Leno Mascia Polymers in Industry from...

Leno Mascia

Polymers in Industry from A----Z

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Leno Mascia

Polymers in Industry from A–Z

A Concise Encyclopedia

The Authors

Dr. Leno MasciaDepartment of MaterialsLoughborough UniversityLoughborough LE11 3TUUnited Kingdom

All books published by Wiley-VCH are carefullyproduced. Nevertheless, authors, editors, andpublisher do not warrant the information containedin these books, including this book, to be free oferrors. Readers are advised to keep in mind thatstatements, data, illustrations, procedural details orother items may inadvertently be inaccurate.

Library of Congress Card No.: applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library.

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists thispublication in the Deutsche Nationalbibliografie;detailed bibliographic data are available on theInternet at http://dnb.d-nb.de.

# 2012 WILEY-VCH Verlag GmbH & Co. KGaA,Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation intoother languages). No part of this book may bereproduced in any form – by photoprinting,microfilm, or any other means – nor transmitted ortranslated into a machine language without writtenpermission from the publishers. Registered names,trademarks, etc. used in this book, even when notspecifically marked as such, are not to be consideredunprotected by law.

Typesetting Thomson Digital, Noida, IndiaPrintingBindingCover Design Adam-Design, Weinheim

Printed inPrinted on acid-free paper

Print ISBN: 978-3-527-32964-9ePDF ISBN: 978-3-527-64405-6oBook ISBN: 978-3-527-64403-2ePub ISBN: 978-3-527-64404-9Mobi ISBN: 978-3-527-64406-3

Dedication

To my grandchildren and their future

Contents

Preface IXAcknowledgements XIOverview Guide XIIIList of Acronyms XXIII

Chapter Entries Pages

A Abrasion Resistance—Azeotropic Copolymerization 1B Back-Flow—Butyl Rubber 24C Calcium Carbonate (CaCO3)—Cyanate Ester 37D DABCO—Dynamic Vulcanization 80E Effective Modulus—Eyring Equation 99F Fabrication— Fusion Promoter 126G Gate—Gutta Percha 153H Halogenated Fire Retardant—Hyperbranched Polymer 157I Impact Modifier— Izod Impact Test 163J J integral— Joint 175K K Value—Kneading 176L Lamella— Lüder Lines 178M M100 and M300—Mylar 191N Nafion—Nylon Screw 215O Oil Absorption—Ozone 225P Paint—Pyrolysis 229Q Q Meter—Quinone Structure 267R Rabinowitsch Equation—Rutile 268S Sag—Syntactic Foam 277T Tack—Tyre Construction 301U Ubbelohde Viscometer—UV Stabilizer 318V Vacuum Forming—Vulcanization 326

VII

W Wall Slip—Work of Adhesion 335X X-Ray Diffraction (XRD)—Xenon Arc Lamp 342Y Y Calibration Factor—Young�s Modulus 343Z Z-Blade Mixer—Zisman Plot 347

References 349

VIII Contents

Preface

Polymers are a well-established class of materials both in the commercial sector andin educational curricula. Polymers are the main component of commercial productsknown as plastics, composites, rubber (or elastomers), surface coatings, fibres andadhesives.

Although many books have been published over the past 50 years or so to satisfythe demands of those concerned with the scientific and technological aspects of thesubject, the author feels that there is a need for a reference text that can provide easyaccess to brief and concise information on the terminology, concepts, principles andindustrial practice related to the constitution, manufacture and properties of poly-mer materials.

A compact encyclopaedia provides the easiest and most rapid route for retrievingboth specific and general information about the subject of interest. This is particu-larly valuable when the reader is interested primarily in the basics of the subject.

Although the central focus of this book is on aspects concerned with the con-stitution, properties and processing of polymer-based materials, the treatmentextends into related areas, including synthesis and characterization. The amountof information and details provided for each entry, therefore, varies according to theanticipated needs and interests of the potential reader within the core areas.

The contents covered by the text have been derived with the view that the fieldspans various disciplines and branches of industry and, therefore, the needs of thepotential reader beyond the boundaries of these areas are served by complementarytexts related to other sectors, such as the petrochemical industry and specificmanufacturing concerns.

The information is presented in two sections. The main part of the book consistsof an ‘‘A to Z encyclopaedic outline’’, which enables the reader to search directly for aparticular topic or item of interest. This is complemented by the preliminary section‘‘Overview’’ and ‘‘Search Guide’’, which should assist the reader to identify thespecific topic or term for the search. All the terms that appear in the ‘‘Overview’’and ‘‘Search Guide’’ are identified as individual entries in the main part of the bookthat follows, so that the reader can scan the entire field and select the topics andaspects of the subject that are of interest.

IX

Acknowledgements

A book that covers such a wide field could not have been written without thecontribution of very many authors over a large number of years. Although credithas been given to authors and publishers, there have been a few occasions where theoriginal source could not be ascertained. Some of the diagrams used in the text havebeen taken from personal lecture notes produced as early as 1970. Many of thesewere extracted from the immensely rich literature provided by the industrial sector,whose identity was not recorded at the time. The author wishes to thank theseanonymous contributors and hopes to be able to overcome any such deficiency inany future editions, if the required information is brought to his attention or isotherwise obtained.

XI

Overview

Additives Modifiers

Materials Properties Processing

Structure Polymerization Morphology Cross-linking

Characterization Degradation

1. Plastics 2. Rubber 3. Adhesives 4. Composites 5. Foams 6. Coatings 7. Functional

polymers

1. Compounding 2. Moulding & Thermoforming 3. Extrusion & Calendering 4. Welding, Prototyping

& Fabrications

1. Chemical structure 2. Crystallinity & heterogeneity 3. Orientation 4. Molecular weights

1. Stabilizers 2. Lubricants 3. Processing aids 4. Colorants 5. Coupling agents 6. Functional additives

1. Impact modifiers 2. Functional fillers 3. Plasticizers 4. Reinforcing fibres 6. Flame retardants

1. Mechanisms & Methods 2. Initiators & Inhibitors 3. Vulcanization & Curatives 4. Ageing & Weathering

Supporting fundamental principles

1. Rheological.. 2. Mechanical.. 3. Electrical… 4. Optical… 5. Barrier… 6. Other properties

jXIII

Search Guide

1. Materials

1.1 Plastics

ThermoplasticsAcetals: Oxymethylene polymer, Polyoxy-methylene, Poly(methylene oxide) (PMO)Acrylics:Poly(methylmethacrylate) (PMMA),

Methylmethacrylate–butadiene–styrene(MBS)Barrier polymers: Phenoxy, Poly(vinylidene

chloride) (PVDC), Ethylene–vinyl alcoholcopolymer (EVOH)Cellulosics: Cellulose acetate, Cellulose

acetate butyrate, Cellulose nitrate, CellulosepropionateFluoropolymers: Perfluoropolymer (PFA),

Polychlorotrifluoroethylene (PCTFE), Poly-tetrafluoroethylene (PTFE), Poly(tetrafluor-oethylene–ethylene) copolymer (PETFE),Poly(tetrafluoroethylene–hexafluoropropy-lene) copolymer (FEP), Poly(vinylidenefluoride) (PVDF or PVF2)High-temperature polymers: Polybenzimi-

dazole (PBI), Poly(ether ketone) (PEK), Poly(ether etherketone) (PEEK),Polyketone,Poly(phenylene oxide) (PPO), Polysulfone (PSU),Poly(ether sulfone) (PES), Poly(phenylenesulfide) (PPS), Poly(ether imide) (PEI)Polyamides: Nylon 6 (PA 6), Nylon 4,6 (PA

4,6), Nylon 6,6 (PA 6,6), Nylon 11 (PA 11),Nylon 12 (PA 12)Polyesters: Caprolactone polymer (PLC),

Poly(butylene terephthalate) (PBT), Polycar-bonate (PC), Poly(ethylene terephthalate)(PET), Aromatic polyesterPolyolefins: Chlorinated polyethylene,

Chlorosulfonated polyethylene, Coupledpolypropylene, Ethylene–carbon monoxidecopolymer (ECO), Ethylene–ethyl acrylatecopolymer (EEA), Ethylene–methylmethac-rylate copolymer (EMA), Ethylene–vinylacetate copolymer (EVA), Ethenoid poly-mer, Polyethylene (LDPE, VLDPE, LLDPE,

MDPE, HDPE, UHMWPE), Polypropylene(PP), Polybutene, Poly(4-methyl pent-1-ene)Styrene polymers: Acrylonitrile–butadiene–

styrene terpolymer (ABS), Acrylonitrile–acrylate–styrene terpolymer (ASA), High-impact polystyrene (HIPS), Polystyrene (PS),Styrene–acrylonitrile copolymer (SAN),Styrene–maleic anhydride copolymer (SMA)Vinyl polymers: Chlorinated PVC, Poly

(vinyl acetate) (PVAc), Poly(vinyl alcohol)(PVA), Poly(vinyl alkyl ether) (PVME),Poly(vinyl butyral), Poly(vinyl carbazole),Poly(vinyl chloride) (PVC, PVC-U), Poly(vinyl fluoride) (PVF), Polyvinylpyridine,Polyvinylpyrrolidone

ThermosetsAmino resins: Melamine formaldehyde(MF), Urea formaldehyde (UF), CaseinEpoxy resins: Bisphenol-A (DGEBA),

Cycloaliphatic, Epoxidized novolac resin,Tetraglycidoxylmethylene p,p0-diphenylenediamine (TGDM)High-temperature resins: Cyanate ester, Dia-

llyl phthalate, Furan resin, PMR, Polyimide,PolybismaleimidePhenolics: Bakelite, Novolac, ResoleUnsaturated polyesters: Resins for compo-

sites, Bulk moulding compound (BMC),Sheet moulding compound (SMC), Vinylester

Other AspectsGel, Recycling, Polymer blend, Thermore-versible gel, Vitrification

1.2 Rubber

Vulcanized/Cross-Linked ElastomersAcrylates: Ethylene–ethyl acrylate terpoly-mer elastomer (EAM)

XIVj 1 Materials

Diene elastomers: Acrylonitrile–butadiene(NBR), Gutta percha, Natural rubber (NR),Polybutadiene (BR), Polychloroprene (CR),Polyisoprene (IR), Styrene–butadiene (SBR)Fluoroelastomers: Hexafluoropropylene

copolymer and terpolymerHydrocarbon (polyolefin) elastomers: Butyl

rubber, Ethylene–propylene rubber (EPR),Ethylene–propylene–diene monomer rub-ber (EPDM), Chlorosulfonated polyethyl-ene (CSM)Silicone rubber: Polydimethylsiloxane

(PDMS, VMQ), Fluorosilicone (FVMQ)Other elastomers: Epichlorohydrin (ECO),

Phosphazene elastomer, Polycarborane–si-loxane, Polyurethanes (PUR)

Thermoplastic Elastomers (TPE)Block copolymers: Styrene–butadiene–styrene (SBS), Styrene–ethylene/butylene–styrene (S-EB-S), Styrene–isoprene–styrene(SIB), Poly(butylene terephthalate-b-tetra-methylene oxide) (TPE-E), Poly(amide-g-alkylene oxide) (TPE-A), Poly(urethane-g-ester/alkylene oxide) (TPU)Dynamic vulcanizates: Thermoplastic

polyolefin (TPO), Plasticized PVC/NBRblend, NR/EPR blend

Other AspectsCoagulum, Crepe, Fluidized bed, Latex,Mastication, Microwaving, Vulcanizate

1.3 Adhesives

Hot MeltsEthylene–vinyl acetate copolymer (EVA),Ethylene–ethyl acrylate copolymer (EEA),Polyamide, Polyester, Phenoxy

Curable AdhesivesAcrylic, Cyanoacrylate, Epoxy, Phenolic

Water-BornePoly(vinyl acetate), Styrene–butadienecopolymer (SBR), Poly(ethylene–vinylacetate) copolymer (VAE)

Pressure-Sensitive AdhesiveElastomer, Tackifier

Other AspectsAdherend, Adhesive test, Adhesive wetting,Anodizing, Debonding, Cold plasma,Corona discharge, Critical surface energy,Critical wetting tension, Joint, Lap shear,Pot life, Tack, Work of adhesion

1.4 Composites

Fibre ReinforcementContinuous fibres: Aramid fibre, Carbonfibre, Glass fibre, Graphite fibreShort fibres: Asbestos, Carbon fibre,

Chopped strandmat laminate (CSM), Glassfibre

Particulate ReinforcementFillers: Barite, Bentonite, Calcium carbon-ate, Carbon black, Channel black, Clay,Fumed silica, Functional filler, Glass flake,Kaolin, Mica, Quartz, TitaniaNanofillers: Carbon nanotube, Exfolia-

tion, Montmorillonite, NanoclayFire retardant andAntitracking: Aluminium

trihydrate, Antimony oxide, Magnesiumhydroxide, Molybdenum oxideOther fillers: Bioactive filler, Magnetic

filler, Molybdenum disulfide, Metal powder

MatrixThermosets: Unsaturated polyester, Epoxyresin, Phenolic, Cyanoacrylate, PMR,PolyimideThermoplastics: Coupled polypropylene,

Polyamide, Poly(ether ketone), Poly(etherimide), Poly(phenylene sulfide)

NanocompositesCeramer, Exfoliated nanocomposite, Organicmodified filler, Organic–inorganic hybrid

Other AspectsDebonding, BET isotherm, Commingledfibre, Composite manufacture, Composite

1 Materials jXV

property prediction (Reinforcement theory),Composite test, Coupling agent, Criticalfibre length,Gel coat,Graphene, Exfoliation,Intercalation, Ion exchange capacity (IEC),Interfacial bonding, Laminate, Low profileadditive, Modulus enhancement factor, Oilabsorption, Prepreg, Reinforcement factor,Size, Sizing/Finishing, Zeta potential

1.5 Foams

AspectsClosed cell, Foam density and properties,Foam formation mechanism, Foam manu-facture, Open cell, Structural foam, Syntac-tic foam

1.6 Coatings

Ac Curable VarnishesAcrylic, Alkyd, Drying resin, Epoxide,Phenolic, Urethane

Water-Borne DispersionsMicroemulsions: Polyurethane, EpoxidePolymer emulsions: Poly(vinyl acetate),

Acrylic

PowdersCurable thermosetting systems: Epoxide, Poly(ester–epoxide), PolyurethaneThermoplastic powders: Polyester, Acrylic

Other AspectsAnodizing, Blistering, Cold plasma, Con-tact angle, Critical surface energy, Criticalwetting tension, Dip coating, Electrolyticdeposition, Electrostatic spraying, Film for-mation, Metallization, Gel coat, Intumes-cent coating, Pinhole, Plating, Pot life,Primer, Roughness factor, Sputtering, Sur-face energy, Work of adhesion, Zisman plot

1.7 Functional Polymers

BiopolymersChitin, Chitosan, Ester–amide polymer,Ethylene–carbonmonoxidecopolymer (ECO),

Poly(lactic acid), Polylactide, Oxo-biodegrad-able polymer, Poly(hydroxy alkanoate), Poly(hydroxybutyrate),Polypeptide,Polysaccharide,Starch

Conductive PolymersPolyacetylene, Polyaniline (PANI),Polypyrrole

Ionomeric PolymersIonomer, Ion exchange resin, Nafion,Polyelectrolyte

Other AspectsCross-linked thermoplastic, Dendrimer,Doping, Engineering polymer, Heat-shrink-able product, Light-sensitive polymer,Liquid-crystal polymer, Shape memorypolymer, Nonlinear dielectric polymer,Piezoelectric polymer, Photoresist, Poly(amic acid), PTC polymer, Spandex fibre

2. Properties

2.1 Rheological properties

RheologyBarus effect, Binghambody, Carreaumodel,Complex viscosity, Consistency index,Converging flow, Couette flow, Deborahnumber, Deformational behaviour, Dieswell, Dilatant fluid, Drag flow, Elongationalflow, Elongation rate, Elongational viscosity,Ellis equation, Extension viscosity, G0 andG00, Gel time (gel point), Melt elasticity,Mooney equation, Newtonian behaviour,Non-Newtonian behaviour, Normal stressdifference, First normal stress coefficient,Plug flow, Power law, Power-law index, Thix-otropy, Trouton viscosity, True shear rate,True viscosity, Viscosity, Zero-shear viscosity

RheometryBagley correction, Brookfield viscometer,Capillary rheometer, Cone-and-plate rhe-

XVIj 2 Properties

ometer, Coaxial cylinder rheometer, Die-exit phenomena,Dynamic (oscillatory)flow,Gelation, Entry effect, Melt flow index (Meltflow rate), Melt fracture, Melt strength,Monsanto rheometer, Mooney viscometer,Parallel-plate rheometer, PVT diagram,Rabinowitsch correction, Sharkskin, Slipanalysis, Slit rheometer, Torque rheometer,Weissenberg rheogoniometer

Other AspectsCritical chain length (Zc), Deformationalbehaviour, Entanglement, Flow curve,Mark–Huggins equation, Radius of gyration,Reptation, Rubbery state, Viscous state

2.2 Mechanical Properties

Elasticity and ViscoelasticityBulk modulus, Compliance, Complexcompliance, Complex modulus, Creep,Creep compliance, Creep curves, Creepmodulus, Creep period, Damping factor,Deflection under load temperature, Defor-mational behaviour, Dynamic mechanicalspectra, Effective modulus, Elasticity, Elas-tic behaviour, Elastic memory, Elastic re-covery, Flexural modulus, Force–deflec-tion curve, Force–deformation curve, For-ce–extension curve, Heat distortion tem-perature (HDT), Hundred-percent (100%)modulus, Kelvin–Voigt model, Load–deflec-tion curve, Load–deformation curve, Loa-d–extension curve, Loss angle, Loss compli-ance, Loss factor, Loss modulus, Loss tan-gent, Master curve, Maxwell model, Modu-lus, M100 and M300, Nonlinear viscoelasticbehaviour, Phase angle, Recovery, Recover-able strain, Reduced time, Relaxation time,Retardation time, Relaxation modulus, Re-laxed modulus, Rubber elasticity, Shearmodulus, Shift factor, Standard linear solidmodel, Tan d, Tangent modulus, Tensilemodulus, Time-dependent modulus,Time–temperature superposition, Visco-elastic behaviour, Voigt model, Young�smodulus

Failure and Fracturea/W ratio, Brittle fracture, Brittle point,Brittle strength, Brittle–tough transition,Cold-flex temperature, Cold flow, Com-pression set, Crack initiation, Cracklength, Crack opening displacement(COD), Crazing, Creep rupture, Criticalcrazing strain, Critical strain energy re-lease rate (Gc), Critical stress intensity fac-tor (Kc), Ductile, Ductile–brittle transition,Ductile failure, Environmental stresscracking, Fatigue life, Flex cracking, Flexlife, Flexural strength, Fracturemechanics,Griffith�s equation, Impact strength, Inter-laminar shear strength (ILSS), J-integral,L€uder lines, Notch sensitivity, Peelstrength, Permanent set, Plastic deforma-tion, Tear strength, Tenacity, Tresca crite-rion, Von Mises criterion, Yield criteria,Yield failure, Yield point, Yield strength,Young�s modulus

Test MethodsBall drop, Bending test, Charpy impacttest, Compression test, Creep test, Dila-tometer, Dumb-bell specimen, Dynamicmechanical analysis (DMA), Dynamicmechanical thermal analysis (DMTA),Extensometer, Falling-weight impact test,Fatigue test, Fracture test, Impact test, Izodimpact test, Mechanical spectroscopy, Mi-crohardness, Notch, Peel test, Pendulumimpact test, Rubber elasticity, Tensile test,Viscoelasticity

Other AspectsAbrasion resistance, Anisotropy, Boltz-mann superposition principle, Compres-sion, Compact tension specimen, Damagetolerance, Damping, Deformation, Delami-nation, Distribution of relaxation times,Distribution of retardation times, Dynamicmechanical spectra, Flexural properties,Friction coefficient, Hardness, Hydrostaticstress, Life prediction, Load, Microvoid,Poisson�s ratio, Rockwell hardness, Rub-bery state, Shear stress, Shore hardness,

2 Properties jXVII

Stiffness, Strain, Strain rate, Stress, Stressconcentration, Tack, Transmissibility, Ten-sor, Torque, Torsion pendulum, Toughness,Vicat softening point, Vickers hardness,Volumetric strain

2.3 Electrical Properties

Low VoltageCapacitance, Clausius–Mossotti equation,Complex permittivity, Conductance, Con-ductivity, Corona discharge, Currentdensity, Dielectric, Dielectric constant,Dielectric properties, Dielectric thermalanalysis (DETA), Direct current, Electrostat-ic charge, Loss angle, Loss factor, Loss tan-gent, Permittivity, Polarization, Resistivity,Specific impedance, Stress concentration,Surface resistivity, Tan d, Volume resistivity

High VoltageBreakdown voltage, Comparative trackingindex (CTI), Dielectric strength, Dry band,Electrical failure, Electric strength, Tracking

Other AspectsDipole, Electronic conductivity, Electrostaticcharge, Ionic conductivity, Polarity, Stressgrading, Nonlinear dielectric, PTC polymer

2.4 Optical Properties

AspectsBackscatter, Birefringence, CIE chromaticitydiagram, Colour, Colour matching, Directreflection factor, Extinction index, Forwardscatter, Gloss, Haze, Light microscopy, Lightscattering, Light transmission factor, Opticalbrightener, Optical microscopy, Optical pathdifference, Orientation, Photoelasticity, Re-flection factor, Refractive index, See-throughclarity,Stressopticalcoefficient,Transparency

2.5 Barrier Properties

AspectsDiffusion, Diffusion coefficient, Fickian be-haviour, Permeability, Solubility, Time lag

2.6 Other Properties

TypesAcoustic: Attenuation, Loss factorFire resistance: Cone calorimeter, Flash

point, Limiting oxygen index, Pyrolysis,Self-extinguishing, Thermal gravimetricanalysisThermal properties: Dilatometer, Dilata-

tion coefficient, Thermal conductivity, Ther-mal expansion coefficient

3. Processing

3.1 Compounding

AspectsBanbury mixer, Decompression zone,Devolatilization, Dispersion, Dispersive mix-ing, Dry blend, Formulation, Master batch,Melting,Miscibility,Mixing,Mixer, Pelletizer,Plastication, Plastograph, Purging, Recipro-cating screw mixer, Thermal degradation,Torque rheometer, Twin-screw extruder

3.2 Moulding and Thermoforming

Machine and MouldsClamping force, Clamping system, Ejectionmechanism, Film gate, Gate, Hot runnermould, Lockingmechanism,Mould design,Nozzle, Nylon screw, Reciprocating screw,Runner, Sprue, Stripper plate

OperationsAir-slip forming, Blow moulding, Cavityfilling, Cavity packing, Compressionmoulding, Co-injection moulding, Drapeforming, Injection blow moulding, Injec-tion moulding, Plastication, Plug-assistedvacuumforming, Purging, Reactionmould-ing, Reaction processing, Resin transfermoulding, Rotational moulding, Stretchblow moulding, Thermoforming, Transfermoulding, Vacuum forming

XVIIIj 3 Processing

Other AspectsBack-pressure, Demoulding, Distortionand Warping, Flash, Gel coat, Internalstress, Moulding cycle, Moulding defect,Pre-form, PVT diagram, Residual stress,Sink mark, Spiral flow moulding, Void,Weld line

3.3 Extrusion and Calendering

ExtruderBarrel, Barrier flights screw, Co-rotating,Counter-rotating, Decompression zone,Devolatilization, Extruder screw, Gearpump, Nylon screw, Twin-screw extruder

Extrusion DiesDie gap, Die lip, Fish-tail die, Land length,Sizing die, Spider leg, Mandrel

Other AspectsAdiabatic heating, Back-flow, Blocking,Blow-up ratio, Blown film, Breaker plate,Calender, Cambering (Roll crowning),Chill-roll casting, Co-extrusion, Crow feet,Extrusion theory, Die analysis, Die drool,Drag flow, Draw ratio, Drawdown ratio,Extrudate, Fish eye, Flow analysis, Flowinstability, Foam extrusion, Lamination,Leakage flow, Parison, Plastication, Plateout, Pressure flow, Purging, Screw–die in-teraction, Surging, Tubular film, Weld line

3.4 Welding, Prototyping and Fabrications

Hot-plate welding, Friction welding, High-frequencywelding,Ultrasonicwelding,Rapidprototyping, Stereolithography, Casting, Ma-chining, Powder sintering, Tyre construction

4. Structure, Morphologyand Characterization

4.1 Chemical Structure

Acid number, Aliphatic, Atactic, Attenuatedtotal reflectance spectroscopy, Block copoly-

mer, Carbonyl index, Chain configuration,Chain regularity, Chain stiffness, Chemicalshift, Configuration, Conformation, Conju-gated double bond, Coordination, Copoly-mer, Critical chain length, Cross-link,Degree of cross-linking, Degree of poly-merization, Dendrimer, Electron spin res-onance, Electron spectroscopy for chemi-cal analysis (ESCA), Free radical, Fluores-cence, Functionality, Head-to-head, Head-to-tail, Heterochain, Hydrogen bond,Hydrophilic, Hydrophobic, Hydroxylequivalent (number), Hygroscopic, Hyper-branched polymer, Infrared spectroscopy(IR, FTIR), Interpenetrating polymer net-work (IPN), Isotactic, Network, Non-polarpolymer, Oligomer, Orientation, Oxiranering, Polarity, Quinone structure, Radia-tion, Radical, Radius of gyration, Ramanspectroscopy, Random copolymer, Sidegroup, Spectroscopy, Spectrum, Syndiotac-tic, Tacticity, UV spectroscopy, X-ray, X-rayphotoelectron microscopy (XPS)

4.2 Crystallinity and Heterogeneity

Amorphous polymer, Atomic force mi-croscopy (AFM), Birefringence, Chainfolding, Cluster, Cold crystallization, Col-loidal, Co-continuous domain, Core andshell, Crystalline polymer, Crystallization,Degree of crystallinity, Dielectric thermalanalysis (DETA), Differential scanningcalorimetry (DSC), Differential thermalanalysis (DTA), Dynamic mechanical ther-mal analysis (DMA, DMTA), Exfoliation,Emulsion, First-order transition, Fractal,Fringe micelle, Intercalation, Lamella, Lightmicroscopy, Light scattering, Melting point,Microscopy, Microcavitation, Microemul-sion, Microvoid, Optical microscopy, Scan-ning electronmicroscope, Secondary crystal-lization, Shish-kebab crystal, Small-angleX-ray scattering (SAXS), Spherulite, Trans-mission electron microscopy (TEM), Unitcell, Wide-angle X-ray diffraction (WAXS),X-ray

4 Structure, Morphology and Characterization jXIX

4.3 Orientation

Anisotropy, Annealing, Biaxial, Birefrin-gence, Draw ratio, Extension ratio, Fibre,Heat settingHeat-shrinkable polymer, Monoaxial,

Monofilament, Optical path difference, Ori-entation function, Wide-angle X-ray diffrac-tion (WAXS)

4.4 Molecular weights

Dispersity index, Distribution of molecularweight, Gel permeation chromatography,Huggins� constant, Intrinsic viscosity, Mo-lar mass, Molecular weight, Monodisperse,Measurement of molecular weight, Mar-k–Houwink equation, Number-averagemo-lecular weight, Osmotic pressure, Osmom-etry, Relative viscosity, Weight-average mo-lecular weight, Size exclusion chromatogra-phy, Staudinger, Ubbelohde viscometer,Viscometer, Viscosity

5. Polymerization Cross-linking and Degradation

5.1 Initiators, Inhibitors and Vulcanization

Accelerator, Activator, Cobalt naphthanateand octoate, Co-agent, Cure time, Curing,Efficient vulcanization, Fatty acid, Kicker,Mechanical degradation, Mercaptan, Micro-waving,Peroxide,Photoinitiator, Post-curing,Scorch time, Retarder, Thiouram, Zinc oxide

5.2 Polymerization and Cross-Linking

MechanismsAddition polymerization, Anionic polymer-ization, Cationic polymerization, Chainstopper, Condensation reaction, Condensa-tion polymerization, Copolymerization,Depolymerization, DMP-30, Free-radicalpolymerization, Ionic polymerization,Metallocene catalysis, Propagation reaction,

Reactivity ratio, Termination reaction,Ziegler catalyst, Ziegler–Natta catalyst

MethodsBulk polymerization, Electron beaming,Emulsion polymerization, Heterophase orHeterogeneous polymerization, Mass poly-merization, Mechanical degradation, Phaseinversion, Photopolymerization, Radiationprocessing, Reaction processing, Seed po-lymerization, Solid-state polymerization,Surfactant, Suspension polymerization

5.3 Ageing and Weathering

Depolymerization, Chalking, Chain scis-sion, Composting, Environmental ageing,Fogging, Hydrolysis, Induction time, Lifecycle analysis, Life prediction, Ozone, Phys-ical ageing, Propagation reaction, Radia-tion, Recycling, Secondary crystallization,Solar radiation, Thermal degradation, Ul-traviolet (UV) light, UVdegradation, Xenonarc lamp, Yellowness index

6. Additives and Modifiers

6.1 Additives

StabilizersAntidegradant, Antioxidant, Antiozonant,Chelating agent, Excited state quencher,Hindered amine light stabilizer (HALS),Hindered phenol, Hydrolysis stabilizer,Lead stabilizer, Metal deactivator, Phenolicantioxidant, Primary stabilizer, Processingstabilizer, Radical scavenger, UV stabilizer

Lubricants and Processing AidsAntiblocking agent, Antifoaming agent,Blocking, Cationic surfactant, Externallubricant, Factice, Flow promoter, Fusionpromoter, Internal lubricant, Low-profileadditive, Lubricant, Peptizer, Stearate, Stea-ric acid, Tackifier, Thickener, Thixotropicagent

XXj 6 Additives and Modifiers

ColorantsAnatase, CIE chromaticity diagram, Dye,Mineral pigment, Pigment, Rutile, Ther-mochromic pigment

Coupling AgentsCompatibilizing agent, Interfacial bonding,Silane, Size (Sizing), Surfactant

Functional AdditivesAntifoaming agent, Antimicrobial (biocidal)agent, Antistatic agent, Antitracking additive,Blowing agent, Flocculant, Fungicide, Nucle-ating agent

Other AspectsAdditive concentrate, Compounding,Fogging, Law of mixtures, Master batch,Miscibility, Mixing, Solubility parameter,Stabilization, Synergism

6.2 Property Modifiers

Fire (Flame) RetardantsAluminium trihydrate, Antimony oxide,Brominated compound, Chlorinated fireretardant, Magnesium hydroxide, Molybde-num oxide

Impact ModifiersAcrylonitrile–butadiene–styrene terpolymer(ABS), Amine-terminated acrylonitrile–butadiene–styrene terpolymer (ATBN), Car-boxylic acid-terminated acrylonitrile–buta-diene–styrene terpolymer (CTBN), Metha-crylate–butadiene–styrene terpolymer(MBS), Liquid rubber, Polymer alloy, Poly-mer blend, Telechelic oligomer

Functional FillersBarite, Bioactivefiller,Carbonblack,Carbonnanotube, Magnetic filler, Metal powder

PlasticizersEpoxidized soya-bean oil, Extender, Low-temperature plasticizer, Non-migratoryplasticizer, Organosol, Primary plasticizer,Reactive diluent, Secondary plasticizer

Reinforcing FibresGlass fibre, Carbon fibre (Acrylic fibre),Aramid fibre

Other AspectsAntiplasticization, Cold-flex temperature,Compatibility, Glass transition tempera-ture, Internal plasticization, Lower criticalsolution temperature (LCST), Miscibility,Mixing, Plasticization, Plastisol, Solubilityparameter, Upper critical solution tempera-ture (UCST)

7. SupportingFundamental Principlesand Terminology

Absorbance, Activation energy, Activationvolume, Alpha transition, Alternating cur-rent, Aprotic polar solvent, Arrhenius equa-tion, Beer–Lambert law, Beta transition,Boundary condition, Case II diffusion,Cluster, Cohesive energy density, Coldplasma, Colligative properties, Colloidal,Conformation, Configuration, Conserva-tion law, Continuummechanics, Coordina-tion, Current density, Deconvolution, Di-rect current, Elasticity, Electromagnetic ra-diation, Empirical, Endothermic, Engineer-ing design, Enthalpy, Entropy, Exothermic,Extinction coefficient, Fickian behaviour,First-order transition, Fluorescence, Frac-tal, Fractography, Free radical, Fundamentalproperty, Gibbs free energy, Hooke�s law,Hydrogen bond, Hydrolysis, Hydrophilic,Hydrophobic,Hydrostatic pressure,Hydro-static stress, Hydrothermal stress, Hygro-scopic, Induction time, Insulation, Interac-tion, Interfacial polarization, Intermolecu-lar, Internal energy, Intramolecular, Isother-mal, Isotropic, Law of mixtures, Linearbehaviour, Linear elastic, Lower bound, Lu-brication approximation, Melting point,Modulus, Momentum, Momentum equa-tion, Morphology, Non-destructive test,

7 Supporting Fundamental Principles and Terminology jXXI

Non-polar, Nuclear magnetic resonance,Ozone, Photoelasticity, Plane strain, Planestress, Plastic, Poiseuille equation, Poisson�sratio, Polarity, Polarization, Polarized light,

Radical, Solar radiation, Spectrum,Stiffness,Stokes equation, Synergism, Tensor, Torque,Transesterification, Van der Waals forces,Vector

XXIIj 7 Supporting Fundamental Principles and Terminology

List of Acronyms

AAA acetoxyacetoanilideABA acetoxybenzoic acidABS acrylonitrile–butadiene–styrene (terpolymer)AC alternating currentACM acrylic rubber, copolymer of ethyl acrylate and butyl

acrylateAED anionic electrolytic depositionAFM atomic force microscopyAIBN azo-bis-isobutyronitrileANA acetoxynaphthoic acidASA acrylonitrile–acrylate–styrene (terpolymer)ATBN amine-terminated butadiene–acrylonitrile oligomerATH aluminium (or alumina) trihydrateATR attenuated total reflectance (spectroscopy)a/W ratio ratio of length of crack (or notch), a, to width of specimen,W,

used in evaluation of the toughness of materialsAZBN azo-bis-dibutyronitrileAZDN azo-bis-dibutyronitrilebis-MPA bis(hydroxymethyl)propionic acidBMC bulk moulding compoundBMI bismaleimide (resin)b.p. boiling pointBP benzophenoneB-stage term used to describe an intermediate state of cure of

thermosetting resins, particularly phenolic systemsBUR blow-up ratioCA cellulose acetateCAB cellulose acetate butyrateCAD computer-aided designCAP cellulose acetate propionateCBT cyclic butylene terephthalateCEC cation exchange capacity

XXIII

CED cationic electrolytic depositionCED cohesive energy densityCFRP carbon-fibre-reinforced plasticsCIE Commission International de l�EclairageCN cellulose nitrateCNT carbon nanotubeCOD crack-opening displacementCP cellulose propionateCPE chlorinated polyethyleneCR chloroprene rubberCSM chlorosulfonated polyethyleneCSM chopped strand matCT compact tension (specimen)CTBN carboxyl-terminated butadiene–acrylonitrile oligomerCTI comparative tracking indexDABCO 1,4-diazabicyclo[2.2.2]octane (tertiary cyclic diamine)DAI diaryliodoniumDAP diallyl phthalateDBP dibutyl phthalateDBTL dibutyl tin dilaurateDC direct currentDCB double cantilever beam (method)DDS 4,40-diaminodiphenylsulfoneDDSA dodecylsuccinic anhydrideDEAP diethoxyacetophenoneDEN double edge notchDETA dielectric thermal analysisDETA diethylenetriamineDGEBA diglycidyl ether of bisphenol A (resin)DIAP diallyl isophthalateDICY dicyanodiamideDIDP diisododecyl phthalateDIOP diisooctyl phthalateDLTDP dilaurylthiodipropionoateDMA dynamic mechanical analysisDMC dough moulding compoundDMF dimethylformamideDMP-30 tertiary amine used as curing agent for epoxy resinsDMPA dimethoxyphenylacetophenoneDMTA dynamic mechanical thermal analysisDOA dioctyl adipateDOP dioctyl phthalateDOS dioctyl sebacateDSC differential scanning calorimetryDSTDP distearylthiodipropionoate

XXIV List of Acronyms

DTA differential thermal analysisDULT deflection under load temperatureEAM ethylene–ethyl acrylate (copolymer)ECO epichlorohydrin–ethylene oxide (copolymer)ECO ethylene–carbon monoxide (copolymer)EDS energy-dispersive scanning (analysis)EDX energy-dispersive X-ray (analysis) (same as EDS)EEA ethylene–ethyl acrylate (copolymer)EM electromagneticEMA ethylene–methyl methacrylate (copolymer)ENF end-notched flexure (test/specimen)EPDM ethylene–propylene–diene monomer (rubber)EPR ethylene–propylene rubberESCA electron spectroscopy for chemical analysisESCR environmental stress cracking resistanceESR electron spin resonanceETER epichlorohydrin–ethylene oxide–diene terpolymerETPV engineering thermoplastic vulcanizateEV efficient vulcanizing (cure)EVA ethylene–vinyl acetate (copolymer)EVOH ethylene–vinyl alcohol (copolymer)EW equivalent weightFEP poly(tetrafluoroethylene–hexafluoropropylene) copolymerFIR far-infraredFKM designation for a fluoroelastomerFRP fibre-reinforced polymerFTIR Fourier transform infraredFVMQ designation for a fluorosiliconeGc critical strain energy release rateGCC ground calcium carbonateGIc, GIIc, GIIIc critical strain energy release rates for fracture

modes I, II and IIIGOTMS c-glycidyloxypropyltrimethoxysilaneGPC gel permeation chromatography, known also as size

exclusion chromatography (SEC)GPTMS c-glycidyloxypropyltrimethoxysilaneGRP glass-reinforced plasticHALS hindered-amine light stabilizerHDI hexamethylene diisocyanateHDPE high-density polyethylene (density 0.935–0.955 g/cm3)HDT heat distortion temperatureHHPA hexahydrophthalic anhydrideHIPS high-impact polystyreneHP-PE high-pressure polyethyleneIEC ion exchange capacity

List of Acronyms XXV

IIR isobutylene–isoprene rubberILSS interlaminar shear strengthIPN interpenetrating polymer networkIR infrared spectroscopyIR isoprene rubberIRH international rubber hardness (scale)Kc critical stress intensity factorKIc, KIIc, KIIIc critical stress intensity factor for fracture modes I, II and IIIK value empirical parameter used for molecular weight of PVCLARC tradename for a variety of PMR products of

NASA-LangleyLCP liquid-crystal polymerLCST lower critical solution temperatureLDPE low-density polyethyleneLEFM linear elastic fracture mechanicsLLDPE linear low-density polyethyleneLOI limiting oxygen indexLP low-profile (additive)M100, M300 modulus of a rubbery material at 100% and

300% extensionMBS methyl methacrylate–butadiene–styrene

(terpolymer blend)MBT mercaptobenzothiazoleMDI diphenylmethane-4,40-diisocyanate [4,40-methylene

diphenylene isocyanate]MDPE medium-density polyethylene (density =

0.925–0.935 g/cm3)MEK methyl ethyl ketoneMF melamine formaldehyde (resin)MFI melt flow index, also known as melt index or melt flow rate

(MFR)MFR melt flow rate, also known as melt flow index (MFI)MNA methylnadic anhydrideMPD m-phenylenediamineMW molecular weightMWD molecular-weight distributionMWNT multiple-walled (carbon) nanotubeN1 first normal stress differenceNBR butadiene–acrylonitrile rubberNBR nitrile rubberNIR near-infraredNMP N-methylpyrrolidoneNMR nuclear magnetic resonanceNR natural rubberODA oxydianiline

XXVI List of Acronyms

PACM 4,40-methylene-bis-cyclohexanaminePAN polyacrylonitrilePANI polyanilinePB poly(but-1-ene)PB polybutadienePBI polybenzimidazolePBT poly(butylene terephthalate)PC polycarbonatePCBT poly(cyclo(butylene terephthalate))PCL polycaprolactonePCTFE polychlorotrifluoroethylenePCTP pentachlorothiophenolPDLA poly(D-lactic acid)PDLLA poly(D,L-lactic acid)PDMS polydimethylsiloxanePE polyethylenePEEK poly(aryl ether ether ketone)PEG poly(ethylene glycol)PE-g-MA polyethylene-graft-maleic anhydridePEI poly(ether imide)PEK poly(aryl ether ketone)PEM proton exchange membranePEN poly(ethylene naphthanate)PEO poly(ethylene oxide)PES poly(ether sulfone)PET poly(ethylene terephthalate)PETFE poly(tetrafluoroethylene–ethylene) copolymerPF phenol formaldehyde (resin)PFA perfluoroalkoxy (polymer)PHA polyhydroxyalkanoatePHB poly(3-hydroxybutyrate)phr parts per hundred parts resinPI polyimidePLA poly(lactic acid)PLLA poly(L-lactic acid)PMDA pyromellitic dianhydridePMDI poly(diphenylmethane-4,40-diisocyanate)PMMA poly(methyl methacrylate)PMO poly(methylene oxide)PMP poly(4-methylpent-1-ene)PMPS polymethylphenylsiloxanePMR polymerization of monomer reactants

(NASA-Langley process)POM polyoxymethylenePP polypropylene

List of Acronyms XXVII

PPG poly(propylene glycol)PPO poly(phenylene oxide)PPS poly(phenylene sulfide)PS polystyrenePSA pressure-sensitive adhesivePTBAEMA poly(2-t-butylaminoethyl methacrylate)PTC positive temperature coefficient (polymer)PTE thermoplastic elastomerPTFE polytetrafluoroethylenePU polyurethanePVA poly(vinyl alcohol)PVAc poly(vinyl acetate)PVB poly(vinyl butyral)PVC poly(vinyl chloride)PVDC poly(vinylidene chloride)PVDF poly(vinylidene fluoride)PVEE poly(vinyl ethyl ether)PVF poly(vinyl fluoride)PVF2 poly(vinylidene fluoride)PVME poly(vinyl methyl ether)PVP polyvinylpyridinePVP polyvinylpyrrolidonePVT pressure–volume–temperature (diagram)Q symbol sometimes used for polydimethylsilicone rubberQ meter apparatus used to measure permittivity and loss factor

of dielectricRF radiofrequencyRIM reaction injection mouldingRMS root mean squareRTD residence time distributionRTM resin transfer mouldingRTV room-temperature vulcanizationSAN styrene–acrylonitrile (copolymer)SAXS small-angle X-ray scatteringSBR styrene–butadiene rubberSBS styrene–butadiene–styrene (thermoplastic elastomer)SEBS styrene–ethylene–butylene (thermoplastic elastomer)S-EB-S styrene–ethylene/butylene–styreneSEC size exclusion chromatographySEM scanning electron microscopySEN single edge notchS-EP-S styrene–ethylene/propylene–styrenesemi-IPN semi-interpenetrated polymer networkSIS styrene–isoprene–styrene (thermoplastic elastomer)SLS standard linear solid (model)

XXVIII List of Acronyms

SMA styrene–maleic anhydride (copolymer)SMS styrene–a-methylstyrene (copolymer)SPI Society of the Plastics IndustrySTO stannous octoateSWNT single-walled (carbon) nanotubesynPS syndiotactic polystyreneTA tertiary amineTAC triallyl cyanurateTAIC triallyl isocyanurateTAS triarylsulfoniumTCP tricresyl phosphateTDCB tapered double cantilever beamTDI toluene diisocyanateTEM transmission electron microscopyTEOS tetraethoxysilaneTERT tracking erosion testTETA triethylenetetramineTg glass transition temperatureTGA thermal gravimetric (thermogravimetric) analysisTGDM tetraglycidoxylmethylene p,p0-diphenylene diamineTHF tetrahydrofuranTIAC triallyl isocyanurateTm melting temperatureTMA thermomechanical analysisTMP 2-ethyl-2-(hydroxymethyl)-1,3-propanediolTMPTMA trimethylolpropane trimethacrylateTMTD tetramethylthiouram disulfideTPE thermoplastic elastomerTPE-A poly(amide-g-alkylene oxide) [g = graft]TPE-E poly(butylene terephthalate-b-tetramethylene oxide)

[b = block]TPMK 2-methyl-1-[4-(methylthio)-phenyl]-2-morpholinopropane-1-

oneTPO acronym for thermoplastic polyolefin elastomerTPP triphenyl phosphateTPP triphenylphosphineTPS thermoplastic starchTPU thermoplastic polyurethane elastomer [e.g.

poly(urethane-g-ester/alkylene oxide)]TX thioxanthoneUCST upper critical solution temperatureUDCB uniform double cantilever beamUF urea formaldehyde (resin)UHF ultra-high-frequencyUHMWPE ultra-high-molecular-weight polyethylene

List of Acronyms XXIX

UL Underwriter�s LaboratoryUP unsaturated polyester (resin)UPVC unplasticized poly(vinyl chloride)UV ultraviolet (light)VA vinyl acetateVAE vinyl acetate ethylene copolymerVLDPE very low density polyethylene (density < 0.92 g/cm3)VLLDPE very low-density linear polyethyleneVOC volatile organic compoundVUV vacuum ultravioletXPE cross-linked polyethyleneXPS X-ray photoelectron microscopy (spectroscopy)XRD X-ray diffractionWATS weighted-average total strainWAXS wide-angle X-ray scattering (diffraction)WLF Williams–Landel–Ferry (equation)

XXX List of Acronyms

A-Z Encyclopedia Outline

A

1. Abrasion Resistance

Also known as wear resistance, a character-isticdescribing theresistanceofamaterial towear, which takes place via the erosion ofsmall particles from the surface as a result ofthe frictional forces exerted by a slidingmember. A suitable measure of the rate ofwear is provided by the ratioV/m, whereV isthevolumeabradedperunit slidingdistanceand m is the coefficient of friction, whichcorresponds to the amount of abraded sub-stance per unit energy dissipated in sliding.The abrasion resistance is measured in anumber of different ways, according to theexpected service conditions of a particularproduct.Themostcommonmethodis touseabrasive papermounted on a rotating drum,allowing contact with a specimen subjectedto a constant load in order to bring about theformation of debris, which gives rise to lossof material by wear.

2. ABS

A blend or alloy consisting of a glassy styr-ene–acrylonitrile random copolymer matrixanddispersedmicroscopic rubberybutadiene–acrylonitrile random copolymer particles,which contain sub-micrometre glassy poly-mer inclusions. The three letters stand foracrylonitrile, butadiene and styrene. Acry-lonitrile–butadiene–styrene (ABS) poly-mers are produced either by blending astyrene–acrylonitrile (SAN) copolymer(glassy major component) with a butadie-ne–acrylonitrile rubber (NBR) copolymer(rubbery component), or by a specially de-signed bulk polymerization method. Thelatter consists of dissolving the rubbery

component in a mixture of the monomersfor the formation of the glassy matrix, fol-lowed by free-radical polymerization, whichproduces the glassy SAN matrix, graftedonto the diene elastomer. At any early stageof the polymerization, there is an inversionof phases, leading to the precipitation ofsmall glassy particles into the diene elasto-mer, which precipitate into larger particles,forming the characteristic morphologicalstructure of these toughened polymersystems. The different particle structuresobtained with the two methods of produc-tion are shown in the diagram.

Structure of rubber toughening particles in ABSpolymers. Left: System produced by blending ofemulsions. Right: System formed bymass polymer-ization. Source: Schmitt (1979).

There are many grades of ABS availablecommercially, differing in rigidity character-istics, which are determined by the amountof rubber used, and also in the degree ofplasticization of the glassy phase by theelastomer component. The glass transitiontemperature (Tg) values are in the region of100–110 �C for the glassy phase and around�40 to �50 �C for the rubbery component.The ordinary polymer grades are opaque,owing to the particle size of the precipitatedparticles being greater than 1mm and to the

Polymers in Industry from A–Z: A Concise Encyclopedia, First Edition. Leno Mascia.� 2012 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2012 by Wiley-VCH Verlag GmbH & Co. KGaA.

j1

substantial difference in the refractive indexvalues for the two components.ABS is widely used in the automotive

industry, as it combines its intrinsic hightoughnesswith the ability to produce surfaceswith a high gloss, and also because of the easewith which parts can be metallized by con-ventional electroplating methods. It is alsoavailable in the form of blends with polycar-bonate, which exhibit better thermal oxida-tion stability and higher rigidity than conven-tional ABS grades. (See Styrene polymer.)

3. Absorbance

A coefficient denoting the fractional inten-sity of radiation absorbed by a body, that is,

absorbance a ¼ flux of radiation absorbedtotal incident flux

:

4. Accelerator

An additive used to speed up the rate ofcross-linking reactions in the curing ofthermosetting resins or elastomers. Forpolyester thermosetting resins, the acceler-ator is usually a cobalt naphthenate or cobaltoctoate in solution. For the case of elasto-mers, the accelerator is a sulfur-containingcompound, such as a thiourea, mercaptanand dithiocarbamate, or a non-sulfur-con-taining compound, such as a urea, guani-dine and aldehyde diamine. The chemicalstructures of typical accelerators for sulfurcuring of elastomers are shown.

In many cases, mixtures of acceleratorsare used to obtain a synergistic effect. Typi-cally, a thiazole type is used with smalleramounts of dithiocarbamate or an amine.

5. Acetal

A term used for poly(methylene oxide)(PMO), represented by the chemical formula�(CH2O)n�. Acetals are crystalline poly-mers with a melting point (Tm) in the regionof 180–190 �C and a Tg around�40 �C. Theyare also available in the form of randomcopolymers containing small amounts ofethylene oxide units. Acetals are widely usedin engineering applications for their highresistance to creep and wear under highloads. They also have a good resistance tosolvents and low water absorption character-istics, which makes them suitable for appli-cations requiring dimensional stability un-der moist environmental conditions. Blendswith up to about 30% polyurethane elasto-mers have been reported to display a goodbalance of engineering properties with re-spect to stiffness, strength, toughness andsolvent resistance.

6. Acid Number

A term used to denote the acid content of apolymer or resin, which is defined as theamount in milligrams (mg) of KOH (potas-sium hydroxide) required to neutralize100 g of polymer or resin.

2j 6 Acid Number

7. Acoustic Properties

Describe the response of amaterial to soundand particularly the absorption of sound. Inpolymers, theabsorptionofsoundtakesplacethrough molecular relaxations. The parame-ter that denotes the capability of a polymer todissipate mechanical energy through vibra-tions, known as the loss factor or dampingfactor (tan d), is also used to describe thesound absorption characteristics of poly-mers.(SeeViscoelasticity.)Themethodsusedto measure acoustic properties are broadlydivided into wave propagation, resonanceand forced vibration methods.Resonance and forced vibration methods

are used to measure the Young�s modulusand shear modulus as viscoelastic para-meters comprising an elastic and a losscomponent. Wave propagationmethods areused, on the other hand, to record the actualsound absorption characteristics of materi-als. Measurements are made by sendingacoustic pulses with duration less than 1msthrough the specimen immersed in a liq-uid, and detecting them by another trans-ducer on the opposite surface.

8. Acrylate Elastomer

(See Acrylic polymer.)

9. Acrylic

Ageneric term formonomers and polymerscontaining acrylate or methacrylate units.(See Acrylic polymer.)

10. Acrylic Polymer

Contains acrylic monomeric units in themolecular chains, represented by the gen-eral formula shown.

Polymers where R is anHatom are calledpolyacrylates, and those where R is amethylgroup are called polymethacrylates. Acrylicsare generally amorphous polymers and areavailable as linear polymers or blends (ther-moplastic), cross-linkable elastomers andcross-linkable adhesives and surface coat-ings. The properties of acrylic polymers arestrongly dependent on the nature of thesubstituent R and R0 groups, as illustratedin the table.

Density(g/cm3) Tg (�C)

Poly(acrylic acid) — 106Poly(methyl acrylate) 1.22 8Poly(ethyl acrylate) 1.12 �22Poly(n-butyl acrylate) <1.08 �54Poly(t-butyl acrylate) 1.00 43Poly(methacrylic acid) — 130Poly(methyl methacrylate) 1.17 105Poly(ethyl methacrylate) 1.12 65Poly(n-butyl methacrylate) 1.06 20Poly(n-hexyl methacrylate) 1.01 �5Polyacrylamide 1.30 165

Source: Data from Mascia (1989).

The data in the table clearly illustratethree important aspects of the structure–-property relationship in polymers, respec-tively chain stiffness (energy required torotate a group attached to the carbon atomin the backbone chain), internal plasticiza-tion (creating free volumes between poly-mer chains) and intermolecular forces. Onthis basis, one notes that polymethacrylateshave a higher Tg than the correspondingacrylates. Increasing the length of the alkyl-group acrylate or methacrylate polymersbrings about a large reduction in Tg throughinternal plasticization. The presence of a

10 Acrylic Polymer j3

carboxylic acid or an amide group causes theopposite effect through the increase in in-termolecular forces by the formation ofinter-chain hydrogenbonds. Themain char-acteristics of acrylic polymers available com-mercially are described below in alphabeti-cal order of the monomer units within thepolymer chains.

10.1 Acrylic Elastomer

Generally available as a random copolymeror terpolymer, typically poly(ethyl–butyleneacrylate) with Tg within the range �30 to�40 �C. These elastomers are well knownfor their resistance to oils, as well as for theiroxidative stability at high temperatures and

in UV light environment. They tend to ab-sorb large quantities of water via hydrolysisof the ester groups. Vulcanization can becarried out by either peroxide curatives, forsystems containing unsaturation in themainchains,orbymetalhydroxides throughsalt formation via carboxylic acid groups.

10.2 Acrylic Adhesive

(See Adhesive.)

10.3 Acrylic Fibre

Produced from polyacrylonitrile (PAN),whichisrepresentedbythechemicalformula

where the CN groups are organized in anatactic configuration, preventing themolec-ular chains from packing in a highly or-dered crystalline lattice. The fibres are pro-duced by solution spinning, because of thehigh viscosity and the rapid decompositionof the polymer at the temperatures thatwould be required for melt spinning. Ther-mal degradation takes place by cyclizationinvolving the pendent CN groups along thepolymer chains, which results in the forma-tion of infusible ladder polymers, as shownby the reaction scheme, and confers on thefibres a certain degree of fire retardancy

Moreover, this particular feature makesPAN fibres suitable for the production ofcarbon fibres due to the dimensional stabil-ity that they acquirewhile they are heated upto the high temperatures required forgraphitization. (See Carbon fibre.)

10.4 Acrylic Flocculant and Hydrogel

Based on polyacrylamide, a water-solublecrystalline polymer represented by the for-mula shown.

4j 10 Acrylic Polymer

10.5 Acrylic Impact Modifier

Based on methyl methacrylate–butadie-ne–styrene (MBS) terpolymer alloys, usedwidely as impact modifiers in rigid PVCformulations. They are produced mainlyfrom emulsions of a styrene–butadienerubber (SBR) elastomer and through graftpolymerization of methyl methacrylatechemically bonded on the surface of thepre-formed SBR particles. The tougheningaction in poly(vinyl chloride) (PVC) com-pounds arisesmostly from themiscibility ofthe acrylic outer layers of the dispersedparticles with the PVC matrix. These arepreferred to ABS impact modifier systemsin applications requiring superior resis-tance to UV light.

10.6 Acrylic Plastic

The most important polymer in this cate-gory is poly(methyl methacrylate) (PMMA),a glassy polymer available either as a ther-moplastic material or as a lightly cross-linked pre-formed product, such as sheetsor rod castings. PMMA is widely for its hightransparency and high resistance to UVlight. It is represented by the formula shownand is usually available as a homopolymergrade. (See Acrylic polymer.)

11. Activation Energy

A term in the Arrhenius equation widelyused to denote the sensitivity of the rate ofchemical or physical processes to changesin temperature. The activation energy (DH)is determined from the slope of the plot ofthe logarithm of the rate of reaction, or rateof physical change, against the reciprocal of

the absolute temperature (T ). This can bederived from the Arrhenius equation,

rate K ¼ A expð�DH=RTÞ;where A is a constant for the system R isthe universal gas constant. (See Arrheniusequation.)

12. Activation Volume

A term in the Eyring equation used todescribe the sensitivity of the yield strengthof materials to changes in applied strainrate. It is an adaptation of the Arrheniusequation for which the activation energyterm (DH) is replaced by the term (DH�ysY), where y is the activation volume andsY is the yield strength. The product ysY

represents the quantity by which the activa-tion energy has been reduced by the appli-cation of the stress required to induce yield(plastic) deformations. (See Yield failure.)The Eyring equation is written as

d«=dt ¼ B exp½ðDH�ysYÞ=RT �;

where d«/dt is the strain rate used in thetest, corresponding also to the rate at whichyielding deformations take place, and B is amaterial constant. (See Eyring equation.)

13. Activator

An additive used in conjunction with anaccelerator for the vulcanization of elasto-mers. Activators consist of metal oxides orsalts of lead, zinc ormagnesium, often usedin conjunction with stearic acid to enhancetheir solubility in the rubber mix.

14. Addition Polymerization

The conversion of monomer to polymerwithout the loss of other molecular species.This is contrary to the case of condensation

14 Addition Polymerization j5

polymerization, which takes place throughthe loss of small molecules, such as water.Typically, addition polymerization takesplace by a free-radicalmechanismor cationicpolymerization.

15. Additive

A substance added to a polymer formula-tion in minor amounts to improve ormodify specific characteristics related tomanufacture and/or end use of products.

16. Additive Concentrate

Amixture of additive and a polymer powder(usually) where the amount of additive pres-ent is much larger than the quantity re-quired in the final formulation. The concen-trate ismixedwith the neat polymer or resinto bring down the amount of additive to therequired level. (See Master batch.)

17. Adherend

A term often used to denote the componentin contact with the adhesive layer.

18. Adhesive

Substance used to stick (bond) two or morecomponents of a product or structure.Adhesives can be divided into �hot-meltadhesives�, based on thermoplastic poly-mers, �curable adhesives�, based on thermo-setting resin, and �pressure-sensitive ad-hesives�, based on elastomeric polymers.Apart from the bonding requirements, anydifference in molecular structure or formu-lation details between polymer composi-tions used for �bulk� components and thoseused for adhesives arises from differencesin the way the two systems have to be

processed or applied. The table lists somepolymers used for adhesives.

Commercial name Chemical nature

Thermoplastic hot meltsPolyesters andpolyamides

Low-crystallinity systems

Phenoxy Poly(glycidyl hydroxyl ether)EVA Ethylene–vinyl acetate

copolymerEEA Ethylene–ethyl acrylate

copolymer

Thermosetting (cold cure and heat curable)Phenolics Mostly modified with NBREpoxy Mostly DGEBA resinsAcrylics Several types available

Pressure-sensitive adhesives (PSAs)Most uncuredelastomers

Contain tackifiers

Water-borne emulsionsPoly(vinyl acetate) Partially hydrolysed

The chemical compositions of polymersused for hot-melt adhesives are similar tothose used for plastics, but they have lowermolecular weights to meet the low-viscosityrequirements for manufacturing purposes.Adhesive grades are usually copolymerscontaining small amounts of carboxylic acidor hydroxyl groups to enhance their affinityand bonding characteristics for the morecommon adherends. Oligomeric systemsused for curable adhesives usually containcomplex mixtures of auxiliary ingredients,and often have a heterogeneous morpho-logy, as ameans of obtaining a good balanceof properties and also to satisfy specificrequirements for a multitude of applica-tions. Acrylic adhesives are usually basedon low-volatility monomers containing per-oxide initiators with a very long half-life.Some very innovative systems have beendeveloped that take advantage of prevailingconditions to accelerate or induce curing in

6j 18 Adhesive

the adhesive. An interesting example is theanionic polymerization of cyanoacrylate ad-hesives, which takes advantage of the slight-ly basic nature ofmany inorganic substratesand the presence of water adsorbed on thesurface to promote cure reactionswithin theadhesives.

19. Adhesive Test

Usually refers to a mechanical test for mea-suring the strength of bonded specimens,which is normally defined as the force re-quired to separate the adherends of a joint,divided by the overall bonded area. Underideal conditions, that is, those in which theactual intrinsic strength of the adhesive is tobemeasured, failure has to take placewithinthe bulk of the adhesive (cohesive failure)and not at the interface between adherendand adhesive (interface failure). This is anessential requirement of structural adhe-sive, and it is for this reason that the surfaceof the adherend is often treated to increasethe interfacial bond strength to the levelrequired to ensure that failure takes placewithin the adhesive. The preparation of thesurface of the adherend usually entails thegeneration of chemical groups that canreact with the adhesive to produce chemicalbonds across the interface. If the adhesive ismechanically strong (i.e. it requires highstresses for fracture), it is unlikely thatcohesive failures can be achieved onlythrough physical bonds at the interface,even when these are strong types such ashydrogen bonds, bearing inmind that thesemay beweakened through the absorption of

water. Nevertheless, the strength values ob-tained depend on geometric factors, such asthe dimensions of the bonded area and thethickness of the adhesive layer. Conse-quently, they cannot be used as fundamen-tal parameters for use in theoretically baseddesign procedures and have to be consid-ered primarily as data for �quality controland specifications�.

19.1 Tensile Test

Typical bonded specimens, known as buttjoints, are shown. These are pulled at con-stant strain rate up to fracture. The bondstrength is calculated by dividing the load tofracture over the bonded area.

Typical axial loaded �butt-joint� specimens:(a) wood-to-wood bond; (b) metal-to-metal bond.

19.2 Shear Test

Also known as �lap shear� to describe thetype of specimen used. Typical specimenstypes are shown.

19 Adhesive Test j7

These are the more widely used tests,mainly because both the specimens and theexperimental procedure are simple. Thestrength of the bonded specimen, knownas the �lap shear strength�, is expressed asthe load to fracture divided by the bondedarea. In these tests the adhesive layer issubjected to a combination of tensile andshear stresses at the interface andwithin theadhesive layer, which vary in the oppositemanner along the bonded length of thelapped area, as shown. The shear stress inthe adhesive layer decreases from a maxi-mum at the edge of the lapped area to zeroin the middle when the bond line is suffi-ciently long. Completely the opposite to thisis the change in axial tensile stress, which ismaximum in the centre and smallest (zero)at the outer edges.

19.3 Fracture Toughness Test: General

The fracture toughness of bonded speci-mens is normally measured using double

cantilever specimens. These are specimenswith a very long bond line subjected to a�crack opening� fracturemode by pulling thebonded cantilevers away from each otherand recording the load during fracture prop-agation along the �bonded line�. The value ofthe critical strain energy release rate Gc iscalculated from a fundamentally derivedequation, using the appropriate values fordC/da (i.e. the rate of increase of specimencompliance C with crack length a). (SeeCompliance and Fracture mechanics.)Two types of specimens are usually used:

. the uniform double cantilever beam(UDCB) specimen, which is known alsoas the thin strip test;

. the tapered double cantilever beam(TDCB) specimen, which is known alsoas the wedged specimen.

The description and geometry of thesetwo specimen types are given below.

Variation of strain in the adhesive layer and the two adherends in a single lap shear test.

8j 19 Adhesive Test

19.4 Fracture Toughness Test: UDCBSpecimen

Double cantilever beam (thin strip) test. The load can be applied either directly at the edge of the strips orthrough a wedge at the open end of the bonded strips.

In UDCB testing, it is important that thetwo adherends undergo only elastic defor-mation during the test to ensure that all theenergy imposed is used only to inducefracture of the adhesive layer. Note that, fora double cantilever beam, the compliance Cis given by the expression

C ¼ D

P¼ 64a3

EWB3;

where D is the deflection, P is the load, a isthe non-bonded distance (cf. crack length),E is the Young�s modulus of the adherend,W is the width of the specimen and B is thethickness of the beam. Differentiating theabove equation with respect to a gives anexpression for dC/da that can be substitutedin the generic equation for Gc, which canthen be calculated from the recorded load tofracture (Pf), that is, the maximum loadrecorded in the test. From the above equa-tion one obtains

Gc ¼ 96P2f a

2

EW2B3:

Note that, when the adherend is veryflexible (compliant), the test is known asthe �T-peel test�. If, on the other hand, one ofthe adherends is very rigid (i.e. very thickand/or the material has a very high modu-lus) and the other is very compliant (i.e. verythin and/or the material has a very lowmodulus), the test is known as the �L- peeltest�. Both tests can be used to measure the

fracture toughness in terms of theGc value,which is given by the formula

Gc ¼ ðPf=BÞð1þ «Þ;whereB is thewidth of theflexible adherendstrip and « is the tensile strain («¼P/BWE).When « is very small, the value of Gc isobtained directly from the ratio Pf/B. Theunit N/m corresponding to this ratio isequal to J/m2, which is the appropriate unitfor Gc.

19.5 Fracture Toughness Test: TDCBSpecimen

Tapered double cantilever specimen for fracturetoughness testing of adhesives.

For TDCB specimens the value of dC/dais given by the expression

dC=da ¼ 6m=EB;

where B is the thickness, E is the Young�smodulus of the beam andm is a function ofboth the height h of the beam and cracklength a, that is,mh3� (1 þ y)h2� 4a2¼ 0,

19 Adhesive Test j9

where y is the Poisson ratio of the beam.The taper of the outer edge of the specimenis estimated by maintaining the value of mconstant so that the height (depth) of thebeam becomes larger as the non-bonded(crack) length increases. The solution ofm gives a slightly concave contour for theouter edge, with the curvature becomingmore pronounced as the non-bonded dis-tance gets smaller. Therefore, by using largevalues of a, the contour of the specimenbecomes approximately linear, that is, thegradient is constant. Typically, if the gradi-ent angle is 11�, then

dC=da ¼ 90=EBh0;

where h0 is the height (depth) of the beam atthe crack tip. This simpler geometry makesit easier to produce specimens for testing.The advantage of the TDCB specimen isthat the fracture load (Pf) remains constantduring fracture propagation, making it pos-sible to measure the rate of crack propaga-tion along the bond line.A slip–stick type of crack propagation

occurs if fracture takes place in a mixedmode, involving cleavage through the bulkof the adhesive layer and debonding at theinterface with the adherend.

Typical force–deformation curves obtained in testswith TDCB specimens.

The TDCB test is particularly useful forfractures induced under fatigue (cyclic load-ing) conditions, so that the crack growth rate

can be measured as a function of the fre-quency and magnitude of the applied load.Using UDCB specimens, on the otherhand, the load to fracture decreases aftercrack initiation because the value of dC/dabecomes smaller with increasing cracklength. For many systems, the fracturetoughness of structural adhesives has beenmeasured also with respect to the long-termstatic and dynamic (fatigue) behaviour,through measurements of the increase incrack length with time and/or loadingcycles.

20. Adhesive Wetting

Wettability is an essential characteristic ofan adhesive to ensure that it completelycovers the surface of the adherend. Thiscondition is satisfied by ensuring that theadhesive and adherend have a similar sur-face energy. In quantitative terms, this re-quirement is to make sure that the so-called�work of adhesion�,WA, is very small. This isrelated to the surface energies, g, betweenthe various phases by the equation

WA ¼ gLV þgSV þgLS;

where the subscripts LV, SV and LS denotethe three interfaces concerned, respectivelyliquid–vapour, solid–vapour and liquid–solid. The surface energy for the solid–liquid interface is lowest when the respec-tive surface energies of the solid (substrate)and the liquid (adhesive) are very similar.Surface energies depend on the chemicalconstitution. Low polarity will give lowvalues for the surface energy. Polytetrafluor-oethylene (PTFE) has the lowest surfaceenergy because of the absence of net dipolesin the structure. Polyethylene (PE) also has avery low surface energy, owing to the ab-sence of net dipoles, but it is not as low as forPTFE. Polymers with very strong dipoles,such as those containing COOHorOH sidegroups or NH groups in the main chains

10j 20 Adhesive Wetting

(e.g. polyamides and polyurethanes), havevery high surface energies. (See Surfaceenergy.) Surface oxidation of PE or PTFEcan introduce polar groups and increaseaccordingly the surface energy. These treat-ments would be used, therefore, to improvethebondingofpolaradhesives,suchas thosebased on epoxy resins. Chemical reactionsacross the interface bring about an increasein the interfacial bonding between adhesiveand adherend, which represents the highestlevel of bonding that can be achieved.

21. Adiabatic Heating

A term used to describe the self-heating of apolymer taking place during intensive mix-ing and extrusion, resulting from the shear-ing action of the rotors of the mixer or thescrew of an extruder.

22. Air-Slip Forming

A technique used in vacuum forming (alsothermoforming) by which air is injectedthrough fine orifices in the cavity of themould in order to prevent sticking and rapidcooling of the polymer sheet during draw-ing. (See Thermoforming.)

23. Aliphatic

A term used in chemistry to describe thelinear connection of carbon atoms to eachother. This implies the absence of benzenerings, a compound containing which wouldbe referred to as �aromatic�. (See Aliphaticpolymer.)

24. Aliphatic Polymer

A polymer containing aliphatic carbonatoms along the backbone of the molecularchains, for example, polypropylene.

25. Alkyd

A type of polyester resin. The term is de-rived from a combination of the wordsalcohol and acid to indicate that it is aproduct resulting from the reaction of analcohol (multifunctional) and a dicarboxylicacid. The latter is usually a mixture of natu-rally occurring fatty acids and aromatictypes. Alkyds are normally divided into oxi-dizing and non-oxidizing types. The oxidiz-ing types are produced from unsaturatedfatty acids, whose double bonds can reactwith oxygen from the atmosphere to pro-duce free-radical species that can causecross-linking reactions. The non-oxidizingtypes are cross-linked by reactions of thefree OH groups in the chains with a ureaformaldehyde or melamine formaldehyderesin, or with multifunctional isocyanates.

26. Allophonate

A type of chemical group formed fromreaction between an isocyanate and a ure-thane group.

27. Alloy

(See Polymer blend.)

28. Alpha Transition Temperature

The alpha (a) transition temperature Ta isthermodynamically classified as a second-ary transition, denoting the temperature atwhich thefirst partial derivative of a primaryfunction, such as the volumeor the enthalpy(@V/@Tor@H/@T), shows a discontinuity.Tais also known as the glass transition tem-perature (Tg) insofar as it represents a ref-erence temperature for the change in thedeformational behaviour of a polymer fromthe glassy state to the rubbery state, which

28 Alpha Transition Temperature j11

entails a reduction inmodulus by a factor of103–104 with increasing temperature.

29. Alternating Current (AC)

A current resulting from the application of acyclic (sinusoidal)voltage.Thecyclicvariationof voltage and current takes place at specificfrequencies. (See Dielectric properties.)

30. Aluminium Trihydrate Al2O3�3H2O

A functional filler used to impart flame-retardant and antitracking characteristics toa polymer. Particle size is in the range2–20mm and surface area in the region of0.1–6m2/g. The amount of water corre-sponds to 34.5wt%, which volatilizes veryrapidly above 220 �Cand reaches about 80%completion at around 300 �C. (See Flameretardant, Antitracking and Filler.)

31. Amine-TerminatedButadiene–Acrylonitrile (ATBN)

An oligomer, also known as liquid rubber,amine-terminated butadiene–acrylonitrile(ATBN) is used for the toughening of epoxyresins. Commercial systems are availablewith molecular weight between 2000 and5000 and with acrylonitrile content around25–35%. (See Epoxy resin, subsection�Reactive toughening modifiers�.)

32. Amino Resin

A resin produced from the reaction of amultifunctional amine and formaldehyde.The most commercially important aminoresins are urea formaldehyde (UF) andmel-amine formaldehyde (MF) resins. Both re-sins are water clear, unlike phenol formal-dehyde (PF) systems. Thenetwork structureof the cured UF resins and the reactionsinvolved are shown schematically.

These are formed from condensationreactions between �CH2OH of the basicresin to produce oxymethylene bridges, asshown in the scheme.

Condensation reactions in the curing of UF resins.

Dense network structure of cured urea formaldehyde (UF) resin.

12j 32 Amino Resin

Similar reactions take place in the cross-linking of MF resins, as shown.

A large number of these oxymethylene bridgesundergo a loss of formaldehyde to produce a densernetwork.

The moulding compounds of both UFand MF resins contain cellulose fillers andadditives, such as pigments, curing cata-lysts, external lubricants and sometimesalso small amounts of plasticizer. For whiteformulations, the cellulose filler is usually ableached variety in order to eliminate thepossibility of producing undesirable tintsfrom impurities. Sometimes MF resins arebutylated in order to increase their shelf-lifewhen used as aqueous solutions or micro-suspensions. In this case the condensationreactions will be preceded by the lossof butanol. For both UF and MF resins,however, the curing reactions rarely go to

completion, so that there will be a substan-tial number of CH2OH groups presentin addition to �NCH2�O�CH2N� and�NCH2N� groups.The use of cellulosic fillers for moulding

powder or paper for laminates not onlyprovides an efficient reinforcing and tough-ening function but also ensures that thewater produced does not result in the for-mation of voids. The strong affinity of waterwith the structural units of amine resins, viahydrogen bonds, allows a substantialamount of water to remain dissolved in thenetwork.

33. Amnesia

A term (jargon) used in the technology ofheat-shrinkable polymers to denote the ex-tent by which the product fails to reach thedimensions it had before being stretched.(See Permanent set.)

34. Amorphous Polymer

The term is used to denote the lack of orderat the supramolecular level. This implies

Network of a highly cross-linked melamine formaldehyde (MF) resin. Source: Ehrenstein (2001).

34 Amorphous Polymer j13

that the molecular chains (thermoplastics)or the macromolecular networks (thermo-sets or cross-linked rubber) have a randomconfiguration, as illustrated in the sche-matic diagram.

35. Anatase

A crystalline form of titanium dioxide (tita-nia) used as the basic component of whitepigments. (See Titanium dioxide.)

36. Anionic Polymerization

A type of polymerization that takes place viathe growth of chains containing an anion inequilibrium with a small-sized counter-ion(cation) originating from the initiator, usu-ally a metal alkyl (e.g. lithium butyl) or analkyl metalamide (e.g. potassamide). Thesteps involved in the polymerization are asfollows.

Step 1. Initiation: Addition of the anionfrom the initiator onto the monomer,

LiBuþH2C¼CHX!Bu�H2

C� CHX�Liþ

Step 2. Propagation: Rapid addition of alarge number of monomer molecules,

Bu�H2C� CHX� Liþ

þ nH2C¼CHX!Bu�H2C�CHX� ðH2C� CHXÞ�n Liþ

Step 3. Termination: Polymer chains reachfull size when the monomer is exhausted orthrough secondary reactions with other spe-cies present, such as solvent.

37. Anionic Surfactant

(See Surfactant.)

38. Anisotropic

A product or specimen exhibiting aniso-tropy. (See Anisotropy.)

39. Anisotropy

Thecharacteristicofaspecimenorproduct inwhichthevalueofagivenpropertyisdifferentinmagnitudewhenmeasured in twoperpen-dicular directions. In the case of cylindricalgeometries such as rods, fibres or tubes, thetwo perpendicular directions of anisotropicbehaviour are the longitudinal and circum-ferential directions. Anisotropy in polymerproducts results from the preferential align-ment of polymer chains and crystallites in aspecificdirection. Inmost cases anisotropy isdeliberately introduced to enhance the prop-erties in one specific direction. In the case offibresandtapes,theorientationisdeliberatelyinducedintheaxial,or longitudinal,directionas a means of increasing the mechanicalstrength in thedirection inwhich theproductwould be subjected to mechanical forces in

Linear polymers (left) and cross-linked polymers (right).

14j 39 Anisotropy

service. (See Orientation.) In the case ofcomposites,anisotropyarisesfromthediffer-ent degree of fibre alignment in two perpen-dicular directions.

40. Annealing

Atermdenoting the thermal treatment (usu-allyat constant temperature followedbyslowcooling)ofaspecimenorproductwithaviewto releasing the internal stresses set up dur-ing moulding or to developing the highestpossible degree of crystallinity. This thermaltreatment serves also to stabilize the dimen-sions and properties of a product prior to itbeing used in service. Annealing is carriedout at temperatures very close to the glasstransition temperature (Tg value) of thepoly-mer if amorphous or just below its meltingpoint (Tm) if the polymer is crystalline. Note,however, that annealingmay induce embrit-tlement of products made from glassy poly-mers through physical ageing and thosemade fromcrystallinepolymers through thethickening of the lamellae.

41. Anodizing

(See Metallization.)

42. Antiageing

(See Antioxidant, Stabilizer and UVstabilizer.)

43. Antibacterial Agent

(See Antifouling additive andAntimicrobialagent.)

44. Antiblocking Agent

An additive that produces roughness on thesurfaces of a soft polymer product, prevent-

ing these from sticking to another throughinterfacial attraction forces. This phenome-non is particularly problematic in the case offlexible films used for plastic bags, as itmakes it difficult to open them. The mostwidely used antiblocking additives consistof fine particles 20–50 nm diameter, usuallyinorganic fillers such as silica, talc, kaolin,calcium carbonate and zeolites.

45. Antidegradant

Ageneric nameused primarily in relation torubber formulations to denote an additivethat improves the resistance to ageing. (SeeDegradation and Stabilizer.)

46. Antifoaming Agent

An additive used to prevent the formation offoams during the mixing of liquid systems.They are also known as defoamers or foamsuppressants. Early systems were primarilyvegetable or mineral oils. Nowadays anti-foaming agents are complexmixtures in theform of hydrophobic solids containing ac-tive ingredients, consisting of a variety ofcompounds derived from water-solublepolymers. They normally contain a liquid-phase component such as mineral or vege-table oils, poly(ethylene glycol), silicone oils(polydimethylsiloxanes) and fluorosilicones(polytrifluoropropylmethylsiloxanes). Theseare particularly effective in non-aqueoussystem particles because of their low surfaceenergy and immiscibility. The other compo-nent is a solid consisting of hydrophobicsilica or hydrocarbon waxes. Antifoamingagents may also contain ancillary ingredi-ents consisting of surfactants, couplingagents, stabilizers and carriers. The latterhave the function of holding the ingredientstogether. In general, the defoamer has asurface energy lower than that of the foam-ing medium and should be immiscible and

46 Antifoaming Agent j15

readily dispersible. The main uses of defoa-mers inpolymer systemsare in coating, latexand emulsion formulations.

47. Antifouling Additive

Known also as biocides and bactericides,these contain chemicals that are toxic tomicroorganisms. These include zinc andbarium salts, as well as mixtures of zincoxide or barium metaborate with thiazolesor imidazole compounds. They are widelyused for marine coatings. More recently,extensive use has been made of the incor-poration of sub-micrometre particles of sil-ver, particularly for furniture and appliancesfor clinical application. (See Antimicrobialagent.)

48. Antimicrobial Agent (Biocidal Agent)

An additive with the ability to inhibit thegrowth of a broad range of microbes, suchas bacteria, moulds, fungi, viruses andyeasts. Antimicrobial activity in polymerscan be attained either by the incorporationof additives or through modifications of thechemical structure. Additives that can beused as antimicrobial agents include anti-biotics, heavy-metal ions (silver or copper),cationic surfactants (quaternary ammo-nium salts with long hydrocarbon chains),phenols and oxidizing agents. An additivethat is frequently used as an antimicrobialagent in polymers is metallic silver, in theform of fine (nano-sized) particles, eventhough it does not release metal ions aseasily as copper. The use of copper isavoided, however, as it can have some dev-astating effects on the heat stability of thepolymer. In order to increase the rate ofrelease of ions, silver salts are sometimesembedded in hydrophilic carrier particles,such as silver-substituted zeolites. Macro-molecular antimicrobial agents used in

polymers include poly(2-t-butylaminoethylmethacrylate) (PTBAEMA) and N-hala-mines grafted onto polymer chains throughacid or anhydride functionalization of thelatter. N-halamines are compounds inwhich one chlorine atom is attached to thenitrogen atom. In both cases the antimicro-bial activity derives from the formation of aquaternary ammonium salt, while the poly-meric nature prevents them from beingeasily extracted by water.

49. Antimony Oxide

Corresponds to Sb2O3 and is used as awhitepigment as a result of its high scatteringpower resulting from its high density (5.7 g/cm3) and as a functional filler in conjunc-tion with chlorinated or brominatedcompounds to impart fire-retardant charac-teristics to polymers. Optimal tinting andflame-retardant properties are achievedwith particle size in the range of 0.2 to 1mm.These systems are generally considered toproduce toxic products under burning con-ditions. (See Flame retardant.)

50. Antioxidant

An additive within the general class of anti-ageing additives or stabilizers. An antioxi-dant reduces the rate of degradation ofpolymers resulting from the action of oxy-gen in the atmosphere on defective sites of amolecular chain. This creates free radicals,which initiate and propagate a series ofreactions resulting in chain scission,cross-linking and formation of oxygen-con-taining chromophore groups, such as car-bonyls. These reactions cause discolora-tions and embrittlement of the product. Anantioxidant reacts with the free radicals toproduce inert compounds, thereby prevent-ing the propagation of degradation reac-tions. The antioxidant activity is regenerated

16j 50 Antioxidant

through secondary reactions so that theycan act as efficient stabilizers even at verylow concentrations (0.1–0.5%). Typical anti-oxidants used in polymers are ortho- andpara-substituted tertiary butyl phenols oraromatic amines. Amine antioxidants areless widely used, as they impart a darkdiscoloration to the products and they arerather toxic, which makes them less attrac-tive for general uses. Typical examples ofphenolic stabilizers are shown.

Example of phenolic antioxidants.

Note that the second example of phenolicantioxidant contains a phosphite group,which provides a synergistic effect with thephenolic unit by acting as a peroxide de-composer. Themore common types of anti-oxidants do not have a built-in peroxidedecomposer and, therefore, they require thepresence of another additive to exert thisfunction. These are typically phosphite andmercaptan compounds, which acceleratethe decomposition of hydroperoxides anddeactivates them through the formation ofstable products.Antioxidants intervene in the degrada-

tion reactions caused by the formation offree radicals in the polymer chains (P)through a series of reactions with oxygen,starting at sites with the weakest CH bond,such as tertiary or allylic carbons. The�initiation� reaction.

PHþO2 !POOH!PO. þ .OH

is followed by rapid propagation reactions

P. þO2 !POO.

POO. þPH!POOHþP.

PHþH. !H2 þP.

P. þP0H!PHþP0.

PHþ .OOH!P. þH2O2

OH. þPH!P. þH2O

Propagation reactions are the most dam-aging reactions insofar as they affect a largenumber of polymer molecules. The antioxi-dant intervenes predominantly at this stageby reacting with the free radicals in thepolymer chains, forming non-reactive pro-ducts, a phenomenon known as quenching.Denoting by AH the antioxidant molecule,either amine or phenol type, the quenchingreaction can be written as

P. þAH!PHþA�

where A� represents a stable (non-reactive)radical. The mechanism for the loss ofreactivity of the A� radicals for the case ofa phenolic antioxidants is as shown.

Note that the stability of the radicals isdue to internal delocalization, making itinaccessible for interacting with polymerchains.The reaction scheme for the action of

secondary stabilizers as peroxide decompo-sers is:

50 Antioxidant j17

Examples of mercaptan and phosphitecompounds used as secondary stabilizersare dilaurylthiodipropanoate (DLTDP) anddistearylthiodipropanoate (DSTDP).

The structures of two phosphite second-ary stabilizers are shown. These are knowncommercially as Weston 618 (left) andUltranox 626 (right).

51. Antiozonant

An additive used primarily in diene elasto-mers to improve the resistance to attackfromozone in the environment, particularlythe ozone generated in electrical motorsand other devices through corona dis-charges. An antiozonant is often a waxcapable of migrating to the surface to forman oxidation-resistant layer.

52. Antiplasticization

Although the term denotes a phenomenonwith the opposite effect to plasticization,

this must not be interpreted in terms of anincrease in the glass transition temperature.Antiplasticization is a phenomenon thatbrings about an increase in modulus at lowtemperatures, as well as embrittlement at

ambient temperatures. In PVC, this isbrought about by the incorporation of smallamounts of plasticizers (typically 5–10 partsper hundred) capable of exerting strongphysical interaction, such asH�bondswiththe Cl atoms in the chains. These interac-tions cause a depression of short-rangerelaxations, normally associated with rota-tional movements of side groups in a poly-mer chain. The effects of the addition of

18j 52 Antiplasticization

small amounts of plasticizer in PVC com-pounds on the variation of modulus withtemperature, shown in the diagram, pro-vides evidence that antiplasticization isessentially a phenomenon occurring at lowtemperatures and that normal plasticizationtakes places at higher temperatures.

Plot of dynamic shearmodulusagainst temperaturefor a PVC sample (curve on the right, triangles) anda sample containing 9wt% tricresyl phosphate(curve on the left, circles). Source: Mascia (1978).

Illustration of effects of antiplasticization of a PVCcompound. Upper curve: unplasticized PVC. Lowercurve: PVC plasticized with 9wt% tricresyl phos-phate. Source: Mascia et al. (1989).

The embrittlement effect due to antiplas-ticization is illustrated in the second dia-gram in terms of the reduction in �criticalcrazing strain� as a function of the CH3OH/H2O ratio, representing the relative affinityof the environmental agent for the polargroups in the polymer.

53. Antistatic Agent

An additive used in polymer formulationsto reduce the build-up of static charges onthe surface of products or structures. Anti-static agents are additives capable ofmigrat-

ing to the surface of a product, forming aconductive path through ionization result-ing from the absorption of moisture in the

53 Antistatic Agent j19

atmosphere. These are usually surfactantsconsisting of long-chain aliphatic amines,amides or quaternary ammonium salts,alkyl aryl sulfonates and alkyl hydrogenpho-sphates. Among other compounds used asantistatic agents are water-soluble ionicallyconductive polymeric compounds, such ashexadecyl ethers of poly(ethylene glycol).(See Surface resistivity.)

54. Antitracking

Preventing the formation of surface trackson the surface of a dielectric, or insulator,subjected to a high voltage. The surfacetracks consist of carbonaceous paths thatare formed as a result of the chemicaldegradation of the polymer, thereby produc-ing very conductive channels capable ofleaking a current to ground. Tracking ofinsulators is often prevented by depositingsuitable oils or greases on the surface, suchas silicone types, as they are thermally stableand do not form carbonaceous residues.

55. Antitracking Additive

An additive that imparts antitracking char-acteristics to a polymer. These are sub-stances that can release large quantities ofwater when the outer surface layers of theinsulator reach temperatures in the regionof 300–400 �C, as a result of the heat pro-duced by the arcs generated by the appliedhigh voltage. Arcs contain very reactive oxy-gen ions, which give rise to extremely rapiddegradation reactions. The most widelyused antitracking additive is aluminiumtrihydrate, Al2O3�3H2O, which loses allthree H2O molecules at around 350 �C,corresponding to about 35wt% weight loss.(See Flame retardant.)

56. Apparent Shear Rate

The shear rate calculated on the basis thatthe polymer melt behaves as a Newtonianliquid. The value of the apparent shear rate,_ga, at the wall can be calculated from theflow rate Q and the dimensions of thechannels, as follows.

. Circular channel: _ga ¼ 4Q=pR3, whereRis the radius of the channel.

. Rectangular channel: _ga ¼ 6Q=WH2,where W is the width of the channel andH is the depth, valid for shallow channels,that is, when W � H.

A shape factor, S, has to be introduced forother situations. Correction has to be madebymultiplying the value calculated from theabove equation by the appropriate shapefactor, S¼ 1 – 0.65(H/W). (See True shearrate and Non-Newtonian behaviour.)

57. Apparent Viscosity

The value of the viscosity (ha) calculated onthe basis that the polymermelt behaves as aNewtonian liquid, that is ha ¼ t= _ga, wheret is the shear stress and _ga is the value of theapparent shear rate.

58. Aprotic Polar Solvent

A solvent without the capability of undergo-ing hydrogen-bonding interactions throughthe involvement of protons.

59. Araldite

A tradename for a variety of epoxy resins.

20j 60 Araldite

60. Aramid

A term used to denote aromatic polyamidefibres, an example of which is shown.

Example of an aramid fibre displaying fibrillationcharacteristics. Source: Ehrenstein (2001).

The chemical structure of a typical poly-amide used for the production of aramidfibre is shown.

These are often identified by the trade-name Kevlar. The molecular chains of aro-matic polyamides are very rigid and areoriented in the axial direction of the fibres,forming strong attractionswith other neigh-bouringmoleculesviahydrogenbonds.Thisprovidesahighstrengthandmodulus,withahighlevelofductility, relativetocarbonfibres(which are extremely brittle) and even glassfibres. Aramids have a very high meltingpoint (around 500 �C) but are susceptible toUV-induced degradation. (See Composite.)

61. Aromatic Anhydride

Frequently used compounds for the produc-tion of polyesters and polyimides and some-times used as curing agents for epoxyresins.

62. Arrhenius Equation

The name of an equation derived by thechemist Arrhenius to describe the variationof the rate of a chemical reaction (K ) as a

function of the absolute temperature (T ).This is written as

K ¼ A expð�DE=RTÞ;where A is a characteristic constant, DE isthe activation energy for the reaction and Ris the universal gas constant. This equationhas been found to apply equally well tophysical processes that involve movementsof some structural constituents, for instancein the case of electronic or ionic conductionand gas diffusion.

63. Asbestos

A magnesium silicate fibre occurring natu-rally in four different forms. The �chrysotile�variety has been used for reinforcement ofthermosetting resins, particularly phenolictypes, in engineering applications such asbrake pads. It consists of fine fibrils packedinto bundles for its high reinforcing effi-ciency due to the high modulus (see themicrograph).

SEM micrograph of chrysotile asbestos fibres.Source: Wypych (1993).

Owing to toxicity issues, asbestos hasbeen largely replaced by other high-perfor-mance reinforcing fibres. (See Composite.)

64. Aspect Ratio

The ratio of the length to diameter of fibresused in composites. Sometimes used also

64 Aspect Ratio j21

for platelet particles as the ratio of thenominal width to the thickness.

65. Atactic Polymer

A term used to denote the lack of a specificorder in the chemical structure of a polymer,such as polypropylene. A polymer with anatactic chemical structure. (See Isotacticpolymer and Tacticity.)

66. Atomic Force Microscopy (AFM)

A microscopic technique that producesimages of the surface topology via the tip ofa scanning probe that measures the atomicforces (attractive or repulsive) against thesurface under examination. Atomic forcemicroscopy (AFM) is particularly useful forexamining surface features of very smalldimensions, for example 10–1000nm. Thetip is placed on a cantilever that will deflect asa result of the atomic surface forces, asshown in the diagram.

The movements are detected by the re-flection of a suitable focused laser beam. Intapping-mode AFM the cantilever is oscil-lated at a certain frequency with an ampli-tude that allows the tip to come into close

proximitywith the surfacewithout touchingit. In most cases a feedback mechanism isemployed to adjust the tip-to-sample dis-tance to maintain a constant force betweenthe tip and the surface of the sample.

67. Attenuated Total ReflectanceSpectroscopy (ATR Spectroscopy)

An infrared spectroscopy technique used toidentify specific chemical groups present onthe surface of a sample, supported on aprism with a very high refractive index,which reflects the incident infrared radia-tion transmitted through the thin film incontact with the prism. (See Infraredspectroscopy.)

68. Attenuation

(See Damping.)

69. Avrami Equation

Originally developed to model the crystalli-zation rate ofmetals during solidification, ithas been found to apply equally well to the

Schematic diagram of the operating principle of an atomic force microscope. Source: Lavorgna (2009).

22j 69 Avrami Equation

crystallization of polymers. The Avramiequation is usually written as

lnð1�wtÞ ¼ Ztn;

where wt is the volume fraction of polymercrystals (also known as the degree of crys-tallinity) at time t, while Z and n are char-acteristic constants for the polymer.

70. a/W Ratio

The ratio of the length of the crack (ornotch), a, to the width of the specimen,

W, used in the evaluation of the toughnessof materials using fracture mechanics prin-ciples. (See Fracture mechanics.)

71. Azeotropic Copolymerization

Conditions in which the composition of themolecular chains of a copolymer (i.e. theratio and position of the two monomerunits) remains the same throughout thepolymerization process.

71 Azeotropic Copolymerization j23

B

1. Back-Flow

The flow that can take place in the oppositedirection to the inlet flow. Back-flow canoccur sometimes through the gate of amould cavity if the pressure is removedbefore the gate is frozen. It also takes placefrequently in the form of leakage flow overthe flights of the screw of an extruder. (SeeExtrusion theory.)

2. Back-Pressure

The pressure exerted against the screw of aninjection moulding machine during itsrotation for the plasticization and transpor-tation of the melt to the front of the barrel.

3. Backscatter

Denotes the scattering of light from thesurface of a flat object, such as a sheet orfilm, impinged by incident rays, causing adeterioration of clarity of objects seenthrough. The term is also used in energy-dispersive scanning (EDS) analysis by ste-reo scanning electron microscopy (SEM).

Backward and forward light scattering from thesurface of a polymer film.

4. Bagley Correction

Represents the pressure drop experiencedby a polymer melt at the entry of the capil-lary of a die used in rheological measure-

ments with a capillary rheometer. In orderto calculate the value of the shear stress atthe wall of the capillary, twall, the entrypressure drop (DPentry) has to be subtractedfrom the total pressure drop, DPtotal, mea-sured by the transducer fitted in the heatingchamber, that is,

twall ¼ ðDPtotal�DPentryÞR=2L;where L andR are the geometric parametersfor the capillary die (L is the length and R isthe radius).

5. Bagley Plot

A plot of the measured pressure (DPtotal)against the ratio L/R in rheological mea-surements carried out for polymer meltswith a capillary rheometer using dies ofdifferent ratios of length (L) to radius (R)and at different apparent shear rates (s�1)for each plot (see diagram). The extrapolat-ed P value for L/R¼ 0 corresponds to theentry pressure drop, which has to be sub-tracted from the measured pressure drop(DPtotal) in calculating the shear stress at thewall, that is,

DPcapillary ¼ DPtotal�DPentry:

(See Bagley correction.)

Example of Bagley plot for different shear rates.


24j

6. Bakelite

Originally a tradename for phenol formal-dehyde moulded products, after the inven-tor Leo Beakeland, it became widely accept-ed as a generic term. (See Phenolics.)

7. Ball-Drop Test

(See Falling-weight impact test.)

8. Bank

A term used to describe the beading ofpolymer melt along the entry side of thefirst nip of the rolls of a calender. Thisprevents the entrapment of air at the inter-face between melt and rolls. (See Calenderand Calendering.)

Formation of the rolling bank by the rotation of thebottom roll at the nip of the calender. Source:Mascia (1989).

9. Barrel

The cylinder enclosing the screw of aninjection moulding machine or that of anextruder.

10. Barrier Flight Screw

Type of screw used in extrusion processes,designedtokeepthesolidbedseparatedfromthemelt pool within the transition zone. Theflow path followed by the solid bed and themelt pool within the unwrapped spirallingchannel of an ordinary screw is shown.

Solid bed and melt pool in an unwrapped screwchannel. Source: Osswald (1998).

Barrier screws prevent the break-up ofthe solid bed and the creation of local per-turbations of pressure and temperature inthe transition zone, which eliminates thepossibility of a pulsating flow occurring atthe die, known as �surging�. There are twoflight designs to achieve these require-ments: �constant solid-bed channel width�,known as theMaillefer screw, and �constantchannel depth�, simply known as the barrierscrew. The separation of the solid bed fromthe melt pool and the cross-sections of thechannels are illustrated.

Schematic diagram of screws with different barrierflights. Source: Osswald (1998).

10 Barrier Flight Screw j25

11. Barrier Polymer

A polymer with the ability to restrict thepermeation of gases, vapours or liquids.The barrier characteristics of polymers areexpressed in terms of their permeabilitycoefficient, which is defined as the molarflux of penetrant through a film per unitthickness. (See Barrier properties.)The barrier characteristics of polymers are

related to theirmolecular andmorphologicalstructure. This is illustrated in the table,which compares the effects of functionalgroup and chain packing on the oxygenpermeability PO2 value (wherein mil ¼1/1000thof an inch, and atm¼ atmosphere).

Effects of functional group

Nature of X in PO2 (cm3/mil 100

inch2 day atm)

–OH 0.01–CN 0.04–Cl 8.0–F 15–COOCH3 17–CH3 150–C6H5 420–H (LDPE) 480

Effects of chain packing

Structure PO2 (cm3/mil 100

inch2 day atm)

(HDPE)

110

150

(P4MePe-1)

4000

Source: Data from Mascia (1989).

In the first series is shown the effect ofdecreasing the polarity of the polymerchains, and in the second is shown theeffect of decreasing the molecular chainpacking within the crystals forming thelamellae. It is known that the polymerswith the highest barrier characteristics to-wards oxygen, carbon dioxide and waterare ethylene–vinyl alcohol (EVOH) copoly-mers, poly(vinylidene dichloride) (PVDC)and liquid-crystal polymers (LCPs). Allpolyolefins, on the other hand, have poorbarrier properties towards the samediffusants. Blending small amounts ofpolyamides with polyolefins, throughappropriate compatibilization methods,has been used as a method for improvingthe barrier properties of the latter polymersfor packaging. The inclusion of exfoliatednanoclays in a polymer is another effectiveway of reducing the permeability of gasesthrough polymer films or coatings, in viewof their intrinsic low permeability, whichprovides an effective barrier through adilution effect, as well as through the crea-tion of long tortuous paths for the diffusionof penetrants, due to their high aspectratio (area/thickness ratio). A chemicalapproach has also been used to reduce thediffusion of oxygen through polymerfilms resulting from the oxygen scaveng-ing characteristics of certain additives,such as cobalt carboxylate salts.

12. Barrier Properties

Properties of packaging films or containersdenoting the resistance to permeation ofgases or liquids. The barrier properties ofpolymers are described by the solubility (S),the permeability coefficient (P) and thediffusion coefficient (D). These parametersare related to each other by the expressionP¼DS. The SI units for permeabilityare mol m/m2 s Pa, while a widely usedunit is the barrer, which corresponds to7.60� 10�9 cm3 cm/cm2 s atm. The mostwidely used penetrants for measurements

26j 12 Barrier Properties

of the barrier characteristics of packagingfilms and containers are oxygen, water andcarbon dioxide.

13. Barus Effect

The swelling of extrudedmelt at the die exit.(See Die swell ratio.)

14. Baryte

A filler based on barium sulfate, BaSO4,used mostly to achieve sound attenuationcharacteristics, arising primarily fromits high density (4.5 g/cm3). The particlesize is in the region of 2–15m. For toxicityreasons, the amount of water-solublebarium salts have to be kept at very lowlevels.

15. Beer–Lambert Law

Describes the absorption of radiation ofmaterials with the equation

logðI0=IÞ ¼ «cl

where I0 is the intensity of the incidentbeam of light, I is the intensity of thetransmitted beam, « is the extinctioncoefficient (a property of the material), cis the concentration of the absorbingspecies and l is the path length. TheBeer–Lambert law is the basis of radiationspectroscopic techniques, which makes itpossible to calculate the concentration ofparticular chemical groups present in asample.

16. Bending Moment

A fundamental concept used for the bend-ing theory of beams. The bending moment(M) is defined as the product of the applied

load (P) and the distance from the point ofsupport.

17. Bending Test

Also known as flexural test, is usually car-ried out in the form of three-point bending,where a beam is supported at the two endsand is loaded in the centre. (See Charpyimpact strength and Flexural properties.)

18. Bentonite

A type of clay used as filler, which containsexfoliatable platelets. (See Nanocompositeand Filler.)

19. BET Isotherm(Brunauer–Emmett–Teller Isotherm)

A theory and a method for measuring thetotal surface area of powders based on theabsorption of gas/vapour molecules,through the relationship between volumeof gas adsorbed and gas pressure at constanttemperature,

pVðp0�pÞ ¼

1Vmc

þ ðc�1ÞpVmcp0

;

where V is the volume of absorbed vapour,Vm is the monolayer capacity of the solidsurface, p is the partial pressure of thevapour, p0 is the saturation vapour pressureand c¼ exp(DHA�DHL)/RT, in which DHA

is the heat of adsorption, DHL is the heat ofvapour condensation, R is the universal gasconstant and T is the absolute temperature.

20. Beta Transition Temperature

The beta (b) transition is a minor transitionoccurringinglassypolymersat temperaturessubstantially below the alpha (a) transition,

20 Beta Transition Temperature j27

which is known as the glass transition (Tg).The b transition is associated with short-range relaxations, arising primarily from ro-tations of side groups attached to the mainpolymer chains. The change inmodulus of apolymerattheb transitiontemperature,how-ever, is quite small:much less than oneorderof magnitude as compared to a change ofthreeorfourordersofmagnitudetakingplaceabove the a (glass) transition temperature.Theseare illustrated in thedynamicmechan-ical spectra.

21. Biaxially Oriented Film

(See Orientation.)

22. Binder

A term widely used for the binding togetherof fibres in mats or fabrics by means of alow-melting-point solid resin or film-forming polymer deposited from a wateremulsion.

23. Bingham Body

A liquid ormelt requiring aminimumshearstress level at the walls of a channel beforeflow starts, known as the yield shear stress.

Schematic representation of a Bingham body flowbehaviour for polymer melts.

24. Bioactive Filler

Afiller that impartsbiocompatible character-istics toapolymer.Typical bioactivefillersarehydroxyapatite and starch. (See Biopolymer.)

25. Biodegradable Polymer

A polymer or a polymer composition thatcan be attacked by microorganisms in theenvironment, causing a breakdown of themolecular structure.

Dynamic mechanical spectra at two frequencies of a glassy polymer showing the a and b transitions.Source: Mascia (1989).

28j 25 Biodegradable Polymer

26. Biopolymer

A biodegradable or biocompatible polymer,which can be classified into naturaland synthetic materials. The majority arenaturally occurring polymers, such as�polysaccharides� (e.g. starch, cellulose,lignin and chitin), �polypeptides� and�proteins� (e.g. gelatin, casein, wheat gluten,silk andwool), and �lipids� (e.g. plant oils andanimal fats). The most widely researchedsynthetic polymers are �modified cellulose�(e.g. cellulose acetate, cellulose propionateandcelluloseacetatebutyrate), �polyesters�(e.g. polyhydroxybutyrate, polyhydroxyalkano-ate,poly(lacticacid)andpolycaprolactone),aswell as mixed aliphatic–aromatic polyesters.Other systems include poly(vinyl alcohol)and �modifiedpolyolefins� (e.g.ethylene–car-bon monoxide copolymers containing bothphoto- and biodegradation catalysts).

27. Birefringence

The difference in the refractive index in twoperpendicular directions, that is, Dn¼ n1�n2, where n is the refractive index, and 1 and2 refer to the directions. This arises from theanisotropic structure of polymer productsresulting from the presence of alignedmolecular chains. Measurement of the bi-refringence is widely used to assess quanti-tatively the degree of molecular orientationin an anisotropic polymer product, such asfibres and tapes, and also in injection-moulded products to determine the level ofresidual stresses through the thickness, asshown in the diagram. (See Orientation.)Birefringence ismeasured directly on spe-

cimens using polarized electromagnetic(EM) radiation bymeasuring the optical pathdifference (or relative retardation,D)with theaid of a characteristic colour chart, known astheMichel-L�evy chart, or an optical compen-sator (i.e. a device with precalibrated andadjustable birefringence characteristics).This is a straightforward method insofar as

the relative retardation is directly proportion-al to the birefringence, that is, D¼ bDn. Aspectrophotometric technique is used tomeasure the relative retardation in thosecases where the birefringence is very high.

28. Bismaleimide Resin (BMI Resin)

A type of resin used as the matrix forcomposites to obtain a high glass transitiontemperature and a high resistance to degra-dation of mechanical properties in high-temperature environments. A variety of dif-ferent types are available commercially,varying from simple resins, such as bis(maleimidophenyl)methane, to more com-plex types, such as adducts (see diagrams).

Bis(maleimidophenyl)methane.

Adduct of maleimide to trimethylphenylindane.

Example of variation of birefringence through thethickness of an injection-moulded specimen.Source: Murphy (1969).

28 Bismaleimide Resin (BMI Resin) j29

The curing and grafting reactions takeplace via a free-radical mechanism. Oftenthese systems are mixed with vinyl estertype resins to reduce costs and optimizeperformance. (See Vinyl ester.)

29. Bisphenol

The bisphenols are a class of raw materialswidely used primarily for the production ofepoxy resins and some aromatic polyesters,including polycarbonate, sometimes usedas an antioxidant. There are three types ofbisphenols, namely bisphenol A, bisphenolF and bisphenol S, consisting of two phenolunits bridged at the para position by, respec-tively, a propylidene group, a hexafluoropro-pylidene group and a sulfone group.

30. Biuret

Chemical group formed from the reactionbetween a urethane group and a urea groupin the production of polyurethanes.

31. Bleeding

A term used for the loss of additive from apolymer when immersed in an aqueousenvironment. The term �leaching� is alsoused to describe the same phenomenon.

32. Blend

(See Polymer blend.)

33. Blistering

A phenomenon observed in surface coat-ings, especially when used for corrosionprotection, and in polyester resin–fibrecomposites (glass-reinforced plastic, GRP),particularly at the interface between theouter gel coat layer and the fibre composite.

In most cases blistering is associated withthe difference in osmotic pressure betweenthe water contained in defect areas, such asvoids or microcracks, and that of the watermedium in the surrounding areas. Theosmotic pressure differential arises fromdisparities in concentration of ions, whichproduces a thermodynamic drive for equil-ibration of ion concentration through thetransportation of water vapour and ions. Forthe case of surface coatings on metals,blistering can occur also through corrosion,which can take place cathodically, when thesurrounding medium is acidic, or anodical-ly, for high-pH environments. In thesecases the transport of water into the blisterareas is driven by electro-osmosis, that is,electropotential gradients rather than os-motic pressure differentials.

34. Block Copolymer

A copolymer in which the two constituentmonomer units are joined in blocks. Theseare divided into consecutive AB types, end-

Schematic of ABA block copolymers, where A re-presents rigid polystyrene blocks (low molecularweight) and B denotes soft polybutadiene blocks(high molecular weight): (a) linear blocks, (b)branched blocks, and (c) star blocks.

30j 34 Block Copolymer

block ABA types and alternating ABABtypes. They may consist of linear blocks oftwo different chains or star blocks compris-ingmore than two linear blocks attached to acommon branched point, as illustrated forstyrene–butadiene–styrene systems.An important feature of block copoly-

mers is their morphological structure aris-ing from the lack of miscibility of the vari-ous blocks in the structure. According to thecomposition and chain lengths of theblocks, the two domains assume differentspatial organization, as indicated.

At the same time, the composition of theblock copolymers can impose different be-haviour with respect to physical properties.There are two aspects that have receivedconsiderable attention in industry. An im-portant area of interest of these systems isthe elastomeric behaviour resulting fromthe large difference in Tg of the two blocks,one producing a rigid dispersed phase(glassy or crystalline), and the other consist-ing of soft (rubbery) domains. The presenceof rigid domains acts as an internallybuilt reinforcement for the rubbery phase,so that the resulting polymer acquiresthe characteristics typical of a conventionalrubber without cross-links in the polymerchains and therefore exerts a thermoplasticbehaviour. For this reason, they arereferred to as �thermoplastic elastomers�.Typical thermoplastic elastomers based onblock copolymers found commercially areshown in the table. (See Thermoplasticelastomer.)

NameRigid phaseblocks

Soft phaseblocks

SBS Polystyrene (glassy) PolybutadieneSIS Polystyrene (glassy) PolyisopreneSEBS Polystyrene (glassy) Poly(ethylene–

butylene)Polyester Poly(butylene

terephthalate)(crystalline)

Poly(tetramethy-lene oxide)

Polyu-rethane

Polyurethanefrom methylenediisocyanate(glassy)

Aliphatic polyes-ter orpoly(tetraethy-lene oxide)

Polyamide Polyamide(crystalline)

Poly(tetramethy-lene oxide)

35. Blocking

A phenomenon describing the sticking offlexible films to each other, as in plasticbags. This is caused by attractive surfaceforces, of van der Waals type, operatingwhen the surface of the films is verysmooth, which allows the touching surfacesto have intimate contact. (See Antiblockingagent.)

36. Blooming

A term used to describe the migration ofadditives, usually solid types, from the bulkto the surface of a product.

37. Blow Moulding

A process used for the production of hol-low articles, such as bottles and contain-ers. These can be produced either by ex-trusion blow moulding or by injectionblow moulding. The operation takes placein two stages, either in-line or separately:production of a parison and inflation intoa cold mould. (See Extrusion.) Examplesare shown of two widely used extrusion

Changes in spatial organization of immiscible do-mains of block copolymers according to A/B ratio.

37 Blow Moulding j31

blow moulding processes. The first is aconventional multiple-cavity process forrelatively small bottles. The second isa process, used for larger containers,involving the accumulation of melt at thefront of the extruder so that the screwcan rapidly extrude the parison through arapid forward movement, thereby prevent-ing excessive cooling and sagging of theparison before the subsequent blowingoperation.

Example of extrusion blowmoulding operationwithmulticavity mould. Source: Muccio (1994).

38. Blowing Agent

An additive used for the production offoams (cellular products). Blowing agentsexert their function by rapidly producinglarge quantities of gas at specific siteswithinthe bulk of a resin ormolten polymer, wherenucleation of the cells takes place. They aredivided into physical and chemical types,depending on whether the blowing actionresults from a rapid evaporation of theadditive or through chemical decomposi-tion of the additive, producing large quanti-ties of gases (usually nitrogen) for the nu-cleation and subsequent growth of cells.Typical physical blowing agents are low-boiling-point hydrocarbons, such as pen-tane (boiling point, b.p.¼ 30–40 �C) andheptane (b.p.¼ 65–70 �C). The use of fluo-rinated hydrocarbons, known as freons (b.p.¼ 25–50 �C), is now generally discour-aged because of environmental issues. Thedirect induced infusion of gases in thepolymer, such as N2 or CO2, is a methodby which physical blowing can be inducedthrough a sudden release of the pressure.The more common types of chemical blow-

Example of extrusion blow moulding with accumulator head. Source: Lee (1998).

32j 38 Blowing Agent

ing agents used for the foaming of elasto-mers and thermoplastics, together withtheir chemical structure and range ofdecomposition temperature, are shown inthe table.

Name Structure

Decompositionrange (�C)(maximumrate)

Azodicarbona-mide

160–200

Azobisbutyro-nitrile

90–115

Benzenesulf-onylhydrazine

95–100

p-Toluenesulfonylsemicarbazide

210–270

39. Blown Film

Also known as tubular film, is produced byextrusion using circular dies. The entire set-up for the production of blown films isillustrated in the diagram.The essence of the tubular film process

is the blowing of a bubble by the inlet ofair through the mandrel of the die andmaintaining a constant pressure insidethe bubble by folding the film via two niprolls. The expansion of the bubble stops atthe so-called �frost line�, which is formedwhen the temperature of the melt reachesthe glass transition, for the case of glassypolymers, or the onset crystallization tem-perature, for crystalline polymers. A degreeof biaxial orientation is introduced in thefilm due to a certain amount of stretchingthat takes place within the rubbery stateof the polymer. The balance betweenlongitudinal and circumferential (trans-verse) orientation can be controlled throughadjustments in blow-up ratio, stretchratio imposed by the take-off rolls andcooling rate.

Schematic diagram of a production line for blown films. Source: Rosato (1998).

39 Blown Film j33

The highest level of orientation is ob-tained by ensuring that most of the stretch-ing of the bubble takes place just below thefrost line in order to minimize the extent ofmolecular relaxations.

40. Blow-Up Ratio (BUR)

This is the ratio of the diameter of the bubbletothediameterofthehollowcylindricaldie,inthe tubular film extrusions of polymerfilms.TheBURisusuallyintheregionof2–4.Inthisprocess a tubular film exiting from the dieis blown out while still in the melt state bythe injection of air through the centre of thedie before being cooled and collapsed by thenip rolls acting as sealant for the bubble.

41. Boltzmann Superposition Principle

A procedure for determining the accumu-lated strain in a specimen, or in an area of a

product, subjected to variable stresses intime. This is based on the principle that anincrease or reduction in the magnitude of astress at a certain time during creep can beaccounted for in the design of the article, onthe basis that resulting change in strain isindependent of the previous history. Theprinciple is illustrated in the diagram,which shows the incremental increase instrain resulting from a stepwise increase inapplied stress.This implies also that the reduction in the

magnitude of an applied tensile stress willresult in a partial recovery and can be con-sidered to be equivalent to the addition of acompressive stress of the same magnitudeas the removed tensile stress. (See Creep.)

42. Boundary Condition

The extreme values that a variable can reachin constrained situations. Particularly usedin calculations involving the integration of afunction in heat transfer and transportphenomena.

43. Breakdown Voltage

Represents the value of the voltage appliedon a polymer insulator, in the form ofspecimen or electrical insulation, thatcauses the local breakdown of the chemicalstructure, resulting in the formation ofconductive paths through the bulk for thecurrent to leak to earth. (See Tracking.)

44. Breaker Plate

Adisc containing a largenumber of orifices,placed between the barrel of an extruderand the die. The function of the breakerplate is to act as a support for �screen packs�,that is, wire gauzes that filter the meltbefore it reaches the die. (See Extruder.)

Incremental accumulation of the strain resultingfrom a stepwise increase in stress level.

34j 44 Breaker Plate

45. Brittle Fracture

A type of failure that results in the formationof two smooth fracture surfaces, whichtakes place at low strains. It occurs in com-ponents that contain geometrical disconti-nuities or defects such as cracks, whichhavethe effect of increasing the stress at the tip ofthe crack and preventing the onset of large-scale deformations (ductile failures). A pic-torial description of the deformations oc-curring in a tensile test specimen of bothbrittle and ductile polymer is shown. Thegraphical representation of brittle and duc-tile failures is shown in the graph.

Changes in tensile specimens after failure: A, brittlefracture; B, ductile failure with necking and colddrawing (typical for rigid polymers); C, ductile fail-ure withmicrovoiding (applicablemostly to failuresof polymer blends).

Schematic representation of brittle and ductile de-formational behaviour of materials up to failure.

46. Brittle Point

The failure mode of polymers changes frombrittletoductilewithincreasingtemperature,and vice versa. The temperature at whichthis takes place is known as the brittle pointor the tough–brittle transition temperature.

47. Brittle Strength

The value of the stress recorded in tensiletests in which the material fails in a brittlemanner is sometimes known as the brittlestrength. This is not a fundamental propertybecause the value recorded depends on thedimensions of internal flaws, usually in theform of cracks. (See Fracture mechanicsand Griffith equation.)

48. Brittle–Tough Transition

A term used to denote the temperature (TB)at which there is a change in deformationalbehaviour from brittle to ductile. This isusually determined from impact tests car-ried out at different temperatures and isidentified by a rapid change in the recordedfracture energy, using themid-point to iden-tify the TB value. This does not correspondto the glass transition temperature (Tg), anddepends on the test method used, particu-larly on the notch tip radius in the case ofIzod or Charpy tests. If fracture mechanicsprinciples are used to measure theGc valueas the fracture toughness parameter, thenthe TB value becomes an invariant parame-ter that depends only on the nature of thematerial, and hence is a fundamental prop-erty of the material, like the Tg.

49. Brominated Compound

These are widely used in polymer formula-tions as fire-retardant additives in conjunc-

49 Brominated Compound j35

tionwith antimony oxide, usually in ratios ofabout 2:1. Typical brominated fire-retardantadditives used as fire retardants are tetrabro-mo-bisphenol A, decabromodiphenyloxideand hexabromo-cyclododecane.

50. Brookfield Viscometer

An instrument used to measure the nomi-nal viscosity of pastes, suspensions andresins. Consists of a spindle rotating in theliquid medium contained in a beaker andrecording the torque developed to maintaina constant rotation speed. The viscosity ofthe liquid is determined from calibrationprocedures using reference liquids ofknown viscosity. The viscosity data obtainedare not accurate for fluids exhibiting non-Newtonian behaviour due to the variationsin shear rate within the fluid.

51. B-Stage

A term used to describe an intermediatestage in the cure of thermosetting polymerproducts (usually phenol formaldehydetypes), which is characterized by a very highviscosity but still capable of flowing underhigh pressures to allow shaping operationsto be carried out before the final (C-stage)cure.

52. Bulk Modulus

A parameter denoting the resistance of amaterial to volumetric deformations, result-ing from applied pressure or hydrostatictension. (See Modulus.)

53. Bulk Moulding Compound (BMC)

A moulding composition containing aboutequal amounts of styrene, an unsaturated

polyester resin, short glass fibres (approxi-mately 5 mm long) and an inorganic filler,usually calcium carbonate. This is some-times referred to as dough moulding com-pound (DMC).

54. Bulk Polymerization

Polymerization of liquidmonomers carriedout in the absence of solvents or water as adispersing medium. This is also known as�mass polymerization�.

55. Butyl Rubber

Butyl rubber, also known as isobutylene–i-soprene rubber (IIR), consists of about97–99.5% isobutylene and 0.5–3.0% trans-1,4-isoprene units, which can be repre-sented with the chemical formula shown.

Commercial grades have an average mo-lecular weight (MW) in the region of300 000–500 000 and a broad molecular-weight distribution (MWD). The lack ofunsaturation and the total absence of tertC�H bonds in the molecular chains giverise to high thermal oxidation stability,while the lack of dipoles provides very gooddielectric properties. A significant charac-teristic of butyl rubber is its ability to crys-tallize under stress, like natural rubber,which provides a high resistance to tearing.Another important feature of IIR is the lowoxygen permeability. These characteristicsmake IIR a suitable material for cables andinner liners for tubeless tyres.

36j 55 Butyl Rubber

C

1. Calcium Carbonate (CaCO3)

A low-cost filler for many different polymercompositions, such as plastics, elastomersand paints. Themain sources are calcite andlimestone refined into particulate fillersthroughvarious routes.CaCO3 fromnaturalsources is often referred to as ground calci-um carbonate (GCC) to differentiate it fromthe purer version, known as precipitatedcalcium carbonate, which is obtained by asynthetic route. Inall cases, thefillerusedforpolymer formulations is invariably coatedwith stearic acid to prevent agglomerationand to improve the dispersion. CaCO3 has adensityof2.96 g/cm3andanaverageparticlesize around 2–3mm, giving a surface area inthe region of 2–10m2/g. The particles havean irregular geometry, with a wide distribu-tionof shape andsize.Somegrades canhavea particle size as low as 0.03–0.05mm and asurface area of 30–90m2/g.

2. Calender

Equipment used to produce sheets or filmsby passing a melt though a series of highlypolished heated rolls and then through cool-ing rolls before being wound or cut to therequired length. The most common rollconfigurations of a calender are the invertedL type and the inclined Z type (shown).

Inclined Z stacking of the rolls of a calender.

3. Calendering

The process used to produce films or sheetsusing a calender. A calendering productionline includes several units for the prepara-tion of the mixes and for the feeding of themelt into the nip of the first set of rolls, aswell as other units for cooling and take-offsystems (see diagram).

The output of a calendering operation,that is, the flow rate of the material pass-ing through the nip of the rolls, is relatedto the velocity of the rolls (U), the gapbetween the rolls (h) and viscosity of themelt (h) by the expression

Q ¼ 2h U� h2

3hdPdx

� ��

Typical calendering line for the production of films. The arrangement of rolls is an inverted L type. Source:Osswald (1998).


j37

where Q is the flow rate per unit width ofthe rolls and dP/dx is the pressure gradientin the nip. The velocityU¼ 2pRN, where Ris the roll radius and N is the roll rotationspeed in revolutions per unit time. Inaddition to calendering as an entire pro-cess, calendering rolls in vertical stacks ofthree are used as polishing and coolingdevices in a sheet extrusion line.

4. Calorimetry

A characterization technique using heat asthe medium to bring about changes in asmall quantity of a polymer sample. (SeeDifferential scanning calorimetry.)

5. Cambering (Roll Crowning)

A term used in calendering processes todescribe the slight concavity of the outersurface of the rolls along the axial directionto counteract the differential thickening ofthe produced sheet at the exit due to swell-ing. (See Calender and Calendering.)

6. Camphor

Anaturalproduct,originally,usedincellulosenitrate compositions to reduce the melt vis-cosity. The chemical formula of camphor is:

7. Capacitance

Definedas the ratioof the charge stored (Q) tothe voltage applied (V) on a specimen placedbetween the electrodes of a capacitor, that is,C¼Q/V. The unit of capacitance is the farad(F). (SeePermittivity andDielectric constant.)

8. Capillary Rheometer

An instrument to characterize the rheologi-cal (flow) behaviour of polymer melts. Itconsists of a cylindrical chamber, in whichthe polymer is fed, heated and then forcedby a drivenpiston toflow through an alignedcapillary die.

Schematic diagram of a capillary rheometer.

The pressure variation that occurs dur-ing flow of the melt from the heatingchamber (reservoir) to the exit of the dieis as shown. The pressure, however, canonly be measured by means of a transducerfitted at the bottom of the reservoir, justbefore the melt enters the capillary die. Theflow rate, Q , is estimated from the velocityof the piston, V, used to force the meltthrough the die, that is, Q¼VA, where A isthe area of the piston. (See Rheology andMomentum equation.)

Pressure profile for the flow of themelt in a capillaryrheometer.

38j 8 Capillary Rheometer

The principle for the measurement of themelt viscosity is based on the possibility ofrelating the measured pressure to the shearstress at the wall of the capillary through theapplication of the momentum equation andcorrecting for the entry pressure drop(DPentry) by the Bagley correction method.(See Bagley correction.) The relationship be-tween shear stress at the wall (twall) and thepressure drop (DP) along the die capillary is

twall ¼ DPR=2L;

whereR is the radiusandL is the lengthof thecapillary.Note that the small pressure drop atthe die exit (DPexit), associated with die swell-ing, can be neglected, as it is quite small. It isnoted that the entry pressure drop decreasesif the entry angle from the reservoir to thecapillary is reduced from 90� to smallervalues, say45�.At thesametime, if the lengthof the capillary is very largewithrespect to theradius, say L/R> 30, the entry pressure dropbecomes quite small relative to the totalpressure drop, so that it can be neglected,making the Bagley correction unnecessary.From the velocity of the piston, it is

possible to calculate the shear rate at thewall ( _gwall) through the relationship be-tween velocity gradient (dV/dt) and flowrate. The velocity gradient is calculated fromthe flow rate through the capillary, which isthe same as the flow rate induced by thepiston in the reservoir. The relationshipobtained on the assumption that the behav-iour is Newtonian is

_gwall ¼ 4Q=pR3:

Bydescribing the behaviour of themelt witha power-law equation, that is,

t ¼ k _gn;

where k is known as the fluidity index and nas the power-law index, the shear rate at thewall becomes

_gwall ¼ð3nþ 1Þð4nÞ

4QpR3

;

where the 4Q/pR3 term is known as theapparent shear rate, on account that it is thevalue calculated on the basis of Newtonianbehaviour. This modification of the equa-tion is also known as the �Rabinowitschcorrection�.Further corrections can be made to in-

crease the accuracy of the calculated shearrate through a slip analysis, which makes itpossible to estimate the velocity of the meltat the wall (Vslip) and is used to calculate thetrue velocity gradient. (See Wall slip andExternal lubricant.) This is done by carryingout experiments with a series of dies withconstant L/R ratio, possibly choosing a largeL/R value (say L/R� 40) and plotting thevalues of 4Q/pR3 against 1/R at each pres-sure (i.e. for each wall shear stress value).

Plot of 4Qtotal/pR3 against 1/R at pressure P.

The rationale for this plot (also known asthe Mooney analysis) is that the total flowrate Qtotal is the sum of the slip flow rateQslip¼VslipA (whereA is the cross-sectionalarea of the channel, pR2) and the shear flowrate. The latter can be obtained by taking theaverage velocity �V shear, which givesQshear ¼ �V shearA (obtained by integratingthe velocity gradient across the channelsection). Therefore,

Qtotal ¼ VslippR2 þðf ð _gÞdr:

This equation can also be written as

4Qtotal

pR3¼ 4ðVslipþ �V shearÞ

R¼ 4Vslip

Rþ _gwall:

8 Capillary Rheometer j39

In the absence of wall slip (i.e. Vslip¼ 0), theshear rate at the wall is equal to 4Q/pR3

irrespective of the radius of the capillaryused. When, on the other hand, slip takesplace (i.e. for conditions when 1/R¼ 0), theshear rate at the wall is the intercept.From measurements made at different

pressures, a series of plots can be made forthe viscosity against shear rates and slipvelocity as a function of shear stress. It isgenerally found that the slip velocity in-creases with shear stress at the wall accord-ing to a power law, that is,

Vslip ¼ btmwall;

where b andm are constants for the polymermelt. Note that the incorporation of externallubricants will increase the values of Vslip

and may also have an effect on the values ofthe two constants, b and m.

9. Capillary Viscometer

An instrument to measure the viscosity ofpolymer solutions as a means of determin-ing the molecular weight.Measurements aremade by recording the

time for the solution to flow from an upperreservoir through a capillary leading to thelowerreservoir.Therecordedtimevaluesarecompared with those obtained for the puresolvent to flow through the same capillary.The viscosity of the solution can be cal-

culated from the relationship between flowrate (Q¼ volume/time) and viscosity (h)given by the Poiseuille equation,

Q ¼ KDp=h;

where K is the geometric constant for thecapillary and Dp is the pressure drop alongthe capillary.

10. Caprolactone Polymer(Polycaprolactone, PCL)

A polymer obtained by the ring-opening po-lymerization of caprolactone. The chemical

structure can be represented with theformula�(OCH2CH2CH2CH2CH2CO)n�.PCL has been developed primarily as a bio-compatible polymer for medical applicationand as a biodegradable polymer. It has a lowmelting point (Tm¼ 60–62 �C), with a de-gree of crystallinity around 50–60% and aTg in the region of�60 �C. At room temper-ature, the properties are similar to those of alow- to medium-density polyethylene, thatis, a Young�s modulus of approximately0.5GPa, tensile yield strength in the regionof 15–18MPa and elongation at break>500%. The water absorption is approxi-mately 0.3%.

11. Carbon Black

Often referred to in the rubber industrysimply as �black�. It consists of agglomeratesof nanosized carbon particles with surfacearea varying from around 25 up to 1450m2/g and size approximately within therange 15–75 nm. The density is in the re-gion of 1.85 g/cm3. Structurally similar tographite, consisting of large sheets of poly-nuclear rings of carbon atoms, which areseparated by electrons and are responsiblefor the high electrical conductivity. Thereare a variety of different types of carbonblacks, varying in chemical andmorpholog-ical structure. They are accordingly classi-fied as �low structure� when the agglomer-ated structure is compact, and as �highstructure� if the structure is porous with amuch higher surface area. Carbon black isusually obtained by the controlled combus-tion of hydrocarbon gases or acetylene. Themore common types are referred to as�furnace blacks�, �lamp blacks� or �thermalblacks� depending on the manufacturingmethod. �Channel blacks� are obtained fromnatural gas, now an obsolete process, andare known to have a surface with an acidiccharacter, which has a repressing effect onsulfur vulcanization.

40j 11 Carbon Black

High-resolution phase-contrast TEMmicrographofa typical �furnace black�. The scale bar represents10 nm. Source: Kraus (1978).

Chemical reactions can take place be-tween functional groups on the surface ofcarbon black, mostly quinonic type, and thefree radicals present in the system duringcompounding and curing operations. Forthis reason, carbon black tends to retard thecuring reactions but provides considerableprotection against oxidative degradation.When carbon black is heated at 2700 �C orhigher in an inert atmosphere, all surfacefunctional groups are removed and thestructure is converted into a crystalline gra-phitic type. The loss of functional groups onthe surface reduces the ability to formchem-ical bonds at the interface, thereby reducingthe reinforcing efficiencywith respect to lowstrainproperties, such asmodulus andabra-sion resistance. This does not have a signifi-cant effect, however, on the ultimatestrength. About 90% is used by the rubberindustry as a reinforcing filler. The rest isused in the plastics industry and in printinginks as a pigment or to produce semicon-ducting products.

12. Carbon Fibre

Widely used as reinforcing fibres for theproduction of composites. (See Compositeand Reinforcement.) Such fibres have agraphene structure resulting from thecontrolled pyrolysis of suitable organic

fibres, such as polyacrylonitrile or cotton,carried out in an inert atmosphere. (SeeGraphene.) The final diameter of the fibresis in the region of 6–10mm. Some low-costcarbon fibres are produced from pitch, a tar-like material. Their mechanical propertiesare largely related to the level of crystallinity.Fibres with a higher modulus and higherstrength are often referred to as graphitecarbon fibres. The morphological structureof carbonfibres is shown in the diagramandmicrograph.

Pictorial description of the internal structure ofcarbon fibres.

Micrograph of a typical carbon fibre. Source: Ehren-stein (2001).

Since the surface of carbon fibres is virtu-ally free of any reactive (functional) groups,special chemical treatments have to used tointroduce some OH, COOH and NH2

groups onto the surface, as a means of pro-ducing chemical bonds with the matrix. Tofacilitate handling of the fibres and to im-prove their wettability with matrix resins,the surface of carbon fibres is usually coatedwith an extremely thin layer of a solid epoxyresin.This reactswith the surface functionalgroups to produce chemical coupling with

12 Carbon Fibre j41

the resin matrix, normally another epoxyresin or a different resin that is compatiblewith epoxy resins. The epoxy coating actsalso as a binder for the �tows� so that theyremain compact and thismakes themeasiertohandleduring theproductionofprepregs.

13. Carbon Nanotube (CNT)

CNTs are extremely fine tubes with a gra-phene structure, produced by chemical va-pour deposition method from unsaturatedhydrocarbons, such as ethylene or acety-lene. They are available as single-walledcarbon nanotubes (SWNTs), consisting ofa single hexagonal layer of graphitic carbonwith a diameter in the region of 20–50 nm,or as multiple-walled carbon nanotubes(MWNTs), with 50–100 nm diameter.The orientation of the graphene layers is

in theaxialdirectionand is symmetricalwiththe central axis in both CNTsystems. CNTsare usually used at very low concentrations(<3wt%) owing to their very high reinfor-cing efficiency and their ability to produceelectrically conductive paths through perco-lation of the high-aspect-ratio nanotubes.The organization of the graphene layers ofan MWNTand a TEMmicrograph of actualMWNT bundles are shown in the diagramand micrograph, respectively.

Graphene layers in anMWNT: (top) armchair stacking;(bottom)zig-zagorganization.Source:Belletal.(2006).

Double-walled carbon nanotubes (diameter 30 nm)from Shenzen (China). Courtesy of D. Acierno,University of Naples, Italy.

14. Carbonyl Index

A parameter used to describe the extent ofoxidation of a polyolefin resulting fromdegradation reactions induced by UV lightand/or by heat. It is simply defined by theequation CI¼ 100A/t, where A is the infra-red absorbance at wavenumbers in the re-gion of 1715–1750 cm�1 and t is the thick-ness of the film used in the experiment.

15. Carothers

Wallace Carothers was the inventor of nylonpolymers and is well known for his funda-mental work on polymers produced by con-densation reactions.

16. Carreau Model

A mathematical model to describe the vari-ation of the viscosity (h) of a polymer meltwith shear rate, as shown in the graph.

42j 16 Carreau Model

Variation of relative viscosity of polymer melts(h/h0) with shear rate according to the Carreaumodel.

The Carreau equation is usually writtenas

h�h0 ¼h0�h¥

½1þðl _gÞ2�ð1�nÞ=2 ;

whereh0 is the viscosity extrapolated to zeroshear rate, hence known as the �zero-shearviscosity�, h¥ is the limiting viscosity at veryhigh shear rates, l is a constant for the melt(known as the characteristic time because ofits units), _g is the shear rate and n is anexponential index (constant) for the melt.

17. Cartesian Coordinates

Also known as rectangular coordinates. Amathematical representation of variables inspace with linear coordinates at right anglesto each other. They are also used to repre-sent the direction of three-dimensionalspace.

18. Case II Diffusion

A type of diffusion of small moleculesthrough a solid, which takes place via anadvancing front layer thatgradually increasesin thickness until it traverses the entiresection of the medium. The actual diffusionbegins after a certain induction time isreached in order to allow an accumulation

of diffusing species on the surface of themedium. In case II diffusion the mass ab-sorbed (Mt) increases approximately linearlywith time (t), whereas for Fickian diffusionMt is proportional to t

1/2. (See Diffusion.)

19. Casein

Aplasticmaterial with the samename as theprotein found in milk and cheese, fromwhich it is produced. Originally obtainedfrom straight polymerization by treatmentwith acid, it was later improved by treatmentwith formaldehyde. It has beenusedprimar-ily for the production of buttons to replacehorn. It is now largely superseded by otherrigid plastics derived from petrochemicals.

20. Casting

A technique for the production of articles bypouring a liquid resin, amonomer or a pasteintoanopenmouldandallowingit tosolidifythrough chemical reactions or diffusion.The term is also used in film extrusion todenote a technique bywhich the extrudate israpidly quenched on chilled rolls. This lattertechnique is called �chill roll casting�.

21. Cationic Polymerization

A type of polymerization carried out withthe use of Lewis acid catalysts, such as BF3,AlCl3, TiCl4 and SnCl4. It can be used for thepolymerization of both unsaturated or cyclicmonomers or oligomers, which becomeactive in association with a proton donorauxiliary. For example

BF3 þH2O!Hþ þBF4OH�

or

BF3 þR2O!R2O�BF3

Cationic polymerization takes place inthree stages.

21 Cationic Polymerization j43

Step 1. Initiation: This takes place by theaddition of H or R to the double bond, or tothe oxygen of an oxirane ring in the mono-mer or resin. For example

RCH ¼ CH2 þBF3=H2O!RCH2

�CH2þBF4OH

�

Step 2. Propagation: For example

RCH2�CH2þBF4OH�þnRCH¼CH2

!ðRCH2�CH2Þnþ1þBF4OH�

Step 3. Termination: For example (transferof ions to monomer)

ðRCH2�CH2Þnþ 1þBF4OH

� þRC

¼ CH2 !ðRCH2�CH2Þn þRCH2

�CH2þBF4OH

�

However, this is only one of many possibletermination reactions. Others include abstrac-tion of a proton from other species present,such as the solvent.

22. Cationic Surfactant

(See Surfactant.)

23. Cavity

The component of amould that receives themelt for the shaping of a moulded part.

24. Cavity Filling

A term that refers to the flow of a polymermelt into the cavities of an injection mould.

24.1 Cavity Filling Mechanism

The mechanism by which the melt entersand flows into a mould cavity is determinedprimarily by the typeandpositionof thegate.Jet filling takes place when the gate is posi-tionedat theopposite endof thecavity so thatthe cavity fills up in a zig-zag fashion. When

themelt emerging from thegate immediate-ly finds an obstruction or a sharp change ofdirection, the turbulence created produces alaminar flow filling mechanism. The twomechanisms are illustrated in the diagram.

Cavity filling mechanisms in injection moulding.Source: Mascia (1989).

The cold walls of the cavity of the mouldproduce a frozen solid layer of �orientedpolymer� chains, owing to the setting-up ofelongational stresses at the flowing front ofthe melt, as shown.

Flow mechanism of polymer melt in the cavities ofan injection mould. Source: Tadmor (1974).

24.2 Pressure Requirements for CavityFilling

Owing to the complexity of the flow path inthe cavities of injectionmoulds, it is difficultto obtain estimates of the pressure require-ments to fill the cavity of a mould withoutthe aid of analytical techniques such as�finite element analysis�. Other difficultiesarise from the non-isothermal nature of theflow and the non-Newtonian behaviour ofpolymer melts, which make it difficult tospecify single values for the viscosity.

25. Cavity Packing

Theflowof polymermelt entering the cavityof an injection mould as a result of the

44j 25 Cavity Packing

volumetric shrinkage taking place whilecooling. Shrinkage is particularly large forthe case of crystalline polymers and can beas high as 20% at atmospheric pressure. Aconsiderably larger pressure is required forcavity packing than for cavity filling to coun-teract the volumetric shrinkage. This can beestimated from the pressure–volume–tem-perature (PVT) diagram of particular poly-mers and makes it possible to design apressure profile for themoulding cycle. (SeePVT diagram.)

26. Cellophane

Film cast from a water-dispersed�regenerated cellulose�, obtained by treatingcellulose with sodiumhydroxide solution inorder to swell the fibrils by allowing water topenetrate between polymer chains. Theproduct is then reacted with carbon disul-fide to form the sodium salt, known as�cellulose xanthate�. The aqueous dope ofregenerated cellulose is cast into films toproduce cellophane.

27. Cellular Polymer

Anothertermforpolymerfoams.(SeeFoam.)

28. Celluloid

Originally a tradename for cellulose nitrateplastic products.

29. Cellulose

A polydisperse linear polysaccharide withthe chemical structure shown.

Chemical structure of cellulose, n¼ 2000–10 000.

Cellulose is the most abundant naturalorganic compound, which is found in cot-ton (95%), flax (80%), jute (60–70%) andwood (40–50%). It is insoluble in mostorganic solvents and decomposes beforereaching the melt state. However, it can beprocessed from aqueous dispersions of re-generated cellulose to produce glossy films(known as cellophane) and fibres (rayon).Cellulose has played an important role inthe development of plastics materials, firstthrough the development of cellulose ni-trate and subsequently for the productionof other esters, such as cellulose acetate(CA), cellulose propionate (CP), celluloseacetate butyrate (CAB) and cellulose acetatepropionate (CAP). These are often mixedwith plasticizers, such as triethyl citrate ordioctyl adipate, to enhance their pro-cessability through a reduction in melt vis-cosity. Attractive features of cellulosic poly-mers include their biodegradability andtheir controlled-release characteristics formembranes and coatings.

30. Cellulose Acetate (CA)

The first thermoplastic material that couldbe moulded and extruded in the melt state.CA is a glassy amorphous polymer, usuallycontaining small amounts of plasticizer toimprove its processing characteristics andto increase its ductility. Produced by theacetylation of the hydroxyl groups presentin cellulose, aimed at interrupting the for-mation of hydrogen bonds, responsible forthe strong intermolecular forces that pre-vent the reaching of the melt state beforethe onset of degradation reactions. (SeeCellulose.)

31. Cellulose Acetate Butyrate (CAB)

A glassy polymer produced by the partialsubstitution of acetyl groups with butyric

31 Cellulose Acetate Butyrate (CAB) j45

groups in the esterification of cellulose.This substitution brings about a more effi-cient internal plasticization than can beachieved by acetylation alone, which makesit unnecessary to use an external plasticizerto improve the processing characteristics ofthe polymer. CAB also has a lower level ofwater absorption than cellulose acetate.

32. Cellulose Nitrate (CN)

A polymer obtained by the nitration of cel-lulose. It represents the first plasticmaterialmade available commercially under trade-names of Parkesine and Celluloid. CN isused mostly in the form of mixtures withcamphor.

33. Cellulose Propionate (CP)

A glassy polymer obtained by esterificationof cellulose with propionic acid. The prop-erties of CP are intermediate between thoseexhibited by cellulose acetate and celluloseacetate butyrate.

34. Cellulosic

A generic term for all cellulose-derivedplastics.

35. Ceramer

A termderived from the combination of twotruncated words, namely, ceramic and poly-mer. It has been used to describe organi-c–inorganic hybrid materials intended foruse in coatings.

36. Chain Configuration (cis and trans)

Denotes the spatial arrangement of two dif-ferent substituent groups on C¼C bonds,

such as the CH2 groups in polybutadiene.The cis configuration refers to thepositionofequivalent groups on both sides of the C¼Cbond, while trans refers to configurationswhere equivalent groups are positioned onopposite sides, as shown.

37. Chain Extension

Atermused todescribe reactions that lead toan increase in the length of a polymer chain.

38. Chain Flexibility

It describes the ease with which a polymerchain can rotate about the constituent C�Cbonds, which is related to the internal ener-gy required for the rotation of segments ofpolymer chains at temperatures above theglass transition.

39. Chain Folding

Mechanism by which lamellae are formedduring the crystallization of polymers. (SeeCrystallinity.)

40. Chain Scission

The breaking of a polymer chain, associatedwith degradation reactions.

41. Chain Stiffness

The opposite of chain flexibility.

46j 41 Chain Stiffness

42. Chain Stopper

An additive or impurity that reacts with agrowing polymer chain during polymeriza-tion, thereby controlling chain length.

43. Chain Transfer

Mechanism by which a free radical attachedto a growing polymer chain, during poly-merization, abstracts hydrogen from a dif-ferent molecule, usually a chain transferadditive, producing a different free radical.

44. Chalking

A term (jargon) used to describe the forma-tion of a brittle layer on the surface of apolymer product as a result of weathering-induced degradation reactions.

45. Channel Black

A grade of carbon black widely used as a UVabsorber additive.

46. Char

A carbonaceous residue formed on the sur-face of a burning polymer, either cellulosicin nature or containing aromatic groupsalong the backbone chains, as in polysul-fones (thermoplastic) or phenol formalde-hyde (thermoset).

47. Charge Density

The quantity of charges present on a unitsurface area of the electrodes of a capacitorcontaining a dielectric.

48. Charge Exchange Capacity

A generic term that quantifies the capabilityof nanoclays to exchange structural cations

with others of similar charge derived fromthe surrounding medium, expressed asmeq/100 g clay.

49. Charpy Impact Strength (and IzodImpact Strength)

Denote the amount of mechanical energyper unit cross-sectional area beneath thenotch that is consumed when a specimenis fractured under impact conditions (seediagram). The use of the term �strength� inthis case is anomalous insofar as strength isnormally expressed in terms of the stress,and not energy, required to fracture a speci-men. The accurate term should be �impacttoughness� forconsistencyofnomenclature.

Geometry of specimen and loading mode in pen-dulum impact tests.

In these impact tests, the load is deliveredat high speed to the specific loading point bya mass placed at the extremity of a pendu-lum. The apparatus records the energy usedin fracturing the specimen by registeringthe loss of potential energy (DU) from thereduction in the height reached by the strik-ingmass after fracturing the specimen. Theloss of energy of the pendulum is, therefore,given by the expression

DU ¼ mgðho�hf Þ;

where m is the mass of the pendulum, hoand hf are the respective heights before andafter fracture of the specimen. (See Fracturetest and Pendulum impact test.)

49 Charpy Impact Strength (and Izod Impact Strength) j47

Principle of pendulum impact tests.

50. Chelating Agent

Additive used to produce complexes or co-ordination products with metal ions in or-der to prevent their catalytic action on thedegradation caused by thermal or UV-induced oxidative reactions.

51. Chemical Blowing Agent

Additive used for the formation of cells inthe production of foams. A gas, usuallynitrogen, is formed at a very fast rate overa relative narrow range of temperatures.Typical chemical blowing agents and thecorresponding blowing temperature rangeare: azo-bis-dibutyronitrile (90–115 �C),azodicarbonamide (160–200 �C) and p-toluenesulfonylsemicarbazide(210–270 �C).

52. Chemical Resistance

Denotes the capability of a polymer to resisteither swelling by solvents or attack bychemicals.

53. Chemical Shift

A term used primarily in nuclear magneticresonance (NMR) analysis to denote theshifting of themagnetic resonance frequen-cy to values lower than the applied externalmagnetic field as a result of the interaction

with the electrons of the molecules of thesubstance examined. (See Nuclear magnet-ic resonance.)

54. Chill-Roll Casting

A processing method for the production ofslit films (see diagram). This processmakesit possible to produce films at a very highproduction rate by operating with the dieheated to high temperatures and with alarge drawdown ratio.

Schematic illustration of the chill-roll casting pro-cess for the production of films. Source: Teegarden(2004).

55. Chitin

An abundant natural product, correspond-ing to poly(N-acetyl-D-glucosamine), foundin the exoskeleton of crustaceans and in-sects, as well as in the cell walls of fungi andmicroorganisms. The structure of chitincan be drawn as

or with a more precise special configura-tion as

Chemical structure of chitin.

48j 55 Chitin

The main commercial sources of chitinare fish shells such as crabs, shrimps andlobsters.

56. Chitosan

Apolymer obtained by the partial deacetyla-tion of chitin, having the chemical structureshown, where the residual acetyl groupsvary between 5% and 70%.

Chemical structure of chitosan.

The molecular weight of chitosan variesaccording to the degree of deacetylation butis generally found to vary from about1� 105 to 5� 105. Chitosan is a biopolymersoluble in dilute acids such as acetic acid orformic acid, and can be plasticized withpolyols, such as glycerol, sorbitol and poly(ethylene glycol), as well as with fatty acids,such as stearic and palmitic acids. Chitosandegrades readily at high temperatures and,therefore, cannot be processed in the meltstate. Normally chitosan is used for coatingsand films cast from dilute acid solutions.

57. Chlorinated Fire Retardant

Examples are chlorinated paraffins, con-taining 30–70% chlorine, chlorinated alkylphosphates and chlorinated cycloaliphaticssuch as dodecachlorodimethanodibenzocyclooctane.

58. Chlorinated Polyethylene

A grade of polyethylene obtained by thechlorination of the polymer chain with chlo-rine gas to improve the chemical resistancetowards polar solvents.

59. Chlorinated PVC

A grade of poly(vinyl chloride) (PVC) ob-tained by the introduction of more chlorineatoms in the polymer chain as a means ofimproving the chemical resistance.

60. Chlorosulfonated Polyethylene

A grade of polyethylene (PE) containing asmall number of SO2Cl side groups alongthe polymer chains. These provide the poly-mer with the ability to become cross-linkedby reaction with magnesium oxide and leadoxide in conjunction with an accelerator.

61. Chopped Strand Mat (CSM)

Mats consisting of chopped glass fibre rov-ings, usually about 5–10 cm long, heldtogether with a binder that will readily dis-solve in the resin in the manufacture ofcomposites. A solid unsaturated polyesterresin is often used as the binder for liquidpolyester resins containing styrene as thecross-linking agent.

62. CIE Chromaticity Diagram

The abbreviation for the Commission In-ternational de l�Eclairage, used to describethe plot of the values x, y or z, as fractions ofthe sum of the three primary colours, R(red),G (green) and B (blue), used in colourmatching, that is

x ¼ R=ðRþGþBÞ;

y ¼ G=ðRþGþBÞ;

z ¼ B=ðRþGþBÞ;where x þ y þ z¼ 1 (see diagram). Thismakes it possible to specify the desiredcolour for a product in terms of the x, yand z values. (See Colour matching.)

62 CIE Chromaticity Diagram j49

CIE chromaticity diagram.

63. Clamping Force

The force that has to be exerted onto themould of an injectionmouldingmachine inorder to prevent the melt escaping throughthe parting line of the mould to form a�flash�. The simplest approach to calculatethe clamping force is to multiply the pres-sure on the melt by the projected area of themould. To take into account the increase inviscosity during cooling, a more elaborateprocedure is required through the use ofvarious dimensionless parameters, such as

b ¼ aðTi�TmÞ;where a is the thermal diffusivity (k/rCp), Tis the temperature, and subscripts i and mstand for injection and mould, respectively.The other important parameter is the di-mensionless time, defined as

t ¼ tfillk=h2rCp;

where tfill is the mould filling time, h is thethickness, k is the thermal conductivityand Cp is the specific heat. The relation-ship between clamping force (F) andthe parameter t is available for differentvalues of b.

64. Clamping System

The mechanical system used in injectionmoulding machines to lock the mould dur-ing the injection of the melt into the cavity.This may be either hydraulic or mechanical(toggle), or a combination of the two. (SeeInjection moulding.)

Typical toggle clamping unit fitted to injectionmouldingmachines: 1, sprue half of mould; 2, fixedplaten; 3, moving platen; 4, adjustable platen; 5, tie-bar; 6, hydraulic cylinder; 7, toggle mechanism.

65. Clarity

The ability of a product or a specimen toallow the details in an object to be resolvedin the image observed. For this reason it issometimes referred to as �see-through clar-ity�. The loss of clarity is related to lightscattered while passing through the object.

66. Clash and Berg Test

An empirical test usually used to determinethe temperature at which a rubbery polymer,such as plasticized PVC or elastomers, ac-quireapredeterminedlevelofflexibilitywhenheated from low temperatures. The tempera-ture at which this takes place is known as the�cold-flex temperature�, which is closely relat-ed to the glass transition temperature.

67. Clausius–Mossotti Equation

Relates the permittivity of a dielectric, «, toits density, r, by the expression

50j 67 Clausius–Mossotti Equation

ð«�1Þ=ð«þ 2Þ ¼ Kr;

where K is a constant for the material.

68. Clay

Agenericnameforavarietyofsilicateminer-als used asfillers. The density is about 2.3 g/cm3 with particle size usually within therange 0.2–10mm and surface area around10–20m2/g. Themorewidely used varietiesare �bentonite�, �kaolin� and �China clay�.Accordingto theoriginandtreatments, clayscanhavedifferentmorphological structure–many are characterized by a platelet geome-try susceptible to delamination.

Micrograph of a clay from J. M. Huber Corporation.Source: Wypych (1993).

Montmorillonite is the principal constit-uent of bentonite, widely used for the pro-duction of nanocomposites in view of thepossibility of exfoliating the platelets intolaminae down to a few nanometres in thick-ness. (See Exfoliated nanocomposite andNanoclay.)

69. Cluster

A term used to describe agglomerations ofsmall structural entities into domains ofnanoscopic dimensions. Examples are theclusters in ionomers consisting of anions

hanging from polymer chains and metalcations added from an external source.

70. Co-Agent

A generic term for an additive used as anauxiliary, as in the case of curatives forelastomers.

71. Coagulum

A large agglomerate found in a latex due tocoalescence of primary suspended particles.

72. Coaxial Cylinder Rheometer

A rheometer consisting of an inner cylinder,known also as the �bob�, which rotates with-in a static outer cylinder, thereby shearingthe fluid in the gap between the two cylin-ders. The shear rate corresponds to thevelocity gradient through the gap. It is alsoknown as the Couette rheometer, namedafter the inventor.

Principle of coaxial cylinder rheometer.

The shear rate is given by the velocitygradient across the gap (Ro�Ri), that is,

_g ¼ rdVdr

;

72 Coaxial Cylinder Rheometer j51

which gives

_g ¼ RoW

Ro�Ri;

where W is the angular velocity. The shearstress t is calculated from the torque devel-opedby the rotating cylinder tomaintain theimposed velocity, using the equation

t ¼ M2pR2

o;

where M is the torque per unit radius dis-tance. The viscosity h is calculated as theratio t= _g.

73. Cobalt Naphthenate and Cobalt Octoate

Usedinadilutesolutionasacceleratorsfor thecold curing of unsaturated polyester resins.

74. Co-Continuous Domain (Co-Continuous Phase)

A term used to describe the spatial configu-ration of the constituent components ofpolymer blends or organic–inorganic hy-brids. The diagram shows an idealized re-presentation of the silica domains in anorganic–inorganic hybrid.

Bicontinuous phases in creamers or organic–inor-ganic hybrids.

75. Co-Extrusion

Extruding two or more polymers through acommon die to produce multilayeredsheets, films and tubular products. The

principle is shown in the diagrams for asheeting die and a tubular die. Note that insheet dies the flow rate of each polymer canbe controlled by individual choke-bar chan-nels. Similarly, the uniformity of the thick-ness of each film can be controlled by indi-vidual spiralling channels in tubular filmdies. (See Extrusion.)

Die systems that bring together the two meltstreams outside the die. Source: Baird and Collias(1998).

Die systems that bring together the two meltstreams within the die just before reaching the dielips. Source: Baird and Collias (1998).

Die systems that bring together the two meltstreams at the die adapter and then spread outand flow through the die in a laminar fashion.Source: Baird and Collias (1998).

52j 75 Co-Extrusion

76. Cohesive Energy Density (CED)

Aconceptused todetermine the solubility ofa polymer in a solvent or the mutual misci-bility of two polymers. Defined as the differ-ence between themolar heat of vaporizationand the molar work of expansion, that is

CED ¼ ðDHvap�RTÞ=Vm;

where DHvap is the latent heat of vaporiza-tion, R is the universal gas constant, T is theambient (absolute) temperature (K) and Vm

is the molar volume of the liquid.

77. Co-Injection Moulding

(See Injection moulding.)

78. Cold Crystallization

A term used in thermal analysis to denotethe crystallization that occurs during theheating scan.

79. Cold Curing

Curing of a thermosetting resin or an elas-tomer carried out at ambient temperature.

80. Cold Drawing

A term used to describe the stretching stageafter the formation of a neck (yield point) intensile tests of ductile thermoplastics. Theevents that follow the yield point areillustrated.Cold drawing introduces monoaxial ori-

entation of the polymer chains and crystal-lite entities (where applicable), which isstabilized by the increase in intermolecularforces, resulting from the reduction in in-termolecular distances.

81. Cold-Flex Temperature

A term used in the technology of plasticizedPVC to denote the temperature at which the

material reaches a certain level of flexibilitywhen heated up from its glassy state. Theterm derives from a standard test, known asthe Clash and Berg test, using a torsionpendulum apparatus.

82. Cold Flow

Large deformations taking place at ambienttemperature. This is sometimes referred toas �creep�.

83. Cold Forming

Anoperation, such as extrusion or compres-sion moulding, carried out at temperatures

Sequence of observations in tensile tests on ductilepolymer. (Top) Stress–strain curves (indicator 2corresponds to the yield point). (Bottom) Tensilespecimens showing necking deformations and colddrawing (indicators 3, 4 and 5).

83 Cold Forming j53

below the melting point of the polymer. Forglassy polymers, cold forming is carried outat temperatures only just above the glasstransition temperature.

84. Cold Plasma

Gas converted to plasma by the applicationof a radiofrequency (RF) field at ambienttemperature and at relatively low pressures(1–100Pa). This causes the ionization of gasmolecules by collision with the high-energyfree electrons generated by the RF fieldthrough a cascade process leading to theformation of plasma. At atmospheric pres-sure and in the absence of an RFfield, a gaswould reach temperatures in the region of3000–5000K to acquire the level of energyassociated with plasma. The type of plasmagenerated depends on the nature of the gasused and can be classified into �noble gas�plasma and �active� plasma. The excitationreactions occurring in a noble gas, such asargon, are well known and can be repre-sented as follows:

i) e� þ Ar¼Arþ þ 2e�

ii) e� þ Ar¼Ar� þ e�

iii) Ar� ¼Ar þ hn

iv) Arþ þ e�¼Ar þ hn

Reaction (i) represents the ionization pro-cess by collision. A cascade will result ifthese reactions occur at a faster rate thanthose in reaction (iv), which represents therecombination accompanied by electro-magnetic radiation emission in the vacuumultraviolet (VUV) region. Reaction (ii) re-presents an interaction during which a col-lision produces not ionization but excitationof the Ar atom, that is, Ar acquires energybut this is not sufficient to cause ionization.The excited atoms (Ar�) thus produced willdecay to the ground state, as shown inreaction (iii) with emission of radiation inthe visible and UV regions of the spectrum.

Note that the net total electrostatic charge onthe ionized gas is actually zero, due to theelectrostatic balance.In �active� plasma there aremany possible

reactions that can take place. It has beenestimated, for instance, that in oxygen plas-ma there are more than 30 possible reac-tions. Within the pressure range 1–100 Pathe electrons have energy of the order of1–10 eV and are present at densities of1015–1018 per cubic metre. In this pressurerange themean freepathof the electrons (i.e.distance travelled without undergoing colli-sions) is sufficiently large for them to gainenergy from the applied electric field at agreater rate than that at which they loseenergy by colliding with atoms and mole-cules inthegas.Theelectronenergiesmaybeexpressed in terms of a �Boltzmann equiva-lent temperature� (Te) defined by the relation

12MeV

2 ¼ 32kTe;

whereMe is themass of the electron,V is theroot mean square (RMS) velocity of theelectrons and k is the Boltzmann constant.Note that neutral atoms and molecules arenot accelerated by the electric field and,therefore, their energy is determined pri-marily by the ambient temperature, with asmall contribution from the collisions withelectrons. Since the RMS velocity of neutralatoms and molecules is much lower thanthat of the electrons, the gas temperature(T) will also be much lower. Typically, theratio Te/Tmay be in the region of 10–100,making RF plasma a suitable expedientfor the treatment of lower-melting-pointma-terials, such as polymers. This means thathighly reactive ions and free radicals can beproduced at quite low temperature, both inthe plasma and on the surface of thematerials to be treated. The reactive inter-actions of plasma with polymers have beenexploited commercially for various types ofsurface treatments, such as cleaning, etch-ing, cross-linking and grafting reactions.

54j 84 Cold Plasma

The reactive species produced on thesurface of polymers are often sufficientlylong-lived to allow further reactions to beinduced after the plasma treatment, therebypermitting the functionalization of surfaceswith chemical species that would decom-pose in a plasma atmosphere, such as un-saturated monomers. There are, however,substantial limitations in the treatment ofthe inner surface of articles such as tubingor open cells of foams, insofar as the meanfree path of the ionized gas species could belonger than the diameter of internal cavitiesso that they will become �deactivated� in theentrance regions through collisions beforereaching the inner surface of the cells ortubing. A sketch of the vacuum chamberand set-up to receive gas and for generatingthe RF field for producing cold plasma isshown.

A plasma chamber for the treatment of polymersurfaces.

85. Cold Set (Compression Set)

A term widely use to denote the lack ofrecovery of a rubber or elastomeric productafter compression.

86. Colligative Properties

Properties of solution depending only onthe number of solute particles and not on

their chemical nature. The main colligativeproperties are lowering of vapour pressure,depression of freezing point and loweringof osmotic pressure. These properties canbe used to determine the molecular weight(molar mass) of a polymer. The relationshipbetween osmotic pressure (P) and number-average molecular weight (M) is

limc! 0

Pc¼ RT

M;

where c is concentration, R is the gas con-stant and T is absolute temperature (K).

87. Colloidal

FromLatin colla,meaning glue.Denotes thestructureless state of very viscous fluids orsoft solids, consisting of sub-micrometreparticles or globules suspended in a fluid ordispersed in another solid. Protective col-loids are agents that prevent the agglomera-tion of dispersed particles or coalescence ofdroplets. (See Suspension polymerization.)

88. Colorant

An additive used to impart colour. Dyes areused to produce the required colorationwhile retaining transparency. Pigments areused to produce opaque coloured formula-tions, created by internal light scattering.(See Dye and Pigment.)

89. Colour Matching

Adjusting the dye or pigment compositionto the exact colour of a reference article orsample. Colour develops as a result of theabsorption of visible light of specific wave-length. The colour seen corresponds to thewavelength of the light that has not beenabsorbed. For instance, red corresponds towavelengths in the region of 750–610 nm,green in the region 550–510 nm, and yellowin the region 590–575 nm.

89 Colour Matching j55

89.1 Dye

For dyeing purposes, the relative amountsof dyes to be used can be estimated fromspectrographic measurements of the absor-bance (also known as the optical density) ofthe colour to be matched,

d ¼ logðI0=ItÞ;where I0 is the intensity of the incident lightand It is the intensity of the transmittedlight. For a three-colour mixture (the maxi-mum number normally required) the opti-cal density at any givenwavelength is relatedto the concentration of each individual dyeby the additivity rule, that is,

d ¼ aACA þaBCB þaCCC;

where aA, aB and aC are the absorbancevalues of dyes A, B and C, defined by Beer�slaw, log(I0/It)¼aCx, CA, CB and CC are themolar concentrations of the dyes to be used,and x is the sample thickness.

89.2 Pigment

For pigmenting, it is necessary to take intoaccount the scattering coefficient (d) in ad-dition to the absorbance (a) to calculate thereflectance (R) at the required wavelength,that is,

2R1�R2

¼ dACA þ dBCB þ dCCC

aACA þaBCB þaCCC:

Note, however, that in the case of crystal-line polymers some scattering takes placealso from the surface of the crystal lamellae,whichmay create considerable errors in thetheoretical predictions of the above equa-tion. (See CIE chromaticity diagram.)

90. Commingled Fabric

A fabric in which the constituent yarns ortows contain a mixture of reinforcing fibresand polymer fibres. The latter will melt toform the matrix of the composite when the

temperature is increased above the meltingpoint of the polymer and forced to flowaround reinforcing fibres by the applicationof an external pressure.

91. Comonomer

Themonomer present inminor amounts ina mixture of two monomers used for theproduction of copolymers.

92. Compact Tension Specimen (CTSpecimen)

Denotes a type of specimen used to deter-mine the fracture toughness of a material.(See Fracture mechanics.)

93. Compatibility

A term often used to denote the partialmiscibility of polymers in blends.

94. Compatibilize

Making two polymers compatible, usuallyimplying that either the chemical structurehas been modified or an additive has beenused to bring about a fine dispersion whenmixed together. (See Polymer blend.)

95. Compatibilizing Agent

An additive or a third component of a poly-mer blend used specifically to enhance thecompatibility of the twomajor components.Denoting the twomajor polymers in a blendby A and B, the structure of the compatibi-lizing agent is often a block copolymer of thetype A–B or A–B–A, so that blocks A willprovide the thermodynamic drive for mix-ing with polymer A, and similarly blocks B

56j 95 Compatibilizing Agent

will be miscible with polymer B. (See Blockcopolymer.)

96. Complex Compliance (and ComplexModulus)

The term �complex� for the compliance andmodulus (known also as dynamic modulusand dynamic compliance) derives from theviscoelastic nature of polymers. It impliesthat both parameters consist of two compo-nents, a �real� part (elastic or storage com-ponent) and an �imaginary� part (viscous orloss component), that is,

E� ¼ E0 þ iE00

and

D� ¼ D0�iD00;

where E� andD� are the �complex� modulusand complex compliance, E0 and D0 are thecorresponding elastic components, whileE00 and D00 are the loss components, andi ¼ ffiffiffiffiffiffiffi�1

p, that is, the complex number.

The denomination of complex modulusand complex compliance derives from theviscoelasticity theory for cyclic loading con-ditions. That is to say, when a sinusoidalsymmetric strain is applied to a specimen,there will be a corresponding sinusoidalstress response over the same cycle withthe same period and frequency. If the ma-terial has an elastic behaviour, then thestress/strain ratio (i.e. the modulus) andthe strain/stress ratio (i.e. the compliance)are constant. Thismeans that the stress andstrains are in phase, so when the stress ismaximum, the strain is alsomaximum; andwhen one of these is zero, the other will alsobe zero. This situation can be elaboratedthrough the appropriate functions. That is,if the applied strain is

« ¼ «0 sinðvtÞ;then the resulting stress has to be

s ¼ s0 sinðvtÞ

for the ratio of the two to remain constant.Here t is the time and v is the angularvelocity, insofar as the corresponding forceand deformation are considered vectors thatrotate in circular motions through positiveand negative quadrants at angular velocityv. The respective maximum values forstress and strain during each cycle are s0

and «0 as shown.

Response of a viscoelastic material to dynamicloads.

Since, for a viscoelastic material, thestress/strain or strain/stress ratios cannotbe constant over theperiod inwhich the loadis applied, the only way this situation can besustained is for the stress and strain curvestobedisplacedwithrespect toeachotherbyaphase angled, as shown in thediagram.Thismeans that the stress associated with anapplied sinusoidal strain at angular velocityv will be described by the equation

s ¼ s0 sinðvtþ dÞ;

which indicates that the strain vector lagsbehind the stress vector by an angle d. Frommathematical considerations, the stressfunctions0 sin(vt þ d) can be decomposedwith respect to the strain function «0 sin(vt)into an in-phase component (elastic compo-nent) and an out-of-phase component (losscomponent). The mathematical analysisproduces expressions for the modulus andcompliance in terms of complex para-meters, respectively E� ¼E0 þ iE00 and D�

¼D0 � iD00, where the magnitude of E00 andD00 provides a measure of the deviation ofthe behaviour of a polymer from elasticbehaviour, which is normally associated

96 Complex Compliance (and Complex Modulus) j57

with the behaviour of metals and ceramics.Alternatively, this deviation can be ex-pressed in terms of the ratio of the losscomponent to the elastic component, that is,

tan d ¼ E00=E0 ¼ D00=D0;

where tan d is also known as the �loss factor�.

97. Complex Permittivity and SpecificImpedance

A concept applied to the capacitance char-acteristics of polymers using similar prin-ciples as those used for the complex modu-lus and compliance in relation to the visco-elastic behaviour of polymers. In alternatingcurrent circuits, the electrical stress is out ofphase with respect to the charge densityof the capacitor component. The propertiesof a dielectric that define its ability to storecharge are the permittivity («) and specificimpedance (Zp), which are defined as fol-lows. In general, permittivity « is

« ¼ charge densityelectrical stress

and relative permittivity «r is

«r ¼ permittivity of dielectricpermittivity of vacuum ðor airÞ ;

which is also known as the dielectric con-stant. The complex permittivity is given by

«� ¼ «0�i«00;

the complex specific impedance is ex-pressed as

Z�p ¼ Z0

p þ iZ00p

and the loss angle as

tan d ¼ «00=«0 ¼ Z00p=Z

0p:

Note that

Z�p ¼

1v «rC1

;

where v is the angular frequency (2pf) andC1 is a constant defined as C1¼C0(d/A). In

this case, C0 is the capacitance of vacuum(or air), d is the distance between the elec-trodes (i.e. the thickness of the dielectric)and A is the area of contact between thedielectric and the electrode.

98. Compliance

A term denoting the deformation character-istics of a structure or a specimen, corre-sponding to the inverse of the stiffness. Forthe case of a beam, for instance, the stiffness(S) can defined in terms of themagnitude ofthe load (P) required to obtain a specifiedlevel of deflection (D). Hence, the ratio S¼P/D is a parameter that defines the rigidity ofa structure in terms of its resistance todeformations. Since the compliance (C) isthe reciprocal of the stiffness, then C¼D/Pand, therefore, C represents a parameterthat defines the flexibility of a structure.The term �compliance�, however, is alsoused to designate the inverse of the Young�smodulus. (See Creep compliance and Com-plex compliance.)

99. Composite

A material consisting of a dispersion ofhigh-modulus fibres or fillers within a line-ar polymer ormacromolecular networkma-trix. The fibres may be short and randomlydispersed or continuous and laid in a highlyordered manner

Random short-fibre composite.

58j 99 Composite

Unidirectional continuous-fibre composite.

In practice, the reinforcing componentof composites can also be in the form ofwebs or fabrics, where yarns or tows offibres are disposed (woven) at 90� (as warpand weft) in equal or different amounts, asshown.

Fabric-type continuous-fibre reinforcement.

100. Composite Fibre

The reinforcing component of polymerma-trix composites is in the form of high-mod-ulus and/or high-strength fibres. The mostwidely usedfibres and theirmain propertiesare shown in the table. (See Fibre reinforce-ment theory.)Particulate fillers are much less effi-

cient than fibres in enhancing the me-chanical properties of the polymer matrixbut are easily processed, particularly whenused in combination with thermoplasticmatrices.

Type offibre

Density(kg/m3�10�3)

Tensilestrength(N/m2�10�6)

Young�smodulus(N/m2�10�9)

Glass, E typea) 2.50 2400 72Glass, S typea) 2.44 2800 86Carbonb) 1.38 1700 190Graphiteb) 1.38 1700 250Aramidsa) 1.44 3600 127

a)Fibre diameter¼ 16–20mm.b)Fibre diameter¼ 6–10mm.

101. Composite Manufacture

Short-fibre composites are processed bycompression moulding or injection mould-ing. In the latter case particular care has tobe taken in the design of the equipmentand moulds in order to minimize fibrebreakage during processing. This usuallyinvolves the omission of non-return valvesin the barrel of injection moulding ma-chines, particularly for thermosetting sys-tems, and the use of large-cavity gates inthe mould. For long-fibre composites mostmanufacturing methods are carried out atlow pressures. Typical processes are shownschematically.

Wet layup technique with spray gun.

Pultrusion process with fibre impregnation.

101 Composite Manufacture j59

Filament winding with fibre impregnation.

Matched-die moulding with resin spreading.

Resin transfer moulding process.

102. Composite Matrix

The component that embeds the reinfor-cing fibres or fillers in a composite. Themost widely used polymermatrices in com-posites are shown in the table.

Thermoplastic polymers

Commercial name –

Chemical natureTm(�C)

Tensilestrength(MPa)

Coupled PP –

Polypropylene graftedwith maleic anhydride

165 30

Nylon – Polyamides 6 and 66 220–260 60PPS –Poly(phenylene sulfide) 280 50PEEK – Poly(ether etherketone)

330 70

Thermosetting resins

Commercial name –

Chemical nature Tg (�C)

Tensilestrength(MPa)

UPE – Unsaturatedpolyesters

80–100 50–60

Epoxy – Glycidylether resins

60–200 50

PF – Phenolformaldehyde resin

100 30

103. Composite Property Prediction

(See Fibre reinforcement theory.)

104. Composite Test

Usually refers to the measurement ofmechanical properties. The tests usedvary according to the type of composites.Long-fibre (or continuous-fibre) compo-sites require special considerations withrespect to the size of the specimens rela-tive to the length and orientation of thefibres. In addition to these requirements,there are also tests specifically designedfor long-fibre laminated systems, as out-lined below.

104.1 Interlaminar Shear Strength (ILSS)

Tests widely used for quality control pur-poses and as screening tests for the evalua-tion of matrices, fibre reinforcement andfibre–matrix interactions. The ILSS test iscarried out in three-point bending using avery short span (S) relative to the thickness(W). This allows the maximum shear stressto be set up between the fibre plies so thatfailureoccurswithin thematrixand/orat thefibre–matrix interface.Forpractical reasons,usually the recommendedS/W ratio is 5 and

60j 104 Composite Test

the ILSS value is calculated from the firstpeak of the load (Pmax) recorded in the test,whichcorresponds to the interlaminarshearfailure, using the formula

ILSS ¼ 0:75Pmax=BW;

whereW is the thickness and B the width ofthe specimen. Usually specimens are 1 cmwide and 3–4mm thick. A schematic illus-tration of the ILSS test is shown.

Interlaminar shear strength test by three-pointbending.

The values obtained for the ILSS of con-tinuous-fibre composites are in the regionof 15–30MPa for polyester resin laminateswith 50% glass fibre content. ILSS values,however, may depend on the thickness ofthe specimen and fabric construction, asthese will affect the complexity of the stres-ses that are set upwithin the laminae, owingto unaccounted interference from normalstresses in the calculation of the failureshear stress using the above equation.

104.2 Compression Strength Measurement

Tests often carried out onhigh-performancecomposites. A practical difficulty experi-enced in performing compression tests onrelatively thin specimens, such as lami-nates, is maintaining the axial alignmentduring the test. Special arrangements areoften made to achieve this through the useof guided grips, which prevent the occur-rence of buckling instabilities in the testspecimen during the test prior to fracture.Failures in compression can occur at stress

levels that are much lower than those expe-rienced in tensile and flexural strength.Typical compression strength values forwoven fabric laminates with 50% glass arein the region of 150–250MPa. The reasonfor this is that failure can take place withinthe matrix and at the interface throughvarious types of internal events, such asmicrobuckling resulting from fibre–matrixdebonding andmicrocracking of the matrixbetween the aligned fibres. In this respect itmust be borne inmind that the �slendernessratio� of the fibres is extremely high and,therefore, buckling of the fibres can occur atvery low compression strains.

104.3 Fracture Mechanics Applied to Fail-ure in a Composite

The very important role of interlaminarfailures in high-performance composites,and the inherent deficiencies of the ILSStests (mentioned earlier), has stimulatedconsiderable interest in the use of fracturemechanics to obtain more appropriate data.In particular, measurements have beenmade to obtain values for the critical strainenergy release rate in both crack-openingmode (GIc) by the double cantilever beam(DCB) method and the in-plane shear fail-ure mode (GIIc) using the end-notched flex-ure (ENF) specimens, as illustrated.

Geometric features of specimens and loadingmode for measuring the interlaminar shear tough-ness of composites.

104 Composite Test j61

The double cantilever beam test is thesame as that described for adhesives. Thesameformulacanbeusedtocalculate theGIc

value fromtherecordedpeak load to fracture(Pf), substituting the Young�s modulus ofthe adherend with the flexural modulus ofthe laminate (Efx). (See Adhesive test.) Inmeasurements of GIIc, the compliance ofENF specimens is given by the formula

C ¼ 2L3 þ 3a3

8Efxth3;

from which is obtained

GIIc ¼ 9P2f a

2C2tð2L3 þ 3a3Þ ;

where all the terms are as defined in thediagram. Note that the flexural complianceC can be measured directly on the ENFspecimen. The two tests can also be usedformeasuring crack growth rate under bothdynamic load (fatigue) and static load(creep) conditions. The values for GIIc areusually larger than for GIc, ranging fromabout 80 to 2000 J/m2. The larger values areobtainable particularly with the use of ther-moplastic matrices.

104.4 Damage Tolerance Test

These tests measure the damage caused byaccidental loading situations, such as im-pacts by falling objects or projectiles, interms of deterioration of some specificproperty within the affected area. Compres-sion tests are often performed on speci-mens containing different extents ofdamage induced by subjecting coupons oflaminate to different levels of impact energyby means of falling projectiles. (See Falling-weight impact test.) The damage toleranceof the laminate can be derived from thestrength retention after impact by con-structing plots of compression strengthversus applied impact energy.

105. Composting

According to the definition provided bythe US Environmental Protection Agency,the term �composting� denotes the con-trolled biological decomposition of organicmaterials in the presence of air to formhumus-like substances. (See Biodegradablepolymer.)

106. Compounding

A term used to describe the mixing of apolymer with additives or other auxiliaries,such as plasticizers and fillers,mainly in themelt state of the polymer. Compoundingmethods can be divided into batch mixingtechniques and continuous extrusion, usu-ally twin-screw extrusion. The typical equip-ment used for industrial-scale compound-ing is shown.

Banbury-type batch mixer. Source: Todd (2010).

62j 106 Compounding

Twin-screw mixing extruder. Source: Todd (2010).

107. Compression

The application of forces that bring about areduction in the dimensions in the direc-tion in which they act. In mechanics, com-pressive stresses and tensile stresses aredistinguishable only for their sign, that is,s¼ tension and �s¼ compression.

108. Compression Moulding

Amoulding process carried out in a verticalpress in which the rawmaterial, in the formof a prepreg, moulding compound, powderor pellets, is placed directly into the cavityand subsequently shaped by the applicationof pressure. Normally only thermosettingplastics and vulcanizable elastomers areprocessed by compressionmoulding, usinga hotmould to allow curing reactions to takeplace in the shortest possible time. Long-fibre thermoplastic composites are also pro-cessed in this manner by placing a pre-heated feedstock in a �cold� mould andapplying the required pressure before theonset of solidification through crystalliza-tion or vitrification in the case of glassypolymer matrices.

Example of compression moulding of thermoset-tingpolymers. Left: feedingof a compactedpreformof polymer mix. Right: cavity filled with melt under-going curing.

109. Compression Ratio

The reduction in volume per unit length ofthe channel of an extrusion screwwithin thetransition (or compression) zone. Since thewidth of the channel along the axial lengthof the screw is constant, then the compres-sion ratio can be calculated as the ratio of theheight of the channel in the feed zone to theheight of the channel in the metering zone.(See Extruder and Extrusion.)

110. Compression Set

A term used to describe the lack of recoverycharacteristics of a rubber or elastomerunder compressive loading conditions. Typ-ically the measurement consists in deter-mining the extent to which a cylindricallyshaped specimen remains permanently de-formed after being subjected to compres-sion stresses for a predetermined period.

111. Compression Test

Test carried out in compression. These arenot widely used for testing polymers, except

111 Compression Test j63

for cases where one wishes to determinethe behaviour of specific materials. (SeeComposite and Compression set.)

112. Compression Zone

The second section of the screw of an ex-truder, in which the root diameter graduallyincreases to compress the melting polymerand to remove the entrapped air. (SeeExtrusion.)

113. Concentric Cylinder Rheometer

(See Coaxial cylinder rheometer.)

114. Condensation Polymerization

Also known as polycondensation, refers tothe reaction or process in whichmonomersor oligomers react to produce linear poly-mers, or polymer networks, through con-densation reactions. Examples of conden-sation polymerization are those used for theproduction of polyesters, polyamides andpolyethers, and phenol formaldehyde, ureaformaldehyde andmelamine formaldehydenetworks. One important feature of poly-condensation is that the polymer chainsgrow in steps so that all the reacting mono-mer species take part in the growth of thepolymer chains right from the start. This isdifferent from addition polymerization re-actions, where a chain grows rapidly to thefinal size and a quantity of free monomer isalways present until full conversion isreached.

115. Condensation Reaction

A chemical reaction that involves the join-ing of one or more molecules, with theelimination of a smaller molecule, usually

water. An example of a condensation reac-tion is the formation of an amide from thereaction of a carboxylic acid (RCOOH) withan amine (R0NH2), that is,

RCOOHþR0NH2 !RCONHR0 þH2O

Another example is the formation of estersfrom the reaction of a carboxylic acid(RCOOH) and an alcohol (R0OH), that is,

RCOOHþR0OH!RCONHR0 þH2O

116. Conductance

Denotes the ratio of the current to thevoltage applied on a dielectric material. Byconverting the current I into current densityI/A, where A is the cross-sectional area, andthe voltage V into stress V/L, where L is thepath length, it is possible to calculate the�conductivity� as the ratio of the currentdensity to the applied stress. Conductivityis a property of the material and is equal tothe reciprocal of the resistivity.

117. Conduction

Represents the flow of heat through thebulk of a solid medium along the path setup by the temperature gradient. It alsodenotes the transportation of electrons, orions, to produce an electric current throughthe application of a voltage gradient acrossthe medium.

118. Conductive Polymer

A polymer capable of conducting an electri-cal current. Such polymers are divided into�extrinsically� conductive polymers, whenthe conductivity arises from the addition ofconductive fillers, and �intrinsically� con-ductive polymers, when the conductivitydevelops fromwithin the polymer structurethrough the dislocation of electrons alongpolymer chains.

64j 118 Conductive Polymer

118.1 Extrinsically Conductive Polymer

The fillers most widely used to developelectron conductivity in commercial poly-mers are grades of carbon black with a highsurface area. The amounts required have toexceed the critical concentration to createpercolation paths for the movement of elec-trons. The particles do not have to makephysical contact but have to be sufficientlyclose to allow electrons to hop across gapsabout 2 nm wide. This phenomenon is of-ten referred to as �tunnelling�. Using con-ductive grades of carbon blacks, theamounts required to bring down the vol-ume resistivity of typical polymers, around1015–1017Wm (ohm metre), to a lower pla-teau in the region of 100–300Wm, that is, aconductivity of about 10�2 S/m (siemensper metre), varies from values as low as1.5 to more than 10wt%, depending on thesystems used. (See Law of mixtures.)

118.2 Intrinsically Conductive Polymer

These are all based on conjugated polymers.The most widely studied in this category ispolyacetylene in its �doped� form. This con-sists of polymer chains containing free ra-dicals formed by controlled oxidation reac-tions that can recombine to form chargecarriers along the chains.

Example of charge carriers on polyacetylene chains.

In effect, the controlled oxidation addsextra electrons, creating �holes�, which rep-resent a position where an electron is miss-ing.When such ahole isfilled by an electronjumping in from a neighbouring position, anew hole is created and so on, allowing thecharge to migrate a long distance. The�doped� form of polyacetylene has a conduc-tivity of 105 S/m,which ismuch higher thanthat achieved with the addition of carbon

black to an �ordinary� polymer and com-pares with values of around 108–109 S/mfor copper. However, there are major draw-backs for these systems that prevent themfrom being used widely, namely their ex-treme susceptibility to oxidative degrada-tion when exposed to air and their poorprocessability. Otherwidely researched con-ductive polymers are listed below.

118.3 Polypyrrole

The structure of the raw polymer is shown,but to achieve a high level of conductivity ithas to be doped with strong acids, such astoluenesulfonic acid.

118.4 Polyaniline

The structure corresponds to that of emer-aldine, which can be dopedwith strong acid.Alternatively, it can be self-doped throughthe incorporation of sulfonic acid groupsalong the polymer chain, as shown.

119. Conductivity

Usually refers to either thermal conductivityor electrical conductivity. Thermal conduc-tivity, K, is the coefficient that relates theheat flux (Q) to the temperature gradient(dT/dx), that is Q¼K(dT/dx). Electrical

119 Conductivity j65

conductivity, r, is the coefficient that relatesthe current density (dI/dA) to the voltagegradient (dV/dL), that is,

dI=dA ¼ rðdV=dLÞ:(See Conduction and Conductance.)

120. Cone-and-Plate Rheometer

Operates by imposing a drag flow onto afluid placed between a rotating or oscillatingshallow cone and a flat plate in order toprovide a constant shear rate within the gap.This is achieved by ensuring that the angleformed by the cone with the plate is lessthan 10�. Under these conditions, the shearrate is given by _g ¼ W=a, where W is theangular velocity and a is the angle betweenthe two surfaces (see diagram).

Schematic illustration of the principle of the cone-and-plate viscometer.

The cone-and-plate rheometer is usedprimarily to evaluate the rheological prop-erties of polymer systems with a relativelylow viscosity, such as resins, solutions,emulsions and pastes. The shear stressacting on the fluid can be calculated fromthe torque (T ) developed by the rotatingspindle using the relationship

t ¼ 3T=2pR3;

where R is the radius of the rotating cone.The viscosity, h, can be calculated as theratio t= _g formeasurementsmade at variousshear rates and temperatures.For operations in the rotational mode, it

is possible to measure also the vertical

thrust on the plate, which can be used toevaluate themelt elasticity characteristics interms of the first normal stress difference(N1) from the relationship

N1 ¼ 2F0=pR2;

where F0 is the �net force� acting on themelt,that is,

F0 ¼ F�PapR2;

where F is the measured force (thrust) andPa is the atmospheric pressure exerted onthe melt at the edge. From the obtained N1

value it is possible to calculate the firstnormal stress coefficient (c1), that is,

c1 ¼ N1= _g2:

Vertical thrust measurements, however, arerarelymade. (SeeNormal stress difference.)For operations made in an oscillatory

mode, the data are displayed in terms of�real� shear modulus G0 and �imaginary�shear modulus G00. The latter correspondsto the �real viscosity� (h0) calculated as theratioG00/v, wherev is the angular velocity ofthe oscillatorymotion. The viscosity data arepresented as a �complex viscosity� (h�),which comprises a real component (h0) andan imaginary component (h00), that is,

h� ¼ h0 þ ih00;

where i ¼ ffiffiffiffiffiffiffi�1p

(the imaginary number).The imaginary term, h00, is directly relatedto G0, that is h00 ¼G0/ v. (See Complexcompliance.)

121. Cone Calorimeter

An apparatus that measures the heatevolved by a burning plaque, using thetechnique of the oxygen depletion calorim-eter. This is to say, the heat released by aburning sample is directly proportional tothe quantity of oxygen used in the process.The name derives from the shape of thetruncated conical heater that is used toirradiate the test specimen.

66j 121 Cone Calorimeter

Cone calorimeter for measuring the burning resis-tance of polymers. Source: Ashton (2010).

122. Configuration

A term used the denote the spatial positionof groups attached to a polymer chain,which gives rise to stereoregularity or tac-ticity designations, such as isotactic poly-propylene. (See Tacticity.)

123. Conformation

A term denoting the configuration of amolecule derived from the rotations withina molecular chain. (See Chain conforma-tion (cis and trans).)

124. Conjugated Double Bond

A term to describe the double bonds thatappear in alternated sequences with singlebonds, as in aromatic rings, or along linearaliphatic chains, as in polyacetylene. Theelectrons in the p orbitals of double bondsare said to be dislocated insofar as they canmove from one p orbital to another withinan aromatic ring or along the conjugationdouble bonds in a polymer chain. (SeeConductive polymer.)

125. Conservation Law

A fundamental law of nature. Conservationlaws are concerned with the conservation of

momentum and energy, forming the basisfor the setting of a constitutive equation forflow analysis and heat transfer in polymerprocessing.

126. Consistency Index

The coefficient relating shear stress to shearrate in the description of the power-lawbehaviour of the flow of pseudoplasticliquids, such as polymer melts,

t ¼ Kðdg=dtÞn;

where t is the shear stress, K is the consis-tency index, dg/dt is the shear rate and n isknown as the power-law index.

127. Contact Angle

The angle formed by a liquid droplet be-tween the tangent to the curvature and theplane on which it rests. It is related to theinterfacial free energy and determines theability of a liquid or a highly deformablebody (D), such as a polymer melt, to wet thesurface of a substrate (S) in air (A). The basicdefinition and the forces related to eachsurface energy term are shown.

The contact angle (u) is related to theinterfacial energy (gSD) and the surfaceenergy of the other two phases (gDA andgSA). The contact angle is obtained from therelationship

gSA ¼ gSD þ gDA cos u:

128. Continuum Mechanics

A branch of engineering science dealingwith definitions and relationships between

128 Continuum Mechanics j67

stress, strain and strain rate, which form thebasis for structural and flow analysis.

129. Converging Flow

Describes the flow of a fluid in channelswhose cross-sectional area decreases alongthe flow path. The most common type ofconverging flow in polymer processing isthat through conical sections of dies orthrough wedged sections of moulds or dies.The occurrence of converging flow is animportant issue in polymer processing in-sofar as it produces an acceleration of thefront of the flowing melt.

130. Coordination

Refers primarily to the formation of strongphysical bonds between the chemicalgroups of an additive or a polymer chainwithmetal ions, often present as impurities.Coordination is also known also as com-plexation or chelation.

131. Copolymer

A polymer containing two different mono-mer units along the chains. The two units(say, A and B) can be arranged in threepossible ways and the copolymers arenamed according to their disposition in thechains. A random or statistical copolymer isone in which the two units are arranged atrandom, or are statistically distributed alongthe chains. A block copolymer is one wherethe two units are arranged in blocks ofspecific lengths. An alternating copolymeris one where the two monomer units are inan alternating sequence along the chains.

. Random copolymer:

AAAAAABBBAABBBBABBAAABAABBBB

. Block copolymer:

AAAAAAAAABBBBBBB

or

AAAAAAABBBBBBBBBAAAAAAA

. Alternating copolymer:

ABABABABABABABABABABABAB

132. Core-and-Shell Structure

A type of structure of polymer particlesconsisting of two or more different typesof polymers, arranged in such a mannerthat one polymer produces a core or nucleusand another polymer forms the outer skinor a shell of the particle.

133. Corona Discharge

Electrical discharges generated by the de-composition of gases, normally air, underthe influence of a high voltage gradient.Their glowing appearance is caused by theformation of highly charged gaseous ions.These discharges can occur in air pockets ofa high-voltage insulation andmay cause thedeterioration of the insulation through ther-mal oxidative reactions. Corona dischargesare deliberately induced on the surface ofpolyolefin films used in packaging, such aspolyethylene or polypropylene, as a meansof producing oxygenated groups on thesurface of the film in order to enhance theiradhesion to printing inks. (See Coldplasma.)

134. Co-Rotating

A termused to denote the configuration andthe relative direction of two parallel screwsused in twin-screw extrusion. Co-rotationimplies that the two screws rotate in thesame direction. The concept is used primar-ily in the extrusion of rigid or unplasticizedpoly(vinyl chloride) (UPVC). (See Counter-rotating.)

68j 134 Co-Rotating

135. Couette Flow

Type of flow, named after the homonymousscientist, that takes place between a station-ary and a moving surface, also known as�drag flow�.

136. Counter-Rotating

A termused to denote the configuration andthe relative direction of two parallel screwsused in twin-screw extrusion. Counter-rota-tion implies that the two screws rotate in theopposite directions, one clockwise and theother anticlockwise. This type of screw con-figuration is most widely used in extrudersused for compounding.

Schematic diagram of intermeshing screws.

137. Coupled Polypropylene

A grade of polypropylene that contains an-hydride grafts along the polymer chains tomake them reactive towards silane couplingagents used in sizes for glass fibres or forthe surface treatment of fillers.

138. Coupling Agent

Reactive additives used to produce a chem-ical bond between the surface of an inor-ganic substrate, such as that of glass fibresor fillers, with a polymericmatrix. Couplingagents are usually alkyl functional trialkox-ysilane compounds, designed to allow thealkoxysilane groups to hydrolyse and under-go condensation reactions with the surfaceof the inorganic substrate, while the func-tional groups attached to the alkyl chain canreact with the organic matrix, as indicatedby the reaction scheme.

Hydrolysis and condensation reactions of alkoxysi-lanes with the surface of an inorganic substrate.

The hydrolysis reactions are catalysedprimarily by acids, while the condensationreactions are much faster under basic con-ditions. The most commonly used silanecoupling agents for typical polymer matrixcomposites are shown in the table.

Name Formula Matrix type

Vinyl triethoxysilane Polyester resins

g-Methacryloxypropyltrimethoxysilane

Polyester resins

g-Aminopropyltriethoxysilane

Epoxy resins, nylons, coupled PP

g-Glycidoxypropyltrimethoxysilane

Epoxy resins, nylons, coupled PP

g-Mercaptopropyltrimethoxysilane

Diene elastomers and EPDM forsilica reinforcement

138 Coupling Agent j69

There are other types of coupling agentsthat are sometimes used in polymer matrixcomposites, particularly the particulatetypes. These are usually esters of titaniumor zirconium, forming a bond with thesurface of inorganic fillers through protoncoordination interactions. They are usedprimarily for their ability to improve thedispersion of fillers, making it possible toincorporate larger quantities in a given for-mulation. This is particularly useful fornon-halogenated fire-retardant formula-tions using magnesium hydroxide or alu-minium trihydrate, which require largequantities of fillers to develop the necessaryfire-retardant characteristics.

139. Crack Initiation

A phenomenon describing the initial for-mation of a crack or the extension of anexisting crack, or notch, in a specimensubjected to a fracture toughness test.

140. Crack Length

The length of an edge notch of a specimen –

single edge notch (SEN) or double edgenotch (DEN) – used for the evaluation ofthe fracture toughness of materials.

141. Crack-Opening Displacement (COD)

Denotes the increase in the separation dis-tance between the two surfaces of a notch intests carried out on very ductile materials.The yield zone formed at the crack tip canbring about a quite large separation of thetwo surfaces of the notch, which can bereadilymeasured. The resistance to fractureof very ductile materials is often expressedin terms of a critical crack-opening displace-ment (COD), representing the increase inseparation distance at which the cracksbegin to grow. (See Fracture mechanics.)

142. Crazing

The formation of crazes, consisting of flatellipsoidal voids (axial length varies fromabout 50 nm to 1mm) lying in the directionperpendicular to the applied stress (pre-dominantly tensile). The upper and lowersurfaces of thewalls of a craze are connectedby fibrils 10–40 nm in diameter, as illustrat-ed in the diagram.

Formation and structure of crazes in glassypolymers.

Crazes observed in a polystyrene specimen testedin tension.

Crazing occurs in glassy polymers attemperatures substantially lower than theirglass transition temperature. Crazing takesplace only when the polymer is subjected topredominantly dilatational stresses. In oth-er words, crazing does not take place undercompression or pure shear stresses. Thephenomenon becomes more prominent inthe presence of a liquid environment withmiscibility parameter similar to that of thepolymer. (See Critical crazing strain.)

70j 142 Crazing

143. Creep

A phenomenon denoting an increase indeformation with time when a structure ora specimen is subjected to a constant load ora constant stress. In the case of polymers,this type of behaviour is associated withviscoelastic deformations.

144. Creep Compliance

Aparameter (C) that denotes the ability of astructure to deflect when subjected to exter-nal loads. It is defined, therefore, as the ratioof the applied load (P) to the resultingdeflection (D), that is C¼P/D. The compli-ance of a structure is equal to the reciprocalof its stiffness (S). The term �compliance� isalso used as a property of the material (D),which corresponds to the reciprocal of theYoung�smodulus, that is,D¼ strain/stress.The value of the compliance of a material isobtained from the gradient of the plot ofstrain against stress. For the case of visco-elastic materials, the compliance increaseswith the time of duration of the applicationof the stress. The standard linear model isoften used to describe the variation of thecompliance as a function of time, which isgiven by the expression

DðtÞ ¼ D0 þðD¥�D0Þ ½1�et=lc �;where D0 is the instantaneous compliance,that is, at time zero, D¥ is the equilibriumcompliance, that is, at time infinity, and lccorresponds to the retardation time, whichis a material constant that determines therate at which the compliance increases fromD0 to D¥. (See Viscoelasticity.)

145. Creep Curve

Plots of the strain as a function of time,normally as linear–log plots, derived fromexperiments carried out on specimens sub-jected to a wide range of stresses at constanttemperature. Normally the tests are carried

out in tension or in a three-point bendingmode. Typical curves obtained are shown inthe graph for a grade of polypropylene test-ed at room temperature.

Creep curves for a typical grade of polypropylene.

146. Creep Modulus

Correspondstotheratiooftheappliedstresstotheresultingvariablestrainmeasuredincreepexperiments. The creepmodulusofpolymersis a decreasing function of the duration of theappliedstress.Thevalueof thecreepmoduluscorresponds to the reciprocal of the creepcompliance, which is regarded as the funda-mental property that characterizes the behav-iour of polymers under creep testing condi-tions. (See Creep compliance.)

147. Creep Period

Corresponds to the part of a creep experi-ment in which the stress remains constantbefore the start of the recovery period. (SeeRecovery.)

Illustration of variation of strain with time duringthe creep period and subsequent creep recovery.

147 Creep Period j71

148. Creep Rupture

Refers to the fracture of a specimen or anarticle resulting from the application of aconstant stress as in creep experiments. Thetime required to induce failure by yieldingor fracture of a specimen at different stresslevels is sometimes measured to assess thetime-dependent fracture/yield resistance ofmaterials, as illustrated.

Failure of polyethylene pipes under pressure atdifferent temperatures (a< b < c < d). Source: Birleyet al. (1991).

149. Creep Test

Tests carried out at constant stress in whichthe strain is measured as function of theduration of the applied stress.

150. Crepe Rubber

The coagulated latex of natural rubber, usu-ally obtained in the form of sheets

151. Criterion

A rationale used to determine the condi-tions under which a certain event may takeplace. For instance, the Tresca criterion andthe Von Mises criterion are used to deter-mine, respectively, the state of stresses and

the magnitude of the distortional energyrequired to bring about failure of productsby yielding. (See Yield strength.)

152. Critical Chain Length (Zc)

The length of polymer chains above whichentanglements are formed. This is an impor-tant parameter with respect to the relation-shipbetweenviscosity andmolecularweight.Below Zc the zero-shear viscosity is directlyproportional to chain length (Z), that is,h0¼K1Z.AboveZc therelationshipish0¼K2Z

3.5,where K1 and K2 are proportionality con-stants, which depend on the chemical natureof the polymer and on the temperature atwhich the viscosity is measured. A log–logplotof thezero-shearviscosityagainstweight-average molecular weight is shown.

Graphical representation of the relationship be-tween zero-shear viscosity and chain length ofpolymers.

153. Critical Crazing Strain

The value of the tensile strain in the direc-tion of the maximum principal stress atwhich crazing takes place in a glassy poly-mer. (See Crazing.)

154. Critical Fibre Length (Lc)

Corresponds to the minimum length of thefibres in a unidirectional composite that is

72j 154 Critical Fibre Length (Lc)

required for the tensile stress acting alongthe length of the fibres to reach the maxi-mum possible value, which corresponds tothe tensile strength of the fibres. For fibrelengths greater than Lc the stress distribu-tion along a fibre (sf) rises from a mini-mum at the fibre ends and reaches aplateau along the middle section, wherethe conditions are isostrain, that is, thestrain in the fibre is equal to the strain inthe matrix. As the fibres get shorter, theportion of the fibres under isostrain con-ditions also becomes smaller, so that, whenthe length of the fibres decreases, andbecomes equal to the Lc value, the maxi-mum stress is reached only in the middlepoint (see diagram).

Variation of tensile stresses acting on the fibres of aunidirectional fibre composite.

Increasing the level of the external stress,the maximum stress in the middle sectionreaches the tensile strength value (s�),which causes the fibres to break and thefracture to propagate rapidly through thematrix. This is illustrated in the first micro-graph, taken on the fracture surface of athermoplastic composite tested in tension,which shows that fibres lying along thedirection of the applied stress break firstand are then pulled out of the matrix over a

distance equivalent to the Lc value of theparticular fibre–matrix combination.

Fracture surface of a thermoplastic composite con-taining glass fibres with length L> Lc. Source: Mas-cia (1974).

For fibre lengths shorter than Lc, thefibres cannot reach the maximum possiblevalue and, therefore, failure occurs at theinterface between fibre and matrix by ashear mechanism, as indicated in the sec-ond micrograph. In this case the compositeundergoes yielding deformation, causingthe rotation of non-aligned fibres along thedirection of the applied stress.

Fracture surface of a thermoplastic composite con-taining glass fibres with length L< Lc. Source: Mas-cia (1974).

Note that, if the fibre–matrix interfacialbond is very strong, failure will take placewithin the matrix near the interface at thepoint when the interfacial shear stressesreach the shear strength of the matrix. Thismakes it possible to obtain an estimate of

154 Critical Fibre Length (Lc) j73

the value of the criticalfibre length by takingthe balance of the tensile force acting withinthe fibre and the shear force acting at theinterface, as shown.

Force balance between tensile stress on a fibre andthe shear force at the fibre–matrix interface whenL¼ Lc.

When the length of thefibre (L) is equal toLc, the average tensile force on the fibres(Ff ) is equal to the average shear force at theinterface (Fmf ), where

Ff ¼ s�fpd

2=4

and

Fmf ¼ �tpdLc2:

Here d is the diameter of the fibre and �t isthe interfacial shear strength or the shearstrength of the matrix when the interfacialbond is sufficiently strong to cause failurewithin the matrix rather than at the inter-face. Making the appropriate substitutionsin the above equation, it is possible to obtainan estimated value of the criticalfibre lengthfrom the expression

Lc ¼ s�f d=2 �t:

A strong interfacial bond and a high matrixstrength are, therefore, required to obtain alow value for Lc, so that the tensile strengthof the composite remains well above thestrength of the matrix. On the other hand,because the propagation of the fracturefrom the fibres to the matrix takes placethrough a pull-out of the fibre from thematrix over a length equal to Lc, a largevalue for Lc becomes beneficial for tough-ness enhancement by providing an increasein the energy absorbed during fracture.

The estimated pull-out energy Uf is relatedto Lc and �t by the expression

Uf ¼ ff�tL2c=12d

The reduction in tensile strength resultingfrom shortening of the fibres in unidirec-tional composites can be estimated througha modification of the law of mixtures forisostrain conditions based on the averagevalue of stress carried by the fibres at thepoint of fracture. When L� Lc the averagestress can be estimated by approximatingthe variation of the stress along the fibre tothe geometry of a trapezium, as seen in thediagram illustrating the concept of Lc. Sincefracture originates in the middle section ofthe fibre at the point where the fibre reachesits ultimate tensile strength, it follows thatthe average stress, �s, carried by the fibres atthis point can be related to the strength ofthe fibre, s

�f , by the expression

�s ¼ s�f ð1�Lc=2LÞ:

This can be used in the law of mixtures forthe strength of the composite, s

�c, which

becomes

s�c ¼ ffs

�f ð1�Lc=2LÞþ ð1�ff Þs

�m;

where s�m is the stress carried by the matrix

at the point of the initiation of the fracture inthe fibres.

155. Critical Strain Energy Release Rate (Gc)

(See Fracture mechanics.)

156. Critical Stress Intensity Factor (Kc)

(See Fracture mechanics.)

157. Critical Wetting Tension

Also known as the critical surface energy,corresponds to the minimum value of the

74j 157 Critical Wetting Tension

surface tension (or surface energy) that isrequired for a liquid to obtain spontaneouswetting of the surface of a solid. (See Zis-man plot.)

158. Cross-Linked Thermoplastic

Linear polymers containing a small num-ber of cross-links between polymer chains,introduced through second-stage reactionsafter a product has been manufactured, oras an intermediate stage for a final processoperation. An example of the latter is thecross-linking of thermoplastic tubes, usual-ly by electron beam radiation, before theseare expanded to produce heat-shrinkabletubes. The polymers that are most widelycross-linked are: polyethylene (cross-linkedpolyethylene, XPE), both low- and high-density types; poly(vinyl chloride), mostlyas a plasticized polymer; poly(vinylidenedifluoride); and thermoplastic elastomers.Cross-linking of thermoplastics is usuallycarried out either directly through free-radical reactions, using peroxides orhigh-energy radiation techniques, or indi-rectly via functional groups grafted ontothe polymer chains. One widely usedtechnique for cables is to graft alkoxysilanefunctional groups onto the polymer chains,allowing the cross-linking reactions to takeplace through the formation of siloxanelinks, which are obtained by hydrolysisand condensation reactions when the pro-duct is exposed to natural atmosphericenvironments.

159. Cross-Linking

A term used to denote the formation ofchemical bonds (cross-links) between poly-mer or oligomer chains, leading to theformation of a network. (See Curing.)

160. Cross-Ply

The variable angle arrangement of unidi-rectionalfibres, or fabrics, in the productionof composites to obtain planar isotropy. Atypical arrangement for cross-plies obtainedin the production of pipes or cylindricalvessels by filament winding is shown.

Cross-ply layout and stresses acting on the fibres ofdifferent layers in filament winding of tubular pro-ducts. The stress on the fibre,sf, is normalized withrespect to the total thickness tf.

161. Crow Feet

Defects on the surface of calendered sheets,particularly in PVC, resulting from the pres-ence of rigid polymer particles, known asgels, dragged by the rotation of rolls, form-ing wakes on the surface of the sheets thatresemble the feet of a crow.

162. Crystalline Polymer

A polymer with a molecular structure con-sisting of a mixture of aligned molecularchains (crystals) and random chains (amor-phous regions).During crystallization, poly-mer chains will fold over at some specificchain length, forming a lamella. Individualpolymer chains enter into the adjacentlamellas via amorphous regions.An illustra-tion of the structure of crystalline polymersand the formation of lamellae is shown.

162 Crystalline Polymer j75

The sketch on the left depicts the earlyinterpretation of the structure of polymercrystals, known as a �fringed micelle�, con-sisting of domains containing aligned seg-ments of polymer chains and others inwhich sections of the polymer chains arecoiled, forming amorphous regions. Thesketches on the right show the actual struc-ture of polymer crystals, consisting of poly-mer chains folding over a well-defined dis-tance to form lamellae of crystals, sur-rounded by amorphous regions consistingof randomly coiled chains. The same poly-mer molecule can participate in the chainfolding process for the formation of lamel-lae as well as being part of the amorphousdomains. The latter are often referred to as�tie molecules�. (See Spherulite.)

163. Crystallinity

Denotes the crystalline state of a polymer.The �degree of crystallinity� of a polymer, onthe other hand, defines the percentage ofcrystalline domain present in a particularsample. This depends on the nature of thepolymer and on the processing conditionsused to produce a given sample or product.The degree of crystallinity of polymers var-ies from about 10% (low-crystallinity poly-mers) to about 60–70% for polymers with ahigh degree of crystallinity.The degree of crystallinity of polymers

has a major influence on most properties,and therefore it is often adjusted to obtain

the best balance of properties for a particu-lar application. (See Ethylene polymer.)

164. Crystallization

Denotes the formation of crystals throughcooling of a polymer melt or a polymersolution. It takes place in two steps, knownas nucleation and growth.Nucleation can bedivided into homogeneous nucleation andheterogeneous nucleation, according towhether the nuclei are formed either spon-taneously or on the surface of impurities orexistingheterogeneitiespresent.Nucleationand growth of crystals take place only whenthe temperature is higher than the glasstransition temperature (Tg). The maximumcrystallization rate takes place at some tem-peraturebetween themeltingpoint (Tm) andtheTg of thepolymer.Thegrowthofpolymercrystals takes place through the formationoflamellae by the folding of molecular chainsin the direction perpendicular to the basalplane. (See Crystalline polymer.)The thickness of the lamellae is between

5 and 50 nm, and is inversely related to thedegree of supercooling from the melt.Supercooling is defined as the differencebetween the equilibriummelting point andthe ambient temperature at which crystalli-zation takes place. In the case of solventcrystallization, the extent of supercooling isassessed with respect to the �equilibrium�dissolution temperature. Crystallizationcan also take place when the polymer isheated from the quenched amorphous stateto a temperature above the glass transitiontemperature. This is often referred to as�cold crystallization�, which can be facilitat-ed by the application of external stresses, asin the injection blow moulding of poly(eth-ylene terephthalate) (PET). Stress-inducedcrystallization can take place also above themelting point of the polymer, as in the caseof stretched natural rubber, and also within

76j 164 Crystallization

the die of an extruderwhen some crystallinepolymers are processed at temperatures justabove their Tm.

165. Curable Adhesive

Systems that will produce cross-links in thefinal structure. (See Adhesive.)

166. Curative

Cross-linking agent used to induce curingreactions. An alternative term for �hardener�for thermosetting resins or �vulcanizingagent� for elastomeric materials.

167. Cure-Meter

A device or an apparatus to evaluate thecuring characteristics of a rubbermix (com-pound). The most widely used commercialsystem is the Mooney viscometer, whichconsists of a rotating bi-conical disc oscillat-ing in a cavity containing the sample. Radialribs on the surface of the disc allow thecontacting rubber sample to oscillate and,therefore, to shear between the static sur-face of the cavity and the moving surface ofthe disc. The basic construction is shown.

Schematic diagram of a rubber cure-meter. Source:Eirich (1978).

The cure-meter records the variation ofthe torque exerted by the disc on the samplewhile it is cured. The temperature of thechamber and the amplitude of the oscilla-tions can be changed at will to suit thenature of the sample examined and to studythe effects of related processing parameters.(See Cure time.)

168. Cure Time

A term denoting the time required by athermosetting resin, or vulcanizable elasto-mer, to develop the required network den-sity for optimum physical properties. Typi-cal curves for the variation of viscosity ortorque to maintain constant the amplitudeof the oscillations of the disc in the rheom-eter used in the measurements is shown.

Cure curves recorded in measurements with anoscillating disc rheometer.

In the diagram the following parametersare identified:

. VM – The minimum torque as an indica-tor of the viscosity of the mix beforecuring. (Note that the initial decrease intorque is an artefact arising from thewarming up of the sample fed into therheometer at room temperature.)

. TS – The �scorch� time, corresponding tothe time required to reach an arbitraryincrease in viscosity, above which thematerial will no longer be workable.

. TC – The �optimum cure� time, arbitrarilydefined as the time required to reach 90%

168 Cure Time j77

of the maximum achievable cross-linkingdensity. It is assumed that a mouldedproduct will continue to cure to the maxi-mum as it cools down naturally afterbeing removed from the mould.

. SlopebeforeTC–Aparameterrelatedtotherate of cross-linking reactions (cure rate).

. TMAX – An indicator of the degree ofcross-links (cross-linking density of thenetwork).

. Slope after TMAX – An indicator of thestability of the network produced. A neg-ative slope, known as �reversion�, resultsfrom the breakdown of cross-links. Apositive slope, known as �marching cure�,indicates that there is a continual increasein the degree of cross-linking, albeit atmuch slower rate due to the depletion ofreactive species present.

The optimum curing conditions for ther-mosets are established ad hoc throughmea-surements of the mechanical properties ofmoulded specimens. Typical changes inmechanical properties for thermoset poly-mers are shown. The indicator line at pointA shows the �optimum cure time� deter-mined in terms of the best balance of prop-erties achievable for a particular system.

Change inmechanical propertieswith reaction timeat a given processing temperature for a rigid ther-moset polymer. Source: Goodman (1998).

169. Curing

A term originally used to describe the re-duction in compression set in rubber with

the addition of sulfur to the formulation.Nowadays it is generally used to denotecross-linking reactions for both thermoset-ting resins and elastomers. In the lattercase, the process is also known as vulcani-zation. Similarly to polymerization, curingreactions can take place by addition or con-densation reactions. The latter is generallyavoided, if at all possible, in order to avoidthe formation of volatiles, which may pro-duce bubbles or have other undesirableside-effects.

170. Current Density

For conduction through the bulk of a me-dium, the current density corresponds tothe intensity of the current flowing throughthe medium divided by the cross-sectionalarea. For surface conduction, the currentdensity is defined as the intensity of thecurrent divided by the width, perimeter orcircumference of the medium. (See Con-ductivity, Volume resistivity and Surfaceresistivity.)

171. Cyclic Butylene Terephthalate

Cyclic oligomers containing a small num-ber of butylene terephthalate units, used forin situ polymerization manufacturingoperations.

172. Cycloaliphatic Epoxy Resin

Type of epoxy resins used to obtain productswith higher transparency and better water-like clarity than aromatic epoxy resins.Widely used also for electrical applicationsbecause of the better tracking resistance,arising from the absence of aromatic ringsin the network, which would give rise to theformation of graphitic polynuclear ringsunder the influence of arcs formed by highelectrical stresses. (See Epoxy resin.)

78j 172 Cycloaliphatic Epoxy Resin

173. Cyanate Ester

Type of thermosetting resin used in adhe-sives or composites for the high Tg valuesachievable through curing reactions involv-ing trimerization of isocyanate groups withthe formation of triazine rings. The reactionscheme shows how these reactions cantake place.

Cyanate esters are often used as mixtureswith epoxy resins to reduce the cure tem-perature and to improve the wettability withgraphite fibres. (See Urethane polymer andresin.)

Scheme for trimerization reactions of isocyanate groups.

173 Cyanate Ester j79

D

1. DABCO

A tertiary cyclic diamine (2,4-diazobicyclo[2.2.2]octane) used as a catalyst for isocya-nate reactions in the production of polyure-thane or as a catalyst for esterification reac-tions in paints. (See Urethane polymer andresin.)

2. Damage Tolerance

A term used to denote the resistance of amaterial to damage caused by loads at levelsthat would cause catastrophic fracture. It isnormally assessed by measuring the deteri-oration in mechanical properties after apanel has been subjected to impact loads.(See Composite.)

3. Damping

The attenuation of oscillatory excitations,mechanical vibrations or sound waves ap-plied to a structure. The phenomenon isalso known as attenuation. (See Loss angle.)

4. Damping Factor

The extent of damping or attenuation that amaterial undergoes is expressed in terms oftan d, which is known as the damping orattenuation factor, where d is known as theloss angle. (See Dynamic mechanical ther-mal analysis and Loss angle.)

5. Debonding

A term used for removing or loosening thebond (adhesion) of adhesives towards theadherend (substrate). Widely used also todenote the loss of adhesion between matrixand fibres or fillers in composites.

6. Deborah Number

A dimensionless number used in rheology,defined as the ratio of the characteristic timeof the material (usually the relaxation timeor retardation time) to the time over whichthe phenomenon examined is considered.

7. Decomposition

Denotes the breakdown of the molecularstructure of a polymer by heat. Widely usedterm in thermogravimetric analysis, wherevarious reference temperatures are identi-fied as relevant features of the decomposi-tion process. For instance the �onset decom-position temperature� is the temperatureat which the incipient loss of matter isobserved in a thermal scan of the analysis.

8. Decompression Zone

The zone of the screw of a compoundingextruder, usually within the region wherevacuum is applied to remove volatiles. Thisis illustrated in the diagram, which showsalso the rapid drop in pressure on the melton approaching the devolatilization zone ofthe screw/barrel assembly.

Extruder with devolatilization port and decompres-sion zone in screw.


80j

9. Deconvolution

A procedure that allows one to distinguishclearly between two merging absorptionpeaks in spectra obtained by spectroscopicanalysis, such as IR or UV spectroscopy.

10. Deflection Under Load Temperature(DULT)

The temperature at which a specimen sub-jected to a specified flexural load (three-point bending mode), when heated at aspecified rate of temperature rise, reachesa specified central deflection. This is alsoknown as the heat distortion temperature.(See Heat distortion temperature.)

11. Deformation

A generic term for the response of a speci-men or structure to amechanical force. Thistakes place in the form of a change in lengthwhen a tensile or compressive force is ap-plied, or as a geometric or torsional distor-tion when the applied forces are shear ortorsional types.

12. Deformational Behaviour

Refers to the different states of a polymerover a wide range of temperatures. Thechanges that take place with increasing

temperature presented as force versusextension curves up to fracture are shown.

The deformational behaviour can also beinterpreted in terms of the deformationalstates of a polymer with changes in temper-ature, illustrated as nominal plots of a pa-rameter representing the deformability, orcompliance, as a function of temperature.It is important to note that the transitionfrom the �glassy� state to the �rubbery� statefor the case of a linear polymer, or onewith avery low cross-link density (as in the case ofelastomers), brings about an increase indeformability by three or four orders ofmagnitude.It is noted that the transition from the

rubbery state to a nominal viscous statetakes place via an intermediate �melt� state.In the melt state a polymer acquiresthe ability to undergo flow while it retainssome of the characteristics of the rubberystate, known as melt elasticity (see dia-gram).

12 Deformational Behaviour j81

Various deformational states of polymers.

13. Degradation

The deterioration of properties or opticaldiscoloration resulting from oxidative reac-tions taking place during processing orenvironmental ageing of a polymer sampleor product. (See Thermal degradation andUV degradation.)

14. Degree of Cross-Linking

Refers to the quantity of cross-links presentin network polymers, such as rubbers (elas-tomers) or thermoset plastics. It is normallyexpressed in terms of the molecular weightof chains between cross-links. For vulca-nized rubber, themolecular weight betweencross-links is in the region of 2000–3000;whereas for thermosetplastics, thevaluecanvarymuchmorewidely but canbe estimatedto be within the range of 300–1000. It has tobe borne in mind that the molecular con-stituents of thermoset plastics are muchmore bulky than those of elastomers.

15. Degree of Crystallinity

Represents the volume fraction of crystal-line domains in a polymer, expressed as apercentage. Can be obtained from thermalanalysis or X-ray diffraction methods. (SeeCrystallinity.)

16. Degree of Polymerization

Represents the number of monomericunits present in a polymer chain. The dia-gram shows the length of a free polymerchain with a degree of polymerizationequal to about 1000. Although this is a fairlylow degree of polymerization for mostcommercial polymers, the actual length ofthe chains is very large, as indicated in thediagram.

A free polymer chain with a degree of polymeriza-tion in the region of 1000.

For polyethylene, for instance, a degreeof polymerization of 1000 corresponds toa molecular weight of 28 000. This isequivalent to a low-molecular-weight gradeused in injectionmoulding. In comparison,an ultra-high-molecular-weight polyethyl-ene (UHMWPE) grade has a degree ofpolymerization in the region of 40 000.However, for polymers containing aromaticunits in the backbone chains, such as poly-carbonates or polysulfones, the degree ofpolymerization is even lower than 1000.

17. Delamination

The breaking up of the interlayers inlaminar composites or other multilayerconstructions.

18. Demoulding

The removal of a moulded part from amoulding process at the end of a cycle.

82j 18 Demoulding

19. Dendrimer

Can be defined as a branchedmolecule witha perfect structural and molar mass regu-larity. The principle used to build up thistype of �perfect� structure through variousstages is illustrated. The concept has beenused to produce industrially useful productsknown �hyperbranched polymers�. (SeeHyperbranched polymer.)

20. Denier

A unit of measurement of the diameter offibres or textile yarns, expressed inweight ingrams per 9000 metre length. (See Tex.)

21. Depolymerization

The reverse process to polymerization.Some polymers, such as poly(tetrafluor-oethylene), poly(methyl methacrylate) andpolyoxymethylene (POM), will depolymer-ize back to the original monomer throughunzipping reactions.

22. Desorption

The loss of volatiles from a substance whenis exposed to an environment where theconcentration of the previously absorbedvolatiles is either zero or very small. (SeeDiffusion.)

23. Devolatilization

The removal of volatiles, particularly water,from a compound. The term also refers tothe section of a compounding extruderwhere a vacuum port in the barrel is usedto remove volatiles from the decompressionzone of the screw. (See Decompressionzone.)

24. Diallyl Phthalate and Isophthalate(DAP and DIAP)

A tetrafunctional unsaturated monomerused for the production of thermosettingresin moulding compositions. The chemi-cal formula is:

DAP and DIAP are primarily used ascross-linking agents for unsaturated polye-sters and as polymerizable plasticizer inPVC formulations. The high reactivity ofthe allyl groups gives rise to networks with ahigh cross-link density and products with avery high glass transition temperature (Tg).

25. Die

The part of an extruder that shapes themelt into the desired geometry. Fitted near

Formation of dendritic molecular structures through condensation reactions. Source: Teegarden (2004).

25 Die j83

the screw tip, a die receives the meltfrom the metering zone of the extruder anddelivers the extrudate to cooling devicesbefore arriving at the take-off units. Theterm �die�, however, is sometimes usedsynonymously with the term mould. (SeeExtrusion.)

26. Die Analysis

Refers to the flow analysis within the die ofan extruder to predict the flow rate (Q) as afunction of the pressure drop (DP) from thedie entry to the screw tip. This can begeneralized by the equation

Q ¼ KDP=h;

where K is a constant related to the geome-try of the die and h is the viscosity of themelt. Because the die is composed of severalsections, the analysis has to be carried outfor each section from knowledge of thepressure profile. In general, the highestpressure drop takes place in the flowthrough the die lips or die gap. Therefore,approximate estimates can be obtained byneglecting the pressure drops arisingbefore the melts enter the die lips or diegap. The calculation of K for the mostcommon types of channels in extrusion diesare shown below for Newtonian flow.

. Circular sections (cylindrical rods):

K ¼ pR4

8L;

where R is the radius and L is the length(for L/R� 1).. Rectangular sections (slit dies):

K ¼ SWH3

12L;

where S¼ 1� 0.65(H/W) is the shapefactor, H is the height of the channel andW is the width of the channel.. Axial annular sections (thin-wall tubulardies):

K ¼ pR4o½1�R4�ð1�R2Þ2=lnð1=RÞ�

8L;

where Ro is the external radius, Ri is theinternal radius, with R¼Ri/Ro, and L is thelength of the channel.

Note that for the case of polymer meltsthe viscosity is dependent on the shearrate and temperature and it is, therefore,difficult to obtain accurate estimates fromthe above equations without a detailedknowledge of the variation of viscosity. (SeeExtrusion and Screw–die interaction.)

27. Die Drool

The build-up of solid deposits at the die exitof an extruder, resulting from the removal of�loose� matter that has accumulated on thesurface during the flow path.

28. Die Exit Phenomena

(See Sharkskin.)

29. Die Gap and Die Lip

The upper and lower walls of the exit chan-nel of a die used in polymer extrusion.These are often adjustable to change thethickness of the extrudate. (See Extrusion.)

30. Die Swell Ratio (B)

The ratio of the diameter of the extrudate tothe diameter of the die for circular capillarydies, that is,

B ¼ DðextrudateÞDðdieÞ :

It is frequently quoted as an empiricalparameter characterizing the elasticityof polymer melts. (See Melt elasticity and

84j 30 Die Swell Ratio (B)

Normal stress difference.) The value of Bdepends on the shear rate ( _g), temperature(T) and the length/diameter ratio (L/D) ofthe die, as shown in the diagrams.

Variation of swell ratio (B) with increasing L/D of acapillary die at two shear rates, _g1> _g2.

Variation of swell ratio (B) with increasing L/D of acapillary die at two temperatures, T2> T1.

The increase in die swell ratio with in-creasing shear rate is related to the higherdegree of molecular orientation of the poly-mer chains during the flow down the capil-lary. The reduction in swell ratio with in-creasing L/D is thought to be due to thegradual relaxation of the molecular orienta-tion acquired in the die entry region. Simi-larly, the reduction in die swell ratio withincreasing temperature results from themore rapid relaxation of molecular orienta-tion before themelt reaches the die exit. Forthe same type of polymer, an increase in

molecular weight results in an increase indie swell ratio. Although the die swell ratiocurves suggest that a limiting constantvalue of B is reached at high L/D ratios,this value is always greater than 1 due to theelastic characteristics of polymer melts. Atthe same time, the limiting value of Bcannot in itself be considered a fundamen-tal property insofar as it cannot predictthe extent of swelling for dies of differentgeometry, such as slit dies.

31. Dielectric

A generic term for an electrical insulatingmaterial, normally for low-voltage circuits.

32. Dielectric Constant

Known also as the relative permittivity, it isdefined as the ratio of the permittivity of adielectric to the permittivity of air. It is,therefore, a dimensionless number. Thepermittivity of air is close to 1, which is thelowest value achievable insofar as it corre-sponds to the value for a perfect dielectric,that is, vacuum. (See Permittivity andDielectric properties.)

33. Dielectric Properties

Properties that define the relationship be-tween an applied electrical stress (voltagegradient along the line of current flow) andthe resulting current density (current perunit cross-sectional area).ForDC situations, the relationship can be

described in terms of �volume resistivity� (r)and �bulk conductivity� (1/r), where

r ¼ ðV=dÞðA=IÞ:A perfect dielectric is one whose volumeresistivity or bulk conductivity is indepen-dent of the duration of the applied voltage(linear behaviour).

33 Dielectric Properties j85

For AC situations, the dielectric proper-ties are described by the �specific im-pedance� (Zp) and �permittivity� («). For aperfect dielectric, the specific impedanceand permittivity are independent of thefrequency of the current in the circuit. Thedeviation from ideal behaviour can bedescribed by models (analogues) consistingof combinations of a �resistor� (perfect di-electric) and a �capacitor� (the componentresponsible for the decrease in volume re-sistivity with time, and associated with lossof electrical energy in AC circuits). Theapproach is similar to that used for theviscoelastic behaviour, using combinationsof a spring (elastic solid) and a dashpot(viscous component).

In this respect, appropriate combinationsof the two elements can be used to modelthe reduction in volume resistivity withtime (the opposite for conductivity) and theincrease in permittivity with frequency (theopposite for specific impedance). The ratioof the constants for the elements deter-mines the time- or frequency-dependentbehaviour in terms of a characteristic time,known as the �relaxation� or �retardation�time, l.For ACcircuits the deviation fromperfect

dielectric behaviour is defined by the losscomponents Z

00p and «00, or the loss tangent

of the phase angle

tan d ¼ Z00p=Z

0p ¼ «00=«0:

Similarly to the viscoelastic behaviour formechanical properties, the variation of thedielectric loss component «00 and tan d atconstant frequency goes through a maxi-

mum with respect to temperature, corre-sponding to the glass transition tempera-ture, Tg. The corresponding variations withrespect to frequency have amaximumwhenthe frequency is equal to 1/l.

34. Dielectric Strength

The value of the electrical stress at whichfailure takes place. Failure denotes the lossof dielectric characteristics through the for-mation of carbonaceous channels or theformation of holes resulting from depo-lymerization reactions, as for PTFE. Thetypical measurement set-up for dielectricstrength is shown in the diagram.

Electrode set-up for measuring dielectric strength.

Note that often the specimen is im-mersed in transformer oil to prevent arcingover the edges of the specimen caused bythe breakdown of air.

35. Dielectric Thermal Analysis (DETA)

Known also as dielectric relaxation spec-troscopy, is a characterization techniquebased on the measurement of the permit-tivity («) and loss factor (tan d) over a widerange of frequencies (f) and temperatures(T). (See Permittivity.) A sample is sub-jected to an AC voltage to induce polariza-tion of the dipoles associated with theconstituent chemical groups. The response

86j 35 Dielectric Thermal Analysis (DETA)

is analysed in terms of the charges gener-ated and loss of input energy, from whichare calculated the two components of thepermittivity, respectively the in-phase («0)and out-of-phase («00) components. InDETA measurements there are two possi-ble transitions that polymers can undergo,varying according to the excitation fre-quency. These are associated with interfa-cial polarization for frequencies around100Hz and with dipolar polarization atfrequencies between 100 and 106Hz. (SeePolarization and Dynamic mechanicalthermal analysis.) The treatment is similarto that developed for the viscoelasticity ofpolymers, using models that can be usedto define fundamental parameters that canbe correlated with the chemical and physi-cal structure. The models consist of acombination of resistors and capacitors torepresent the actual behaviour between thetwo extremes exhibited by each individualelement. The vector diagram for the twocomponents of the current resulting fromthe applied voltage, respectively Ic (out-of-phase component, representing the charg-ing current) and Ie (in-phase component,representing the loss current), gives thephase angle d, known as the loss angle.

Vector diagram of electric current resulting from anAC voltage applied to a dielectric.

The input and response signals are usedto generate the data required to calculate theparameters representing the frequency-related dielectric characteristics of polymersin terms of the components of the complexpermittivity «*, that is, «* ¼ «0 � i«00, where iis the imaginary number (

ffiffiffiffiffiffiffi�1p

), «0 is the in-phase component and «00 is the out-of-phase(loss) component, so that tan d ¼ Ie/Ic andalso tan d¼ «00/«0. A transition ismanifestedas a rapid decrease in the «* or «0 values anda peak in the tan d or «00 values with increas-ing excitation frequency – see diagram forpoly(methyl methacrylate) (PMMA).

Variation of dielectric tan d with frequency at different temperatures for aPMMA sample. Source: Koppelmann (1979).

35 Dielectric Thermal Analysis (DETA) j87

36. Diene Elastomer

A homopolymer or copolymer based on adiene monomer. The latter are available asrandom copolymers requiring conventionalsulfur vulcanization for curing, or as blockcopolymers in the form of thermoplasticelastomers. The more widely used systemsare described below.

36.1 Polybutadiene (Butadiene Rubber, BR)

Polymer chains with mostly cis-1,4-, sometrans-1,4- conformations and small amountsof vinyl-1,2- typeunits, as depicted. Producedby a number of polymerization techniques,giving a variety of grades with differentmolecular structure, molecular weight andpolydispersity. The grades with the highestcis-1,4- conformation gives the lowest Tg,around �90 �C and a melting point of ap-proximately þ 1 �C.

The polymer does not exhibit stress-in-duced crystallization at room temperature,although the tendency to stress crystalliza-tion increases with increasing amount of1,2- units in the polymer chains, resultingin a decrease in wear resistance. The aver-age molecular weight of commercial BR isin the region of 250 000–300 000. Such BRsare mainly used in blends with naturalrubber (NR) and styrene–butadiene rubber(SBR) in sulfur vulcanization compounds,primarily for use in tyre manufacture.

36.2 Polyisoprene

The polymer constituent of natural rubber(NR) and synthetic polyisoprene (isoprene

rubber, IR). Both have chains with a cis-1,4-configuration content greater than 92%.The chemical formula is:

The molecular weight of both syntheticIR and NR is very high, in the region of(1� 1.5)� 106, and they have similar prop-erties. The density is 0.934 g/cm3 and IRundergoes crystallization if cooled slowlyfrom about 10 to �35 �C. Stress-inducedcrystallization, on the other hand, can takeplace at higher temperatures. NR has to bemasticated in order to reduce the molecularweight and render it compoundable andprocessable. Its main use is for the produc-tion of tyres.

36.3 Polychloroprene Rubber (ChloropreneRubber, CR)

Sometimes also known as �neoprene �, isessentially poly(2-chlorobutadiene), whichcan be represented by the formula:

Some commercial grades may containsmall amounts of 2,3-dichlorobutadiene,acrylonitrile or styrene, as a means ofcontrollingthecrystallizationcharacteristicsof the polymer. Contrary to all other dieneelastomers, the vulcanization of CR is notcarried out using sulfur but through reac-

88j 36 Diene Elastomer

tions with metal oxides involving the scis-sion of the C�Cl bond. Typical oxides areMgO, ZnO and PbO or Pb2O4, even thoughthe cross-linking reactions are assisted bythe addition of conventional accelerators,such as thiuram or mercaptans. The maincharacteristics of CR are flame retardancyandoil resistanceduetothepresenceof largequantities of chlorine in the structure.

36.4 Styrene–Butadiene Rubber (SBR)

A general-purpose rubber containing23–40% styrene and 60–77% butadiene asrandom copolymers, represented by theformula:

There aremany grades available commer-cially, varying according to the method ofpolymerization used, and broadly known asE-SBR (emulsion-polymerized) and L-SBR(solution-polymerized). The difference instructure can be quite substantial, owingmainly to variations in trans-1,4- conforma-tion and vinyl-1,2-butadiene content. Theglass transition temperature, Tg, is usuallyin the region of �50 �C and increases withthe styrene content of the polymer chains.E-SBR has a molecular weight in the range250 000–800 000 and is used mainly inblendswith polybutadiene (BR) in tyreman-ufacture. This combination brings about asubstantial decrease in the Tg value. L-SBRis a purer grade with a less broadmolecular-weight distribution and is less branchedthan E-SBR. It is characterized by a higherabrasion resistance and a lower heat build-up thanE-SBR.Owing to the randomnatureof the chain structure, SBR does not exhibitstress-induced crystallization and, there-fore, the products have inferior mechanical

properties than natural rubber or syntheticpolyisoprene rubber.

36.5 Acrylonitrile–Butadiene Rubber (NBR)

Also known as nitrile rubber, is a based onrandom copolymers with acrylonitrile con-tent in the range 18–51%, represented bythe formula:

There are also many variations in gradesavailable due to differences in trans-1,4-conformation and vinyl-1,2-butadiene con-tent. The Tg varies from about �10 to �40�C with increasing butadiene content. Ow-ing to the random structure and the lack ofuniformity of polymer chains NBR does notexhibit stress-induced crystallization and,therefore, relies on the use of carbon blackreinforcement to achieve adequate strengthcharacteristics. They are widely used inblends with natural rubber, polybutadieneand EPDM rubbers. An important charac-teristic is the resistance to mineral oils dueto the high polarity of the chains, resultingfrom the presence of the acrylonitrile units.The polar nature of the chains makes NBRmiscible with poly(vinyl chloride) (PVC)and the phthalate plasticizers, which arewidely used for low-voltage insulation inwire and cable applications.

37. Differential Scanning Calorimetry (DSC)

A technique that measures changes in heatflow to and froma sample contained in a cellwhile it is undergoing chemical or physicalchanges. This is done by comparison to areference sample, which remains stableduring the same scan at a constant rate oftemperature rise (see diagram).

37 Differential Scanning Calorimetry (DSC) j89

Schematic diagram of a DSC cell.

Themeasurements are usually made in anitrogenatmosphere,unless it is intendedtoexamine the effects of an oxidative environ-ment. Heats of reaction are more usuallymeasured with isothermal scans, whilephysical transitions, such as the glass tran-sition temperature and the melting point,are determined with a ramp scan. The mea-sured enthalpy can be used to measure thedegree of crystallinity of a polymer fromknowledge of the corresponding heat offusion for a fully crystalline sample, nor-mally estimated from theoretical calcula-tions. The weight fraction of crystalline con-tent is equal to the ratio of the measuredenthalpy to that of the fully crystalline sam-ple. The thermogram shows the glass transi-tion (Tg) in the formof a sharp increase in thebaseline of the heat flow, corresponding tothe increase in specific heat DCp, and a peakassociated with the endothermic heat flow,which results from the melting of crystals.

Thermogram of a polymer examined by DSC.

Melting takes place over a range of tem-peratures owing to the non-homogeneity of

the crystals present and is completed at thepeak temperature, taken as the thermody-namicmelting point (Tm). The diagram alsoshows the endothermic oxidation of thepolymer, which takes place at highertemperatures.

38. Differential Thermal Analysis (DTA)

A technique thatmeasures the difference intemperature between an inert referencematerial and the sample arising from heatchanges in experiments carried out in aheating scan in the measuring apparatus.(See Differential scanning calorimetry.)Endothermic events will bring about a re-duction in temperature of the sample exam-ined relative to the reference sample. Theopposite changes are recorded if the ther-mal process is exothermic.

39. Diffusion

A termused to denote the transport of gasesor liquids through a solid medium. Thereare various types of diffusion. The morecommon are the Fickian and the case IItypes. Fickian diffusion takes place througha random movement of the diffusant mo-lecules, driven by concentration gradientsthrough the thickness. Case II diffusiontakes place via an advancing front layer,which gradually increases in thickness untilit traverses the entire cross-section of themedium, driven by the hydrostatic tensionahead of the swollen advancing front layer.

40. Diffusion Coefficient (or Diffusivity)

The coefficient (D) that relates the rate ofdiffusion (F) of gases or liquids through asolid medium under steady-state condi-tions, generally known as Fick�s law, thatis, F¼D(dc/dt), where dc/dt is the concen-tration gradient. The diffusion coefficient

90j 40 Diffusion Coefficient (or Diffusivity)

can be measured from experiments carriedout on thin sheets or films either by moni-toring the amount of diffusant that has beentransported through the medium and plot-ted against time, or by measuring the massuptake of the sample through absorptionwhen immersed in the diffusant.For the first case, the mass (Mt or Ft)

transported through the medium is approx-imately related to D by the expression

Mt ¼ DC0

xðt�x2=6DÞ ;

whereC0 is the concentration of diffusant atthe surface and x is the thickness of thefilm.The quantity x2/6D, known as the �time lag�(L), can be used to calculate the value ofD. Atypical graph obtained from the above plot isshown.

Concept of �time lag� (L in diffusion phenomena).

For absorption experiments, the massuptake of diffusant (Mt or Ft) is approxi-mately related to D by the expression

Mt

M1¼ 4

p1=2ðD t=x2Þ1=2;

fromwhich thevalueofD canbeobtainedbymeasuring themass uptake with time (t) upto equilibrium toobtain the value ofM1 (i.e.the maximum amount absorbed by thesample).This equation is valid, however, only

forMt/M1 ratios up to 0.5, so that the valueof D can be estimated from the gradient ofthe initial part of the curve obtained from theplot of Mt/M1 against (t/x2)1/2, where x isthe thickness (see diagram). The time forMt/M1¼ 0.5 is known as the �half-time�.

Concept of �half-time� in diffusion phenomena.

A linear diffusion behaviour implies thatthe value of D does not depend on the con-centration of diffusant C0 used in the mea-surements.Thevalidityof theassumptionofFickianbehaviourofdiffusion throughpoly-mer samples can be checked by carryingout experiments with samples of differentthickness. All the data on the plot should fallon the same curve up to the �half-time�.The variation of the coefficient of diffu-

sion with temperature obeys the Arrheniusequation on account of the nature of thephenomenonas aphysical rate process. (SeeArrhenius equation and Activation energy.)

41. Dilatant Fluid

A fluid whose viscosity increases with shearrate. This is the opposite of pseudoplasticbehaviour. (See Rheology.)

42. Dilatation Coefficient

Equivalent to the volumetric expansioncoefficient.

42 Dilatation Coefficient j91

43. Dilatometer

Anapparatus used tomeasure the change inlinear dimensions of a sample resultingfroma change in temperature. (See Thermo-mechanical analysis.)

44. Dimensional Stability

A term used to describe the resistance of apolymer product to changes in dimensionas a result of the action of external environ-mental agents, such as moisture or heat.

45. Dip Coating

A technique used to produce coatings onarticles through immersion into the coatingfluid or dispersion, which can be carried outas a continuous operation.

46. Dipole

A concept used to describe the imbalance ofelectron density along a chemical bond,arising from the difference in electronega-tivity between the atoms involved in thebond considered. Dipoles can be dividedinto �permanent dipoles� and �induceddipoles�. The latter refer to the polarizationof a chemical bond arising from neighbour-ing species. Dipoles are indicated as d� ifthere is an excess of electrons on a particularatom or dþ if there is a defect of electrons.

47. Direct Current (DC)

Acurrent resulting from the application of aconstant voltage.

48. Direct Reflection Factor

Defined as the ratio of the lightflux reflectedfrom a surface to the incident light flux, it

characterizes the ability of a product toreflect light.

49. Direct Transmission Factor

Known also as the specular transmittance, itis defined as the ratio of the light fluxtransmitted to the incident light flux. Itdenotes the light transmission characteris-tics of a medium.

50. Dispersion

A term used to denote the state of distribu-tion of an additive of filler into the bulk ofthe polymer.

51. Dispersity

Normally refers to the breath of the distri-bution of themolecularweight of a polymer.

52. Dispersity Index

Also known as polydispersity, denotes theratio of the weight-average to the number-average molecular weight and provides ameasure of the spread of the distribution ofmolecular weight, based on the assumptionthat the distribution is Gaussian (i.e. statis-tically symmetrical).

53. Dispersive Mixing

A term used to describe the mixing ofadditives through a dispersive action. (SeeMixing.)

54. Distortion and Warping (Moulding)

Planar deviations of a large-area moulding(moulded part) from the geometry of themould cavity, which arise from theeffect of cooling rate on the density of a

92j 54 Distortion and Warping (Moulding)

crystalline polymer or a rigid thermosetting�compound�.A higher cooling rate produces a larger

amountof cross-links ina thermosetting resinand a lower degree of crystallinity in a crystal-linepolymer. Inboth cases, this brings about alower density of the moulded part.The diagram shows that a flat geometry is

maintained if the cooling rate at the twosurfaces, S1 and S2, is the same (left). On theother hand, if the cooling rate at surface S1 islower than that at surface S2, the mouldedpart has to bow inwards in order to accom-modate the difference in density.

Effect of differential cooling between the oppositesurfaces of a flat moulded part. Source: Mascia(1989).

Warping in moulded parts, on the otherhand, results primarily from the orientationofpolymermolecules, orfibre reinforcementinthecaseofcomposites,eventhoughthetwotypes of morphological orientation have theopposite effect. In the diagram, depicting acomparison of side-feed gates with centralfeeding, it is shown that the direction of theorientation coincides with the direction offlow of the melt while feeding the cavity.

Orientation direction of polymer molecules or re-inforcing fibres in filling a mould cavity. Source:Mascia (1989).

For the case of molecular orientation, theshrinkage that takes place during cooling ofthe moulded part is greater along the orien-tation direction (owing to molecular relaxa-tions taking place during cooling) than inthe transverse direction. For the case of adisc-shaped cavity, a side-gate melt inlet hasa main flow path along the diameter A–B ofthe disc. Owing to the differential shrinkagein the two perpendicular directions, aftercooling, the diameter A–B will be smallerthan the diameter C–D. This situation isaccommodated by an inward bowing (dis-tortion) of the moulded disc. For the case ofcentre-fed cavities, the molecular orienta-tion and the associated linear shrinkage aregreater in the radial direction than in thetransverse direction, which corresponds tothe circumferential direction. The implica-tions are that, in the absence of radial ori-entation, the geometrical relationshipC¼ 2pR (C is the circumference and R is theradius) holds both before and after cooling.When radial orientation occurs, on the oth-er hand, the extent of shrinkage in the radialdirection becomes greater than that alongthe circumferential direction. This situationresults in the relationship C> 2pR, whichcan only be accommodated if the disc as-sumes an out-of-plane hyperbolic–parabolic(figure-of-eight) �warped� geometry.The situation is completely reversed for

both types of gates if the orientation iscaused by the alignment of fibres, as in thecase of short-fibre composites with a matrixthat does not bring about molecular orien-tation (e.g. thermosetting resins) and, there-fore, is not susceptible to differentialshrinkage. This is because the shrinkagealong the fibre orientation direction is nowless than along the circumferential direc-tion. The case of glass-reinforced thermo-plastics represents an ideal solution to dis-tortions and warping problems, insofar asthe shrinkage associated with fibre orienta-tion and that resulting from molecular ori-entation tend to take place in opposite direc-

54 Distortion and Warping (Moulding) j93

tions and therefore will minimize or eveneliminate the differential shrinkage. Inpractice, the differential shrinkage iscompletely eliminated with the incorpo-ration of small quantities of mica flakeswhose plate-like geometry reduces theextent of orientation of the reinforcing fi-bres by creating greater turbulence alongthe flow direction.

55. Distribution of Molecular Weight

(See Molecular weight.)

56. Distribution of Relaxation Times

Defines the spread of relaxation times for alarge number of models acting in series,either Maxwell or standard linear solid(SLS) models, as a means of describingmore accurately the properties of polymerswith respect to their linear viscoelastic be-haviour. A single model, characterized by asingle value of the relaxation time, predicts arapid change in the relaxation moduluswhen the duration of the experiment ap-proaches the value of the relaxation time ofthe model (i.e. t¼l). Since this is not suffi-ciently close to the true behaviour of poly-mers, a large number of elements (con-nected in series), each exhibiting a differentrelaxation time, are used in the model toproduce a bland decrease in relaxationmod-ulus, which provides a more realistic de-scription of the true behaviour of polymers.Themathematical equation for the variationof the relaxation modulus with time, E(t),for an infinite number of SLSmodels actingin series becomes

EðtÞ ¼ E1 þð1�1

Hðln lÞ e�t=l dðln lÞ;

where H(lnl) is a parameter known as thedistribution of relaxation times and E1 isthe modulus at infinite time, known also asthe relaxed modulus.

57. Distribution of Retardation Times

Defines the spread of retardation times for alarge number of models acting in series,either Kelvin–Voigt or standard linear solid(SLS)models, as ameans of describingmoreaccurately the viscoelastic behaviour of poly-mersundercreepconditions.Asimplemodelcharacterized by a single value of the retarda-tion timeresults inaveryrapidincreaseinthecreep compliance when the duration of theexperiment approaches the value of the retar-dation timeof themodel (i.e. t¼l).Since thisis not sufficiently realistic, a large number ofelements (connected in series), each exhibit-ing a different retardation time, are used inthe model to obtain a more bland change inthe creep compliance in order to bring thepredictions of the model closer to the actualbehaviour of polymers. The mathematicalequation for the variation of the creep com-pliance with time, for an infinite numberof SLS models acting in series, becomes

DðtÞ ¼ D0 þð1�1

Lðln lÞ½1�e�t=l� dðln lÞ;

where L(lnl) is a parameter known as thedistribution of retardation times and D0 isthe compliance at time zero, known also asthe instantaneous compliance.

58. DMP-30

Tradename for a tertiary amine used as acuring agent for epoxy resins, that is, 2,4,6-tris(dimethylaminomethyl)phenol. The phe-nolic hydroxyl group enhances the reactivity.The corresponding DMP-30 tri-(2-ethyl)-hexoate salt has been used in resins forelectrical applications in order to improveadhesion to metal components.

59. Dog-Bone Specimen

Also known as dumb-bell, is a type of speci-men used in tensile tests. A typical example

94j 59 Dog-Bone Specimen

is shown. The waist section ensures thatfailure takes place in an area subjected touniaxial tension. When rectangular speci-mens are used in tensile tests, failure islikely to take place at the clamps, wherespurious triaxial stresses arise from thecombination of the clamping forces and theapplied tension.

Dog-bone shaped specimen for tensile tests.

60. Doping

A term used to denote the enhancement ofspecific properties by the addition of smallamounts an additive. A typical example isthe addition of very small amounts of strongacids to an intrinsically conductive polymer,such as polyaniline, to increase the electrontransfer efficiency along the conjugateddouble bonds.

61. Dough Moulding Compound (DMC)

(See Bulk moulding compound.)

62. Drag Flow

Also known as Couette flow, is a type of flowproduced between two surfaces, one ofwhich is stationary while the other is mov-ing. When the two surfaces are sufficientlyclose, the flow produces a linear velocitygradient, corresponding to a state of con-stant shear rate across the gap. This type offlow occurs very often in polymer proces-sing and melt mixing operations. For in-stance, the flow in the channels of themetering zone of an extruder takes placeby the rotation action of the screw against

the stationary wall of the barrel. (See Extru-sion theory.)

63. Drape Forming

A technique used in vacuum forming (ther-moforming) using a male mould. The arti-cle is formed by the application of vacuumto draw the sheet against the contours of themale mould after the sheet is �draped�(pushed into shape). (See Thermoforming.)

64. Draw Ratio (or Extension Ratio)

The ratio of the final length after drawing asample or product (usually in the form offilaments, tapes or films) to the originallength. In manufacturing processes, thiscorresponds to the ratio of the velocity ofthe two sets of rolls used to draw theproduct.

65. Drawdown Ratio

The ratio of the velocity of an extrudate at theexit of the tensioning rolls to the velocity ofthe melt through the die. It is normallyestimated from the ratio of the final cross-sectional area of the extrudate to the corre-sponding area at the die lips.

66. Drawdown Resonance

The formation of regular diameter fluctua-tions in an extrudate arising by the drawingof the polymer melt from the die. Thisphenomenon occurs under conditions inwhich the drawdown ratio exceeds a criticalvalue. This phenomenon occurs primarilyin the production of fibres, filaments or castfilms. (See Melt strength.)

66 Drawdown Resonance j95

Undulations in diameter of filaments or thicknessof films resulting from drawdown resonance.

67. Dry Band

A term applied to the formation of a dryzone on the surface of high-voltage insula-tors subjected to surface contaminationwith salt solutions. (See Tracking.)

68. Dry Blend

Amixture of PVCpowder (suspension type)and plasticizer, which is forced to occupythe internal pores of the PVC particlesthrough high-speed mixing operations.

69. Drying Resin

An alkyd resin containing large amounts ofan unsaturated vegetable oil. The term�drying� derives from their ability to becomeincreasingly less tacky during curing, due tocross-linking reactions within the oilcomponent.

70. Dual Sorption

Phenomenon related to the dissolution ofgases in glassy polymers, consisting of twosorption components, hence the term �dualsorption�. One corresponds to the amountof gases occupying free volumes within

polymer chains, known as the Henry solu-bility; while the other corresponds to theamount of gas residing in microcavities,known also as Langmuir absorption. Bothterms are related to pressure according tothe equation

Ct ¼ SDpþ C0Hbp

1þ bp;

where Ct is the total concentration of gas orvapour absorbed, SD is the solubility coeffi-cient, C0

H is the void absorption constant, bis the void affinity constant and p is thepressure.

71. Ductile

A term used to describe the ability of amaterial to undergo large deformationthrough yielding, known also as plastic de-formations. (See Brittle fracture.)

72. Ductile–Brittle Transition

(See Brittle point and Brittle–toughtransition.)

73. Ductile Failure

Failures occurring through yielding or plas-tic deformations. (See Load–extensioncurve.)

74. Dumb-Bell Specimen

(See Dog-bone specimen.)

75. Dye

A colouring agent that is molecularly mis-cible or dispersible on the nanometre scale,which permits the polymer to develop a

96j 75 Dye

colour without losing its transparency.(See Colorant and Colour matching.) Thechemical structure of some typical dyesused for the coloration of transparent poly-mers is shown below.

. Spirit-soluble: Salts of organic bases, forexample, Zapon Fast Scarlet GG:

. Oil-soluble: Various non-ionic aromaticcompounds containing alkyl groups toimprove compatibility, for example, OilOrange C.1.24:

76. Dynamic Mechanical Thermal Analysis(Dynamic Mechanical Analysis)

Abbreviated to DMTA or DMA, denote testscarried out under cyclic loading conditions,where the stress applied to a specimen andthe resulting strain vary in a sinusoidalmanner with time at a certain frequency.DMTA and DMA tests measure also the

phase angle resulting from the delayedresponse to the applied stress, which arisesfrom the viscoelastic behaviour of polymers.This makes it possible to calculate the com-ponents of the complexmodulusover awiderangeof frequencies and temperatures. (SeeViscoelasticity.) The plots of these para-meters against frequency or temperatureprovide fingerprints for the dynamicmechanical behaviour of polymers, knownas �mechanical spectra�. From these it ispossible to obtain valuable informationabout the chemical and morphologicalstructure.

77. Dynamic Mechanical Spectra

Plots for the variation of the loss tangent(tan d), or loss modulus (E00 or G00), withtemperature (T) and oscillation frequency(v). Typical dynamicmechanical spectra aredepicted, which show the variation of theelastic modulus (E0) and the loss modulus(E00) with angular velocity at two differenttemperatures (T2 and T1).Note that, in cyclic phenomena, the an-

gular velocity v is related to the frequency fby the expression v¼ 2pf. The glass transi-tion temperature of the polymer (Tg) isobtained from the maximum of the E00 plotagainst temperature. Often the tan d value(tan d¼E00/E0) is plotted against tempera-ture. Themaximum, in this case, occurs at a

Variation of elastic and loss moduli with angular velocity at two different temperatures (T2 > T1).

77 Dynamic Mechanical Spectra j97

slightly higher temperature. The modulusand compliance functions are obtainedthrough mathematical operations on therelationships for stress and strain, that is,the function

s ¼ s0 sinðvtþ dÞcan be expanded to

s ¼ s0 cos d sinðvtÞþs0 sin d cosðvtÞ;which means that the associated vector hasbeen decomposed into two vectors forminga phase angle of 90� with respect to eachother. Relative to the strain vector,

« ¼ «0 sinðvtÞ;the first term represents the in-phase com-ponent and the second term is the out-of-phase component. This equation can bewritten in �complex� notation, that is,

s ¼ s0 sinðvtÞþs00 cosðvtÞ;where s0 corresponds to the stress compo-nent that is in-phase with the �complex�strain,

«� ¼ «0 sinðvtÞ;ands00 corresponds to the stress componentout-of-phase with respect to the strain.

78. Dynamic (Oscillatory) Flow

A drag flow that takes place in cone-and-plate and parallel-plate rheometers operatedin an oscillatory mode. The results are ob-tained in terms of the complex viscosity h*

and the melt elasticity parameter G0. (SeeViscosity.)

79. Dynamic Vulcanization

A procedure whereby one of the compo-nents of a blend is an elastomer that isvulcanized, or partially vulcanized, duringthe mixing process, while the other compo-nent remains non-cross-linked. This proce-dure is often used for the production ofthermoplastic elastomers where the non-cross-linked component is a thermoplasticpolymer. The procedure is also used as ameans of improving the dispersion of fillersin the blend and also to restrict the locationof the filler primarily to one phase. Thephase contrast micrograph, taken on adynamic vulcanized blend of natural rubber(NR) and an ethylene–propylene copolymer(ethylene–propylene rubber, EPR) showsthat the phases are co-continuous.

Phase contrast micrograph of a dynamicallyvulcanized NR–EPR blend. Source: Tinker andJones (1998).

98j 79 Dynamic Vulcanization

E

1. Effective Modulus

The modulus value (Eeff) used for fractureanalysisunderplanestrainconditions, thatis,

Eeff ¼ E=ð1�n2Þ;where E is Young�s modulus and n isPoisson�s ratio.

2. Efficient Vulcanizing Cure (EV Cure)

An elastomer formulation containing ahigh accelerator-to-sulfur ratio in order toprovide large amounts of monosulfidecross-links. Semi-efficient vulcanizing curesystems have an accelerator-to-sulfur ratiothat is intermediate between EV cure sys-tems and ordinary sulfur cure systems.

3. Ejection Mechanism

The assembly of a mould that provides amechanism for the ejection of mouldedparts from the cavities, consisting of ejectorpins fitted onto the ejector plate. A simpleexample of the operation of ejector pins isshown in the diagram with reference tocompression moulding of thermosettingpolymers.

Pin ejection of moulded parts in transfer mouldingoperations. Source: (N. M. Bikales, Ed., Moldingof plastics: Encyclopedia reprints, 1971, Wiley -Interscience).

For the removal of a thin moulding,where there is a risk that the pins coulddamage the moulded part, ejection is car-ried outwith theuse of a �stripper plate�. Theprinciple of operation of a stripper plateejection is shown.

Stripper plate ejection mechanism. Source:(Unidentified original source).

4. Elastic Behaviour

Indicates that the Young�s modulus and theshear modulus of a material are indepen-dent of both the loading history and themagnitude of the applied load. This meansthat the load–deformation relationship (seediagram) is linear and the gradient of theplot of the two variables is invariant irre-spective of the duration of the applied load(force) or whether it acts in a static ordynamic manner.

Force–deformation diagram for an elastic material.

5. Elastic Memory

A term that is sometimes used to describethe partial recovery of the deformationimposed on a polymer melt upon removal


j99

of the stress. This manifests itself in theform of swelling when a polymer meltemerges from the die of an extruder orcapillary rheometer. (See Die swell ratio,Barus effect and Melt elasticity.)

6. Elastic Recovery

The instantaneous recovery component ofa linear viscoelasticmaterial. (SeeViscoelas-ticity and Recovery.)

7. Elasticity

A characteristic of materials denoting theability to recover an imposed deformationwhen the applied force or stress is removed.In theoretical mechanics, the term is usedalso to denote conditions in which the im-posed strains are small and the deforma-tions are directly proportional to the appliedforces. (See Elastic behaviour and Rubberelasticity.)

8. Elastomer

A semi-scientific term for rubber, that is,polymers with a glass transition tempera-ture (Tg) well below room temperature andcontaining physical or chemical cross-links.Accordingly, they are known as either ther-moplastic elastomers or vulcanized elasto-mers, depending onwhether themain com-ponent is a linear polymer with reinforcingcrystalline domains (physical cross-links) ora polymer containing a small number ofchemical cross-links.

9. Electric Strength

The value of the electric stress at whichelectrical failure occurs. (See Dielectricstrength.)

10. Electrical Failure

Failure of a dielectric or insulating compo-nent via the formation of conductive chan-nels either through the bulk or over thesurface. (See Tracking.) For polymers thatdo not carbonize as a result of thermaldegradation, failure can take place throughthe formation of holes resulting from local-ized depolymerization. A typical example ispolytetrafluoroethylene (PTFE).

11. Electrical Properties

Properties describing the behaviour of apolymer under the influence of electricalstresses. Electrical stress is defined as thevoltage gradient in the direction of the cur-rent, which is also known as the �electricfield�. (See Dielectric.)

12. Electrolytic Deposition

A method for depositing polymer coatingson highly conductive substrates fromwater-borne solutions, emulsions or dispersions.The outer surface layers of the polymerparticles contain ions. On the applicationof a voltage, those ions anchored on thesurface of the polymer particle, or attachedto the polymer molecules in solution,migrate to one electrode, transporting thepolymer, while the counter-ion migrates tothe other electrode. The surface of the poly-mer may contain either positive ions(cations), usually protonated amine types,or negative ions, normally carboxylate an-ions. Accordingly, the deposition process isknown as cationic electrolytic deposition(CED) or anionic electrolytic deposition(AED). In addition to the deposition of theions, there are also electrolytic chemicalreactions taking place at the respectiveelectrodes.

100j 12 Electrolytic Deposition

. For CED:

2H2O þ 2e� ! H2 þ 2OH� (cathodicreaction)polymer–NR2H

þ þ OH� !polymer–NR2 þ H2O

. For AED:

2H2O ! 4Hþ þ O2 þ 4e� (anodicreaction)polymer–COO� þHþ ! polymer–COOH

A schematic diagram for the cathodicelectrodeposition is shown. Note that theoxygen and hydrogen gases formed duringthe electrolysis play an important role indetermining the thickness of the final coat-ing. These gases produce a cellular struc-ture in the deposited wet polymer coating,which contributes to building up a resis-tance to the deposition of additional poly-mer through the formation of an isolatinglayer for the electrode where the polymer isdeposited.

13. Electromagnetic Radiation

Radiation that includes visible light, UVandIR, with wavelengths ranging from 200 to760 nm. The amount of energy (E) carriedby radiation is related to the frequency (n) by

Planck�s law, that is, E¼ hn, where h isPlanck�s constant.

14. Electron Beaming

A method used for hardening thermoset-ting unsaturated oligomers, such as vinylesters, and to produce cross-links in poly-meric or elastomeric products obtained byextrusion, using high-energy electrons�beamed� onto the product. Electron beam-ing is a low-temperature curing method,sometimes referred to as radiation proces-sing. The bombarding of aliphatic poly-mers, or oligomers, with highly energeticelectrons introduces very reactive free radi-cals in the molecular chains, which caninteract with similar radicals from a differ-ent chain to form new covalent bonds andultimately lead to the formation of cross-links.The presence of unsaturated groups, as

either functional groups or structural

defects (cf. linear polyethylene), reduces theenergy levels required to produce the freeradicals, while the flexibility of the polymerchains provides the favourable conditionsfor the chain-to-chain interactions requiredfor the formation of cross-links via radical

Schematic illustration of cathodic deposition.

14 Electron Beaming j101

recombination reactions. For the cross-link-ing of linear polymers, a co-agent (alsoknown as �pro-rad�), consisting of a multi-functional unsaturated monomer, such astriallyl isocyanurate, is invariably used toreduce the energy levels to promote theformation of free radicals and to speed upthe rate of cross-linking.Aromatic groups in the polymer chains,

on the other hand, have a high capacity todissipate the absorbed energy through elec-tron delocalization. At the same time, therestriction that aromatic groups impose onmolecular relaxations, owing to the rigidityof thepolymer chains, provides obstacles forinter-chain interactions and prevents theformation of cross-links. The latter appliesto all polymerswith ahighTg, even if they arecapable of producing free radicals by chainscission. Good examples are poly(methylmethacrylate) (PMMA) and polystyrene(PS). For polymers such as polypropylene(PP), despite the low Tg of the amorphousphase, the rate of chain scission reactions isalwaysmuch faster than the rate of intermo-lecular interactions, so that they ultimatelyundergo degradation reactions with deteri-oration of mechanical properties.

15. Electron Microscopy

(See Scanning electron microscopy andTransmission electron microscopy.)

16. Electron Spectroscopy for ChemicalAnalysis (ESCA)

A technique that identifies the elementspresent on the surface of a sample, exceptforHandHe.Asample is subjected tosoftX-raysunderhigh-vacuumconditions, and theemitted electrons are collected by an electro-static energy analyser and detected as afunction of the kinetic energyEK, producinga spectrum. The intensity of the peaks is

proportional to the number of atoms withinthesampledvolume, fromwhich thesurfacecomposition can be deduced.

17. Electron Spin Resonance (ESR)

A spectroscopic technique that detects thetransitions induced by electromagneticradiation between the energy levels of elec-tron spins in the presence of a static mag-netic field. The method can be used todetect species containing one or more un-paired electrons, such as the free radicalsthat are generated by the scission of poly-mer chains.

18. Electronic Conductivity

Conductivity arising through the move-ment of electrons in the direction of theapplied electrical stress.

19. Electrostatic Charge

Charges accumulated on the surface of apolymer as a result of contact with a non-conductive surface. Positive charges denotean electron donor characteristic of the sur-face, while negative charges indicates anelectron acceptor behaviour. The electrostat-ic charging characteristics of polymers arerelated to their dielectric constant. General-ly a polymer with a high dielectric constantacts as an electron donor (positive chargingbehaviour). Most thermoplastics show highcharging tendencies owing to their highsurface resistivity, which is above 1014

W/&, which prevents the acquired chargesfrom leaking to earth. On the other hand,polymer formulations containing antistaticagents, or carbon black, have negligiblecharging characteristics in view of theirrelatively low surface resistivity, which isbelow 1010 W/&.

102j 19 Electrostatic Charge

20. Electrostatic Fluidized Bed Coating

(See Powder coating and Electrostaticspraying.)

21. Electrostatic Spraying

A process by which polymer powder ischarged electrostatically in its passagethrough the nozzle of a gun and, as aconsequence, becomes attracted onto a me-tallic object connected to earth. When aspecific coating thickness has built up, theexcess powder falls off the coating throughrepulsion from the similarly charged outerparticles of the coating. This is caused by theinsulation created by the coating, whichprevents them from being discharged toearth. After this stage the coated object istransferred to an oven for curing (thermo-sets) or sintering (thermoplastics).

Schematic diagram of electrostatic spray coating.Source: Mascia (1989).

22. Ellis Equation

An equation that describes the variation ofthe viscosity (h) of a polymer melt with theimposed shear stress (t), that is,

h=h0 ¼ 1þðt=t*Þn�1;

where h0, t* and n are empirical constants.

23. Elongational Flow

Known also as extensional flow, arises as aresult of tensile stresses acting on amelt, as

in the case of fibres or films drawn from thedie by the take-off rolls. Elongational flowarises also in converging flow situationsowing to the increase in velocity of the meltas it flows towards the exit. In this case themelt undergoes both shearflow,manifestedas a velocity gradient through the cross-section of the channel, and elongationalflow, resulting from the axial velocitygradient.

24. Elongational Viscosity

Defined as the coefficient that relates anelongational (tensile) stress to the resultingelongational rate (axial velocity gradient),that is,

s ¼ hEðd«=dtÞ;where s is the elongational stress, hE is theelongational viscosity and d«/dt is the elon-gation rate.For ideal (Newtonian and incompress-

ible) liquids, the elongational viscosity isthree times greater than the shear viscosity.In polymermelts, the elongational viscosityis many times greater than the shear viscos-ity. The discrepancy diminishes with in-creasing temperature. An apparatus formeasuring the elongational viscosity ofpolymer melts is shown in the section onmelt strength. (see Melt strength.)

25. Empirical

An adjective usually used in relation to atest, methodology or property. An empiricalproperty is one that is not derived fromfundamental considerations and, therefore,it varies according to the test method orthe geometry of the specimen used in thetest. Typical empirical mechanical proper-ties are scratch resistance, hardness, impactstrength and abrasion resistance.

25 Empirical j103

26. Emulsion

A sub-micrometre suspension of monomerdroplets or polymer particles in a liquid,usually water. In the case of a monomeremulsion, the suspended droplets are stabi-lized against coalescence by the micelleformed by the surfactant, which entraps themonomer (hydrophobic component) in thecentre layers of a multitude of verticallyoriented surfactant molecules. The individ-ual particles of an emulsion are very small(about 30–100 nm) but they tend to aggre-gate into larger microscopic secondary par-ticles, which are responsible for the milkyappearance, resulting from the scattering ofthe impinging visible light. The TEM mi-crograph, showing an OsO4-stained dieneelastomer emulsion, indicates that the sizeof discrete particles is in the region of50–100 nm.

TEM micrograph of OsO4-stained particles of adiene elastomer emulsion. Source: Kampf (1986).

27. Emulsion Polymerization

A very widely used polymerization methodfor vinyl, styrene and acrylic monomers.A liquid monomer is dispersed in watercontaining amounts of surfactants in ex-cess of the critical concentration requiredto form micelles to entrap the monomermolecules. A water-soluble initiator, suchas potassium persulfate or hydrogen per-oxide, is used to initiate the polymerizationwithin the micelles. The initiator is attractedinto the micelles by the thermodynamic

drive derived from the polymerizationreaction, producing polymer particles swol-len with monomer. As monomer micellesare converted into polymer particles, newmonomermicelles are created at the expenseof monomer droplets, because the initiationand growth of polymer chains occur prefer-entially in the monomer micelles. All thecomponents present during emulsionpolymerization are shown in the diagram.

Species present during emulsion polymerization.

28. Encapsulation

Aprocess by which a component is coveredcompletely through a large inlet andentrapped by either a paste or a curingresin in a mould. The process is particular-ly used for the protection of delicate elec-tronic devices.

29. Endothermic

An adjective for chemical or physical pro-cesses that absorb heat from the surround-ing atmosphere.

30. Energy-Dispersive Scanning Analysis(EDS or EDX)

An analytical technique for detecting atomson the surface of a specimen during exam-inations by scanning electron microscopy

104j 30 Energy-Dispersive Scanning Analysis (EDS or EDX)

(SEM). (See Scanning electronmicroscopy.)Characteristic X-rays have well-definedenergies from different atoms. Thus analyt-ical information can be obtained from anX-ray spectrum.

31. Engineering Design

A methodology that seeks to determine thedimensions and to optimize the geometryof an article from fundamental principlesand/or through rational use of experimentaldata available for the candidate materials.The most widely used engineering designprinciple is the prediction of the deflectionresulting from an applied load, or thedetermination of the maximum load thata structure can support. The general designequation is

D ¼ ðP=EÞ� functionðn; geometric parametersÞ;

where D is the deflection, P is the load, E isYoung�s modulus and n is Poisson�s ratio ofthe material. For instance, the deflectionof a thin centrally loaded circular platesupported at the rim is calculated by theequation

D¼ðPr2=Ed3Þ ½3ð3þnÞð1�n2Þ=4pð1þnÞ�;where r is the radius and d is the thickness.

31.1 Estimation of Deflection

The above design equations indicate that,for elastic materials, it is necessary to knowonly two constants, E and n, to be able toperform the design calculations. The non-linear viscoelastic behaviour of polymers,coupled with their sensitivity to tempera-ture changes, means that a large amount ofdata is needed to solve the equations for thewide range of possible conditions that thedesigned article is likely to encounter inservice. While the variations of Poisson�sratio are not large enough to make a

substantial difference to the calculatedload–deflection values, this is not the casewith respect to changes in Young�s modu-lus. The nonlinear viscoelastic behaviourmakes it necessary to know the value of themodulus for the particular loading history.(See Nonlinear viscoelastic behaviour.)Particularly important is to know whetherthe product is likely to be subjected tocontinuous or intermittent loads.For the latter case it is also necessary to

know the length of the recovery periodrelative to that of the application of the load(creep period). The plot of strain versus log(total creep time) at two different stresslevels (s2 >s1) shows that the accumulatedstrain from creep periods is reduced sub-stantially if there are intermittent longrecovery periods (dashed curves). The lowerdashed curves for a given stress level indi-cate that, the longer the recovery time rela-tive to the creep time, the lower the accu-mulated strain. (See Creep curve.)

Schematic representation of the creep behaviour ofpolymers under continuous and intermittent load-ing conditions.Here, tR is the ratio of recovery time/creep time, known as the reduced time.

The availability of these creep curves at arange of temperatures of interest makes itpossible to determine the value of the creepmodulus, E, as the reciprocal of the compli-ance, which is the ratio of accumulatedstrain to applied stress. Any discrepancyarising for the calculated creep modulus atdifferent stress levels results from the non-linear viscoelastic behaviour. Reasonableestimates can be obtained for differentconditions through interpolations andextrapolation procedures.

31 Engineering Design j105

31.2 Estimation of Maximum AllowableLoad

The maximum load that a structure cantolerate is determined either by the stipula-tion of themaximumallowable deflection orby the strain level that would lead to failurethrough yield deformations or brittle frac-ture. Themaximumdeflection can be deter-mined by external factors or materials lim-itations, such as the occurrence of crazingphenomena.Inthiscase,knowingthevaluesof critical crazing strain for the particularserviceconditions, thecorrespondingvaluesfor the deflection of the article can be esti-mated and set as the maximum deflection.(See Crazing.) The load that would bringabout failure by yielding, on the other hand,can be determined from available data onstrength as a function of loading time atdifferent temperatures. (SeeCreeprupture.)

32. Engineering Polymer

A polymer that has characteristics suitablefor the production of components expectedto be subjected to high stress levels. Anengineering polymer generally has a highmodulus andhigh strength, aswell as a highresistance to wear, and is capable of tolerat-ing changes in temperature without loss ofperformance. Typical engineering polymersare polycarbonate, polyamides, acetals andaromatic polymers in general.

Examples of components made from engineeringpolymer. Source: ICI (1965).

33. Enthalpy

Theheat component (H) of the total internalenergy (E) of a system, that is,

E ¼ Hþ pV ;

where p is the pressure acting on the systemand V is the volume. Very often the changein the pV termduring a process, particularlythose involving solids or liquids, is verysmall, so that the change in internal energybecomes equal to the change in enthalpy(heat content) of the system.

34. Entropy

A theoretical concept related to the degree ofdisorder in a system. It is used in the secondlaw of thermodynamics to determine theconditions that have to be satisfied for theoccurrence of chemical and physicalphenomena, written as

DG ¼ DE�TDS;

where DG is the change in Gibbs free ener-gy, DE is the change in internal energy, T isthe absolute temperature (K) and DS is thechange in entropy;DE is equal to the changein enthalpy (DH) if the pressure is low andthere isnochange involume. (SeeEnthalpy.)Since an event will occur only if it leads to adecrease in free energy, the conditions aresatisfied if there is a decrease in enthalpy,corresponding to an exothermic process,and an increase in entropy through a higherlevel of disorder.Note that polymerization is a favourable

process despite the reduction in entropythat results from the much higher order,and lower degrees of freedom, of themonomeric units in a polymer chainrelative to the free monomer. The favour-able thermodynamic conditions, therefore,arise from the dominance of the decrease(negative change) in enthalpy due to theexothermic nature of the polymerization

106j 34 Entropy

reactions. The melting of polymer crystals,on the other hand, is favoured by the largeincrease in entropy resulting from the highdisorder acquired by the polymer chains inits liquid (melt) state, despite the endother-mic nature of the melting process, whichrequires heat (an increase in enthalpy) toovercome the intermolecular forces holdingthe chains within the lamella of the crystals.In thermodynamics terms, therefore, melt-ing takes place because the term TDS islarger than DH. Note, in any case, that�entropy� is a purely theoretical parameterand cannot be measured experimentally.

35. Entry Effect

An expression used to describe the pressuredrop occurring in theflow of a polymermeltat the entry of a die. Thismay be the cause oferrors in the calculation of the shear stressesat the walls of a die. For this reason, aspecific procedure has to be used to esti-mate the pressure drop resulting from�entry effects�. (See Bagley correction.)

36. Environmental Ageing

A term that refers to the deterioration ofthe properties of a product resulting fromthe action of environmental agents, such astemperature, oxygen, UV radiation, mois-ture and pollutants in the atmosphere.Polyolefins and diene elastomers are par-ticularly prone to degradation reactionscaused by the combined action of oxygenand UV light. Condensation polymers,such as polyesters, polyamides and polyur-ethanes, are also prone to degradationreactions caused by hydrolysis, which isaccelerated by acidic or basic environ-ments. Two brief schemes of degradationreactions induced by environmental ageingare shown.

Cross-linking and chain scission resulting from UVdegradation of vinyl polymers.

Oxygen-assisted UV degradation of polystyrene.

37. Environmental Stress Cracking

A phenomenon related to fracture inducedby environmental agents, which is entirelydue to physical factors. The term was origi-nally used to describe the fracture of poly-ethylene bottles induced by detergents. It isnow more generally used to denote theadverse effect of some environmentalagents on the fracture toughness of poly-mers. The standard test, known also as theBell test, was originally devised specificallyto assess the environmental stress crackingresistance (ESCR) of low-density polyethyl-ene. ESCR is an empirical test that can give

37 Environmental Stress Cracking j107

misleading results, particularly when usedto test themore rigid grades of polyethylene.In the latter cases, the bending of the speci-mens into an arch produces very largestrains in the outer layers, which can easilyexceed the levels that bring about �yielding�(left-hand diagram). This will reduce theelastic (stored) energy in the notched regionof the specimen. Another oddity of the Belltest in terms of fundamental principles isthe insertion of a central cut (notch) alongthe bending direction, which creates a verycomplex state of stresses that cannot berationalized in a manner that would allowfor variations in the geometry of the speci-men. A more rational approach has beenused in devising a test at low strains withnotches across the width of the specimen,which can be carried out with a simple jig(right-hand diagram).

Typical methods for measuring ESCR: (left) high-strain standard test; (right) low-strain test for rigidpolymers.

Fundamentally, ESCR has to be evaluatedin terms of the decrease in the value offracture toughness parameters of a polymer,Kc orGc, brought about by a particular envi-ronment. (See Fracture mechanics.) Forglassy linear polymers, stress cracking isaggravated by the presence of solvents in theatmosphere, which can bring about a reduc-tion in the strain required to induce crazingand also accelerate the conversion of crazesinto cracks. (See Crazing.) For glassy cross-linked polymers, solvents can also have a

detrimental effect on the fracture resistance,even though the phenomenonwillmanifestitselfwithout the visible formationof crazes.Environmental stress cracking phenomenaobserved in glassy polymers may also beconnected to localized antiplasticization ef-fects caused by the solvent, which may beconsidered as the underlying cause of thedecrease in the critical strain for crazing, orthe general reduction in fracture toughnessdue to localized restrictions on molecularrelaxations at the crack tip.

38. Epichlorohydrin Rubber(Epichlorohydrin–Ethylene OxideCopolymer, ECO)

Consists essentially of epichlorohydrinand ethylene oxide copolymers, having therepeating units:

Cross-linkingis inducedviareactionswithsome of the pendent�CH2Cl groups, usingthiourea andmixtures withmetal oxide acidacceptors, such as MgO and Pb3O4. Someterpolymers (epichlorohydrin–ethylene oxi-de–diene terpolymer, ETER) containingsmall amounts of diene units are also avail-able, which can be vulcanized with sulfur-basedcurativesandperoxides.Thepolyetherconstituentunits confer ahighpolarity to thepolymer chains,which provides a high resis-tance to oils. The randomdistribution of thecomponents prevents the formation of crys-talline structure, either thermally or stress-induced. TheTg value is in the region of�30to�40 �C, depending on the ratio of the twomain structural components.

39. Epikote

Tradename for a variety of epoxy resins,known also as Epon.

108j 39 Epikote

40. Epoxidation

A chemical reaction that introduces epoxygroups into a polymer or oligomer. Anexample of epoxidation is the conversion ofunsaturated groups in a diene elastomer toepoxy groups through controlled oxidationreactions.

41. Epoxide

An synonym for epoxy resins.

42. Epoxidized Soya Bean Oil

An epoxidized oil used as a reactive internalplasticizer for epoxy resin formulations andas a co-stabilizer for PVC.

43. Epoxy Equivalent (or EpoxideEquivalent)

The weight of resin in grams that containsone gram equivalent (mole) of epoxygroups. For an unbranched epoxy resin, thiscorresponds to half the number-averagemolecular weight.

44. Epoxy Group

Also known as an oxirane ring, correspondsto a strained ether ring between either twoadjacent CH groups or consecutive CH andCH2 groups. (See Epoxy resin.)

45. Epoxy Resin

A thermosetting resin containing two ormore epoxy groups, respectively referred toas bifunctional or multifunctional epoxy re-sins.Monofunctional epoxy compounds arealso available but are used only as reactive

diluents for conventional epoxy resins inorder to reduce the cross-linking density ofthe cured products. This has the effect ofreducing the glass transition temperature(Tg), which also results in an increase in theductility of thefinalproduct.A typicalmono-functional epoxy diluent (PGE) is shown.

Phenyl glycidyl ether (PGE).

The most common type of epoxy resin isthe diglycidyl ether of bisphenol A (DGE-BA), represented by:

where thevalueofn varies fromabout 0.2 forliquid resins to values between 5 and about20 for solid resins. Better thermal oxidativestability can be achieved by replacing thepropylidene group, CH3�C�CH3, of thebisphenol A unit with the CF3�C�CF3group contained in bisphenol F.Among the multifunctional resins, the

most widely known are the epoxidized no-volacs and tetraglycidoxylmethylene p,p0-diphenylene diamine (TGDM), which areboth shown.

Structure a typical epoxidized novolac resin.

Structure of TGDM.

Multifunctional epoxyresinsgiveahighercross-linking density than conventional

45 Epoxy Resin j109

bifunctional resins. The use of an aromatichardeneras acuringagentproducesnetworkswith a high glass transition temperature.Other types of epoxy resins are the ali-

phatic and cycloaliphatic resins. Thesestructures give cured products with rubberyor high flexibility characteristics. The struc-tures of one typical aliphatic and two typicalcycloaliphatic epoxy resins are shown.

Typical aliphatic epoxy resin produced from poly(propylene glycol).

Typical cycloaliphatic epoxy resin: vinyl cyclohex-3-ene.

Typical cycloaliphatic epoxy resin: 3,4-epoxycyclo-hexylmethyl-3,4- epoxycyclohexane carboxylate.

These cycloaliphatic resins are widelyused for high-voltage electrical applicationsowing to their high tracking resistance incomparison to aromatic-type resins. Theabsence of aromatic rings reduces the pos-sibility of forming polynuclear graphiticstructures, which are responsible forthe formation of conductive �tracks�. (SeeTracking.)

45.1 Hardener for Epoxy Resin

The main types of hardener can bedivided into anhydrides and multifunc-tional amines. Other hardeners are usedfor very specific reasons.

45.2 Anhydride

These hardeners exert a �curing� functionby reacting with epoxy resins first throughring opening of the epoxy groups either viathe reaction of carboxylic acid groups (pres-ent as impurities) and/or via the reactionwith carboxylate ions (formed by the inter-action of the anhydride with a tertiaryamine used as catalyst). The opening of theepoxy ring is followed by esterification re-actions between the anhydride groups andthe newly formed hydroxyl groups, which isalso catalysed by the tertiary amine catalyst(see diagram).

Reaction scheme for the ring opening of the anhy-dride groups by tertiary amines and subsequentreaction with epoxy groups.

The most widely used anhydride hard-eners are shown. Note that aromaticanhydrides are not normally used as solehardeners owing to their low reactivity withthe resin.

Typical anhydride curing agents: (left) tetrahy-drophthalic anhydride; (right) methylnadicanhydride.

110j 45 Epoxy Resin

Dodecylsuccinic anhydride (DDSA) issometimes used when a higher flexibility isrequired. This results from the internal plas-ticizationeffectcausedbythedodecylgroups.

Dodecylsuccinic anhydride.

45.3 Amine Hardener

These hardeners react directly with the ep-oxy groups but do not react with the hydrox-yl groups. So while amines react muchfaster than anhydrides, the resultingcross-linking density is lower. The reactionscheme of primary and secondary amineswith epoxy groups is shown.

Reaction scheme for the curing of epoxy resins withamine hardeners.

45.4 Aliphatic Amine Hardener

Themore common types are diethylenetria-mine(DETA),H2N–CH2CH2–NH–CH2CH2–

NH2, and triethylenetetramine (TETA),H2N–CH2CH2–NH–CH2CH2–NH–CH2–NH2,used primarily for cold-curing adhesives.Another type that could enter this classifica-tion is dicyanodiamide (DICY), which existsin three tautomeric forms, as shown.

DICY is used in quantities much smallerthan the amounts expected from cross-link-ing reactions alone, which suggests that thereactions take place primarily throughhomopolymerization, involving ring open-ing of the epoxy groups to produce longsequences of linear polyethers, also knownas phenoxy structures.

45.5 Cycloaliphatic Amine Hardener

These are very reactive and therefore aresuitable for cold-curing systems. The cyclicstructure confers a higher rigidity to thenetwork than linear aliphatic hardeners,thereby imparting a higher Tg value for thecured products than those obtained withthe use of DETA or TETA. A widely usedcycloaliphatic amine hardener is 4,40-meth-ylene-bis-cyclohexanamine (PACM), whosestructure is shown.

Structure of PACM.

45.6 Aromatic Amine

These are used to obtain cured productswith high Tg values, resulting from therigidity of the aromatic rings in the network.These are slow curing systems and there-fore require high-temperature conditionsfor the curing reactions to go to completion.Typical aromatic amine hardeners arem-phenylenediamine (MPD) and 4,40-dia-minodiphenylsulfone (DDS). The struc-tures of these hardeners are shown.

Tautomeric forms of DICY.

45 Epoxy Resin j111

Note that MPD is often used in the formof eutectic mixtures in order to reduce themelting point so that it can be more easilyhandled in manufacturing. DDS, on theother hand, is widely used for curing mul-tifunctional epoxy resins in matrices forcarbon fibre composites for aerospace ap-plications, owing to the very high Tg valuesachievable as a result of the chain stiffeningeffect of the �SO2� groups.

45.7 Ketimine

Chemically, ketimines can be regarded as�blocked� amines. Since the C¼N bond isreadily hydrolysed to the original ketoneand amine, they can be regarded as �latent�curing agents. These are useful for one-potresin systems in view of the long pot lifeachievable, resulting from the delay of thecuring reactions, which can only take placeafter the hydrolysis step required to gener-ate the amine. A typical ketimine, as a�blocked amine hardener, is shown.

45.8 Polyamide Hardener

These are amines based on polyamides,produced from the reaction of dimerizedor trimerized fatty acids from vegetable oilswith polyamines. For the example shown,the reaction takes place by a Diels–Aldermechanism between 9,12- and 9,11-linoleicacids.

Typical amine-functionalized polyamide.

Although they can act as curing agents intheir own right, polyamide hardeners are tobe regarded primarily asflexibilizers for usein mixtures with other amine hardeners.

45.9 Catalytic Curing Agent

These consist of Lewis bases andLewis acids.Lewis base curatives for epoxy resins includetertiary amines, such as o-(dimethylamino-methyl)phenol and tris-(dimethylamino-methyl)phenol and its salt, as well as imidaz-ole compounds. Although these are referredto as �catalysts�, they are true hardeners inso-farastheyreactwiththeresinandremainpartof the structure of the cured products. Thereaction mechanism for the curing of epoxyresins with Lewis bases is illustrated.

Mechanism of curing reactions with imidazoles.

112j 45 Epoxy Resin

Lewis acid catalysts function as curingagents by forming coordinated structureswith the oxygen atom in the epoxy group,which facilitates the transfer of a protonfor the opening of the epoxy ring. Thesecuratives are usually complexes of borontrifluoride with amines, such as mono-methylamines. Owing to their extremelyhigh reactivity, they are often used to speedup the curing rate in conjunction with an-hydride hardeners.

45.10 Polysulfide

These are end-terminated thiol oligomersused particularly as flexibilizing curingagents. A typical polysulfide curing agentis shown. Curing takes place through theepoxy ring opening reaction by mercaptan�SHgroups on the end of chains, as shown.

Typical polysulfide, where n¼ 2–26.

Curing by a mercaptan group.

45.11 Reactive Toughening Modifier

These are low-molecular-weight polymerswith terminal functionalities consisting of�COOHor�NH2 groups, often referred toas �liquid rubbers� to indicate that they are inthe liquid state, which makes them easy todissolve in an epoxy resin. The most widelyused systems are random copolymers ofbutadiene and acrylonitrile, with molecularweight in the region of 2000–10 000, knownas carboxyl-terminated butadiene–acryloni-trile oligomer (CTBN) for carboxylic acidfunctionalized systems and as amine-termi-nated butadiene–acrylonitrile oligomer(ATBN) for systems with amine functional-ity. The acrylonitrile content is in the regionof 25–40% for both systems. The procedure

that has to be used to induce the precipita-tion of rubbery particles during curing is toreact the functionalized modifier with alarge excess of epoxy resin in the presenceof a selective catalyst, such as triphenylpho-sphine (TPP), before the hardener is addedfor the subsequent curing stage. This reac-tion produces telechelic extension to themolecular chains of the modifier, as shownin the scheme.

Reaction scheme for the telechelic extension of aliquid elastomer modifier. Source: Riew (1989).

Many other systems have been studied.The most interesting among these are thetelechelic extended polydimethylsiloxanesandperfluoroetheroligomers,owingtotheirvery thigh thermal and UV stability, whichwould overcome the deficiency of diene-based liquid rubbers. These ABA-type oligo-mers are very immiscible and thereforehaveto be telechelically extended by reactionwithfunctionalized miscible segments in orderto acquire the necessary �compatibility�,evidenced by the formation of a transparentepoxyresinmixturepriortocuring.Sincethecentral segments of theses ABA oligomersare not molecularly miscible with the epoxyresin, theyprovideready-madenuclei for theprecipitation of the rubbery particles, whichcan take place at much lower levels of addi-tion than forCTBNorATBNsystems.Thesesystems,however, arenot available commer-cially. The multicomponent morphologicalstructure observed in precipitated rubberyparticles in aDGEBAresin containing about4–5% of a hydroxyl-terminated perfluor-oether, cured with methylnadic anhydride(MNA) is shown.

45 Epoxy Resin j113

Structure of �soft� particles derived from a teleche-lically extended perfluoroether oligomer in an epoxymatrix. Source: Zitouni (1994).

Note that the morphology of the precipi-tated particles of these telechelic perfluor-oether systems resembles the structureobtained through phase inversion of acry-lonitrile–butadiene–styrene (ABS) andhigh-impact polystyrene (HIPS) polymersproduced from mass polymerization, exhi-biting also the characteristic broad distribu-tion of particle size. (See Phase inversion.)

45.12 Epoxy–Silica Hybrid

These are epoxy resins containing finethree-dimensional domains of organo-modified silica produced in situ via thesol–gel process. These can be produced byfunctionalizing the epoxy resinwith a trialk-oxysilane to about the 10% level, as shown,and then mixing with a siloxane precursor,containing tetraethoxysilane (TEOS).

Small amounts of water and g-glycidox-ylpropyltrimethoxysilane are added to theTEOS precursor, respectively, to inducehydrolysis of the ethoxysilane groups and

to compatibilize the organic and inorganicdomains. The latter is assisted by the use ofa rapidly reacting amine hardener, such asPACM, for the curing of the epoxy resindomains. (See Organic–inorganic hybrid.)

46. Ester–Amide Polymer

Aclass of biodegradable polymers producedfrom condensation reactions of 1,4-butane-diol, adipic acid and hexamethylenedia-mine, with varying ester/amide ratios.These have a melting point in the range of120–180 �C and a Tg varying from �40 to�5 �C. Accordingly, the mechanical proper-ties are related to the degree of crystallinity,which is determined by the ester/amideratio. In general, they are quite flexible,intermediate between low-density polyeth-ylene (LDPE) and medium-density polyeth-ylene (MDPE).

47. Esterification

Reaction resulting in the formation ofesters, usually from reaction between acarboxylic acid, a glycol and a hydroxyl-containing oligomer.

48. Ethenoid Polymer

Polymers derived from alkylene mono-mers, such as ethylene, propylene, butylene

and isobutylene. These polymers are alsoknown as polyolefins. Their main feature isthe hydrocarbon nature of the polymerchains, which confers to them a highly

Reaction of an amine bis(propyltrimethoxysilane) with an epoxy resin.

114j 48 Ethenoid Polymer

non-polar nature due to the total absence ofdipoles.

49. Ethylene Polymer

Polymers with ethylene units as the maincomponents of the polymer chains. Theyare either homopolymers or copolymers ofethylene and small amounts of a higherolefin (butene, hexene or dodecene), whichproduce short branches along the backbonechains. These branches are introduced as ameans of controlling the density throughvariations in the degree of crystallinity. Ac-cordingly, these polymers are divided intolow-density polyethylene (LDPE), knownalso as high-pressure polyethylene (HP-PE),very low-density linear polyethylene(VLLDPE), linear low-density polyethylene(LLDPE), medium-density polyethylene(MDPE), high-density polyethylene (HDPE)and ultra-high-molecular-weight polyethyl-ene (UHMWPE). Thefirst polyethylene thatwasmade available commercially was LDPEproduced by a high-pressure method, con-taining irregular long branches attached onthe main chains. The LLDPE, MDPE andHDPE types are produced by Ziegler–Nattaor �metallocene� polymerization methods.HDPE can also be produced by the Phillipsprocess. The typical characteristics of poly-ethylenes are summarized in the table.

Polyethylenetype

Averagedensity(g/cm3)

Degree ofcrystallinity

(%)

Meltingpoint(�C)

LDPE 0.925 >30 110VLLDPE 0.915 >30 115LLDPE 0.925 30–45 125MDPE 0.9330 45–55 128HDPE 0.945 55–70 138UHMWPE 0.940 55–65 137

Note that, while the melting point variesconsiderably with the degree of crystallinity

for the various types of polyethylene, the Tgvalue remains fairly constant at around�100 �C. The increase in density, resultingfrom the higher degree of crystallinity, alsobrings about an increase in modulus (rigid-ity) and yield strength, as well as in increasein opacity of the products. Thewide range oftypes of polyethylene available commercial-ly is complemented by an even wider rangeof different grades varying in molecularweight and molecular-weight distribution.The number-average molecular weight canvary by a factor of 100 across the wholerange, from as low as 30 000 for someeasy-flow injection moulding grades to3 000 000. The different grades are identi-fied by the density (degree of crystallinity),melt flow index (MFI, an empirical param-eter related to the averagemolecularweight)and sometimes also melt flow ratio (i.e. theratio of two MFI values obtained with loadsof 5.00 and 2.16 kg, respectively). The meltflow ratio is related to the molecular-weightdistribution. (See Melt flow index.)The increase in density, from LDPE to

HDPE, brings about large changes in prop-erties such as modulus, strength, solventresistance and barrier properties. Increas-ing molecular weight results in improve-ments in environmental stress crackingresistance and toughness at low tempera-tures. One of the attractive properties ofUHMWPE, for instance, is the extremelyhigh toughness at cryogenic temperatures(the highest of all knownmaterials), and thegenerally high wear resistance at tempera-tures up to about 60–70 �C, owing to acombination of low coefficient of frictionand toughness. The grades with the highestmolecular weight, that is, above 1 000 000,cannot be processed by the conventionalmethods used for thermoplastics in view ofthe very high melt viscosity.One notable difference between the orig-

inal LDPE and the relatively new LLDPE iswith respect to the rheological properties,which require some adjustments in the

49 Ethylene Polymer j115

processing conditions and equipment fea-tures in switching from one type to another.LLDPEhasaviscositywitha lowershear-ratesensitivity than LDPE (higher power-lawindex). On the other hand, the elongationalviscosity of LLPE increases to a lesser extentwith increasing extension ratio than LDPE.Both aspects are relevant for the productionof films, where both types of polyethyleneare extensively used. Frequently, differentgrades of polyethylene, particularly LDPEand LLDPE, are blended to tailor the prop-erties to specific end-use (e.g. better tearstrength) or process requirements (e.g.improved melt drawdown characteristics).All types and grades of polyethylene arecharacterized by excellent dielectric proper-ties, due to the complete absence of polargroups or polarizable structural features.The additives used in grades for cable appli-cations have to be carefully chosen to avoiddeterioration in dielectric losses even whenused at very low levels of addition. Further-more, the lackofpolargroups in thepolymerchains confers an extremely high resistanceto water absorption for all grades of polyeth-ylene, along with other polyolefins.

49.1 Ethylene–Carbon MonoxideCopolymer (ECO)

These usually contain less than 5% CO.They have been produced for applicationsrequiring rapid degradation reactions whenexposed to UV radiation. These can beutilized for the production of biodegradablepackaging films. (See Biopolymers.)

49.2 Ethylene–Vinyl Alcohol Copolymer(EVOH)

These copolymers are obtained by thehydrolysis of ethylene–vinyl acetate (EVA)copolymers.Widely used in packagingfilmsas a barrier layer and/or as binding layerfor sandwich constructions of polar andnon-polar polymers, such as polyethylene

and a polyamide. The ethylene content ofcommercial EVOH polymers is usuallywithin the range 30–50 mol%. The meltingpoint decreases with increasing ethylenecontent within the region of about165–185 �C.

49.3 Ethylene–Ethyl Acrylate Copolymer(EEA)

Similar characteristics to EVA but with bet-ter thermal oxidative stability. (See latersubsection in this entry on ethylene–vinylacetate copolymers.)

49.4 Ethylene–Ethyl Acrylate TerpolymerElastomer (EAM)

Copolymers of ethylene containing largequantities of an acrylate comonomer anda small amount of an acidic monomer, suchas acrylic acid, as a means of introducingreactive sites for cross-linking with the ad-dition of a diamine. (See Ionomer.)

49.5 Ethylene–Methyl MethacrylateCopolymer (EMA)

Very stable copolymer widely used to pro-duce master batches and for coatings byextrusion due to its capability of resistingvery high processing temperatures.

49.6 Ethylene–Propylene Rubber (EPR)

Random copolymers with very low level ofcrystallinity and rubber-like characteristics.The chemical structure is shown, where themolar ratio of ethylene to propylene isaround 1–1.5 : 1.

Chemical structure of an EPR rubber.

The absence of unsaturated groups in themolecular chains prevents EPR from being

116j 49 Ethylene Polymer

cross-linked by conventional sulfur vulcani-zation methods, requiring the use of perox-ide curative systems. Cross-linking takesplace via the formation of free radicalsresulting from abstraction of the hydrogenatom of the tert CH group.

49.7 Ethylene–Propylene–Diene MonomerRubber (EPDM)

Produced from a terpolymer consisting pri-marily of ethylene and propylene units withminor amounts of a diene monomer tointroduce unsaturation in the chains, sothat it can be vulcanized by conventionalsulfur-based rubber curatives as well as byperoxide initiators. The diene monomer isusually either hexane-1,4-diene (type I),dicyclopentadiene (type II) or 4-ethylidene-norbornene (type III). The schematic chem-ical structure of these diene monomericunits in an EPDM chain is shown.

Various types of unsaturated groups along EPDMchains for cross-links by a free radical mechanism.

49.8 Ethylene–Vinyl Acetate Copolymer(EVA)

Random copolymers containing 10–30%vinyl acetate (VA) units along with the pre-dominant ethylene units. Designed toreduce the level of crystallinity and toincrease the polarity in the polymer chains,thereby producing a more rubbery materialwith a lower melting point, as well as ex-hibiting a higher resistance to hydrocarbonsolvents. At the upper end of the range ofVA

content, these copolymers are very rubbery,comparable to plasticized PVC.Grades withhigher levels of VA are also available and areused primarily as adhesives and coatings,due to the higher affinity for polar sub-strates, through hydrogen-bonding interac-tions, making them particularly suitable forthe production of hot-melt adhesives. Theycan also be readily cross-linked with perox-ides and high-energy radiation, makingthem suitable for low-voltage cable insula-tion. Copolymers with very high VA con-tents, up to about 90%, are used for themanufacture of emulsion paints and softadhesives. (See Vinyl polymer.)

50. Excited-State Quencher

An additive that interacts with photo-excitedpolymermolecules and brings them back totheir ground state by dissipating theacquired energy through harmless infraredradiation. These are typically nickel com-plexes, normally used as co-stabilizers forUV protection. (See UV stabilizer.)

51. Exfoliated Nanocomposite

Composites formed when the silicate nano-layers of a clay are individually dispersedwithin a polymer or resin matrix throughtwo consecutive processes, known as inter-calation and exfoliation. The originallayered silica clay contains aggregates ofprimary layers, also known as tactoids. Thelayer thickness is around 1 nm, while thelateral dimensions of the platelets can varyfrom a 30nm to several micrometres. Thetactoids are characterized by moderate sur-face charges, known as the cation exchangecapacity (CEC) expressed as mequiv/100 g(mmol/100 g). The structure of a typicalinterlayered nanoclay is shown.

51 Exfoliated Nanocomposite j117

A cationic surfactant is used to exchangethe alkali or alkaline-earth cations on thesurface of individual silicate layers withquaternary ammonium cations of the sur-factant, which provides the driving force forthe intercalation of the silicate layers withthe long aliphatic chains of the ammoniumcation. After mixing with a resin or a poly-mer, the intercalated layers are separatedand become dispersed in the matrix toproduce a nanocomposite. The varioussteps and structures of the nanofiller areillustrated in the diagram.

Themicrographs show an example of themorphology of exfoliated nanoclays in apolymer matrix nanocomposite.

Bright-field TEM micrographs of 6wt% Cloisite15A* dispersed in polyamide 6 by intermeshingtwin -screw extrusion [*montmorillonite intercalat-edwith dimethyl-dihydrogenated tallow–quaternaryammonium cations (125mequiv/100 g clay),Southern Clay Product]. Source: Courtesy ofD. Acierno, University of Naples, Italy.

52. Exothermic

An adjective for a chemical or physicalprocess that gives out heat to the surround-ings, as a result of the temperature risecaused by events of the process.

53. Expanded Polystyrene

Foams usually produced from physicallyblown polystyrene beads.

54. Extender

A liquid containing both aliphatic and aro-matic components, often referred to as �oil�,used in rubbers to improve the processingcharacteristics, as well as the dispersion ofadditives and reinforcing filler. At the sametime, an extender acts also as a plasticizerand/ordiluent insofaras itdecreasesboththeTg and the modulus of the cured elastomer.

55. Extension Ratio

Known also as the draw ratio, correspondsto the ratio of the final length of a specimendivided by the initial length, after beingstretched. (See Draw ratio.)

118j 55 Extension Ratio

56. Extensional Flow

Also known as elongational flow, representsthe flow arising from the action of tensilestresses. It can take place as a unidirectionalor planar flow depending on whether thetensile stresses are monoaxial or biaxial.(See Elongational flow.)

57. Extensional Viscosity

(See Elongational viscosity.)

58. Extensometer

A device that it is attached to a tensilespecimen to record the localized extensionduring a tensile test.

59. External Lubricant

Additive used to reduce the friction and ad-hesion of a polymer melt with the surface ofthe processing equipment. (See Lubricant.)

60. External Plasticization

The lowering of the glass transition temper-ature of a glassy polymer by the addition of aplasticizer. (See Plasticization and Internalplasticization.)

61. Extinction Coefficient

The constant, «, in the Beer–Lambert law,which relates the intensity of absorbed light(I) to the concentration of absorbing species(c), that is,

logðI=I0Þ ¼ «Zc;

where I0 is the intensity of the incident lightand Z is the thickness of the mediumreceiving the light.

62. Extinction Index

A coefficient, n00, related to the light trans-mission characteristics of a polymer via theequation

I=I0 ¼ expð�4pn00Z=lÞ;

where I is the intensity of the transmittedlight, I0 is the intensity of the incident light,Z is the sample thickness and l is thewavelength. The extinction index n00 corre-sponds to the imaginary component of therefractive index n� (n� ¼ n0 � in00), where i isthe complex number (


).

63. Extrudate

The product that emerges from the die of anextruder.

64. Extruder

Known also as single-screw extruder, is theequipment used to extrude a polymer meltthrough a die. It consists of an Archime-dean screw rotating inside a heated barrel,performing the following operations: (a) �feeds�the cold polymer granules or powder arriv-ing from the hopper, (b) �melts� the solidpolymer, and (c) �delivers� it to the die, aswell as acting as a pump to force the meltthrough the die, where it acquires the shapeof the extruded product.

Example of a single-screw extruder. Source: Uni-dentified original source.

64 Extruder j119

65. Extruder Screw

The screw of a single-screw extruderconsists of three zones, respectively, the�feed zone� (near the feeding hopper), the�compression or transition zone� (centralsection) and the �metering zone� (near thedie). There is also a reliance on themeteringzone to stabilize the flow stream arrivingfrom the transition zone and to enhance themixing of additives and fillers. This is par-ticularly important for operations whereadditives are incorporated directly into thepolymer without passing themixes througha preceding compounding operation. Spe-cial mixing devices (see diagram) are at-tached to the end of the screw or within themetering zone for this purpose.

Mixing devices attached to screws of extruders.Source: Unidentified original source.

Some extruders operate with screws char-acterized by a sudden compression, as inthe case of nylon screws, which have a longfeed zone, a very short transition zone (overhalf a turn of the screw) and a relativelyshort metering zone. (See Nylon screw.) Insome other extruders the sudden transitiontakes place after a relatively short feedsection where the barrel contains circum-ferential grooves to induce rapid melting ofthe granules through frictional forces (seediagram). This is followed by a long meter-

ing zone, which is particularly advanta-geous for the production of thermoplasticfoams using chemical blowing agents. Sucha system allows the pressure to build up veryrapidly so that, if the blowing agent starts todecompose the gases formed are dissolvedinto the polymer melt rather than escapingthough the spaces between granules andthen through the hopper.

Grooved barrel extruder. Source: Scholtz (2009).

Another variant of screws for polymerextrusion is the type used for rubbers. Thefeedstock can be in the form of a striparriving directly from a two-roll mill in linewith an internal mixer. Alternatively, themass of rubber compound can be force- fedinto the extruderby a reciprocatinghydraulicram.

66. Extrusion

A continuous process that produces articlesof unlimited length and with a constantcross-section, for example, pipes, sheetsand profiles. The most common type ofextruders for polymer extrusion is the singlescrew type. (See Extruder.) The layout of atypical extrusion line for the production ofsheets is shown, as an example.

Sheet extrusion line using a unit with three coolingrolls. Source: Rosato (1998).

120j 66 Extrusion

67. Extrusion Die

The shaping component of an extruderfitted to the exit end of the barrel. Sketchesof typical dies used for polymer extrusionare shown.In dies used for tubular extrusions, there

is an air inlet in the centre of the die toprevent collapse of the walls of the tubularmelt as it emerges from the die. This featureis not required for systems fitted with avacuum sizing die.

Die used for tubing and pipe extrusion. Source:McCrum et al. (1988).

Die used for the production of tubular films. Source:Unidentified original source.

The problemarising from the difficulty ofobtaining a uniform flow rate along thecircumference of the die has been overcomeby means of spiralling channels before themelt reaches the annular die lips at the exit.The rotation of themelt before reaching the

die exit also has the function of destroyingthe weld lines formed by the flow streamafter leaving the spider legs section, whichis used to fit the central mandrel to the bodyof the die.

Principle of flow through spiral mandrel dies.

The die for wire coating is also known as apressure wire die, which indicates that themelt is forced on the wire surface by thepressure inside the die. Vacuum is applied atthewireentry to removeanyair that becomesentrapped at the interface with the wire. Fordies where the melt tubing is impinged onthe wire at the exit of the die, the applicationof vacuum also assists the drawing of themelt against the surface of the wire.

Die used for wire coating. Source: Baird and Collias(1998).

A cross-section of a typical sheet die, fea-turing a flexible lip adjustment, is shown(where b is a transverse channel for flowequalization). The overall thickness of theextruded sheet can be adjusted by closing oropening the die gap by a push–pull actionimposed on the die lips by a series of bolts.The flow rate through the restriction sectioniscontrolledbythechoke-barinthesameway.

67 Extrusion Die j121

Diewith flexible lips for sheet and flat film extrusion.Source: Unidentified original source.

The features for the lateral spreading of aflow of melt delivered by the screw of anextruder to a die via a fish-tail-shaped chan-nel (indicators 3 and 4 in diagram) carryingthe melt to the die lips is shown. A largertrough parallel to the die lips (indicator 2 inthe diagram) is often provided to accommo-date a flexible choke-bar, which is used as ameans of controlling the flow rate in zonesacross the width. This is to ensure that themelt at the die lip is subjected to a constantpressure across the width so that the thick-ness of the sheet at the die exit is uniform.Themain equalization of pressure along thewidth of the die, however, has to be achievedby an appropriate design of the angle of themanifold channel feeding themelt to thedielips.

Sketch of spreading flow in sheet dies via a fish-tail-shaped channel. Source: Michaeli (1992).

Both tubular dies and sheet dies can beused to produce multilayer films using dif-ferent polymers delivered to a common diefromseparate extruders. (SeeCo-extrusion.)

68. Extrusion Theory

Refers to the analysis of the feeding, melt-ing and pumping action of the screw indelivering the melt to the die entry of anextruder.

68.1 Analysis of Events in the Feed Zone

The theoretical analysis of the feed zone of asingle-screw extruder assumes that thegranules or powder particles are compactedtogether within one or two turns of thescrew flights to form a solid plug that slidesforward by virtue of the difference in fric-tion forces between the root surface of thescrew and the inner surface of the barrel.From an analysis of the forces developed,the average velocity of the plug (Vz) is relat-ed to the velocity of the screw surface (Vb) bythe expression

Vz ¼ Vb tan u=ðtan bþ tan uÞ;where u is the helix angle of the screwchannel and b is an angle defining the axialmovement of the plug along the channel interms of changes in position of the plug as itmoves forwards.The volumetric conveying rate of the feed

section of the screw (G) is calculated bymultiplying the velocity Vz of the plug bythe cross-sectional area of the channel, fromwhich an expression for the solid conveyingrate (Gs) can be obtained, for example,

Gs ¼ rsp2NHfD0ðD0�Hf Þtan u tan b=

ðtan uþ tan bÞ;where rs is the density of the solid plug,N isthe screw rotation frequency, Hf is thechannel depth andD0 is the screw diameter.

122j 68 Extrusion Theory

The solid conveying angle b can be estimat-ed from the expression

cosðuþbÞ ¼ ðfs=fbÞ½2ðHf=WÞþ 1�þ ðHf=fbÞdðln PÞ=dz;

where fs is the coefficient of friction againstthe screw, fb is the coefficient of frictionagainst the barrel, W is the width of thechannel, and d(lnP)/dz is the slope of theplot of logarithmic pressure against dis-tance from the entry.

68.2 Melting and Flow within the TransitionZone

Before the polymer reaches the meteringzone, it has to be fully melted to avoidthe entrapment of air, which would causethe formation of bubbles in the extrudate.The melting of the polymer plug arrivingfrom the feed zone takes place via the for-mation of amoltenfilm at the barrel surface.This is scraped by the ploughing action ofthe screw and forced to flow into a melt poolformed at the side wall at the upstream sidechannel of the screw. In the diagram isshowna schematic cross-sectionof the chan-nels in the transition zone. Note that thematerial flows along the channel from rightto left in the axial direction of the screw.

An expression for the melting rate isobtained from the mass balance:.

rate of meltingper unit distance

¼ rate of flowinto melt pool

¼ rate of melt poolflowing downstream

This involves also a heat transfer analysisto determine the rate of melting of thepolymer at the barrel surface. The finalexpression for the reduction in the size ofthe solid plug as it moves downstreambecomes

XW

¼ c

A¼ A=c� 1

1�½ðZ=ZTÞðA=cÞð2�A=cÞ1=2�

( )2

;

where X/W is the ratio of solid bed width tochannel width, c is a parameter containingthe heat transfer characteristics and solidplug conveying rate, and Z/ZT is a dimen-sionless ratio, corresponding to the frac-tion of the melting distance considered, Z,relative to the total melt distance, ZT. Themelting of the solid bed, however, starts inthe feed zone and extends into the meter-ing zone, as shown by the data in thegraphs.

Melting mechanism of polymer powder or granules in the transition zone of an extruder. Melt flow takesplace from right (feed zone) to left (metering zone). Source: Adapted from Maddock (1959).

68 Extrusion Theory j123

Plots of X/W versus number of turns of the flightsalong the screw. Source: Osswald (1998).

68.3 Flow Analysis in the Metering Zone

The metering zone has two functions. Onefunction is to dampen any pressure oscilla-tions that arise from pressure fluctuationscreated by the breaking up of the solid bedin the transition zone. This is necessary inorder to avoid surging of themelt (unsteadyflow) through the die. The flow rate throughthe metering zone, hence the pumpingcapacity of the extruder, is calculated on thebasis of a model that assumes that thechannel of the rotating screw and the innersurface of the barrel can be unravelled andflattened. Flow is assumed to result fromthe sliding of the barrel surface over thescrew channel, at an angle corresponding tothe helix angle of the flight of the screw (seediagram).

Velocity components of themelt at the inner surfaceof the barrel sliding over the screw channel andsymbols. Source: Mascia (1989).

The analysis consists in setting theappropriate momentum equation and

obtaining a solution for steady-state condi-tions, that is, the velocity does not changewith time and, therefore, remains constantalong the length of the channel. (SeeMomentum equation.) The analysis alsoassumes that the velocity is constant acrossthe width of the channel and that the onlyvelocity gradient along the flow path is theone corresponding to the shear rate throughthe depth of the channel. Assuming a New-tonian behaviour, the solution leads to anexpression for the velocity of a particle with-in themelt at a distance y from the bottomofthe channel in the form of

Vz ¼ yH

Vbz� yðH�yÞ2h

dPdz

;

where Vbz is the component of the meltvelocity (Vb) in the Z-direction at the barrelsurface. The flow rate (Q) can then becalculated as the product of the velocity andthe cross-sectional area of the channel,which yields the expression.

Q ¼ VbzWH2

�WH3

12hdPdz

;

whereh is the viscosity of polymermelt, dP/dz is the pressure gradient along the chan-nel length and H is the height of thechannel.The first term of the flow rate equation

corresponds to the �drag flow rate� (QD),which represents the maximum pumpingcapacity of the screw. The second term isknown as the �pressure flow rate� (QP),which represents the reduction in flow ratealong the channel of the screw resultingfrom the building of the pressure due tothe restrictions caused by the die. The pres-sure flow equation can be elaborated to takeinto account back-flow taking place throughthe clearance d between the flights and thebarrel (see diagram) and theVbz velocity canbe related to the screw revolution frequency,

124j 68 Extrusion Theory

N (revolutions per second). The flow rateequation can be written as

Q ¼ QD�QP;

where

QD¼aNd=H and QP¼bDP=hð1�d=HÞ:

The two constants a and b are known as the�screw characteristics� insofar as they de-scribe the geometric features of the screw.To take into account the non-Newtonianbehaviour of polymer melts, the viscosityterm h has to be replaced with a function ofthe shear rate. (See Power law and Carreaumodel.)Quite often the viscosity term is replaced

by a more complex polynomial equation,obtained from experimental data, whichtakes into account also the effect of temper-ature. Note that the flow restrictions im-posed by the die can be quantified by aparameter w, sometimes referred to as thethrottle ratio, which is defined as the ratio ofthe pressure flow (QP) to the drag flow (QD).The theoretical value of w varies from 0 forQP¼ 0 (open discharge conditions, that is,conditions in the absence of a die) to 1 forQP¼QD (closed discharge conditions, thatis, conditions when the die is completelyblocked). In the latter case, the only netpossible flow is that resulting from leakageflow over the flights of the screw. This is asituation analogous to batch rotary mixers.Hence, themixing efficiency of an extrusion

operation is often defined in terms of thethrottle ratio. (See Screw–die interaction.)

69. Eyring Equation

Relates the change in yield strength of amaterial to strain rate and temperature. TheEyring equation is written as

d«=dt ¼ B exp½ðDH�ysYÞ=RT � ¼ _«Y;

where d«/dt is the applied strain rate, whichis equal to the strain rate _«Y experienced bythe material during yielding, B is a materialconstant,DH is the activation energy, y is theactivation volume,sY is the yield strength ofthe material, R is the universal gas constantand T is the absolute temperature. The dataarepresented asplots ofsY/T versus log( _«Y),from which the values for the activationvolume and activation energy are obtained,as shown in the diagram. (See Activationvolume and Arrhenius equation.)

Eyring plots for determining the activation energyand activation volume for yielding failures. Source:McCrum et al. (1988).

69 Eyring Equation j125

F

1. Fabrication

A term used to describe the construction ofa structure by assembling and joining vari-ous components. (See Tyre construction.)

2. Factice

A termused for softeners or processing aidsfor rubber. Factices consist of unsaturatedoils (vegetable and animal types) that havebeen reacted with sulfur or mercaptans.

3. Falling-Weight Impact Test

Used to measure the impact strength ofmaterials by dropping a mass on to a speci-menfromacertainheight.Thisisalsoknownas the ball-drop test. (See Impact strength.)

4. Fatigue Life

A term widely used for fatigue tests on rubber,denoting the number of cycles required tofracture a specimen subjected to dynamic loads.

5. Fatigue Test

A term introduced in the early part of thenineteenth century to denote the failure ofmetal components when subjected to cyclic

loads, over a long period of time, at stresslevels below the tensile strength values ob-tained from standard laboratory tests. Oftenfatigue tests are classified as static fatiguetests, also known as creep rupture tests,when the stress is kept constant, or dynamicfatigue tests, if themagnitude of the appliedstress varies periodically with time. For theconvenienceof equipment construction, theimposed strain is allowed to vary sinusoidal-ly with time, with the upper and lower limitsremaining constant during the test. Whenthe upper and lower limits are both eitherpositive (tension)ornegative(compression),the stress cycle is called �fluctuating�. Whenthe stress changes sign during a cycle, thetest is known as �reversed� cycle fatigue.There are two cases of reversed and fluc-

tuating cycles used in practice. The first is asymmetrical reverse cycle, in which themean stress is zero, and the upper andlower limits are equal in magnitude butdiffer in sign. The second is a fluctuatingcycle in which the mean stress is half themagnitude of themaximum stress, with theminimum stress equal to zero. This lattertype is widely used for testing rubber sam-ples in tension. The results of fatigue testsare usually presented as linear–log orlog–log plots of the applied stress versusnumber of cycles to failure, known as S-Ncurves, as illustrated in the diagram.

Schematic illustration of fatigue S-N curves: (left) linear–log, (right)log–log.


126j

Fatigue tests are rarely carried out onthermoplastic polymers, unless the oscilla-tion frequency is sufficiently low to preventlarge increases in temperature caused bytheheat generated through internal friction.In practice, dynamic fatigue tests are carriedout on structural adhesives, composites andvulcanized rubber.

6. Fatty Acid

A term for long-chain aliphatic carboxylicacids derived from natural products. Forinstance, oleic acid is a fatty acid obtainedfrom vegetable oils. However, the term isfrequently used more generally andincludes aliphatic acids with shorter chainlengths, such as stearic acid and lauricacid.

7. Feed Zone

(See Extruder and Extrusion.)

8. Fibre

Very fine filament normally produced inbundles known as yarns, tows or rovings.Fibres are produced by processes generallyknown as �spinning�, which can be in theform of a mechanical method, consisting offibrillation procedures, such as those usedfor natural fibres and polypropylene, �wet�spinning and �melt� spinning. A schematicdiagram of a typical melt spinning processis shown.

Melt spinning process for linear polymers. Source:Adapted from Teegarden (2004).

Note that the drawdown ratio from thespinneret to the godet rolls is extremelyhigh, so that the orifices of the spinneretcan be as a large as a few millimetres indiameter. For the production of inorganicfibres, such as glass fibres, the flow of meltthrough the spinnerets takes place by gravi-ty feed, possibly assisted by air pressure;while for polymer-based fibres, the melt isdelivered to the spinnerets by an extrudervia a gear pump. The details of the applica-tion of the size (or finish) on the fibres canvary fromone process to another dependingon both the nature of the fibres and themedium for depositing the coating on thefibres. The process formaking carbonfibresis a second-stage operation in which theprecursor fibres, acrylic fibres, rayon orpitch fibres, are pyrolysed at very high tem-peratures in an inert atmosphere.Note that the high modulus and high

strength of inorganic fibres derive from theintrinsically very high internal forces, bothwithin rigid networks and between molec-

8 Fibre j127

ular constituents joined by covalent andionic bonds. The attainment of high-modu-lus and high-strength characteristics in or-ganic fibres relies on the molecular chainsbecoming aligned along the axis of the fibre(monoaxial orientation) so that externalforces can be transmitted along the strongcovalent bonds of the polymer chains. (SeeOrientation.) In the case of carbon fibresand carbon nanotubes, the graphene layersare aligned in planes along the fibre axis, sothat forces are transmitted along the cova-lently bonded hexagonal rings, therebyavoiding stresses being transferred betweenthe graphene planes, which are held togeth-er by dynamic dipoles created by the freemovement of electrons. (See Graphene andCarbon nanotube.)

9. Fibreglass

An alternative name for glass fibre. (SeeGlass fibre.)

10. Fibre-Reinforced Polymer (FRP)

A composite consisting of a polymer rein-forced with fibres exhibiting much highermodulus and strength than the polymerused. (See Composite). Fibres are laid with-in a polymeric matrix either unidirection-ally or in the form of random mats or aswoven fabrics.

11. Fibre Reinforcement Theory

A theoretical analysis that relates the prop-erties of composites to the properties of thefibres and those of the matrix, particularlymodulus and strength.

11.1 Estimation of Young�s Modulus:Unidirectional Continuous Reinforcement

In the analysis it is assumed that (i) bothphases (fibres and matrix) behave elastical-ly, (ii) both phases have the same Poisson�sratio, so that no spurious (triaxial) stressesdevelop from an externally applied axialstress, and (iii) there are no movements atthe interface, that is, there is perfect fibre–-matrix bonding.

Longitudinal direction External stressesapplied along the direction of the fibresproduce strains along the fibres of the samemagnitude as in thematrix, that is, isostrainconditions («c¼ «f¼ «m). (See Law of mix-tures.) It follows that the stresses are sharedbetween the fibres and the matrix and,therefore, the stresses (s) on the compositeare equal to the sumof the stresses acting onthe two components weighted by theirrespective volume fractions (f), that is,

sc ¼ ffsf þð1�ff Þ sm;

where subscripts c, f and m stand for com-posite, fibre and matrix, respectively. Divid-ing by «c gives the equation for the Young�smodulus, that is,

Ec ¼ ffEf þð1�ff ÞEf ;

which corresponds to the upper limit valuepredicted from the law of mixtures.

128j 11 Fibre Reinforcement Theory

Transverse direction External stressesapplied in the direction perpendicular tothe fibre direction bring about conditionsthat vary from isostress at the equator toisostrain at the poles. Between these posi-tions, around the fibre circumference, theconditions are predominantly shear type, asshown in the diagrams.

The stress conditions at three positionsaround the circumference of the fibreswhen external stresses are applied in thetransverse direction are shown in the threediagrams.

Position 1: sc¼sf¼sm (isostress).

Position 3: «c¼ «f¼ «m (isostrain).

Position 2: «c 6¼ «f 6¼ «m, sc 6¼ sf 6¼ sm.

The mixed stress conditions depicted inthe last diagram are reflected in the term ofthe equation for the prediction of the trans-verse modulus, which is

where E is Young�s modulus, n is Poisson�sratio, G is the shear modulus,

Kf ¼ Ef

2ð1�nf Þ ; Km ¼ Em

2ð1�nmÞ ;

Gf ¼ Ef

2ð1þ nf Þ ; Gm ¼ Em

2ð1þ nmÞ ;

and C is the contiguity factor (distancebetweenfibres, stacking); for isolatedfibres,C¼ 0, and for fibres in close contact, C¼ 1.

11.2 Estimation of Young�s Modulus:Unidirectional Short-Fibre Reinforcement

When the fibres are not continuous, but arealigned in one direction, the externally

Eð?Þc ¼ 2½1�nf þðnf�nmÞð1�ff Þ�

� ð1�CÞKf ð2Km þGmÞ�GmðKf�KmÞð1�ff Þ2Km þGm þ 2ðKf�KmÞð1�ff Þ

� �

þCKf ð2Km þGf ÞþGf ðKm�Kf Þð1�ff Þ

Km þGf�2ðKf�KmÞð1�ff Þ ;

11 Fibre Reinforcement Theory j129

applied tensile forces in the direction of thefibres produce isostrain conditions only inthe central section of the fibres. The regionaround the fibre ends are subjected to sheardeformations, as indicated in the diagram.The fibre ends can be considered as�ineffective� in the transfer of the stressesfrom the matrix to the fibres and, therefore,will bring about a reduction in modulusrelative to that estimated for continuousfibres.

An equation that is more widely used forthe estimation of the modulus of short-fibrecomposites is known as the Halpin–Tsaiequation, and it can be used to calculate boththeYoung�smodulusandtheshearmodulus:

Mc

Mm¼ 1þ jhff

1�hff;

where

h ¼ ðMf=MmÞ�1ðMf=MmÞþ j

;

Mc is the composite modulus (Ec, Gc),Mf isthe fibre modulus (Ef, Gf),Mm is the matrixmodulus (Em, Gm), and j is a geometricfactor that depends on fibre length andloading conditions, with j¼ 2(l/d) for theprediction of the longitudinal Young�s mod-ulus and j¼ 1 for the prediction of the shearmodulus.It is noted that for j¼1, that is, l/d ! 1

(continuous fibres), the Halpin–Tsai equa-tion reduces to the upper limit of the law ofmixtures, that is, the longitudinal modulus.For j¼ 0, that is, l/d ! 0 (fibres in thetransverse direction), on the other hand, the

Halpin–Tsai equation reduces to the lowerlimit, that is, the �reciprocal� lawofmixtures.

Angular dependence of modulus The varia-tion of the modulus of unidirectional fibrecomposites between the longitudinal andtransverse directions can be derived fromconsiderations of the equilibrium of forces.Converting forces into related stressesand introducing geometrical considerationsfor the strains, the following expression can

be obtained

EL=Eu ¼ cos4 uþðEL=ETÞ sin4 uþðEL=GLT�2nLTÞ cos2 u sin2 u;

where Eu, EL and ET respectively are theYoung�s modulus in direction u and in thelongitudinal and transverse directions, GLT

and nLTare the shearmodulus andPoisson�sratio related to the planes of the fibre direc-tions, and u is the angle formed by thedirection of the fibres and that of the exter-nally applied stress.

11.3 Estimation of Young�s Modulus:Modulus of Random Fibre Reinforcement

When the fibres are arranged in morethan one direction as fabric reinforcementand ply laminates, the modulus for eachdirection can be obtained by averaging pro-cedures taking into account the fraction offibres present in each of the directionsconsidered. For planar random fibre com-posites, the modulus will be the same in alldirections in the plane and can be calculateddirectly from the general averaging proce-


dure of a function, that is,

�E ¼ 1p=2

ðp=2

0

EðuÞ du:

11.4 Estimation of Tensile Strength:Unidirectional Continuous Reinforcement

Longitudinal direction Stresses applied inthe longitudinal direction produce isomet-ric deformations in the fibres and matrix,that is, «c¼ «f¼ «m. Under these condi-tions, the stress acting on the composite isshared between the stress acting on the twophases, which can be calculated from thelaw of mixtures, that is,

sc ¼ ffsf þð1�ff Þsm;

whereff is the volume fraction offibres and(1�ff) is the volume fraction of matrix. Ifthe fracture strain of the fibres is lower thanthat of thematrix, then the composite breaksthrough fracture propagation through thematrix at the point when the fibres break.Therefore, the law of mixtures can be ap-plied to calculate the fracture stress for thecomposite, s*

c , from the tensile strength ofthe fibres, s*

f , and the value of the stress onthematrix corresponds to atwhich the strainis equal to the fracture strain of the fibres,s0

m, as shown in the diagram.

Stress versus strain curves for fibres, matrix andunidirectional continuous fibre composite.

Therefore, the law of mixtures for frac-ture conditions can be written as

s*c ¼ ffs

*f þð1�ff Þs0

m:

Assuming elastic behaviour for both com-ponents up to fracture conditions, the stres-ses can be calculated from the respectiveYoung�s modulus, that is,

s*c ¼ ff«

*f Ef þ «*f ð1�ff ÞEm;

where «*f is the strain at which the fibresbreak.

Transverse direction When the stresses areapplied in the transverse direction to thefibres, either failure will take place withinthe matrix (if the interfacial fibre–matrixbond is very strong), or fracture will start atthe interface and propagate through thematrix. For the first case, the strength ofthe composite is the same as the strengthof the matrix; while for the second case, itwill be even lower. Therefore, the expres-sion for the strength of the composite inthe transverse direction can be written ass*c � s*

m.

11.5 Estimation of Tensile Strength:Unidirectional Short-Fibre Reinforcement

In short-fibre composites, the stress alongthe length of the fibre is not constant, butrises from a minimum at the fibre end to amaximum in the centre.

Longitudinal direction When the length ofthe fibres is greater than the critical fibrelength (Lc), the conditions in the centralregion are isostrain type and, therefore,fracture starts within the fibres at the pointwhen the stress reaches the tensile strength

11 Fibre Reinforcement Theory j131

of the fibres. It follows that the averagestress, �s; carried by the fibres at the pointof fracture can be related to the strength ofthe fibre, s*

f , by the expression

�s ¼ s*f ð1�Lc=2LÞ;

which can be used in the law ofmixtures forthe strength of the composite, s*

c , whichbecomes

s*c ¼ fff

*f ð1�Lc=2LÞþ ð1�ff Þs0

m;

where s0m is the stress carried by the matrix

at the point of the initiation of the fracture inthe fibres. If the strain at break of the fibresis lower than that of the matrix, the value ofs0m can be estimated from its Young�s mod-

ulus, that is, s0m ¼ Em«f .

When the fibre length is much smallerthan Lc, fracture takes place by a shearmechanism initiated either at the interfaceor within the matrix adjacent to the fibres.

Transverse direction When stresses are ap-plied in the transverse direction, failuretakes place within the matrix, even thoughit may originate by the breaking of theinterfacial fibre–matrix bond. Therefore,the strength of the composite is practicallyequal to the strength of the matrix.

11.6 Angular Tensile Strength ofUnidirectional Fibre Composites

When an external tensile force is applied atan angle u to the direction of the fibres, theinternal forces can be resolved into twovectors, in the plane along the directions ofthe fibres, and in the plane perpendicular tothe fibres, respectively, as indicated in thediagram.

Vector analysis of forces acting on planes paralleland perpendicular to the fibre direction. Source:Mascia (1974).

When the angle is very small, fracturetakes place in the plane perpendicular to thefibres, and the strength is practically thesame as the longitudinal strength of unidi-rectional composites. At larger angles, be-tween around 15� and 75�, fracture occurspredominantly through shear slip along theplanes between the fibres, as shown.

Shear failure of unidirectional fibre composites.

The theoretical analysis assumes that Fsis the shear force responsible for the failurealong one of the planes between the fibres.The value of Fs at failure can be estimatedfrom knowledge of the interlaminar shearstrength, tm�f, that is, Fs¼ tm�f A00, whereA00 is the area of the failure plane. Thestrength of the composite at angle u is su¼Fa/A. Substituting Fs¼Fa cos u and A¼A00

sin u, one obtains the following expressionfor the strength of the composite:


su ¼ tm�f

sin u cos u:

At very large angles, between around 75�

and 90�, fracture occurs in the planebetween thefibres by a cleavagemechanism,so that, as the angle approaches 90�, thevalue of the stress that causes fracturebecomes equal to the transverse strength ofthe unidirectional fibre composite. Thetheoretical equation for the strength, su, asa function of the angle, u, becomes

su ¼ sT=cos2 u;

where sT is the strength in the transversedirection to the fibres. The overall variationin strength from 0� to 90� is shown sche-matically in the diagram.

Prediction of the angular strength of unidirectionalfibre composites.

In view of the high sensitivity to shearfailures of unidirectional fibre composites,productsareusuallyproducedwithcross-plyconfigurationsorwith fabric reinforcement.

12. Fickian Behaviour

A type of diffusion of gases or vapoursthrough afilmor sheet that can be describedby Fick�s law. Accordingly, a plot of themassM of a sample at time t, under steady-statediffusion conditions (normalized with re-spect to the mass reached at absorptionequilibrium, Mt/M1), against the square

root of time is linear. The validity of theFickian behaviour assumption can be ascer-tained by making measurements on sam-ples of different thickness (L). The plot ofMt/M1 against t1/2/L would produce a sin-gle curve. (See Diffusion.)

13. Filament Winding

A manufacturing method used to producehollow products such as pipes and vesselsusing continuous reinforcing fibres. (SeeComposite.)

14. Filler

A term for inorganic particles obtained bycomminution of low-cost natural minerals.The term derives from their poor reinforcingefficiencyso that theirmain function is to �fill� apolymer compound in order to reduce theoverall cost. Some fillers are also made by asynthetic route.Under this category are includ-ed fillers used for their functional properties,such as fire retardancy or electrical character-istics. The main features of fillers used inpolymer formulations are shown in the table.

Types Features

Talc, mica, glass flakes Platelet geometryCalcium carbonate, chinaclay

Quasi-spherical

Carbon black, fumedsilica, nanoclays

Very irregular

Aluminium trihydrate,magnesium hydroxide

Quasi-spherical

Silicon carbide, zincoxide, barites

Quasi-spherical

In terms of mechanical properties, thereinforcement efficiency of fillers is quite lowand only elastomers display substantial in-creases in modulus and strength. The equa-tionsnormallyused for thepredictionof shear

14 Filler j133

modulus and viscosity have a certain similari-ty. For instance, Kerner�s equation for theshear modulus of particulate composites is

Gc=Gm ¼ 1þ ½15wpð1�nmÞ=wmð8�10nmÞ;whereGc/Gm is the shearmodulus reinforce-ment factor (subscripts c and m stand forcomposite and matrix), wp and wm are thevolume fractions for the particles and matrix,and nm is Poisson�s ratio of thematrix. One ofthe more widely used equations for melt vis-cosity, attributed to Kitano, is

hc=hm ¼ ½1�wp=wpk��2;

wherehc/hm is the viscosity �increment factor�at low shear rates, wp is the volume fraction ofthe particles and wpk is the maximum volumefraction of the filler particles, known as thepacking fraction. (See Reinforcement factor.)Thefigure shows a comparison of the strengthreinforcement efficiency of differentfillers in avulcanized rubber.

Plot of tensile strength versus filler content ofa vulcanized rubber for different types of fillers(numbers in brackets correspond to the surfacearea of the filler, m2/g). Source: Wypych (1993).

Thedata show agood correlation betweentensile strength and surface area of the fillerand also a substantial increase in strengthresulting from the promotion of chemicalbonds between filler and matrix, as can beinferred from the data obtained with Hysil(silica) and carbon black. The further datashow the effect of filler concentration ofdifferent types of fumed silica on the vis-cosity of an unsaturated polyester resin.

Effect of filler concentration on the viscosity of anunsaturated polyester resin for various grades offumed silica (numbers on the curves represent thesurface area, m2/g). Source: Wypych (1993).

The data illustrate the strong influence ofsurface area on viscosity and reveal theimportant role of surface charges. The pres-ence of OH groups confers a strong hydro-philic character to the surface of the parti-cles, which can immobilize the neighbour-ing resin molecules through strong hydro-gen-bonding interactions. Note that thechemical nature of the surface of the silicaparticles can be readily changed by treat-ments with silane coupling agents. (SeeCoupling agent.)

15. Film Extrusion

(See Extrusion, Blown film and Chill-rollcasting.)

134j 15 Film Extrusion

16. Film Formation

A term used to describe the formation of a�solid� coating on a substrate through depo-sition of a polymer from a solution or dis-persion in a liquid medium. The mecha-nism for the formation of a film from apolymer dispersion is shown schematically.

Film formation of coatings from dispersions.Source: Adapted from Denkinger (1996).

After evaporating the water from the de-posited coating, the polymer particles fusewith each other to produce a continuousfilm. For this to take place, the polymermolecules from adjacent particles have todiffuse across the interface and the voidsbetween particles have to disappear. Thelatter event takes place through a balancebetween the reduction of surface energy andtherateofenergydissipationbyviscousflow,which implies that the ambient temperaturehas to be higher than the glass transitiontemperature (Tg) of the polymer to ensurethat molecular diffusion can take place at arealistic rate. (See Powder sintering.)The film formation characteristics of a

polymer dispersion are described by anempirical parameter known as the �filmformation temperature� (Tf). The value ofTf is measured experimentally by casting afilm on a long plate heated in such a way asto provide a linear temperature gradientalong its length. The Tf value is obtainedby recording the position, hence the tem-perature, of the �frost� line that is observed

across the width of the film, which resultsfrom the disappearance of voids and bringsabout the natural transparency of the poly-mer in the coating. For crystalline polymers,film formation takes place at temperaturesTf above the melting point Tm. In any case,the film formation temperature can be re-duced by the incorporation of plasticizers,which remain permanently embedded in thefilm.Note that, while continuousfilms can beformed readily from solutions, the removal ofresidual solvent may be very slow and notcomplete if the Tg of the polymer is muchhigher than ambient temperature. For thecase of crystalline polymers, the evaporationof solvent may result in the growth of largecrystals, which can produce a �grainy� orpowdery coating instead of a continuous film.

17. Film Gate

A channel in the form of a thin slit feedingthe flat cavity of an injection mould. (SeeGate and Mould.)

18. Fire Retardant

(See Flame retardant.)

19. First-Order Transition

Corresponds to the transition from a highlyordered state of a solid (the crystalline state)to a highly disordered state (the liquid state),that is, the melting transition. Thermody-namically, a first-order transition is definedas the temperature at which a primary vari-able, such as volume or enthalpy, shows asudden jump. (See Alpha transition tem-perature and Beta transition temperature.)

20. Fish Eye

Adefect found in sheets due to the presenceof �gel spots�, which are dragged by the

20 Fish Eye j135

action of the calendering rolls to form awake resembling the eye of a fish. (See Gel.)

21. Fish-Tail Die

An extrusion die to produce sheets or flatfilms. The term derives from its geometricfeatures,whichare characterizedby the abili-tytodeliverthemelttothedielipsatauniformrate in order to ensure a constant thicknessacross the width. (See Extrusion die.)

22. Flame Retardant

Additives used to reduce the susceptibilityof polymers to be ignited by a flame. Thereare three main types of additives that can beused to induce flame retardancy in polymerformulations.

22.1 Combustion Inhibitors (or ChemicalFlame Retardants)

These are the traditional fire retardantadditives, consisting of mixtures of highlyhalogenated compounds and antimony ox-ide, with optimum weight ratio at around2 : 1, derived from the relationship illustrat-ed in the diagram.

Optimized quantities of synergistic components offlame retardant formulations. Source: Mascia(1974).

At high temperatures, the halogenatedcompounds decompose into volatile pro-ducts, consisting of highly reactive speciesthat will intervene in the combustion reac-tions by quenching the free radicalsformed by the pyrolysis of the polymer.These reactions retard the rate of flamepropagation and cause the flame to extin-guish itself. The addition of antimonyoxide (Sb2O3) enhances the efficiency ofthe above intervention through the pro-duction of antimony oxychloride �fumes�capable of adsorbing the very reactive radi-cal species in the combustible gases. Themost common types of halogenated flameretardant additives are chlorinated paraf-fins (C10�C30), derivatives of hexachloro-and hexabromocyclopentadiene, tetrabro-mododecane and pentabromotoluene.

22.2 Oxygen Diluents (or Physical FlameRetardants)

These are additives that give out large quan-tities of incombustible gases, such as water,just before the exposed polymer front ap-proaches its ignition conditions in terms oftemperature and oxygen concentration. Thetypical additives that operate on this princi-ple are aluminium trihydrate and magne-sium hydroxide. (See Aluminium trihy-drate, Magnesium hydroxideAntitrackingadditive.) These additives very rapidlyrelease 30–35wt% water at temperaturesaround 300–400 �C, which reduces the con-centration of oxygen available for the com-bustion of volatile products at the heatedfront. Since the dehydration of inorganicoxides is an endothermic process, a certainamount of heat will be removed, therebycausing a reduction in temperature in theexposed zone, which also delays the attain-ment of the conditions required to startignition. Another additive exerting a similarfunction is melamine, and its salts, such asmelamine cyanurate, which sublime at

136j 22 Flame Retardant

around 300–400 �C and therefore dilute themixture of oxygen and combustible gasesformed by pyrolysis reactions at the exposedpolymer front. It is possible that for somepolymers the pyrolysis products may evenreact with the melamine vapour to formmore stable products.

22.3 Heat and Oxygen Barrier Promoters

These are also known as intumescent char-forming additives due to their ability toproduce a layer of char as a result ofphysical and chemical interactions with thedecomposing polymer front. (See Intumes-cent coating.) This can act as a heat andoxygen barrier for the polymer beneath,thereby slowing down the rate of formationof combustible gases from the polymer.Other additives can form a protective bar-rier layer primarily through the formationof an inorganic glass coating. Typical ad-ditives of this type are mixed salts of zincsulfate, potassium sulfate and sodium sul-fate, ammonium perborate and zinc phos-phate glasses. Silica gels and nanoclayshave also been found to provide someprotection by this mechanism.

23. Flash

A thin film of polymer formed at the edge ofamoulded article, resulting from the flow ofmelt between the contacting surfaces of twoparts of themould, consisting of punch andcavity parts.

24. Flash Point

Corresponds to the self-ignition tempera-ture of combustible liquids. It is an impor-tant parameter in choosing solvents or plas-ticizers in situations where there could befire hazards, 300–400 �C.

25. Flex Cracking

A term denoting the fracture of a flexiblesheet by bending.

26. Flex Life

A term to denote the fatigue life of rubberunder cyclic loading conditions. (SeeFatigue life.)

27. Flexural Modulus

The modulus of a material measured inthree-point bending experiments. By apply-ing a load (P) at the centre of a freelysupported beam and measuring the result-ing deflection (D), the Young�s modulus (E)is calculated from fundamental considera-tions. Provided the measurements aremade within the applicability of the under-lying theory, requiring a large span-to-thick-ness ratio (i.e. S/W > 16) and small deflec-tions (i.e. S/D> 10), it is

E ¼ PL3=4DBW3:

The calculated value should be the sameas that obtained from tensile or compres-sion tests. However, because the limitingconditions imposed by beam theory cannotbe easily imposed in practical measure-ments on polymers, the E value obtainedfrom a flexural test can be somewhat higherthan that obtained froma tensile test.Hencethe reason for identifying the value obtainedas �flexural� modulus.

28. Flexural Properties

Mechanical properties measured by meth-ods involving the application of the load in athree-point bendingmode, hence the termsflexural modulus and flexural strength.

28 Flexural Properties j137

Deflection of a beam loaded in a three-point bend-ing mode. Source: Courtesy of M. Baldwin (2003),EU Mercurio Project.

The three-point bending mode is a con-venient way of evaluating the mechanicalproperties of rigid materials due to thesimplicity of the specimens required, typi-cally rectangular bars. Provided that thedeflections incurred are small and thespan-to-thickness ratio is large, normallygreater than 20 : 1, the recorded forces canbe used to calculate the outer skin stresses atthe two opposite sides of the loading point(respectively, compression and tension),from which fundamental properties, suchas modulus and yield strength, can be esti-mated. The analysis of a centrally loadedfreely supported beam at low levels ofdeflections makes it possible to calculatethe strain, «, and the stress,s, at the loadingpoint on both the compression and tensionsides of the beam, that is

« ¼ 6WðD=L2Þ and s ¼ 32ðPL=BW2Þ;

where P is the load, B is the width,W is thethickness and D is the central deflection.

29. Flexural Strength

The strength of a material measured inthree-point bending experiments. By in-creasing the load at the centre of a freelysupported beamup to the point at which thematerial fails by yielding (PY), the yieldstrength (sY) can be calculated from funda-

mental considerations, provided the mea-surements aremadewithin the applicabilityof the underlying theory, requiring a largespan-to-thickness ratio (i.e. S/W > 16) andsmall deflections (i.e. S/D > 10). The equa-tion is

sY ¼ 3PYS=2WB2;

where B is the width of the rectangularspecimen. The calculated value should bethe same as that obtained from tensile orcompression tests. However, because thelimiting conditions imposed by beam theo-ry cannot be easily imposed in practicalmeasurements on polymers, the sY valueobtained from a flexural test can be higherthan that obtained from a tensile test. Fur-thermore, the tests are widely used to mea-sure theflexural strength even, or especially,when the material fails in a brittle manneror by a complex fracture mechanism, as incomposites. In this case, the flexuralstrength values calculated from the aboveformula canbe considerably higher than thevalues obtained from tensile tests.

30. Flocculant

(See Flocculation.)

31. Flocculation

A phenomenon or process by which parti-cles are kept in suspension, or preventedfrom forming agglomerates, when dis-persed in a fluid medium. The ability ofsuspensions to flocculate is determined byconsiderations based on both the surfacecharacteristics of the particles and thesedimentation velocity. (See Zeta potentialand Stokes equation.) The dispersion ofparticles takes place through repulsionscaused by surface charges of equal signand exhibiting a high zeta potential. This

138j 31 Flocculation

characteristic has to be combined with thestability against sedimentation, through therequired balance of particle size, the densityof the particles and the viscosity of themedium, as stipulated by Stokes law. Thedesirable increase in viscosity of water-borne dispersions is often achieved throughthe addition of water-soluble polymers,known as flocculants, possessing polaritycharacteristics �compatible� with the surfacecharges of the particles.

32. Flow Analysis

Analysis of the flow of polymer melts basedon the conservation of momentum. In theanalysis of the flow of polymer meltsthrough channels, it is usually assumed thatthe rate of change in momentum is negligi-ble, even in situations where there is a largechange in cross-sectional area along theflow path. This is allowable in view of thevery high viscosity of polymer melts, whichmakes the rate of change in velocity, dV/dt,very small compared to the force required tomaintain the flow. (See Momentum equa-tion.) An example of the use of the momen-tum equation in the flow analysis of poly-mer melts is to obtain a relationship be-tween pressure and flow rate.

A comparison of the flow though cylin-drical and slit dies is shown. From theequations shown, the respective expres-sions for the flow rate (Q) are obtained as

Q ¼ðR02prVzðrÞ dr and

Q ¼ðH=2

02WvzðyÞ dy;

where trz and tyz are the shear stresses atdistances r and y, and dP/dz is the pressuregradient along the flow direction.

33. Flow Curves

Plots of shear stress against shear rate,usually on a log–log scale to obtain straightlines, obtained from rheological measure-ments on polymer melts. (See Power lawand Power-law index.)

34. Flow-Induced Crystallization

The formation of crystals taking place infibre spinning from a melt, a solution or agel through the combined effect of cooling,or solvent evaporation, and the applicationof tensile forces to draw the extrudate.

34 Flow-Induced Crystallization j139

35. Flow Instability

Fluctuations in the flow rate of a polymermelt emerging from a die. These can arisefrom �fractures� at the die entry resulting ina cyclic slip–stick effect at the walls of thedie. (See Melt fracture.) In extrusion, flowinstability may arise from a phenomenonknown as �surging�, which is caused by thebreaking up of the solid bed in the transitionzone. This event creates pressure fluctua-tions within the channel of the meteringzone that can be transmitted all the waydown to the exit of the die, which will bemanifested as periodic thickness fluctua-tion in the extrudate. (See Extrusion theory.)

36. Flow Promoter

A term sometimes used to denote an addi-tive capable of enhancing the flow charac-teristics of a polymer melt through externallubrication or a reduction in viscosity.

37. Fluid Bed (Fluidized Bed)

A bath consisting of small particles (usuallyglass Ballotini spheres about 0.15–0.25mmdiameter) suspended in inert hot gas, usedprimarily for thecontinuousvulcanizationofrubber products, such as tubings or profiles.

38. Fluorescence

Aphenomenawhereby characteristic chem-ical groups in molecules absorb incidentlight and re-emit part of it as radiation ata lower frequency. Fluorescent dyes, forinstance, absorb UV light and re-emit it inthe visible range. The origin of fluorescencelies within the conjugated double bonds inwhich the delocalized p–electrons are ableto absorb energy with relative ease. Thistechnique is often used to detect degrada-

tion in PVC products, which results in theformation of conjugated double bonds.

39. Fluoroelastomer (also known as FKM)

Fluoroelastomers (known under the shortform FKM) are produced from copolymeri-zation or terpolymerization of hexafluoro-propylene (CF2¼CFCF3) in combinationwith vinylidene fluoride (CH2¼CF2) andeither perfluoro(methyl vinyl ether)(CF2¼CFOCF3) or tetrafluoroethylene(CF2¼CF2). The Tg value varies between�35 and �50 �C depending on composi-tion. Themain attribute offluoroelastomersis their thermal oxidative stability, whichmakes them suitable for continuous use upto 200 �C. Fluoroelastomers can be curedwith diamines in combination with a metaloxide, such as CaO andMgO, as acid accep-tor. The amine can abstract a fluorine atomfrom the molecular chains, producing thedesired cross-links, producing HF as by-product. Systems that can be cross-linkedwith peroxides or by electron beaming arebased on terpolymers with minor amountsof vinyl compounds containing brominegroups. Free radicals are produced as aresult of the scission of the weak C�Brbond, which produces HBr as by-productand, therefore, these polymers also requirea metal oxide to act as acid absorber.

40. Fluoropolymer

A polymer containing fluorine atoms at-tached to an aliphatic polymer chain. Exam-ples are homopolymers and copolymers oftetrafluoroethylene, vinylidene fluoride andpolyhexafluoropropylene.

41. Fluorosilicone (also known as FVMQ)

(See Silicone rubber.)

140j 41 Fluorosilicone (also known as FVMQ)

42. Foaming Agent

(See Blowing agent.)

43. Foam

Aproduct containing large quantities of regu-larly sized and evenly distributed voids,known as �cells�. Foams are divided into�closed cell� foams and �open cell� foams,according to whether the voids are totallyoccluded within the polymer matrix or areinterconnected to form co-continuous phasesof air and polymer. The density of foamsranges from about 300–700kg/m3 for struc-tural foams (produced by injection mouldingof thermoplastics) down to about 3–5kg/m3

for free rising foams from liquid resin sys-tems. The dimensions of the cells can varyfromabout0.2mmfor closedcellsup toaboutto 2–3mm for open cells. The typical struc-tures of cells is shown in the micrographs.

All polymers can be processed to producecellular structures using similar methods.Two exceptions to this are the manufactureof polystyrene foams by the expandablebeads method, and the production of�syntactic foams�, consisting of rigid mi-

cro-balloons (Ballotini spheres) embeddedin a polymermatrix. Themechanism for theformation of foams consists in the nucle-ation of �gas clusters� by the blowing agentand the subsequent growth of a large num-ber of cells, through the rapid evolution ofgases. These can be generated eitherthrough the decomposition of a chemicalblowing agent or by the sudden evaporationof fine droplets of a liquid or dissolved gas,known as physical blowing. When foamingis carried out with chemical blowing agents,the formationofclustersandthesubsequentgrowth of cells takes place by the spontane-ous chemical decomposition of the blowingagent toproducevery rapidly a largequantityof gases. (See Blowing agent.)

44. Foam Density and Properties

An interesting feature of the production offoams is the possibility of estimating the

Foam cell structures: (left) expanded polystyrene; (middle) expandedpolyethylene; (right) flexible polyurethane. Source: Unidentified original source.

44 Foam Density and Properties j141

amount of blowing agent that would berequired to produce foam with a specifieddensity, on the basis that the contribution ofthe weight of gas in the foam is negligibleand, therefore, the density of the foam, rf, isdirectly proportional to the volume fractionof the polymer, that is rf¼wprp, where wp isthe volume fraction of the polymer in thefoam and rp is the density of the polymer.(See Law of mixtures.) The volume fractionof gas in the foam, wgas, therefore, is(1�wp), a quantity that can be estimatedfrom the decomposition reaction of a chem-ical blowing agent or from the solubility–-pressure relationship of the foaming gas inthe polymer. Alternatively, the density canbe calculated from theweight fraction (v) as

1=rf ¼ vgas=rgas þvp=rp:

Solubility diagrams can be used to esti-mate the pressure required to infuse theminimum amount of gas in the polymer, aswell as selecting the right gas for a particularpolymer in order to obtain foams of thedesired density. Another interesting featureof foams is the possibility to estimate therequired foam density in order to achieve aspecified change in properties, caused bythe replacement of a fraction of polymerwith gas. For instance, it is possible to usethe Clausius–Mossotti relationship to esti-mate the required density (r) of a cellularstructure in order to obtain a certain per-mittivity value («) for a dielectric material,that is,

ð«�1Þ=ð«þ 2Þ ¼ kr;

where k is a proportionality constant relatedto the chemical nature of the dielectric.It is also possible tomake also some quite

precise predictions for the thermal conduc-tivity of foams for use in thermal insulation.This can be done, for instance, by consider-ing that the heat transfer rate by conductionis given by the equation

Q ¼ AðDT=XÞ½wgasKgas þð1�wgasÞKsolid�;

where A is the surface area, DT is thetemperature difference, X is the thickness,wgas is the volume fraction of the gas in thecells and K is the thermal conductivity.Knowing that rsolid>> rgas one obtains

Q ¼ AðDT=XÞrsolid½wsolidKgas þðKsolid�KgasÞwfoam;

from which it is predicted that the heattransfer by conduction decreases linearlyas the density of the foam decreases.Although it is more difficult to make

accurate estimates for the change inYoung�smodulus, a reasonable relationshiphas been found using the expression

Efoam=Esolid ¼ ðrfoam=rsolidÞn;

where the exponent n has values between 1and 2, depending on the cell structure,particularly whether the foam is an opencell or closed cell type. From this it is clearlydeduced that the modulus changes morerapidly with increasing gas fraction than therelated change in density.Ontheotherhand, ifabendingsituationis

considered for the case of sandwich or struc-tural foams (i.e. foams with a solid outerskin), there are substantial stiffness advan-tages to be derived on weight basis argu-ments. The deflection of a rectangular canti-lever beam, y, is given by the expression

y ¼ ð4PL3=bÞð1=Eh3Þ;

whereP is the applied load, L is the length ofthe beam, E is the Young�smodulus, b is thewidth and h is the thickness of the beam. Ifthe length and width of the beam are keptconstant, then the deflection resulting fromthe applied load P can be written as y¼ k/Eh3, where k is a proportionality constant.From this it is deduced that the reduction indeflection, y, resulting from an increase in hthrough foaming is much greater than theincrease that results from a decrease inmodulus.

142j 44 Foam Density and Properties

45. Foam Formation Mechanism

For foaming operations carried out bymeans of physical blowing agents, the for-mation of �gas clusters� can be nucleated bythe incorporation offine inorganic particles,typically talc or silica, or particles of solidorganic compounds, such as citric acid(decomposing at 150–170 �C), as well as

inorganic acids, such as boric acid andsodium hydrogencarbonate. The clustershave to reach a critical number and sizebefore they can grow into cells capable ofcreating the required conditions for theexpansion process to occur. These condi-tions are determined by the equation

drdt

¼ g

hf

dðDPÞdt

� �;

where g is the surface energy and h is theviscosity of the surroundingmedium, whilef (d(DP)/dt) denotes a time function of thedifference in pressure (DP) between the gasin the cells and that of the surroundings. Itis noteworthy that the surface energy (g) isimportant only for low-viscosity reactivesystems. For the case of polymer melts, thepredominant factor is the viscosity, h. Thesize of the cells is controlled, and becomedimensionally uniform, through the diffu-sion of gas from small cells into larger ones,driven by the pressure differential. This setsup a dynamic process of size reductionand size growth and stabilization, till thefirst leads to vanishing of cells, while the

latter is controlled by the conditions set bythe equation for dr/dt¼ 0. These conditionsare determined by two possible events: (i)the viscosity becomes infinite through cool-ing of the melt (thermoplastics) or the for-mation of cross-links (thermosetting re-sins), or (ii) the pressure differential be-tween adjacent cells is eliminated whenthey burst to form interconnected cells.

Images of growing cells and the formationof interconnected cells are shown.Diffusion of gas from internal cells into

the atmosphere is prevented by the forma-tion of a solid skin on the outer layers of thefoam. The solid skin is formed by thecollapse of local cells caused by the rapidFickian diffusion of gas in these areas. Theouter solid skin helps to maintain at alltimes a pressure differential between theinner cells and the surroundings. Whenfoaming is induced by the injection of gasesin a cross-linked thermoplastic, it is therubbery plateau modulus that controls thegrowth of the cells, as the polymer deformsthrough elastic deformations and notthrough flow. This has significant implica-tions on the mechanical properties of thefoams, insofar as the polymer in the walls ofthe cells is in a state of biaxial orientation.

46. Foam Manufacture

Four typical methods for the production offoams are illustrated.

Cell growth (left) and formation of interconnected cells (right)during the production of foams. Source: Unidentified original source.

46 Foam Manufacture j143

Set-up for the injection moulding of foams with anaccumulator to achieve a rapid transfer of the meltinto the cavity. Source: Scholtz (2009).

Injection moulding of structural foams with amould that can be opened to allow for the expan-sion of cells to take place after injection of the melt.Source: Michaeli et al. (2009).

Extrusion of foams with gas injected in the mixingsection at the front of the barrel. Source: Michaeliet al. (2009).

Reaction injection moulding of a two-componentpolyurethane foam. The process can be used on acontinuous basis for the production of foamboards. Source: Lee (2009).

47. Fogging

Haziness of the glass surfaces of the pas-senger compartment of a motor vehicle.The phenomenon is due to condensationof volatiles, such as plasticizers or residualsolvents from polymer products, causingbackward light scattering from depositeddroplets.

48. Force–Deflection Curve

A curve obtained in measurements of theflexural properties of rigid polymers or com-posites by three-point bending methods.

49. Force–Deformation Curve

A curve obtained in compression tests onpolymers and elastomers, or rubber.

144j 50 Force–Deformation Curve

50. Force–Extension Curve

A curve obtained in measurements of thetensile properties of polymers or compo-sites in tensile tests.

51. Formica

A tradename for phenolic–paper laminate.

52. Formulation

Detailed list of type and amount of specificingredients used in a polymer compound orresin mixture. The quantities used arebased on parts per hundred polymer, nor-mally abbreviated to phr,where �r� stands forresin, owing to the traditional reference tothermosetting resin systems.

53. Forward Scatter

Represents the scattering of light from thesurface of the medium at the exit side of theincident light flux (see diagram).

Illustrationof forwardandbackward light scattering.

54. Fractal

Amathematical term that is used to charac-terize the features of a fractured surface thatcannot be described by image analysis tech-niques in geometrical terms.

55. Fractography

The visualization, description and interpre-tation of images obtained by examination of

fractured surfaces of polymers, adhesives orcomposites. A very smooth surface denotesthe occurrence of a brittle fracture, while anuneven surface with asperities denotes aductile failure, taking place through local-ized plastic deformations. (See Fracturemechanics.) For the case of fibre compo-sites, the appearance of �clean� fibre frag-ments is a manifestation of poor interfacialbonding.

56. Fracture Mechanics

A branch of science specifically devoted toestablishing the principles and conditionsfor the fracture of products and to measure-ments of the related fundamental proper-ties of structural materials. The concepts offracture mechanics have been developedfrom studies of large plates containing acentral crack of dimensions much smallerthan the plane dimensions of the plate, thatis, a/W� 0, where a is the length of thecrack and W is the width of the plate. Notethat the central crack simulates the effects ofnatural defects in a material, arising duringmanufacture or during its service life. If theplate is subjected to a tensile stress s0, therewill be stress intensification at the crack tipin the way shown.

Stress intensification near a crack tip.

56 Fracture Mechanics j145

56.1 Concept of �Stress Intensity Factor�

If the plate is very thin, the stresses in thethickness direction, sz, are very small and,therefore, do not have any effect on thefracture of the plate. This is known as theplane stress condition, as there are onlystresses acting in the x and y directions ofthe plate. In such a case, the variation of thetwo stresses, sx and sy, with distance fromthe tip of the crack can be related to thedimensions of the crack by

sy ¼ Kffiffiffiffiffiffiffiffi2px

p and sx ¼ Kffiffiffiffiffiffiffiffi2px

p ;

that is,sy¼sx, where x is the distance fromthe crack tip and a is half the crack length.Here K ¼ s0

ffiffiffiffiffiffipa

pis known as the �stress

intensity factor�, and is a factor that com-bines the effect of the size of the crack(defect) and the magnitude of the externallyapplied stress (s0) on the intensification ofthe stress ahead of the crack tip. The con-ditions that give rise to brittle fracture, thatis, catastrophic crack propagation, can beexpressed in terms of the critical stressintensity factor, Kc. For the testing of realis-tic specimens, that is, those with finitedimensions, the equation relating K tostress and geometric factors is written as

K ¼ Ys0ffiffiffia

p;

where Y¼ f (a/W) so that Y ¼ ffiffiffip

pfor

a/W ! 0. This is to say, Y is a geometricalfactor that depends not only on the a/Wratio but also on the manner in which theexternal stress are applied, for example,tension or bending.

56.2 Concept of �Strain Energy ReleaseRate�

A rectangular specimen of an elastic mate-rial containing a single edge notch (SEN),subjected to a load, will store energy (U)equal to the area under the load–deflection(P versus D) curve. that is, U ¼ 1

2PD. From

the definition of specimen compliance, C¼D/P, the equation becomes U ¼ 1

2P2C.

Load and stored energy at constant deformation D

for specimens at two different crack lengths.

If the crack extends from an originalvalue a1 to a value a2, at constant deforma-tion (as in the diagram), therewill be releaseof energy DU, which will make the loadacting on the specimen drop from the origi-nal P1 value to a new P2 level. The specificenergy released from the specimen as aresult of the crack extension is DU/B(a1�a2), where B is the specimen thickness andB(a1� a2)¼BDa (crack extended area). Ifthe crack extension (a1� a2) is infinitesi-mally small, then the associated energyrelease rate will also be infinitesimallysmall, and the ratio dU/B da is known asthe �strain energy release rate�, G. Note thatthe strain energy release rate,G, can be usedinstead of the surface energy term 2g in theGriffith equation, giving s ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

GE=pap

.Substituting in this equation the expressionK ¼ Ys

ffiffiffia

p, one obtains a relationship be-

tween K and G in the form of K2¼EG. Thevalue of the strain energy release rate,G, canbe related to the load at the point when crackextension begins by

G ¼ P2

2BdCda

;

where dC/da is the rate of increase of thespecimen compliance with crack length.This expression can be readily derived by

differentiating CP¼D (constant) and

146j 56 Fracture Mechanics

substituting in dU/B da. When conditionsare reached for fracture to occur at a cata-strophic rate, the value of the strain energyrelease rate is known as theGc value, that is,the critical value. From the above discus-sion, it can be inferred that the critical strainenergy release rate,Gc, can be measured byrecording the load at which fracture occursfor a particular type of specimen, from aknowledge of the gradient dC/da at any pre-specified value of the crack length. The dC/da value is obtained from a calibration curveof the variation of the compliancewith cracklength for the same type of specimen andloading conditions as used for the fracturetest. In principle there are three possibletypes of fracture modes, as shown in thediagram.

Fracture modes I, II and III for the evaluation offracture toughness.

Mode I is the most widely used for theevaluation of the fracture toughness ofmaterials. Mode II is sometimes used tomeasure the interlaminar fracture toughnessof composites. Mode III is very rarely used.

57. Fracture Test

Destructive tests to measure the ultimatestrength (stress at fracture) or the fracturetoughness of a material. The strength ismeasured either on rectangular specimensfor tests in three-point bending (flexuraltests) or using dumbbell-shaped specimensfor the case of tensile tests. (See Brittlestrength.) Compression tests to measure

strength are more widely used for high-performance composites than for conven-tional moulded polymer specimens. In allthese cases the tests are carried out at lowdeformation rates using universal tensiletesting machines. Fracture toughness ismeasured both at low deformation rates,using the same equipment, or at high speed,using pendulum or falling-weight (balldrop) testing equipment. (See Charpyimpact strength.) In these tests one usuallymeasures an empirical property, such as theultimate tensile strength (stress at break) orthe impact strength in terms of a specificenergy to fracture (i.e. fracture energyrecorded divided by cross-sectional area ofspecimen). With the introduction of frac-ture mechanics in the field of polymers inthe 1970s, fracture tests have been adaptedto measure fundamental parameters, suchas Kc and Gc, instead of other empiricalparameters. (SeeFracturemechanics.) Testsat low speeds are carried out with the aid ofcompact rectangular specimens, as shown.

Single edge notch (SEN) specimens and loadingmodes in fracture toughness tests.

The Y values required to calculate Kc

are obtained from the solution of a generalpolynomial

Y ¼ C0�C1ða=wÞþC2ða=wÞ2�C3ða=wÞ3 þC4ða=wÞ4:

The values of the constants C0, C1, C2, C3

and C4 are obtained either experimentallyor theoretically, assuming linear elastic

57 Fracture Test j147

behaviour. For the specimens shown, thevalues of the constants are given in the table.

Specimentype C0 C1 C2 C3 C4

Tension(compact)

1.99 �0.41 18.70 �38.48 53.85

Three-pointbending(L/W¼ 8)

1.96 �2.75 3.66 �23.98 25.22

Three-pointbending(L/W¼ 4)

1.93 �3.07 14.53 �25.11 25.80

The specific equations for Kc can be writ-ten directly in terms of the recorded fractureload Pf, knowing s for the appropriate test.

. Tests in tension:

s0 ¼ Pf=BW;

therefore

Kc ¼ YPf

BW

ffiffiffia

p:

. Tests by three-point bending:

s0 ¼ 23PfBW

2=L;

therefore

Kc ¼ 3YPfL2BW2

ffiffiffia

p:

57.1 Pendulum Test

SEN rectangular specimens, shown on theright-hand side of the previous diagram, canalso be used in Charpy and Izod tests tomeasure the fracture toughness of a mate-rial in terms of its Gc value. (See Charpyimpact strength and Fracture mechanics.)With this approach, the energy recorded tofracture specimens (U) with different cracklengths is recorded and plotted against theproduct fBW, where f is a geometricalcalibration factor that depends only on the

a/W ratio and on the span-to-thickness(S/W) ratio, as shown in the diagram.

Variation of factor f with a/W ratio at three S/Wratios in three-point bending tests. Source: Plati andWilliam (1973).

The plot of the energy recorded to frac-ture specimens of different crack lengthsagainst the product fBW gives a straightline. The slope of the straight line producedcorresponds to the Gc value of the material,that is, U¼GcfBW. This equation isderived from the definition

G ¼ P2

2BdCda

by letting

f ¼ CdC=dða=WÞ

� ��1

;

where C is the compliance of the specimenat a specific a/W ratio. The values of f canbe obtained experimentally or can be calcu-lated theoretically assuming linear elasticbehaviour for the material tested.A typical plot for the calculation of Gc

from Charpy or Izod impact tests is shownin the diagram. The straight line obtainedfrom the plot does not go through the ori-gin, as the energy recorded by the instru-ment also includes the energy used to pro-pel the specimen after fracture (i.e. the valueof the energy at the intercept), which isconstant and independent of crack length.(See Pendulum impact test.)

148j 57 Fracture Test

Plot obtained fromCharpy impact tests on a PMMAcast sheet. Source: Plati and William (1973).

57.2 Falling-Weight (Ball Drop) FractureTests

In these tests, a sheet or disc is rested on acylindrical support. A striker, or projectile,with a hemispherical tip is dropped from agiven height on the sheet at themidpoint, asshown.

Sketch of the falling-weight (ball drop) impact test.

The evaluation of the impact strength ofthe material is carried out either by the�staircase method� or on a �probability offailure� basis at several levels of input ener-gy, known as the �probit� method. The stair-case method consists of starting with acertain energy level (U¼mgh) and examin-ing whether or not this is sufficient to causefracture of the sheet.With the �probit�meth-od, a number of specimens (usually 10) aresubjected to impact at each of a series ofinput energies, and the fraction of speci-mens that have fractured at each level isrecorded. These values are plotted againstthe input energy level, and the value that

corresponds to 50% failure is used as theimpact strength of the sheet. If a sufficientlylarge number of specimens is tested and thenumber of levels of input energies is realis-tic (at least five), the failure distributioncurve should be of Gaussian type. Conse-quently, the plot of �per cent failures� versus�energy input� gives a sigmoidal curve. Themedian of the fracture energy (the so-calledF50 value) gives a measure of the impactstrength.

Probit plot for falling weight impact tests.

Nowadays most falling-weight apparatusare fitted with a load cell at the striker so thatthe force can be measured directly duringthe event and the energy can be computedfrom the area within the force–deformationcurve recorded. The deformation is normal-ly calculated from the velocity of the striker,assuming that it remains constant duringthe test. A typical force–deflection tracerecorded in falling-weight impact tests isshown.

Typical force–deformation curve recorded in aninstrumented falling-weight impact tester. Source:Ehrenstein (2001).

57 Fracture Test j149

The trace identifies thepeak load,which isnormally assumed to correspond to crackinitiation, and the rapidreduction in the loadduring the penetration of the indenter. Therespective areas under the curve are alsorecorded and act as empirical parametersfor the fracture toughness. The instrumentcan also be used for measuring the funda-mental fracture toughness parameters, Kc

andGc, by using notched rectangular speci-mens tested in a cantilever mode, as in Izodtests, or in a three-point bending mode, asexplained forCharpy tests. (SeeFracture testand Fracture mechanics.)

58. Free Radical

Chemical species containing an �odd�(unpaired) electron, formed by the symmet-rical splitting of a covalent bond. Freeradicals are very reactive, and for this reasonthey are used widely as initiators for poly-merization. They are, however, also thecause of the rapid degradation reactionsinduced thermally or by UV light.

59. Free-Radical Polymerization

The reaction or process leading to the for-mation of high-molecular-weight polymers(thermoplastics) or networks (thermosets)from unsaturated monomers or oligomersvia an �addition� mechanism. Polymeriza-tion takes place in three stages.

Step 1. Initiation: The initiator (usually per-oxides or azo-bis-isobutyronitrile, AIBN)decomposes to produce two free radicals,which add on to a double bond of themonomer(s) or oligomer molecules to startthe polymerization, for example,

ROOR ! 2RO. (peroxy radical) and then

RO. þ H2C¼CHX ! ROH2C�CHX.

(growing radical)

Step 2. Propagation:

ROH2C�CHX. þ nH2C¼CHX ! RO(H2C�CHX)nþ 1

. (high-molecular-weightchains)

Step 3. Termination: This represents thecessation of growth of the polymer chainsthrough the extinction of free radicals, thatis,

RO(H2C�CHX)n. þ RO(H2C�CHX)n�1

.

! RO(H2C�CHX)n(XHC�CH2)n�xOR(combination)

or

RO(H2C�CHX)n. þ .(XHC�CH2)n�xOR

! RO(H2C�CHX)n�H2C¼CHX þ(XHC�CH2)n�xOR (disproportionation)

However, termination often takes placethrough reactions of a growing polymerchain with other active species present,sometimes the solvent or additives useddeliberately to control the size of polymermolecules. Other side reactions are alsolikely to take place alongside the propaga-tion and termination reactions. In anycase, a feature of free-radical polymerizationis the presence of both original monomer(s)or oligomer at all times until the total con-version takes place. The use of mixtures ofmonomers results in the formation of ran-dom copolymers, whose composition de-pends on the relative reactivity of the mono-mers present and varies during the course ofthe polymerization reactions.

60. Free Volume

The volumetric fraction of spaces within thebulk of a polymer that is not occupied bymolecular chains. These spaces are formedby the vibrational motions of segments ofthe polymer chains. The concept of freevolume is used to explain the more rapidvolumetric expansion taking place at tem-

150j 60 Free Volume

peratures above the Tg (glass transitiontemperature). The value of the free volume( f ) increases linearly with temperature, T,according to the equation

f ¼ f0 þaðT�T0Þ;where a is the expansion coefficient andsubscript 0 denotes a reference point. AboveTg, the value ofa ismuchhigher than that ofthe polymer in its glassy state.

61. Friction Coefficient

A parameter that denotes the resistanceoffered by the surface of a material to thesliding, or rubbing, action of a contactingobject. The diagram shows the forces in-volved in defining the friction coefficient.From these, it is clear that the force Pproduces a compressive stress (s¼P/A) atthe contact surface, while the drag force Fsproduces a shear stress (t¼Fs/A), where Ais the contact area. The coefficient of friction(m) is defined as m¼ t/s.

Forces involved in friction phenomena.

From the diagram, it can be observed thatthere are two coefficients of friction, a staticcoefficient (ms), related to the forces in-volved in starting the sliding action, andanother, known as the dynamic coefficientof friction (md), for situations where theforces considered are those involved in themovement of the sliding object. The latter isthe parameter most widely used for com-parison and design purposes. Themd valuesare usually slightly higher than the ms va-lues. The coefficient of friction of a polymeris dependent not only on temperature butalso on the sliding velocity and the magni-

tude of the load exerted on the object. Thecoefficient of friction measured at roomtemperature for the more common engi-neering polymers is around 0.2, with theexception of polytetrafluoroethylene(PTFE), for which the m value is about0.04–0.05.

62. Fringe Micelle Crystal

(See Crystalline polymer.)

63. Fumed Silica

Very fine amorphous silica particles withhigh surface area and high purity, obtainedby precipitation from a sodium silicatesolution through acidification. Used primar-ily as an antiblocking additive for films. (SeeFiller.)

64. Functional Filler

Fillers used in polymers to modify proper-ties other than mechanical properties.Typical functional fillers are fire retardants,antitracking fillers and conductive carbonblacks.

65. Functional Polymer

Polymers exhibiting �special� characteris-tics, such as intrinsic electronic conductivityand piezoelectric behaviour.

66. Functionality

A term that denotes the number of reactivegroups or atoms present in reagents, suchas monomers, oligomers, resins or hard-eners. For instance, a monomer such asethylene or styrene has a functionality equal

66 Functionality j151

to 2 insofar as the double bond can open toform two free radicals or two ions, whichcan react to produce linear polymers. Areagent such as triethylenetetramine,

NH2 � CH2CH2 � NH� CH2CH2�NH� CH2CH2 � NH2;

on the other hand, has a functionality equalto 6, as there are six active hydrogen atomsin the amine functionality, capable of pro-ducing macromolecular networks with ahigh cross-linking density when used as ahardener for epoxy resins.

67. Functionalization

A chemical reaction that introduces func-tional groups (reactive groups) into a poly-mer, resin or oligomer.

68. Fundamental Property

Refers to a property defined and derivedfrom fundamental principles. The valuequoted for a fundamental property is inde-pendent of the test method used and of thegeometry of the specimens used in the test.

69. Fungicide

An additive used to depress the growth ofmicroorganisms. (SeeAntimicrobial agent.)

70. Furan Resin

Resins produced from condensation reac-tions of furfuryl alcohol in the presence ofan acid catalyst to produce linear oligomers.

These oligomers can cross-link via con-densation reactions in the presence of astrong acid to form a three-dimensionalnetwork.

71. Fusion Promoter

An additive used particularly in rigid PVCformulations in order to accelerate the fu-sion (melting) of particles in the screwchannels of an extruder or injection mould-ing machine. Fusion promoters are alsoknown as processing aids.

152j 71 Fusion Promoter

G

1. Gate

A small channel for the transfer of the meltfrom the runners to the cavities of a mould.Different types of gates are shown hereschematically. (See Runner.)

Various types of gates used for the inlet of polymermelt into the cavity of an injection mould.

2. Gear Pump

Apumpfitted between the barrel and the dieof an extruder to increase the output and toprevent surging and irregular output. Gearpumps are used primarily for the extrusionof low-viscosity melts in the production offibres and films. A schematic illustration isshown.

Positioning of a gear pump between screw tip anddie. Source: Muccio (1994).

3. Gel

Describes the state of a polymer solution, aresin or an organic–inorganic hybrid that isintermediate between a solid and a liquid.Although the viscosity of a gel tends toinfinity (the fluid loses its ability to flow),a gel is highly deformable. Gels consisting

of mixtures of polymer and solvent, or poly-mer and plasticizer, are known as �thermo-reversible� gels, which denotes their abilityto go from the solid to the liquid state bychanging the temperature. Gels derivedfrom cross-linked polymers are called�thermo-irreversible� gels owing to theirinability to go back to a liquid state byincreasing the temperature. The term �gel�is also used to describe hard particles foundin films, consisting of domains of cross-linked polymer, which are responsible fordefects usually known as �fish eyes�. (SeeFish eye.)

4. Gel Coat

A term used to describe the coating of glass-reinforced plastic (GRP) hand-layup lami-nates produced by covering the inner sur-face of themould prior to spraying the resinand the chopped glass rovings. Gel coats areusually based on resins that cure to a toughcoating, and normally contain all the addi-tives required to impart the required surfacecharacteristics to the laminates, such aspigments, UV absorbers and antifoulingagents.

5. Gel Permeation Chromatography (GPC)

A technique used to measure the molecularweight and molecular-weight distributionof polymers, which is also known as sizeexclusion chromatography (SEC). (SeeMolecular weight.)

6. Gel Time (or Gel Point)

Denotes the time taken for a thermosettingresin to assume the characteristics of a gel,


j153

through the formation of cross-links. The�gel state� represents the transitional statebetween solid and liquid,which is identifiedby the point at which flow ceases as a resultof the very rapid increase in viscosity. Asketch of a typical curve representing thechange in viscosity with time for a liquidthermosetting system is shown.

Change in viscosity with time for a typical thermo-setting system. Source: Goodman (1998).

The initial decrease in viscosity resultsfrom an increase in temperature, arisingfrom the exothermic nature of the reactions.The subsequent mild increase in viscositytakes place via the formation of isolatedregions of highly branched or lightlycross-linked nuclei dispersed in the fluid,forming a �sol�. As the number and dimen-sions of these domains increase, a stage willbe reached at which they become immobi-lized and produce a �gel�, which is mani-fested as a very sudden and rapid increase inviscosity (gel point). The time required bythe system for this to happen corresponds tothe �gel time�. A fundamental definition of�gel time� can be derived from considerationof viscoelasticity principles under dynamic(cyclic) loading conditions. In these situa-tions, it is possible to carry out the analysisin terms of either the complex shearmodulus (G* ¼G0 þ iG00, where G00 is theviscous component) or the complex

viscosity (h* ¼h0 � ih00, where h00 is theimaginary viscosity associated with themeltelasticity component, that is, h00 ¼G0/v).The change that takes place in cross-link-able systems, from a liquid to a solid-likestate, can be envisaged to have reachedthe transition point (gel point) for condi-tions in which G0 ¼G00 or h0 ¼h00 or tand¼G00/G0 ¼h00/h0 ¼ 1. (See Viscoelasticbehaviour, Dynamic mechanical thermalanalysis and Complex compliance.)

7. Gelation

The event that leads to the formation of a gelfrom a liquid. This term is also used in PVCtechnology to denote the fusion of particleswithin the screw channels of an extruder orinjection moulding machine, as well as theconditions achieved by a PVC paste in thefirst stage of a manufacturing process.

8. Gibbs Free Energy

Also known simply as free energy (G). It is aparameter of the second law of thermody-namics that defines the relationship be-tween the internal energy (E) of a systemand its entropy (S), that is G¼E�TS,where T is the absolute temperature (kel-vins). The concept is widely used in polymerscience to determine whether certain phe-nomena are likely to occur. These includedeterminations of the solubility of a poly-mer in a solvent or the miscibility of aparticular combination of two polymers. Itis used as well to characterize the physicaltransitions of polymers resulting fromchanges in temperature.

9. Glass Bead

Thesearehollowbeads,sometimesknownasmicrospheres orBallotini spheres, capable of

154j 9 Glass Bead

providing apparent densities ranging fromthat of solid glass around 2.3 g/cm3 down to0.1 g/cm3.Mostlyproduced fromachemical-ly inert variety of silica–alumina glass.

10. Glass Fibre

Fibres used primarily for the production offibre-reinforced polymers. Glass fibres areusually made from E glass, which has thefollowing composition: silicon dioxide,53%; calciumoxide, 21%; aluminiumoxide,15%; boron oxide, 9%; magnesium oxide,0.3%; and other oxides, 1.7%. The structureis basically a lime–alumina–borosilicateglass consisting of a three-dimensional net-work of silica and other oxides. The letter Eoriginates from the original designation for�electrical grade� for its superior electricalproperties compared to ordinary alkali glass(A glass). There is also considerable use of Sglass fibres (the letter S stands for �strong�)for the production of high-performancecomposites owing to their higher modulusand higher strength than E glass fibres.Another variety, known as C glass fibres(C stands for �chemically resistant�), issometimes used for applications requiringstronger resistance to strong acids and alka-lis. (See Composite.) Glass fibres have amonolithic amorphous structure as shownin the micrograph.

Typicalmonolithic structure of a glass fibre. Source:Ehrenstein (2001).

The commercial grades are coated with athin layer (about 0.3–0.5 mm) of a �size� toenable them to be handled during their

production and the manufacture of compo-sites. (See Size.) The diameter of glassfibresvaries according to applications, from about6mm to about 20mm.

11. Glass-Filled Polymer

Polymers reinforced with short glass fibres.(See Composite.)

12. Glass Flake

A platelet type of filler, usually made fromchemically inert C glass, with a thicknessaround 3mm and lateral dimensions of0.5–3mm. Glass flakes are widely used incoatings to provide barrier characteristicsand chemical resistance to acids and alkalis.

13. Glass Transition Temperature

Also known as the glass–rubber transition(Tg), represents a reference temperature forthe transition from the glassy state to therubbery state. The Tg is thermodynamicallyclassified as a second-order transition. (SeeDeformational behaviour.)

14. Glassy State

This is the state of polymers at temperaturesbelow the glass transition temperature. Inthe glassy state, the polymer acquires itshighest achievable Young�s modulus, usu-ally around 3GPa. (See Deformationalbehaviour.)

15. Gloss

A property that denotes the shiny appear-ance of a surface, which is defined as theratio of the intensity of light reflectedwithin

15 Gloss j155

a certain angle from a surface (usuallyaround 45�) to the incident light.

16. Graft Copolymer

Ablock-type copolymer inwhich the secondcomponent emerges as a side chain fromthe backbone of the host polymer.

17. Graphene

The name for the structural sheet units ofgraphite lying in parallel planes at approxi-mately 0.334 nm distance, separated byelectrons in p–orbitals. The grapheneplanes are staggered as shown.

Stacking of graphene structural units in graphite.Source: Bell et al. (2006).

18. Graphite

A crystalline form of carbon characterizedby a graphene layered structure found in

carbon fibres. (See Carbon fibre andComposite.)

19. Griffith Equation

An equation that relates the strength (s*) ofa brittle material to the size of internalcracks and to the intrinsic properties of thematerial, respectively, the surface energy (g)and Young�smodulus (E). For a thin infiniteplate containing a central crack (a), theGriffith equation is usually written in theform

s* ¼ffiffiffiffiffiffiffiffiffiffi2g Epa

r;

where a is the length of the central crack.(See Fracture mechanics.)

20. Gum Stock

The mixture of elastomer with all auxiliaryingredients and additives before curing.

21. Gutta Percha

A natural polyisoprene rubber. (See Naturalrubber.)

156j 21 Gutta Percha

H

1. Halogenated Fire Retardant

These arefire retardant additives containingeither bromine or chlorine. (See Flameretardant.)

2. Hardener

The component of a resin mixture used toproduce the network in cross-linked poly-mer products, normally known as thermo-sets. (See Epoxy resin.)

3. Hardness

An empiricalmechanical property denotingthe resistance of a polymer to the penetra-tion of a sharp device made from a materialwith amuch higher Young�s modulus, suchas ametal, glass or ceramic. In standard testmethods, the hardness is numerically ex-pressed in arbitrary units specifically de-rived from the method used.Themost widely used standard testmeth-

ods formeasuring the hardness of polymersare the Shore hardness (scales A and B) forsoft polymers and the international rubberhardness (IRH) for elastomers, both ofwhich use a needle penetration device.For rigid polymers, the most widely used

methods are the Rockwell hardness (scale R,L,MandE) and the Brinell hardness, both ofwhich use a sphere penetration approach toassess the resistance to indentations.Widelyused by research workers is the Vickershardness, which is based on the penetrationof a diamond-shaped indenter. Thehardnessvalue is expressed in terms of the load re-quired to induce a specified amount of pen-etration of the �indenter� from the surfaceinto the bulk of a specimen.For surface coatings, the hardness is of-

ten measured by the �pencil� test, which

identifies the minimum pencil hardnessthat can cause a scratch on the surfaceunder specified conditions. More recently,nano-indentometers have been developedto measure the hardness in a manner simi-lar to the Vickers method using a very fineindenter subjected to very small loads.

4. Haze

An optical property of polymer products,such as films, that describes the milky ap-pearance resulting from the forward scatter-ing of light from the surface at angles withinthe range of 2.5–90�. For this reason, haze isoften referred to as �multi-angle scatter�,defined as the fraction of the total transmit-ted light. The scattering of light from thesurface of films is usually attributed to sur-face irregularities resulting from the forma-tion of spherulitic crystals. This is confirmedby the photograph,which shows an image oftext seen through a polyethylene film exhi-biting haze. The details of the print increaseconsiderably in the central area of the filmcoveredwith a drop of cassia oil owing to thegood match in refractive indices of the twomedia, which prevents the scattering of lightfrom the surface of the film.

Evidence for the association of haze with surfacelight scattering. Source: Ross and Birley (1974).


j157

5. Head-to-Head

A termused in polymerization to denote theformation of a chemical bond between twofree radicals attached to the side containinga bulky group (a position), such as in sty-rene or vinyl chloride, for example,

ClCH�CH2�ClCH�CH2

�CH2CHCl�CH2CHCl�This type of reaction takes place primarily

as chain-to-chain recombination or termi-nation reactions.

6. Head-to-Tail

A termused in polymerization to denote theformation of a chemical bond between afree radical at the end of a growing polymerchain containing a bulky group, such as instyrene or vinyl chloride, and the unhin-dered end of a monomer molecule, so thatthe resulting polymer chain will have alter-native heads and tails, for example,

�CH2CHCl�CH2CHCl�CH2CHCl�

7. Heat Build-Up

A term used in the rubber industry todenote the conversion ofmechanical energyinto heat under cyclic loading conditions.(See Loss angle.)

8. Heat Distortion Temperature (HDT)

An empirical parameter that denotes theresistance of a polymer to deformations athigh temperatures. It is measured by stan-dard three-point bending methods on speci-mens immersed inaninert liquidandheatedat a constant heating rate. The central deflec-tionisplottedasafunctionofthetemperatureand the HDT value is registered as the tem-perature at which a certain specified deflec-tionisreached.Thevaluesfortheappliedload

and the target deflection are determined bythe specific standardmethod, usually 1mm.

Typical HDT apparatus: A, heating liquid; B, testspecimen; C, applied load;D, deflectionmonitoringdial gauge; E, thermometer; F, stirrer. Source:Unidentified original source.

9. Heat Setting

An operation carried out on filamentaryproducts after they have beendrawn inorderto achieve dimensional stability.Heat settingis carried out by allowing the filaments toretract slightly by the application of heat attemperatures just below themelting point ofthe polymer in order to develop the maxi-mum level of crystallinity through second-ary crystallization and to relax any polymerorientation within the amorphous regions.

10. Heat-Shrinkable Product

Products usually in the form of flexibletubing, tapes or sealable wrappers that willshrink when heated above the glass transi-tion temperature (Tg) for an amorphouspolymer or above the melting point (Tm)for a crystalline polymer. This behaviourderives from the natural characteristic ofthe molecules in oriented polymers, whichare driven by the second law of thermody-namics to assume a random coiled config-uration to achieve the most stable high-entropy state. In practice, the polymer isusually slightly cross-linked to convert theminto a rubber at the required shrinkage

158j 10 Heat-Shrinkable Product

temperature, thereby protecting the productagainst damage and loss of dimensions.

11. Heterochain

A polymer chain where the constituentscontain a mixture of carbon and otheratoms, for example, in polyesters, poly-ethers, polyamides and polysulfones.

12. Heterogeneous Blend or Mixture

Ablend ormixture of polymers that consistsof two or more distinct phases. This situa-tion arises when two or more polymers arenot completely miscible.

13. Heterogeneous Nucleation

(See Crystallization.)

14. Heterogeneous Polymerization(or Heterophase Polymerization)

A generic term for polymerization takingplace in a two-phase medium. This termincludes the polymerization of liquidmono-mers in suspension or emulsion in water orsupercritical CO2.

15. High-Density Polyethylene (HDPE)

A polyethylene with density between 0.935and 0.955, which is related to the degree of

crystallinity, usually in the range 0.55–0.70.The higher degree of crystallinity in HDPE,relative to that in the correspondingmedium-and low-density polyethylene grades, isresponsible also for the higher rigidity andlower transparency. (See Ethylene polymer.)

16. High-Impact Polystyrene (HIPS)

(See Styrene polymer.)

17. High-Temperature Polymer

A polymer with a glass transition tempera-ture Tg > 150 �C or a melting temperatureTm > 300 �Cand exhibiting a high resistanceto thermal oxidation to enable it to be usedcontinuously at high temperatures. (SeePolybenzimidazole, Polyimide, Polyketone,Polysulfone, Poly(phenylene sulfide) andPoly(amic acid).)

18. Hindered Phenol

Type of antioxidant based on phenol com-pounds in which the ortho and para posi-tions are occupied by tertiary butyl groups toproduce a hydrogen-free carbon atom in thearomatic ring. This is to stabilize the freeradical formed on the phenolic oxygen afterthe hydrogen atom has been abstracted inthe reaction with a free radical on the poly-mer chains formed through degradationreactions. The mechanism is illustrated.

Mechanism for the free-radical quenching byphenolic antioxidants.

18 Hindered Phenol j159

19. Homogeneous Blend

A blend of polymers exhibiting only onephase at microscopic level. This situationarises when two or more polymers arecompletely miscible.

20. Homopolymer

A polymer containing only one monomericunit along the molecular chains.

21. Hooke�s Law

Alaw thatdescribes the relationshipbetweenthe applied force and the resulting deforma-tion of an elastic material. Accordingly, thedeformation is directly proportional to theapplied force, normally referring to forcesacting in tension or compression. Hooke�slaw forms the basis onwhichYoung�smodu-lus is defined by converting the force into therelated stress and the deformation into therelated strain. (See Elastic behaviour.)

22. Hot-Melt Adhesive

(See Adhesive.)

23. Hot Runner Mould

An injection mould in which the runnerregion of the mould is kept hot by externalheaters in order to prevent the containedpolymer from solidifying along the actualmoulded part. The ejected moulded partdoes not contain the usual sprue, therebyreducing the amount of polymerwaste. (SeeGate and Runner.)

Example of hot runner mould used for injectionmoulding of thermoplastics. Source: McCrum et al.(1988).

24. Huggins Constant

A constant in the relationship betweenthe intrinsic solution viscosity and theviscosity number, used in the determina-tion of the molecular weight of polymers,that is,

ðh2�h1Þ=h1c ¼ ½h� þ kc;

where k¼ k0[h]2 and k0 is known as theHuggins constant, with values between0.3 and 0.4. (See Molecular weight.)

25. Hundred-Percent Modulus (100%Modulus)

The tensile modulus of a rubber or elasto-meric material calculated by taking the val-ue of the nominal stress at 100% extensionin the force–extension curve.

160j 26 Hundred-Percent Modulus (100% Modulus)

26. Hydrogen Bond

The strong physical interaction between twogroups from adjacent molecules or seg-ments. These involve the attraction of ahydrogen atom chemically linked to anelectronegative atom (usually N, O or halo-gen) from onemolecule with an electroneg-ative atom from another molecule. Hydro-gen bonds can also occur within a polymerchain (intramolecular hydrogen bonds), asin the case of polyamides, which provide agood example to illustrate how hydrogenbonding can affect the properties and be-haviour of polymers. In this case, a stronginteraction occurs between the hydrogenatom of the amide group of one molecularsegment and the carbonyl group of theamide groupof anothermolecular segment.These interactions are responsible for thehigher melting point of polyamides relativeto that of polyesters with similar structure.One notes that the absence of such hydro-gen atoms in the polyester chains can onlyprovide polar attractions, which are weakerthan hydrogen-bonding interactions.

27. Hydrolysis

The process by which chemical bonds with-in a polymer chain, or macromolecularnetwork, are broken by the action of water.Hydrolysis is, therefore, the reverse ofcondensation. (See Condensation reaction.)When hydrolysis takes place within thepolymer chains, as in the case of polyesters,polyamides, polyurethanes and polyimides,hydrolysis brings about a decrease in themolecular weight of the polymer, whichcauses a deterioration in mechanicalproperties.

28. Hydrolysis Stabilizer

Additives used to enhance the stability of ahydrolysable polymer, such as polyesters or

polyurethanes, against degradation broughtabout by hydrolysis. The more widely usedhydrolysis stabilizers are based on stericallyhindered polycarbodiimides, which can re-act with water, according to the scheme:

In the case of polyesters, the polycarbo-diimide stabilizer can react also with anycarboxylic acid groups present at the end ofthe chains, thereby reducing their catalyticactivity on the rate of hydrolysis. The reac-tion of carbodiimides with carboxylic acidtakes place according to the scheme:

29. Hydrophilic

A substance that attracts water, behaviourthat is driven by the formation of hydrogenbonds between water molecules and highlypolar groups in the substance.

30. Hydrophobic

A substance that does not attract or absorbwater, behaviour arising from the presenceof non-polar groups as in hydrocarbons andespecially fluorocarbons.

31. Hydrostatic Pressure

Pressure applied evenly in all threedirections.

32. Hydrostatic Stress

Tensile or compressive stresses evenly ap-plied in all three directions.

RN C NR + H2O → RNH—CO—NHR————

32 Hydrostatic Stress j161

33. Hydrothermal Stress

Internal stresses created in a product bychanges in temperature.

34. Hydroxyl Equivalent (Number)

Defines the quantity of hydroxyl groupspresent in oligomers, resins or polymers,which corresponds to the weight in gramscontaining one gram equivalent (mole) ofhydroxyl groups.

35. Hygroscopic

Capable of absorbing water, a characteristicrelated to the ability of water molecules toform hydrogen bonds with hydrophilicgroups present in products.

36. Hyperbranched Polymer

Polymers whose chains branch out in threedimensions from a central multifunctionalunit, continuing to form regularly struc-tured branches as the chains grow in suc-cessive steps into highly ramified polymer

molecules. Hyperbranched polymers areusually polyesters or polyamides, or mixedtypes, obtained from condensation reac-tions. Hyperbranched polymers are gener-ally brittle and are used primarily as func-tionalized modifiers for thermosetting res-in systems, producing regions with a well-defined structure and providing featuresthat may give rise to enhanced propertiesand rheological behaviour. An example ofthe structure of a hyperbranched polymer isshown.

Hyperbranched aliphatic polyester produced fromthe polycondensation of bis(hydroxymethyl)propio-nic acid (bis-MPA) with 2-ethyl-2-(hydroxymethyl)-1,3-propanediol (TMP).

162j 36 Hyperbranched Polymer

I

1. Impact Modifier

A general term for an auxiliary component ofa polymer or resin formulation used to in-creasethetoughnessofproducts.Inthecaseofthermoplastics, an impact modifier is incor-porated into a brittle polymer matrix aspre-formed �toughening� particles. The com-position and morphology of the particles aredesigned in such a way as to promote stronginterfacial bondsbetween the tougheningpar-ticles and the surrounding polymer matrix,thus promoting an efficient stress transfermechanism between the two phases. In thisway the localized strain energy resulting fromimpacts can be redistributed through the bulkvia the toughening particles, thereby prevent-ing the formation and propagation of cracks.An example of this �toughening� mechanismis theuseofacrylicorABSimpactmodifiers inrigidPVCformulations. There are, however, anumberof theories thathavebeenputforwardfor the toughening mechanism of polymersand, indeed, more than one mechanism canoperate, depending on the nature of the poly-mer. For HIPS and ABS, for instance, it hasbeenproposed that toughening takesplace viathe formation of crazes through the matrixbetween rubber particles, as amechanism forabsorbing the strain energy (see diagram).

It is possible, however, that the forma-tion of crazes represents a �second-stage�event, which follows the energy absorp-tion mechanism by molecular relaxationwithin the �interphase� regions, consist-ing of miscible domains of the two com-ponents. For thermosetting resins, theparticles that bring about the tougheningof the matrix are generated in situ throughthe addition of specially designed oligo-mers that react with the resin and hard-ener. The rubbery particles are nucleatedbefore �gelation� of the resin takes placeand grow into larger particles as a resultof the migration of reactive species fromthe surrounding resin mixture. Thegrowth of precipitated particles ceaseswhen the surrounding matrix �gels�through the formation of a continuousnetwork. The infusion of reactive species,such as the hardener, from the surround-ing resin into the precipitated particlesmay nucleate the formation of other par-ticles, which remain quite small owing tothe constraints imposed by hardening ofthe matrix surrounding the larger particleagglomerates. (See Epoxy resin and Phaseinversion.)

2. Impact Strength

Denotes the resistance of a material toimpact loads, normally expressed in termsof the energy required to induce fracture ofspecific specimens. In this respect the term�strength� is a misnomer insofar asstrength normally denotes the value of thestress (force per unit area) required tofracture a specimen. Impact strength isusually measured with the use of pendu-lum equipment or by falling-weight meth-ods. (See Impact test, Fracture test andFracture mechanics.)

Crazes formed between dispersed particles of ahigh-impact polystyrene sample. Source: Unidenti-fied original source.


j163

3. Impact Test

Tests carried out by delivering loads at veryhighspeed.(SeeCharpyimpactstrength,Izodimpact test and Falling-weight impact test.)

4. Induction Time

A generic term used to denote the delaytime for the start an event or process. Threespecific examples of induction time experi-enced in polymer systems follow.

a) Degradation and stabilization The oxy-genuptake of a polyolefin sample can bemeasured prior to reactions that lead tothe formation of carbonyl groups in thechains, induced thermally or by theaction of UV light. The efficiency of astabilizer can, therefore, be assessed interms of the increase in induction timethat it brings about in a sample, asillustrated in the diagram.

Evolution of combined oxygen with ageing time.

b) Inhibition of polymerization The in-hibition of polymerization or curingreactions by free radicals can beachieved using quinone. Very smallamounts of inhibitor are added to anunsaturated monomer or oligomer toreact with the initial free radicals byexposure to light and/or oxygen inorder to convert them into inactiveradicals. (See Antioxidant.) In this re-spect, inhibitors must bedistinguished from retarders, whichdecrease the rate of reactions rather

than increasing the induction time forthe reaction to take place.

c) Liquid and gas absorption Solvent canbe taken up by a glassy polymer samplevia a case II diffusion mechanism. Thediagram shows the absorption of tetra-hydrofuran (THF) in three samples of�modified� epoxy resin systems. The toptwo curves refer to a homogeneousglassy structure, the second relating tothe same resin containing pre-formedsilica particles. In both cases absorptiontakes place without an induction time.On the otherhand, in the third sample, adistinct induction time and a large re-duction in total amount of absorbedTHF are observed. There, the silica wasformed in situ as three-dimensional do-mains, which represents a typical struc-ture of organic–inorganic hybrids. (SeeOrganic–inorganic hybrid.)

0 20 40 60 80 100

0

10

20

30

40

50

60

70

80

Immersion time in THF (Days)

Epoxy Resin-A1170 Epoxy Resin-A1170 + 15% SiO2 (Pre-Formed)

H - A1170 - 15% SiO2 (Sol-Gel)

Wei

ght i

ncre

ase

(%)

Solvent uptake of an epoxy–silica hybrid. Source:Prezzi (2003).

5. Infrared Spectroscopy (IR or FTIR)

An analytical technique, known also as vi-brational spectroscopy, used to identify spe-cific chemical groups. The technique de-tects the transition between energy levelsin molecules resulting from vibration ofinteratomic bonds within a chemical group.At low temperatures, molecules exist intheir ground vibrational state. Therefore, inorder to bring them to a higher energy state,it is necessary for them to absorb energy

164j 5 Infrared Spectroscopy (IR or FTIR)

from the surroundings. In vibrational spec-troscopy, this is done by subjecting a sampleto electromagnetic (EM) radiation of a rangeof frequencies (a procedure known as scan-ning), and monitoring the intensity of thetransmitted radiation. Chemical groupswillabsorb energy at specific frequenciesthrough resonance with the natural vibra-tions of the constituent atomic bonds,so that they can be identified through acalibration procedure, which involves scan-ning a compound of known composition.For a standard IR analysis, the wavelengthof the EM radiation is in the range2.5–25mm, corresponding to a frequencywith wavenumber 4000–40 cm�1. (Notethat the wavenumber in cm�1 is equal to104/wavelength inmm.) The spectral posi-tion of the most common chemical groupsin polymers that can be characterized by IRspectroscopy is indicated in the diagram.

Some spectrometers operate in the near-infrared (NIR) region 0.7–2.5mm (4000–1400 cm�1) and others in the far-infrared(FIR) region 50–800mm (200–12 cm�1). Atypical IR spectrumobtained fromapolymersample is shown.

Typical infrared spectrum of a polymer.

In order to speed up the calculationsrequired to process the acquired data, amathematical technique, known as Fouriertransforms, is often used in the software.The technique is referred to as Fouriertransform infrared (FTIR) spectroscopy.

6. Inhibitor

An additive used to reduce the susceptibilityof reactive species, such as monomers andresin–hardener mixtures, to undergo poly-merization reactions during storage. Thefunction of an inhibitor is to react with anactive radical to give products with muchlower reactivity.Aclassical inhibitor for free-radical polymerization is benzoquinone.Although hydroquinone is often used as amonomer �stabilizer�, it relies on the pres-ence of oxygen to be transformed into an

inhibitor through oxidation to quinone. Ineffect, the inhibitor increases the inductiontime for the onset of propagation reactions.

7. Initiator

Anadditive thatstarts thereactions leadingtopolymerizationornetwork formationinfree-radical reaction systems. (See Free radicaland Peroxide.)

8. Injection Blow Moulding

A moulding technique for the productionof containers, consisting of two separate

Spectral position, as absorption wavenumber (cm�1), for (CC) and (CX) valencyvibrations. Source: Kampf (1986).

8 Injection Blow Moulding j165

processes: respectively, the production ofthe �pre-form� by injection moulding, andthe subsequent �blowing� operation into thefinal dimensions. This allows the blowingprocess to take place under highly con-trolled temperature conditions so that theoptimum level of orientation can be intro-duced in the walls of the containers. Alongitudinal pre-stretching operation is fre-quently used in order to obtain a well-bal-anced degree of biaxial orientation bythe blowing operation. For this reason, theprocess is also known as �stretch–blowmoulding�. The most widely used polymerfor injection blow moulding applications ispoly(ethylene terephthalate) (PET). In thiscase the heating of the pre-forms for theblowing operation is carried out in-line byinfrared radiation to temperatures in theregion of 110–115 �C.

Sequential operations in injection blowmoulding ofbottles: (top) injection moulding of pre-forms;(bottom) stretch–blow operation. Source: Uniden-tified original source.

9. Injection Moulding

A technique used primarily for mouldingthermoplastics. It is carried out by pumpinga melt at high speed (producing shear ratesaround 104 s�1) into the cold cavities of amould, where the polymer is allowed to coolto a suitable temperature before the

moulded parts are ejected from the mould.The ejection temperature is below the glasstransition temperature (Tg) for a glassy poly-mer and well below the melting point (Tm)for a crystalline polymer.The injection process involves three con-

secutive operations carried out in a screw–-barrel assembly similar to that used forextrusion. (See Moulding cycle.) First thepolymer granules or powder are fed from ahopper into the feeding section of the screw.Then melting takes place while the screwrotates, delivering at the same time therequired amount of melt to the front of thebarrel via a non-return valve, which resultsin a pressure build-up in the melt at thenozzle. The screw then stops rotating andcomes forward at high speed, as a plunger,to inject the melt into the cavities of themould through the nozzle of the injectionunit of themachine connected to themouldinlet, via a �sprue�, runners and gates. (SeeRunner and Gate.) A diagram of an injec-tion moulding machine, showing also themould with a hydraulic locking mecha-nism, is shown.

In injection moulding of thermosettingplastics or rubber compounds, themould isat a higher temperature than the barrel inorder to produce fast �curing reactions� afterthe cavity has been filled. The heat generat-ed by friction in the injection unit andduring the flow through the nozzle and thesprue–runner–gate sequence in the mould

Simplified drawing of an injection moulding ma-chine for thermoplastics, showing the plasticizingand injection unit (right), and the mould and hy-draulic locking mechanism (left). Source: Uniden-tified original source.

166j 9 Injection Moulding

brings the temperature to the level requiredfor curing the polymer in the cavities. Ejec-tion takes place while the part is still hotowing to the cross-linked nature of theproduct, which prevents distortion of themoulded part during ejection. The screw,nozzle and mould channels carrying themelt to the mould cavities have to be de-signed in such a way as to prevent curingbefore the melt reaches the cavities. Forthis reason, obstructive features, such as anon-return valve at the front of the screw,have to be excluded. A ram-type injectionunit is sometimes used for compoundsthat are too sensitive to the heating inducedby the shearing action of the plasticizingscrew.There are several variants for the injec-

tion moulding of thermoplastics, two ofwhich are described here.

a) Co-injection moulding This is used toobtain two-layer or three-layer mouldedparts. This technique, also known as�sandwich moulding�, is designed insuch a way as to enable the first shotentering the cavity to form the outerskin of a three-layer structure. After thisevent, the second unit injects the otherpolymer through the same �sprue� ofthe mould, so that the incoming meltwill flow through the central region,pushing the outer layers against thewalls of the mould. The main steps areillustrated schematically.

Principle of co-injection, whereby the second poly-mer (B) drives the first polymer (A) into the outersections. Source: Osswald (1998).

One variant of the co-injection processis gas-assisted moulding, where the in-ner component is a gas (e.g. nitrogen),which �blows up� the molten polymeragainst the cavitywalls to producehollowsections. Another version is the produc-tion of sandwich foamed mouldings,where the inner polymer contains ablowing agent to nucleate the formationof �gas cells� and subsequent expansioninto a foam.

b) Structural foam moulding This con-sists in the rapid injection of a meltcontaining the blowing agent into fair-ly thick section cavities of the mould,whereby the rapid cooling of the meltat the walls of the mould forms a solidouter skin. In this way, foaming isrestricted primarily to the inner sec-tions. (See Foam and Mould.)

10. Insulation

A component of a structure or an electricalcircuit that prevents the escape of energy tothe surroundings. The main type of insula-tion involving the use of polymers are: (a)thermal insulation, which prevents heatfrom escaping through the walls of a struc-ture, and (b) electrical insulation, whichprevents the leakage of current from a cir-cuit. (See Foam, Thermal conductivity andDielectric.)

11. Interaction

This term is often used to describe theattractions between certain groups or atomspresent in polymer chains. Interactions canbe intermolecular (between different mole-cules) or intramolecular types. The strengthof the interactions varies from the weakesttype, known as van der Waals, occurring innon-polar polymers, to the strongest typeinvolving electrostatic forces between

11 Interaction j167

cations and anions, known as ionic interac-tions. Between the two there are dipole–di-pole interactions and hydrogen bonds. Thethree main types of interaction are shownschematically. (See Hydrogen bond, Dipoleand Ionomer.)

12. Intercalation

A term used to describe the insertion ofchemical species into a crystal lattice con-taining empty lattice sites. (See Exfoliatednanocomposite and Nanofiller.)

13. Interfacial Bonding

A term that describes the attractive forcesbetween the surfaces of two different ma-terials in contact with each other. Typicalexamples of interfacial bonding in polymer-based products are in laminates, adhesivesand composites. Although destructive me-chanical tests are usually used to assess theinterfacial bond strength, it is often difficultto discern from the results the relative con-tributions by the bulk of the adhering ma-terial and the actual interfacial bonding. Theinterlaminar shear strength test and lapshear test are described elsewhere. (SeeComposite test and Adhesive test.) An as-sessment of the interfacial bonding be-tween fibres and matrix in composites canbe obtained with the use of dynamic me-chanical tests, in view of the large interfacial

surface area. (See Dynamic mechanicalthermal analysis and Law of mixtures.)Under �perfect� bonding conditions at the

fibre–matrix interface of a composite, thereis no contribution to viscoelastic losses fromthe fibres owing to their elastic nature.

Consequently, the loss component of thecomplex modulus of the composite (E

00c) is

directly proportional to the volume fractionof the matrix (ff), that is,

E00c ¼ ð1�ff ÞE

00m:

For �poor� bonding situations, there will beadditional losses resulting from the friction-al (sliding) movements at the interface,which gives rise to an additional term inthe loss modulus equation, that is,

E00c ¼ ð1�ff ÞE

00m þE

00m-f ;

whereE00m-f represents therelated increase in

loss modulus associated with energy lossesat the interface. By comparing the dynamicmechanical spectrum obtained for the ma-trix component without fibres to that for thecorresponding composites, it is possible tocalculate thetheoreticalvalues forE

00m-f overa

wide temperature range of the spectrum.Any discrepancy between themeasured andcalculated E

00c values can be attributed direct-

ly to interfacial losses. The schematic dia-gram indicates that very poor interfacialbonding can give rise to large values for

168j 13 Interfacial Bonding

E00m-f , particularly at temperatures around

the Tg of the matrix. It follows that thestrength of the interfacial bond can be quan-tified as the difference between the mea-sured E

00c and that calculated from the law

of mixtures for E00f ¼ 0. The larger the dis-

crepancy, the lower the strength of the inter-facial bond.Note that thegeometric arrange-mentof thefibres is expected tohaveaminoreffect on the measured E

00c value.

Effects of descriptive strength of interfacial bond onloss modulus of composites relative to the matrix.Source: Constructed from Mascia (1974).

14. Interfacial Polarization

This term refers to the polarization of di-poles present at the interface between fillerand polymer or between the amorphousand the crystalline domains of a polymer,which results from an externally appliedvoltage. This is often the cause of unexpect-ed higher losses than expected in polymerswith low polarity.

15. Interlaminar Failure

Failures taking place by the breaking of thebond between layers of laminates. (SeeDelamination.)

16. Interlaminar Shear Strength (ILSS)

The stress required to break the bond be-tween fibre layers in continuous-fibre com-posites. (See Composite test.)

17. Internal Energy

The total energy of a material, usually takento be the sum of the thermal energy(enthalpy) and the product of external pres-sure and volume of the material, that is,E¼H þ PV. (See Gibbs free energy.)

18. Internal Lubricant

A long-chain alkyl compound with a hydro-philic terminal group that is miscible withthe polymer at low concentrations and re-duces the melt viscosity. (See Lubricant.)

19. Internal Mixer

The term indicates that mixing takes placeinside a closed chamber for a specific lengthof time.An internalmixer is in effect a batchmixer. (See Compounding and Mixer.)

20. Internal Plasticization

Denotes the lowering of the glass transitiontemperature (Tg) through random copoly-merization with a monomer containingflexible side groups, which results in anincrease in the overall flexibility of the poly-mer chains and greater free volume. (SeePlasticization and Plasticizer.)

21. Internal Stress

A generic term used to denote the stressesthat are set internallywithin a product either

21 Internal Stress j169

during processing or through subsequentageing. Internal stresses normally arisefrom the differential thermal expansion orcontractions between adjacent layersstrongly bound to each other. In injectionmoulding of thermoplastics, the low tem-perature of the mould causes a much morerapid cooling of the outer surface layerthan the inner layers, owing to thelow thermal conductivity of polymers. Bythe time the inner sections are cold enoughfor the moulded part to acquire sufficientrigidity to be ejected, the outer layers willbe subjected to a much lower temperaturedrop than the central section. Accordingly,it is expected that the inner sections wouldundergo a much greater amount of shrink-age than the outer layers, were this notprevented by geometrical constraints. As aresult, the outer layers will be subjected tocompressive stresses and the inner sec-tions will be in tension, as shown in thediagram.

Illustration of development of internal stresses ininjection-moulded articles.

This situation is particularly evident forthe case of crystalline polymers, whichundergo amuch greater volumetric contrac-tion during cooling than glassy polymers. Inaddition to the differences arising purely onthe basis of natural contraction, the fastercooling rate in the outer layers results in alower degree of crystallinity (hence, lower

density) than in the central regions, owingto the direct relationship between degree ofcrystallinity acquired by the polymer andthe cooling rate from the melt state. Theexistence of internal stresses can be verifiedby observations made on samples when theouter layers are removed from one of thesurfaces by machining devices. This causesa previously flat moulding to bow outwardsas a result of the tensile stresses in thecentral regions.In any case, themagnitude of the internal

stresses locked in as �residual stress� isdetermined also by the extent of stressrelaxation taking place while the mouldedpart cools to ambient temperature. In thisrespect, although the differential thermalcontraction for glassy polymers is muchless than for crystalline polymers, theirhigh glass transition temperature reducesthe extent of stress relaxation during cool-ing, which may ultimately result in a largermagnitude of �frozen� internal stresses. Thepresence of metallic inserts in mouldedproducts is another cause for the develop-ment of internal stresses in polymer pro-ducts, owing to the large difference in ther-mal expansion coefficient between the twomaterials. The large shrinkage taking placewithin the bulk of a polymer during cool-ing, especially for the case of crystallinepolymers, creates compressive stresses onthe metal insert, which have to be counter-acted by tensile stresses in the surroundingpolymer area. This can also happen for thecase of thermosetting polymers, as a resultof the large shrinkage that occurs duringcuring. In general, these types of stressesare relatively small in thermoplastic pro-ducts, because of the molecular relaxationsthat take place both during processing andin service.The existence of internal stresses in

moulded products can be examined undera polarizing microscope, owing to the an-isotropy resulting from the small amount ofmolecular orientation of the polymer chains

170j 21 Internal Stress

in the regions of internal stresses. An ex-ample is shown.

Residual stresses in a polycarbonate mouldingviewed through crossed polarizers. Source: Birleyet al. (1991).

22. Interpenetrating Polymer Network(IPN)

A type of network formed in a mixture ofnetworking systems, which consist of twomolecular interpenetrating domains of sub-micrometre dimensions. The nanosized di-mensions of the domains is apparent fromthe transparent appearance of such a net-work mixture, while the heterogeneity ofthe networks is clearly identifiable in dy-namic mechanical and dielectric spectro-grams by the presence of two distinct �loss�or tan d peaks. The chemical interconnec-tion of the two networks is identified by thenarrowing of the distance between thesepeaks relative to those exhibited by theindividual networks in isolation. IPNs canalso be formed by single systems with dif-ferent functionalities capable of producingnetworks by a dual mechanism.

23. Intramolecular

Features and events taking place withinpolymer chains. Examples of these are theintramolecular hydrogen bonds betweenthe chains of polyamide (nylon) molecules

within the lamellae of crystals, which areresponsible for their high melting point.

24. Intrinsic Viscosity

A concept used for determining the molec-ular weight of polymers from measure-ments of the solution viscosity. (See Molec-ular weight.)

25. Intumescent Coating

A coating formulation that forms a carbo-naceous (char) foamwhenheatedup tohightemperatures. This provides a heat barrierfor the substrate, thereby reducing the tem-perature and, therefore, also the rate atwhich the formation of combustible vola-tiles are formed by pyrolysis. A typical intu-mescent formulation will contain: (i) thechar-forming component, usually a poly-hydric alcohol, a polyphenol or a polysac-charide; (ii) a blowing agent, usually dicyan-diamide, melamine, urea or guanidine; and(iii) an acid, such as phosphoric acid or aLewis acid. (See Flame retardant.)

26. Ion Exchange Capacity (IEC)

Ameasureof the total contentofexchangeableions in layered silicate minerals and in ionexchangeresins,expressedasmilliequivalentsof ion per gram of sample (meq [ion]/g). (SeeIon exchange resin and Nanoclay.)

27. Ion Exchange Resin

Cross-linked resins or polymers containingionizable groups attached to the molecularchains. Accordingly they can be anionic orcationic. The anionic groups are usuallySO3

�, whereas the more frequently usedcations are ammonium types. The solidresin, usually in the form of beads, can

27 Ion Exchange Resin j171

exchange ions with those from the sur-rounding solution, for example

M�Aþsolid

þ Bþsolution

>M�Bþsolid

þ Aþsolution

These resins are frequently used to purifysolutions by removing unwanted ions, forinstance, in the deionization of water. Themost common type of ion exchange resinsare based on cross-linked polystyrene, pro-duced from copolymerization of styreneand divinylbenzene. These are subsequent-ly functionalized to produce the ion ex-change capability. Typical structures areshown.

The resin on the left exchanges Hþ

ions with a cations from the surroundingsolution, while the resin on the rightexchanges Cl� ions with different anions,or OH�, from the solution. The originalions in the resin will be regeneratedthrough appropriate treatments, afterthey have been depleted of their originalions.

28. Ionic Conductivity

(See Membrane and Polyelectrolyte.)

29. Ionic Polymerization

A type of polymerization that takes placethroughtheuseofionicinitiators.(SeeAnionicpolymerization and Cationic polymerization.)

30. Ionomer

A term used to describe those polymerscontaining �clusters� of ionic species derivedfrom the partial neutralization of acidgroups dispersed as pendent groups alongpolymerchains. Inadditiontoclusters, thereare also �multiplets� within the surrounding

matrix, consisting of small regions of dis-persed ionic species. The most widelyknowncommercially available ionomers arethose based on ethylene methacrylic acid(about 10–15mol%) copolymers containingsodium or zinc carboxylate clusters. Thechemical structure of the polymeric anionsand the formation of clusters are shown.

Poly(ethylene methacrylate) anion.

172j 30 Ionomer

Ionic clusters of zinc or sodium carboxylate.

It must be noted, however, that not all thecarboxylic acid groups are converted to car-boxylate anions. The presence of ionomericdomains confers to the non-polar polymers(such as polyethylene) better resistance tonon-polar liquid environments (such asoils) and provides a greater elastomericcharacter to ethylene–acrylate copolymers,with improved mechanical properties. An-other case of an ethylene-based ionomer isrepresented by sulfonated EPDM elasto-mers. These contain only about 1mol%sulfonate groups, which act primarily asphysical cross-links and, therefore, make itunnecessary to carry out the usual vulcani-zation step. A quite different family of io-nomers is that based onpolytetrafluoroethy-lene containing ionic clusters of ionizedsulfonic acid (Hþ and �O3S ions), intro-duced along the chain in the form of asulfonated perfluoroether copolymer.These are known commercially as Nafionand are widely used as membranes. (SeeNafion.)

31. Isostrain Conditions

A term used to describe the deformationconditions of two or more contiguousphases under stress, where the magnitudeand type of strain are the same in eachphase. From this it results that the totalstress is the sum of the stress acting on

each phase. These conditions are used tostipulate the upper limits (bounds) for theprediction of the Young�s modulus of lami-nates and unidirectional fibre composites.(See Law of mixtures.)

32. Isostress Conditions

Atermusedtodescribe theconditionsof twocontiguous phases, whereby the magnitudeand typeofstressesare thesame.Fromthis itresults that, formembers undermechanicalstress, thetotalstrainis thesumofthestrainsdeveloped by each phase, so that

«c ¼ w1«1 þð1�w1Þ «2;where w1 is the volume fraction of the high-modulus (reinforcing) phase. (See Law ofmixtures.)

33. Isotactic Polymer

A term used to describe the stereoregularconfiguration of polymers containing sidegroups. (See Tacticity.)

34. Isothermal

Denotes events taking place under condi-tions in which the temperature is constant.The kinetics of chemical reactions or physi-cal phenomena, such as crystallization, areusually carried out to obtain a fingerprint ofthe time evolution of the events monito-red, as well as to determine the relatedrate constants and activation energy. (SeeArrhenius equation.)

35. Isotropic

The state of a product or a specimen whoseproperties are equal in all three directions inspace.

35 Isotropic j173

36. Izod Impact Test

Measurement of the impact strength ofa material using rectangular specimens

clamped as a cantilever and impacted at thefree end by a mass delivered by a swingingpendulum. (See Impact strength.)

174j 36 Izod Impact Test

J

1. J integral

A fracture mechanics term used to denotethe involvement of the loss of potentialenergy from a specimen in relation tomaterial behaviour that does not satisfy therequirements of linear elastic fracture me-chanics (LEFM), that is, a linear relation-ship between force and deformation up tothe point at which fracture takes place. Alack of linearity is often found in situationswhere excessive yielding takes place in thecrack region, so that a curve is generated,instead of a straight line, in the force–deformation relationship. The J integral isdefined as the rate of loss of potentialenergy (U) from a specimen of thicknessB with respect to the increase in cracklength (a), that is,

J ¼ @U=@A�@a ! 0;

where A is the newly formed crack area(A¼Ba). For conditions in which the crackpropagates at constant extension (u), theJ integral can be written as

J ¼ uB@PY

@a;

where PY is the load at the yield point.

For tensile tests on specimens withsuitable dimensions, the equation becomesJ¼U/B(W–a), while for three-point bendingtests, using the appropriate specimen geom-etry, the equation is J¼ 2U/B(W– a), whereU is the total energy involved in the fractureof the specimen (area under the force–deformation curve) and W is the specimenwidth. When applied to fracture conditions,the value of J is the fracture toughnessparameter, equivalent to Gc for LEFM,representing the resistance of a ductile ma-terial to fracture propagation. For both cases,theunits are J/m2. (SeeFracturemechanics).

2. Jeffamine

A tradename for a series of difunctional andtrifunctional amine-terminated polyethers,used for curing of epoxy resins and for theproduction of polyureas in polyurethanesystems.

3. Joint

An adhesive bonded structure or specimen,used to measure the adhesion strength.


j175

K

1. K Value

An empirical parameter used in industry torepresent the molecular weight of PVC.

2. Kaolin

A group of minerals used in particulateform as filler in polymer compositions andpaper. Kaolin is essentially an aluminiumsilicate, consisting of alternating ionicallyinteracting layers of alumina and silica.

3. Kapton

A tradename for polyimide films.

4. Kelvin–Voigt Model

A model for the viscoelastic behaviour ofpolymers. It consists of a spring and adashpot acting in parallel, as shown.

When a load (or stress) is applied to themodel, the dashpot causes a retardation ofthe otherwise instantaneous response of thespring. As a result, the extension (or strain)will increase with time in a curved fashionuntil it reaches the equilibrium value. If theload (or stress) is removed after the creepperiod t1, the deformation (or strain) willrecover also in a curved fashion owing to theretardation of the retraction of the spring bythe back-flow of the liquid in the dashpot, asshown.

The Kelvin–Voigt model (often referredto as the Voigt model) describes, therefore,the behaviour of a material that exhibits adelayed or retarded elasticity similar to thebehaviour displayed by polymers. The ad-vantage of having a model of this nature isthat it can be used to obtain an analytical(mathematical) expression to represent therelationship between stress, strain andtime. In examining the response of theKelvin–Voigt model, one notes that thestress (s) is shared between the spring anddashpot, that is,

sapplied ¼ sE þsh: ð1ÞThe strain for the wholemodel («), on the

other hand, is equal to the strain in thespring, which is also equal to the strain inthe dashpot, that is, «¼ «E¼ «h. Substitut-ing sE¼ «E and sh¼h d«/dt into (1)gives the constitutive equation for themodel as

s ¼ «Eþh d«=dt; ð2Þwhich can be solved to produce an equationfor the strain as a function of time, that is,

« ¼ ðs=EÞ ½1�e�tE=h�: ð3ÞThis equation describes the increase in

strain with time resulting from the appliedstress, as shown in the previous diagram.Note that the term s/E corresponds to the


176j

maximum strain that the model can reach,that is, at t ! 1, and can be replaced by thesymbol «V, where the subscript V stands forVoigtmodel. It is also important to note thatthe ratio h/E has the units of time, and isknown as the �retardation time�, l. Conse-quently, the increase of strain can be writtenas

« ¼ «V½1�e�t=l�: ð4ÞThe constitutive equation can be solved

also for conditions s¼ 0 at t¼ t1, that is, the�recovery� period. The equation for the re-sidual (remaining) strain becomes

« ¼ «1½1�eðt�t1Þ=l�; ð5Þwhere «1 corresponds to the strain at time t1,that is, at the end of the �creep� period, and tis the total time, that is, from the start of thecreep period.Obviously, one can divide bothterms of (3)–(5) by the constant appliedstress (s) and obtain an expression thatdescribes the linear viscoelastic behaviourin terms of the �creep compliance�, so thatfrom (4) one obtains the expression

DðtÞ ¼ D1 ½1�e�t=l�; ð6Þwhere D1 is the creep compliance fort ! 1, known also as the �equilibriumcompliance�. The physical meaning of theretardation time can be taken to representthe time required for the compliance to

reach the value D1(1� 1/e), which is ap-proximately equal to two-thirds of its maxi-mum value, D1.

5. Kevlar

A tradename for aromatic polyamide fibres.

6. Kicker

A term (jargon) used to denote an auxiliaryadditive that speeds up the decompositionof the main additive. The latter can be aninitiator of a free-radical polymerization orcuring process, and it can refer to the de-composition of a chemical blowing agent inthe production of foams. The term �kicker�is also used to describe the role of mercap-tobenzothiazole (MBT) in speeding up thesulfurless vulcanization of a diene elasto-mer by tetramethylthiouram disulfide(TMTD) in order to produce monosulfidiccross-links.

7. Kneading

Describes the action of the blades on a meltor dough to induce mixing. (See Mixer andCompounding.)

7 Kneading j177

L

1. Lamella

Thecrystalformedbychainfoldingduringthecrystallization of polymers. Individual poly-merchains canparticipate in the formationofmore than one lamella through interlayers ofrandom coiled chains forming the amor-phous domains. (See Crystalline polymer.)

2. Laminate

Aproduct in the form of a sheet made up oflayers of similar or dissimilar materials.Typical components of laminates are paper,wood and chopped strand glass-fibre mats.

3. Lamination

A process for the production of laminatedproducts. An example of the production oflaminated extruded sheets is shown.

Example of film to sheet lamination. Source: Rosato(1998).

4. Land Length

A term used to denote the length of theparallel section of a die at the exit. (SeeExtrusion die.)

5. Lap Shear

A generic term for mechanical tests onadhesives use lap joints. (See Adhesive test.)

6. LARC

A tradename for a variety of products madeatNASA-Langley via a technological processknown as polymerization of monomerreactants (PMR).

7. Latex

A dispersion of elastomeric polymer parti-cles in water, consisting of aggregates ofnano-dimensioned primary particles. Parti-cles have to be electrostatically charged toexert repulsive forces and prevent coagula-tion by interfacial diffusion during storage.This is usually achieved when the pH of themedium is greater than 7. Processing of alatex is normally carried out by spreading ordip coating techniques, where coagulationtakes place by removing the water by evap-oration. Once the particles are in continualcontact, the thermodynamic drive (reduc-tion in free energy) for molecular diffusionacross the particles results in the formationof a continuous film or coating on anadherend substrate.

8. Law of Mixtures

A generic name for a type of law that stipu-lates that the physical properties of a mix-ture, or an array of ordered assemblies, canbe estimated to be equal to the �weighted�algebraic sum of the properties of the indi-vidual constituents. The weighting isexpressed in terms of a fractional amount


178j

relative to the total, which can be taken as avolume fraction or weight fraction, depend-ing on whether the particular property isrelated to geometric dimensions or to themass of the material. The summation re-sults from the principle that, when an exter-nal �excitation� is applied to a mixture, the�response� of themixture as a whole entity isequal to the sum of the responses derivedfrom the individual components. It is possi-ble to distinguish two situations: one formixtures with isotropic properties, and theother for anisotropic properties. In the lattercase, the principle of the law of mixturesmakes it possible to estimate the upper andlower limits (bounds) of theproperties of themixture with respect to the direction of theexcitation relative to the orientation of thecomponentsof themixture.Thisprinciple isnow illustrated by examining the responseof a laminar composite to: (i) mechanicalforces, in order to derive expressions for theupper and lower bounds of themodulus of acomposite; (ii) temperature gradient, to es-timate the thermal conductivity; (iii) the fluxof gases through a multilayered film ormembrane, to determine its permeability;and (iv) electrical potential (voltage), as ameans of deriving expressions for the vol-ume resistivity of a layered dielectric. Thelaw of mixtures can also be used to makeestimates for mass-related properties.

8.1 Upper Limit for Modulus of Composite

If forces applied to the composite are trans-mitted along the plane of the laminae, thelongitudinal extension is the same through-out the various laminar components and,therefore, the total forces acting on the com-posite are equal to the sum of the forcesacting on the individual components.Taking into account the cross-sectional areaof individual laminae, the forces can beconverted to stresses, so that the stress act-ing on the composite becomes equal to thesum the stresses on each component, nor-

malized by their volume fraction. This canbe illustrated by reference to the diagram.

Illustration of isostrain conditions, arising from theequality of the extensions for each phase.

The diagram shows that a force applied inthe direction of the laminae produces anextension dLc that is equal in magnitude forall laminae (phases). Dividing dLc by thelength (L) gives the longitudinal strain,which is equal in both phases, that is, wehave an �isostrain� situation:

dLc ¼ dL1 ¼ dL2;

dLc ¼ dL1 ¼ dL2 ;L L L«c ¼ «1 ¼ «2:

In this case the total force acting on the�composite� is the sum of the forces actingon the two phases. By dividing the forcesby the cross-sectional area of the compo-nents, one derives an expression for themechanical stress acting on the composite,corresponding to the weighted algebraicsum of the stresses acting on each phase,that is,

Fc ¼Xi¼n

i¼1

F1 þXi¼n

i¼1

F2

and therefore

sc ¼ f1s1 þð1�f1Þs2:

8 Law of Mixtures j179

Dividing the stress terms by «c (where «c¼ «1¼ «2) gives an expression for the upperlimit of the Young�s modulus of a compos-ite, that is,

Ec ¼ f1E1 þð1�f1ÞE2;

which is the widely used law ofmixtures forthe prediction of the modulus of acomposite.

8.2 Lower Limit for Modulus of Composite

If the applied forces act through the planesof the laminae, they will have the samemagnitude in each lamina and, therefore,the total extension is the sum of the thick-ness increase of each individual lamina.Translating these conditions into relatedstresses and strains, and taking into accountthe volume fractions, one obtains the law ofmixtures for the strain acting on the com-posite.

Illustration of isostress conditions, arising from theequality of the forces and interfacial areas for eachphase.

The elucidation of this principle can beobtained by considering the diagram andthe related deductions:

Fc ¼ F1 ¼ F2 and Ac ¼ A1 ¼ A2:

Since

s ¼ F=A;

then

sc ¼ s1 ¼ s2:

Hence the total deformation is the sum ofthe deformations occurring in each phase,that is,

dLc ¼X

dL1 þX

dL2;

and the total strain is theweighted algebraicsum of the strain in each phase, that is,

«c ¼ f1«1 þð1�f1Þ«2;where the subscript c refers to the compos-ite, 1 and 2 to the two respective compo-nents, and f is the volume fraction of thecomponents, for example,

f1 ¼volume of phase 1

total volume:

From the above it follows that the Young�smodulus of the composite under isostressconditions is given by the equation

1Ec

¼ f1

E1þ ð1�f1Þ

E2;

which corresponds to the lower limit of themodulus of a composite.The comparison between the upper and

lower limits of reinforcement is shown inthe diagram for a two-component compos-ite, where Ef¼modulus of phase 1 andEm¼modulus of phase 2, with Ef/Em ratiosequal to 10 and 100, plotted in terms of themodulus enhancement factor, Ec/Em, as afunction of the volume fraction of phase 1,ff.

10.90.80.70.60.50.40.30.20.10φf

Ec

/Em

0

2

4

6

8

10

12

14

16

18

20

Ef / Em = 100

Ef / Em = 10

Comparison of upper limit and lower limit ofmodulus enhancement factor of composites.

From the diagram, it can be deducedthat, for a composite in which the modulusratio of the two components E2/E1¼ 10,

180j 8 Law of Mixtures

under isostrain conditions one can achievea three-fold increase in modulus with avolume fraction of the high-modulus com-ponent of about 0.2. A volume fractionaround 0.8, on the other hand, would berequired to achieve the same level of rein-forcement under isostress conditions. Thediagram also indicates that under isostrainconditions the reinforcing efficiency wouldincrease enormously when the modulusratio of the two components increased,E2/E1¼ 100. There is hardly any substantialincrease in reinforcing efficiency if thesame was done under isostress conditions.

8.3 Thermal Conductivity

. Isoflux conditions These are situationswhere heat is transferred through theplanes of the laminated structure, whereeach layer receives the same quantity ofheat from an external source. This is thesituation where heat is transferredthrough the laminae of the composite.The resultant effect is that the overalltemperature gradient is the sum of thegradients in the individual layers, that is,

DT=DX ¼ ðdt=dxÞ1 þðdt=dxÞ2;so that the expression for the overall ther-mal conductivity, Kc, becomes

1Kc

¼ f1

K1þ ð1�f1Þ

K2;

which corresponds to the �lower limit�.. Isothermal gradient conditions These si-tuations arise when heat is transferredalong the planes of the laminae of thecomposite, so that the total heat flux is thesum of the heat flux along each laminarcomponent. Consequently, the equationfor the thermal conductivity of the com-posite becomes

Kc ¼ f1K1 þð1�f1ÞK2;

which corresponds to the �upper limit�.

8.4 Permeability

. Isoflux conditions Diffusion and heattransfer obey the same scientific laws andboth are treated as transport phenomena.Consequently, all the considerationsabove for thermal conductivity apply alsoto the prediction of the permeability coef-ficient of laminates. Isoflux conditionsimply that the permeation rate throughthe thickness of a laminated structure isthe same as that occurring through eachlamina. In other words, there is no loss ofpermeating species through the interface.This leads to the lower limit equation forthe permeability (Pc) of a two-layer lami-nated structure as

1Pc

¼ f1

P1þ ð1�f1Þ

P2:

For a multilayer structure it is simply aquestion of writing the related weightedalgebraic sum of the inverse of the per-meability of each component, that is,

1Pc

¼ f1

P1þ f2

P2þ f3

P3þ � � � þ fn

Pn:

. Isoconcentration gradient Note that theother extreme condition corresponding toisoconcentration gradient conditions isunlikely to be encountered in practice inview of the thin sections of the constituentlaminae.

8.5 Volume Resistivity of CompositeDielectric

. Isostress conditions In a laminar compos-ite, when a voltage is applied along adirection parallel to the planes of thelaminae, the resulting current is the sumof the currents transmitted by each phase,so that the total volume resistivity willcorrespond to that derived for the lowerlimit of the law of mixtures, that is,

8 Law of Mixtures j181

1rc

¼ f1

r1þ ð1�f1Þ

r2:

. Isocurrent condition If the voltage is ap-plied across the laminae of the composite,the current density is equal in each lamina.Hence the total voltage gradient is the sumof the voltage gradients that exist througheach lamina. This results in an expressionfor the volume resistivity of the compositecorresponding to the upper limit, that is,

rc ¼ ffrf þð1�ff Þrm:

8.6 Mass-Related Properties

An example of a mass-related property isdensity. In this case, deviations from addi-tivity predictions based on weight fractionscanonly arise if thepresenceof voidshasnotbeen taken into account, or if there areinteractions between the two componentsthat lead to a change indensity ofoneorbothof them, causing changes in degree of crys-tallinity (thermoplastics) or an increase incross-linking density (thermosets). Theequations derived from the law of mixturesfor the density of composites (d) differ ac-cording to whether volume fractions (w) orweight fractions (v) are considered. Theequations are

dc ¼ wf df þð1�wf Þ dmand

1dc

¼ vf

dfþ ð1�vf Þ

dm;

where the subscripts c, f and m stand forcomposite, filler and matrix.There are cases where the law of mix-

tures has been applied on an empiricalbasis, that is, without any theoretical rea-sons to justify its applicability. One suchcase is the prediction of the glass transitiontemperature Tgb of a homogeneous blend,known as the Fox equation, written as

1Tgb

¼ v1

Tg1þ v2

Tg2;

where v1 and v2 are the respective weightfractions of the two components of theblend. Note, however, that deviations fromthe above equations are often quantifiedwith the addition of an interaction term,so that the above equation would be rewrit-ten as

1Tgb

¼ v1

Tg1þ v2

Tg2þ kv1v2;

where k is an empirical interaction param-eter for the particular system considered.

9. Lay-Flat Film

This term refers to tubular films insofar asthey are flattened at the nip of the take-offrolls. (See Blown film and Blow-up ratio.)

10. Lead Stabilizer

(See PVC.)

11. Leakage Flow

The flow that takes place within the clear-ance between the flights of the screw andthe barrel of an extruder. This occurs in theopposite direction to the flow in the chan-nels (i.e. back-flow). (See Extrusion theory.)

12. Life Cycle Analysis (or Assessment)

A methodology that seeks to identify theenvironmental impact of a product by con-sidering the environmental effect at everystage of its life cycle. This includes theimpact of extracting the rawmaterials, trans-forming them into new products, usingthem and then disposal and/or recycling.

13. Life Prediction

The estimation of the longevity or service-ability of a product from accelerated tests

182j 13 Life Prediction

carried out at higher temperatures. Themethodology is based on the principle thatthe deterioration of the properties of a ma-terial results fromdegradation reactions thatcan be related directly to the ambient tem-perature by the Arrhenius equation. (SeeArrhenius equation.) In this respect the timeto failure tf (i.e. the longevity) is inverselyrelated to the rate of the reactions that causethe deterioration in properties. Therefore,the Arrhenius equation can be written astf¼B exp(DE/RT), where B and DE are para-meters related to the structure of the mate-rial and its interactionwith the environment,R is the universal gas constant and T is theabsolute temperature. Therefore, if the time,tf, required to produce a specified reductionin a selected property (usually a 50% reduc-tion in ductility) ismeasured, after the speci-mens have been exposed to an environmentat different temperatures, an Arrhenius plotcan be made to obtain the extrapolated tTvalue for the expected life at ambient tem-perature T. Alternatively, the lifetime (tT) canbe specified (usually between 5000 and20 000 hours) and the extrapolation is madeto obtain the temperature Tt, representingthe maximum temperature at which thearticle can be used in the particular environ-ment considered, as shown in the diagram.

Example of Arrhenius-type plot for the life predic-tion of polymers in a particular environment.

This method works particularly well withcross-liked polymers, as they can be ex-posed to very high temperatures withoutdistortions or destruction of the shape ofthe specimens used in the tests. The meth-od is even more accurate for vulcanizedrubber, as the extrapolation is carried outfrom data obtained within the same defor-mational state of the polymer, whichis characterized by a constant activationenergy. This may not be the case for glassycross-linked polymers, where the extrapo-lation may cross two deformational states,that is, rubbery and glassy, that have differ-ent activation energies. Hence the extrapo-lation used for these situations may pro-duce much less reliable predictions. A �ruleof thumb� is sometimes used to estimatethe life prediction from a few acceleratedtests at higher temperature. This assumesthat the life expectancy of a product in-creases two-fold for every 10 �C decrease intemperature.

14. Light Microscopy

A microscopy technique that uses visiblelight, occasionally UV light, as the incidentradiation to view an object through magni-fying �lenses�. Variousmethods of examina-tion are available:

a) direct illumination;

b) dark-field observations, whereby onlythose rays diffracted in the object con-tribute to the formation of the image;

c) phase contrast microscopy, by whichobservation of objects is made with theuse of a plate in the image sideto produce a �90� phase shift in thezero-order diffraction maximum;

d) fluorescence microscopy using UVlight to detect objects, or features with-in the object, capable of emitting fluo-rescent radiation; and

14 Light Microscopy j183

e) polarization microscopy, a techniquethat is widely used for morphologicalexaminations and quantitative estima-tion of the amount of orientation inpolymer products.

In these examinations, two polarizingfilters are used, that is, a polarizer and ananalyser at right angles to each other. Thepolarizer is placed between the light sourceand the condenser, and the analyser is be-tween the objective and the eyepiece. Thesample is placed in such a way that themajor refractive indices are at 45� and135� to the direction of the polarizer. Thepolarized incident light is split into twowaves of equal amplitude in the directionparallel to the directions of themajor refrac-tive indices, traversing the sample withdifferent velocities and, after emergingfrom the sample, combine to form an ellip-tically polarized wave. However, only theportion of polarized light that travels paral-lel to the analyser is transmitted. The differ-ence T in optical path lengths nd in thesample (where n is the refractive index andd is the thickness) is a measure of theanisotropy, that is,

T ¼ ðn1�n2Þd:When T¼a l (where a¼ 0,� 1, � 2, . . .,and l is the wavelength) the emerging waveis polarized in the direction of the polarizerand cancelled. For isotropic samples T¼ 0and the image appears dark. This gives riseto the classical �isogyral cross� (�Maltesecross�) images of spherulites present incrystalline polymers. (See Spherulite, Ori-entation and Birefringence.)

15. Light Scattering

A term that denotes the reflection of light inmultiple directions from the surface of ob-jects, such as particles, whose refractiveindex is greater than that of the surrounding

medium, provided that the dimensions ofthe scattering centres are larger than thewavelength of the light. Light scatteringtechniques have been used for measuringthe weight-average molecular weight ofpolymers in solution and to examine themorphology of polymers in the solid state.Neither technique iswidely used these days,as there are more rapid and more accuratemethods available.

16. Light-Sensitive Polymer

A polymer capable of absorbing light (visi-ble or UV), which results in the productionof cross-linked structures. A typical exampleis poly(vinyl cinnamate), where the unsa-turation in the side groups produces thelight-absorbing characteristics of the poly-mer through the formation of conjugateddouble bonds with the benzene ring and, atthe same time, provides sites for the pro-duction of cross-links. The structure of de-rivatives of cinnamic acid is shown. (SeeUVstabilizer.)

Derivatives of cinnamic acid, where Y¼COOH;and X and Z are other substituents.

Cross-linking of polymers by light can bebrought about also with the use of light-absorbing additives, such as difunctionalazides, which decompose (releasing nitro-gen) into very reactive free radicals that willreact with labile hydrogen atoms in thepolymer chains, as indicated schematically.

Cross-linking of polymers with azides through lightabsorption.

184j 16 Light-Sensitive Polymer

Light-sensitive polymers are used inphotofabrication (e.g. photoresist) and forthe formation of printing plates and micro-circuits. (See Photoresist polymer.)

17. Light Transmission Factor

An index, T, that defines the intensity oflight transmitted through amedium, that is,T¼ 1� Fabs�Fsc, where Fabs and Fsc, re-spectively, are the fractions of the intensityof light absorbed and scattered by the me-dium. (See Optical properties.)

18. Limiting Oxygen Index (LOI)

A parameter that describes the fire resis-tance of a polymer and is defined as theconcentration of oxygen (%) in an oxygen–-nitrogen mixture capable of sustaining theburning of a polymer specimenmounted ina draft-free chamber. The higher the LOIvalue of a polymer, the greater is its fireresistance. A typical apparatus is shown.

Apparatus formeasuring the LimitedOxygen Index,Method ASTM 2863. Source: Courtesy of ASTMInternational (formerly American Society for Test-ing and Materials).

19. Linear Behaviour

Denotes a relationship between two vari-ables that remains the same irrespective ofthe value or magnitude of the variableconsidered.

20. Linear Elastic

Denotes the behaviour of a material forwhich the stress is proportional to theresulting strain at all times and irrespectiveof the type and level of stress applied. Thisimplies that there is no loss of strain energyunder cyclic loading conditions. (See Elasticbehaviour.)

21. Linear Polymer

A polymer whose molecular chains are notlinked and do not contain long-chainbranches.

22. Linear Viscoelastic

A viscoelastic behaviour by which the timedependenceof themodulusorcomplianceofa polymerdoesnot change irrespective of thelevel of stress or strain that is imposed on astructuralmemberThisimpliesthatthereisalinear relationshipbetween stress and strain.(See Viscoelasticity, Viscoelastic behaviourand Nonlinear viscoelastic behaviour.)

23. Liquid-Crystal Polymer (LCP)

A polymer containing regular rod-like rigidunits, known as mesogenic units, whichcan assemble in ordered arrays when thepolymer is in its melt state or in solution.

23 Liquid-Crystal Polymer (LCP) j185

The mesogenic units may be either locatedwithin molecular chains or attached as pen-dent groups to flexible polymer chains, asshown in the diagram.

Schematic representation of the organization ofmesogenic units in liquid-crystal polymers.

The liquid-crystal domains, known as themesophase, are not true crystals insofar asthe order of the constituent units is onlyshort-range. When the mesophase is dis-persed in the polymer melt, they are alsoknown as thermotropic LCPs. Examples ofthese LCPs are polyesters and poly(esteramide)s whose mesophase is obtained withthe use of acetoxybenzoic acid (ABA), acet-oxynaphthoic acid (ANA) and acetoxyace-toanilide (AAA). The synthesis and struc-ture of a typical polyester-based LCP avail-able commercially is shown.

Reaction schemeand structure of a typical polyesterLCP available commercially.

When the mesophase is dispersed in apolymer solution, they are called lyotropicLCPs. An example of a lyotropic LCP is poly(p-phenylene terephthalamide)s dissolvedin sulfuric acid, used for the production ofreinforcingfibres, known as �Aramids�. (SeeComposite.)

24. Liquid Rubber

Low-molecular-weight polymers or liquids,containingNH2 orCOOHend groups, usedto increases the toughness of thermosettingresins, particularly epoxy resins. (SeeAmine-terminated butadiene–acrylonitrileand Epoxy resin.)

25. Load–Deflection Curve

A graph obtained when performing flexural(three-point bending) tests presented in theform of plots of the recorded load (force)against the central deflection of the speci-men up to the point of fracture. Theseprovide a fingerprint of themechanical char-acteristics of the material, by calculating theouter-skin values of the stress from theapplied load, and the strain from the deflec-tion at the point where the load has beenapplied. For three-point bending tests, stressis given by s¼ 3PL/2WB2 and strain by«¼ 6BD/L2, where P is the load, D is thecentral deflection, L is the span, andB andWare respectively the thickness and width ofthe rectangular specimen. From the load–ex-tension curve it is possible to calculate: (i) theYoung�s modulus from the slope of thetangent to the curve starting from the origin(Young�s modulus¼ stress/strain); (ii) theyield strength (if failure is not brittle) takenas the stress value at the peak or at the pointthere is a rapid change in slope; and (c) theyield strain as the value of the strain corre-sponding to the yield stress. Note, however,that the equations that are normally used forthe calculation of the outer-skin centralstress and strain, on both the tension andcompression sides of the specimen, havebeen derived on the basis that the deflectionis very small. This may bring about consid-erable errors in the estimate of the yieldstrength and yield strain of polymers fromflexural tests. For this reason the data ob-tained in these tests are quoted as flexural

186j 25 Load–Deflection Curve

values, and are generally higher than theequivalent data obtained from tensile tests.

26. Load–Deformation Curve

A graph obtained when performing com-pression tests presented in the form of plotsof the recorded load (force) against thereduction in thickness of the specimen.Compression tests are rarely used for mea-suring fundamental properties of polymers,such as Young�s modulus or yield strength.They are more usually used for the evalua-tion of specific characteristics of materialsunder compression loads, such as, for in-stance, the fibre–matrix debonding in com-posites or the compression set of rubbers.

27. Load–Extension Curve

A graph obtained when performing tensiletests presented in the form of plots of therecorded load (force) against the extensionof the specimen up to the point of fracture.These provide a fingerprint of the mechani-cal characteristics of the material, as shownin the diagram.

By converting the required values for theload into stress (load/cross-sectional area)and extension into strain (extension/initialgauge length of the specimen), it is possibleto calculate: (i) the Young�s modulus fromthe slope of the tangent to the curve startingfrom the origin; (ii) the yield strength (iffailure is not brittle) taken as the stress valueat the peak or at the point there is a rapidchange in slope; (iii) the yield strain as thevalue of the strain corresponding to theyield stress; (iv) the extension at break asthe strain at break, expressed as a percent-age of the total extension divided by thegauge length; (v) the tensile strength atbreak, known also as the ultimate tensilestrength; and (vi) the relative toughness bytaking the area under the curve up to thepoint of fracture.

28. Locking Mechanism

A mechanical device designed to open andclose the mould of an injection mouldingmachine. (See Injection moulding.)

Typical mould locking mechanism for in-jection moulding machines: 1, mould; 2, 3and 4, fixed plates; 5, tie bar; 6, togglemechanism. Source: Birley et al. (1991).

29. Loss Angle

The angle, d, formed between the stress andthe strain in dynamic mechanical tests aris-ing from the viscoelastic behaviour of poly-mers. The value of the loss angle liesbetween 0, corresponding to that for an

Schematic illustration of the behaviour of differentpolymers in a tensile test. Source: Mascia (1974).

29 Loss Angle j187

ideal solid (elastic material), and p/2, whichis equivalent to the value for an ideal liquid(Newtonian). For structural polymers, thelossangleat lowtemperaturesismuchcloserto 0 than to p/2. (See Dynamic mechanicalthermal analysis and Viscoelasticity.)

Representation of elastic behaviour in cyclic stresssituations involving tension and compression: thestress is always in phase with the strain.

Representation of viscoelastic behaviour in cyclicstress situations involving tension and compres-sion: stress and strain are always out of phase.

The same concept applies to the angleformed between the voltage gradient (elec-trical stress) acting on a dielectric and theresulting current density in an alternatingcurrent field. The theoretical values also liebetween 0 and p/2, corresponding respec-tively to the values of an ideal dielectric(resistive material) and that of a capacitor.The electrical loss angle values for non-

polar polymers, such as polyethylene, aremuch closer to zero than the mechanicalloss angle of any rigid polymer. For bothsituations, that is, mechanical and electricalstresses, the loss angle values are usuallyquoted as loss tangent (tan d). (See Dielec-tric thermal analysis and Insulation.)

30. Loss Factor

Another term for the loss tangent or tan d.(See Loss angle.)

31. Loss Modulus

The imaginary component of the complexmodulus of polymers. (See Dynamicmechanical thermal analysis andViscoelasticity.)

32. Loss Tangent

(See Loss angle.)

33. Low-Density Polyethylene (LDPE)

Polyethylene with density in the range0.910–0.925 kg/m3. (See Ethylene polymer.)

34. Low-Profile Additive (LP Additive)

A polymer that is usually mixed with anunsaturated polyester resin in the produc-tion of bulk moulding compounds andsheet moulding compounds. The role ofthe LP is to prevent the formation of slightundulations on the surface resulting froman uneven distribution of the resin/fibreratio in the uncured pre-impregnatedchopped strand glassmats. An LP functionsby migrating towards the surface during

188j 34 Low-Profile Additive (LP Additive)

curing as a result of its reduced solubilityin the cross-linked resin, which allows it tofill the gaps created at the interface with thewalls of the mould. A variety of polymershave been used as LP additives, includingpoly(vinyl acetate), poly(vinyl chloride) andacrylic polymers. These additives havebeen found to have beneficial effects alsowith respect to the control of mouldshrinkage.

35. Lower Bound

Corresponds to the lower limit value of theproperties of composites predictable by thelaw of mixtures. (See Law of mixtures.)

36. Lower Critical Solution Temperature(LCST)

The temperature corresponding to themin-imum in the curves of temperature versusvolume fraction representing the borderbetween the miscible region and the two-phase region. (See Miscibility.)

37. Lubricant

An additive used in polymer formulationsto enhance the processing characteristics ofpolymers by reducing the friction betweenthe melt and the walls of the processingequipment. There are two types oflubricants:

a) External lubricants are additives thatexhibit a limited miscibility at hightemperatures with the polymer, so thatthe molecules can diffuse to reach thesurface of the metal equipment, form-ing a multi-molecular layer or micelleattached to the surface of the processingequipment.

Migration of fatty-acid-type lubricants to the surfaceof the equipment and the formation of amicelle anda weak boundary layer. Source: Mascia (1974).

The intermolecular forces within themicelle formed are very weak and canbe easily overcome by the action of theshear stresses at the wall of the proces-sing equipment, thereby providing alubrication mechanism for the flow ofthe high-viscosity polymer melt. Exter-nal lubricants are usually high-molecu-lar-weight fatty acids, amines, amidesor metal soaps, containing 12–18 car-bon atoms in the aliphatic chain. Inmore recent years, hydrocarbon waxes,consisting of low-molecular-weight co-polymers of ethylene with highly polarcomonomers, have also been used forthis purpose. These do not form mi-celles but produce a low-viscosity inter-layer between the melt and the metalsurface.

b) Internal lubricants have a certain levelof miscibility with the polymer and willbring about an appreciable reduction inmelt viscosity. An internal lubricant,however, isusuallyused inamounts thatexceedthesolubility limit inthepolymer,so that the soluble portion reduces themelt viscosity (from which the term�internal lubricant� is derived) and therest migrates to the surface of the pro-cessing equipment to produce lubrica-tion. An example of the use of internal

37 Lubricant j189

lubricant is the incorporation of stearicacid in rigid PVC formulations. Some-times two different lubricants, an internallubricant and an external lubricant (long-chain carboxylate salt, which is almosttotally insoluble in the polymer), are usedinpolymerswith ahighmelt viscosity thatare susceptible to thermal degradation,such as PVC and heavily filled thermoset-ting moulding compounds.

38. Lubrication Approximation

An approximation made in the solution offundamental flow equations through chan-nels of variable cross-sectional area along the

flow path. The approximation requires thattherewill be no change in theaxial velocity onthe basis that the rate of change in momen-tumisverysmall. (SeeMomentumequation.)

39. L€uder Lines

Also known as shear bands, these consist ofdislocated shear planes observed on speci-mens tested under plane-strain compres-sion conditions. They are often used tosupport the theory that the onset of yieldingfailures takes place through shear deforma-tions along the plane where the shear stres-ses are highest. (See Yield failure.)

190j 39 L€uder Lines

M

1. M100 and M300

Terms denoting the modulus of rubberymaterials at 100% and 300% extension. (SeeRubber elasticity.)

2. Machining

A manufacturing operation by which anarticle is produced by mechanically remov-ing material, using a cutting device, knownas a tool. Thermoplastics have to be in theirglassy state to be able to tolerate the highlocal heat generated by the interfacial stres-ses and to ensure that the resulting temper-ature rise at the cutting surface does notbring the polymer into the rubbery state. Forthe same reason, crystalline polymers musthave a fairly highmelting point to be able tobe machined. The cutting speed, rake angleof the tool and thickness of the chip have tobe carefully controlled to prevent excessivetemperature rises, which would bring thepolymer into the rubbery state. Machiningoperations include drilling and blanking.

3. Macromolecule

A generic term for large molecules with reg-ularly spaced monomeric units, arrangedeither linearly (polymers), inhighlybranchedfashion or in the formof an infinite network.

4. Magnesium Hydroxide

An inorganic filler, with particle size withinthe range 0.5–5mm, used primarily as anon-toxic fire retardant additive at levels inthe region of 40–65 wt%. (See Flame retar-dant.) It is also used, however, as a cross-linking agent for chloroprene rubber,

chlorosulfonated elastomers and some fluor-oelastomers. (SeeCuringandVulcanization.)

5. Magnetic Filler

Afiller used to impartmagnetic properties topolymers. The magnetic moment of thecompound produced is directly proportionalto the volume fraction. Themost commonlyused magnetic filler is magnetite (Fe3O4).Normally, a loading of 25–45 vol% (corre-sponding to 60–80wt%Fe3O4) is required toobtain polymeric magnets. Other magneticfillers includebariumferrite,Alnico (analloyof aluminium, nickel and cobalt, with someiron and copper), samarium cobalt and rare-earth iron borides.

6. Mandrel

The core part of a tubing die or pipe die.For the case of cross-head blow mouldingdies, the mandrel and die assembly can besubjected to programmed cyclic verticalmovements to adjust the die gap as ameansof increasing the flow rate. In this way it ispossible to compensate for the reduction inthe wall thickness, caused by sagging due tothe weight of the parison, thereby ensuringthat the produced container has a uniformwall thickness along its length. The mecha-nism of thickness adjustment withmovablemandrel is shown.

Schematic diagram of a movable mandrel.


j191

Mandrels can also be made to rotateduring extrusion of tubular products as ameans of destroying the weld lines formedby the spider legs and to achieve a uniformpressure gradient in the flow directionalong the entire circumference. Rotatingmandrels can also be used to produce spe-cial products, such as nets or perforatedtubings, as shown in the diagram. (SeeExtrusion die and Blow moulding.)

Example of extruded products made with the use ofrotating mandrels. Source: Rosato (1998).

7. Mark–Houwink Equation

An equation for the relationship betweensolution viscosity, [h], and the molecularweight of a polymer, corresponding to theso-called �viscosity-average molecularweight�, Mv, that is,

½h� ¼ KMav ;

where K and a are characteristic constantsfor a specific type of polymer that have to bedetermined experimentally. (See Molecularweight.)

8. Mass Polymerization

Known also as bulk polymerization, this isthe polymerization of a monomer in theabsence of any solvents or otherfluidmedia,such as water or supercritical CO2. Thistype of polymerization is used primarily for

systems that can be polymerized by anaddition polymerization mechanism, thatis, without the elimination of volatile spe-cies. Althoughmass polymerization is com-monly used for the production of castings inmoulds, coatings, adhesives or matrices forcomposites, it is often used also for contin-uous polymerization in reactors for theproduction of moulding powders. One ofthe difficulties of bulk polymerization is theheat of reaction, which can produce largetemperature rises. For this reason, thismethod of polymerization is restricted tovery thin sections, as indicated by the ex-amples given earlier. (See Polymerization,Curing and Cross-linking.)

9. Master Batch

A polymer compound, usually in granularform, containing large quantities of addi-tives. A master batch is pre-mixed in smallamounts with a virgin polymer (i.e. one freeof additives) at the processing stage, as ameans of incorporating additives into poly-mer products without having to undergo anexpensive compounding operation. Onemaster batch can often be used for a varietyof polymers.

10. Master Curve

A curve for the variation of a deformationalparameter (e.g. modulus or compliance)with time of duration of an applied load,derived by the extrapolation of experimentalresults obtained at higher temperatures.(See Time–temperature superposition.)

11. Mastication

An operation carried out on raw natural rub-ber as a means of reducing the molecularweight. (SeeMechanochemicaldegradation.)

192j 11 Mastication

12. Matrix

The polymer phase of a composite. (SeeComposite.)

13. Maxwell Model

A mechanical analogue, consisting of aspring and a dashpot connected in series,used to model the stress relaxation behav-iour of polymers when held under constantstrain, as shown.

If a strain («) is suddenly imposed ontothe Maxwell model and is held constant intime, it will be observed that at time zero (t0)the spring will stretch instantaneouslywhile the dashpot will remain in its originalposition. As time progresses the spring willretract because the force acting on it willcause the liquid in the dashpot to flow. Thismeans that the force (and correspondingstresssE) on the spring decreaseswith time.The stress sh acting on the dashpot isalways equal to that acting on the spring,so that s¼sE¼sh. This stress will gradu-ally decay until the spring has retractedcompletely and the stress becomescompletely relaxed (i.e. becomes equal tozero). This �stress relaxation� situation isillustrated in the diagram.

Illustration of the relaxation of stresses according tothe Maxwell model.

With this model it is possible to obtain aconstitutive equation for the stress relaxa-tion process, noting that, at any time t,the total imposed strain « is the sum of thestrain on the spring and that on the dashpot,

« ¼ «E þ «h; ð1Þ

that is, the strain is shared between the twocomponents. Note that the correspondingrates at which the strain increases with time(d«/dt) are also additive. The constitutiveequation is derived by making the appro-priate substitutions in (1), that is,

ðd«=dtÞE ¼ ð1=EÞ ds=dt and ðd«=dtÞ h

¼ s=h;

where E is the modulus of the elastic solidrepresented by the spring and h is theviscosity of the liquid in the dashpot.The solution of the resulting constitutive

13 Maxwell Model j193

equation for the condition «¼ constantbecomes

s ¼ s0 eð�tE=hÞ; ð2Þ

wheres0 is the stress at time zero, while theratio h/E can be replaced by a constant l,known as the �relaxation time�, as it has theunits of time. Dividing both sides of theequation by «, which is constant (i.e. inde-pendent of time), and rewriting (2) in termsof themodulus as a function of time, knownas the �relaxation modulus�, one obtains

E ¼ E0 e�t=l: ð3Þ

Fromthepreviousgraph it canbe inferredthat if, at time t1, the strain is to be instan-taneously forced to become equal to zero,this would require an equal stress in theopposite direction (i.e. a compressivestress). The applied compressive stress,however,woulddecay tozeroat infinite time.This is because the relaxation rate is deter-minedonlyby the relaxation timel,which isconstant and independent of the directionalnature of the stress. It is understood thatthese are generalmodels and, therefore, canbe used for either tension, compression orshear deformations, so that the derivedequations would be identical. For shear de-formation situations, for instance, onewould use the symbol G for the modulus.

14. Mechanical Properties

Properties that characterize the response ofamaterial tomechanical stresses, expressedin terms of stress at failure (strength), gra-dient of the plot of stress versus strain(modulus) and parameters related to theenergy required to cause fracture (tough-ness). (See Fracture mechanics.)

15. Mechanical Spectroscopy

Atechnique fordetermining thedeformation-al characteristics of polymers when subjectedto cyclic stresses. The data are presented as

plots of the complexmodulus and lossmodu-lus, or tan d, against temperature. (SeeDynamic mechanical thermal analysis.)

16. Mechanochemical Degradation

Degradation reactions that take place bycontinually shearing a polymer melt. Forpolymers that degrade by chain scission viafree-radical reactions, such as polyisoprenerubber and polypropylene, mechanochemi-cal degradation is often used as a techniquefor deliberately decreasing the molecularweight of a polymer. In the case of polypro-pylene, the technique is used to produce theso-called�controlledrheologygrades�,mostlyused for the production of fibres. An earlyexampleofmechanochemicaldegradation isthe �milling� of natural rubber to reduce themolecularweight inorder tomake it process-able in the melt state. This operation is gen-erally known as �mastication�, which is aprocess carried out at low temperatures inorder to ensure that degradation is inducedby the high shear stresses developed duringshearing,whichcanincreasefurtherthrough�stress-induced� crystallization effects. Theprocess is further assisted by the infusion ofoxygen from the atmosphere. Mechano-chemical degradation has also been used toenhance the compatibility of polymers in theproductionofblends,owing to thepossibilityof producing a certain amount of graft copo-lymers through chain transfer reactions.These will subsequently act as compatibili-zers for the unaffected polymer chains.

17. Melamine Formaldehyde

Abbreviated to MF, a thermosetting resinobtained from the reaction of melaminewith formaldehyde. (See Amino resin.)

18. Melt

The state of a polymer at temperaturesabove that of the rubbery plateau. It

194j 18 Melt

represents the liquid sate of the polymer, asit denotes the ability of the polymer to flow,which is manifested through a net move-ment of molecules from one site to another.Flow takes place via rotations of chain seg-ments involving uncoiling and reptationmovements. (See Deformational behaviourand Non-Newtonian behaviour.)

19. Melt Elasticity

A term used to describe a characteristic ofpolymermelts that causes partial recovery ofthe imposed deformation when the stressesare removed. Amanifestation of this behav-iour is the swelling of an extrudate at the exitof a die,where thewall shear stress suddenlyvanishes due to the elimination of the pres-sure gradient that existed during the flowthough the die. The die swell ratio (i.e. forcircular dies, diameter of extrudate/diame-ter of die) is frequently quoted as an empiri-cal parameter characterizing the elasticity ofpolymer melts. (See Die swell ratio andNormal stress difference.) The phenome-non originates from the long-chain natureof polymermolecules, which have to under-goacertaindegreeof alignmentduringflow.The consequence of the recovery charac-

teristics of polymer melts can be illustratedby the swelling of an extrudate emergingfrom a die. At the die exit, the pressure onthe melt becomes equal to the atmosphericpressure and, therefore, the pressuregradient (and also the associated shearstress at the wall) becomes equal to zero.The sudden removal of the �flow stresses�causes the partially aligned molecules toretract back into a random configuration,resulting in a lateral swelling of the extru-date. This indicates that, during the flow ofthe melt through the die, other stresses aredeveloped in the direction perpendicular tothe flow direction, which can be directlyassociated with swelling.Indragflowsituations, as in thecaseof the

flow in rotational rheometers, the effect is

evidenced directly from measurements ofthe pressure at walls. This pressure is notexperiencedbyNewtonian liquids.Aparam-eter, known as the normal stress coefficient,c1, is defined to describe the melt elasticitycharacteristics of the flow of polymers, thatis,c1 ¼ N1= _g

2,where _g is the shear rate andN1 is the difference between the normalstresses acting along the flow direction andthat perpendicular to the flow direction.In dynamic flow situations the shear

stress (t) lags behind the shear rate ( _g) bya phase angle (d), so that if _g ¼ _g0 sinðvtÞthen t ¼ t0 sinðvt�dÞ, where v is theangular velocity and vt is the angle ofdeformation at time t. This results in anequation for the viscosity in complex nota-tion in the form of h* ¼h0 � ih00, where h0

is the real viscosity component, i is thecomplex number (


) and h00 is theimaginary component of the viscosity(a measure of the melt elasticity character-istics), corresponding to G/v, where G theelastic shear modulus.

20. Melt Flow Index (MFI)

Also known as the melt index or melt flowrate (MFR), is an empirical parameter thatdescribes the ease of flow of polymer melts.It is defined as the grams of polymer ex-truded in 10minutes through a capillary dieof specified dimensions, resulting from anexternally applied load. The temperature atwhich the measurements are made and themagnitude of the applied load varies accord-ing to the nature of the polymer. For thesame polymer, the value of the MFI is oftenmeasured at two different loads. The con-ditions to be used are stipulated by appro-priate standard testmethods. For the case ofpolyethylene, irrespective of its density, themeasurements are made at 190 �C and thetwo loads normally used are 2.16 and 5.0 kg.A typical set-up for the apparatus used formeasuring the MFI of polymers is shownschematically.

20 Melt Flow Index (MFI) j195

Schematic diagram of the apparatus for measuringthe melt flow index of a polymer. Source: Osswald(1998).

21. Melt Fracture

A phenomenon that manifests itself in theform of undulations or gross deformities inextrudates, particularly those obtained fromorifices with a small cross-sectional area.These are associated with die-entry instabil-ities, which create pressure fluctuations as aresult of a slip–stick effect on the wall of thedie. If the die length is not sufficiently large,thepressurefluctuationswillnotdampenoutby the time the melt reaches the die exit andwill create gross distortions in the emergingextrudate.Thesecan takedifferentgeometricshapes, as shown in the photographs.

It is widely accepted that melt fractureoccurs when the shear stress at the wall ofthe capillary in the entry region reaches acritical value,which depends on the viscosityand, therefore, on the molecular weight ofthe polymer. The higher the viscosity (hencethe lower the temperature and the higher themolecular weight), the lower the value of thecritical shear stress formelt fracture to occur,(tw)cr. While the value of the critical shearstress for melt fracture decreases with in-creasing temperature, owing to the reduc-tion in melt viscosity, the product of wallshear stress for melt fracture and weight-averagemolecularweight (Mw) remains con-stant, that is, (tw)crMw¼ constant. This im-plies that it is possible to alleviate the meltfracture problem either by increasing theprocessing temperature or by using a poly-mer with a lower molecular weight.

22. Melt State Polymerization

Refers to the increase in molecular weightof condensation polymers that can bebrought about through extension reactionsduring processing.

23. Melt Strength

A term that denotes the capability of apolymer melt to resist fracturing at the exit

Examples of extrudate distortions resulting from melt fracture at the die entry of a capillary die.

196j 23 Melt Strength

of the die when it is drawn by the take-offequipment. Although it does not have thesame meaning as melt fracture, the twocharacteristics are related. (See Drawdownresonance.) A typical test for evaluating thedrawdown characteristics, as well as elonga-tional viscosity and melt strength of poly-mer melts, is illustrated.

Schematic diagram of the apparatus used to mea-sure the elongational viscosity, melt strength anddrawdown properties of polymer melts. Source:Minoshima et al. (1980).

The drawdown characteristics are as-sessed by recording the maximum drawratio that can be achieved, determined fromthe ratio of peripheral velocity of the take-offroll to the exit velocity of the melt emergingfrom the extrusion die. In these experi-ments, it is also possible to measure theforces for drawing the filament at differentdrawing speeds, with the aid of a�tensiometer�. The critical drawdown ratiocan be estimated from the ratio of thevelocity of the filament at drawing rolls tothat at the die exit (manifested as a regularwaving pattern along the length), while themelt strength is calculated by recording theforce at which the filament breaks awayfrom the die. From a plot of the stress

(calculated from the recorded force) againstdrawing rate of the filament between dieand rolls, it is also possible to obtain anestimate of the elongational viscosity of themelt. (See Elongational viscosity and Meltfracture.)

24. Melting

Denotes the change from solid-like behav-iour to a state in which flow can take place.In the case of crystalline polymers, meltingtakes place through the breaking up ofcrystals. In general melting results from theincrease in heat content, which increasesthe internal energy associated the with ro-tational movements of molecular chains. Inthe case of amorphous polymers, this takesplace via a gradual increase (rather than asudden jump) in enthalpy.

25. Melting Point (Tm)

The temperature at which the crystals of asolid are disrupted to become a liquid. Thisis also known as a first-order transitioninsofar as it is a transition that occurs viaa sudden increase in enthalpy (heat con-tent), as shown.

Change in enthalpy with temperature for an idealcrystalline solid.

Polymers differ from ideal crystallinesolids insofar as melting takes place overa wide range of temperatures, so that the

25 Melting Point (Tm) j197

enthalpy starts to increase more rapidlywhen melting of the crystals begins andslows down again with a discontinuity inthe trace at the point when the melting ofthe crystals is complete. The temperature atwhich the latter takes place is taken as themelting point, as shown.

Change in enthalpy with temperature for a crystal-line polymer.

Amorphous polymers do not have athermodynamically definable meltingpoint, hence the transition from the rubberystate to the melt state should be regarded asthe �flow temperature�.

26. Membrane

Films with selective characteristics withrespect to permeation of liquids or gases.(See Nafion.)

27. Memory Polymer

Apolymer that, after stretching and coolingto ambient temperature, will regain its orig-inal dimensions when reheated. (See Heat-shrinkable product, Deformational behav-iour and Cross-linked thermoplastic.)

28. Mercaptan

Chemical compound containing the groupSH. (See Vulcanization.)

29. Mercerization

A process named after the inventor, JohnMercer, involving the treatment of cellulosewith alkalis (mostly sodium hydroxide) toallow swelling of thefibres through penetra-tion of water between the polymer chains.

30. Metal Deactivator

An additive used to reduce the catalyticdegradation effect of metal ions, present inpolymer products in the form of impurities,which may also be contained in other com-ponents of the formulation, such asfillers orpigments. Metal deactivators act as�complexing� agents (known also as�chelating agents�) so that the ions becomeimmobilized and will not reach the radicalspresent on polymer chains, whichmay havebeen generated by oxidative degradationreactions. The most widely used complex-ing agents in polymers are organic phos-phines or phosphites and more highlynitrogenated organic compounds, such asmelamine, bis-salicylidene diamines andoxamides. (See Chelating agent.)

31. Metal Powder

Used as filler for the production of conduc-tive compositions. Many metals have to beexcluded or suitably coated to prevent the

198j 31 Metal Powder

migration of metal ions into the polymermatrix, which could adversely affect thethermal oxidation stability. A wide rangeof different of particle sizes and geome-tries can be obtained through variousmanufacturing routes, including conden-sation of metal vapours, atomization ofmolten metal and electrolytic depositionfrom metal compounds.

32. Metallization

The process by which a thin metal layer isdeposited on the surface of a polymer prod-uct. There are several methods used for themetallization of polymers, the main ones ofwhich follow.

a) Vacuum deposition is carried by evap-orating a metal, usually aluminium,heated by tungsten filaments, and de-positing the atomized metal layers un-der vacuum on the cold surface of apolymer substrate. Often the metal lay-er is in the form of a sandwich betweentwo layers of a lacquer, a base coat toprovide a smooth surface, and a top coatfor the protection of the metal coating.The top coat is necessary as the metalparticles do not form a continuous filmandmay be abraded very easily from thesurface of the substrate.

b) Electroplating is a rigorous processthat involves several steps, respectivelysurface preparation, electroless deposi-tion of copper or nickel, followed by theelectrolytic deposition of the finalmetallayer. This is to make the surface con-ductive for the subsequent electrolyticdeposition. A good bond with the sub-strate is achieved by etching the surfacewith strong oxidizing acids, which cre-ate pits and crevices for the electrolesscopper coating. Chemical bonds mayalso be formed through salt formationwith the carboxylic acid groups, but

these tend to be unstable and produceblistering in service. (See Blistering.)Polymers containing etchable inclu-sions, such as alloyed diene elastomerparticles, as in ABS, usually provide thebest sites for the creation of the requiredcrevices.Crystallinepolymers relyon thehigher etchability of the amorphous re-gions, relative to the crystal lamellae, tocreate the features required for the me-chanicalkeyingof themetal coating.Thesubsequent electroless deposition is car-riedoutbycopperornickel salt solutionswith a reducing agent, such as formalde-hyde, in a caustic soda solution at pHaround 11–13. Other additives may beused to control the reactions, such ashydrazine, or auxiliaries, such as phos-phites, to increase the ductility of themetalliccoatings.Theelectroplatingpro-cess per se may include several stepsdepending on the performance require-ments of the plated product. A chromi-umplate deposition for automotive exte-rior trimcanbemadeupofseveral layerswith different thicknesses in the follow-ing order (thickness values in mm): elec-troless copper 0.75, copper or nickelstrike 2.5, copper plate 20, semi-bright/bright nickel 21, nickel for microporouschromium 2.5, and chromium 0.25 (in-formation from Margolis, 1986). Themultilayered structure of the coatingsillustrates also the complexity of the en-tire procedure involved in electroplatingoperations, which often include severalintermediate and final treatments.

c) Hot stamping is carried out via thetransfersofmetal coatings, usually in theform of labels or images, from a filmcarrier by application of localized heatand pressure from a tool or �die� (madein metal or silicone rubber) onto a coldsubstrate.Thecarrierfilm(orfoil)ismadefromahigh-melting-pointpolymer, suchas poly(ethylene terephthalate).

32 Metallization j199

33. Metallocene Catalyst

Evolved fromZiegler–Natta catalyst systemsused for the production of narrow molecu-lar-weight polyolefins by a gas-phase poly-merization technique. Metallocenes arecomplexes of transition metals, mostly zir-conium or titanium, and two cyclopentadie-nyl (Cp, C5H5) ligands coordinated in asandwich structure. The compounds usedas catalysts are derivatives containing anintramolecular bridge between the Cprings. By varying the details of the substitu-ent groups around the Cp rings, and othersconnected to the metal ion, it is possible tocontrol the type and sequence of the stereo-regularity in the polymer chains, whichprovides the chemist with the ability to�tailor� the molecular structure to differentproperty requirements, particularly trans-parency and toughness. An elucidation ofthe mechanism for building up isotacticpolypropylene chains from the �active� sitesof the catalyst is shown.

Mechanism for the polymerization of olefins bymetallocene catalysis. Source: Adapted fromKaminsky et al., as cited in Ugbolue (2009).

34. Methylnadic Anhydride (MNA)

A curing agent for epoxy resins, having thechemical structure shown. (See Epoxy resin.)

35. Mica

A platelet reinforcing filler with excellentdielectric properties, derived mainly from�muscovite�, essentially an aluminium sili-cate mineral with density of 2.8 g/cm3.Although it is possible to produce sheetsa few centimetres wide for special electricalapplications, the filler variety is available inthe form of flakes about 1–3mm thick and10–500mm wide. A micrograph of a micafiller sieved through a 200 mesh net isshown.

Micrograph of a muscovite mica filler. Source:Wypych (1993).

Because of the fairly high aspect ratio,mica fillers display a fairly high reinforcingefficiency without the orientation featuresprovided by glass fibres. For this reasonmica is often used in combination withglass fibres in mouldable thermoplasticcomposites, as a means of reducing thewarping that results from differentialshrinkage associated with the monoaxialorientation of the fibres.

36. Microcavitation

Aphenomenon describing the creation of amultitude of small voids during ductiledeformations of heterogeneous materials,such as HIPS, ABS, or particulate compo-sites with poor interfacial bonding.

200j 36 Microcavitation

37. Microemulsion

A dispersion of solid particles or liquiddroplets in a liquid medium, distinguishedfrom an ordinary emulsion by their ther-modynamic stability and their nanostruc-ture. The latter feature is responsible fortheir optical transparency.

38. Microhardness

Hardness measured with small indentersand to low levels of penetration.

39. Micrometre (Micron)

A linear dimension corresponding to 10�6

m. The usual symbol formicrometres ismm(sometimesm alone is used for micron).

40. Microscopy

A technique that takes magnified views ofgeometric features of specimens. Theimages can be taken by reflection of incidentradiation (reflectionmicroscopy) or by trans-mission of incident radiation (transmissionmicroscopy). (See Light microscopy, Trans-mission electron microscopy and Scanningelectron microscopy.) The range of hetero-geneities that can be examined by the vari-ous microscopic techniques is indicated inthe diagram.

Working range of various microscopy techniques:A, polymer coils as amorphous or crystalline do-mains; B, nanocomposites; C, composites andpigmented polymers; D, foams and laminates.Source: Kampf (1986).

41. Microvoid

Small voids present in polymer products.Microvoids are frequently found in compo-sites as a result of air entrapment duringthe impregnation of the fibres with resin.Microvoids are also formed in crystallinepolymers and polymer blends subjected tohigh stresses, owing to the development ofhydrostatic tensile stresses at the interfacebetween crystals and amorphous domains,or between the glassy and rubbery domainsof blends such as HIPS. The formation ofmicrovoids is usuallymanifested as whiten-ing regions in the stressed areas.

42. Microwaving

Using a very energetic form of radiation atvery high frequencies (2–15 GHz), primar-ily for the continuous vulcanization of rub-ber, also known as ultra-high-frequency(UHF) vulcanization. It follows the sameprinciples as dielectric heating, whichrelies on the energy losses to generate heat.Specific additives are often used to increasethe dielectric losses to the required levels.(See Dielectric, Polarization and Lossangle.)

43. Mineral Filler

A filler from mineral sources. (See Filler.)

44. Mineral Pigment

A pigment from mineral sources. (SeeColorant.)

45. Miscibility

A term used to describe the ability of acombination of two polymers, or an additiveand a polymer, to form homogeneous mix-tures, that is, the components become

45 Miscibility j201

intimately dispersed at the molecular level.Miscibility is achieved under conditions inwhich the related free energy of mixing(DGm) is negative. According to the secondlaw of thermodynamics,

DGm ¼ DHm�TDSm;

where DHm is the heat of mixing, T is theabsolute temperature andDSm correspondsto the change in entropy. For mixtures of apolymer and an additive, the heat of mixingcan be calculated theoretically from knowl-edge of the respective solubility parametersof the components of the mixture, that is,

DHm ¼ w1w2V1ðd1�d2Þ;where w1 and w2 are the respective molarvolume fractions,V1 is the volume occupiedby the polymer, while d1 and d2 are thesolubility parameters. For the case of mix-tures of two polymers in which the volumefractions of the two components are notvastly different, it is more appropriate touse the Flory–Huggins equation to calculatethe heat of mixing, that is,

DHm ¼ kTx012n2w1;

where n2 is the number of molecules ofpolymer 2, k is the Boltzmann constant andx0

12 is a characteristic interaction parame-ter. The term kTx0

12 represents the differ-ence between the enthalpy of one moleculeof polymer 1 when surrounded by mole-cules of polymer 2, and that of onemoleculeof polymer 2 when surrounded by mole-cules of polymer 1.From the above considerations it follows

that, since mixing results in an increase inentropy, the ability of the two components toform a homogeneous mixture is favoured ifthe heat of mixing is negative, that is, whenheat is evolved during mixing. Even so,however, the Flory–Huggins equation failsto predict the possibility of phase separationtaking place with changes in temperature.The related theories have later taken into

account the change in free energy withtemperature and have stipulated that phaseseparation can take place at a �critical solu-tion temperature�, Tc. There are two curvesthat represent the boundary between a mis-cible (single-phase) system and a two-phasemixture, known respectively as binodal andspinodal phase separation. The idealizeddiagram of critical solution temperature asa function of the volume fraction of thecomponents shows that there can be anupper critical solution temperature (UCST)and a lower critical solution temperature(LCST). Accordingly, phase separation takesplace when the second derivative of the freeenergy with respect to volume fraction isequal to zero, that is,

@2ðDGmÞ=@w2 ¼ 0;

wherew2 is the volume fraction of theminorcomponent. A schematic diagram of thephase separation conditions is shown.

Schematic diagram showing the boundaries be-tween miscibility and phase separation as upper(UCST) and lower (LCST) critical solution tempera-tures. Source: Unidentified original source.

46. Mixer

Equipment and devices used for mixingcomponents of a polymer formulation.These can be �static mixers�, for systems

202j 46 Mixer

where the required breaking up and move-ment of the components takes placethrough a series of complex channels. Moreusually, mixing is carried out in �rotationalmixers�, where the stretching and move-ment of the components takes place be-tween the stationary walls andmoving wallsof channels, that is, the surfaces of rotors.The majority of mixing devices includeboth complex flow paths and rotationfeatures.An example of a staticmixer is the �Kenic�

mixer, which consists of a tube containinghelical elements of alternating reverse pitchat 90� to each other, as illustrated.

Flow pattern in a Kenic static mixer. Source: Bairdand Collias (1998).

In aKenic staticmixer the elements of thefluid entering the channel are stretched andfolded through helical rotations so that ele-ments in the centre are distributed to thewall, while the fluid at the wall is moved tothe centre along the flow path. In this way astream entering the first element is splitinto two streams and each of them is furtherdivided as the fluid moves along the chan-nel, as illustrated in the diagram.

Consecutive stretching, splitting and refolding into32 layers in a static mixer. Source: Baird and Collias(1998).

Rotational mixers can be dived into lami-nar flow mixers, operating at relatively lowspeeds, which are used for high-viscosity

fluids, such as pastes and melts, and turbu-lence mixers, used mainly with liquiddispersions and powders. The extent, ordegree, of mixing in laminar flow mixersis determined by the weighted-average totalstrain (WATS) that a fluid element under-goes during mixing, and the residence timedistribution (RTD). These two parametersare related to the average velocity of thefluid. For a simple shearing situation expe-rienced by a melt in a drag flow betweenparallel plates, the total strain, g, can becalculated from the velocity of the plate, Vz,the gap,H, between the stationary plate andthe moving plate, and the duration of theflow, t (i.e. the residence time), as g¼ (Vz/H)t. For the case where the flow pattern iscomplex, each term is taken as an averagevalue.

46.1 Melt Mixer

The first melt mixing device to be used inindustry was the two-roll mill, originallyused for the mastication of natural rubberand for the incorporation of vulcanizingagents. It has been widely used also forplastics, particularly for laboratory work.The rolls rotate in the opposite directionand at different speeds at a ratio between1.5 and 3.0 in order to create a velocitygradient (shear rate) across the gap. Therolls are heated to the required tempera-ture, allowing a few degrees temperaturedifference between the two surfaces to en-sure that the melt will preferentially adhereto one roll and form a continuous band,known as the �hide� or �crepe�. A rollingbank is formed between the two rolls by thedifferential velocity, where new material iscontinually fed from the hide. To ensurethatmixing takes place also across thewidthof the rolls, the hide has to be cut frequentlyat an angle, so that the rolling bank breaksup and re-forms with fresh material. Themechanics of the operation is shown in thediagrams.

46 Mixer j203

For compounding operations of rubbersand many soft thermoplastics and blendswith elastomers, the most widely used pro-cess is the internal mixer. In essence theinternal mixer operates on the same princi-ple as the two-roll mill with a built-in mech-anism for continually cutting, folding andtransferring the melt contained in thechamber from one rotor to another. This isassured by feeding a volume of melt that isless than the actual volume of the chamber(the volumetric ratio is known as the fillfactor). The role of the ram is primarily tofeed the polymer and keep a seal on thechamber while mixing takes place. For themixing of rubber compounds, at the end ofthemixing cycle themelt is transferred ontoa two-roll mill, from which it is removed inthe form of a sheet or as strips.

Principle of mixing in an internal mixer. Source:Matthews (1982).

In the case of thermoplastics, the melt isdischarged into an extruder where it is pel-letizedas itexits themulti-orificedie (die-face

cutting) and immediately drenched in waterfor cooling. Alternatively the laces formedbythe die are cooled and then cut (lace cutting).For thermoplastics the most widely usedmixers for compounding are twin-screw ex-truders and the reciprocating interrupted-flight single-screw extruder. (See Com-pounding and Twin-screw extruder.)

Illustration of the discharge of a mix from an inter-nal mixer into an extruder. Source: Matthews(1982).

Some co-rotating twin-screw extrudersmay contain sections containing intermesh-ing self-wiping kneading blocks or otherforms of mixing elements to enhance themixing efficiency by the creation of multidi-rectionalflowpatterns. Photographs of thesespecial sections of the twin screw are shown.

Kneading blocks (left) and mixing elements (right)of intermeshing co-rotating twin screws. Source:Baird and Collias (1998).

An illustration of the operation principleof the reciprocating screw extruder withinternal pins (usually referred to as a Kokneader) is shown. The screw has the nor-mal rotational movement with an addition-

Principle of operation of a two-roll mill. Source:Matthews (1982).

204j 46 Mixer

al reciprocating action extending over thelength coinciding with the incidence of thepin–slot arrangement. These produce bothintensive and extensive mixing due to thecomplex flow pattern as well as the shear-ing of the melt in the intermesh of thebarrel pin and flight slot of the screw. Sincethe reciprocating action of the screw pro-duces a pulsating drag flow pattern, themelt is transferred at the end of the mixingchannels to the metering zone of a conven-tional single-screw extruder to smooth outthe pulsations before the melt reaches theexit orifice die for granulation.

Reciprocating action of a screw with interruptedflights and barrel pins of a Ko kneader. Source:Matthews (1982).

46.2 Paste Mixer

There are basically two types, the �parallelshaft� mixer, known also as the Z-bladeblender, and the �planetarymixer�. Schematicdiagrams are shown.

Paste mixers: (left) Z-blade blender; (right) paddleplanetary mixer. Source: Matthews (1982).

Note that, in the planetary mixer, theimpeller shaft not only rotates in the nor-mal way but also moves in a circular patharound the vertical central line of the mix-ing vessel. Inmany cases themixing vesselalso rotates and, for this reason, thesemixers are sometime known also as �pony�mixers.

46.3 Low-Speed Powder Mixer

A common type is the �ribbonmixer�, whichoperates at low speeds using spiral blades,as illustrated.

Low-speed powder mixer: (left) general layout of aribbon blender; (right) other blade designs. Source:Matthews (1982).

46.4 Fluid Dispersion Mixer

A widely used mixer for dispersion of solidparticles, such as suspensions in low-viscosity fluids, is the three-roll mill. Thebreaking up of agglomerates takes place inthe very small gap between the rolls, whichoperate at fairly high speeds. While the firsttwo rolls rotate in opposite directions, thelast roll can operate in either direction.The dispersion adheres to the rollers bysurface tension effects rather than drippingthrough the gap.More than one passmay benecessary to obtain the desired degree ofparticle break-up and dispersion.

Typical set-up of a three-roll mill. Source: Matthews(1982).

There are also mixers that operate at veryhigh speed, referred to as �colloid mills�,which operate as continuous mixers. Inten-sive shear is achieved by the high rotational

46 Mixer j205

speed of the rotors,which are placed in closeproximity to a stator to provide high shearrates. One type of colloid mill comprises ahollow cylinder that rotates at high speedwithin another concentric cylinder, formingonly a small gap between the surfaces of thetwo. The fluid enters at one end and isforced to exit at the other end throughcentrifugal forces and rotor design (left-hand diagram). Another type is the �disccolloid mill�, which is based on the sameprinciple but employs two circular discsinstead of cylinders (right-hand diagram).The fluid suspension is fed through thecentre and leaves tangentially at the bottomend by high centrifugal forces, which canproduce peripheral speeds of the order of60–70 m/s.

Cylindrical (left) and disc-type (right) colloid mills.Source: Matthews (1982).

46.5 High-Speed Powder Mixer

These produce mixing through the forma-tion of vortices created by impellers rotatingat very high speed. The main differencebetween the different types of high-speedpowder mixers is the design of the impellerand drive system.

Example of drive and impeller arrangement forintensive powder mixers (left) and the flow patternof powder (right). Source: Matthews (1982).

The frictional forces created by repeatedimpacts causes a considerable increase intemperature, which can be very useful inproducing a better dispersion of solid ad-ditives with a low melting point. This fea-ture is exploited in the production of PVCdry blends as a means of speeding up theinfusion of plasticizer into the microporesof the powder particles. This assists theformation of a solid skin on the outer sur-face of the particles, thereby enhancing thefree-flowing characteristics of the powder. Athermocouple is used to record the temper-ature continuously, which serves as ameansof monitoring the mixing cycle and forstopping the rotors to discharge the powderinto a larger cooling chamber operating atlower agitation speed.

47. Mixing

An operation or process that reduces thenon-uniformities, concentration gradientsor size of dispersed components, whichleads to the randomization of the system,driven by the increase in entropy that thesystem is seeking to achieve. The compo-nents can be considered in terms of individ-ualmolecules, as in the case of the formationof solutions (liquid–liquid and solid–liquid),or supramolecular entities that can break upto limiting dimensions, as in the case ofimmiscible liquids, a dispersion of solidparticles in a liquid, or particles intermixedwith other solid particles. Accordingly, themovement of components to different partsof the flow field can take place by moleculardiffusion or redistribution of phases. (SeeMiscibility.) The latter can take place through�intensive mixing� (requiring external forcesfor the breaking up of the constituent com-ponents) or by �extensive mixing� (requiringonly the transportation of components, suchas particles, along the imposed flow field).Extensivemixingincludesoperationsthatareoften referred to as distributive, simple mix-

206j 47 Mixing

ing or blending, whereas intensive mixingincludes terms such as compounding anddispersive mixing. Another term frequentlyused in mixing operations is �kneading�,where randomization of components takesplace through continually elongating andfolding layers over one another. (See Mixer.)

48. Modulus

A property of materials that denotes theirresistance to the deformations resultingfrom the application of external forces.There are three parameters required to fullydefine this behaviour, respectively: Young�smodulus (E), shear modulus (G) and bulkmodulus (K).

48.1 Young�s Modulus

Defined as the gradient of the plot of stressversus strain for conditions below thoseleading to yielding or fracture, that is, E¼stress/strain (s/«). Stress is the force actingon a unit cross-sectional area (s¼ F/A) andstrain is the extension per unit length («¼dL/L), where dL denotes an extension that ismuch smaller than the length. In the case ofpolymers, the gradient is taken either fromthe tangent of the straight line taken at theorigin (tangent modulus), or as the ratio ofthe stress at a pre-specified level of strain(usually 1–2%) divided by the strain (secantmodulus), as shown in the diagram.

Stress versus strain plot for materials failing byyield.

Formostmaterials, the Young�smodulusmeasured in tension is equal to that mea-sured in compression. For an idealmaterial,that is, one with an elastic behaviour andisotropic properties (equal in all directions),the Young�smodulus is constant and can bedescribed by a single coefficient. Steel andglass behave very closely to an ideal materi-al, hence one can find in the literature orhandbooks the values of their Young�smod-ulus, that is, 200GPa for steel and 70GPafor glass. The Young�s modulus of wooddepends on the type of wood but also onwhether the Young�s modulus is measuredalong the grain (longitudinal direction) oracross the grain (transverse direction);hence one usually finds a range of valuesquoted, typically 2–40GPa.

48.2 Shear Modulus

Defined as the ratio of shear stress, t, toshear strain, g, that is G¼ t/g. An illustra-tion of shear deformations occurring by in-plane displacements and through torsions isshown. In either case the force acts in thedirection of the plane and shear stress isdefined as the force divided by the area.

Shear deformation by in-plane shear (left) andthrough torsion (right).

Shear strain is determined by the extentof distortion, expressed in terms of thedisplacement of the plane relative to thedistance from the fixed plane. This is alsoequal to the tangent of the angle of thedistortion, dX/Y, or the extent of circumfer-ential torsion, dC/C. These normalized dis-tortions correspond to the tangent of the

48 Modulus j207

angle, B, formed by the distortion and thetorsion, respectively.

48.3 Bulk Modulus

When a component is subjected to threeperpendicular tensile or compressive stres-ses, one can consider the total change involume to calculate the volumetric strainusing the concept of �bulk modulus�. Thedefinitions of the terms involved are asfollows.

. volumetric strain

«v ¼ «1 þ «2 þ «3

. mean stress (hydrostatic tension orpressure)

sm ¼ s1 þs2 þs3

. bulk modulus

K ¼ sm=«v

The bulk modulus can be related toPoisson�s ratio y, shear modulus G, andYoung�s modulus E, through the followingexpressions:

E ¼ 3K ð1�2yÞ and K ¼ 2Gð1þyÞ=3ð1�2yÞ:

Poisson�s ratio is the ratio of the lateralstrain to the longitudinal strain, resultingfrom a uniaxial tension or compressionstress s1, that is, y¼ «1/«2¼ «1/«3. Notethat the value of Poisson�s ratio is related tothe volumetric expansion (tension) or con-traction (compression) that results fromthe application of the stress. The maxi-mum value (denoting no change in vol-ume) is 0.5, which corresponds to the valueobtained for rubbers. For crystalline poly-mers, such as polypropylene or HDPE, thevalue is in the region of 0.40–0.42, whilefor glassy polymers, such as polystyreneand polycarbonate, the value is around0.33–0.55.

49. Modulus Enhancement Factor

Denotes the increase in modulus of a poly-mer resulting from reinforcement withfibres or fillers. It is defined as the ratio ofthe modulus of the composite (Ec) to themodulus of the matrix (Em). The graphshows the effects of the strength of thefibre–matrix interfacial bondon the variationinEc/Em ratio as a function of the duration ofthe applied load for the case of a thermoplas-tic matrix composite. Comparison is madewith the ideal behaviour expected from acomposite exhibiting elastic behaviour andwithout fibre–matrix interactions.

Variation of modulus enhancement factor with theduration of the applied load for thermoplasticcomposites. Source: Derived from author�s unpub-lished work and Mascia (1974).

50. Molar Mass

(See Molecular weight and Degree ofpolymerization.)

51. Molecular Weight

Abbreviated to MW, corresponds to themass of a molecules expressed in grams.This is the same as molar mass. The molar

208j 51 Molecular Weight

mass of ethylene, C2H4, is 28 (i.e. 2� 12þ 4� 1). Themolarmass,MW, of amould-ing grade of polyethylene can be as high as280 000, which corresponds to 10 000ethylene units in the chain. (This is knownas the degree of polymerization.) The MWof an ultra-high-molecular-weight grade, onthe other hand, can be 10 times higher. Forpolymers, the size of the molecules is notuniform but statistically distributed over awide range. The distribution can be sym-metrical or skewed at either side of themedian value. Normally an average valueis reported for MW and, preferably, alsothemethod used for themeasurement. Thedifferent average molecular weights are de-fined according to the way the average iscalculated.The �number-average� MW is the aver-

age calculated on the basis of the numberof molecules Ni having molecular weightMi. Calling ai the fraction of moleculeswith molecular weight Mi, the equationfor calculating the number-average MWis

�Mn ¼X

aiMi ¼X NiP

Ni

� �Mi ¼

PNiMiPNi

:

If the weight fraction of such molecules,wi, is used for the computation of the MW,then the expression for the �weight-average�MW becomes

�Mw ¼X

wiMi ¼X WiP

Wi

� �Mi ¼

PWiMiPWi

;

and, therefore,

�Mw ¼P

NiM2iP

NiMi:

If all the molecules are equal in size, thetwo averages are the same, and the polymeris said to be monodisperse, that is, Mw/Mn¼ 1. With broadening of the distribu-tion, which is usually the case, this ratiobecomes larger than 1 and the system is saidto be polydisperse. The ratioMw/Mn, there-

fore, quantifies the degree of polydispersity.The diagram depicts the MW curve for asystem that exhibits a distribution skewedtowards low MWs and normalized withrespect to Mn, in which are reported thevarious averageMWvalues. In this diagramthere appears also an Mz average, whichrepresents the degree of skewness of thecurve. For a symmetric distribution thisvalue would be the same as Mw.

Typical molecular-weight distribution of a polymer,showing various average molecular weights on thecurve, respectively Mn, Mv, Mw, MGPC and Mz.Source: Ver Strate (1978).

Note that, for the particular polymer re-presented in the diagram, the measuredvaluesMv (from solution viscositymeasure-ments) and MGPC (from gel permeationchromatography) are both higher than Mn,and MGPC is even higher than Mz. For thelatter, the molecular-weight values are ex-pressed in terms of polystyrene equivalentsand not in absolute terms.

51.1 Measurement of Average MolecularWeight

There are different ways of measuring av-erage molecular weight. The more widelyused are �solution viscosity� to measure the�viscosity-average molecular weight�, Mv,and �gel permeation chromatography� fordetermination of the entire molecular-weight distribution. There are also meth-

51 Molecular Weight j209

ods specifically designed for particular sys-tems, such as, for instance, end-groupanalysis for polymers or resins containingfunctional end groups that can be mea-sured by titration methods or by spectro-scopic techniques. Typical systems thatmake use of end-group analysis are epoxyresins, unsaturated polyesters, CTBN andATBN, polyamides and polyols. The mo-lecular weight is calculated from basicprinciples, for example,

½mole equivalent of functional groups�¼ weight of sample=molecular weight:

This method has some practical limita-tions for high-molecular-weight polymersowing to the very low concentration offunctional groups in the samples that canbe used for chemical analysis. There arealso several empirical methods that areused to measure parameters related tomolecular weight, but these are used pri-marily for quality control purpose. Theseinclude �K value� and �viscosity number� forPVC, MFI for polyolefins and styrene poly-mers, and �intrinsic viscosity� for polya-mides and PET. In most cases, relation-ships are available to convert these para-meters to nominal number-average molec-ular weight.

51.2 Solution Viscosity Method

Themethod is based on theMark–Houwinkrelationship between the intrinsic viscosityand molecular weight, [h]¼KMa, where kand a are constants that depend only on thenature of the polymer. The viscosity of dilutepolymer solutions at different concentra-tions, and that of the solvent, are measuredwith specifically designed viscometers,such as the Ostwald and Ubbelohde visc-ometers, by simply recording the time forthe solution to flow between two marks inthe capillary, as shown.

Oswald (left) and Ubbelohde (right) viscometers.Source: Unidentified original source.

The relationship between the ratio of theviscosity of the solution, h2, to the viscosityof the solvent, h1, and the polymer concen-tration, c, is given by the expression

h2=h1 ¼ 1þ ½h�cþ kc2 þhigher-order terms;

where [h] and k are constants, and thehigher-order terms are very small relative to theprevious first- and second-order terms. Theequationcan, therefore,be rearranged togive

ðh2�h1Þ=h1c ¼ ½h� þ kc;

so that a plot can be made of (h2�h1)/h1cagainst concentration, c. This will give astraight line, whereby the intercept corre-sponds to the value of [h], known as the�limiting viscosity number� or �intrinsicviscosity�, while the slope gives the value ofk. These parameters depend on molecularweight, which is known for most polymersfrom the Mark–Houwink equation. The vis-cosity-average molecular weight so obtainedis related to the number-average value by theexpression

�Mv ¼P

NiM1þaiP

NiMi

� �1=a

:

For the special case where a¼ 1, the viscosi-ty-average MW would correspond to theweight-average value. In practice, the valueofa is between0.5 and0.8 and, therefore, theviscosity-average MW is lower than theweight-average value, but higher than thenumber-average value.

210j 51 Molecular Weight

51.3 Gel Permeation ChromatographyMethod

Themethod relies on the ability of a column(packed with a porous cross-linked polymergel swollen with solvent) to retard the rate offlow of a dissolved polymer to an extent thatdependsonthesizeof thepolymermolecules(i.e. theirmolecular weight). Pores consist ofregions of the network with a low degree ofcross-linking, therefore, containing largeramounts of solvent. Smallermolecules expe-rience a greater reduction in flow rate and,therefore, take longer to elute through such acolumn than larger (higher-molecular-weight) species. This effect results from theability of smaller molecules to take up posi-tions in the smaller pores of the gel and,therefore, theyareretainedlongerinapackedcolumnthanthelargermolecules,thattakeuppositions in the larger pores. Detectors areemployed to record the retention time ofspecies of differentmolecularweightswithinthe column and produce elution curves, re-presenting the concentration of polymer inthe eluted solvent. The detectors normallyused includerefractive indexmeasurements,low-angle light scattering, UV and IR radia-tion. A typical elution curve obtained bymea-suring the increase in refractive index overthatofthesolvent,whichisproportionaltotheconcentrationofthepolymereluted,isshown.

Example of an elution curve (GPC chromatogram).Source: Ver Strate (1978).

The conversion of the elution curves intoa molecular-weight distribution curve (i.e.concentration, or weight fraction, versusmolecular weight) is achieved bymeasuring

the elution time of standard solutionscontaining fractionatedmonodisperse poly-mers of known molecular weights. A col-umn has to be calibrated with a series ofwell-characterized polymer solutions, usu-ally solutions of monodisperse polystyrene.For this reason, the molecular weight of thepolymer examined is referred to as�polystyrene equivalent molecular weight�.

52. Molybdenum Oxide

Corresponds to Mo2O3, widely used as asmoke suppressant in fire retardant poly-mer formulations. The Mo2O3 acts as acatalyst for the oxidation reactions occur-ring at high temperature, so that less carbo-naceous matter (smoke and soot) isproduced during combustion.

53. Molybdenum Disulfide

MoS2 used as a solid lubricant in engineer-ing polymer grades, such as PTFE, toenhance the wear resistance.

54. Momentum

A mathematical concept related to movingbodies or the flow of gases or fluids. It is theproduct of mass (m) times velocity (V ), thatis, M¼mV.

55. Momentum Equation

A fundamental equation on which all flowcalculations are based. It corresponds toNewton�s second law, which states that therate of change of momentum of a movingbody is equal to the sum of all forces (F )causing the motion, that is,

d ðmVÞdt

¼X

F;

where m is the mass and V is the velocity.(See Flow analysis.)

55 Momentum Equation j211

56. Monodisperse Polymer

A polymer with dispersity index equal to 1,indicating that all polymer chains have thesame molecular weight.

57. Monofilament

Filamentary products containing only onefilament.

58. Monomer

Chemical compound used for the produc-tion of polymers by polymerization reac-tions. For instance, styrene is the monomerrequired to produce polystyrene.

59. Monsanto Rheometer

An instrument used to evaluate the curingcharacteristics of a rubber gum. (See Cure-meter.)

60. Montmorillonite

A nanoclay consisting of hydrated sodiumcalcium aluminium magnesium silicatehydroxide, (Na,Ca)(Al,Mg)6(Si4O10)3(OH)6�nH2O, used primarily for the production ofpolymer nanocomposites. The interestingcharacteristic of montmorillonite for nano-composites is the layered structure of alter-nating silica tetrahedra and alumina octa-hedra, as shown.This structure allows the penetration of a

cationic surfactant (a quaternary ammoniumcompound) between the layers through theexchange of surface cations (known as inter-calation), which brings about the separationof the layers (known as exfoliation) intoplatelets with a thickness of a few nano-metres, when they are incorporated into apolymer. (See Exfoliated nanocomposite andIntercalation.)

61. Mooney Equation

An equation that relates the increase inviscosity of a polymer resulting from theincorporation of a particulate filler, that is,

lnðhc=hmÞ ¼ KcVf =ð1�Vf =wmaxÞ;where hc and hm are the respective viscosi-ties of composite and matrix, Kc is a geo-metric constant for the filler particles, Vf isthe volume fraction of the filler, and wmax isthe packing factor (defined as the ratio of thetrue volume to the apparent volume occu-pied by the filler).

62. Mooney–Rivlin Equation

(See Rubber elasticity.)

63. Mooney Viscometer

An apparatus used to evaluate the curingcharacteristics of a rubber. (See Cure-meter.)

64. Morphology

A term used to describe the characteristicheterogeneous nature of a polymer, such asthat arising from the presence of crystallinedomains, fillers or other fine componentsnot molecularly miscible with the hostpolymer.

65. Mould

Thecomponentofamouldingequipmentormanufacturing line that provides the shapeof the product. It consists of two �halves�,respectively, the �fixed half� attached to thestationary part (often referred to as platen)and the �movinghalf� attached to themovingpart. The impressions formed between thetwo �halves� are known as cavities. (SeeCompression moulding, Injection mould-ing and Transfer moulding.)

212j 65 Mould

66. Mould Design

Two important aspects to consider inmoulddesign are the �flow analysis� for cavity fillingand the heat transfer for �cooling� themoulded part. There are two aspects thatneed special consideration in cavity filling,the formationof a solid skin as themelt frontmoves forwards from the gate and the radialflow path. (See Cavity filling.) In terms ofpressure requirements, the main consider-ation is the packing pressure, while the solidskin formation is particularly important forthe moulding of fibre-reinforced polymers,as it has considerable effect on the anisotro-py resulting from the orientation of thefibres in the outer layers. (See PVTdiagram.)

67. Mould Shrinkage

The amount of shrinkage (linear%), relativeto the dimensions of themould cavities, thata polymer undergoes in a high-pressuremoulding operation. (See PVT diagram.)

68. Moulding

A shaping process that produces articlesthrough deformations induced on a mate-rial feedstock within the confines of thecavities of a mould through the applicationof pressure. The most commonly usedmoulding processes for the processing ofpolymers are compressionmoulding, trans-fer moulding, injection moulding and blowmoulding. (See Compression moulding,Transfermoulding, Injectionmoulding andBlow moulding.)

69. Moulding Cycle

The sequences and times required for thevarious steps of a moulding operation. Thesequential events that take place in a typicalinjectionmoulding operation are illustrated.

Various stages of an injection moulding cycle.Source: Osswald (1998).

The moulding cycle starts with the injec-tion of the melt from the front end of thebarrel into the cold mould by a rapid for-wardmotion of the screw (events A and B inthe diagram). The screw then rotates toplasticate the cold polymer granules resid-ing in the feed zone, and to convey thepolymer melt in the metering zone to thefront of the barrel. In doing so it also movesaxially back into the previous position (eventC). The mould opens and the mouldedparts, together with runners and sprue, areejected from the cavity (event D).The cycle time is the total time required to

carry out the sequence of events shown inthe diagram.The time for themould to openand close in order to eject the parts is knownas the �dead� time and is usually the shortestfraction of the total time. The longest part ofthe cycle is the �cooling time�, which isdefined as the time between injecting themelt and opening the mould. This is due tothe intrinsically low thermal conductivity ofpolymers. The only effective expedientavailable to shorten the cycle time is tooperate with the lowest possible mouldtemperature, which is limited by the

69 Moulding Cycle j213

freezing of the melt while flowing into thecavities of the mould, preventing the cavityfrom being filled completely.In relation to the heat transfer analysis,

for determining the cooling time, althoughthermal diffusivity is a predominant factor,there is not a very large variation in thevalues exhibited by polymers, deriving fromtheir chemical structure. More importantin this respect are the temperature at whichthe moulded part can be ejected (TD) andthe temperature at which the polymerceases to flow, that is, the onset temperaturefor the rubbery state (TR), when the viscositybecomes extremely high. (See Deforma-tional behaviour.) The latter determines themaximum flow path length achievable andthe minimum pressure required to obtain asatisfactory weld of two meeting meltfronts. Neither temperature (TD and TR)can be defined from fundamental princi-ples, nor can they be measured experimen-tally with any degree of accuracy to producedata that can be used universally. An equa-tion that has been widely used for estimat-ing the minimum cooling time for amoulded part, and that would require aknowledge of the value of TD, is

tcooling¼ðh2=paÞln½ð8=p2ÞðTM�TWÞ=ðTD�TWÞ�;

where h is the thickness, a is the thermaldiffusivity, TM is the melt temperature, TW isthe mould temperature and TD is the allow-able ejection temperature. The value of TD isparticularly difficult to specify, as it may de-pend also on the ejector system used forremovingthemouldedpartsfromthecavities.

70. Moulding Defect

Visual defects that appear in a mouldedpart, particularly in the injection mouldingof thermoplastics. The more common typeof defects are (i) weld lines, (ii) sink marks,(iii) internal voids, (iv) distortions, and(v) warping. (See Weld line.) Sink marks

and internal voids are experienced particu-larly in relatively thick sections of amouldedpart produced from a crystalline polymer orthermosetting �compound�. These defectsarise primarily as a result of the differentialcooling rate between the outer skin layersand the middle section of a moulded part,which results in a differential densitythrough the thickness due to different de-grees of crystallinity or cross-linking densitydeveloped. In both cases the faster coolingin the outer layers gives a lower density thanthe slow cooling rate in the middle. Thediagram shows that the type of defects, thatis, whether in the form of sink marks (in-ward suction of the outer surface layers) orinternal voids, depends on the modulus ofthe polymer, which determines the rigidityof the moulded part.

Illustration of the consequences of differential den-sity through the thickness of a moulded part.Source: Mascia (1989).

71. Mullins Effect

A term used to describe the strain softeningbehaviour of filled rubbers attributed to thedeterioration of the adhesion of the polymerchains from the surface of filler particles.

72. Mylar

A tradename for biaxially oriented films ofpoly(ethylene terephthalate).

214j 72 Mylar

N

1. Nafion

A tradename for a particular ionomer, usedprimarily for the production of the protonexchange membrane (PEM) for fuel cells,consisting of polytetrafluoroethylene back-bone chains with regularly spaced perfluor-oether side chains terminated by sulfonicgroups. The chemical structure can berepresented by the following formula.

The term Nafion has become almost ahousehold name, like nylon, used even inscientific publications. There are, however,several other perfluoroether-based mem-branes available commercially. The impor-tant parameters that characterize the struc-ture of Nafion are (i) the equivalent weight(EW), corresponding to the number ofgrams of dry Nafion per mole of sulfonicacid groups contained in the structure, and(ii) the ion exchange capacity (IEC), whichrepresents the number of milliequivalentsof Hþ ions present per gram of polymer.This can, therefore, be related to averageEW as IEC¼EW/1000.The morphology of hydrated Nafion con-

sists of ionic clusters, about 4 nm in diame-ter, containing the sulfonated perfluor-oether side chains, which are organized asinverted micelles arranged in a lattice andinterconnected by narrow channels, about1 nm in diameter. Both the diameter of theclusters and that of the interconnectingchannels increase with the absorption ofwater, so that the movement of protons orhydronium ions (H3O

þ ) from one cell toanother can readily take place under theinfluence of an externally applied voltage.The amount of water absorbed, and theassociated swelling of the membrane, are

controlled by the surrounding crystallinehydrophobic polytetrafluoroethylene do-mains. The actual detailed morphologicalstructure and the proton conductivity arecontrolled by the amount of water absorbed.At low water contents, not all the �SO3Hgroups are dissociated, and the interactionbetween water molecules via hydrogenbonds is somewhat low, so that the protonsor hydronium ions will not be able to movevery fast.

2. Nanoclay

A term used for clay fillers that can beexfoliated to produce platelets with thick-ness in the region of 3–20 nm.

3. Nanocomposite

A composite containing reinforcing agentswith at least one dimension in the region of3–100 nm.

4. Nanofiller

A term used to describe a filler that can beexfoliated to produce platelets with thick-ness in the region of 3–20 nm.

5. Nanometre

A linear dimension corresponding to10�9 m. The symbol for nanometre is nm.

6. Natural Rubber

Rubber obtained from the sap of manydifferent types of trees in the form of a


j215

water-based latex. Themost common type isfrom the tree known as Hevea brasiliensis,which is what is usually referred to as�natural rubber�. The chemical structurecorresponds to the cis–1,4–polyisopreneconfiguration. The other naturally occur-ring latex, known as �gutta percha�, corre-sponds to the trans–1,4–polyisoprene con-figuration, a harder rubber originally usedfor cable insulation, which has been re-placed by polyethylene. The structures ofthe two types are shown.

Natural rubber has a degree of polymeri-zation in the region of 5000 and a broadmolecular-weight distribution. The natural-ly occurring latex has a solids content in therange 25–45%, which is precipitated into acoagulum with the addition of acetic acidand rolled into sheets, known as crepe.(See Rubber and Elastomer.)

7. Network

A term used to describe the cross-linkedstructure of a thermoset polymer or that of avulcanized elastomer.

8. Newtonian Behaviour

Characteristic of liquids whose shear flowbehaviour can be described by Newton�s

law, which stipulates that the shear stress(t) acting on a lamina of fluid during flow isdirectly proportional to the shear rate ( _g)corresponding to the velocity gradient (dV/dt) in the plane perpendicular to the flowdirection, that is, t¼h dV/dt, whereh is theshear viscosity, also known as the Newtoni-an viscosity, which is a parameter thatdefines the resistance of a fluid to flow anddepends only on temperature. Any devia-tion from this characteristic gives rise to anon-Newtonian behaviour. In the case ofpolymer melts, the viscosity decreases withincreasing shear rate, giving a characteristicthat is often referred to as pseudoplasticbehaviour. (See Rheology.)

9. Nomex

A tradename for a paper made from anaromatic polyamide, represented by thechemical structure shown. These polymershave a very high melting point and a highresistance to thermal oxidative degradation,coupled with intrinsic fire retardant proper-ties. (See Aramid.)

The aromatic polyamide,m-phenylene isophthalamide.

10. Non-Destructive Test

A test that does not result in any changes inchemical structure, or in the destruction, ofthe specimen used for the examination.

11. Nonlinear Dielectric Polymer

Consists of a polymer composition thatexerts dielectric characteristics at low vol-tages but becomes conductive when thevoltage increases substantially above the

216j 11 Nonlinear Dielectric Polymer

line voltage. These systems are useful,therefore, for the production of devices forthe protection of circuits against overloads.A good example is their use in the construc-tion of cable joints and terminations inorder to provide a mechanism for the leak-age of spikes of current resulting fromlightning strikes, which would otherwisecreate failures in the insulation throughtracking. The high nonlinearity of the resis-tivity in relation to the applied voltage can bebrought about through the incorporation ofintrinsically nonlinear fillers, such as sili-con carbide, iron oxide or zinc oxide.Another way to produce a nonlinear dielec-tric is via the incorporation of carbon blackat levels just below the critical concentrationto achieve percolation conditions.A crystalline polymer is preferable for

this purpose as it would enable the filler tobe located predominantly within the amor-phous regions, thereby reaching the re-quired threshold conditions at lower levelsof addition than would be required with anamorphous polymer.At low voltages, the current cannot be

transmitted across the conductive carbonblack particles, as these are separated by anon-conductive polymer interphase. On in-creasing the voltage, the conditions areeventually reached whereby electrons canbe transferred through the separatingdielectric gap by a �tunnelling� effect, there-by producing conductive paths. Cross-linking the polymer can bring about anincrease in the stability of the nonlinearcharacteristics by preventing changes in themorphological structure. These could resultfrom overloads in the circuit, which wouldraise the temperature of the dielectric.

12. Nonlinear Viscoelastic Behaviour

Denotes a deformational behaviour bywhich the relationship between stress and

strain, at any given temperature, dependsnot only on the duration of the excitationor the history of the deformation but alsoon the level of stress and strain. The differ-ence between linear and nonlinear visco-elastic relationships between stress andstrain is shown in the diagram. The isochro-nous relaxation modulus (stress/strain attime t¼ constant) decreases with increas-ing level of stress used to produce the strainconsidered. Similarly, the isochronous com-pliance (strain/stress at time t¼ constant)increases with increasing level ofstrain considered. The time indicated onthe various curves increases in the ordert1 < t2< t3 < t4.

Linear and nonlinear stress–strain relationship un-der isochronous conditions.

The implication of the nonlinear visco-elastic behaviour of polymers is that it is notsufficient to specify a single value for thecompliance ormodulus for a given specifiedtemperature and duration of the load actingon thematerial. It is required to specify alsothe level of stress or strain. In other words,the modulus will be stated as E(T, t, «) andthe compliance as D(T, t, s), where theappropriate values of T, t, « and s arespecified. It is worth noting that the devia-tion of D or E from the linear behaviour

12 Nonlinear Viscoelastic Behaviour j217

becomes increasingly more pronounced athigher temperatures and at longer times.Thismeans that the compliance ormoduluscurves split up into divergent curves as timeincreases.

Nonlinear variation of relaxation modulus E (top)and creep compliance D (bottom) with time at twodifferent temperatures (T2> T1), two strains («2> «1)and two stress levels (s2>s1).

It has to be borne in mind that, since thenonlinearity becomes a prominent featureonly at fairly high strain levels, it becomesan important consideration only under con-ditions where the modulus is relatively low.It is unlikely, therefore, that substantialnonlinearity will be experienced for the caseof engineering polymers (e.g. polyamides,polycarbonates, acetals and PEEK). It iseven less likely in the case of structural

adhesives and composites, where the strainlevels reached are quite low.In any case the level of strain in engineer-

ing products is deliberately kept at low levelsas a safety factor, as a means of preventingthe occurrence of fracture failures arisingfrom defects, such as crazing and micro-voids. (See Crazing.)

13. Non-Migratory Plasticizer

A type of plasticizer that does not diffuseeasily intoadjacentorsurroundingmaterials.

14. Non-Newtonian Behaviour

A behaviour of fluids by which the relation-ship between shear stress and shear rate,defining viscosity, is not linear. This is to saythat the ratio of shear stress to the shear rate,that is h¼ t/g, at any given temperature, isnot constant but is a function of the shearstress acting on the fluid. Polymermelts aretypical fluids exhibiting non-Newtonianbehaviour. The most widely used modelsto describe the relationship between shearstress and shear rate for polymer melts arethe power-law equation and the Carreaumodel. Note that the flow behaviour of aliquid affects the velocity profile through thechannels. In the absence of slip or lubrica-tion, the velocity at the wall is zero and risesto a maximum in the centre. For a Newto-nian liquid, the velocity profile is parabolic,giving rise to a linear increase in velocitygradient from zero at the centre to a maxi-mum at the wall. For liquids such aspolymer melts exhibiting a power-law orCarreau behaviour, the velocity profilebecomes flatter towards the centre, result-ing in a curved increase in velocity gradient,rather than a linear one, from the centre tothe maximum at the wall.

218j 14 Non-Newtonian Behaviour

Velocity profile of liquids flowing through cylindricaland rectangular (slit) channels: (left) Newtonianbehaviour; (right) power-law and Carreaubehaviour.

15. Non-Newtonian Liquid

A liquid that does not exhibit Newtonianbehaviour.

16. Non-Polar Polymer

A polymer whose chemical structure doesnot contain polar groups, or where the polargroups are arranged in such a way as not toproduce permanent dipoles along themolecular chains. Typical non-polar poly-mers are the polyolefins (PP, PE, TPO andEPDM) and PTFE. Note that in the case ofPTFE there are four symmetric C–F groupsin each monomeric unit, each of whichproduces individually a strongdipolearisingfrom the large difference in electron densitybetween the two atoms forming the C–Fbonds. However, the dipoles so formed aresymmetrical and act in the opposite direc-tion, so that they cancel each other and,therefore, produce a zero dipole moment.

17. Normal Stress Difference

The difference between normal stresses,exhibited by polymer melts and solutions,

acting perpendicularly to the drag flowdirection. This phenomenon is usuallyillustrated by observations of the upwardflow along a rotating spindle immersed in aviscous polymer solution, as depicted inthe diagram.

Upward rising of a polymer solution around arotating spindle, attributed to stresses acting in theperpendicular direction to the rotational flow.

Since this phenomenon does not occurwhen the solvent alone (a Newtonian fluid)is subjected to the same rotational flow, it isclear that the solvent does not exhibit thenormal stress characteristics of the polymersolution (a viscoelastic fluid). The behaviouris attributed to the melt elasticity of polymermeltsandsolutions.While therotationalflowis caused by the imposed shear stress (t)exerted by the torque on the spindle, theupward motion results from the resultingdifference in normal stresses (sQ�sL¼�N1, whereN1 is known as the �first normalstressdifference�).Theparameterthat isusedto determine the melt elasticity characteris-tics of polymer melts and solutions in dragflow situations is known as the �first normalstress coefficient� c1, which is related to theshear rate _g (associated with the shear stresst) by the expression c1 ¼ N1= _g

2.

18. Norrish I and Norrish II

These are mechanisms for the chain scis-sion of polymer chains caused by the pres-ence of carbonyl groups as a result of theabsorption ofUV light. The carbonyl groups

18 Norrish I and Norrish II j219

may already be present in the chain asconstituent units of a copolymer derivedfromanolefinicmonomer and carbonmon-oxide, or they may be formed through oxi-dation reactions along the polymer chainsof a hydrocarbon or other ethenoid poly-mers. The two mechanisms are shown.

It is noted that, whereas the Norrish Imechanismproduces carbonmonoxide as aby-product, the Norrish II mechanism pro-duces double bonds along the polymerchains.

19. Notch

An artificial crack machined in a specimenused to evaluate the fracture resistance char-acteristics of materials. Notches can be slittypes or V types. The latter are more widelyused to measure the impact strength ofmaterials with pendulummethods, such asCharpy and Izod.

20. Notch Sensitivity

Denotes the reduction in fracture energyobserved when a notch is introduced into aspecimen. Although the phenomenon is

not amenable to interpretations in terms offracture mechanics principles, it is oftenused by design engineers as a criterion forthe selection of materials for the manufac-ture of articles that are likely to be subjectedto impact loads in service.

21. Novolac

A phenol formaldehyde resin that does notcontain CH2OH groups and, therefore, re-quires the addition of a hardener capable ofgenerating formaldehyde, typically hexam-ethylene tetramine, to produce cross-linksfor the network in moulded products. (SeePhenolic.)

22. Nozzle

A device fitted in front of an injectionmoulding machine or spraying equipment.

Nozzle position of an injection moulding unit rela-tive to the sprue of themould. Source: Unidentifiedoriginal source.

220j 22 Nozzle

23. Nuclear Magnetic Resonance (NMR)

A spectroscopic analytical techniqueinvolving the monitoring of absorbed oremitted electromagnetic (EM) radiation ofa compound, in the radio-frequencyrange between 900MHz and 2 kHz, bystimulated transitions between energylevels in the system, which are influencedby the environment of the nuclei. Nuclearmagnetic resonance (NMR) arises fromthe interaction of the applied EM radiationwith nuclear spins when the energy levelsare split by the external magnetic field.For this to happen it is essential that thenuclei of the atoms possess a nuclearspin, which arises when there is an oddnumber of protons or neutrons. For thevast majority of polymers, the hydrogenatoms in the molecular chains have thesecharacteristics and, for this reason, the tech-nique is often referred to 1H NMR, wherethe 1 denotes the number of protonsinteracting.

24. Nucleating Agent

An insoluble additive used to nucleate theformation of crystals in polymers cooledfrom the melt state. This is also referred toas heterogeneous nucleation insofar as theformation of crystals starts at heteroge-

neous sites, that is, at the surface of theparticles of nucleating agent. Nucleatingagents are mainly inorganic in nature, typi-cally silica, talc, clay, metal oxides andpigments in general. Organic nucleatingagents are solids with a high melting point,particularly salts such as sodium, potassi-um or aluminium benzoate.A nucleating agent accelerates the forma-

tion of crystal nuclei when the polymer iscooled from the melt, which is manifestedin an increase in the temperature for theonset of the crystallization process, as indi-cated in the thermogram.

DSC thermogram for samples of polypropylenecooled from 200 �C at a rate of 8 K/min: (a) samplewithout nucleating agent; (b) sample containing 1%sodium p-tert-butyl benzoate. Source: Jansen (1990).

The larger number of nuclei that areformed in the presence of nucleating agentsbrings about a reduction in the size of thesperulites, as shown in the micrographs.

Effect of a nucleating agent on the size of spherulites in polypropylene samples: (left) without nucleatingagent; (right) with nucleating agent. Source: Jansen (1990).

24 Nucleating Agent j221

The smaller spherulites bring about anenhancement in optical clarity, owing to thereduced amount of internal light scattering,and an increase in fracture toughness,whicharises from the great ability of the crystals todissipate strain energy through sliding ofcrystals before the formation of cracks. It isimportant tonote,however, that thepresenceof a nucleating agent has only a marginaleffect, if any, on the actual rate of crystalliza-tion, as shown in the thermograms for theisothermal crystallization of samples of poly(ethylene terephthalate) (PET) at 100 �C onsupercooled samples in the glassy state.(Note that the Tg of PET is around 75 �C.)

Cold crystallization isotherms for samples of PETcontaining 0.5% of different types of nucleatingagents: (a) sample without nucleating agent;(b) TiO2; (c) SiO2; (d) kaolin; (e) talc. Source:Jansen (1990).

The isotherms are plots of the degree ofcrystallinity (i.e. fraction of crystallinedomains) as a function of time. The diagramshows that the rate of increase in degree ofcrystallinity is practically the same in allcases, while the samples with nucleatingagents start to crystallize much sooner. Thedata shown highlight the very strong nucle-ating power of talc relative to other inorganicmineral particles.

25. Nucleation

A termused to describe the formation of the�nuclei�, in the shape of nanoscopic poly-

meric domains, relative to the crystalliza-tion of polymers from the melt or solution,as well as the phase separation of two mis-cible polymers on cooling from the meltstate through evaporation of the solventfrom a solution mixture. This term is alsoused for the initial step in the formation ofcells in the production of foams.

26. Nucleation and Growth

A mechanism for the formation of a partic-ulate morphology in polymer blends result-ing from phase separation of one of thecomponents, frequently in the form of net-works, to produce the �nuclei�, followed bytheir growth into particles. This mechanismis widely found in the toughening of athermosetting resin frommisciblemixtureswith appropriate oligomers. During curingthere is a precipitation of cross-linked spe-cies from this latter component before gela-tion of the surrounding resin matrix takesplace, which brings about the formation(nucleation and growth) of toughening par-ticles. (See Impact modifier.) The term�nucleation and growth� is also used forcrystallization phenomena and for the for-mation of cells in the production of foams.

27. Number-Average Molecular Weight

Also known as number-average molarmass, corresponds to the molecular weightof a polymer where the average is based onthe number of molecules taken to calculatethe average value. (See Molecular weight.)

28. Nylon

A term for aliphatic polyamides derivedfrom an early tradename for the homony-mous synthetic fibres.

222j 28 Nylon

The general structure of aliphatic poly-amides produced from dicarboxylic diacidsand diamines, known as polyamide x,y, PAx,y or nylon x,y, where x and y are thenumber of CH2 groups in each monomerunit, is represented by the formula:

The structure of polyamides producedfrom a,v-amino acids or from the corre-sponding cyclic amide, known as PA x ornylon x, where x is the number of CH2

groups in themonomer unit, is representedby the formula:

The linear structure of aliphatic polya-mides allows these polymers to form crys-talline domains through close packing, as inthe case of linear polyethylene, while thepresence of amide groups in the molecularchains produces strong intermolecularforces, via the formation of hydrogenbonds, which are responsible for the veryhigh melting point in comparison to linearpolyethylene. The number of hydrogenbonds that can be produced and, therefore,the value of the melting point depends onthe distance between and the symmetryof the amide groups along the chains. Thiseffect is illustrated in the table, for the twotypes of polyamides.

Nylonx,yþ2

Meltingpoint (�C)

Nylonxþ1

Meltingpoint (�C)

Nylon 4,6 278 Nylon 6� 2256,6� 265 7 2358,6 235 8 1957,7 205 9 2108,8 215 10 1789,9 177 11� 19010,10 206 12� 175

�See text.

An even number of CH2 groups in thechains can produce one hydrogen bond forevery repeating unit, while an odd numberof CH2 groups will only produce a maxi-mum of one hydrogen bond for every tworepeating units. The latter will, therefore,result in polymers with a lower meltingpoint. The two most important aliphaticpolyamides available commercially, usedmostly for the production of fibres or asengineering thermoplastics, are nylon 6,6and nylon 6, nylon 11 and nylon 12. Theglass transition temperature (Tg) values ofthe more common polyamides are approxi-mately 60 �C for PA 6, 70 �C for PA 6,6, and50 �C for PA 11 and PA 12. More recently anylon 4,6 has also been introduced. Nylonsare also available in the form of blends withethylene–methacrylic acid ionomers andother ethylene–acrylate copolymers, aswell as nitrile rubber. The reactivity of theamine end groups in polyamides has beenexploited for the production of blends withnon-polar elastomers, such as EPR andEPDM, by grafting the latter polymers withmaleic anhydride, resulting in substantialimprovements is impact strength over theblends with ethylene–acrylate copolymers.The number of amide groups per unit

length of a polymer chain also affects theamount of water that the polymer can ab-sorb, which is generally high in comparisonto other polymers. Nylon 11 and nylon 12exhibit lower water absorption than nylon6,6 and nylon 6. Grades in the form ofblends are often produced as a means ofreducing further the water absorption char-acteristics, as well as increasing the impactstrength (as already indicated). Mouldingswith very large cross-sections are producedin the form of castings by �activated anionicpolymerization� of caprolactam and can beobtained with very high molecular weightsto achieve a very high resistance to abrasionand wear. The water absorption character-istics of nylons requires that the mouldingsare �normalized� to the equilibrium water

28 Nylon j223

absorption level in accordance with theexpected level of humidity in the environ-ment in which they are used. A comparisonof the amount of water absorbed by thedifferent types of nylons is shown inthe plot against the relative humidity in theenvironment. (See Polyamide.)

Water absorption of different types of nylons:(a) PA 6; (b) PA 6/6,6/6,10; (c) PA 6,6; (d) PA6,10; (e) PA 11. Source: Domininghaus (1992).

29. Nylon Screw

An extruder screw comprising a long feedzone and a very short compression zonewith a large compression ratio. This is dueto the high melting point of nylons, partic-ularly nylon 6,6, and the low viscosity of thepolymer in its melt state.

Typical features of a nylon screw used in extrudersand injection moulding machines. Source: Uniden-tified original source.

224j 29 Nylon Screw

O

1. Oil Absorption

An empirical measure of the surface area ofpowders, such as fillers, often using dibutylphthalate (DBP) as the oil for the test. DBPdisplays good wetting characteristics owingto the high polarity of the phthalate group. Atorque rheometer is often used for this test,which records the torque during mixing ofthe oil with the filler under cold conditionsto form a paste. Amaximum in the torque isregistered when the oil completely fills thecrevices between the particles. The oil ab-sorption characteristics of the filler are ex-pressed asmillilitres of DBP per 100 g filler.

2. Oligomer

A short-chain polymer containing around5–20 monomeric units.

3. Open Cell

Interconnected cells of a polymer foam.Open cells are widely found in foams pro-duced from thermosetting systems. (SeeFoam.)

4. Optical Brightener

An additive used to mask yellow discolora-tions in polymers, which may arise throughdegradation reactions occurring during pro-cessing. These are fluorescent organic sub-stancesthatabsorbUVradiationatthefarendof the visible spectrum (300–400nm) andre-emit it at the lower end of the spectrum(450–550nm). Typical optical brightenersused in polymer formulations are vinylenebisbenzoxazoles and benzosulfonamidederivatives of 4–naphthotriazolylstilbene.

5. Optical Microscopy

A microscopic examination method usingincident visible light. (See Microscopy.)

6. Optical Path Difference

Also known as the relative retardation. (SeeOrientation and Refractive index.)

7. Optical Properties

Properties concerned with the response of amaterial towards visible light. The mostwidelymeasured optical properties for poly-mers are light transmission factor, refrac-tive index, specular reflectance or gloss,haze and see-through clarity. (See Lighttransmission factor, Refractive index,Gloss,Haze and See-through clarity.)

8. Organic–Inorganic Hybrid

A term used to describe compositions con-sisting of two distinct nano-phases, wherethe inorganic phase is usually a metal oxideproduced in situ by the sol–gel process.Often the organic and inorganic domainsform co-continuous phases. A typical mor-phology of an epoxy–silica hybrid is shownin the micrograph.

TEM micrograph of an organic–inorganic hybridbased on epoxy–silica. Source: Prezzi (2003).


j225

9. Organic-Modified Filler

A filler that has been treated with an organicadditive either to form deposits on the sur-face of the particles or to penetrate into thegalleries of the structural layers of the fillerto produce the exfoliation of the constituentplatelets. Fillers are coated with stearic acidor with an organic stearate to prevent themfrom becoming agglomerated when dis-persed into a polymer. Sometimes the filleris coated with a functional organotrialkox-ysilane as a means of increasing the adhe-sion between the filler particle and thepolymer matrix.

10. Organosol

A plastisol containing an organic solvent(usually white spirit) as diluent. Not widelyused in view of the toxicity implicationsarising from volatilization of the solvent.(See PVC and Plastisol.)

11. Orientation

A term used to describe the alignment ofpolymer molecules or reinforcing fibreswithin a composite, relative to a referenceaxis. Accordingly, orientation can be mono-axial or biaxial, depending on whether themolecules or fibres preferentially alignalong one direction or lay within a plane.The orientation of molecular chains takesplace when the polymer is deformed in therubbery state or in the �plastic� state duringcold drawing after the yield point. Whenorientation is induced in the rubbery state,the polymer has to be cooled down to�freeze-in� the molecular alignment. Thisis achieved by the development of suffi-ciently strong intermolecular forces, viathe reduction in intermolecular distances,

which prevent the recoiling of the molecu-lar chains into the random configuration,which is the thermodynamically stablestate. This occurs naturally for deforma-tions carried out in the �plastic� state, owingto the lower temperature of the polymerenvironment during the deformations thatinduce molecular orientation.

12. Orientation Function

A parameter that quantifies the degree ofalignment of polymer chains relative toreference axes. An orientation function isdefined in terms of the deviation of theaverage vector formed by the projection ofmolecules on a specific axis relative to itsrandom configuration. The monoaxial ori-entation function ( f *) for a specific direc-tion, say direction x, can be described by avector (representing the axis of symmetry ofthe average special configuration of poly-mer molecules) forming equal angles withrespect to the other two directions, in thiscase y and z, giving

f * ¼ f ðx=yÞ ¼ f ðx=zÞ ¼ 12ð3 cos2a�1Þ

and f ðy=zÞ ¼ 0;

where a is the average angle formed by theprojection vector. Thismeans that themono-axial orientation function f * increases from0 for the unoriented state, where the specialconfiguration of polymer molecules is ran-dom (for which cos2a¼ 1/3), to 1 for perfectmonoaxial orientation (for which cos2a¼ 1,i.e. for a¼ 0).The orientation state of crystalline poly-

mers has to be represented by two orienta-tion functions, one for the amorphousphase and one for the crystalline phase. Forthe latter, the reference vector, representingthe spatial configuration of polymer mole-cules, is the crystal axis, which coincideswith the direction of the chain folds.

226j 12 Orientation Function

Accordingly, the overall orientation can betaken as the algebraic average of the twoorientation functions calculated by thelawofmixtures based on the relative volumefractions of the two phases. Measurementsof the orientation functions can be made byvarious methods. The most widely usedmethod is based on measurements of thebirefringence exhibited by the orientedsample. In this case the orientation functionis equal to the ratio of the measured bire-fringence to the calculated maximum bire-fringence corresponding to the full align-ment of the molecules along the referenceaxis, that is a¼ 0. (See Birefringence.)

13. Osmometry

A method for determining the molecularweight of polymers from measurements ofthe osmotic pressure of solutions at varioussoluteconcentrations. (SeeMolecularweightand Osmotic pressure.)

14. Osmotic Pressure

The pressure generated in a pure solvent asa result of infusion of a solute from anadjacent solution through a membrane.Alternatively, the pressure can be createdby the diffusion of solvent into the solution.Whether the solvent or the solutes migratethrough the membrane depends on thenature of the system. For the case of poly-mer solutions, it is the solvent that perme-ates through the membrane, owing to thevery small size of the solvent moleculesrelative to the size of polymer molecules.This phenomenon is caused by the thermo-dynamic drive towards concentration equi-librium, which allows the solvent to pene-trate into the solution, thereby creating anexpansion of the solution.

Schematic illustration of the generation of a pres-sure, p, in the solution of �cell� C, (seen as a rise inthe height of the liquid in the capillary), derived fromthe arrival of solvent from �cell� A, diffusing throughthe membrane B.

This phenomenon has been exploited forthe measurement of the number-averagemolecular weight of polymers, Mn, exploit-ing the unique characteristic of osmoticpressure as a colligative property, that is, aproperty that depends only on the �number�of molecules (N) present. This is related tothemolecular weight,M, and to the concen-tration of the polymer in the solution by theexpression N¼NAc/M, where NA is theAvogadro number (6.023� 1018 moleculesper gram of polymer). The actual procedureinvolves measuring the osmotic pressureresulting from solutions at different con-centrations and plotting p/c against c. Thevalue of p/c at c¼ 0, obtained by extrapola-tion, corresponds to RT/Mn, where R is theuniversal gas constant and T is the absolutetemperature. (See Colligative propertiesand Molecular weight.)

15. Oxirane Ring

Also known as epoxy group. (See Epoxyresin.)

16. Oxo-Biodegradable Polymer

A polymer capable of undergoing a con-trolled rapid UV-induced oxidative degrada-

16 Oxo-Biodegradable Polymer j227

tion and produce low-molecular-weight bio-degradable species, through the formationof alcohol, ketone, aldehyde, ester and acidgroups. Polymers containing C¼C doublebonds and tertiary hydrogen atoms alongthe molecular chains are particularlyprone to oxidative degradation. The pro-cess can be accelerated by the incorpo-ration of additives consisting of salts oftransition metals. Polymers containingsmall amounts of carbon monoxide alongthe polymer chains, such as ethylene–COcopolymers, have also been produced tomeet these specific requirements.

17. Oxymethylene Polymer

A polymer containing repeating methyleneoxide along the molecular chains. Thesepolymers are abbreviated to PMO, that is,poly(methylene oxide). They are knowncommercially as �acetals� and are regardedas engineering polymers. (See Acetal.)

18. Ozone

Formed from the reaction of atomic oxygenwith molecular oxygen, that is,

OþO2>O3;

which is reversible. Within the conditionsin which polymers are used, the atomic

oxygen for the forward reaction originatesby the splitting of molecular oxygenthrough the adsorption of light with wave-length less than 240 nm. This radiation canderive either from sunlight or by electrical(corona) discharges from electrical cir-cuits. The reverse reaction takes place asa result of the absorption of light at higherwavelength, such as visible light and infra-red at wavelengths up to 1200 nm. There-fore, the quantity of ozone actually formeddepends on the prevailing conditions.The presence of ozone in the atmosphere

can accelerate considerably the degradationof polymers, particularly those containingdouble bonds along the polymer chains,such natural rubber and all diene-type elas-tomers. The atomic oxygen formed from thedecomposition of ozone can also react withwater to form hydrogen peroxide, which willrapidly decompose into two hydroxyl radi-cals and attack the polymer chains by ab-stracting a hydrogen atom, thereby startingthe initiation of the polymer degradationreactions. (See Thermal degradation andUV degradation.) These reactions cause thebreakdown of the original molecular struc-ture of the polymer, that is,

H2O2 þ hn! 2HO.

then

HO. þ��CH¼CH�� !��–CH–C�� þH2O

228j 18 Ozone

P

1. Paint

Generic term for polymer solutions andemulsions used to deposit coatings.

2. Parallel-Plate Rheometer

A rheometer used formeasuring the viscos-ity of polymer melts at low shear rates.It operates on the drag flow principle,whereby a shear rate (velocity gradient) isimposed on the melt placed between astationary plate and a rotating disc (seediagram). It can be made to operate in arotational mode or in a dynamic oscillatoryfashion. The shear rate and shear stress varyfrom zero at the centre to a maximum atthe edge of the circular plate.

Schematic diagram of parallel plates and variationof shear rate ( _g) and shear stress (t) with distancefrom centre (0) to edge of disc (R).

Owing to these variations, the viscosity,h,has to be estimated from the values of theshear stress and shear rate at the edge of therotating plate, that is, h ¼ tðRÞ= _gðRÞ. Inview of the non-Newtonian behaviour ofpolymer melts, the shear stress cannot in-crease linearly from the centre. However,for simplicity, this aspect is often ignored,and the viscosity is expressed as an�apparent viscosity�, based on the assump-tion of a linear change. The shear rate and

shear stress are calculated from the periph-eral velocity gradient and torque recordedon the spindle that drives the plate, that is,

_gðRÞ ¼VðRÞh

¼ 2pWRh

and tðRÞ ¼ 3T2pR3

;

whereV(R) is the peripheral velocity, h is thegap distance,W is the angular velocity of thespindle,T is the torque andR is the radius ofthe rotating cone.With some equipment it is also possible

tomeasure the vertical thrust, fromwhich itis possible to calculate the first normalstress difference N1 and the first normalstress coefficient, c1, that is, c1 ¼ N1= _g

2.(See Normal stress difference.) These lattermeasurements, however, are rarely made.For operationsmade in an oscillatorymode,the data are displayed in terms of �real� shearmodulusG0 and �imaginary� shearmodulusG00. The latter corresponds to the �realviscosity� h0, calculated as the ratio G00/v,where v is the angular velocity of the oscil-latory motion. The viscosity is calculated asa complex viscosity, h*, comprising a realcomponent h0 and an imaginary compo-nent h00, that is, h* ¼h0 � ih00, wherei ¼ ffiffiffiffiffiffiffi�1

p(the imaginary number). The

imaginary term, h00, is directly related toG0,that is,h00 ¼G0/v, which is a directmeasureof a fundamental parameter for the meltelasticity characteristics of the polymer.(See Complex compliance and Viscosity.)

3. Parison

(See Blow moulding.)

4. Parkesine

The first tradename for cellulose nitrateproducts, given by the inventor Alexander


j229

Parkes. The term �Celluloid� was used laterin the USA for similar materials.

5. Particulate Composite

Containmicrometre-sized particles (knownas filler) for reinforcement. (See Compositeand Filler.)

6. Paste

A term generally used to describe a veryviscous suspension of PVC particles inplasticizer. (See PVC.)

7. Peel Strength

A parameter that characterizes the resis-tance of flexible adherend to debondingfrom the substrate. The peel strength isexpressed as the recorded force divided bythe thickness of the adherend. (See Fracturemechanics and Adhesive.)

8. Peel Test

Measures the force required to separateeither a thin flexible adherend from a rigidsubstrate, the test being known as the�L-peel test�, or two thin flexible adherends,inwhich case the test is known as the �T-peeltest�. (See Adhesive.)

9. Pelletizer

The unit of a compounding line that pro-duces pellets after the melt emerges in the

form of a �strand� from the die of theextruder. An example is shown.

Example of a strand pelletizer. Source: Rosato(1998).

Pelletizers are also widely used forproducing tablets, pellets or �pre-weighed�feedstock of thermosetting moulding pow-ders, as well as for compacting fine particu-late fillers, such as carbon black. For thesesystems the pelletizers work on the cold-compaction principle using plunger–cavitycomponents. The �green strength� of thepellets is often increased with the use ofbinders deposited on the surface of theparticles.

10. Pendulum Impact Test

A test in which the load is delivered at highspeed by a mass placed at the extremity of apendulum to a specific loading point of asupported or clamped specimen. The appa-ratus records the energy used in fracturingthe specimen by registering the loss ofpotential energy (DU) from the reductionin the height reached by the striking massafter fracturing the specimen. The loss ofenergy of the pendulum is, therefore, givenby the expression DU¼mg(ho� hf), wherem is the mass of the pendulum, and ho and

230j 10 Pendulum Impact Test

hf are the respective heights before andafter fracture of the specimen.

Principle of pendulum impact tests. Source:Unidentified original source.

The specimen is loaded either as a canti-lever beam (Izod tests) or in a three-pointbendingmode (Charpy tests). In either casethe load is applied in the direction thatcauses crack propagation from the initialartificial notch, as shown.

Geometry of specimens and loading modes inpendulum impact tests. Source: Unidentified origi-nal source.

11. Peptizer

An additive used to assist the breakdown ofpolymer chains during the mastication ofraw rubber stock. Efficient peptizers consistof Fe, Co, V and other transition-metalcomplexes. However, these are not widelyused, as they will also affect the thermaloxidative stability of the vulcanized rubber.Themore commonly used peptizers are thetraditional types, such as pentachlorothio-phenol (PCTP) and its zinc salts (Zn PCTP).

12. Perfluoroether Polymer (PFA)

These are crystalline perfluoroalkoxy (PFA)copolymers of tetrafluoroethylene, whichcan be represented by the formula

where R is the fluoroalkyl group, CnF2nþ 1.The melting point of these polymers isaround 300 �C, which is only slightly lowerthan that of PTFE. This allows PFA to beprocessed by conventional thermoplasticmethods, owing also to the lower viscosityassociated with the reduction in molecularweight. PFA retains many of the character-istics of PTFE, except for coefficient offriction.

13. Permanent Set

A term used to denote the amount by whicha rubber sample fails to recover its originaldimensions after removing the appliedload. For instance, the difference betweenthe length shortly after retraction and theoriginal length, expressed as a percentage ofthe original length, is called the �tensionset�. The same calculation applied to tests in

13 Permanent Set j231

compression gives the �compression set�.When the same reasoning is applied tothe retraction of heat-shrinkable productsafter increasing the temperature above thatused in the expansion process, this gives anestimate of what is sometimes known as�amnesia�.

14. Permeability

Aparameter (P) that describes the pressure-related rate of permeation of a gas or liquidthrough a medium, normally a sheet, filmor membrane, that is, F¼Pdp/dx, where Fis the mass diffusion rate and dp/dx is thepressure gradient through the thickness ofthe medium. Permeability is related to thediffusion coefficient (D) and the solubility(S) by the expression P¼DS. It is a widelyused parameter to describe the barrier prop-erties of films in packaging, which are oftenmultilayer structures that can be specificallydesigned to achieve the desired level ofpermeability. The overall permeability value(Pc) can be calculated from the permeabilityvalues of the individual layers by the appli-cation of the basic principles of the law ofmixtures under isoflux conditions, that is,the rate of permeation is the same througheach layer, which corresponds to a situationin which the total pressure gradient is thesum of the pressure gradients through eachindividual layer. For a three-layer film, forinstance, this gives an expression for thepermeability (Pc) in the form of

1=Pc ¼ t1=P1 þ t2=P2 þ t3=P3;

where ti is the fractional thickness of eachindividual film, ti, relative to the total thick-ness, ttotal, that is, ti¼ ti/ttotal, and the digits1, 2 and 3 refer to each of the three layers.Note that the units of permeability arem3/m s Pa. Similarly to the diffusion coef-ficient, the variation of the permeabilitywith temperature is described by the Arrhe-nius equation using the concept of activa-

tion energy as the fundamental parameterthat characterizes the sensitivity of the per-meability to changes in temperature. (SeeActivation energy.)

15. Permittivity

A property of a dielectric material («) thatcharacterizes the capability of a dielectric tostore charge in an electric field. Permittivityis defined as the ratio of the charge densityQ/A (whereQ is the charge accumulated incoulombs and A is the surface area) to theapplied stress V/L (whereV is the appliedvoltage and L is the thickness of the dielec-tric), that is, «¼ (Q/V)� (L/A) in F/m,where Q/V corresponds to the capacitance.In an alternating field the permittivity isexpressed as a complex parameter, that is«* ¼ «0 � i«00, where i is the complex num-ber. The imaginary term «00 corresponds tothe deviation of a dielectric from a purecapacitor, corresponding to the amount ofelectrical energy dissipated as thermal en-ergy. This characteristic can also be de-scribed in terms of the phase angle (knownalso as the loss angle) between the chargeand loss vectors, that is, tan d¼ «00/«0. Theseparameters vary with the frequency of thealternating field, and are modelled with ananalogue consisting of a resistor and acapacitor. The variation of the related para-meters with the product vt (where v is thefrequency and t is the relaxation time) isshown. (See Complex permittivity andDielectric properties.)

Variation of permittivity parameters of a dielectricwith vt. Source: Hoffmann et al. (1977).

232j 15 Permittivity

16. Peroxide

An agent used as curative for unsaturatedelastomers and as initiator for free-radicalpolymerization of monomers and resins.Peroxy R–OO–R0 compounds undergohomolytic scission when heated or exposedto UV irradiation, producing two free radi-cals, R–O. and R0–O.. These are highlyreactive towards double bonds and will startthe initiation stage of polymerization andcross-linking reactions. The decompositioncharacteristics of peroxides are describedby their �half-life�, thl, and a nominal�decomposition temperature�, Td. The thlvalue corresponds to the time taken for theperoxide to reach 50% conversion into freeradicals, while the Td value is the approxi-mate temperature at which the peroxideundergoes the maximum decompositionrate. Typical peroxides used as polymeriza-tion initiators and curatives for elastomersare shown.

There are also systems available contain-ing multiple peroxide groups, which there-fore provide a high yield of peroxy radicals.Examples of these are shown.

A widely used peroxide for low-tempera-ture curing reactions, as in the case ofunsaturated polyesters for use in compo-sites, is methyl ethyl ketone (MEK) perox-

ide, which is believed to contain amixture ofmonomeric and dimeric compounds, re-presented by the chemical structure shown.

Formulae of commercial grades of MEK peroxide.

17. Peroxide Decomposer

Known also as a secondary stabilizer, theseareusedincombinationwithantioxidants forthe stabilization of polymers against degra-dation by thermal or UV-induced oxidationreactions. (See Stabilizer and Antioxidant.)

18. Phase Angle

(See Loss angle.)

19. Phase Inversion

A phenomenon observed during the masspolymerization of certain reactive mixtures,such as the curing of CTBN-toughenedepoxy resins and in the production ofhigh-impact polystyrene (HIPS) and acrylo-nitrile–butadiene–styrene (ABS) terpoly-

mer alloys. The phenomenon is driven bythe tendency of a system to minimize itsinternal energy through thermodynamicconsiderations of the physical stability of

19 Phase Inversion j233

miscible mixtures. During the course ofpolymerization involving two components,the originally miscible system can undergophase separation through loss of miscibilityas the molecular weight increases. This isalso driven by the system seeking to mini-mize its energy through a reduction inviscosity, achievable via the precipitation ofpolymer particles from themisciblemixture.If at a later stage these conditions arise again,the precipitation of one component maybring about the redissolution of the other,driven again by the resulting reduction inviscosity. These two events are identified inthe diagram, related to the production ofstyrene–butadiene block copolymers.

A situation similar to this can arise inthe curing of epoxy resins containing apre-reacted liquid rubber modifier. In thiscase, however, phase inversion will takeplace within the phase-separated particlesafter the surrounding epoxy matrix hasreached gelation conditions. At this pointthe remaining hardener in the epoxy matrixcan still diffuse into non-cross-linkedprecipitated particles, thermodynamicallydriven by the reaction possibilities with the

telechelic epoxy end groups of the liquidrubber. (See Epoxy resin.)

20. Phenol Formaldehyde

(See Phenolic.)

21. Phenolic

A generic term for resins based on phenolformaldehyde. Those known as �novolac�contain around 5–10 phenol groups joinedby methylene groups. Others, known as�resole�, consist of 2–4 methylolphenol

units with methylene and dimethyleneether bridges.

Chemical structure of a typical novolac phenolicresin.

Data recorded during the production of a styrene–butadiene diblock copolymer through the polymerizationof styrene units linked to a pre-formed polybutadiene. Source: Echte et al. (1981).

234j 21 Phenolic

Chemical structure of a typical resole phenolicresin.

Novolacs are mainly used for the produc-tion of moulding powders mixed withstoichiometric amounts of a hardener con-sisting of cyclic hexamethylenetetramine,(CH2)6N4, known asHEXA, and wood flouras reinforcing filler. Curing takes placethrough hydrolysis of HEXA, to produceformaldehyde and ammonia, that is,

ðCH2Þ6N4 þH2O! 6CH2Oþ 4NH3

The CH2O in turn enters the networkthrough addition reactions on the benzenering of the phenolic groups to form methy-lol groups. Sometimes paraformaldehyde(a low-molecular-weight polymeric form offormaldehyde) is used as hardener. Curingcarried out at high temperatures duringmoulding (from around 150 �C) tends todecompose the less stable dimethyleneether and dimethylene amine bridges intomore stable methylene links, producing atighter network. Undoubtedly some con-densation reactions take place also betweenmethylol groups in the phenolic resin and

the –OH groups in the cellulose units ofwood flour. The gaseous products formedduring curing tend to be absorbed by thewood flour, although some may remaindissolved in the actual phenolic network,owing to the hydrophilic and acidic natureof the phenolic groups.Resoles are used in coatings, composites

(paper and cotton fabric reinforcement) andadhesive formulations, often as water solu-tions. For these systems curing takes placeat low temperatures through direct conden-sation reactions of the methylol groups,giving rise to considerable formation ofdimethylene ether linkages, unless the pro-ducts are post-cured at high temperatures.Strong acids are used, for example, phos-phoric acid or p-toluenesulfonic acid, toprovide a catalytic action for the cross-link-ing reactions. For coating applications,resoles are often etherified with methanol,ethanol or butanol, to produce resins thatare more soluble in less polar solvents andto enhance their compatibility with otherresins (e.g. epoxy, polyester and rosin re-sins) in mixed systems or with reactiveplasticizers (e.g. liquid polybutadiene). Thecuring reactions occur via the formation ofquinone methide units, some of whichremain permanently in the structure, givingrise to the formation of dark-coloured pro-ducts, for example.

Reaction mechanism for the formation of cross-links during curing phenolic resins.

21 Phenolic j235

Reaction mechanism for the grafting of polybutadi-ene chains on phenolic resins during curing.

Moulding compoundsmay contain woodflour asfiller or other natural products, suchas olive kernel flour. Special products mayalso contain inorganic fillers and fibres,including mica flakes (for electrical grades)and graphite for components subjected tofriction, such as bushings. In additionto resin and hardener, the formulationscontain a lubricant, an accelerator andsometimes a plasticizer. NBR elastomerparticles are sometimes used to improvethe impact resistance. Particularly relevantin this respect is the ability of phenoliccompounds to cross-link diene elastomers.(See Vulcanization.) This practice is widelyused for formulations used in structuraladhesives. Phenolic resins are also widelyused for high-performance compositesbased on yarn and fabric reinforcement, ascotton, aramid and glass fibre fabrics.

22. Phenolic Antioxidant

Antioxidants based on ortho- and para-hindered phenols. (See Antioxidant andStabilizer.)

23. Phenoxy Resin

An end-capped high-molecular-weight ep-oxy resin. A glassy polymer with Tg around80 �C, used primarily in hot-melt adhesivesand as toughening agents in epoxy powdercoatings.

24. Phillips Process

A polymerization method for the produc-tion of high-density polyethylene (firstdeveloped at Phillips Petroleum), whichuses a chromium-based catalyst depositedon porous, high-surface-area metal oxideparticles. The calcination of the particles ataround 500–600 �Cbrings the chromium toits hexavalent form,which is responsible forchemisorption and subsequent initiationreactions for the polymerization of the eth-ylene monomer. (See Ethylene polymer,Ziegler catalyst and Metallocene catalyst.)

25. Phosphazene Elastomer

Based on polymers containing phosphorusand nitrogen atoms along the backbonechains, with alkoxy side groups containingfluorine atoms, as indicated by the formulaon the right.

Two polyphosphazenes.

Polyphosphazenes are cross-linked via afree-radical mechanism with peroxides orhigh-energy radiation. They have a Tg in theregion of �80 �C and are mainly used fortheir very high resistance to oils.

26. Photodegradation

Degradation induced by UV light. (See UVdegradation.)

27. Photoelasticity

A methodology used for stress analysis,using a model structural component pro-duced from a glassy polymer, such as poly-carbonate or a cured epoxy resin. The strain

236j 27 Photoelasticity

resulting from the application of a stressbrings about a small alignment of molecu-lar chains, which is sufficient to create acertain amount of anisotropy that can bequantified by measuring the related bire-fringence. The photoelastic characteristicsof a birefringent material can be expressedin terms of a �stress optical coefficient� (C)defined as

n1�n2 ¼ Cðs1�s2Þ ¼ 2Ctmax;

where (n1� n2) is the difference in refrac-tive index in two reference directions, sdenotes the principal stress and t is theshear stress. The isochromatic fringes ob-served in the product represent the contourlevels of maximum shear stress, whichidentify the areas of stress concentrationand make it possible to quantify the stressdistribution in the product.

28. Photoinitiator

A polymerization or curing initiator activat-ed by UV light. (See Initiator and Freeradical.) Photoinitiators absorb light in theUV–visible range (250–450 nm) and convertthe absorbed radiation energy into chemicalenergy. This produces reactive intermedi-ates, such as free radicals and reactive ca-tions, which initiate the polymerization orcuring reactions of functional monomersand oligomers. Photoinitiators for radicalpolymerization can act through bond cleav-age, usually a-cleavage of an aromatic ke-tone group present in the photoinitiator(Norrish I cleavage) or by intermolecularhydrogen abstraction from a hydrogen do-nor by the photoinitiator (Norrish II cleav-age). (See Norrish I and Norrish II.)Typical initiator systems of Norrish I type

are dimethoxyphenylacetophenone (DMPA)and diethoxyacetophenone (DEAP).

Initiators of Norrish II type are usuallybenzophenone (BP) with a tertiary amine(TA).

These initiators are less sensitive to airinhibition than the Norrish I types. (SeePhotopolymerization.) Typical cationicphotoinitiators are -onium salts, that is,diaryliodonium (DAI) or triarylsulfonium(TAS) salts, with PF6

� and SbF6� counter-

ions.

When irradiated with UV light, thesesalts produce strong protonic acids, whichinitiate the cationic polymerization of sys-tems such as epoxy resins and vinyl ethers.Some photoinitiators operate in combina-tion with a photosensitizer, particularlywhen visible light is used to initiate the

28 Photoinitiator j237

polymerization reactions. The photosensi-tizer absorbs energy from a light source andtransfers it to the co-initiator, producingfree radicals.A typical example is the use of photoini-

tiator, 2–methyl-1–[4–(methylthio)-phenyl]-2–morpholinopropane-1–one (TPMK).

This absorbs light in the 275–325 nmrange and is used in conjunction with thiox-anthone (TX) as photosensitizer, which hasits main absorption at 380–420 nm.

(Information provided byA. Priola andM.Sangermano, Politecnico di Torino, 2011.)

29. Photooxidation

(See UV degradation.)

30. Photopolymerization

Polymerization induced by radiation, usu-ally UV. Photopolymerization can take placeby a free-radical or a cationic mechanismdepending on the chemical nature of thereactive species. Photopolymerization is thebasis of important commercial processes,with a wide range of applications. Free-radical photopolymerization is carriedout with unsaturated monomers with theaid of photoinitiators capable of absorbinglight at certain frequencies and producingfree radicals, which induce polymerizationin the same way as for thermally inducedpolymerization. (See Photoinitiator.) The

most important monomers used for free-radical photopolymerization are acrylates,methacrylates and unsaturated polyesters.Cationic photopolymerization can be per-formed using mainly epoxy monomers andvinyl ethers. Usually polyfunctional mono-mers or oligomers are employed to producehighly cross-linked polymer networks. It isnoteworthy that oxygen in the atmosphereinhibits photopolymerization by the free-radical mechanism. Bimolecular radicalphotoinitiators are, however, less sensitiveto air inhibition. (See Photoinitiator.)Conversely, cationic photopolymerizationis not susceptible to oxygen inhibition.

31. Photoresist Polymer

Polymers used in the fabrication of integrat-ed circuits usingUV light to induce cleavageof the polymer chains so that the polymerbecomes soluble in solvents. A typical ex-ample is shown for photoresists based onpolyimides. Through the absorption of UVlight, the strain in the four-membered ringconnecting the two imide groups causes itto split.

Structure of a typical polyimide used as aphotoresist.

Splitting of polyimide chains through UVabsorption.

32. Physical Ageing

Denotes the slight increase in density ofglassy polymers, both linear and cross-

238j 32 Physical Ageing

linked types, when exposed for long periodsto temperatures below the glass transitiontemperature (Tg). This is entirely a physicalprocess that arises purely from the thermo-dynamic drive of the polymer to acquire theminimum internal energy. In the case ofcrystalline polymers, this is achievedthrough crystallization, including second-ary crystallization processes taking placeduring ageing at temperatures between Tgand the melting point of the polymer. Forglassy polymers, the systemseeks to achievethe most stable state (lowest energy state)consistent with the lowest level of freevolumes, which can be brought aboutthrough the closer packing of molecularchains. This is manifested as a suppressionof relaxations in both the b and a transi-tions, as shown in the diagram for rigidPVCsamples.

Effect of physical ageing on the low-temperature btransition and high-temperature a transition forrigid PVC. Source: Mascia and Margetts (1987).

The rate at which physical ageing takesplace depends on the difference betweenthe Tg of the polymer and the ambienttemperature, and goes through amaximumat a temperature just below the Tg. In theprocessing of linear glassy polymers, themelt is usually cooled at a fast rate, whichbrings the polymer into its glassy statebefore reaching the minimum internalenergy. Hence, the system will seek toachieve this state through an �ageing� pro-cess. In the case of cross-linked glassy poly-mers, the �curing� reactions that take placeafter gelation require sufficiently large free

volumes to allow the reactive groups tointeract through chain rotations. In so do-ing, an unstable state is set up, which isprone to physical ageing similarly to glassylinear polymers. This is particularly appli-cable for systems cured at temperatureslower than the Tg of the final product, thatis, the so-called �cold-cured� or �ambient-cured� systems. Physical ageing can beconsidered as a reversible process insofaras it can be erased by heating the polymer totemperatures just above Tg and cooling itdown slowly to ambient temperatures. Theinternal energy interpretation of physicalageing is supported by thermal analysisthrough observations made in a DSCheating scan. Upon reaching temperaturesjust above the Tg of the polymer, a smallendothermic peak is developed immediate-ly after the rapid decrease in the heat flowtaking place during the glass transition.The effect of physical ageing on propertiesreflects the typical changes expected froman increase in density, such as increasedbrittleness of the polymer.

33. Physical Blowing Agent

(See Blowing agent.)

34. Piezoelectric Polymer

Apolymer that exhibits piezoelectric behav-iour, that is, a characteristic of certain ma-terials to generate a small current under theinfluence ofmechanical stresses. Among allthe commercially available polymers, onlypoly(vinylidene fluoride) (PVDF) and, to amuch lesser extent, nylon 11 (PA 11) arecapable of exhibiting piezoelectric behav-iour. In the case of PVDF, there are largedipoles arising from the vast difference inelectron density between the CH2 and CF2in the repeating units owing to the polymor-phic nature of the crystals. The piezoelectric

34 Piezoelectric Polymer j239

behaviour is acquired after drawing afilm toalign the polymer chains and subsequentlyapplying a very large electrical stress(around 5000 kV/cm) to store charge on thedipoles. In this way, when a mechanicalstress is exerted onto the film, the positionof the dipoles is altered, causing the gener-ation of an electric current through chargetransfer. Main applications include micro-phones, earphones, loudspeakers and bur-glar alarms. (See Poly(vinylidene fluoride).)

35. Pigment

An additive used to impart colour and opac-ity to a polymer. Pigments can be eitherinorganic or organic. The latter are pro-duced from dyes that are made insolublewith binders or carriers. Because of theinteraction between the light scattering andlight absorption characteristics of pig-ments, the prediction of colour obtainedfrom a mixture of pigments is more com-plex than the simple additive and subtrac-tive colour mixing relationships availablefor dyes. (See Colour matching.) Invariably,white colours are obtained with the use oftitania pigments (rutile and anatase) andblack with carbon blacks. Other inorganicpigments include cadmium sulfides andlead chromates for yellows, and chromiumoxide for greens. Apearl appearance is oftenobtained with the use of metal flakes, suchas aluminium flakes and copper–zinc alloyflakes. Examples of organic pigments areshown.

Three organic pigments: (top) Yellow 151, 13980,Monoazo; (middle) Blue 15:3, 47160, Phthalocya-nine; and (bottom) Red 122, 73915, Quinacridone.

36. Pinhole

Small holes appearing in films or coatingsthat result from the presence of particleimpurities during production, which maycreate an interfacial tear, leaving behind ahole.

37. Pinking

A coloration developed in polymer productsafter exposure to UV light. This arises fromthe fluorescent characteristics of someamine additives, such as the hinderedamine light stabilizers (HALS) used as UVstabilizers.

240j 37 Pinking

38. Plane Strain

A termusedwidely in fracturemechanics todenote conditions by which the strains re-sulting from applied stresses are confinedto the plane, that is, there is no change inthickness and, therefore, the strain in thethickness direction is zero. This situationarises in areas surrounding the crack tip of athick specimen, owing to the absence ofstress on the free surfaces of the crack.(See Fracture mechanics.)

39. Plane Stress

A termusedwidely in fracturemechanics todenote conditions by which the stressesaround the crack tip are planar. This impliesthat there no stresses acting in the thicknessdirection, hence plane stress conditionsare stated as sz¼ 0. A similar descriptionis used within the context of yield criteria.This situation arises when the specimensare very thin, so that the stress-free state ofthe two outer surfaces of the specimenpredominates through the entire thickness.A gradual transition from plane stress toplane strain conditions takes place withincreasing thickness of the specimen. (SeeFracture mechanics and Yield criteria.)

40. Plasma

(See Cold plasma.)

41. Plastic

A term introduced in the late nineteenthcentury to describe man-made rigidorganic materials, later to be recognized aspolymers. Plastics are classified as�thermoplastics� when they are producedfrom linear polymers, and are capable ofexhibiting a reversible melt state, which

allows them to be shaped repeatedlythroughmelting and cooling. Plastics basedon cross-linked, or network, macromolecu-lar systems are known as �thermosets�,owing to the irreversible nature of the melt-ing process used to shape manufacturedproducts. Prior to becoming thermosets,the organic components are multifunction-al reactive oligomeric compounds, knownas �thermosetting resins�, which can bemade to flow and can be shaped at tempera-tures above their �softening point�.

42. Plastic Deformation

Deformation occurring through yielding, aphenomenon normally associatedwith duc-tile behaviour of materials. (See Yieldcriteria.)

43. Plastication

A term used to describe the melting ofpolymer granules along the transition zoneof an extruder or injection moulding ma-chine, as shown in the diagram.

Schematic description of the three events takingplace along the channels of the screw of an extruder.Source: Unidentified original source.

44. Plasticization

A phenomenon or mechanism to describethe lowering of the glass transition temper-ature (Tg) of a polymer, usually a glassypolymer. (See Plasticizer.)

44 Plasticization j241

. Internal plasticization This is broughtabout by modification of the chemicalstructure of the polymer either by creatinggreater chain flexibility within the back-bone of polymer chains, or through theintroduction of side groups that reducethe strength of intermolecular forcesand increase the free volume. The princi-ple can be illustrated by examiningthe reduction in Tg with increasinglength of the alkyl ester group in polya-crylates, from methyl (Tg¼ 6 �C), ethyl(Tg¼� 24 �C), propyl (Tg¼� 45 �C) tobutyl (Tg¼� 55 �C). In the case of poly(vinyl chloride) (PVC), for instance, inter-nal plasticization is achieved in copoly-mer grades with vinyl acetate (VA), whichdecreases the Tg according to the como-nomer content from 82 �C down to about75 �C (with around 20–25% VA). It isnoted that the reduction inTg in copolymergrades of PVC is not as large as in thepolyacrylate examples, owing to the lowerincidenceof longer side groups introducedvia the incorporation of VAunits. For ther-moset polymers, plasticization can bebrought about through chemicalmodifica-tions resulting in a reduction in the cross-linking (network) density. This is usuallyachieved by the incorporation of a compo-nent with a lower functionality, which isoften known as a reactive plasticizer.

. External plasticization A reduction in theTg of an existing polymer can also beobtained by external plasticization, con-sisting of the addition of a miscible mo-nomeric or oligomeric compound(known as a plasticizer) as a means ofreducing the strength of the molecularattractions between polymer chains.

In the case of crystalline polymers, plasti-cization is confined primarily to the amor-phous phase, but some of the plasticizer canpenetrate into the lamellar constituentsof thecrystals.This increasestheamountofdefects,thereby reducing the temperature for the

onset of melting of the crystals. When thedegree of crystallinity is low, and the quantityof plasticizer added is very large, the crystalsmay accommodate a considerable amount ofplasticizer, so that theoverallmeltingprocesswill take place at much lower temperatures.This is a technique used to produce the so-called �thermo-reversible gels�.

45. Plasticizer

An additive, usually liquid, consisting ofhigh-molecular-weight monomeric com-pounds or low-molecular-weight polymers,which is mixed with a polymer (usually aglassy polymer) to produce a miscible mix-ture exhibiting a lower glass transition tem-perature than the original polymer. The pres-ence of plasticizer molecules dispersed be-tween polymer chains reduces the overallintermolecular forces by a dipole screeningmechanism, or increases the �free volume�throughthecreationofobstacles tomolecularpacking.Dipole screeningnot onlydecreasesthe Tg but also produces a broadening of themodulus–temperature curve, and provides ahigher level offlexibility at low temperatures.Plasticizers have been classified in a num-

ber of ways, using different criteria. Awidelyused classification is according to the plasti-cization efficiency, defined in terms of thereduction of glass transition temperatureachieved for a given weight fraction of plasti-cizer, which is determined primarily by in-crease in free volume. Another classificationismade on the basis of the level ofmiscibilitywith the host polymer. Accordingly, a�primary plasticizer� is one that is misciblewith the polymer over the entire concentra-tion range, while a �secondary plasticizer� isonly miscible at low concentrations. Plastici-zersarealsodistinguishedas�non-migratory�types if theyexhibit a high resistanceeither tomigration intoadjacentmaterialsor toextrac-tion by liquid environments. These are usu-ally polymeric in nature and exhibit slow

242j 45 Plasticizer

diffusion owing to the large size of the mo-lecules. Polymers that are available as plasti-cizedgrades, inorderofplasticizerconsump-tion, are PVC (>80%), nitrile rubber, neo-prene rubber, cellulosics and polyamides.The following are the main types of plastici-zers available, in order of consumption.

. Dialkyl phthalates

where R is either octyl (DOP), isooctyl(DIOP) or isododecyl (DIDP)

. Dialkyl aliphatic estersRO�CO�(CH2)nO�CO�Rwhere R is octyl, and n¼ 2 for adipate(DOA) or n¼ 8 sebacate (DOS)

. Triaryl phosphate

where R1, R2 and R3 are typically phenyl(TPP), cresyl (TCP) or a mixture of thetwo groups

. Poly(propylene adipate) (See Polyester)

. Sulfonamides

Their main characteristics and uses areshown in the table.

46. Plastisol

A term for PVC paste.

47. Plastograph

A laboratory apparatus with the geometricalfeatures of an internal mixer (Banburytype), also known as a torque rheometer,used to study the fusion and gelationcharacteristics of polymers and elastomers.The apparatus records the temperature ofthe mixture and the torque exerted by therotors to maintain a constant speed in amixing run. (See Mixer and Torquerheometer.)

48. Plate-Out

An industrial term (jargon) used todescribe the formation of �hard� deposits ofadditives or impurities present in apolymer formulation on the metal surfaceof the processing equipment. These canmar the surface of manufactured products,such as calendered sheets. Plate-out deposi-tions are particularly likely to take placeif any of the additives are miscible withthe external lubricant.

Plasticizer nature Plasticizer type Plasticizer names Polymers plasticized

Phthalates General purpose,Primary types

dioctyl (DOP),diisododecyl(DIDP), dibutyl (DBP)

PVC, nitrile rubber, neoprenerubber, cellulosics,poly(vinyl acetate)

Dialkyl esters Low temperature,Secondary types

dioctyl adipate (DOA),dioctyl sebacate (DOS),

PVC

Phosphates Flame retardant,Primary types

triphenyl (TPP), tricresyl(TCP)

PVC, cellulosics,nitrile rubber,neoprene rubber

Polyesters Non-migratory,Secondary types

poly(propylene adipate),(MW¼ 1500–3000)

PVC

Sulfonamides Secondary types N-ethyl SA, o- and p-tolueneSA, formaldehyde SA resin

polyamides

48 Plate-Out j243

49. Plating

A term used to describe the deposition of ametallic layer on the surface of an article byan electrolytic deposition method.

50. Plug-Assisted Vacuum Forming

A techniqueused in thermoforming of rigidpolymer sheets. (See Thermoforming.)

51. Plug Flow

A type of flow with a flat velocity gradientprofile, originating from slip phenomena atthe walls of the flow channel and/or result-ing from very pronounced pseudoplasticbehaviour of the polymer melt, that is, alow power-law index. (See Non-Newtonianbehaviour.)

52. PMR

Abbreviation for a technology (developed atNASA-Langley) known as �polymerizationof monomer reactants�, used to describesystems consisting of carbon fibres impreg-nated in a stoichiometric mixture of anaromatic anhydride or a methyl ester (usu-ally perfluoroisopropylidene diphthalic an-hydride) with an aromatic diamine as ameans of producing the required polyimidethrough in-situ polymerization during themanufacture of composites.

Perfluoroisopropylidene diphthalic anhydride(6FDA).

Other systems used for adhesivesconsist of mixtures of a polymeric aromatic

diamine with norbor-5-ene-2,5-dicarboxylicmethyl monoester, cured in two stages. Thefirst stage produces a reactive end-cappedprepolymer, such as

which cures further through free-radicalpolymerization of the end groups.

53. Poiseuille Equation

An equation first derived by Poiseuille forthe volumetric flow rate (Q) of a Newtonianliquid through a circular channel, that is

Q ¼ pR4DP=8hL;

where R is the radius, DP is the pressuredrop along the length L of the channel andhis the viscosity of the fluid.

54. Poisson Ratio

The ratio of the lateral strain to the longitu-dinal strain resulting from uniaxial tensionor compression deformations. The defini-tion is illustrated in the diagram.

Illustration of the concept of Poisson ratio.

244j 54 Poisson Ratio

Note that thePoisson ratio varies from0.5for materials that undergo no volumechange, such as rubber, to about 0.3–0.35for a glassy polymer, due to volumetricchanges, that is, expansion in tension andcontraction in compression. (SeeModulus.)

55. Polarity

Denotes the presence and strength of di-poles in a solvent, auxiliary component orpolymer.

56. Polarization

Aphenomenon and a parameter describingthe response of a material to excitations byan electromagnetic field. The total polariza-tion is the sum of various terms, respective-ly, electronic, atomic, orientation and inter-facial. The contribution of each polarizationterm to the permittivity of the material isrelated to the frequency of the applied stim-ulus. (See Permittivity.) At low frequencies,as in the case of an AC voltage, the predom-inant polarizations are interfacial polariza-tion, resulting from the response of slow-moving charges at interfaces with filler par-ticles or reinforcing fibres, and dipolar po-larization, resulting from the movement ofpermanent dipoles in the structure. Thetype of polarization that takes place at dif-ferent frequencies is illustrated.

Variation of permittivity with frequency of appliedstimulus. Source: Unidentified original source.

57. Polyacetylene

A polymer with the structure�(CH¼CH)n�CH¼CH�produced by the Zieglercatalysis of acetylene. The conjugated dou-ble bonds form the basis for developing anintrinsically high electronic conductivity bya variety of doping methods. (See Conduc-tive polymer.)

58. Poly(Amic Acid)

A polymer precursor for the production ofpolyimides, normally available inN-methyl-pyrrolidone (NMP) or dimethylformamide(DMF) solution to prevent imidizationreactions occurring during storage. (SeePolyimide.) NMPandDMFmolecules form

58 Poly(Amic Acid) j245

physical bridges through hydrogen bond-ing. Internal imidization reactions occuruntil the temperature is increased to about150 �C. At this temperature the solvent–amic acid bridges break down and conver-sion to polyimide begins to take place viainternal condensation reactions (imidiza-tion), as shown.

A widely used poly(amic acid) for theproduction of films, wire coatings and in-terlayer insulation in microelectronics isproduced from the reaction of pyromelliticdianhydride (PMDA) and oxydianiline(ODA), which can be represented by

59. Polyamide

Polymers produced by the condensationreactions of a dicarboxylic acid and a di-amine or via internal condensation reac-tions of an a,v–amino acid, both throughthe intermediate formation of a salt in anaqueous medium. The monomers can beeither aliphatic or aromatic in nature.Aliphatic polyamides can also be obtainedby ring opening polymerization of a cyclicamide in the presence of water, or by eitheranionic or cationic polymerization. They aregenerally referred to as �nylons�. (SeeNylon.) Also available are aromatic polya-mides in which the high chain stiffness,coupled with the strong intermolecular

forces resulting from the amide groups, hasbeen exploited for the production of poly-mers with a high melting point, in theregion of 500 �C. These can only be pro-cessed by solution processing techniques inconcentrated sulfuric acid for the produc-tion of high-strength fibres or papers. (SeeAramid and Nomex.)

60. Polybenzimidazole (PBI)

Aheat-resistant polymer used for high-tem-perature applications. The typical structureof PBI is as shown:

61. Polybutadiene

(See Diene elastomer.)

62. Poly(But-1-ene) (PB)

A polyolefin represented by the formulashown, where the CH2–CH3 side groupappears on the same side along the polymerchain providing an isotactic structure.

It can crystallize in two forms, respective-ly, type II, which is a soft rubber-like poly-mer that is obtained on cooling from themelt state, and type I, resulting from atransformation of type II after aboutone week standing at room temperature.

246j 62 Poly(But-1-ene) (PB)

The transformation takes place at maxi-mum rate at about 30 �C. Type I has a highermelting point, in the region of 125–130 �C,and also a higher density in the region of0.91–0.92 g/cm3. It has a high resistance tocreep,manifested by a small rate of increasein strain with time under stress, whichmakes it attractive for tubings and pipes.Some copolymers with a lower meltingpoint are also available.

63. Poly(Butylene Terephthalate) (PBT)

(See Polyester.)

64. Polycarbonate (PC)

A glassy engineering thermoplastic poly-mer with a Tg in the region of 150 �C,represented by the formula shown.

It is widely used for applications requir-ing a combination of desirable characteris-tics, such as rigidity, creep resistance,toughness and transparency, as well as highresistance to UV light. Special branchedgrades are used for the production of DVDsowing to their ability to exhibit very lowwarping in injection moulding. This arisesfrom the absence of molecular orientation,which results in a uniform shrinkage dur-ing cooling in the mould. The lack of orien-tation also results in a lack of internal stressand the absence of birefringence patternsunder polarized light, which makes it anexcellent candidate for optical devices.Polycarbonate ismisciblewith a variety of

polymers, notable among which is poly(bu-tylene terephthalate). Mixing the two to-gether with the addition of semi-miscibleacrylate elastomer, which forms particulate

rubbery inclusions, results in a well-balanced combination of useful properties,such as retention of modulus and strengthat high temperature, toughness at low tem-peratures, oil/fluid resistance and goodthermal oxidative and UV stability. Widelyused in the automotive industry are blendswith acrylonitrile–butadiene–styrene (ABS)terpolymer alloys, utilizing the miscibilityof the styrene–acrylonitrile (SAN) polymercomponent with polycarbonate and allow-ing the immiscible butadiene–acrylonitrileelastomer component to form rubberyinclusions to increase the impact strength.The micrograph shows the presence ofspherical rubbery inclusions derived fromABS and also a zone surrounding theseparticles consisting of a semi-misciblemixture of polycarbonate and the SANcomponent, chemically bonded to therubber particle.

Electron micrograph of a blend of polycarbonateand ABS. Source: Herpels (1989).

65. Poly(Carborane–Siloxane)

Linear polymers containing carbon, siliconand boron in the backbone chains, withuseful elastomeric properties, which can beused continuously at temperatures up to300 �C. They can be formulated, processedand vulcanized in the same way as conven-tional silicone elastomers. The chemicalstructure of the base polymer is shown.

65 Poly(Carborane–Siloxane) j247

66. Polychloroprene


67. Polychlorotrifluoroethylene (PCTFE)

A polymer with a melting point around215 �C, a Tg in the region of 45 �C and adensity of 2.1 g/cm3. PCTFE has an excep-tional thermal oxidation resistance and ex-tremely good barrier properties towardswater vapour. The chemical structurecan be represented by the formula–[CClFCF2]n– but it is also available as analternating copolymer with ethylene. Al-though it was intended to be a processablepolymer equivalent to PTFE, it falls short ofthese expectations in terms of coefficient offriction and chemical resistance. The polar-ity arising from the substantial difference inelectron density between the Cl and Fatomsattached to the same C atom also bringsabout considerable deterioration in electri-cal properties relative to PTFE.

68. Polyelectrolyte

Polymers containing ionic side groups inthe molecular chains. These can form saltsand can perform like any electrolyte capableof producing ionic conduction through dis-sociation and movement of the counter-ions, if sufficiently small in size, hoppingfrom one ionic group to another. Examplesof cationic and anionic polyelectrolytes areshown.

Cationic polyelectrolyte: poly-(4-vinylpyridine) qua-ternized with butyl bromide.

Anionic polyelectrolyte: sodium polyacrylate.

Both are examples of linear polyelectro-lytes that will dissolve in water. There arealso examples of polyelectrolytes in the formof cross-linked networks, whichwill swell inwater to produce �gels� and produce amech-anism for the exchange of ions with inor-ganic electrolyte solutions, as illustrated.

Swollen ionic �gel� in equilibrium with an electrolytesolution. Source: Flory (1953).

The free anions can associate with thecations fixed on the network and also movefreely from one cationic site to anotherthrough dynamic associations. In this waythe swollen ionic gel acts as its own mem-brane, preventing the fixed cations fromdiffusing into the surrounding solution.

248j 68 Polyelectrolyte

This produces a mechanism for the ex-change of anions from another solution.(See Ion exchange resin and Membrane.)Polymer electrolytes without solvents,

known as solid polymer electrolytes, areused in lithium batteries. These are basedon poly(ethylene oxide) containingdissolved lithium salts, such as lithiumperchlorate, LiClO4, and lithium bis(tri-fluoromethylsulfonyl)imide, Li[N(SO2CF3)2](commonly known as TFSI). The ionicconductivity arise from the ability of Liþ

ions to form coordination bonds withthe closely spaced ether groups along thepolymer chains, thereby producing paths forthe Liþ to hop along while maintainingcharge neutrality with the neighbouringanions. Special copolymer grades of poly(ethylene oxide) (PEO) are usually usedin order to destroy the crystallinity of stan-dard PEO as a means of enhancing themobility of Liþ , thereby increasing theconductivity.

69. Polyester

Polymers containing repeating ester groupsin the backbone chains. These are producedboth as thermosetting resins (for alkyds andunsaturated polyesters) and as linear ther-moplastic polymers (aliphatic, aromatic ormixed aliphatic–aromatic). The linear ali-phatic polymers are used primarily as hot-melt adhesives owing to their quite lowmelting point (e.g. poly(ethylene succinate),Tm¼ 108 �C) or as polymeric plasticizers (e.g. poly(ethylene glutarate), Tm¼ 10 �C, orpoly(ethylene adipate),Tm¼ 50 �C). The dif-ference in melting point arises from thedifferent number of CH2 groups of thediacid used, which is two for the succinate,three for the glutarate and four for theadipate. These follow the trend that smallerand even numbers of CH2 give highermelt-ing points than larger and odd numbers,owing to the lower packing density of the

latter molecules in the respective crystallattices.The mixed aliphatic–aromatic polymers,

in particular poly(butylene terephthalate)(PBT; Tm¼ 222 �C, Tg¼ 40–45 �C) andpoly(ethylene terephthalate) (PET; Tm¼ 265�C, Tg¼ 72–78 �C), are used primarily forfibres, plastics and films. PET is commer-cially used in much larger quantities thanPBT primarily on account of its lower cost.PBT crystallizes at a much faster rate thanPETand is much tougher in the unorientedcrystalline state. For this reason, PBT is usedwidely for injection moulding, particularlyas a glass-fibre-reinforced grade. PET isused mostly for the production of fibres,biaxially drawn films and injection blowmoulding of bottles and containers. For thelatter application, advantage is taken of theability of PET to be moulded into amor-phous pre-forms that can be stretched ataround 100–110 �C to undergo stress-in-duced crystallization, which brings aboutenormous increases in strength and tough-ness, as well as a high level of optical trans-parency. Poly(ethylene naphthanate) (PEN)has been introduced in recent years as it hasa Tg in the region of 125 �C, owing to thehigh chain stiffness brought about by thebulky naphthanate rings. The main use ofPEN is for the production of biaxially drawnfilms for motor insulation. Thermoplasticaliphatic–aromatic polyesters have beenused also for the production of a variety ofengineering polymer alloys for use in theautomotive industry and electrical and elec-tronic components. Themain advantages ofusing polyesters for the production of alloysfor automotive applications, for instance,are their high melting point, which makespossible their use in high-temperature paintstoving operations, as well as their resis-tance to oils.High-Tg amorphous polyesters are pro-

duced, with the used cycloaliphatic glycols,such as dimethylolcyclohexane, utilizingthe rigidity provided by the aromatic and

69 Polyester j249

cyclohexane rings in the backbone of thepolymer chains. Even higher Tg values areexhibited by polyesters made via polycon-densation of diphenols with a mixture ofterephthalic acid and phthalic anhydride,often referred to as polyarylates. In thesesystems, the lack of symmetry of the con-stituent units of the polymer chains pre-vents the development of crystallinity, asindicated by the example shown.

Linear polyesters are also synthesized asmulti-block copolymers for the productionof thermoplastic elastomers, where the hard(crystalline) domains of poly(butylene tere-phthalate) have a melting point (Tm) withinthe range of about 170–210 �C. The softdomains consist of low-molecular-weightsegments of poly(tetramethylene oxide)with a glass transition (Tg) in the region of�80 �C. (See Thermoplastic elastomer.)

70. Poly(Ether Imide) (PEI)

(See Polyimide.)

71. Polyethylene

(See Ethylene polymer.)

71.1 Ethylene Copolymer

(See Ethylene polymer.)

71.2 Ethylene–Methacrylic Acid IonomericCopolymer

(See Ionomer.)

72. Poly(Ethylene Terephthalate) (PET)

(See Polyester.)

73. Polyhydroxyalkanoate (PHA)

A family of biopolymers synthesized bymany bacteria. The most common is poly(3–hydroxybutyrate) (PHB). In order toovercome the excessive brittleness inherentto PHB, due to the high degree of crystal-linity, copolymers are usually produced tointroduce long-chain side groups, such aspoly(hydroxybutyrate-co-hydroxyvalerate) orpoly(hydroxybutyrate-co-hydroxyhexano-ate). (See Biopolymer.)

74. Polyimide (PI)

A class of polymers well known for theirgood properties at high temperature and fortheir very high resistance to thermal oxida-tion and to absorption of solvents. However,they are susceptible to hydrolytic degrada-tion under acidic conditions. There are twomain types of polyimides widely used com-mercially, as follows.

. Curable systems These are produced ei-ther from poly(amic acid) solutions orfrom reactive monomers, and are usedfor coatings, asmatrices for composites orin the production of films. (See Poly(amicacid).) The chemical structures of the twopolyimides most widely used for coatingsandmicroelectronics interlayers, or in theform of films, are shown. The first, de-rived from poly(amic acid) solution, has aTg in the region of 280 �C, whereas theother, obtained from diphenyl dianhy-dride, has a Tg value that can be greater

250j 74 Polyimide (PI)

than 300 �C. Both PIs have a service tem-perature rating greater than 250 �C.

. Thermoplastics systems These are usedfor themanufacture ofmoulded or extrud-ed products. The main polymer in thisclass that is available commercially is poly(ether imide) (PEI), which is a glassy poly-mer with a Tg in the region of 230 �Cand aservice temperature rating around 180 �C.Its chemical structure is shown.

Structure of the thermoplastic, poly(ether imide).

75. Polyisobutylene

(See Butyl rubber.)

76. Polyisocyanurate

(See Urethane polymer and resin.)

77. Polyisoprene


78. Polyketone

These are aromatic ether ketones with ahigh melting point and an exceptionallyhigh thermal oxidative stability, which al-lows them to be processed by conventionalthermoplastics processing techniques, albe-

it at higher temperatures. Adding thesecharacteristics to the high ductility even inthe crystalline state makes poly(aryl etherketone)s unique among all the processablearomatic polymers. The crystallinity pre-vents solvent absorption and embrittlementthrough crazing phenomena. The twomainsystems available commercially are poly(ar-yl ether ketone)s (PEK) and poly(aryl etherether ketone)s (PEEK) represented by theformulae shown.

The properties are remarkably similar,with PEK exhibiting a slightly higher Tg andhighermelting point. The values are respec-tively in the region of 145 �C and 335 �C,with densities of 1.265 g/cm3 for the amor-phous polymers, obtained by melt quench-ing, and about 1.32 g/cm3, depending onthe degree of crystallinity.A major use of poly(aryl ether ketone)s is

for matrices for advanced carbon-fibrecomposites.

79. Poly(Lactic Acid) (PLA)

A biopolymer obtained by condensationreaction of lactic acid. (See Polylactide andBiopolymer.)

80. Polylactide

Corresponds to poly(lactic acid) producedfrom ring opening polymerization of lac-tide. Poly(lactic acid) and polylactide arechemically the same (known as PLA) andcan also readily depolymerize thoroughhydrolysis down to the original monomer.The polymerization and depolymerizationreactions are shown.

80 Polylactide j251

Because two stereoisomeric forms of lac-tic acid exist, there are three forms of PLA:poly(L–lactic acid) (PLLA), corresponding tothe syndiotactic structure; poly(D–lactic ac-id) (PDLA), equivalent to the isotactic struc-ture; and poly(meso-lactic acid), also knownas poly(D,L–lactic acid) (PDLLA), as it con-tains equimolecular amounts of D- andL–lactic acid units. While PLLA and PDLAare crystalline, with similar characteristics,the PDLLA form is amorphous. Polymeri-zation conditions can be adjusted to pro-duce a variety of PLA, containing differentratios of L to D monomeric units, whichgives polymers with different levels of crys-tallinity and properties. Both the meltingpoint (Tm) and glass transition temperature(Tg) of the polymer vary according to thedegree of crystallinity. Reported values forTm are between 120 and 200 �C, which varynot only according to composition but alsodepending on the thermal history of thesample.

81. Polymer

A term first introduced in the early part ofthe nineteenth century by the Swedish sci-entist Berzelius for siloxane compoundscontaining several repeating units. The

term became more widely used followingthe work of the German scientist Staudin-ger, when he illustrated that natural rubber,as well as synthetic products derived fromthe polymerization of monomers, con-tained many thousand repeating units. Healso devised a method for measuring themolecular weight of polymers by the well-known solution viscosity technique. Ini-tially, the term �high polymers� was used toemphasize the very high-molecular-weightfeature of these organic compounds.

82. Polymer Alloy

A term used to describe �well-compatibi-lized polymer blends�.

83. Polymer Blend

A mixture of two or more polymers. Theproperties of polymers can be improved byblending with auxiliary components, suchas plasticizers, or with other polymers toobtain the so-called �polymer blends� or�polymer alloys�.

. Miscible blends are mixtures of two ormore polymers that are miscible at

252j 83 Polymer Blend

molecular level andwill exhibit propertiesthat are intermediate between those of thepolymer components. These includeproperties such as glass transition tem-perature, light transmission and gas/vapour permeability. These types ofblends are widely found in the fields ofadhesives and coatings.

. Heterophase polymer blends are mix-tures of two or three polymers that areeither totally immiscible or semi-misci-ble, so that they form two distinct phases,as shown.

Particulate dispersed blend (left) and co-continu-ous phase morphology blend (right).

The morphology of polymer blends can beeither a particulate type (left), where theminor component becomes the dispersedphase, or in the form of co-continuousphase systems (right). In particulate poly-mer blends, normally the continuous phaseis a glassy polymer and the dispersed phaseis a rubbery polymer. Either component canbe a linear or cross-linked polymer. Theseblends are normally produced to increasethe fracture toughness of glassy polymers.Typical systems are high-impact polysty-rene (HIPS) and acrylonitrile–butadiene–styrene (ABS) terpolymer blend.

84. Polymerization

The process or chemical reactions that leadto the formation of polymers from the con-stituent monomer components.Polymerization processes can be classi-

fied in a number of ways, but more usually

into condensation and addition polymeriza-tion. (See Condensation polymerizationand Addition polymerization.) In the firstcase, single monomer units or a mixture oftwo or more monomer units add to oneanother with the loss of water, or otherspecies, derived from the combination ofend groups in the monomer units involvedin the reaction, for example,

n HO�M�H!�ðMÞn�þ n H2O

or

n HO�M�Hþ n HO�CM�H!�ðM�CMÞn�þ n H2O

In addition polymerization,monomer unitsproduce polymer chains by the direct addi-tion of monomer units to one another.Addition polymerization can be furtherdivided into free-radical polymerization andionic polymerization. (See Free-radicalpolymerization, Anionic polymerizationand Cationic polymerization.)Polymerization can also be divided into

homopolymerization, when only onetype of monomer unit is used for the for-mation of polymer chains, and copolymeri-zation, when two or more different mono-mer units are used to produce polymerchains. (See Polymer and Copolymer.)Free-radical polymerization can be carriedout in different ways: (i) from suspension oremulsion of monomer in water, (ii) in solu-tion using either a solvent that dissolves thepolymer or one that allows the polymer toseparate out as a dispersion in solvent, and(iii) mass or bulk polymerization, wherethe polymer is either soluble in the mono-mer or phase-separates at a certain level ofconversion.

85. Poly(4-Methylpent-1-ene) (PMP)

An isotactic polyolefin represented by theformula:

85 Poly(4-Methylpent-1-ene) (PMP) j253

It was the first crystalline polymer thatwas found to be completely transparent,owing to the similar density of the crystal-line and amorphous regions (in the regionof 0.83 g/cm3). The bulky side groups,CH2CH(CH3)2, along the chains provideconsiderable rotational hindrance, whichresults in a polymer with a very high melt-ing point at around 245 �C.

86. Polyol

A general term to describe hydroxyl-termi-nated oligomers, usually polyether types,known also as polyglycols. The more com-mon polyglycols are poly(ethylene glycol)(PEG) and poly(propylene glycol) (PPG).The structure of these is shown.

There are also polyester types, such aspoly(ethylene adipate) and other mixed ar-omatic–aliphatic polyesters. Multifunction-al polyols (trifunctional types in particular)are available to produce network structures,such as those in polyurethanes.

87. Polyolefin

A polymer produced from olefin mono-mers. Themore common types are polyeth-ylene and polypropylene, but there are sev-eral other types of considerable importance.

88. Polypeptide

Apolymer composed of protein-type aminoacid units linked by peptide (amide) bonds.(See Biopolymer.)

89. Poly(Phenylene Oxide) (PPO)

This polymer is obtained by a unique poly-merization method based on the catalyticoxidation of 2,6-dimethylphenol, accordingto the scheme

PPO is an amorphous polymer with Tg inthe region of 190–210 �C and a high meltviscosity. The polymer is susceptible to rap-id decomposition at temperatures above Tgowing to the formation of conjugatedmethide groups, followed by a rapid oxida-tion of the methyl groups.Since PPO is miscible with polystyrene,

blends are produced as ameans of reducingthe processing temperature and the meltviscosity. Although this considerablyreduces the Tg, the blends can still be usedup to temperatures of about 120–130 �C.More usually commercial blends are pro-duced using mixtures with high-impactpolystyrene (HIPS) to benefit from the en-hanced toughness resulting from the rub-bery polybutadiene inclusions. More ther-mally stable blends are produced with theuse of thermoplastic elastomers based onstyrene block copolymers. Other blendswith low-melting-point polyamides are alsoproduced to improve the solvent and oilresistance for use in the automotive andelectrical and electronics industry. In thesesystems, compatibilization is achievedthrough the formation of graft copolymersvia free-radical decomposition reactions.(See Polymer blend.)

90. Poly(Phenylene Sulfide) (PPS)

A crystalline aromatic polymer representedby the structure

254j 90 Poly(Phenylene Sulfide) (PPS)

The quoted melting point is 288 �C andthe Tg is 93 �C. The polymer is extremelybrittle and is, therefore, used mainly as afibre-reinforced grade for load-bearing ap-plications in compression, or as the matrixfor advanced composites, owing to the re-tention of properties up to high tempera-tures and the high resistance to solvents andchemicals, arising from the high level ofcrystallinity.

91. Polypropylene (PP)

A polyolefin represented by the formulashown, where the CH3 group appears onthe same side along the polymer chain,providing an isotactic configuration.

It is produced by Ziegler–Natta andmetallocene catalysis and is available asrandom and block copolymer grades withethylene. Through many ethylene–propy-lene combinations within the blocks, andmolecular-weight diversity, it is possible totailor the structure to achieve a wide varia-tion of optical, mechanical and rheologicalproperties. Themelting point of PP is in therange of 170 �C for homopolymers, down to135 �C for copolymers, while theTg remainsat around �15 �C.PP is a polymer with a reasonably high

rigidity, having a Young�s modulus in therange 1–2GPa, depending on density,which varies from 0.90–0.91 g/cm3 accord-ing to the degree of crystallinity. The lack ofpolarity has two contrasting effects, provid-ing excellent electrical properties but poorresistance to mineral oils. The presence oftertiary C�H groups along the polymerchain makes it vulnerable to attack by freeradicals, leading to poor thermal and UVstability. On the other hand, this featurehas provided the opportunity to deliberately

induce chain scission in the chains to pro-duce the so-called �controlled rheology�grades with low molecular weight and lowpolydispersity, which results in a very lowmelt viscosity. This is a desirable character-istic for the production of fibres and flatfilms, as well as coatings. Unlike all poly-ethylene grades, PP does not suffer fromenvironmental stress cracking problems.(See Polyolefin.)

92. Polypyrrole

(See Conductive polymer.)

93. Polysaccharide

(See Biopolymer.)

94. Polystyrene

(See Styrene polymer.)

95. Polysulfone

These are glassy aromatic polymers with avery high Tg. The two main types foundcommercially are as follows:

. Poly(aryl sulfone) designated as PSU,with a Tg in the region of 190 �C, andrepresented by the formula

Structure of a poly(aryl sulfone).

. Poly(ether sulfone) with a Tg around230 �C, and represented by the formula

Structure of a poly(ether sulfone).

95 Polysulfone j255

Even higher Tg values have been achievedby introducing very rigid biphenyl groupsinto the polymer chains. The absence ofhydrocarbon segments in the polymer con-fers a very high thermal oxidative stability.Even for the case of poly(aryl sulfone)s, theCH3 groups are quite resistant to thermaloxidation. They have a very poor resistanceto UV light owing to very strong absorptionby the SO2 groups. Another major difficultywith these polymers is their susceptibility tobrittle failure occurring through crazing,which is exacerbated in the presence ofsolvents.

96. Polytetrafluoroethylene (PTFE)

Aunique polymer produced by conventionalsuspension and emulsion polymerizationwith free-radical initiators, resulting in poly-mers with exceptionally high molecularweights due to the lack of chain terminationreactions. At the same time, the absence ofchain transfer reactions during polymeriza-tion allows the formation of linear chainsfree of any branches. These conditions resultin a highly crystalline polymer with a veryhigh melting point (327 �C), a very highstability to thermal and UVdegradation, andan excellent resistance to solvents. The com-plete lack of net dipoles along the chains, dueto internal cancellation of local C–F dipolesacting in opposite directions, confers on thepolymer excellent dielectric characteristics.Coupled with lack of reaction possibilities athigh temperatures to produce graphitic(char-like) residues, thepolymeralsoexhibitsan extremely high resistance to tracking fail-ures at high voltages, particularly in thepresence of environmental pollution, whichis the main weakness of most polymer in-sulators. The presence of four �heavy� fluo-rine atoms in each repeating unit, togetherwith the fairly high degree of crystallinity,results in a polymer with a high density, inthe range 2.14–2.20 g/cm3.

One of the most outstanding features ofPTFE is its very low coefficient of friction.With values as low as 0.04, it has often beensaid to be equivalent to �wet ice on ice�. PTFEis a soft and ductile polymer, which main-tains a high ductility even at very low tem-peratures. In general, it suffers from a lowyield strength and apoor resistance to creep,which has prevented it from being usedmore widely in structural applications.A major factor that has limited the uses ofPTFE is its extremely high melt viscosity,which requires high pressures and the gen-eration of high shear stresses to promoteflow. This can result in large rises in tem-perature, which can lead to rapid depo-lymerization reactions at temperaturesabove 400 �C, with the formation of highlytoxic volatiles. The diagram, representingthe mechanical spectrum of the deforma-tional behaviour of PTFE, shows that themodulus values at high temperatures arequite low and are associated with two sec-ondary transitions.

Dynamic modulus and mechanical loss factor ofPTFE. Source: Domininghaus (1992).

These secondary transitions bring aboutphase transformations, which is a rare oc-currence in polymers. The transition at19 �C is associated with the transformationof the triclinic crystals into a less-orderedhexagonal packing. This is manifested assudden peaks in the coefficient of thermalexpansion. The transition at very low tem-peratures is a characteristic transition relat-ed tomolecular relaxationswithin the amor-phous phase (glass transition), while the

256j 96 Polytetrafluoroethylene (PTFE)

transition at 127 �C is again associated withthe amorphous phase, but is an actual phys-ical transition of physical states, from amor-phous solid to supercooled liquid state.PTFE is available in many different grades,many of which contain inorganic fillers orfibre reinforcement to enhance the me-chanical properties. Fillers include (i) mo-lybdenum sulfide and graphite as solidlubricants to increase the wear resistance,(ii) carbon fibres and glass fibres for rein-forcement, and (iii) bronze particles to im-prove several characteristics, such as creepandwear resistance, aswell as increasing thethermal conductivity to reduce rises in tem-perature arising from frictional contacts.

97. Poly(Tetrafluoroethylene–Ethylene)Copolymer (PETFE)

Acopolymer containing 25%ethylene, char-acterized by a very high melting point(about 280 �C), an exceptional thermal oxi-dative stability (service temperatures up toabout 200 �C) and high resistance to sol-vents. These characteristics are close tothose exhibited by PTFE, with Tm around330 �C and a service temperature up to250 �C. Unlike PTFE, the PETFE copoly-mers can be processed by conventionalpolymer processing methods and havemuch better mechanical properties thanPTFE, except for the coefficient of friction.

98. Poly(Tetrafluoroethylene–Hexafluoropropylene) Copolymer (FEP)

A copolymer containing small amounts ofhexafluoropropylene in the chains to dis-rupt the chain regularity and create lessperfect crystals as a means of reducing themelting point to temperatures below that ofPTFE. A comparison is shown of the struc-tures of hexafluoropropylene monomerunits (left) and tetrafluoroethylene units(right).

The compact nature of the pendent CF3group does not create large changes in thepacking of the molecular chains, so that thepolymer retains its ability to formcrystalsandthedensitydoesnot decrease verymuch, thatis, fromabout 2.2 for PTFE to 2.15 g/ cm3 forFEP. At the same time the melting pointdecreases sufficiently to enable the polymerto be processed by the conventionalmethodsused for thermoplastics, albeit atmuch high-er temperatures.As a result of thedecrease indegree of crystallinity, however, the polymersuffers from deterioration in mechanicalproperties, particularly with respect to thecoefficient of friction, which is much higherthan that of PTFE.

99. Polythiophene

A researched intrinsically conductive poly-mer, represented by the formula

100. Poly(Vinyl Butyral)

(See Vinyl polymer.)

101. Poly(Vinyl Carbazole)

(See Vinyl polymer.)

102. Poly(Vinylidene Chloride) (PVDC)

A crystalline polymer with a melting pointin the range 198–205 �C. The chemical

102 Poly(Vinylidene Chloride) (PVDC) j257

structure can be represented with the gen-eral formula

PVDChas a lowpermeability to gases andliquid additives used for aromatization andflavouring of food, which makes it verysuitable as a coating or lining material forfilm packaging and containers. Due to thesusceptibility to decomposition throughdehydrochlorination, followed by rapidthermal oxidation, the melt processablegrades are in the form of random copoly-mers with ethyl acrylate or acrylonitrilemonomers, as a means of reducing thedegree of crystallinity and melting point.Copolymers with vinyl chloride or vinylacetate are used the form of water emul-sions as surface coatings for paper, polymerfilms and containers.

103. Poly(Vinylidene Fluoride) (PVDFor PVF2)

A crystalline high-molecular-weight poly-mer exerting polymorphism due to thepresence of a substantial amount of head-to-head sequences of monomeric units inthe polymer chains, which gives rise todifferent crystal structures with meltingpoints in the range of 154–184 �C, Tgaround�40 �C and a density of 1.78 g/cm3.The mechanical properties, for example,modulus, yield strength and ductility, aresimilar to those of HDPE. However, PVDFhas a much greater resistance to solventsand amuchhigher stability towards thermaloxidation and UV-induced degradation, ow-ing to the presence of CF2 groups andthe total absence of double bonds and ter-tiary CH groups in the molecular chains.The general molecular structure can berepresented by the formula

The large difference in electron densitybetween two adjacent CH2 and CF2 groupsalong the polymer chain creates a very largedipole, which is responsible for the verylarge dielectric constant, the highest of allcommercial thermoplastics. For this rea-son, PVDF can only be used as a secondaryinsulation or as a protective component inwire and cables. The large dipoles, however,confer on PVDFa unique characteristic thathas been exploited for the production ofpiezoelectric devices. There are availablealso a large number of copolymers withvarying amounts of hexafluoropropyleneunits, to obtain more flexible products, dueto the reduction in crystallinity, while main-taining the high resistance to thermal andUV degradation.

104. Post-Curing

A treatment of cross-linked polymer pro-ducts carried out at high temperatures tooptimize the desired properties.

105. Pot Life

A practical term used to describe the avail-able time for the processing of a thermoset-ting resin system. A certain amount ofreactions in cross-linkable systems can betolerated before the viscosity increases tolevels that render the systemunprocessable.Pot life is related to the more preciselydefined concept of gel time. (See Gel time.)

106. Powder Coating

Aprocess for producing coatings from �dry�powders. A widely used powder coatingprocess is �electrostatic spraying�, whichtakes place in successive stages, compris-ing: (i) electrification of the powder by pass-ing it through thenozzle of a �gun� subject to

258j 106 Powder Coating

a high-voltage electricfield; (ii) dispersion ofthe charged particles through electrostaticrepulsions; and (iii) deposition of a thinlayer of powder on the substrate via electro-static attractions, which are connecting theconductive object to earth. These threestages of the process for producing thecoatings from dry powder are illustrated.

Schematic diagram of electrostatic spray coatingset-up. Source: Mascia (1989).

A uniform coating is achieved as a resultof the powder coating layer, formed on thesubstrate, which begins to repel the incom-ing charged particles when a certain thick-ness is reached. This is due to the insulatingeffect produced, which prevents the incom-ing particles from being discharged toearth. In the final stage the coated objectedis transferred to an oven for sintering. (SeePowder sintering.)Another important powder coating pro-

cess is �fluidized bed coating�, which in-volves the immersion of a heated objectinto afluid bed of suspended powder, whichmelts and sinters the powder coating. Asecond heating stage may be required tocomplete the thermofusion operation. Avariant to the conventional fluidized bedcoating described above is a techniqueknown as �electrostatic fluidized bed coat-ing�, which charges the particles as a meansof obtaining better control of the thicknessof the coating. At the same time this makesit possible to use an earthed metal article toattract the charged particles, so that thedeposited powder coating can then be sin-tered as a separate step.

107. Powder Sintering

A technique mostly used for the processingof PTFE, which consists in producing a pre-form by compaction in cold conditionsand then raising the temperature abovethe melting point of the polymer for asufficient length of time to allow moleculardiffusion across the grains. Upon cooling,crystallization takes place over the entiremass, which erases the previous interfacialboundaries. This can be done also as acontinuous process by ram extrusion inline with a sintering oven set-up. (SeePolytetrafluoroethylene.)

108. Power Law

A response that, when raised to the power n,becomes a linear function of the excitation.A typical example is the relationship be-tween shear stress, t, and shear rate, _g,for the flow of polymer melts, that is,t ¼ k _gn. This implies that a log–log plot ofthe shear stress against shear rate producesa straight line with gradient equal to n. (SeePower-law index and Non-Newtonianliquid.)

109. Power-Law Index

The exponent n of the power-law relation-ship between shear stress, t, and apparentshear rate, _g, for the flow of a polymermelt,that is, t ¼ k _gn. The value of n decreasesfrom1 (forNewtonian behaviour) to around0.3–0.4 for most polymer melts. The valueof n is obtained from a log–log plot of shearstress against apparent shear rate derivedfrom rheological measurements, as shownin the diagram.

109 Power-Law Index j259

Typical log–log plot of shear stress against apparentshear rate at three different temperatures,T1 < T2 <T3.

The diagram shows that the power-lawindex is not affected by changes in temper-ature within the range of temperatures usedfor the common processing operations,such as injection moulding and extrusion.(See Capillary rheometer, Rabinowitschequation and Viscosity.)

110. Pre-form

A small thick-walled precursor for theproduction of bottles by injection blowmoulding.

Typical pre-form used for the production of PETbottles.

111. Prepreg

A term (jargon) for resin-impregnated re-inforcing fibres or fabrics used for themanufacture of structures by compressionmoulding. During the production of pre-pregs, usually the resin is partially reactedwith the hardener in order to increaseviscosity by increasing the molecular

weight of the oligomeric components ofthe resin.

112. Pressure-Sensitive Adhesive (PSA)

(See Adhesive.)

113. Primary Plasticizer

(See Plasticizer.)

114. Primary Stabilizer

(See Stabilizer.)

115. Primary Transition

(See Transition and Glass transitiontemperature.)

116. Primer

A term used to describe a coating depositedon the substrate before the main coatinglayer is applied. A primer coating can havemany functions depending on the systemconsidered. It can simply act as an interfa-cial layer to enhance the adhesion of theprimary coating with the substrate or it canhave a functional role, such as corrosionprotection through the slow release of in-hibitors. For the case of porous substrates,the primer can used to seal the surface inorder to prevent the primary coating frompenetrating deeply.

117. Processing

A term used to describe any operation onthe polymer involved in the manufacture ofproducts.

260j 117 Processing

118. Processing Aid

An additive or auxiliary component of aformulation used to enhance the processingcharacteristics of a polymer or elastomer.

119. Processing Stabilizer

(See Stabilizer.)

120. Propagation Reaction

The reaction step taking place immediatelyafter the initiation step. The propagationstep is followed by a termination step, oftenvia chain transfer reactions. The processesinvolving propagation reactions are poly-merization and thermal degradation reac-tions, such as thermal and UV-assisted oxi-dation reactions.

121. Proton Exchange Membrane

(See Nafion.)

122. Pseudoplastic

A term describing the behaviour of polymermelts by which the viscosity decreases withincreasing shear rate during flow. Thisarises from a nonlinear relationship be-tween shear stress and shear rate, which isusually modelled by a power-law expressionor the Carreau equation. (See Non-Newtonian behaviour.)

123. PTC Polymer

The abbreviation PTC stands for �positivetemperature coefficient�, which refers to therapid increase in resistivity (i.e. positivegradient) experienced by certain polymer

products above a specific temperature. Thephenomenon is reversible, so that the poly-mer regains its high conductivity when iscooled down to the original temperature.The sudden change in the current densitythrough the material at some specific tem-perature, therefore, produces a �switch�effect in the circuit when a PTC polymeris used to separate the conducting elements.Since the switch effect is reversible, a PTCpolymer can be used as a temperature reg-ulator in heaters.The PTC characteristics are obtained by

the incorporation of a conductive filler, usu-ally carbon black, in a crystalline polymer inamounts just enough to reach the percola-tion threshold for the formation of conduc-tive channels for theflowof the current. Thethreshold conditions for the percolation ofthe conductive particles are reached at fairlylow concentrations, as these are confinedentirely within the amorphous regions. Theswitching to a non-conductive polymertakes place when the melting point of thepolymer is reached. The large thermal ex-pansion caused by the melting of the crys-tals breaks up the contact between the car-bon black particles, thereby interrupting theflow of current, as shown schematically.

Illustration of the breaking up of the contact currentmechanism due to thermal expansion during themelting of polymer crystals. Source: Unidentifiedoriginal source.

123 PTC Polymer j261

Further expansion of thematrix when themelting of the crystals is complete causesthe total disruption of the conductive paths.In order to achieve reversibility of theswitching characteristics, the polymer hasto be cross-linked as a means of achievingstable morphology through the preventionof the migration and possible agglomera-tion of the conductive particles. At the sametime, to ensure that the threshold condi-tions are reached at the lowest possibleconcentration of conductive particles, it ispreferable to cross-link the polymer at lowtemperatures, using high-energy radiationtechniques, such as electron beaming.

124. Pultrusion

(See Composite manufacture.)

125. Purging

A term used to describe the removal ofresidual polymer from the barrel of an ex-truder or injection moulding machine aftercompleting a particular processing opera-tion or changing to a new polymer. Purgingis usually carried out by passing through thenew polymer until the barrel is completelyfree of the previously used polymer. Thisoften involves the use of an intermediatepolymer that is more miscible with the firstpolymer and has a higher melt viscosity,in order to allow the removal of residues in�stagnation spots� of the flow channels.

126. PVC

Abbreviation for poly(vinyl chloride). (SeeVinyl polymer.) Available in two forms: rigidgrades, known as PVC-U, do not containplasticizers but may be in the form ofblends; and plasticized grades, known asPVC-P. The latter are available as com-

pounds, dry blends (jargon specific to PVCpowders) or pastes, also knownas plastisols.Flexible PVC grades are rubbery and, there-fore, contain a large amount of plasticizer tobring the Tg down to values below �20 �C.The amount of plasticizer used is usuallyhigher than 20% and can be as high as 80%for very flexible formulations. The latter ismade possible by the presence of crystaldomains that are swollen by the plasticizer,without bringing them into solution, there-by creating a strong thermo-reversible gel.(See Gel.) The use of small amounts ofplasticizer to reduce primarily the melt vis-cosity is not generally recommended, as itmay give rise to the �antiplasticization� phe-nomenon, which brings about considerableembrittlement in the final product. Theplasticizers used are normally: diphthalateesters of long-chain alcohols (e.g. octyl,nonyl or dodecyl phthalates); tricresyl phos-phate; and secondary plasticizers, usuallyused in combinationwith the above primaryplasticizers, namely, dioctyl adipate anddioctyl sebacate, as well as low-molecular-weight aliphatic polyesters derived from thecondensation reactions of both adipic acidand sebacic acid with ethylene glycol. (SeePlasticizer.)In all formulations, whether rigid (PVC-

U) or flexible (PVC-P) types, in addition toproperty modifiers, such as fillers, fire re-tardants and antistatic agents, there are anumber of other essential additives thathave to be incorporated into the mixes asa means of assisting processing operationand to improve the service performance ofproducts. Predominant among these addi-tives are the thermal stabilizers, which havebeen specially developed to enable PVC tobe processed at the highest possible tem-perature. Other important additives forPVC-U formulations are lubricants and pro-cessing aids.PVC grades are also widely used in the

form of melt blends as a means of improv-ing the processing characteristics of the

262j 126 PVC

polymer or themechanical properties of theproducts. Examples of blends of PVC withsmall amounts of other polymers as ameth-od for improving the processing character-istics follow:

a) the addition of small amounts high-molecular-weight poly(methyl methac-rylate) (PMMA), which functions as aprocessing aid by speeding up thefusion of PVC particles in extrusionoperations, because PMMA is fullymiscible with PVC and, therefore, theoptical transmission characteristics arenot impaired;

b) the addition of ethyl acrylate–methylmethacrylate copolymers, chlorinatedpolyethylene (CPE) or ethylene–vinylacetate (EVA) to increase the meltstrength in extrusion and to enhancethe drawdown characteristics of foilsand sheets for thermoforming.

Another important reason for producingPVC blends is to improve the fracturetoughness and impact strength. Typical isthe addition of 5–15% of specially formulat-ed acrylonitrile–butadiene–styrene (ABS)or methyl methacrylate–butadiene–styrene(MBS) terpolymer alloys, exploiting themis-cibility of the styrene–acrylonitrile copoly-mer component of ABS and the PMMAcomponent of MBS. This assists the disper-sion of butadiene–styrene rubber particlesand provides a strong bond with the glassyPVC matrix, through the misciblePVC–PMMA interphases. Well known alsoare blends of PVC and nitrile rubber (NBR)to improve the resistance to oils andfluids, as well as increasing the flexibilityof products, such as hoses, belting andwires and cables.

126.1 Dry blend

Dry blends are PVC porous powders thathave been made to adsorb large quantities

of a plasticizer through high-speed mixingat high temperature. In this way the plasti-cizerfills up themicroporeswithin particlesabout 100–150mm diameter. These are pro-duced by specially devised polymerizationtechniques. One of these is known as�microsuspension�, and another is two-stage bulk polymerization. The latter takesadvantage of the fact that PVC is not solublein its monomer and therefore will precipi-tate out at about 5–10% conversion. Thesuspension obtained in the first high-speedreactor is transferred to a second reactorwhere more monomer and initiator areadded to continue the polymerizationreactions. The process is stopped at about80% conversion to outgas the unreactedmonomer.

126.2 PVC paste

These consist of emulsion PVC particles(20–150mm) dispersed in plasticizer. Whenthe temperature is increased, the plasticizerfirst migrates into the spaces between theprimary particles, 0.1–0.2mm diameter, togel the paste (i.e. a soft solid state. Thestructure of a typical emulsion particle usedfor pastes is shown. After gelation, theplasticizer diffuses into themolecular struc-ture to produce the plasticized polymer.

Micrograph of a PVC emulsion particle. Source:Wilson (1995).

126 PVC j263

126.3 Heat stabilization of PVC

This requires special consideration owingto the unique degradation mechanism ofvinyl polymers, as shown.

From the reaction scheme, it can be de-duced that stabilizers for PVC have to fulfilthe following functions:

a) absorb and neutralize the HCl evolvedas ameans of arresting the autocatalyticchain reactions, as well as preventingthe corrosion of processing equipment;

b) prevent oxidative reactions at the �weak�allyl groups formed in the first step ofthe evolution of HCl, as well as disruptthe conjugated double bonds, whichgive rise to discoloration; and

c) substitute active Cl atoms in the allylposition after the formation of HCl.

Originally the stabilization of PVC ad-dressed primarily the first requirement,

with the use of additives consisting of basiclead salts and weak basic soaps, such asbasic lead carbonate (PbO�PbCO3), tribasiclead sulfate (3PbO�PbSO4�H2O) and dibasiclead phosphite (2PbO�PbHPO3�1/2H2O).

Stabilization through displacement oflabile Cl atoms from the chains has beenachieved with the use of miscible metalcarboxylates, such as mixed cadmium bari-um laureates

Cd½OCOC11H22�2Ba½OCOOCOC11H22�2

The disruptions of the conjugated doublebonds formed in the chains from the unzip-pingeliminationofHClcanbeaccomplishedwith the use of mercaptides and maleateesters, through the mechanism shown.

The mercaptides can also assist thestabilization of PVC by acting as free-radicalquenchers in the simultaneous oxidationreactions. The more recent stabilizers areorgano-tin and organo-phosphite compounds

264j 126 PVC

that act primarily through the displacement ofthe labile Cl atom, according to the schemeshown.

The more widely available systems aredibutyl-tin maleate and dibutyl-tin mercap-tides, respectively, represented with thechemical formulae shown.

The majority of PVC formulations makeuse of mixtures of stabilizers, as they actsynergistically, which is to say that the com-bined effect of two or more stabilizers ismuchgreater than is achievablewith theuseof single stabilizers at equal levels of addi-tion. It has also been found that the additionof epoxy compounds, such as epoxidizedsoya bean oil, can enhance further the syn-ergistic action of the combination of con-ventional stabilizers. (See Vinyl polymer.)

127. PVC Paste

(See PVC.)

128. PVT Diagram

The term refers to plots of the specific vol-ume of polymer melts against temperatureat different levels of pressure. The data areused to produce a pressure profile for aninjection moulding cycle as a means ofcontrolling the volumetric shrinkage of aninjection-moulded part, as shown in thediagramforaparticulargradeofpolystyrene.

Plots of the specific volume of a polystyrene meltagainst temperature at different levels of pressure,and programmed pressure profile during cooling.Source: Osswald (1998).

The number sequence from 1 to 4 indi-cates the programming of the hold-on pres-sure on the polymer melt. The trace from 4to 5 represents the natural path of thevolumetric shrinkage of the polymer in thecavity due to further cooling, which causesthe moulded part to shrink away from thewalls of the cavities, thereby allowing thepressure to fall off to reach atmosphericconditions. The shrinkage taking place atatmospheric pressure corresponds to theactual �mould shrinkage� experienced by themoulded part. From a close analysis ofthe PVT curves, it can be inferred that, ifthe injection pressure were to be increasedto 1000 bar, the extent of mould shrinkagewould decrease to zero, so that the dimen-sions of the moulded part become exactlythe same as those of the cavity of themould.In the diagram are reported the PVTdata

for a polyamide 6,6 (PA 6,6), which is acrystalline polymer and undergoes a muchhigher level of natural shrinkage than poly-styrene (amorphous polymer). The datasuggest that the application of a high pres-sure would not be possible to compensate

128 PVT Diagram j265

for the high shrinkage resulting from thecrystallization of the polymer. This meansthat while for glassy amorphous polymerthe linear mould shrinkage is usuallyaround 0.5–0.8%, for crystalline polymersthe shrinkage values are in the regionof 1–2%.

Plots of the specific volume of a polyamide 6,6 meltagainst temperature at different levels of pressure.Source: Osswald (1998.)

129. Pyrolysis

The breaking down of polymer chainsinto low-molecular-weight species when

exposed to high temperatures. The mecha-nism and type of products formed dependon the nature of the polymer and the envi-ronmental conditions, particularly onwhether pyrolysis is carried out in an inertenvironment, such as nitrogen, or anoxidizing environment, such as oxygen orair. The thermal decomposition of somepolymers occurs via a depolymerizationmechanism producing the original mono-mer. For some polymers, such a polytetra-fluoroethylene (PTFE), poly(methyleneoxide) (PMO) and poly(methyl methacry-late) (PMMA), pyrolysis can produce a100% yield of monomer. In other cases,such as polystyrene (PS) and poly(ethyleneoxide) (PEO), the monomer yield is muchless and is largely dependent on the envi-ronmental conditions. The pyrolysis of vinylpolymers, such as PVC and poly(vinyl ace-tate), in an inert atmosphere, takes place bythe formation of the conjugated unsatura-tion along the chains, as follows:

Other polymers, such as cellulosics, poly-acrylonitrile (PAN) and phenolics producecarbonaceous residues and a variety of vol-atile products.

266j 129 Pyrolysis

Q

1. Q Meter

An apparatus used to measure the permit-tivity and loss factor of a dielectric at fre-quencies up to about 70MHz.

2. Quartz

The crystalline version of silica, SiO2. Itfinds very little use in polymer compounds.

3. Quencher

An additive used to interact with activatedspecies to bring them down to a lowerenergy state, thereby making them lessreactive. Quenchers are widely used forstabilization of polymers against UV-induced degradation. The absorption of UVlight brings a molecule (A) to an excitedstate (A*), known also as the triplet state.The collision of an excited molecule with a

quencher (Q) brings it back to the groundenergy state, known also as the singlet state,through the release of the absorbed energyas IR radiation, that is,

Aþ hvðUVÞ!A*

A*þQ!AþQþ hvðIRÞQuenchers used in combination with

primary UV stabilizers are usually nickelcomplexes. There are, however, toxicity im-plications to be considered.

4. Quinone Structure

This is formed in phenol derivatives, suchas those used to produce phenolic resinsand antioxidants, as a result of reactionswith oxygen. They are responsible for thedevelopment of discoloration with a yellow-ish or even brown tint. (See Phenolicantioxidant.)


j267

R

1. Rabinowitsch Equation

An equation used to calculate the true shearrate at the wall ( _gw) of a capillary rheometerin studies of the flow behaviour of polymermelts, based on a power-law behaviour,

_gw ¼ 3nþ 14n

4QpR3

� �;

where n is the power-law index, Q is thevolumetric flow rate and R is the radius ofthe capillary. (See Non-Newtonian behav-iour and Power law.)

2. Radiation

Can be defined as the energy emitted froman electronic or magnetic field and trans-mitted in the form of waves according toPlanck�s law, that is, E¼ hy, where E is theenergy and y is the frequency of the radia-tion waves, and h is known as Planck�sconstant (with the value 6.63� 10�34 J s).The frequency is equal to the velocity (c)divided by the wavelength of the radiation

(l), that is, y¼ c/l. The energy levels emit-ted by different types of radiation and theassociated wavelength of the radiation areshown in the table.

The energy for laser radiation has notbeen given, as it depends on thewavelength,which varies according to the source(1mW–10W). The actual energy level oflaser radiation is not much different fromthat of visible light, but it is highly concen-trated on very small areas (10mm2–1mm2).The power associated with laser radiation istherefore very high, 107–108W/m2, whilethat of sunlight reaching Earth is about103W/m2. From these data it is easy to seewhy laser light can be used to melt and etchthe surface of materials.

3. Radiation Processing

A term used to induce reactions in oligo-mers (resins) or linear polymers to producecross-linked molecular structures or tofunctionalize the surface of existing poly-mers through grafting reactions. Usuallythe mechanism is a free-radical type butcationic initiators have also been used forthe cross-linking of specific epoxide oligo-mers. Radiation sources used vary fromUV(100–1000 nm wavelength) to electronbeaming (10�4–10�1 nm). Ionizing radia-tion emitted from electron beams is veryenergetic (0.5–2.5 MeV, with a power of upto 20 kW) and can penetrate depths to3–4mm,whereas UV light can only be usedeffectively to induce reactions to a maxi-mum of about 0.5mm from the surface.The absorption of radiation brings themolecules to their excited state, which canin turn cause bond cleavage to produce freeradicals or ions. (See Photopolymerization.)

TypeWavelength

(nm)Energy(kJ/mol)

Far ultraviolet 100 1196Vacuum ultraviolet 200 598Mercury lamp 254 471Solar cut-off 295 406Mid-range ultraviolet 350 341End of ultraviolet range 390 306Blue-green light 500 239Red light 700 171Near infrared 1000 120Infrared 5000 24Hard X-rays, softgamma-rays

0.05 2.4· 106

Hard gamma-rays 0.005 2.4· 107

Source of data: Wypych (2008).


268j

The radiation dose is measured in eitherkilograys (kGy) or megarads (Mrad): 1 Gy¼ 1 J/kg¼ 1Ws/kg¼ 100 rad, hence 1 kGy¼ 10�1 Mrad. The irradiation of polymersfrom high-energy sources can result incross-linking as well as chain scission orboth reactions simultaneously, dependingon the structure of the polymer andwhetheradditives are present. These are classified as�pro-rads� if they enhance the yield of cross-linked structures (multifunctional mono-mers), or �anti-rads� if they absorb radiationand, therefore, act as screens for the poly-mer chains. The latter additives are usuallyaromatic amines or sulfides, and phenols orquinines. The most widely used pro-radsare trimethylolpropane trimethacrylate(TMPTMA), triallyl cyanurate (TAC) andtriallyl isocyanurate (TAIC). The polymersthat cross-link more readily are those con-taining unsaturation along the chains or asside groups. The ability of linear polyethy-lenes to be cross-linked readily by radiationmethods is due to the presence of structuraldefects, consisting primarily of vinyl andvinylidene groups. Vinyl polymers can alsocross-link readily due to the weakness of thetertiary C�H bonds, which undergo homo-lytic scission to produce free radicals. Con-versely, the complete absence of unsatura-tion or tertiary C�H groups in the polymerchains results mainly in chain scission re-actions.Typical among these arepoly(methylmethacrylate) and polytetrafluoroethylene.Polymerssuchaspolystyrene,polypropyleneand polyamides will undergo extensivechain scission alongside some degree ofcross-linking.

4. Radical

A term used to denote chemical speciescontaining anunpaired electron, called �freeradical�, which results from the breaking ofcovalent bonds. A typical example is thehomolytic scission of a peroxide initiator

for the free-radical polymerization of unsat-urated monomers, that is,

HO�OHþ heat=UV! 2.OH

5. Radical Scavenger

An additive that reacts with free radicalspresent on polymer chains and prevents theonset or continuation of propagation reac-tions, which could lead to the degradation ofproperties. The most common type of sca-vengers are also known as primary stabili-zers and are based on hindered phenols orhindered amines.

6. Radius of Gyration

A theoretical concept in polymer sciencedenoting the root-mean-square distance ofa particular atom or group in a polymerchain from the centre of gravity. This pa-rameter is used tomeasure the effective sizeof polymer molecules.

7. Raman Spectroscopy

A vibrational spectroscopy technique basedon the use of intense monochromatic radi-ation in the visible region to promote thetransition in energy levels through vibra-tions of primary bonds. A small fractionof the incident radiation is scattered at adifferent wavelength. Such a change inwavelength is known as the �Raman shift�,which forms the basis for the characteriza-tion of the molecular structure of polymers.(See Infrared spectroscopy.)

8. Random Copolymer

A term used to describe a copolymer inwhich the two monomeric components are

8 Random Copolymer j269

distributed at random along the polymerchain. This type of copolymer is also knownas a statistical copolymer, identified as –

(A-stat-B)n– for a random copolymer con-taining A and B units. Most copolymersused for commercial products are randomtypes. (See Block copolymer.)

9. Rapid Prototyping

A series of different processing methodsused to make prototypes without having tomachine or join together small units. It isalso used for producing items in the manu-facture of special articles that cannot beeconomically produced by conventionalmouldingmethods. (See Stereolithography.)

10. Rayon

A fibre based on regenerated cellulose. (SeeCellophane.)

11. Reaction Moulding

(See Reaction processing.)

12. Reaction Processing

A generic term for manufacturing or com-pounding processes involving chemical re-actions between the components. Allmouldingprocesses involving the formationof cross-links, therefore, fall in this category.

Example of structural reaction injectionmoulding: athermosetting liquidmixture is injected into a cavitycontaining a glass-fibre pre-form. Source: Muccio(1994).

Compounding techniques are some-times used to induce some chemical mod-ifications of the polymer chains, particu-larly for the purpose of introducing func-tional groups. A typical example is thegrafting of acid groups along the molecu-lar chains of a polyolefin through graftingreactions with maleic anhydride or acrylicacid.

13. Reactive Diluent

Amiscible monofunctional component of aresin mixture, used to reduce the viscosityand to decrease the glass transition temper-ature (Tg) of the cured products. (See Epoxyresin.)

270j 13 Reactive Diluent

14. Reactivity Ratio

A concept used in free-radical copolymeri-zation to control the composition and ran-dom distribution of the twomonomer com-ponents. The definition is based on the rateconstants k for the addition of a monomermolecule to a growing chain containing thereactive radical. These are denoted asmono-mer reactivity ratios r1 and r2, defined asr1¼ k11/k12 and r2¼ k22/k21, where the vari-ous rate constants are for the various possi-ble reactions, that is, k11 for the addition ofgrowing chain M1

. onto monomer M1, k12for the addition of growing chain M1

. ontomonomer M2, k22 for the addition of grow-ing chainM2

. ontomonomerM2 and k21 forthe addition of growing chain M2

. ontomonomer M1.

15. Reciprocating Screw

The screw of an injection moulding ma-chine, which slides back while it rotates to�plasticate� the polymer granules and delivera predeterminedamountofmelt to the front.Then the screw is pushed forwards at a highspeed to inject the melt through the nozzleinto the cavities of the mould, via the sprueand runners. (See Injection moulding.)

16. Recoverable Strain

Themagnitude of the total strain that can berecoveredafterremovingthestressinacreepexperiment. For linear polymers, the straincan recover completely if the applied stresshas not reached, or closely approached, theconditions causing failure by yielding.

17. Recovery

A term used to denote the period that fol-lows the removal of the stress in creep

experiments. During this period, the straindecreases and can recover totally after a longperiod, usually about 10–20 times longerthan the creep period. (See Creep.)

18. Recycling

A term that denotes the reuse of polymerspreviously manufactured. Recycling can bedivided into three categories:

. primary recycling if the recycled polymeris used to produce the same article;

. secondary recycling if the polymer is re-used for the manufacture of articles dif-ferent from those used previously; and

. tertiary recycling when the polymer isused for other purposes, such as inciner-ation to produce heat, or being pyrolysedto produce chemicals.

19. Reduced Time

A concept related to creep experiments tonormalize the time after removing the load,known as the recovery time (t1), to the timeunder load, known as the creep time (t). Thereduced time tR is, therefore, defined as

tR ¼ ðt�t1Þ=t1:

20. Reflection Factor

The ratio of the flux of reflected light (Fr)from the surface of a sheet or film to thefluxof incident light (Fi), that is, R¼Fr/Fi,where F¼ I/A, I is the intensity of lightand A is the surface area from which thelight is reflected.

21. Refractive Index

Aparameter that denotes the characteristicsof a material related to the change in the

21 Refractive Index j271

velocity of the transmitted light. The dia-gram shows that the incident light is partlyreflected from the upper surface and partlyfrom the surface at the exit side.

Reflection and refraction of light in passing througha transparent medium.

The transmitted beam of light is�refracted� through a reduction in the pathangle determined by the nature of the ma-terial, Thus, the refractive index n(l) isdefined as

nðlÞ ¼ sin isin r

;

where i is the angle of incidence and r isthe angle of refraction. The refractive indexn(l) decreases with increasing wavelengthof light. For PMMA, for instance, the valueof n(l) is 1.50 at 450 nm and about 1.49at 650 nm wavelength. The refractiveindex decreases also with increasing tem-perature, with the greatest change takingplace upon reaching the glass transitiontemperature.

22. Regulator

Additives that are more reactive than thegrowing polymer chains during the courseof polymerization so that small amountscan be used to stop the growth of polymerchains in order to reduce and control themolecular weight of the polymer produced.Typical chain regulators are carbon tetra-chloride and pentaphenylethane.

23. Reinforcement

A method for increasing the modulus andstrength of a material, brought about by theincorporation of high-modulus and/orhigh-strength fibres, such as glass fibresand carbon fibres. (See Composite andFibre reinforcement theory.)

24. Reinforcement Factor

The ratio of the value of the modulus orstrength of a composite to the correspond-ing value of the matrix. The reinforcingfactor gives a measure of the efficiency ofthe reinforcing agent used in producing acomposite.

25. Relative Permittivity

A dimensionless parameter that relates thepermittivity of a dielectric («d) to that of air(«air), which is approximately equal to thepermittivity of vacuum. The relative permit-tivity of a dielectric is also known as thedielectric constant, K, and is defined asK¼ «d/«air.The value of the relative permittivity of

most polymers varies from about 2 to 5. Thelowest values are obtained with non-polarpolymers, such as polyethylene types, poly-tetrafluoroethylene and polypropylene.Even lower values are achievable with cellu-lar products, owing to the presence of air inthe cells. Higher values are obtainedthrough the absorption of water. The poly-mer with the highest intrinsic permittivityis poly(vinylidene difluoride), with aK valueof approximately 8. (See Permittivity.)

26. Relative Viscosity

The ratio of the viscosity of a solution to theviscosity of the solvent. A concept used in

272j 26 Relative Viscosity

measurements of the molecular weight ofpolymers.

27. Relaxation Modulus

Modulus value obtained from experimentscarried out at constant strain, resulting inthe decay of stress with time, known asstress relaxation. (See Viscoelastic behav-iour and Standard linear solid.)

28. Relaxation Time

Aconcept used in viscoelasticity theory. (SeeMaxwell model and Standard linear solid.)

29. Relaxed Modulus

The value of the relaxationmodulus for timetending to infinity. (See Standard linearsolid.)

Variation of relaxation modulus with time: E0 is theinstantaneous modulus (t¼ 0); E¥ is the relaxedmodulus (t¼¥).

30. Reptation

A term that describes themechanism of themovements of polymer molecules relativeto each other in order to produce flow whenthe temperature is increased above the

rubbery state and, therefore, reaches themelt state. The constraints due to theircoiled configuration and entanglements in-duce the molecules to dissipate their inter-nal energy through serpentinemotions con-fined within a curvilinear cylinder path,which causes them to slip past each other.

Schematic illustration of the serpentine motions(reptation) of polymer molecules in the melt state.Source: Elias (1993).

31. Residual Stress

(See Internal stress.)

32. Resin Transfer Moulding (RTM)

A manufacturing method for composites,consisting of a reinforcing fibre pre-formplaced in the cavity of a mould. A resin isinjected into the interstices between thefibres and the removal of air is assisted bythe application of vacuum. (See Composite.)

33. Resistivity

(See Surface resistivity and Volumeresistivity.)

34. Resole

(See Phenolic.)

35. Retardation Time

Aconcept used in viscoelasticity theory. (SeeKelvin–Voigt model and Standard linearsolid.)

35 Retardation Time j273

36. Retarder

An additive used in rubber compounds toslowdown the rate of cure, hence increasingthe �scorch time�. Typical retarders are di-phenyl nitrosoamine, salicylic acid, benzoicacid and phthalic anhydride.

37. Rheology

A branch of science that is concerned withthe non-Newtonian behaviour of liquids.(See Non-Newtonian behaviour.)

38. Rheometer

An apparatus used to study the rheologicalproperties of polymer melts.

39. Rheopectic

A term that denotes the rheological behav-iour of certain fluids whereby the viscositydecreases with the duration of the imposedshear rate.

40. Rockwell Hardness

Hardness value for rigid polymers obtainedfrom measurements involving the penetra-tion of a steel ball into sample supported ona massive hard base. (See Hardness.)

41. Rosin

A naturally occurring resin also known ascolophony, found in trees, mostly pine spe-cies. Rosin essentially consist of a series ofso-called resin acids, which contain unsa-turation and carboxylic acid functionalities.The main acid components of rosin areabietic acid, neoabietic acid and dehydroa-

bietic acid. Rosin is usually modifiedthrough reactions with the functionalgroups into useful resins for coatings. No-table among these are the products obtainedby the reaction of rosin with maleic anhy-dride. The acid and anhydride functionalgroups can be reacted with polyhydric alco-hols to produce the so-called maleic resins,which are essentially a type of alkyd resin.

42. Rotational Moulding

Also known as rotomoulding, is a processfor the production of hollow mouldings atatmospheric pressure from polymers in theformofpowder. Thepowder is fed into a pre-heated mould, which rotates, at low speed,in one or two directions in order to spreadthe polymer along the wall of the mould,where it melts and sinters. A typical set-upfor the rotation of the mould is shown.

Typical set-up for the rotation of the mould inrotomoulding. Source: Osswald (1998).

During flow, the melt is subjected only togravitational forces, as the centrifugal forcesare negligible, because the rotational speedis low. Note that there is virtually no flow ofthe melt, as it adheres to the surface of themould and remains in place due to therelatively high viscosity. Nevertheless thetemperature has to be very high in orderto cause a rapid melting of the powder and

274j 42 Rotational Moulding

also to effectively remove the voids betweenparticles through surface tension effects.The melting and fusion of the particles

are, in effect, events similar to those experi-enced in a �free� sintering process, hence theparameter that controls the extent of flow ofthemelt and the removal of the air entrappedbetween particles is the ratio of surface en-ergy (g) to melt viscosity (h). In order toobtain the highest possible g/h ratio, theprocess relies on the contrasting sensitivityof these two properties of polymers to in-creases in temperature, which is very low forsurface energy and very high formelt viscos-ity. Before the powdermelts and sticks to thesurface of the mould, the spreading of thepowder takes place by rolling movementsundergravitational forces.As the shear stres-ses arising from gravitational forces on themelt are very low, there are severe limitationsfor the filling of small cavities in a mould, sothat the topographic features of the articlemust be free of intricate asperities.To complete a moulding cycle, the mould

passes through four stages: (i) the articlefrom the previous run is removed; (ii) thenfresh powder is fed into the mould; (iii)the mould is heated by external sources;and (iv) this is followed by a cooling stageusing the spray of fine jets of cold water.

43. Rubber

A term derived from the erasing character-istics of the constituent polymer, whichexists in a �rubbery state� at ambient tem-peratures. The constituent polymers of rub-ber products are also known as elastomers.

44. Rubber Elasticity

A term used to denote the total reversibilityof the high elongations displayed by poly-mers in their rubbery state, as shown in thediagram.

Pictorial description of the stretching and recoveryof the cross-linked polymer chains of an elastomer.Source: Unidentified original source.

The term has acquired special signifi-cance in the mechanics of materials, as ithas required the modification of the classi-cal theory of elasticity based on infinitesimaldeformations. To emphasize the differencefromclassical elastic behaviour, rubber elas-ticity is sometimes referred to as rubber-likeelasticity. Rubber elasticity has acquired aspecial role also in thermodynamics, as ithas made it possible to calculate the changein entropy with the stretching out of poly-meric chains. From the second law of ther-modynamics,

dA ¼ �S dT þ f dL�PdV ;

whereA is the free energy,S is the entropy,Tis the absolute temperature, f is the appliedforce, L is the length of the specimen, P isthe external pressure andV is the volume ofthe stretched specimen. Through appropri-ate theoretical considerations, and knowingthat there is no change in volume, it isdeduced that the change in entropy withincrease in the length of the specimen isequal to the change in force per increase intemperature, that is,

ðdS=dLÞT ¼ �ðdf =dTÞL:This relationship implies that the force act-ing on a stretched rubber specimen in-creases linearly with temperature if thelength is kept constant, a behaviour thatarises entirely through the reduction in theentropy of the stretched polymer chains.Mechanics considerations require a redefi-nition of strain, from the classical elasticity,that is, «¼ (dL/L)dL! 0. This is accom-plished by considering the extension ratio(l) as the parameter related to the appliedstress, that is,l¼ L/L0, where L0 is the initial

44 Rubber Elasticity j275

length of the specimenwhen the stress,s, iszero. From fundamental considerations, anexpression is derived for the relationshipbetween stress and extension ratio, knownas the Mooney–Rivlin equation, that is,

s ¼ ðCþC0=lþC00l2Þðl�1=l2Þ:

The terms C0 and C00 are characteristic con-stants of the rubber, dependingon thechem-ical constitution of the polymer, the cross-linking density, and type and level of rein-forcement. From the above relationship, it isdeduced that the gradient of the plot ofs/(l� 1/l2) against 1/l in the linear regioncorresponds to the shear modulus of therubber. The diagram shows that there is astrong deviation from linearity at large ex-tension ratios, owing to strain hardeningphenomena, such as stress-induced crystal-lization.

Mooney–Rivlin plot for rubber elastic behaviour.Source: Sato (1969).

Since the concept of Young�s modulusused for small strains is not valid for largerubber extensions, in practice the termsM100 and M300 are used instead, which cor-

respond to the value of the nominal stress (i.e. force/original cross-sectional area) dividedby the nominal strain, (100DL/L), at 100%and 300% extension, respectively. These areempirical values that are useful for qualitycontrol and materials specifications.

45. Rubbery State

The state of a polymer above the glasstransition temperature. (See Transition andDeformational behaviour.)

46. Runner

The channel that connects the sprue to thegates of an injection mould, as shown. (SeeInjection moulding, Mould and Gate.)

Example of channels feeding the melt into thecavities of an injection mould in sequence: sprue,runner and gate. Source: McCrum et al. (1988).

47. Rutile

(See Titania.)

276j 47 Rutile

S

1. Sag

A term used to denote the thinning of thepolymer melt emerging from an extrusiondie, or a polymer sheet in thermoformingprior to the application of vacuum or drap-ing the sheet on to the mould.

2. Scanning Electron Microscopy (SEM)

A technique capable of providing muchlargermagnifications than lightmicroscopy(more than 1000 times). The method isbased on the use of a beam of high-energyelectrons, produced from a filament andaccelerated by a high voltage, to producesecondary electrons and/or backscatteredelectrons, as well as X-rays, when focusedon a sample.

Schematic representation of events occurringwhena sample is bombarded with high-energy electrons.Source: Unidentified original source.

The backscattered electrons are primarybeam electrons (high-energy electrons) thathave been elastically scattered by the nucleiin the sample and escape from the surface.Thus they can be used to obtain an elemen-tal composition contrast in the sample.Secondary electrons are emitted with low

energy from the upper surface layers of thesample (a few nanometres deep), whichproduces topographic images of the samplesurface.Non-conductive materials, such as poly-

mers, have to be coated with a thin layer ofhighly conductive and inert metal, such asgold, using a sputtering technique. Thesample is usually fractured after refrigera-tion in liquid nitrogen so that the fractureplane reproduces all the asperities arisingfrom the heterogeneities in the structure.Chemical etching or chemical staining aresometimesused to enhance the topographiccontrast resulting from the presence of twophases, even when the chemical composi-tion is uniform and the heterogeneity arisesfrom the existence of crystalline and amor-phous domains of the same polymer.Chemical staining is carried out in sampleswhere one of the components contains do-mains of a diene rubber, such as ABS orHIPS. The technique takes advantage of theability of osmium tetroxide to react withaliphatic double bonds so that only thedomains containing the diene elastomerwill be �stained� with heavy-metal ions. Thereaction scheme for the staining process isshown.

Chemical staining of diene elastomer domains inpolymer blends.

3. Scorch Time

The time at which the value of the torquereaches a certain pre-specified value in


j277

evaluating the curing characteristics of arubber mix using a cure-meter, such as theMooney viscometer. This parameter givesan indication of the length of time that arubber mix maintains its processing char-acteristics at a specific temperature. (SeeCure-meter.)

4. Screw–Die Interaction

A term used to describe the relationshipbetween flow rate and pressure for themetering zone of the screw and that forthe die of the extruder as a means ofobtaining the operating conditions for anextrusion operation. The net flow rate of themelt through the metering zone can bewritten as (drag flow – pressure flow), thatis, Qscrew¼QD�QP, where QD¼aN andQP¼bDP/h. The two constants a and b areknown as the �screw characteristics� insofaras they represent the geometric features ofthe screw, and N is the screw speed inrevolutions per second. The flow ratethrough the die can be written as Qdie¼KDP/h, where DP is the head pressure andh is the viscosity of the melt for bothequations. The operating conditions aredetermined from the flow balance Qscrew¼Qdie, as there are no leaks of the melt inother parts of the extruder. The main diffi-culties in the solution of these equations forpolymer melts arise from the shear stressand temperature dependences of the termh, resulting from their non-Newtonian be-haviour, which cause considerable devia-tions from linearity in the flow rate (Q )against pressure (DP) plots for both thescrew and the die sections, as shown inthe diagram.

Plots of flow rate versus pressure drop for (a) thescrew metering zone and (b) the die of anextruder, where N is the number of screw revolu-tions per second, R is the nominal radius of thedie and L is the length of the die lips. Source:Birley et al. (1991).

The curves in the upper diagram are forthree different screw speeds, while thecurves at the bottom are for two differentdie constants, K. The operating conditionscorrespond to intercepts of the two plots,which give the values of theflow rate and thepeak pressure between the die and themetering section of the screw at differentscrew speeds (N).

5. Secant Modulus

The ratio of stress to a pre-specified strain(say 1%) from a force–deformation curveobtained in tensile tests. (See Young�smodulus.)

278j 5 Secant Modulus

6. Secondary Crystallization

The term refers to the continuation of thecrystallization process taking place at lowtemperatures. Secondary crystallizationtakes place primarily in the formof a lamellathickening process, but can also be associ-ated with the formation of additional crys-tals of very small lateral dimensions, withspecific melting characteristics. Some spe-cific features of the secondary crystalliza-tion process include a linear increase inboth the melting temperature of secondarycrystals and the glass transition tempera-ture with the logarithmof the crystallizationtime. (See Crystallization.)

7. Secondary Plasticizer

An auxiliary plasticizer. (See Plasticizer.)

8. See-Through Clarity

A term used in the packaging industry todenote the characteristics of a film thatallows fine details of an object placed atsome distance from the film to be seen.This property is related to the presence oflarge surface irregularities, such as�sharkskin� and �orange peel�, which causeforward scattering of light at very smallangles (between 1� and 1.5�). (See Opticalproperties.)

9. Seed Polymerization

A term sometimes used for an emulsionpolymerization that starts from an existingpolymer emulsion. A new monomer ispolymerized on the surface of existingparticles to produce an outer shell or a

chemically bonded (compatibilized) mix-ture of two polymers.

10. Self-Extinguishing

A term used to describe the fire retardantcharacteristics of polymers, whose behav-iour is characterized by their capabilityof allowing a propagating flame to auto-extinguish.

11. Semi-IPN

An interpenetrating polymer network (IPN)structure consisting of a linear polymer anda cross-linked polymer. (See Interpenetrat-ing polymer network.)

12. Shape Memory Polymer

(See Heat-shrinkable product.)

13. Sharkskin

A type of defect found on the surface ofextruded products, formed as the meltemerges from the die. The typical appear-ance of a polymer filament with sharkskinsurface defects is shown in the photograph.

Sharkskin defects on the surface of a filamentemerging from the die of a capillary rheometer.

13 Sharkskin j279

Smoother defects, known as �orangepeel�, are sometimes found on the surfaceof extruded products, particularly if thesehave been stretched out, as in blowmouldedcontainers or tubular films. These types ofdefects arise as a result of the acceleration ofthe outer polymer layers at the exit die inorder to catch up with the velocity in thecentre due to the change from the parabolicflow profile within the die to a constantvelocity within the filament after the die.This brings about a form of melt fracturelocalized at the surface due to the rapidstretching of the polymer outer layers. (SeeMelt fracture and Melt strength.)

Mechanismfor the formationof sharkskindefects inan extrudate at the die exit. Source: Mascia (1989).

14. Shear Modulus

The coefficient that relates the shear stress,t, to the resultant shear strain, g, that is,G¼ t/g. (See Modulus.)

15. Shear Rate

A concept used in rheology to denote thevelocity gradient perpendicular to the flowdirection. (See Rheology and Viscosity.)

16. Shear Stress

(See Stress.)

17. Shelf-Life

A term used to describe the storage stabilityof a cross-linkable system, expressed interms of maximum time that can elapsebefore being used.

18. Shift Factor

Also known as the �time–temperature shiftfactor�, this is a term to denote the amountof displacement of a creep or stress relaxa-tion curve, for experiments carried out at agiven temperature, along the time axis tooverlap with the corresponding curve ob-tained for experiments at a different tem-perature, as a means of producing a mastercurve. The master curve represents an ex-trapolation of the data to low temperaturesfrom data obtained at higher temperatures.(See Master curve and Time–temperaturesuperposition.)

19. Shish-Kebab Crystal

Type of structure that is intermediate be-tween a fringed micelle and chain folding.(See Crystallinity.)

20. Shore Hardness

A measure of the hardness of soft or rub-bery polymers. (See Hardness.)

21. Side Group

A group attached to the backbone of apolymer chain.

280j 22 Side Group

22. Silane

A generic name for alkoxysilane com-pounds, normally in relation to couplingagents for composites. (See Couplingagent.)

23. Silica

A filler represented by the formula SiO2,usually with very small particle dimensions.(See Filler.)

24. Silicone Fluid

Essentially low-molecular-weight polydi-methylsiloxanes (PDMS) or polymethylphe-nylsiloxanes (PMPS), whose constituentunits are represented by the chemical for-mulae shown.

Both have a wide service temperaturerange, from about �60 to þ 200 �C. Thephenylmethyl silicones have lower com-pressibility and a higher thermal oxidativestability, as well as being more resistant tohigh-energy radiation. The molecularweight varies widely depending on the re-quired viscosity, which covers the rangefrom about 5 cSt to 2� 106 cSt. The rangeof uses is illustrated in the diagram.

Applications of silicone fluids in relation to viscosityand molecular weight. Source: Bieleman (1996).

25. Silicone Rubber

A rubber containing silicon and oxygenatoms in the backbone of the constituentpolymer chains, often identified with theletter Q. The most important silicone elas-tomers are based on high-molecular-weightpolydimethylsiloxane (PDMS, also referredto as MQ) or polymethylphenylsiloxane(PMPS, and also PMQ). Cross-linking reac-tions can take place either via alkoxy oracetoxy functional groups, usually forroom-temperature curing, or by free-radicalreactions via pendent vinyl groups (knownalso as VMQ). The former mechanism re-lies on the hydrolysis of the alkoxy or acetoxysilane groups along the backbone chains,induced by moisture in the atmosphere,followed by condensation reactions, bothcatalysed by acid additives, such as aceticacid or organo-tin compounds. These reac-tions are normally carried out at room tem-perature, known as room-temperaturevulcanization (RTV), producing either analcohol or acetic acid as by-products, asshown in the reaction scheme.

25 Silicone Rubber j281

Reaction scheme for RTV condensation reactions of silicone elastomers. Source: Pocius (2002).

The limitations of one-component sys-tems requiring moisture for the initiationof the polymerization reactions are over-come by two-component systems. Curingof the latter systems takes place via directcondensation reactions between hydroxylgroups, catalysed by organo-tin com-pounds, such as dibutyl tin dilaurate (DBTL)and stannous octoate (STO). Both one- andtwo-component systems are mainly used assealants and adhesives. The free-radicalcross-linking reactions, on the other hand,are catalysed by peroxides and are mainlyused for high-temperature cure as inmoulded products. They contain about0.5–1.0% pendent vinyl groups along the

chain, introduced through copolymeriza-tion with the required amounts of methyl-vinylsiloxane monomer. For sealant andliner formulations, modern silicones usecure reactions based on platinum-catalysedvinyl addition of silane hydride to a vinylsi-lane, controlled by the addition of an inhib-itor, as shown in the reaction scheme.In effect the inhibitor retards the reac-

tion, through complexation reactions withthe catalyst, thereby prolonging the storagelife of the uncured system. The inhibitor–catalyst complex breaks down when thesystem is heated, releasing the catalyst forthe reaction.

282j 25 Silicone Rubber

Reaction scheme for the silane hydride cross-linking of vinyl-functionalized silicone elastomer. Source:Pocius (2002).

Silicone elastomers have a wide servicetemperature range and a high thermal oxi-dation stability, as well as excellent dielectricproperties and a high resistance to tracking.Owing to their very lowTg (around�120 �C)they retain their rubber-like characteristicsdown to very low temperatures. They suffer,however, from low resistance to solventsand poor mechanical strength. Unlike mostother elastomers, PDMS systems cannot bereinforced with carbon black, but only withfumed silica. Better resistance to oils, and tonon-polar solvents in general, is achieved bythe fluorosilicone corresponding to poly-methyltrifluoropropylsiloxane, known alsoas FMQ (FVMQ for the vinyl-functionalizedsystem), which is prepared and cured in the

same way as conventional PDMS. Thechemical structure of FMQ is shown.

The presence of the fluorinated sidegroups, however, increases to some extentthe Tg and impairs the mechanical proper-ties relative to PDMS systems.

26. Sink Mark

(See Moulding defect.)

26 Sink Mark j283

27. Size (or Sizing)

A term for coatings deposited on fibresduring manufacture, sometimes referredto as �finishing�. Starch has traditionallybeenused to treat thesurfaceofcottonfibresto prevent them from fluffing and has alsobeenused initially in theproductionof glassfibres for the same reason. The hydroxylgroups in starch provide a natural affinityfor the SiOH groups on the surface of glassfibres. Later starch was replaced with poly(vinyl acetate), deposited fromdiluted emul-sions. Over the last 10–20 years, there havebeen considerable new developments in thetype of polymer emulsions and/or disper-sions used for the �sizing� of fibres in orderto �tailor� the interphase for specific fibre–-matrix combinations. The emulsions usedfor coating fibres contain a number of ad-ditives, such as lubricants, antistatic agents,pH controllers, plasticizers and silane cou-pling agents. The term �size� or �sizing� isused to describe the overall composition ofthe coating on the fibres, which containsabout 80% polymer and 20% additives. Theamount of size used on fibres is about0.5–2.0%, giving a coating thickness in theregion of 0.1–0.5 mm. The micrograph re-veals the type of morphological heterogene-ity in size coatings on the surface of glassfibres that may arise from the presence ofthemultitude of additives and, possibly, alsofrom the poor fusion of the polymer parti-cles deposited from the emulsion.

SEM micrograph of a glass fibre taken from acommercial roving. Source: Demirer (2000).

Sizes have to bemisciblewith the resin orpolymer used as the matrix for compositesso that chemical bonding can take placethrough reactions with the silane couplingagents anchored on the surface of glassfibres. (See Coupling agent.)

28. Size Exclusion Chromatography (SEC)

(See Gel permeation chromatography.)

29. Sizing Die

An auxiliary die placed after the extrusiondie, whose functions are (i) to prevent thecollapse of the melt at the die exit beforethe extrudate is cooled, and (ii) to providethe final dimensions to a tubing or a pipe.Two typical sizing die systems are shown inthe diagrams.

Typical sizing dies for tubings and pipes. Source:Rosato (1998).

The system shown at the top operatesthrough a perforated brass jacket that allowsthewater to get to the surface of thepipe andact as a coolant and lubricant. Vacuum isapplied to draw the surface of the pipe againstthe cooling jacket, thereby ensuring that thepipe does not flatten under gravity forces. Inthe adjacent cooling tank there are also cali-brating rings tomonitor theouter diameter ofthe extruded pipe. The take-off unit is oftenused to draw down the extrudate to the rightdimensions. The system at the bottom oper-ates by direct cooling of the extrudate byspraying fine jets of cold water immediatelyit emerges from the extrusion die.

284j 29 Sizing Die

30. Slip–Stick Effect

A phenomenon associated with the occur-rence of �melt fracture� of polymer meltsabove a critical shear stress value. (See Meltfracture.)

31. Slit Rheometer

A pressure rheometer for studying the rhe-ological properties of polymer melts, usinga slit die instead of the usual capillary die. Aslit die makes it possible to insert pressuretransducers along the channel length forrecording the pressure at different positionsalong the flow path before themelt emergesfrom the die. From the linear plot of pres-sure against distance from the entry, oneobtains (i) the gradient dP/dL, which isrequired to calculate the shear stress at thewall, that is, tw¼ (h/2) dP/dL, and (ii) theresidual pressure at the die exit (Pexit), whichis associated with die swelling and corre-sponds to the first normal stress differenceparameterN1, related tomelt elasticity. (SeeNormal stress difference.)

Plot of pressure against distance along the lengthLD of the die of a slit rheometer.

The shear rate at the wall ( _gw) is obtainedfrom the expression _gw ¼ 6Q=Wh2, whereQ is thevolumetricflowrate, andWandharethe width and height of the channel. Fromthe data it is possible to obtain the meltviscosity, h ¼ tw= _gw, and the first normal

stress coefficient, c1 ¼ N1= _g2w, at different

shear rates, obtained throughchanges in thevolumetric flow rate. Often the slit die isfitted to a small extruder so that measure-ments can bemade under conditions closerto those found in polymer processing opera-tions. (See Capillary rheometer and Meltelasticity.)

32. Small-Angle X-Ray Scattering (SAXS)

A technique widely used for the characteri-zation of nanosized domains in polymers,such as the lamellar structure of crystals andthe geometric features of inorganic do-mains in nanocomposites. The principle ofSAXS examinations is illustrated.

Schematic diagram of the principle of SAXS mea-surements. Source: Lavorgna (2009).

A selected wavevector of incident mono-chromatic radiation, Ki, is impinged ontothe sample and the scattered intensity,Kf, iscollected as a function of the scatteringangle 2Q. The relevant parameter that isrequired to analyse the interaction with thescattering domains is the vector q, repre-senting the difference between the incidentand scattered vectors, that is, q¼Ki�Kf,obtained from the equation

q ¼ ð4p=lÞsinQ:

From knowledge of the scattering vectorq, it is possible to calculate the diffractionspacing (d) using the equation d¼ 2p/q. Thescattered intensity I(q) is the Fourier trans-form of the correlation function of the elec-tron density r(r), which corresponds to theprobability offinding a scattering domain inposition r in the sample if another scatteringelement is located at position 0. SAXS ex-periments are designed to measure I(q) at

32 Small-Angle X-Ray Scattering (SAXS) j285

very small scattering vectors and plots areobtained for I(q) against scattering vector, q.An example of such plot is shown in thediagram for some experiments on silica-hybridized Nafionmembranes, which wereused to calculate the fractal size Dm of thesilica domains.

Example of a log–log plot of scattered intensityagainst vector q from SAXS experiments. Source:Lavorgna (2009).

Usually the data are normalized using thescattering invariant, INV, defined as theintegral of the scattered intensity, that is,

INV ¼ð10IðqÞq2 dq:

In thediagramare shown linear plots for thesame samples used to calculate the separa-tion distance between organic and inorgan-ic domains, as a bimodal distribution withmean values, respectively, 2.1 and 3.7 nm.

Example of plots of INV against vector q derivedfrom SAXS experiments. Source: Lavorgna(2009).

33. Solar Radiation

Radiation from the Sun reaching the Earth.Only about 5% of all the radiation reachingthe Earth gets through the atmosphereto the surface. Radiation with wavelengthin the range 290–400 nm of the spectrumcan be absorbed by many polymers and caninduce oxidative degradation reactions.

34. Solid-State Polymerization

A termusually used todenote the increase inthe molecular weight of poly(ethylene tere-phthalate) (PET) by advancing the condensa-tion reactions, through thermal treatment ofthe granules under vacuum at temperaturesjust below the melting point (Tm¼ 265 �C).

35. Solid-State Processing

Type of processing operation for thermo-plastics carried out at temperatures eitherjust above the Tg of a glassy polymer orbetween the Tg and Tm of a crystallinepolymer. A typical example of solid-stateprocessing is the stretch blow moulding ofPET bottles and containers.

36. Solubility Coefficient

Aparameter, S, that denotes the solubility ofa gas or liquid in a solid relative to theapplied pressure, that is, S¼C/P, whereC is the volume of gas or liquid dissolvedin unit volume of polymer and P is theapplied pressure. (See Permeability.)

37. Solubility Parameter

A parameter, d, that describes the solubility(or miscibility) characteristics of polymers,additives or solvents. The definition is d¼E/y, where E is the internal energy per unitvolume and y is the volume of the molecule.

286j 37 Solubility Parameter

The solubility of additives in polymers, or themiscibility of two polymers in a mixture, isthermodynamically possible if the two com-ponentsof themixturehave similarsolubilityparameters.Thevalueofthesolubilityparam-eter is related to intermolecular interactionsand corresponds to the sum of three terms,respectively, polar (dP), hydrogen bonding(dH) and non-polar or dispersive (dD).

38. Spandex Fibre

The term refers to elastomeric fibres wherethe fibre-forming component is a long-chain polymer consisting of more than85% segmented polyurethane. The softblock is a macroglycol (linear polyol), whilethe hard block is formed from diphenyl-methane-4,40-diisocyanate (MDI) and hy-drazine (H2NNH2) or ethylene diamine(H2NCH2CH2NH2), according to the reac-tion scheme shown. (See Urethane poly-mer, Block copolymer and Fibre.)

Reaction scheme for the synthesis of block copo-lymers for the production of spandex fibres.

39. Specific Impedance

A parameter that describes the capability ofa dielectric to store electric charge in analternating electric field. The complex

specific impedance (Z*p) is related to the

capacitance (C*) and is defined as

Z*p ¼ 1

vC*ðd=AÞ ;

wherev¼ 2p f (f is the frequency),C* ¼Q*/V (i.e. stored charge/applied voltage), d isthe distance between the electrodes andA isthe area of the electrodes. The impedanceZ*p is related to the relative permittivity («*r )

by the expression

Z*p ¼ 1

v«*rC1:

(See Permittivity.)

40. Spectrum

A termused to describe the detailed features ofthe variation of a physical parameter within arange of related causes or excitations. An ex-ample is the absorption spectrumof a polymerto display the details of the absorption of a

certain type of radiation (e.g. infrared) as afunction of wavelength or wavenumber.

41. Spherulite

A term used to describe the organization ofcrystals of polymers, emanating from a cen-tral nucleus, as shown in the micrographs.

41 Spherulite j287

Typical appearance of spherulites in a crystallinepolymer viewed in a polarizing microscope.

Opticalmicrographof a spherulite of polyoxymethy-lene sample etched with 37%HCl solution. Source:Ehrenstein (2001).

The lamellae of folded-chain crystals em-anate from a central nucleus in a spiralfashion as indicated schematically.

Lamellar helical stacking of folded crystal domainswithin a spherulite. Source: Ehrenstein (2001).

42. SPI Gel Time

Amethod used to determine the gel time ofunsaturated polyester resins, devised by theSociety of the Plastics Industry (SPI) inthe USA. It consists of recording the timetaken for the temperature of a specificamount of resin, contained in a test tubeimmersed in a water bath maintained at50 �C, to rise to a pre-specified value as aresult of the exothermicity of the cross-linking reactions.

43. Spider Leg

These are the three sections of a tubingor pipe die that holds the central pinfixed on the main body of the die. (SeeExtrusion die.)

44. Spiral Flow Moulding

A technique used to evaluate the flow char-acteristics of polymers for injection mould-ing. The cavity of the mould is a graduatedspiral that is fed from the central sprue andchannels out to the open. The procedureinvolves measurements of the length of thespiral under different conditions to com-pare the moulding characteristics of differ-ent materials.

288j 44 Spiral Flow Moulding

45. Sputtering

A technique used to deposit a thin layer ofmetal or silica on articles or films throughvaporization induced by a high-temperaturefilament. (See Metallization.)

46. Stabilization

Although generally the term denotes theprocess or method that renders a systemstable, within the polymer context it mainlyrefers to the use of stabilizers to prevent theoccurrence of degradation reactionsthrough the incorporation of additives,which are known as stabilizers. (See Ther-mal degradation, UV degradation, Stabiliz-er and Vinyl polymer.)

47. Stabilizer

An additive used to prevent or retard thedegradation of polymers. Stabilizers func-tion in a number of different ways accord-ing to the cause and mechanism of thedegradation. In this respect they are broadlydivided into:

a) light orUVstabilizers if they protect thepolymer against the degradation effectsof sunlight in combination with atmo-spheric oxygen; and

b) processing stabilizers when their inter-vention prevents degradation duringmanufacturing operations, involvingthe combined effect of high tempera-ture and oxygen.

Stabilizers that protect the polymer byreacting with the free radicals producedfrom the interaction of oxygenwith polymerchains are usually called �antioxidants� or�primary stabilizers�. The stabilizers that actas peroxide decomposers are referred to as�secondary stabilizers�, insofar as they are

used in conjunction with a primary stabiliz-er to provide a synergistic effect. (SeeAntioxidant and UV stabilizer.) Special sta-bilizers can be used to protect polymersagainst degradation resulting through hy-drolysis reactions, which cause chain scis-sion and a reduction of molecular weight.(See Hydrolysis and Hydrolysis stabilizer.)Stabilizers are sometimes classified in a

manner that reflects both their chemicalnature and the type of protection that theyafford. For instance, HALS is the abbrevia-tion for �hindered amine light stabilizers�.The chemical classification of stabilizers isapplied particularly to additives used informulations of PVC and other vinyl poly-mers. In this case, stabilizers are classifiedas �acid absorbers� if their function is toprotect the equipment against the corrosiveaction of the acid formed, as well as mini-mizing the autocatalytic effect that they haveon the actual formation of the acid fromdecomposition of the polymer chains.These stabilizers are further classified intolead, cadmium, barium, zinc or tin types todescribe the chemical nature of the metalcomponent of the compound used as addi-tive. (See PVC and Stabilization.)

48. Standard Linear Solid (SLS)

A hybrid model that combines the relaxa-tion characteristics of the Maxwell modeland the creep behaviour of the Kelvin–Voigtmodel, as shown in the diagram.

Standard linear solid (SLS) model.

The SLS model is more realistic thaneither the Maxwell model or the Kelvin–Voigtmodel for the linear viscoelastic behav-iourofpolymers insofaras it canexhibitboth

48 Standard Linear Solid (SLS) j289

the stress relaxation and the creepbehaviourof polymers. Note that the Kelvin–Voigtmodel does not exhibit stress relaxationcharacteristics. At the same time, the solu-tion of the constitutive equation for theMaxwell model applied to creep situations(constant stress input) produces an unreal-istic linear increase in strain from time zeroand a residual constant strain when remov-ing the stress after a creep period.The physical interpretation of the SLS

model with respect to stress relaxationsituations is shown.

Stress relaxation characteristics of the standardlinear solid (SLS) model.

The SLSmodel indicates that, if a strain isapplied instantaneously at time zero, andheld constant, there will be an exponentialdecay of the resulting stress, reaching aconstant value at infinite time. In this re-spect the SLS model differs from the Max-well model, which predicts completerelaxation of the stress. However, ifthe strain is forced to go to zero at timet1, the resulting compressive stress willrelax completely at infinite time.The constitutive equation for the SLS

model can be written as a generic expres-sion for the variation of stress,s, and strain,«, with time, t, such as

a0sþ a1ds=dt ¼ b0«þ b1d«=dt;

where the constants a0, a1, b0 and b1 can berelated to the two spring constants andthe dashpot of the SLS model, resulting inthe expression

Em þEv

Em

� �sþ h

Em

dsdt

¼ hd«Et

�Ev«;

where Em is the modulus of the Maxwellcomponent, Ev is the modulus of Kelvin–Voigt component andh is the viscosity of thedashpot component. Solving the equation

for «¼ constant (stress relaxation condi-tions) gives an expression for the variationof the relaxation modulus with time, E(t), as

EðtÞ ¼ E1 þ ðE0�E1Þ expð�t=lRÞ;where E1 is the modulus at infinite time,knownalso as the relaxedmodulus (ER),E0 isthemodulus at time zero, known also as theinstantaneous modulus, and lR¼h/(Em þEv) is the relaxation time.Solving the constitutive equation for s¼

constant (creep conditions), an equation forthe compliance D(t) is obtained in the form

DðtÞ ¼ D0 þðD1�D0Þ½1�expð�t=lcÞ�;where D0 is the instantaneous compliance,D1 is the compliance at infinite time, andlc¼h/Ev is the retardation time.

290j 48 Standard Linear Solid (SLS)

The physical interpretation of the SLSmodel for creep conditions is illustrated inthe diagram in terms of the variation of thestrain as a function of time during the creepperiod and after removing the stress (i.e.recovery period). The diagram shows thatthere is an instantaneous increase in strain(i.e. at time zero) followed by a retardedincrease towards equilibrium at infinitetime. If the stress is removed at a certaintime, there will be an instantaneous recov-ery of the strain imposed at the start of thecreep period, followed by an exponentialretardation of the strain before the condi-tions of complete recovery are reached.

Evolution and recovery of strain for the standardlinear solid (SLS) model under creep conditions.

49. Starch

A polysaccharide consisting of a mixture ofamylase (linear polymer) and amylopectin(a highly branched polymer), as shown.

Chemical structure of (a) amylose and (b) amylo-pectin. Source: Rudnik (2008).

Natural starch contains 15–30% amylosewith an average molecular weight (MW)that varies from 250 to 5000, and 70–85%amylopectin with MW varying within therange of 10 000 to 100 000.Heating starch ina closed vessel containing about 15% water

49 Starch j291

to temperatures above 100 �C produces arigid thermoplastic polymer (thermoplasticstarch, TPS) with a glass transition temper-ature (Tg) in the region of 60 �C (after dry-ing), which results from the destruction ofthe original crystalline structure. This re-structured form of starch can be injectionmoulded into products with rigidity similarto that exhibited by polypropylene orHDPE,and can be plasticized using a variety ofplasticizers, such as glycerol and poly(eth-ylene glycol). The TPS form of starch can beblended with other biodegradable polymerssuch as polycaprolactone, poly(lactic acid),poly(vinyl alcohol), poly(hydroxybutyrate-co-valerate) and poly(ester amide)s to tailorthe properties to specific product require-ments. (See Biopolymer.)

50. Staudinger

A German scientist who devised the firstmethod for measuring the molecularweight of polymers. After this work, theterm �high polymers� became widely usedto describe the long-chain macromolecularcompounds, which are now known simplyas �polymers�.

51. Stearate

Usually as an inorganic salt of sodium, zincand calcium types, used as external lubri-cants in polymer formulations.

52. Stearic Acid

An additive used in conjunction with zincoxide to �activate� the vulcanization of elas-tomers. Also used as a dispersing aid forfillers and as an internal lubricant in PVC-Uformulations.

53. Stereolithograpy

A technique widely used for the rapid pro-duction of prototypes. In this process, usu-ally a thermosetting resin, such as an epoxyresin containing specific photoinitiators,is used to build up three-dimensionalshapes through sequential cross-linking re-actions of successive thin layers of resins bymeans of a focused laser beam, usuallyoperating in the UV range. The movementof the laser beam is programmed via acomputer-aided design (CAD) system. Theprinciple is illustrated in the diagram.

Principle of stereolithography prototyping. Source:Chua et al. (2003).

The same technique can also be usedwith thermoplastics capable of absorbingradiation within the limits of the powergenerated by the laser, to generate sufficientheat to melt a thin layer of polymer powder.Typical polymers used are polyamides, par-ticularly nylon 11 or nylon 12, polycarbonateand thermoplastic elastomers.

54. Stiffness

A general term used to describe the resis-tance of a structure to bending deforma-tions. It can be quantified through thedefinition of a stiffness coefficient (S) asthe ratio of the applied load (P) and theresulting deflection (D), that is, S¼P/D.The reciprocal of the stiffness coefficient isknown as the �compliance�.

292j 54 Stiffness

55. Stokes Equation

An equation used to determine the sedi-mentation time of particles suspended in aliquid medium through calculations of thesedimentation velocity (V ), that is,

V ¼ d2ðr�r0Þg18h

;

where d is the particle diameter, r is theparticle density, r0 is the density of themedium, g is the gravity constant and h isthe viscosity of the medium.From an examination of this equation,

for instance, one can predict the beneficialeffects of reducing particle size and in-creasing the viscosity of the suspendingmedium with flocculants as a means ofimproving the stability of suspensions. Itmust be noted, however, that the Stokesequation assumes that there are no inter-active forces acting between particles,which are determined by their zeta poten-tial value. Consequently, the equation canonly be used for dilute suspensions, that is,volumetric concentrations up to about 3%.Empirical modifications can be used forestimations related to suspensions withhigher particle concentrations. For concen-trations between 3% and 10%, the calculat-ed velocity is corrected by a factor equal to(1�ws)

4.5, where ws is the volume fractionof the solid particles. Another limitation ofthe Stokes equation arises from deviationsof the particles from the assumption ofspherical geometry.

56. Strain

A concept used in engineering mechanicsto take into account the dimensions of acomponent or specimen subjected to defor-mations. Accordingly, strain («) is definedas the change in linear dimension dividedby the original dimension. Strains can bedivided into:

a) normal strain (compression or tension)when the change in dimension takesplace along the direction of the force,that is, «¼ dL/L;

b) shear strain when the deformationcauses a distortion of the geometry(e.g. a square section becomes rhom-boidal) without changing the volume,that is, g¼ dX/L¼ tana, where dX isthe change in dimension perpendicu-lar to the length (L), so thata representsthe deviation of the angle from theoriginal 90� angle formed by the sur-faces of the body deformed; and

c) volumetric strain («V) when there is achange in dimensions in three perpen-dicular directions, which gives «V¼«1þ «2 þ «3.

57. Strain Rate

The rate of change of strain with time, avariable used in tensile tests carried out tomeasure the strength or evaluate the tough-ness of materials.

58. Stress

A concept used in both mechanical andelectrical engineering to take into accountthe dimensions of a component or speci-men over which a mechanical force acts orthe distance over which a voltage is applied.A mechanical stress (s) can be simply de-fined as the force (F) divided by the area (A),while an electrical stress, j, is the voltage (V)divided by the distance (L). Inmore rigorousterms, these should bewritten as the ratio ofinfinitesimal quantities, that is, s¼ dF/dAand j¼ dV/dL.

58.1 Mechanical Stress

Thereare three typesofmechanical stresses:(i) normal stress (tensile or compressive)

58 Stress j293

when the force acts perpendicular to a sur-face; (ii) shear stress when the force actsparallel to a surface; and (iii) hydrostaticstress (pressure p or hydrostatic tensionsH)when three forces, equal in magnitude, actin three perpendicular directions over anarea. The different types of stress that canact on a body are shown in the diagram.

Identification of normal stresses and shear stressesthat can act on a body.

Stress is a tensor quantity requiring twodigits for identification: the second digit in-dicates the direction of the force, while thefirst denotes the area over which the force isapplied. For instance, sxx denotes a normalstress acting indirectionxonaplaneperpen-dicular to direction x, which is often identi-fied simply as sx. On the other hand, sxy

denotesaforceactingindirectionyonaplaneperpendicular todirectionx. Thismeans thatsyx is a shear stress, which is more usuallyrepresented by the symbol txy. If three stres-ses acting in perpendicular directions aredifferent in magnitude, then the hydrostaticstress component is taken as the averagevalue, that is, sH¼ (sx þ sy þ sz)/3.

58.2 Electrical Stress

The same arguments can be made withrespect to electrical stresses.

59. Stress Concentration

A term used to describe the intensificationof stresses (mechanical or electrical) arising

when there are sharp discontinuities in thegeometry of a product or specimen. Thesediscontinuities can be in the form of Vnotches or sharp edges. Stress concentra-tions are experienced particularly in joints,irrespective of whether they are mechanicalor electrical. An example of stress concen-trations in electrical components is shownin the diagram for the case of a shieldedcable at the point where the insulation hasbeen cut to produce a joint.

Stress concentrations in a cable where the insula-tion is stripped for the preparation of a joint.Source: Mascia (1989).

60. Stress Grading

A design aimed to attenuate the stress con-centration, mechanical or electrical, arisingwhen two adjacent components of a struc-ture, or a circuit, are made from materialswith vastly different Young�s moduli(mechanical structures) or volume resistiv-ities (electrical circuits). Stress grading isachieved by introducing an interlayer com-posed of a material with an intermediatemodulus or resistivity.

61. Stress Optical Coefficient

(See Photoelasticity.)

62. Stress–Strain Curve

A plot of stress against strain data obtainedfrom mechanical tests and usually used tocalculate the Young�s modulus of thematerial.

294j 62 Stress–Strain Curve

63. Stretch Blow Moulding

(See Injection blow moulding.)

64. Stripper Plate

A mechanism used to eject concave or hol-low thin-walledmouldings from the cavitiesof an injection mould. When the mouldopens, the stripper plate pushes the mould-ings away from the respective cores by ex-erting forces along the ribs of individualmouldings. (See Ejection mechanism.)

65. Structural Foam

A foamwith a solid skin obtained from rigidpolymers. (See Foam.)

66. Styrene–Butadiene Rubber (SBR)


67. Styrene–Butadiene–Styrene (SBS)Thermoplastic Elastomer

(See Thermoplastic elastomer.)

68. Styrene–Isoprene–Styrene (SIS)Thermoplastic Elastomer

(See Thermoplastic elastomer.)

69. Styrene Polymer

A polymer containing a predominant num-ber of styrene units in the polymer chains.These include both the homopolymer andcopolymers, which are described below.

69.1 Polystyrene (PS)

Available commercially predominantly asan atactic homopolymer, where the benzene

side groups are distributed at random inspace. (See Tacticity.) PS is glassy polymer(amorphous, although often referred to as�crystalline� due to its transparency). Thechemical structure of PS is represented bythe formula:

The glass transition temperature is in theregion of 100 �C and the density is 1.05 g/cm3. It is produced predominantly by bulkor suspension free-radical polymerization.Apart from the main use for the productionof injection-moulded articles, it is widelyused for the manufacture of foams (knownas expanded polystyrene, as it is producedfrom expandable beads containing pentaneas blowing agent) and also for the produc-tion of biaxially oriented films.

69.2 Syndiotactic Polystyrene (SynPS)

Polystyrene can also be polymerized with aNatta catalyst to produce stereospecific poly-mers with a high melting point. In parti-cular, the syndiotactic version has beencommercialized in recent years for the pro-duction of films. SynPS has a melting pointof 273 �C and a Tg around 100 �C.

69.3 Styrene Copolymer

A variety of random copolymers, producedby free-radical polymerizationmethods, areavailable in the plastics industry, as well asfor coatings and binders. The comonomerchosen varies according to the desiredchange in Tg or to improve the chemicalresistance, particularly in relation to thesusceptibility to crazing. Copolymers witha-methylstyrene (styrene–a-methylstyrene,SMS) and acrylonitrile (styrene–acryloni-trile, SAN) have a Tg around 115–120 �C.The structure of SAN can be represented bythe formula:

69 Styrene Polymer j295

SAN also provides a better resistancethan PS to crazing in hydrocarbons andvegetable oils. Improved weathering resis-tance is achievedwith the use of copolymersof methyl methacrylate without any signifi-cant changes in the Tg. Copolymers andterpolymers with other acrylate esters, onthe other hand, are more widely used aswater emulsions for coatings and binders,as these exhibit a considerably lower Tg.

69.4 Styrene–Maleic AnhydrideCopolymer (SMA)

These may be considered as functionalizedpolystyrene grades insofar as they contain a

small number of succinic anhydride units(5–10%) in the backbone chains, obtainedby copolymerization of styrene with maleicanhydride. This method makes it possibleto introduce a larger quantity of anhydridefunctional groups on the polystyrene chainsthan by post-polymerization grafting tech-niques. The presence of reactive anhydridegroups in the chains can be exploited in anumber of ways, particularly in improvingthe adhesion characteristics towards rein-forcing fillers and fibres.

69.5 High-Impact Polystyrene (HIPS)

Represents a wide range of toughenedgrades of polystyrene containing particlesof essentially polybutadiene (PB) rubberchemically bonded to the surroundingglassy polystyrene (PS) matrix. These areproduced by dissolving the elastomer instyrene monomer and conducting a free-radical polymerization in bulk. The freeradicals produced by the initiator can alsoattack the PB chains, thereby producing aquantity of grafted block copolymer actingas compatibilizer for the immiscible PS andPB homopolymers. By varying the molarratio of reactants and the polymerizationconditions, as well as the reaction proce-dure, it is possible to obtain a wide range ofPS–PB alloys with different morphologicalstructures, as shown in the micrographs.

Morphological features of several types of HIPS. Source: Courtesy of BASF.

The details of the morphological struc-ture can have a predominant effect on prop-erties. For instance, the top left and topcentre micrographs are typical HIPS ob-tained through conditions that lead to phaseinversion during the course of polymeriza-tion. (See Phase inversion.) Typically, thedispersed rubber particles of these systemscontain occluded sub-micrometre sizedparticles of glassy polystyrene. Note that,

296j 69 Styrene Polymer

whereas the systems with large particles(micrographs at the top) are opaque in viewof the large difference in refractive indexbetween particles and matrix, the system atbottom left, containing fine discrete parti-cles of PB, produces translucentmouldings.The HIPS shown in the bottom right mi-crograph was produced by an anionic solu-tion polymerization method, producing avery fine lamellar rubber phase, resulting inproducts that are completely transparent.This is due to the fact that the dimensionsof the dispersed scattering centre of the PBrubber particles are smaller than the wave-length of visible light. Owing to some inevi-table plasticization effect provided bysolubilized grafted PB chains in the sur-rounding PS matrix, all HIPS grades tendto exhibit a somewhat lower Tg than that ofpure PS.

69.6 Acrylonitrile–Butadiene–Styrene (ABS)Terpolymer Alloy

Consists of compatibilized two-phaseblends with an acrylonitrile–styrene copol-ymer as the main glassy component and abutadiene–acrylonitrile copolymer as thedispersed rubber component. The rubberparticles contain inclusions of glassy poly-mer, which act as reinforcement to counter-act the reduction in Tg brought about by thepresence of miscible components of themain copolymers. Similarly to HIPSthere is a wide range of different gradesavailable commercially, varying in levels ofrubber modification and method used toproduce the blends. (See ABS.)

69.7 Acrylonitrile–Acrylate–Styrene (ASA)Terpolymer Alloy

Consist of compatibilized two-phase blendsof a styrene–acrylonitrile copolymer with anacrylate rubber, produced in the same way

as ABS. The replacement of the polybutadi-ene elastomer with an acrylate rubber, suchas copolymers of butyl acrylate–ethyl acry-late, brings about large improvements inthermal oxidation stability and resistance toUV light, as well as in the resistance tomineral oil.

70. Surface Energy (Surface Tension)

Forces and energy on the surface of a liquidor solid, arising from the imbalance ofmolecular interactions between moleculesin the bulk and those at the surface. Themolecules exposed to the surface will attractor repelmolecules from the environment. Ifthe latter is air (or any gas), the number ofmolecules that can interact with those of thesolid or liquid surface is very small, so thatan imbalance of energy between bulk andsurface still remains. In the case of liquids,the presence of surface forces is evidencedby the tendency of a free liquid droplet toassume a spherical geometry, which givesthe lowest surface per unit volume. Surfaceenergy plays a crucial role in the under-standing of adhesion phenomena. Thesurface energy (g) of water at room temper-ature is 72mJ/m2, which is quite high dueto the strong hydrogen bonds between mo-lecules in the bulk. The value decreaseswiththe reduction in strength of intermolecularforces, so that for glycerol the value of gbecomes 63mJ/m2 and for a typical epoxyresin the value is 47mJ/m2. The values goright down when the intermolecular forcesare weak, as in the case of hexane, wherethere are only van der Waals forces actingbetween molecules, giving a surface energyaround 18mJ/m2.The surface energy of the most common

types of polymers are shown in ascendingorder in the table. For comparison thevalues for wood and iron are also reported.

70 Surface Energy (Surface Tension) j297

For these, the g values are very high, owingto the very large number of hydrogen bondsand covalent bonds in wood, and the strongionic interactions in iron.

SubstrateSurface energy

(mJ/m2)

Polytetrafluoroethylene (PTFE) 18.5Polytrifluoroethylene 22Poly(vinylidene fluoride)(PVDF)

25

Poly(vinyl fluoride) (PVF) 28Polyethylene 31Polypropylene 31Polystyrene 33Poly(vinyl alcohol) (PVA) 37Poly(methyl methacrylate)(PMMA)

39

Poly(vinyl chloride) (TVC) 39Poly(vinylidene chloride)(PVDC)

40

Poly(ethylene terephthalate)(PET)

43

Poly(hexamethylene adipa-mide) (nylon 6,6)

46

Epoxy resin (cured) 45Wood 200–300Iron �2000

Source of data: Wake (1992).

71. Surface Resistivity

Denotes the resistivity of a dielectric, whichcharacterizes its capability to �resist� theflow of a current over the surface. Since�resistivity� is defined as the ratio of electri-cal stress to the resulting current density,the related formula for surface resistivity(rS) can be derived from first principles asfollows. One has stress¼ voltage (V) perunit distance, and surface current density¼ current (I) per unit frontal width. Usingthe apparatus and specimen geometryshown, the final equation for rS becomes

rS ¼ ðV=gÞ ðP=IÞ ¼ ðP=gÞRS;

where RS is the surface resistance (V/I), P isthe average perimeter of the guarded elec-trode (2pDaverage) and g is the gap distancebetween the inner electrode and the guardring. Note that the dimensions of surfaceresistivity are ohm/square (W/&), wheresquare (&) indicates that the property isrelated to the surface characteristics, so thatit can be differentiated from volume resis-tivity, which is a bulk characteristic of thedielectric. The schematic diagram for theelectrical circuit measurement of the sur-face resistivity is shown, where G repre-sents the galvanometer for measuring thecurrent (I) resulting from the appliedvoltage (V).

Circuit formeasuring the current flowing across thegap between the inner electrode and the guard ring.

The geometric setup for the electrodes(top and bottom) and the guard ring isshown. Note that the function of the guardring is to ensure that only the current flow-ing through the gap between the electrodeand the guard ring is recorded by the galva-nometer. The circuit arrangement shownallows any leakage of current flowing overthe edge of the plaque to go to earth.

298j 71 Surface Resistivity

Top electrode and guard ring attached to the plaqueused as specimen for measuring surface resistivity.

72. Surfactant

Agent used to reduce the surface energy ofliquids or the interfacial energy betweensolid and liquid or between liquid and liq-uid. There are three types of surfactants:

a) Anionic surfactants consist of long ali-phatic chains (hydrophobic) andSO3

�Naþ (hydrophilic) end groups.The most common type is dodecylben-zene sodium sulfonate.

b) Cationic surfactants are mostly ammo-nium quaternary salts (bromides orchlorides) of long-chain hydrocarbons,used primarily as emulsifying agentsfor emulsion polymerization and asexfoliating agents for nanoclays. Anexample is CxHyNH4

þBr�, wherex¼ 12–18 and y¼ 25–37.

c) Amphoteric surfactants is the termused to describe the non-ionic natureof a class of surfactants, consistingmostly of block copolymers containingchains of polydimethylsiloxane and apoly(alkylene oxide), such as those de-rived from ethylene or propylene oxide.

73. Surging

A term used to describe a pulsating outputof an extruder, resulting from the break-upof the solid bed within the transition zone.This creates a temperature perturbation andlocal flow instability, which gives rise to afluctuating pressure at the die entry and apulsating flow rate through the die. Thephenomenon can be prevented by usingscrews with a very long metering zone toensure that the flow instability vanishes bythe time the melt reaches the die, or byusing a �barrier� screw. (See Extrusion theo-ry and Barrier flights screw.)

74. Suspension

Particles of a liquid or solid dispersed in aliquid medium, usually water. Sedimenta-tion of the particles does not take place if thedensity of the two components is not toodifferent. The stability of a suspension canbe increased by means of surface-activeagents, also known as protective colloids.These have two different types of chemicalgroups, each one of which is capable offorming strong bonds, or associations, withthe other component of the suspension. It isalso possible to increase the stability ofsuspensions by allowing charges to be ac-cumulated on the surface of the droplets orparticles so that their agglomeration or coa-lescence is prevented through inter-particlerepulsions. This is sometimes referred to as�electrostatic stabilization�. (See Suspensionpolymerization.)

75. Suspension Polymerization

A type of polymerization whereby a mono-mer is dispersed in water to form stabledroplets in the region of 10–1000 mm, de-pending on the nature of the monomer andthe type of surface-active agent, that is, the

75 Suspension Polymerization j299

suspension stabilizer. Suspension polymer-ization is an effective way of maintainingconstant the temperature of the polymeriz-ing species, as it allows theheat developed tobe dissipated into the surrounding water,which can be effectively controlled throughappropriate heat exchangers in the form ofcooling jackets or other devices. The initia-tor for the polymerization is dissolved in themonomer particles; alternatively, polymeri-zation is induced by photocatalysis with theuse of UV light. In this respect, therefore,suspension polymerization is similar tobulk ormass polymerization. Formost vinylmonomers, the stability of the monomersuspension is achieved with the addition ofpoly(vinyl alcohol), containing a certainamounts of acetate groups. (See Vinyl poly-mers.) The stability is achieved by virtue ofthe �OH groups forming strong associa-tions with water, while the more hydropho-bic acetate groups are solubilized into theouter surface layers of the monomer dro-plets, as shown.

Schematic illustration of the spatial organization ofpoly(vinyl alcohol) in a suspension of monomer inwater. Source: Denkinger (1996a).

In most cases the polymer formed re-mains dissolved in the monomer until therequired, or maximum, degree of conver-sion is achieved. The free monomer is thenexpelled through suitable drying proce-dures in the final stage of the polymeriza-tion when the polymer particles areseparated from the water. In some cases,however, the polymer formed precipitatesout of the monomer, while still remainingwithin the suspended particles. For the caseof PVC, this situation is exploited for theproduction of porous polymer particles,used for the production of the so-called �dryblend� grades. (See PVC.)

76. Syndiotactic

(See Tacticity.)

77. Synergism

The combined response or effect producedby two additives or components of apolymer formulation that is substantiallygreater than the weighted sum of the effectsof the individual components.

78. Syntactic Foam

A cellular product produced with the use ofhollow Ballottini spheres. (See Foam.)

300j 78 Syntactic Foam

T

1. Tack

A term used in the rubber industry todescribe the sticking of a rubber gum (priorto vulcanization). This is an important char-acteristic for fabrications of rubber articles,as it allows stacks of various cuttings toremain in position during manufacturingoperations. The term is also used in relationto adhesives.

2. Tackifier

An additive, usually a resin (phenolic, cou-marone–indene and terpene types), used inrubber mixes or hot-melt adhesives andpressure-sensitive adhesives in order to en-hance the �tack� of a gum or adhesive tapes.

3. Tacticity

A term used to describe the spatial positionof symmetrical side groups attached to amonomeric unit of polymer chains, such asthe position of CH3 groups in polypropyl-ene. Accordingly, when each unit has thesame spatial configuration along the chains,the polymer is said to be �isotactic�. Whenthe CH3 groups are arranged in an alternat-ing fashion, the polymer is said to be�syndiotactic�; and if they assume a randomconfiguration, the structure is said to�atactic�. The spatial configuration of isotac-tic and syndiotactic polymers is shown.

Isotactic and syndiotactic configurations. Bold (thintriangular) and dashed C–X bonds denote the spa-tial position of the X group, respectively, above andbelow the reference plane (of the paper).

Note that the regularity of the spatialposition of the CH3 groups in isotactic andsyndiotactic systems allows the chains to bepacked close to each other into crystallinedomains. Usually, this is not possible if thestructure is atactic, owing to the steric hin-drance effects of the side groups.

4. Talc

A magnesium silicate filler derived fromrocks known as soapstone or stealites. Talcis essentially aluminium silicate, with den-sity in the range 2.58–2.83 g/cm3, depend-ing on the origin and grade. There are avariety of particles in talc fillers, rangingfrom platelets, through rods to irregularlyshaped particles, which provides a certainlevel of reinforcement capability. The typicalgeometric features of talc particles is shownin the micrograph.


j301

Micrograph of a talc filler, from Rheox Inc. Source:Wypych (1993).

The average particle size and surface areaof talc fillers are in the range 1–8mm and3–20m2/g. (See Filler.)

5. Tan d

Also known as tangent delta. (See Lossfactor, Dynamic mechanical thermal analy-sis and Dielectric thermal analysis.)

6. Tangent Modulus

The modulus calculated by drawing a tan-gent on the stress–strain curve through theorigin. The modulus is calculated as thegradient of the resulting straight line. Thetangent modulus is sometimes known asthe �initial modulus�. (See Modulus.)

7. Tear Strength

A term used to denote the resistance of aflexible material to tearing. Tests are nor-mally carried out to measure the resistanceto propagation of an existing crack intro-duced into a rectangular specimen, which isstretched in a tearingmode, as shown in thediagram.

Tear test for flexible materials.

The case where the force remains con-stant during fracture (smooth tearing) isan example of fracture taking place with-out a change in compliance of the speci-men during crack propagation, as the loadis supported only in section I of thespecimen, while section II is not sub-jected to stresses. This type of fracturetakes place when the rate at which thespecimen is stretched is higher than therate at which the crack would propagatenaturally, so that the crack has to be�driven� in order to advance. This situa-tion arises when fracture takes place withthe formation of a fairly large yield zone atthe crack tip (e.g. polyethylene film) andin the case of rubber, provided that thecrack advances along a linear path in thedirection of the applied load. For thesetearing conditions, the strain energy re-lease rate, G, is given by

G ¼ �2ðdW=dAÞ;where W is the total strain energy in thespecimen and A is the surface area of thecrack formed. Under constant-complianceconditions this equation becomes

G ¼ 2F=B;

where F is the force associated with thepropagation of the crack and B is the thick-ness of the specimen. Consequently, thetear strength, expressed as force per unitthickness, corresponds to the fundamentalfracture toughness parameter G, (strainenergy release rate), expressed as energyper unit area. (See Fracture mechanics.)

302j 7 Tear Strength

Force–extension curves recorded in tear tests.

When the natural rate of crack propaga-tion is higher than the rate at which thespecimen is stretched, fracture takes placevia theso-calledslip–stickmechanism,man-ifested in the form of a zig-zag force–defor-mation traceduring fracturepropagation. Inother words the force drops when the crackstarts to propagate, owing to the recovery ofthe deformation at the crack tip, and risesagain when the extension in the specimenagain reaches the condition required forthe propagation of the crack. In the caseof a slip–stick tear, the value of the forceto be used in the equation for the calcula-tion of the tear strength is taken as theaverage between the oscillating values.(See Adhesive test.)

8. Teflon

Tradenameforpolytetrafluoroethylene(PTFE).

9. Telechelic Oligomer or Polymer

Systems containing functional groups at thechain ends that can be used to extend thelengthof thechain through further reactions.

10. Tenacity

A term used to denote the tensile strengthof fibres or filaments, in grams per denier(g/denier) or newtons per tex (N/tex). (SeeDenier and Tex.)

11. Tensile Modulus

Modulus measured in tension. Corre-sponds to the Young�s modulus if measure-ments are made at small extensions. Underthese conditions, the value of the modulusmeasured in tension is equal to the valueobtained in compression. (See Modulus.)

12. Tensile Test

A test carried out in tension.

13. Tensor

Aquantity (excitation or response) that has amagnitude, a direction and a position rela-tive to a surface. An example of a tensorquantity is �stress�, as it has a magnitude(say, n pascals), a direction (x, y or z inCartesian coordinates) and a position rela-tive to a reference plane (xy, xz or yz). Forthis reason, two letters or digits are requiredto describe its spatial position. For example,sxx denotes a normal stress (tension orcompression) that acts in the x directionand is located in the plane perpendicular tothe x direction. On the other hand, sxz is ashear stress that acts in direction z and liesin the plane perpendicular to direction x.(See Stress.)

14. Termination Reaction

A reaction that stops the growth of poly-mer chains during polymerization. (SeePolymerization.)

15. Tex

A unit used to describe the dimension offibres (cross-sectional area), filaments andweaving tapes. The �tex� is defined as thenumber of grams of the product per 1000metre length. Other units also used are

15 Tex j303

�decitex� as the weight in grams per 10 000metres and �denier� as the weight in gramsper 9000 metres. (See Denier.)

16. Thermal Conductivity

The coefficient that relates the heat flux (H)through a slab of material to the imposedtemperature difference (DT) between thetwo opposing surfaces, that is,

H=A ¼ KDT=X ;

where A is the surface area and X is thethickness. The thermal conductivity (K) ofpolymers is much lower than that of metalsowing to the absence of free-moving elec-trons to transfer the thermal energy in thedirection of the temperature gradient.

17. Thermal Degradation

A term that denotes the breakdown of themolecular structure of a polymer by theaction of heat. In most cases this resultsfrom oxidative reactions with atmosphericoxygen. In other cases, such as vinyl poly-mers, different reactions may take placeeither prior to, or simultaneous with, ther-mal oxidation reactions.

18. Thermal Expansion Coefficient

A coefficient that relates the linear or volu-metric expansion (DX) to changes in tem-perature (DT), that is, DX¼aDT, where a isthe linear or volumetric expansioncoefficient.

19. Thermal Gravimetric Analysis (TGA)

A technique that measures the change inweight of a sample with changes in temper-ature, under chosen environmental condi-tions, such as nitrogen, air or oxygen. This

technique is particularly useful to measurethe loss of volatiles resulting from degrada-tion reactions. Normally measurements aremadeinatemperaturerampmode,but itcanalso beused isothermally for kinetic studies.

20. Thermal Oxidation

(See Thermal degradation.)

21. Thermochromic Pigment

Type of pigment that changes colour revers-ibly at specific temperatures. There are twocommon types.

a) Liquid crystals with a twisted nematicmesophase. The change in colour whena temperature is reached arises from theincrease in crystal spacing, producingreflections at different wavelengths,whichareperceivedasachangeincolour.

b) Leuco dyes used in the form of micro-encapsulations 3–5mm in diameter.These have a less accurate temperatureresponse than liquid crystals.

22. Thermoforming

A generic name for processes involving theheating of a sheet, or a tubular product, tothe rubbery state of the polymer and draw-ing it by the application of vacuum to pro-duce the desired shape, often assisted bymechanical devices. The product is cooledwhile still under a state of external stressesin order to prevent recovery of the imposeddeformation through relaxation of the ac-quired molecular orientation. A character-istic feature of thermoforming is that thedeformations produce molecular orienta-tion, which imparts dimensional instabilityif the product were to be used at hightemperatures. On the other hand, the ori-entation can be controlled as a means ofincreasing the mechanical strength and

304j 22 Thermoforming

toughness of the article. Examples of sheetthermoforming processes are briefly dis-cussed and shown schematically.In negative (female) vacuum forming,

the required shape is acquired through thesimple application of vacuum to draw thesheet into a cavity. The formed article isremoved after the vacuum is released.

Negative (female) vacuum forming. Source: Un-identified original source.

In air-slip vacuum (male) forming, afterheating the sheet to the required tempera-ture, air is used to inflate and pre-stretch thesheet. Vacuum is then applied to draw thesheet onto a male mould, where is cooledbefore the vacuum is released and themoulded part removed.

Air-slip vacuum (male) forming. Source: Unidenti-fied original source.

In plug-assisted thermoforming, the pre-heated sheet is drawn into a cavity through

the combined use of a �plug� and vacuum toachieve larger draw ratios than is possible byother methods.

Plug-assisted forming. Source: Osswald (1998).

Note that �stretch blow moulding� meth-ods can be described as thermoformingof a tubular product. (See Injection blowmoulding.)

23. Thermofusion Process

This can be described as a manufacturingprocess by which articles are produced viathe interfacial fusion of smaller compo-nents. These processes comprise powderfusion operations, such as powder sinter-ing, powder coating and rotational mould-ing, as well as welding processes. (See Pow-der sintering, Powder coating, Rotationalmoulding and Welding.) �Perfect fusion� ofthe components brought into contact withone another is achieved if the overall adhe-sive forces acting across the interface be-come equal to the cohesive forces actingwithin the bulk of the components. If theadhering components are chemically simi-lar, perfect fusion would be achieved simplyby removing all surface irregularities andheterogeneities at the interface, so that thematerial at the interface cannot be distin-guished from the material in the bulk. Inorder to achieve this structural state, therehas to be molecular diffusion across theinterface of the individual components.Chemical similarity of the fusion compo-nents can be interpreted also in terms interms of mutual miscibility, determined bysimilarity in the values of the solubilityparameters.

23 Thermofusion Process j305

This may not be a sufficient requirementin the case of crystalline polymers insofar asthe two components, although miscible inthemelt state,may segregate at the interfacethrough differential crystallization insteadof co-crystallization. An example of the lat-ter situation is the fusion of high-densitypolyethylene (HDPE) to polypropylene(PP), which exhibit similar solubility para-meters but do not crystallize into commoncrystal cells on cooling. This results in adifferential surface energy of the compo-nents at the interface, which prevents theachievement of �perfect fusion�, as a state ofthe material where the interface cannot bedistinguished from the bulk. For the com-bination HDPE/PP, for instance, the differ-ence in solubility parameters is only in theregion of 5%, whereas the ratio of surfaceenergy for HDPE and PP is greater than 2.

24. Thermogram

A term used to describe the plot of an eventas a function of temperature, such as theweight of the sample inTGAor theheatflowin DSC experiments.

25. Thermomechanical Analysis (TMA)

A technique that measures the changes indimensions of a sample as result of changesin temperature, using a dilatometer. Theanalysis is particularly useful formeasuringthe glass transition temperature (Tg) and thelinear expansion coefficient of polymersbelow the Tg.

26. Thermoplastic

A polymer that will melt and flow at hightemperatures, evidenced by the net dis-placement of entire molecules relative toeach other through a reptation mechanism.To be able to fulfil these conditions, the

polymer must not contain chemical cross-links. Hence, for a cross-linked polyethyl-ene product, while it is crystalline and willmelt at high temperatures, the moleculesexist in the form of a low-density networkand cannot bemade to flow. The reasonwhysome thermoplastic products are cross-linked after processing, therefore, is toachieve this particular state so that they canbe used at temperatures above theirmeltingpoint. (See Heat-shrinkable product.)

27. Thermoplastic Elastomer

A synthetic rubber that has the processingcharacteristics of a rigid thermoplastic poly-mer. There are several types of thermoplas-tic elastomers.

27.1 Block Copolymer Elastomer

These constitute the main class of thermo-plastic elastomers, consisting of ABA-typeblock copolymers,where theAblocks consistof rigid units (glassy amorphous domains,usually polystyrene,Tg¼ 95 �C, or crystallinerigiddomains),whiletheBblocksarerubberylinearpolymersof variouscompositions.TheB units of the main types of thermoplasticelastomers are polybutadiene (Tg¼�90 �C),polyisoprene and isobutylene (Tg in the re-gion of�60 �C). (See Block copolymer.)Other systems are obtained by the hydro-

genation of the central units consisting ofcopolymers of butadiene and isoprenesto produce systems known as styrene–ethylene/propylene–styrene (S–EP–S) andstyrene–ethylene/butylene–styrene (S–EB–S).The removal of the unsaturation in thecentral rubbery blocks provides a greaterresistance to thermal and UV-induced oxi-dative degradation. The polystyrene con-tent of these block-copolymer elastomers isusually in the region of 30–40%. The mo-lecular weight of the central rubbery unitsis usually greater than 100 000, whereas themolecular weight of the end polystyrene

306j 27 Thermoplastic Elastomer

units is in the region of 7000–10 000.Highermolecular weights of the PS blocks wouldproduce large rigid domains, which willhave an adverse effect on many properties,particularly transparency. The manner inwhich the rigid blocks of polystyrene pro-duce physical cross-links between the high-molecular-weight (diene) segments of theblock copolymer chains is illustrated.

Physical cross-links provided by the strong attrac-tive forces between the segregated segments of therigid domains.

TEM micrographs of typical ABA blockcopolymers obtained on commercial ther-moplastic elastomers are shown. Note thatthe black-stained domains correspond tothe rubbery phase. Those with a lower ex-tent of phase interpenetration ((a) and (b))are softer elastomers owing to the moreprominent effect of the co-continuous rub-bery domains.

TEMmicrographs of different types of thermoplas-tic elastomers produced from ABA block copoly-mers. Source: Unidentified original source.

27.2 Multi-Block Copolymer

These elastomers are based on a multi-block copolymer with an (H–E)n structure,where H represents the hard segments,which are often crystalline thermoplastics,and E represents the rubbery (soft) seg-ments, with an amorphous structure. TheH segments are formed from polymerswith a regular repeating unit structure,that is, . . .AAAAAAAAAAA. . ., capable offorming crystalline domains with meltingpoint well above room temperature.The soft E segments are formed frompolymers with an irregular (random) ar-rangement of monomeric units, that is,. . .ABBAAABAABBBBAAB. . ., which pro-duce domains with a Tg well below roomtemperature. The composition and size ofeach block are distributed at random with-in macromolecular linear chains with dif-ferent molecular weights. The resultingblock copolymers have a complex morpho-logical structure consisting of ill-definedlamellae interconnected with chains con-taining both soft and hard segments. Thepresence of crystals immersed in theamorphous domain not only provides astrain-hardening behaviour exhibited byconventional cross-linked rubber, but willalso act as reinforcing filler.The most important types of elastomers

based on multi-block copolymers usuallycontain hard blocks consisting of eitherpolyurethanes, polyesters or polyamides.The soft segments are either aliphaticpolyethers, such as polyoxytetramethy-lene, polyoxypropylene and polyoxyethy-lene, or polymers produced from the con-densation reactions of adipic acid or se-bacic acid with different types of long-chain glycols. The hard blocks of polyesterelastomers are usually polybutylene tere-phthalate; those used for polyamide arethe same as those used for conventionalnylons, that is, PA 6, PA 11, PA 12 or PA6,6. The hard segments of polyurethaneelastomers are urethane blocks obtained

27 Thermoplastic Elastomer j307

from the reaction of diphenylmethane-4,40-diisocyanate (MDI) and 1,4-butane-diol. (See Polyester, Polyamide, Nylon andUrethane polymer and resin.) In the caseof polyolefin-based thermoplastic elasto-mers, the hard crystalline blocks are eitherisotactic polypropylene or linear polyeth-ylene (HDPE type), while the soft seg-ments are made of random copolymersof ethylene and propylene (EPR) with aglass transition around �60 �C.

27.3 Dynamic Vulcanizate

These have a structure, both chemical andmorphological, quite different from that ofblock copolymers. Themorphological struc-ture consists of a fine continuous phase of across-linked elastomer (usually EPDM) in amatrix and dispersed particles of a hardthermoplastic polymer component (usuallypolypropylene). The thermoplastic-like pro-cessing characteristics are likely to be de-rived from phase inversion when the crys-talline component melts. This not only re-sults in a large volumetric expansion of thelinear polymer domain but also produces amechanism for the dissipation of the im-posed mechanical energy through molecu-lar movements. The reptation movementsof the linear polymer chains will �drag�along the cross-linked elastomeric domainsby imposing on them sequential chain ex-tension and recovery motions. These dy-namic vulcanizates are obtained by mixingthe non-cross-linked (or partially cross-linked) elastomer with the thermoplasticpolyolefin at high shear rates in order toinduce grafting reactions between the twocomponents and to induce the requireddegree of cross-linking in the elastomerphase. The choice of vulcanizing agent isvery important as a means of controllingboth the cross-linking reactions and theresulting morphology.

27.4 Plasticized Glassy Polymer

These are thermoplastic elastomers, typi-fied by plasticized PVC, derived from theconcept that the addition of sufficientamounts of plasticizer can reduce theglass transition temperature (Tg) to valueswell below room temperature. In order toachieve strain-hardening characteristics oftypical elastomers, the glassy polymermust contain a certain degree of crystal-linity, so that the swollen crystals can act asreinforcing domains. For the case of PVC,these characteristics are often enhancedby incorporating into the formulation an-other polymer, usually a specially designednitrile rubber (NBR) or a multi-block poly-urethane or a chlorinated polyethylene.These polymers are intrinsically rubberyin nature and are �compatible� with PVC.At the same time, they have the capacity tointroduce more efficient reinforcing do-mains than is achievable with swollenPVC crystals alone.

28. Thermoset Polymer

A glassy polymer based on cross-linkedmacromolecular organic networks, whichprevents flow occurring when heated tohigh temperatures.

29. Thermosetting Resin

A term used to describe a certain type ofmultifunctional reactive organic compo-nent, usually oligomeric compounds,which can be made to flow and be shapedat temperatures above their �softeningpoint�. Subsequent cross-linking reac-tions produce networks that make up theglassy characteristics of �thermoset�polymers.

308j 29 Thermosetting Resin

30. Thickener

An additive used to increase the viscosity ofa solution through chain extension reac-tions. An example is the use of magnesiumhydroxide to chain-extend an unsaturatedpolyester resin through the formation ofmagnesium carboxylate salts, which in-crease the molecular weight of the originalresin. The term �thickener� is often usedsynonymously with thixotropic agent. Forinstance, various cellulose-derived thick-eners, such as hydroxyethyl cellulose andcarboxymethyl cellulose, are often added towater solutions to increase the viscosity.This takes place by the formation of inter-molecular hydrogen bonds between poly-mermolecules through bridges of aggregat-ed water clusters. Other thickeners includepolyurethane systems obtained by chainextension of hydroxyl-terminated block co-polymers with diisocyanates. These pro-duce hydrophilic groupswithin the polymerchains (e.g. polyethers or polyesters) andhydrophobic groups at the chain ends (e.g.oleyl or stearyl). The resulting structuresdevelop surface activity characteristics sothat they will produce micelles when dis-persed in water in concentrations above acritical value.In contrast to monomeric surfactants, a

polymeric thickener can form more thanone micelle, joined by polyurethane seg-ments. The viscosity increase arises, there-fore, through a reduction in the mobility ofwater molecules due to the association thatthey form with the micelles and the repul-sions from the hydrophobic components.These types of thickeners are widely usedto increase the viscosity of emulsions,where the hydrophobic component formsassociations with the outer layers of poly-mer particles, while the hydrophilic part ofthe molecules becomes swollen with water.This structure can �hold� different polymerparticles together through polymeric chain

bridges. Such associations can be formedalso with other components of a polymerformulation, such as filler or pigment par-ticles, as shown schematically.

Immobilization of particles within an emulsion ordispersion through many micelles formed by thesame thickenermolecule. Source: Bieleman (1996).

31. Thickening

A term used to describe the increase inviscosity of a liquid resin or paste, achievedthrough chain extension reactions or bymeans of additives.

32. Thiouram

A vulcanizing agent for rubber. (SeeVulcanization.)

33. Thixotropic Agent

An additive that increases the viscosity atlow shear rates of a resin as a result of theformation of hydrogen bonds with polargroups within the resin. These interactions,however, break down at higher shear rates,causing the viscosity to decrease. Thixotro-pic agents are mixtures, usually based onhigh-surface-area silica mixed with glycolsor glycerols as a means of enhancing theirdispersion in the resin.

33 Thixotropic Agent j309

34. Thixotropy

A phenomenon related to the increase inviscosity of a fluid or suspension resultingfrom continual shearing.

35. Tie Molecule

(See Crystalline polymer.)

36. Time-Dependent Modulus

A term used within the context of visco-elasticity to describe the decrease in mod-ulus with time, resulting from molecularrelaxations.

37. Time Lag (Diffusion)

(See Diffusion and Induction time.)

38. Time–Temperature Superposition

A principle originating from the theory oflinear viscoelasticity, which describes theequivalence of the effects of increasing theduration of the time under load, at a giventemperature, to that of increasing the tem-perature at constant duration of loads. Thisconcept arises from the verification that thecurves representing the variation of the re-laxationmodulus, or creep compliance,withtime at different temperatures are similar tothose expressed as a function of tempera-ture, measured over a constant duration ofthe applied strain or stress. The rationale forthis principle derives from the realizationthat the time and temperature dependencesof the modulus and compliance functionsare primarily determined by the ratio of theduration of the load (t) to the characteristictime (l), which is a parameter for the mate-rial. This ratio, sometimes referred to as the

Deborah number, corresponds to the t/lconcept in the Maxwell, Kelvin–Voigt andstandard linear solidmodels. Examining themodulus and compliance curves (see dia-gram) at temperatures TR and T1, T2 and T3(where TR <T1 <T2 <T3), it is clear that, bysliding the curves for temperatures T1, T2andT3 along the time axis, they can bemadeto overlap the curve at temperature TR. Indoing so one has, in effect, kept the values ofthe compliance constant and changed thetime tuntil thevalueofl is reachedforwhichthe t/l ratio has become the same as for thecurve at temperature TR. The movement(shift) that has been made along the timeaxis to make the curves overlap is known asthe time–temperature shift factor aT.

Horizontal shifting of modulus–log(time) curves athigh temperatures (T3, T2, T1) towards that ob-tained at room temperature, the reference temper-ature, TR.

A more precise procedure would alsomake a vertical shift to account for the smallchanges that the temperature would haveon the time-independent components ofthe modulus. However, this effect is verysmall and can be neglected. The time–tem-perature superposition principle can beused, therefore, to develop an extrapolationprocedure for the estimation of the modu-lus and compliance values at long times,based on experiments carried out over shortperiods of time at higher temperatures.The argument for the stress relaxationmod-ulus or compliance as a function of timeapplies equally well for plots of the complex

310j 38 Time–Temperature Superposition

modulus, or complex compliance, with thereciprocal of the frequency (or angular ve-locity) at different temperatures. A similarshift factor aT would apply to make thecurves overlap into a master curve.In this case the amount of shifting, that

is, the aT value, required to obtain theoverlap from one temperature to anothercan be calculated from knowledge ofthe activation energy, DH. With the use ofthe Arrhenius equation, one can derive theexpression for aTover a given temperatureinterval, that is,

log aT ¼ ðDH=2:303RÞ½1=T1�1=T2�:The activation energy DH can be obtainedfrom a very rapid test under dynamic load-ing conditions, carried out over a widerange of frequencies and temperatures. Anempirical approach to obtain the values ofaTwas used byWilliams, Landel and Ferry,who derived an expression known as theWLF equation, that is,

log aT ¼ ½�C1ðT�TgÞ�=ðC2 þT�TgÞ;where C1 and C2 are constants for thematerial and loading conditions (i.e. creepor stress relaxation).

39. Titanate

(See Coupling agent.)

40. Titanium Dioxide (Titania, TiO2)

A white pigment in two forms, �rutile� and�anatase�,whicharecrystallographicallysim-ilar (tetragonal structure) but with a ratherdifferent density, respectively 4.2–5.5 and3.9 g/cm3. The particles have a complexstructure, with a predominance of Al2O3,SiO2 and ZnO in the outer layers to blockthe diffusion of Ti ions, which would have astrong catalytic effect on the degradation of

polymers, irrespective of whether it is ther-mally or UV-induced. The average particlesize is in the regionof 0.2–0.3mminorder toachieve the optimum light scattering char-acteristics, which are largely derived fromthe very high refractive index, equal to 2.6.

41. Torque

The product of a shear force and the dis-tance over which the force is applied. Aconcept widely used in rotation and torsionsituations.

42. Torque Rheometer

An apparatus consisting of a small internalmixer, comprising kneading rotors within achamber,whichcontainsaspecificamountofpolymer and other ingredients. The appara-tus records the torquedevelopedby themixerrotorsand the temperatureof themeltduringmixingandcontinual shearingof themelt. Inthis respect, it can be considered as a toolcomplementary to a cure-meter for the char-acterization of rubber mixes, as well as avaluable apparatus for studying the mixingcharacteristics of polymer blends and partic-ulate composites. Although the term�rheometer� is amisnomer, insofar as it doesnot involve measurements of flow rates orshear rates, the variation of torque and tem-peraturewith timeprovide valuable informa-tionaboutthefusion(melting)characteristicsof a mixture as well as other events that maytake place duringmixing, such as cross-link-ing and degradation reactions.

43. Torsion Pendulum

An apparatus used to characterize the dy-namic mechanical properties of polymersby subjecting a specimen to free dampingtorsional oscillations.

43 Torsion Pendulum j311

A schematic illustration of the components of adamping torsion oscillation apparatus: S is thesample; P is the inertia disc; TC is the temperaturecontroller; other parts are electronic devices.Source: Hoffmann et al. (1977).

From the decay of the amplitude (A) ofthe oscillations, it is possible to obtain thelogarithmic decrement (D), from which theloss factor (tan d) can be calculated, that is,A¼A0 exp(�pt) and p¼ ic� a (wherei ¼ ffiffiffiffiffiffiffi�1

p, c is the angular frequency of the

oscillation and a is a constant). Thus

D ¼ ln½An=ðAn þ 1Þ� ¼ ln½ðAn þ 1Þ=ðAn þ 2Þ¼ p tan d ¼ pG00=G0:

Damping of oscillations of the pendulum disc dueto the viscoelastic behaviour of the polymer sample.

The elastic (G0) and loss (G00) componentsof the complex shear modulus, on the otherhand, are calculated from the applied mo-ment of inertia (I) and the angular frequen-cy of the torsion oscillations (c):

G0 ¼ Icu

l2ð1�4p2Þ andG

00 ¼ ilc2

pu;

where l¼ 2pa/c and u is a geometric(shape) factor for the specimen.

44. Toughness

The resistance of a material to fractureexpressed in energy terms. (See Fracturemechanics and Impact strength.)

45. Tow

A term (jargon)widely used in the context ofcarbon fibre composites to describe a col-lection of fibres for filament winding or forthe production of woven fabrics.

46. Tracking

A type of failure that occurs in dielectrics,whichoccursvia theformationofconductive(carbonaceous) surface channels, usuallybrought about by the presence of surfacecontaminants, such as salts. A �dry band� isformed on the surface of high-voltage insu-lators when exposed to surface contamina-tion, usually salt solutions, which representthe type of atmospheric conditions prevail-ing in areas near the sea. The local heatgenerated by the high voltage causes theevaporation of the water over a small area,thereby producing a drastic reduction of thesurface conduction across a narrow non-conductive zone, known as a �dry band�.These conditions result in the formation ofarcs across the dry bands, which bring aboutrapid thermal degradation reactions, withthe formation of carbonaceous conductivesurface tracks.The latter is obviously related to the

thermal decomposition mechanism of thepolymer. Aromatic units within a polymerchain are particularly prone to form carbo-naceous tracks. Polymers such as polyte-trafluoroethylene (PTFE), poly(methylene

312j 46 Tracking

oxide) (PMO) and poly(methyl methacry-late) (PMMA), on the other hand, depoly-merize completely under the influence ofthe arc formed across the dry bands. Whileinsulators made of PTFE would simplycreate eroded paths and holes as a resultof the depolymerization, those made ofPMO and PMMA would catch fire becauseof the high flammability of the products,consisting predominantly of monomers.The resistance to tracking of polymers is

usually assessed by tests measuring thecomparative tracking index (CTI). The CTIvalue corresponds to the voltage required tocause failure by surface tracking with theapplication of 50 drops of a 0.1% NH4Clsolution onto the surface of a specimensubjected to a voltage gradient between twochisel-shaped electrodes. A test that is con-sidered to produce results that approachmore closely the type of failures experiencedin service is the tracking erosion test(TERT). The test is carried out on an in-clined specimen where a 1% NH4Cl elec-trolyte solution is run in small drips over thelower surface to ensure that it forms only athin surface layer.

Inclined-plane method for measuring the trackingand electrical erosion resistance of polymers.Source: Mascia (1989).

The voltage is increased in steps untilfailure takes place due to the formation ofsurface tracks that leak the current to earth.Alternatively, the extent of erosion produced

through a series of localized surface failuresis monitored at different time intervals bymeasuring the weight loss. (See Antitrack-ing additive.)

47. Transesterification

A reaction that takes place between estersfrom two different compounds, causing anexchange of carboxylate substituents. Thiscan happen duringmelt mixing and proces-sing of polymer blends, where the transes-terification mechanism may be exploited toenhance the compatibility of the compo-nents through the deliberate production of�compatibilizing� block copolymers.

48. Transfer Moulding

Aprocess used formoulding thermosettingmoulding powders and bulk mouldingcompounds (BMC), as well as vulcanizableelastomers. The latter uses a different sys-tem for removing the moulded part. Theprinciple consists in feeding the rightamount of pre-heated pellets or powder intothe �pot� of a hot mould, from which it isquickly �transferred� into the cavities of themould via the sprue, runners and gates. Atypical set-up is shown in the diagram.

Schematic diagram of a transfer mould with anintegral pot contained in the plate between theplunger carrying plate and the cavity plate. Source:Unidentified original source.

One of the main advantages of transfermoulding over compression moulding is

48 Transfer Moulding j313

the much lower cycle times achievedthrough shear heating of the melt duringthe flow through the various channels. Theprocess is still slow and less versatile thanscrew injection moulding, which has grad-ually replaced the traditional transfermoulding process.

49. Transition

Thechange fromonestate toanother,usuallybrought about by a change in temperature.There are twomajor transitions encounteredin polymers, respectively, the glass–rubbertransition (secondary transition) and themelting transition (primary transition). (SeeGlass transition temperature and Meltingpoint.)

50. Transmissibility

A term used within the context of dampingof oscillations in situations such asmachinemounts used to isolate a structure fromvibrations. The effectiveness of the isolationis expressed in terms of the transmissibility,T, which is the ratio of the transmitted forceto the applied force. This is related to thedynamic mechanical property of the rubbermount by the expression

T2 ¼ 1þ ½tan dðvÞ�2½1�ðv=v0Þ2G0ðv0Þ=G0ðvÞ�2 þ ½tan dðvÞ�2 ;

where v is the actual frequency of thevibrating system, v0 is the resonance fre-quency,G0(v0) is the storage shearmodulusat the resonance frequency, and G0(v) andtan d(v) are the shear modulus and losstangent of the rubber at frequency v. Fromthis it can be deduced that machinemountshave to be designed to have a resonancefrequency considerably lower than the fre-quency of the vibrating member fromwhich isolation is required.

51. Transmission Electron Microscopy(TEM)

An electron microscopy technique using ahigh-energy electron beam to produce sec-ondary electrons and/or backscattered elec-trons, as well as X-rays, when focused on asample. (See Scanning electron microsco-py.) Using samples less than a few micro-metres thick, the scattered electrons pro-duced are partially absorbed and partiallytransmitted through the object, forming animage of the physical heterogeneity of thesample down to about 1 nm, depending onthe nature of the sample. In the case ofpolymers, the samples have to be extremelythin because of their low �mass thickness�resulting from their low density (i.e. massthickness¼ density� thickness of sample).The technique is more applicable, there-fore, for polymers containing inorganic het-erogeneities, as in nanocomposites and or-ganic–inorganic hybrids.

52. Transparency

The ability of a material to transmit visiblelight. (see Optical properties.)

53. Tresca Criterion

(See Yield criteria.)

54. Trouton Viscosity

Corresponds to the elongational, or exten-sional, viscosity. For incompressible New-tonian fluids, the Trouton viscosity is threetimes the value of the shear viscosity.

55. True Shear Rate

The value of the shear rate for the flow ofpolymer melts, which takes into account

314j 55 True Shear Rate

their non-Newtonian behaviour. Assumingthat the behaviour of the melt follows apower law, one can write t ¼ K _gn, wheren is the power-law index, which is a param-eter that describes the deviation from New-tonian behaviour. For Newtonian liquidsn¼ 1, while for a polymer melt the valueof n is usually in the range 0.3–0.6. (SeeApparent shear rate and Non-Newtonianbehaviour.) The true shear rate ( _gT) can becalculated from the value obtained assum-ing Newtonian behaviour, known as theapparent shear rate ( _ga)

. circular channel _gT ¼ ½ð3nþ 1Þ=4n� _ga

. rectangular channel _gT ¼ ½ð2nþ1Þ=3n� _ga

56. True Viscosity

The value of the viscosity of polymer melts,at a given shear rate, which takes into ac-count their non-Newtonian behaviour, thatis, hT ¼ t= _gT, where t is the shear stressand _gT is the value of the �true� shear rate.(See True shear rate and Non-Newtonianbehaviour.)

57. Tubular Film

(See Blown film.)

58. Twin-Screw Extruder

Extruder with two parallel screws mountedin a barrel with connected double bores.Twin-screw extruders are classified accord-ing to the degree by which the screws inter-mesh and the relative direction of theirrotation. Accordingly, they are known as

(a) intermeshing counter-rotating, (b) inter-meshing co-rotating and (c) non-intermesh-ing counter-rotating types, respectively, asillustrated.

Illustration of rotational directions and flight inter-meshing in twin-screw extrusion. Source: Baird andCollias (1998).

The sweeping of the melt through the C-shaped cavities of an intermeshing counter-rotating type twin-screw extruder is illus-trated.

Melt sweeping action of the screw flights of anintermeshing counter-rotating twin-screw extruder.Source: Baird and Collias (1998).

While in single-screw extruders the trans-port of both solid feed and melt takes placeby the drag action of the screw, the convey-ing mechanism in intermeshing twin-screw extruders is mostly by positive dis-placement. The maximum flow rate,Q, canbe estimated, therefore, from the equationQ¼ 2pNV, where p is the number of parallelflights,N is the screw speed (revolutions perunit time) and V is the volume of the closedC-shaped channel carrying the material.The actual geometry of the C-shaped cham-ber for each of the two intermeshing screwsis shown.

58 Twin-Screw Extruder j315

Geometry of a single C-shaped chamber used tocalculate the flow rate of an intermeshing counter-rotating twin-screw extruder.

The diagram shows that there are severalleakageflows taking place through the inter-meshes of the screws, which take place inthe opposite direction to the displacementflow. Thus the flow rate equation for theintermeshing counter-rotating twin-screwextruder can be written as

Q ¼ 2p NV�2½Qf þQt þ pðQc þQsÞ�:

Leakage flows in intermeshing counter-rotatingtwin-screw extruder.

59. Two-Roll Mill

(See Mixer.)

60. Tyre Construction

The fabrication of the pneumatic tyre is oneof the most complex operations in the man-ufacture of polymer products. The typicalstructural components are shown in thediagram.

Typical structural components of a tyre. Source:Novac (1978).

The diagram shows that a tyre has thefollowing basic components:

a) Tread representing the wear-resistantcomponent that provides traction, silentrunningandlowheatbuild-up.Thecom-positionof the treadcomponent isdiffer-ent from the rest of the tyre and usuallyconsists of a blend of oil-extended SBRandpolybutadieneelastomerandnaturalrubber, compounded with carbon black,curatives, oils and other auxiliary addi-tives. The geometrical features of thetread consist of circumferential ribs andgrooves, speciallydesigned foroptimumtraction and direction control withmini-mum heat build-up.

b) Sidewalls corresponding to the struc-tural components between the treadand the beads, provide support for theweight of the vehicle. The rubber iscompounded to provide a high fatigueresistance (flex life) and weatherresistance.

c) Shoulder comprising the upper por-tion of the sidewall below the edge ofthe tread. It is the component that

316j 60 Tyre Construction

controls the cornering characteristicsof the tyre.

d) Bead consisting of high-strength steelwire formed into hoops functioning asanchors for the plies and holding theassembly onto the rim of the wheel.The cross-section of the bead conformsto the flange of the wheel to prevent thetyre from rocking or slipping on therim.

e) Plies consisting of layers of rubber-im-pregnated fabric cord, which extendsfrom bead to bead and provides me-chanical reinforcement for the tyre.

f) Belts or breakers consisting of narrowlayers of tyre cord under the tread of

the crown of the tyre. These have thefunction of resisting deformations inthe footprint (i.e. the contact with theroad).

g) Liner consisting of a thin layer ofrubber inside the tyre to provide a sealagainst the escape of compressed air.This is very important in tubeless tyreconstruction.

h) Chafer consisting of narrow strips ofmaterial around the outside of thebead to protect the cord against wearand cutting by the rim, and to distrib-ute the flex above the rim, as well aspreventing moisture and dirt gettinginto the tyre.

60 Tyre Construction j317

U

1. Ubbelohde Viscometer

Used to measure the solution viscosity of apolymer for measuring its molecularweight. (See Molecular weight.)

2. Ultrasonic Welding

A welding technique that uses ultrasonicpulsations. (See Welding.)

3. Ultraviolet Light (UV Light)

(See Electromagnetic radiation, Radiation,Solar radiation, UV degradation, UV spec-troscopy and UV stabilizer.)

4. Uniaxial Orientation

The alignment of the constituents of thestructure of a material in one or two direc-tions, usually the molecular chains of apolymer or the reinforcing fibres of a com-posite. A typical example is the molecularorientation of polymers in fibres or fibrillat-ed tapes. (See Orientation function.)

5. Unit Cell

A concept used in crystallography to de-scribe a regularly repeating element fromwhich a crystal is formed through paralleldisplacements in three dimensions. Therelative positions of atoms within a unit cellare constant from cell to cell.

6. Unplasticized PVC

Refers to PVC formulations that do notcontain a plasticizer and are often referredto as rigid PVC or PVC-U.

7. Unsaturated Polyester Resin (UP Resin)

A resin obtained from polycondensationreactions between glycols and acid anhy-dride monomers, which contains doublebonds at regular intervals along the back-bone chains. The resin is usually dissolvedin a liquid unsaturated monomer that actsas a solvent–hardener for the curing reac-tions by a free-radical mechanism. Theseresins are used primarily as matrices forglass fibre composites and for coatings. Inthe latter case they are often referred to asalkyds. Some use of UP resins is also madefor castings and as binders for artificialstone from inorganic aggregates. The mostwidely used UP resins are produced asalternating copolyesters of propylene glycolphthalate–fumarate, as depicted in thechemical formula.

Alternating copolyester structure of UP resins.

The solvent–hardener is usually styrene,at around 40wt%. Other monomers aresometimes used as hardeners. A schematicdiagram that illustrates the structure of thesolvated resin before curing and that ofcross-linked products is shown.


318j

Schematic structure of a UP resin solvated withstyrene monomer (top) and the resulting networkafter curing (bottom). Source: Ehrenstein (2001).

Variants of standard UP resins are ob-tained by replacing, partially or totally, theortho-phthalate units in the chain with othersaturated diesters. The following are typicalreplacements for o-phthalic anhydride:

a) adipic or succinic anhydride to increasethe flexibility;

b) isophthalic acid to reducewater absorp-tion and increase the resistance tohydrolysis; and

c) tetrabromophthalic anhydride or hexa-chloro-endo-methylene tetrahydrophtha-lic anhydride (known as chlorendicanhydride) to produce fire retardantresins.

Alternatives to styrene as the solvent–hard-ener are: (i) methyl methacrylate for betterweathering resistance; and (ii) divinylben-zene or diallyl phthalate to increase the Tgthrough an increase in the cross-linkingdensity. Curing reactions are induced byperoxide initiators with varying decomposi-tion temperature, depending on the appli-cation. Room-temperature cure resins forcomposites usually use methyl ethyl ketone(MEK) peroxide activated with a cobalt or-ganic salt or complex. Higher-temperatureperoxides, such as benzoyl peroxide, areused inmoulding compounds, such as bulk

moulding compound (BMC) and sheetmoulding compound (SMC), as these areprocessed under pressure at higher tem-peratures. Sometimes an inhibitor (alky-lated phenols, cresols or quinones) is usedto increase the storage stability of the resin.Magnesium oxide is also used in thesecompounds to increase the viscosity of theresin at ambient temperature tomake themeasier to handle.

8. Upper Critical Solution Temperature

(See Miscibility.)

9. Upper Limit

(See Law of mixtures.)

10. Urea Formaldehyde Resin (UF Resin)

(See Amino resin.)

11. Urethane Polymer and Resin

These are systems that contain urethanegroups in the polymer chains or networks.These systems are often abbreviated to PU(for polyurethane). Urethane groups areformed from the reaction of an isocyanateand a hydroxyl group, that is,

A linear polymer is obtained, therefore, ifa difunctional isocyanate and a glycol arereacted together. A cross-linked polymer isformed if one or both reactants aremultifunctional.

11 Urethane Polymer and Resin j319

11.1 Polyisocyanate

The majority of isocyanates used in indus-trial products are aromatic. Themorewide-ly used systems are toluene diisocyanate(TDI), respectively, 2,4-TDI and 2,6-TDI,and diphenylmethane-4,40-diisocyanate(4,40-MDI). The structure of these isocya-nates is shown.

Apart from the linear structure, the4,40-MDI has a lower volatility than bothTDIs, which is advantageous in manyapplications owing to the toxicity of iso-cyanates. Even lower volatility can beachieved with the polymeric diisocyanatepoly(diphenylmethane-4,40-diisocyanate)(PMDI), represented by the followingchemical structure:

Although in the majority of cases cross-links are produced using multifunctionalhydroxyl compounds, known as polyols,higher-functionality polyisocyanates aresometimes used for the same purpose. Atypical multifunctional diisocyanate is theadduct of TDI to trimethylolpropane, hav-ing the following structure:

Aliphatic polyisocyanates are primarilyused for light-fast products, such as coat-ings or fibres, owing the low UV stability ofaromatic isocyanates, which give rise todegradation and discolorations through theformation of quinoids and conjugated dou-ble bonds, as shown.

The most widely used aliphatic diisocya-nate is hexamethylene diisocyanate (1,6-HDI), OCN�(CH2)6�NCO.In general, aliphatic isocyanates are less

reactive than aromatic isocyanates. For thisreason, their reactions are usually catalysedwith either organo-tin compounds, such asdibutyl tin dilaurate (DBTL), and tertiaryamines, such as 1,4-diazabicyclo[2.2.2]octane (DABCO):

The ability of isocyanates to reactwith anyhydrogen atom that can be ionically ab-stracted from a chemical compound pro-vides the opportunity to synthesize a wide

320j 11 Urethane Polymer and Resin

range of products. There are also side reac-tions that can occur, such as the reactionwith water:

This reaction is utilized in the productionof flexible foams, owing to the formation ofCO2, which acts as an �internal� chemicalblowing agent and assists in the formationof cells deriving from an external physicalblowing agent.At the same time, the resulting amine

reacts very rapidly with other isocyanategroups to produce urea groups, that is,

The H atoms in the urea groups can alsoreact with isocyanates to produce biuretgroups. Other reactions of isocyanatesinclude those leading to the formation ofallophonate groups through reactions withthe hydrogen atom in the urethane groupand those with itself leading to the forma-tion of cyclic dimers and trimers or tocarbodiimides with the elimination of CO2.The trimerization reaction is often exploitedfor the production of cyanate ester resinsused in formulations for high-temperatureadhesives, that is,

Isocyanates can also react with phenols,«-caprolactam, oximes and secondaryamines. The reversible nature of these

reactions is exploited for the production ofthe so-called �blocked isocyanate� prepoly-mers to protect the isocyanate groupsagainst reactions with water during storage.When they are subsequently heated, theisocyanate groups are formed again, so thatthey can react with other components.Blocked isocyanates are particularly usefulfor the production of one-pack systems forcoatings or adhesives.

11.2 Polyol

The most widely polyols are aliphatic poly-ether and polyester types. Polyethers aremostly obtained by the addition of cyclicethers, such as ethylene oxide or propyleneoxide, to bifunctional starter molecules ei-ther alone or mixed with multifunctionalstartermolecules to produce either linear orbranched systems. Typical starters are eth-ylene glycol, 1,2-propanediol, trimethylol-propane, glycerol and sugar. Polyester-typepolyols are produced from combinations of

Trimerization of diisocynates.

11 Urethane Polymer and Resin j321

various diacids and glycols with differentamounts of glycerol, neopentyl glycol ortrimethylolpropane to produce systemswith different degrees of functionality (usu-ally 2–4) and molecular weight (normallywithin the range 500–5000). For coatingapplications, hydroxyl-functionalized poly-acrylates are widely used in combinationwith aliphatic polyisocyanates. Typical acryl-ic polyols are produced from hydroxyethylacrylate and methacrylate and also fromhydroxypropyl methacrylate.

11.3 Polyurethane Adhesive and Coating

Both systems are available as one- or two-component systems. The one-componentsystems require blocking of the isocyanategroups to overcome the possibility of re-actions taking place during storage. Thedisadvantage of these systems lies in theregeneration of the blocking agent, suchas phenol or caprolactam, when the pro-ducts are cured. The released blockingagents remain dispersed in the system asdiluents.Some systems make use of moisture

infusion for curing at ambient tempera-tures. These are based on isocyanate-termi-nated prepolymer, which will react readilywith water to produce CO2 and a diamine(see the reaction schemes above). Water-borne systems, on the other hand, are spe-cifically designed to allow them to be dis-persed in water without undergoing curing.(See Water-borne coating.) The prepolymermay contain ionic groups in the structure toallow the use of ionic surfactants for thestorage stabilization of the dispersion, oralternatively the polyol component can bespecially designed to make it compatiblewith non-ionic surfactants.

11.4 Polyurethane Elastomer

The original polyurethane (PU) elastomerswere designed to match the technology of

conventional rubbers so that they could bevulcanized by sulfur curatives or peroxides.These were referred to as �millable PUelastomer� and were produced as systemswith superior solvent resistance and higherthermal stability than NBR or chloroprenes.Subsequently liquid thermosetting cast sys-tems with high tensile strength and hightear strength were introduced, which werethen followed by thermoplastic polyure-thane elastomers (TPUs), processed by con-ventional extrusion and injection mouldingtechniques. More recently, high-pressureimpingement mixing machines havebecome available for the production of castthermoset elastomers by reaction injectionmoulding (RIM).The chemical structures of themainunits

of cured PU elastomers are quite similar,differing in details regarding either the spe-cificgroupsforcross-linkingor thecontrolofthe rate of curing to suit the particular pro-cess. Millable PU elastomers are essentiallyABA-typeblockcopolymersproducedfromapolyol, containing a few double bonds forfree-radical cross-linking reactions, and anaromatic isocyanate, such as TDI or MDI.TPUs with similar properties are producedfrom the reaction of saturated linear polyols,polyetherorpolyester type (soft blocks),withan isocyanate-terminated prepolymer (hardblocks), obtained from the reaction of MDIwithaglycolextender,suchas1,4-butanediolor 1,6-hexanediol, ethylene glycol or diethy-lene glycol. TPUmade frompolyethers havea high hydrolytic stability, while those con-taining polyester blocks exhibit a higherresistance to mineral oils.TheRIMproducts are producedprimarily

fromaromatic diamine extenders, instead ofglycol extenders, in order to achieve fasterreaction rates, so that the cycle time forcuring can be reduced. These are oftenreferred to as polyurethane–urea RIM sys-tems. In order to increase further the rates ofreactions for RIM systems and to obtain aneven higher thermal stability, the OH

322j 11 Urethane Polymer and Resin

terminal groups in the polyol can bereplaced with amines, and are referred toas polyurea RIM systems.

11.5 Polyurethane Fibre

(See Spandex fibre.)

11.6 Polyurethane Foam

PU foams are divided into flexible and rigidfoams.Flexible foams are produced using TDI

(or MDI/PMDI mixtures), trifunctionalpolyether polyols (MW range 3000–6500)and water. The blowing action takes placethrough the formation of CO2 gas derivedfrom the reaction of isocyanates with water,producing a coarse open-cell foam struc-ture. A finer cell structure is obtained withthe addition of physical blowing agents,such as methylene chloride and fluorocar-bons, although these are nowadays replacedwith less toxic systems.Rigid foams are produced from MDI or

PMDI and either polyether or polyesterpolyols, using traditional chlorofluorocar-bon physical blowing agents, which areincreasingly being replaced by non-fluori-nated systems, such as dimethyl ether.

12. UV Degradation

This term denotes oxidative decompositionof the molecular structure of a polymercaused by the absorption of UV light. Themost harmful radiation in the solar spec-trum is that within the wavelength range290–400 nm, where there is sufficient ener-gy to breakmost chemical bonds of aliphaticpolymer chains. The degradation reactionstake place in several steps.

a) Initiationstep: productionof freeradicalsas a result of the absorption of UV light,that is,

PHðpolymer chainÞ þ UV!P. þH.

b) Propagation step: reaction of radicalswith other polymer chains, that is,

P. þO2 !POO.

and

POO. þPH!POOHþP.

c) Termination step: deactivation of freeradicals, that is,

P. þP. !P

P. þPOO. !POOP

and

POO. þPOO. !POOPþO2

These degradation reactions can beexemplified by reference to the UV degra-dation of polystyrene, as shown. (See Nor-rish I and Norrish II and Environmentalageing.)

Formation of radicals resulting from the absorptionof UV light by polystyrene.

Reaction of free radicals with atmospheric oxygen.

Formation of hydroperoxide groups by the reac-tion of peroxy radicals with other polymer chains(PH), propagating the formation of free radicals.

12 UV Degradation j323

Decomposition of hydroperoxide groups as a firststep in the formation of carbonyl groups andmolecular scission.

13. UV Spectroscopy

A spectroscopic analysis using radiation inthe UV region, 200–600 nm, and some-times up to the visible range. In theseregions there is a strong radiation absorp-tion by double bonds (e.g. the C¼Ogroup at280 nm and the conjugated double bonds ofaromatic rings and in polyacetylene seg-ments of aliphatic chains, often producedby degradation reactions in vinyl polymers).

14. UV Stabilizer

An additive used to slow down the degrada-tion of polymers induced by UV light. UVstabilizersareclassifiedintotwomaingroups.

14.1 UV Absorber or Screening Agent

These can absorb UV light more easily thanpolymers, thereby reducing the amount ofenergy available to cause the decompositionof polymer chains. Absorption of the dam-agingUV light takes theUVabsorber into itsexcited state (higher energy level) and theabsorbed energy is then released as lessharmful radiationwithin the infrared region.The most effective UV absorbers are carbonblack followed by metal oxide pigments.Pigments act also as screeners ofUV light

by internal scattering at the interface withthe polymer. For this mechanism to beeffective, the diameter of the particles mustbe smaller than about 1mm. Some pig-ments, such as titanium oxide, are coatedto prevent the diffusion of metal ions intothe polymer as a means of alleviating their

catalytic effect on the propagation reactionsfor the degradation.In general, UV stabilizers are used in

combination with antioxidants such as phe-nolic and hindered amine light stabilizer(HALS) types to obtain a synergistic effect.The structure of a typical HALS is shownbelow:

The more widely used organic UV stabi-lizers are derivatives of 2-hydroxybenzophe-none and hydroxybenzotriazole. The chem-ical structures of these compounds areshown.Additional groups, particularly chlo-rine, could be attached to the other benzenering as a means of enhancing the UVabsorption efficiency of the compound.

(a) Hydroxybenzophenone and (b) hydroxyphenyl-benzotriazole. Note that R and R0 are long-chainaliphatic segments to make them more easilydispersed in the predominantly aliphatic polymers.

Other compounds with strong UV ab-sorption characteristics are derivatives ofhydroxyphenyl-S-hydrazine. The commonfeature of these additives is their ability toform internal hydrogen bonds and the for-mation of a conjugated structure as a light-absorbing mechanism, as shown.

Mechanism for UV absorption and dissipation ofenergy as IR radiation (reverse transformation).

324j 14 UV Stabilizer

14.2 Excited-State Quencher

These additives exert a UV stabilizationfunction by deactivating the photoexcitedgroups of a polymer chain (chromo-phores) through the dissipation of theabsorbed energy as harmless infraredradiation. The more widely known excit-ed-state quenchers used for UV stabiliza-

tion are nickel complexes such as thoseshown.

Typical excited-state quencher.

14 UV Stabilizer j325

V

1. Vacuum Forming

A shaping process involving the applicationof vacuum todrawaheated sheet against thecontours of a cavity or male part of a mould.(See Thermoforming.)

2. Van der Waals Force

A force acting between molecules throughinteractions between the dipoles within themolecular structure. These are weakerforces than those arising through hydrogenbonds or by ionic attractions.

3. Vector

An excitation or response that can take placein three directions without a specified posi-tion or location.A typical example of a vectoris a force, which can act in any one or allthree directions but does not have a startingposition. An applied force, however, can bedecomposed into three spatial componentsacting at right angles to each other.

4. Velocity Gradient

The change of velocity with respect to posi-tion within the channel in which the flowtakes place. In shear flow the velocity gradi-ent occurs perpendicular to the direction offlow, while for elongational flow the velocitygradient takes place along the flow direc-tion. (See Viscosity.)

5. Velocity Profile

The profile that the velocity vector of a liquidassumes within the flow channels. (SeeNon-Newtonian behaviour.)

6. Vent

Small bore holes in moulds to allow theescape of air when themelt enters the cavity.

7. Vicat Softening Point

An empirical parameter used as a measureof the resistance of a polymer to the pene-tration of sharp hard objects at high tem-peratures. It is measured bymonitoring thepenetration of a loaded needle into a disc-shaped specimen, supported on a rigid plateand fully immersed into an inert liquid. Thetemperature is increased at a constant rateby heating the liquid, and the penetration ofthe needle is measured and then plottedagainst temperature. The Vicat softeningpoint is defined as the temperature at whicha specified penetration of the needle (usu-ally 1 mm) is recorded. This value is oftenvery close to the glass transition tempera-ture of the polymer (Tg). (See Heat distor-tion temperature.)

8. Vickers Hardness

(See Hardness.)

9. Vinyl Ester

Originally used to describe products ob-tained from the reaction of an epoxy resinwith acrylic acid or methacrylic acid as ameans of converting the epoxy groups intounsaturated (vinyl) groups:


326j

The introduction of vinyl groups allowsthe resin to be cross-linked by a free-radicalmechanism using either peroxide initiatorsor radiation sources, such as UV light orelectron beaming. Often a vinyl ester resinis used as a mixture with another multi-functional monomer in order to increasethe cross-linking density and/or to enhancethe rate of cure. The term is nowadays usedin a more general way to describe a widerange of oligomers containing unsaturatedend groups, notable among which are thepolyurethane types. Other vinyl esters fromcycloaliphatic epoxy resins are used to ob-tain products that can be curedwith cationicphotoinitiators.

10. Vinyl Polymer

These are polymers produced from vinylmonomers, covering a very wide range ofproducts. Thepolymers are producedmostlyby free-radical polymerization and are pre-dominantly atactic. The polarity, size andflexibility of the vinyl substituent group havea dominant effect on the capability of thepolymer chains to form a crystal lattice, andon the glass transition temperature for thecaseof amorphouspolymers.Themost com-mon types of vinyl monomers are brieflydiscussed below.

10.1 Poly(Vinyl Acetate) (PVAc)

An amorphous polymer with a Tg in theregionof 28 �C, represented by the chemicalformula:

PVAc is usually available in the form ofwater emulsions for use in formulations foradhesives and coatings, particularly forporous materials, such as wood, paper andfabrics. PVAc is also the startingmaterial forthe production of poly(vinyl alcohol).

10.2 Poly(Vinyl Alcohol) (PVA)

A water-soluble polymer with the followingchemical structure:

PVA is produced by the hydrolysis of poly(vinyl acetate) (PVAc), –(CH2CHCOOCH3)n–.The preparation of the polymer by thisindirect route is due to the instability ofvinyl alcohol, which converts readily toacetaldehyde. PVA has biocompatibilityand biodegradation characteristics. Com-mercial products are available with varyingdegrees of hydrolysis, with the vinyl alco-hol component dominating over the resid-ual vinyl acetate groups, that is,

ðCH2CHCOOCH3ÞnþxH2O

!ðCH2CHCOOCH3Þn�xðCH2CHOHÞxþxHOCOCH3

where x� n�x.Biodegradable grades are often available

in the form of blends with starch and, possi-bly, a plasticizer. The fully hydrolysed gradesof PVA are crystalline polymers with a Tm inthe region of 240 �C and a Tg around 90 �C.

10.3 Poly(Vinyl Butyral) and Poly(VinylFormal)

These two polymers are produced by react-ing poly(vinyl alcohol) with the respective

10 Vinyl Polymer j327

aldehyde, and they are represented by thechemical formulae:

The main application of poly(vinyl butyr-al) is for the production of laminated safetyglass for automotivewindshields. Poly(vinylformal), on the other hand, is used primari-ly in lacquers.

10.4 Polyvinylcarbazole

A glassy polymer with a Tg greater than200 �C, represented by the chemical formu-la:

It is mainly used for paper impregnationfor application in capacitors.

10.5 Poly(Vinyl Alkyl Ether)

Various crystalline polymers with an atac-tic molecular structure, represented by theformula:

The Tm and Tg values are respectively 145and �13 �C for poly(vinyl methyl ether)(PVME) and 86 and �19 �C for poly(vinylethyl ether) (PVEE).

10.6 Poly(Vinyl Chloride) (PVC)

A glassy polymer produced by free-radicalpolymerization in emulsions (e.g. gradesfor pastes) and suspensions (e.g. grades fordry blends). (See PVC.) The chemical struc-ture is represented by the formula:

The Cl atom take up random spatialpositions (atactic configuration) except forsome sequences in which chlorine takes upa syndiotactic configuration. Therefore,although the polymer is predominantlyamorphous and glassy with a Tg in theregion of 80 �C, there are a small amountof crystalline domains (around 5–10%) witha broad melting transition occurring attemperatures higher than the range nor-mally used for processing. The quoted Tmvalue is 212 �C. The crystals have a densitysimilar to the surrounding amorphous re-gions (around 1.4 g/cm3), as the moleculesare not tightly packed owing to the syndio-tactic configuration of the segments respon-sible for the formation of crystals. This doesnot cause any internal light scattering andtherefore the products are intrinsicallytransparent.Commercially the molecular weight of

poly(vinyl chloride) is specified in terms ofthe K value (named after Fikentscher)

328j 10 Vinyl Polymer

obtained from measurements of the solu-tion viscosity. Typical values range fromabout 40 to 85, corresponding to number-average MW¼ 40 000–90 000 and weight-average MW¼ 70 000–500 000. A �viscositynumber� is also used as an indication of themolecular weight of PVC.

10.7 Poly(Vinyl Fluoride) (PVF)

A crystalline polymer with melting point inthe region of 200 �C and a Tg around 20 �C.PVF is represented by the formula:

Although essentially an atactic polymer,the small size of the fluorine atom makes itpossible for the polymer chains topack into acrystal lattice despite the atactic configura-tion. PVF is available mainly in the form offilms, requiring a solution casting techniqueowing to excessive thermal decomposition athigh temperature, resulting in the loss ofHF(a very toxic gas). PVF is transparent to bothvisible and UV light and has a high resis-tance to outdoor weathering conditions.

10.8 Polyvinylpyridine

There are two types, respectively poly(4-vinylpyridine) and poly(2-vinylpyridine),depending on the position of the nitrogenof the pyridine ring relative to the vinylgroup of the monomer. Both polymers areamorphous, owing to the atactic structure,with different Tg values, respectively 153 �Cfor poly(4-vinylpyridine) and 102 �C poly(2-vinylpyridine). The formula for the latter isshown below:

A major attraction of these polymers istheir ability to form quaternary ammoniumsalts with carboxylic acid compounds, there-by providing a mechanism for producingwater-soluble products, which become in-fusible under dry conditions. This has cre-ated a wide interest in the production ofmicrospheres for encapsulation, owing tothe possibility of polymerizing the water-soluble monomers by gamma radiation,also in combination with water-solubleacrylic monomers.

10.9 Polyvinylpyrrolidone

A rigid brittle polymer soluble inwater, witha Tg in the region of 160 �C, represented bythe chemical formula:

It is used primarily as a binder for medi-cal and cosmetic products.

11. Virial Coefficient

A coefficient that is sometimes added to anequation to account for the deviation fromideal behaviour. An example is the variationof the osmotic pressure (p) of a solutionwith temperature, that is,

p=c ¼ RT ½A1 þA2cþA3c2 þ . . .�;

where c is theconcentrationofsolute,R is theuniversal gas constant, T is absolute temper-ature,andA1,A2,A3 andhigher termsare thevirial coefficients.ThevaluesofA1,A2 andA3

are equal to zero for an ideal solution.

12. Viscoelastic Behaviour

A termused to describe the time-dependentmechanical properties of polymers. Where-

12 Viscoelastic Behaviour j329

as for elasticmaterials the Young�smodulusand shearmodulus are constant, the relatedvalues for polymers vary with the durationof the applied stress. The terms �viscoelasticbehaviour� and �viscoelasticity� derive fromcombining the two words �viscous� and�elastic�, which are related to the modelsnormally used to describe the time-depen-dent behaviour of polymers. These modelsuse a dashpot for the viscous deformationsand a spring for the elastic response (see thesubsection on modelling that follows).The viscoelastic behaviour of polymers

arises from the molecular structure (whichallows the applied forces to be transmittedinternally through rotations of segments ofthe polymer chains) and to the predomi-nance of weak Van der Waals intermolecu-lar forces. The rotation of polymer chainsand their uncoiling in the direction of theacting forces take place through a sequenceof events that require time to reach a newequilibrium position. This is a characteris-tic time that depends on the intrinsic natureof the polymer molecules, such as rigidity(i.e. energy required to rotate the chains)and the strength of the intermolecularforces. Restrictingmolecular rotations, withthe introduction of cross-links or by theincorporation of bulky groups into the poly-mer chains, is a method used in polymersynthesis to attenuate the viscoelastic char-acteristics of polymers. The various move-ments of individual polymer chains in re-sponse to external forces are illustrated inthe diagram.

Schematic illustration of the movements of poly-mer chains in the direction of the applied stress.Source: Mascia (1974).

12.1 Modelling the Viscoelastic Behaviourof Polymers

Such models consist of combinations of aspringandadashpotaccordingtotheloadingconditions. The extension of the spring(hence the strain) is directly proportional totheapplied load (hence thestress) and, there-fore, represents the �elastic component�. Theproportionality constant is Young�s modu-lus, that is,

E ¼ s=«:

A dashpot is a cylinder with a frictionlesspiston capable of moving in either directionby allowing the liquid to flow from one partto the other through an orifice in the piston.An applied force will cause the piston tomove at a rate that is directly proportional tothe viscosity of the liquid within the cylin-der. When the force is removed, the pistonstops instantaneously and the extensionproduced by the applied load does notrecover at any time thereafter. Again, onecan replace the force with stress and thedeformation rate with strain rate, so that thecharacteristic constant for the dashpot is theviscosity, h. This can be used to representthe �viscous component� of the viscoelasticbehaviour, that is,

h ¼ s

d«=dt:

The combination of a spring and a dash-pot in series (known as the Maxwell model)gives isostress conditions for the responseof the two elements and is used tomodel thetime-dependent stress relaxation behaviourof polymers. (See Maxwell model.) Thecombination of the elastic and viscouselements in parallel, known as the Kelvin–Voigt model, is used to describe the time-dependent creep and recovery behaviour ofpolymers. (See Kelvin–Voigt model.) Ahybrid combination, known as the standardlinear solid, is used tomodel both the stress

330j 12 Viscoelastic Behaviour

relaxation and creep behaviour of polymers.(See Standard linear solid.) The individualmodels mentioned here contain details ofthe physical interpretation and underlyingequations.

13. Viscoelasticity

A theory used to analyse and characterizethe time-dependent deformational behav-iour of polymers, under different loadingconditions. Static loading conditions areused to describe the time-dependent evolu-tion of the strain resulting from the appli-cation of a constant stress, and the time-dependent relaxation (decay) of the stressunder conditions in which the strain is keptconstant. Cyclic loading conditions are usedfor the dynamic mechanical analysis of theviscoelastic behaviour of polymers. (SeeViscoelastic behaviour.)

14. Viscometer

An apparatus used to measure the viscosityof liquids or low-viscosity emulsions, sus-pensions or pastes. The apparatus used formeasurements made on high-viscosityliquids is generally known as a rheometer.The more widely used viscometers for poly-mer systems are the Ubbelohde viscometerfor solutions, such as those for measure-ments of molecular weights, and the Brook-field viscometer for emulsions and pastes.

15. Viscosity

A property that denotes the resistance of aliquid to flow. Viscosity, h, is defined as theratio of the stress, s, acting on the liquid tothe related strain rate, d«/dt (or velocitygradient, dV/dy), that is,

h ¼ s

d«=dt¼ s

dV=dy:

For shear flow situations, the viscosity isknown as the shear viscosity, or simplyviscosity, and the strain rate corresponds tothe shear rate, while the velocity gradientcorresponds to the gradient perpendicularto the flow direction, as shown.

Velocity gradient in shear flow.

For elongational flow conditions, the vis-cosity is known as the elongational viscosity,or extensional viscosity, and the strain ratecorresponds to the elongational rate, wherethe velocity gradient is experienced alongthe direction of flow, as shown. (See Elonga-tional flow.)

Velocity gradient in elongational flow.

For Newtonian liquids, there is an exactrelationship between the elongational vis-cosity (he) and the shear viscosity (hs), thatis,he¼ 3hs. For polymermelts, on the otherhand, the elongational viscosity is manytimes greater than the shear viscosity,depending on the temperature and molec-ular weight of the polymer. Under dynamicor cyclicflowconditions, thenon-Newtoniannature of the flow behaviour of polymerscan be expressed in terms of a complexviscosity, h*, comprising a real component,h 0, and an imaginary component, h 00, thatis, h* ¼h0 � ih00, where i ¼ ffiffiffiffiffiffiffi�1

p(the imag-

inary number). The imaginary term, h00,arises from the melt elasticity characteris-tics and is directly related to G0, the realcomponent of the shear modulus when thebehaviour is expressed in complex solid-like

15 Viscosity j331

characteristics, that is,h00 ¼G0/v, wherev isthe angular frequency of the oscillatorymotion.The viscosity of liquids in general

decreases exponentially with temperatureand follows very closely the Arrhenius equa-tion, as shown by the plots of the zero-shearviscosity against the reciprocal of the abso-lute temperature in the diagram. The datashow that the viscosity of poly(vinyl butyral)(PVB) is muchmore sensitive to changes intemperature than is polyethylene, that is,PVB has a much higher activation energy.(See Arrhenius equation.)

Change of viscosity of polymer melts with absolutetemperature for two grades of polyethylene (I) andpoly(vinyl butyral) (II). Source: McKelvey (1957).

16. Viscous Flow

Flow is a term generally used to denoteirreversible deformations in polymers. Flowoccurs by the displacement of entire mole-cules, which takes place through reptationmovements, involving segments of the poly-mer chains. These molecular movementsare feasible only when the polymer is in themelt state and, therefore, viscous flow has tobe differentiated from what is sometimesknown as �plastic flow�, which takes place atlow temperatures through yielding and cold-drawing deformations. In the latter case, the

molecules stretch out in the direction of theapplied forces and assume an oriented con-figuration. (See Cold drawing and Yieldfailure.)Contrary to viscousflow, plasticflowdeformations of polymers are recoverableowing to the instability of the orientation ofthe polymer chains, which will recoil back totheir original random position in order toregain their stable (high-entropy) configura-tion when the temperature is increasedabove the glass transition temperature ormelting point of the polymer.

17. Viscous State

A state of matter in which flow can takeplace. Within the context of the deforma-tional behaviour of polymers, the viscousstate can be considered to correspond to thestate in which melt elasticity vanishes andthe flow assumes a Newtonian behaviour.

18. Visible Light

(See Radiation.)

19. Vitrification

The state that a thermosetting resin systemdevelops subsequent to �gelation�, when thesystem reaches the glassy state, that is, theTg assumes a value greater than ambienttemperature.

20. Void

These are extensively found in compositesdue to the difficulty of expelling completelythe air entrapped between the fibres by theresin during manufacture. Voids are alsofound sometimes in thick sections ofinjection-moulded thermoplastics articles.(See Moulding defect.)

332j 20 Void

21. Voigt Model

(See Kelvin–Voigt model.)

22. Volume Resistivity

Aproperty that describes the resistance of adielectric material to the flow of an electriccurrent through the bulk. From the generaldefinition of resistivity, that is, r¼ electricalstress/current density, a formula can bederived for the volume resistivity (rV) frommeasurements made on the electricalcircuit shown, that is,

r ¼ ðV=dÞðA=IÞ ¼ ðA=dÞRV;

where A is the average area of the top andbottom electrodes and d is the thickness ofthe plaque used as specimen. Note that thedimensions of volume resistivity are ohmmetre (Wm). (See Surface resistivity.)

Circuit for measuring the current flowing betweenthe top inner electrode and the bottom electrode(i.e. through the thickness of the plaque).

The geometric set-up for the electrodes(top and bottom) and the guard ring isshown.

Top electrode and guard ring attached to the plaqueused as specimen for measuring volume resistivity.

23. Von Mises Criterion

(see Yield criteria.)

24. Vulcanizate

A rubber sample or article that has gonethrough a vulcanization process.

25. Vulcanization

A termused in the rubber industry to denotean operation that produces cross-linksthrough theuse of sulfur and sulfur-contain-ing curatives (vulcanizing agents). The termderives fromVulcan, theGreek god offire, todenote the use of heat to �cure� the rubber.Originally, vulcanization was carried out bythe addition of sulfur. It was later discoveredthat the cure rate could be increased consid-erably by incorporating zinc oxide in theformulation and increased further again bythe addition of a fatty acid, such as stearic

25 Vulcanization j333

acid, and the use of an �accelerator�. The fattyacid is absorbed on the surface of the zincoxide particles and produces the desirablequantities of zinc ions, which activate theaccelerator through the formation of com-plexes. The various type of cross-links be-tween polymer chains obtained in the vul-canization of rubber with sulfur are shown.

Sulfur cross-links in vulcanized rubber. Ac standsfor accelerator molecule.

A typical reaction scheme showing theparticipation of the accelerator in the for-mation of sulfur cross-links between elasto-mer chain is shown.

Reaction scheme for the formation of sulfur cross-links involving the action of the accelerator.

Diene rubbers can also be cross-linkedwith phenolic compounds, particularlydiphenol type, such as resorcinol formalde-hyde resins. These isomerize to quinoneswith the formation of allylic double bondsthat can react readily with the unsaturationof the diene elastomer chains, as shown.

Reaction between resorcinol formaldehyde resin and the chain of a diene rubber.

334j 25 Vulcanization

W

1. Wall Slip

A term used to describe the non-zero veloc-ity of polymer melts at the surface of theflow channel. (See Rheology and Mooneyequation.)

2. Warping

(See Distortion and warping.)

3. Water-Borne Coating

A coating deposited from a micro-suspen-sion of a polymer in water. The polymer isspecially designed through synthesis ormodification of existing polymers to pro-duce ammonium salts, which provides thedesired level of �affinity� for water. An ionicsurfactant is used to stabilize the dispersionagainst segregation and agglomeration. Af-ter removing the water by drying or throughan electrolytic separation process, the coat-ing is �stoved� or cured at high temperaturesto induce cross-linking reactions with othercomponents. (See Electrolytic deposition.)This operation also drives off the ammoniafrom the carboxylate salt. In other cases,such as epoxides, the required ammoniumsalts are produced from amine-extendedepoxy resins with the addition of a weakmonomeric carboxylic acid, such as lacticacid. For electrolytic coating deposition, thechoice of type of ion bound to the polymerparticle depends on whether a cathodic oranodic deposition process in used. Water-bornepolyurethane systems arewidely usedin view of the excellent mechanical proper-ties, suchasabrasion resistance,providedbyurethane blocks within the final polymernetwork. Both one-pack and two-pack sys-tems are used. In two-pack systems, one

component contains a blocked isocyanate,and the other contains the polyol, so that,after drying out thewater, reactions can takeplace between the polyol of one pack and theunblocked isocyanate groups in the otherpack. (See Urethane polymer and resin.)

4. Weak Boundary Layer

An interlayer between an adhesive and theadherend, which prevents a joint fromreaching the maximum achievable bondstrength. Weak boundary layers are usuallyformed from contaminants that are eitherpresent in the atmosphere (typically water)or exude out from the bulk of the adherend.In the case of polymer adherends, the for-mation of a weak boundary layer is oftencaused by the migration of external lubri-cants to the surface during processing. Inmoulded products, the mould release agentused to ease the ejection of a moulded partcan give rise to the formation of a weakboundary layer if it is not soluble in theadhesive.

5. Weathering

A term used to describe the deterioration ofthe properties of materials or the perfor-mance of products brought about byadverse climatic conditions. The damagingatmospheric agents in the weather includeradiation (mainly the UV range), tempera-ture, oxygen, moisture, contaminants andrainfall. The deterioration of materials byexposure to weather conditions is duealmost entirely to chemical reactions, partic-ularly oxidation through reactions of atomicoxygen with tertiary H�C bonds, CH¼CHbonds, and the hydrolysis of groups withinthe backbone chain of a polymer, such as


j335

esters, amides, imides and urethanes. Oxi-dation reactions are accelerated by the actionof UV light (wavelength in the range280–400 nm) and metallic contaminantspresent in other components of a formula-tion, such as fillers. The hydrolytic degrada-tion reactions, on the other hand, are highlysensitive to the presence of acidic or basiccontaminants in the environment. (SeeHydrolysis and Degradation.) The extent ofdegradation due to weathering varies widelyin different parts of the globe and also be-tween summer and winter months. Thecause of the seasonal variations is rooted inthe difference in the intensity of light fallingon Earth, as illustrated in terms of the varia-tion of the �irradiance� (radiation power) as afunction of the wavelength within the UVregion in the diagram.

Typical solar spectrum for summer and winterseasons. Source: Brennan and Fedor (1988).

Weathering affects the outer surface of aproduct and gradually progresses to a limit-ing depth depending on the material andenvironmental conditions. It takes placethrough a combination of chemical reac-tions and erosion or loss of products of thedegradation process as volatiles or leachablecompounds. The diagram shows a plot ofthe absorbance of carbonyl groups, mea-sured on a polyethylene pipe, as a functionof the distance from the surface (depth)after one year�s exposure to natural weather.

Carbonyl absorbance of samples of a polyethylenepipe, taken at different depths from the surface,after one year�s exposure to natural weather.Source: Allen et al. (1997).

The degradation reactions cause severeembrittlement of the outer surface layers,with the formation of small craters andcracks. This is illustrated for a sample ofpolypropylene examined at different timesof exposure to tropical weathering condi-tions. In this case a thin skin of polymer,possibly a highly oriented layer, was foundto be highly susceptible to degradation.

Degradation of the outer surface layers of a poly-propylene sample exposed to tropical weather.Source: Bedia et al. (2003).

The presence of degraded outer layers(a feature known as �chalking�) causes se-vere embrittlement of the entire sample orproduct owing to the high stress intensifi-cation caused by the crevices and cracks.This is illustrated in the diagram in the formof plots of theflexural strengthmeasured onweatheredABS sheets after removing layersof different thickness from the exposedsurface, relative to the flexural strength ofthe original sample.

336j 5 Weathering

Change in flexural strength of ABS sheets, weath-ered for two, three and five years, as a functionof thethickness of the layer removed from the surface.Source: Watanabe et al. (1981).

Natural weathering evaluations are proneto large variations in climatic conditions andmay take too long for the evaluation of newformulations or for comparison of differentsystems. For this reason, laboratory testsfrequently use sources that emit light thatfairly closelymatches the solar spectrum. Insome systems there is also the possibility ofintroducing other climatic variants, such asspraying water or salt solution, as well asbeing able to operate at higher temperaturesto accelerate the degradation reactions. Themain sources of UV light for laboratoryweathering tests are: carbon arc, xenon arc,fluorescent UV lamps, metal halides andmercury lamps. Filters are frequently usedto fine-tune the wavelength of the radiationused for the tests relative to some localnatural light conditions.

6. Weight-Average Molecular Weight

The average molecular weight calculated onthe basis of the weight fraction of polymerchainsofspecificsize. (SeeMolecularweight.)

7. Weissenberg Rheogoniometer

This is also known as the cone-and-platerheometer. (SeeCone-and-plate rheometer.)

8. Weld Line

The line that identifies the location of twomelt fronts that have come into contact toform a weld. Apart from welding processes,weld lines are observed in extrusion blow-moulded containers at the �pinch� line, andin injection-moulded products at thosepoints where two melt fronts meet withinthe cavities of the mould, as shown.

Typical weld line in injection-moulded products.Source: Unidentified original source.

Weld lines are also found in extrudedtubular products at the points within thedie where themelt fronts are reunited afterseparation by the �spider legs� before reach-ing the die lips. The typical geometry of thespider legs used for fixing the inner core ofthe die to the outer body is shown. (SeeExtrusion die.)

Spider legs joining the central core of a tubular dieto the main body. Source: Rosato (1998).

9. Welding

A manufacturing or fabrication processby which two or more, usually large,

9 Welding j337

components are brought into contact andjoined together by promoting moleculardiffusion across the interface through arapid localized increase in the tempera-ture. This implies, therefore, that onlythermoplastic products or componentscan be welded. (See Thermofusion pro-cess.) The main welding processes usedfor plastics are briefly described.

9.1 Hot Gas Welding

A technique used for large-area fabrica-tions adopted from the oxy-acetylene weld-ing of metals, using hot gas (usually heat-ed air or nitrogen) to raise the temperatureof the welding rod and the V-grooveformed by adjacent edges of the compo-nents of the jointed parts. The diagramshows an example of how the welding rodcan be guided into the welding groovethrough a nozzle.

Schematic illustration of hot gaswelding of plastics.Source: Bernam (1988).

The welding rod is chemically similar tothe parts used for fabrication, but with aslightly lower viscosity in order to ensurethat the groove is filled completely.

9.2 Hot Plate Welding

A simple technique that uses a hot metalplate to heat the parts to be welded, thenforcing the two components against eachother for a sufficient length of time to allow

the weld to be formed. This technique isalso known as butt fusion, as illustrated.

Illustration of the principle of hot plate welding.

Theprincipleofhotplateweldinghasbeenwidely exploited for the joining of pipes andhas been elaborated through the use of sock-ets to enhance the performance of the joint, atechniqueknownaselectrofusion.Thesocketis often heated electrically by inserting acoiled wire element into the actual socket sothat it can be connected to a power source toproduce the required heat for melting theinnersurfaceof thesleeve,aswellas theoutersurface of the pipe fronts, as illustrated.

Typical set-up for electrofusion welding of plasticpipes. Source: Stafford (1988).

9.3 Friction Welding

The principle consists of heating the joiningfronts throughmechanical friction producedby vibrating or spinning one of the partsagainst the other. The principle is illustrated.

338j 9 Welding

Principle of friction or spin welding. Source:Dunkerton (1988).

9.4 High-Frequency (RF) Welding

The principle is based on the ability ofpolymers with a high dielectric loss factor(tan d) to generate heat under the influenceof an AC field produced by a generator witha 2–5 kW output. The electrical energy lossW (W/cm3) that is converted to thermalenergy for heating the welding area can becalculated from

W ¼ 0:555� 10�12 � f � tan d� F2;

where f is the frequency (standard value of27MHz) and F is the electric field or elec-trical stress (V/cm). This technique iswidelyused for the welding of flexible PVC sheetsowing to the very high loss factor and thelow temperature required to inducethe required molecular diffusion throughthewelding surfaces. The electrodes used toapply the RF field to the welding area arealso used to exert the pressure for thethermofusion.

9.5 Ultrasonic Welding

A technique that uses ultrasonic pulsations(frequencies between 20 and 50 kHz) gen-erated by a piezoelectric crystal, amplifiedand transmitted via a metal sonotrone

known as the �horn�, to the welding area ofthe polymer component supported on arigid metal base. The set-up is illustrated.

Set-up of an ultrasonic welding device. Source:McCrum et al. (1988).

Welding takes place as a result of thetransformation of the mechanical energydelivered by the horn to thermal energy,which heats up the polymer in the weldingarea. This technique takes advantage of thelow thermal conductivity of polymers,which ensures that only the contact regionsreach high temperatures. For polymerswith a high damping factor (tan d value),the horn has to be close to the welding area(near-fieldmode). For glassy polymerswithlow attenuation or damping characteristicsat ambient temperatures, the horn can beapplied at fairly high distances from thewelding area (far-field mode), which isparticularly attractive for welding hollowcomponents, as shown.

9 Welding j339

Example of �far-field� ultrasonic welding. Source:Mascia (1989).

10. Wide-Angle X-Ray Diffraction (Wide-Angle X-Ray Scattering, WAXS)

A technique used to measure the degree ofcrystallinity and orientation in polymers.The measurements are based on the prin-ciple that X-rays are diffracted from a sys-tem of parallel equidistant lattice planes ofcrystals if the Bragg equation is satisfied,that is,

nþ l ¼ 2d sin #;

where n is an integer that defines the orderof diffraction, l is the wavelength of theincident X-rays, t is the angle of diffraction,and d is the spacing between lattice planes,as shown in diagram.

Diffraction of X-rays at a set of lattice planes in acrystalline substance.

Themeasured diffractedX-ray intensityFfrom the sample analysed is plotted as afunction of 2t. An amorphous material ex-hibits a broad spectrum of diffraction,whereas a crystalline substance is identifiedby sharp diffraction peaks. Since crystalline

polymers consist of mixtures of amorphousand crystalline domains, the resulting spec-trum consists of a superimposed combina-tion of both types of spectra, as shown.

X-ray diffraction of a low-density polyethylenesample. Source: Unidentified original source.

From measurements of the overall dif-fracted intensity of the two components (Fcand Fa), through integration over appropri-ate intervals, it is possible to calculate therelative proportions of crystalline (Xc) andamorphous domains (Xa), that is, Xc¼ aFcand Xa¼ 1� Fc¼ bFa, where a and b areconstants determined by suitable calibra-tion measurements. With the goniometrictechniques normally used for probing thecrystallinity in polymers, it is possibleto identify also whether the constituentdomains are oriented, and to calculate thevalues for the respective orientation func-tions for the crystalline and amorphousregions. The photographs below show thetypical X-ray patterns for an isotropic crys-talline polymer and for the same polymerafter being stretched longitudinally to intro-duce orientation.

X-ray flat chamber photographs on polypropylene:(left) isotropic sample; (right) stretched sample at12 : 1 draw ratio. Source: Kampf (1986).

340j 10 Wide-Angle X-Ray Diffraction (Wide-Angle X-Ray Scattering, WAXS)

11. WLF Equation

The abbreviation stands for Williams–Landel–Ferry, the three authorswhoderivedthe equation. They used an empirical ap-proach to obtain values of the shift factor aTfor the production of master curves fromisochronous creep or stress relaxation ex-periments carried out at various tempera-tures. The procedure is based on the time–-temperature equivalence of the viscoelasticbehaviourof polymers.TheWLFequation iswritten as

log aT ¼ ½�C1ðT�TgÞ�=ðC2 þT�TgÞ;where C1 and C2 are constants for themate-

rial and loading conditions (i.e. whethercreep or stress relaxation). (See Time–temperature superposition.)

12. Wood Flour

A filler obtained by the comminution ofwood. Mainly used as a reinforcing fillerfor phenolic moulding powders.

13. Work of Adhesion

(See Adhesive wetting.)

13 Work of Adhesion j341

X

1. X-Ray Diffraction (XRD)

(See Wide-angle X-ray diffraction andSmall-angle X-ray scattering.)

2. X-Ray Photoelectron Microscopy (X-RayPhotoelectron Spectroscopy, XPS)

An analytical technique used for surfaceanalysis, based on the principle that an atomexcited by photons with energy level hnfrom monochromatic X-rays will knock anelectron out of the L shell. This (photo)electron possesses a kinetic energy equalto hn�EL, where EL is the characteristicenergy of the L shell of a specific atom. XPSanalysis makes it possible to determine thechemical nature of the atom from experi-mental measurements, from which the en-ergy EL can be calculated from the overallkinetic energy.

3. X-Rays

Rays produced by the acceleration of elec-trons emitted from a heated cathode in ahigh vacuum using a high voltage(3–100 kV) and allowing them to impingeon an anode (usually water-cooled). Thekinetic energy of the electrons is mainlyconverted into heat, but part of it is emittedas X-rays. These X-rays possess a character-istic energy distribution (spectrum) that isdependent on the excitation voltage usedand on the nature of the anodic material.(See Radiation.)

4. Xenon Arc Lamp

A source of light that simulates naturaldaylight through the use of appropriatefilters. Xenon arc lamps are widely used foraccelerated weathering tests.


342j

Y

1. Y Calibration Factor

A geometrical parameter that takes intoaccount the geometry of the specimen, thecrack length, a, and the width of the speci-men, W, in the calculation of the stressintensity factor (K), that is, K ¼ Ys

ffiffiffi

ap

,where s is the applied stress. (See Fracturemechanics.)

2. Yellowness Index

An empirical parameter used to describethe extent of degradation of a polymer thattakes place through weathering and is man-ifested by the development of a yellow tint. Itis determined using UV spectroscopy bymeasuring the absorption in thewavelengthrange 570–590 nm. Some standard testscompare the absorbance of the polymer tothat of magnesium oxide, as a referencepoint.

3. Yield Criteria

Criteria to determine the conditions thatbring about yield failure in multiaxial stresssituations. (See Yield failure.) The mostcommonly used criteria are the Tresca crite-rion and the Von Mises criterion. Althoughthese were originally used for metals, theyhavebeen found toapply equallywell to rigidpolymers. Small modifications have beensuggested to improve the accuracy of thepredictions of these criteria for polymers.

3.1 Tresca Criterion

According to this criterion, yielding takesplace when the maximum shear stress(tmax) reaches a critical value (tcrit), whichis determined by the nature of the material.

(See L€uder lines.) The Tresca criterion isusually written as

tmax ¼ ðsmax�sminÞ=2 ¼ tcrit;

where smax and smin are themaximum andminimum principal stresses acting alongthe main axes. Since the yield strength (sY)of a material is measured under uniaxialstress conditions, that is, tension or com-pression, the application of this criteriongives tmax¼smax/2¼ tcrit because smin

(stress in other principal directions) is zero,whilesmax corresponds to the yield strengthof the material, sY. For situations where theyield strengths in tension and compressionare equal, as in the case of most metals, theTresca criterion can be represented graphi-cally with the identification of contours forthe magnitude of the principal stresses thathave to be reached for yielding failures. Thediagram shows the graphical description ofthe yielding conditions by the Tresca crite-rion for plane stress conditions, that is,when one of the principal stresses is zero(as is often the case when the thickness ofthe structure or product is very small).

Tresca criterion for plane stress conditions formaterials where the yield strength in tension isequal to the yield strength in compression. Source:Adapted from Mascia (1989).


j343

For materials, such as polymers, wherethe yield strength in compression is greaterthan the yield strength in tension, thegraphical representation is modified in themanner shown in the diagram.

Tresca criterion for plane stress conditions forpolymers, where the yield strength in tension islower than the yield strength in compression.Source: Mascia (1989).

3.2 Von Mises Criterion

This criterion states that yielding conditionsare reached when the maximum distortion-al strain energy reaches a critical valuedetermined by the nature of the material.For materials where the values of the yieldstrength in tension and compression areequal, the Von Mises criterion can be writ-ten in terms of the corresponding principalstresses as

ðs1�s2Þ2 þðs1�s3Þ2 þðs2�s3Þ2 ¼ 2s2Y;

where s1, s2 and s3 are the three principalstresses. For plane stress conditions, that is,when s3 is equal to zero, the Von Misescriterion becomes

s21 þs2

2�s1s2 ¼ s2Y:

The graphical representation of this equa-tion is an inclined ellipse at 45� with respecttothetwoaxesofprincipalstressess1ands2.The diagram shows a graphical compari-

son of the Tresca and Von Mises criteria,

which indicates that they predict very simi-lar conditions for yielding, with amaximumdiscrepancy around 14% occurring in thetension and compression quadrants.

Comparison of Tresca and Von Mises criteria formaterials where the yield strength in tension isequal to the yield strength in compression.

4. Yield Failure

A failure arising from large unrecovereddeformations when the stress reaches acritical value, known as the yield strength.This is exemplified in the diagram, wherethe yield failure conditions are identified asthe yield point.

Graphical representation of conditions leading toyield failure and identification of the yield point.

344j 4 Yield Failure

When the applied load is lower than thevalue required for reaching the yield point,the deformations are reversible (i.e. thestrain recovers when the stress is removed).After exceeding the yield point, on the otherhand, only a small part of the deformationrecovers. The largest part of the deforma-tion, corresponding to the plastic strain, «P,remains after the load is removed. This isidentified in the diagram by the arrow afterthe yield point. Yield failures take placethrough the sliding of planes of crystallamellae with the uncoiling of random tiemolecules, followed by the alignment of thecrystals in the direction of the applied stress,as depicted in the diagram.

Yield failure mechanism for crystalline polymers.

For the case of amorphous (glassy) poly-mers,yieldingalso takesplace throughsheardeformations along the planes where theshear stresses are highest, as exemplified bythe formation of L€uder lines shown in thediagram for a polystyrene sample in a testcarried out under plane stress conditions.

L€uder lines as evidence for the shear deformationsin yield failure of glassy polymers. Source: Bucknall(1977).

5. Yield Point

The point that identifies the failure by yield-ing in load–deformation curves, normallyobtained by tensile tests. In some cases theyielding conditions cannot be easily identi-fied as a maximum or a clear discontinuityon the load–deformation curve. A tech-nique, known as the Considere construc-tion, is sometimes used to assign a precisevalues of the stress and the strain on astress–strain curve at which yielding occurs.This is rarely done in the case of polymers.

6. Yield Strength

The value of the stress at which yieldingtakes place, calculated as the load/originalcross-sectional area of the specimen, nor-mally from tensile tests. As there can be asubstantial amount of deformation beforethe yield point is reached, the actual value ofthe stress, based on the actual cross-section-al area of the specimen, can be appreciablyhigher. Although the value of the true stresscan be calculated from the value of thenominal stress, this is not normally done.

7. Young�s Modulus

A material property defined as the propor-tionality coefficient between an appliedstress and resulting strain in either tensionor compression, for conditions below thosethat cause failure either by yielding or brittlefracture, that is,

Young�s modulus ¼ stress=strain:

The Young�s modulus of polymersdecreases with the duration of the appliedload, owing to their viscoelastic behaviour.Even for a typical engineering polymer,such as poly(ether sulfone) (PES), the creepmodulus decreases from about 3 GPa forvery short durations of applied load (say,about one minute) to less than 1 GPa when

7 Young�s Modulus j345

the load is maintained for a very long time(say, about two years).The value of the Young�s modulus allows

a design engineer to estimate the deflectionresulting from an applied load. Forinstance, in the case of a cantilever beam,the deflection D can be calculated using theformula

D ¼ ðP=EÞ½L3=6bd3�;where P is the applied load, E is the Young�smodulus,L is the length of the beam, b is thewidth and d is the thickness. With thisformula, the designer can choose the mostappropriatematerial, knowing themodulus

values. To contain the amount of deflectionresulting from the applied load, the design-er can either choose a material with highermodulus or increase the width or thicknessof the beam. The latter is usually the pre-ferred choice, because of the cubic relation-ship instead of a linear one with respect towidth ormodulus. The use of typical designequations for rigid polymers implies thatone cannot assign a specific value to thesematerials for the Young�s modulus becausethe value would depend on the loadinghistory, which has to be known in order touse an appropriate value to perform thecalculations. (See Modulus.)

346j 7 Young�s Modulus

Z

1. Z-Blade Mixer

A typical design for mixing doughs andpastes. (See Mixer.)

2. Zero-Shear Viscosity

The value of melt viscosity of polymerswithin the Newtonian plateau at low shearrates, that is, shear rates tending to zero.(See Non-Newtonian behaviour.)

3. Zeta Potential (or z Potential)

Aparameter used to characterize the level ofcharge on a surface, particularly objectswith a high surface-to-volume ratio, suchas particles and fibres. The z potential is auseful parameter inflocculation, as itmakesit possible to determine the optimum pH ofthe suspension medium to achieve thehighest stability. These conditions aredetermined by the chemical nature of thesurface of the particle, which can vary con-siderably from one filler to another, asillustrated.

Zeta potential of water suspension of various fillersas a function of pH of the suspending medium.Source: Schroder (1991).

From an examination of the isoelectricpoint (at which the z potential is equal tozero) of the different fillers, one can deduce

that the glass surface is strongly acidic,while that of MgO is very basic. The surfaceof TiO2, on the other hand, is practicallyneutral. The z potential of the filler, there-fore, determines the nature of chemicalspecies that can be adsorbed on the surface,which is particularly useful for the surfacetreatment of fillers as a way of improvingtheir dispersion characteristics in polymercompounds and preventing agglomerationsin liquid suspensions.

4. Ziegler Catalyst

A coordination-type catalyst (known also asa Ziegler–Natta catalyst) used for the poly-merization of linear polyethylene (LLDPEandHDPE) and for stereoregular polymers,such as isotactic PP. The most commontype is a coordination complex producedfrom the interaction of aluminium trialkylcompounds and titanium tetrachloride toform a complex of the type:

Polymerization of an olefin takes placethrough the break-up of the coordinationcomplex by the polarization effect of thep-electrons in the double bond of themono-mer, as shown.

As a consequence, this causes the split-ting of the double bond, with the formation


j347

of a positive charge:

This is then followedby the lengthening ofthe chain (propagation reaction) through theaddition of successive monomer units at theTi side of the complex. The isotactic configu-rationofthesidegroupsinthepolymerizationof an a-olefin arises from the spatial restric-tions imposed by the catalyst on the additionof successivemonomerunits at the coordina-tion complex side of the growing chain.

5. Zinc Oxide

An additive used in combinationwith a fattyacid, usually stearic acid, as an acceleratorfor the sulfur vulcanization of rubber. (SeeAccelerator.) It has a high level of purity(99.99% ZnO) and is also used in combina-tion with magnesium oxide to cross-linkchloroprene rubbers. It has a density of5.6 g/cm3 and particle size around

0.1–0.4mm, with a specific surface area ofabout 10–20m2/g. The grade used as anaccelerator for the vulcanization of rubber isoften coated with stearic acid or propionicacid to assist its dispersion.

6. Zisman Plot

Aplot of the contact angle (cos u) formed bya series of liquids on a solid surface againstthe surface energy of each liquid. This pro-duces an approximately straight line thatcan be extrapolated to cos u¼ 1 (i.e. u¼ 0),which corresponds to the conditions forspontaneous wetting of the surface of thesolid. The value of the surface energy forwhich u¼ 0 is known as the �critical surfaceenergy� or �critical wetting tension�. The plotis based on an empirical equation put for-ward by Zisman in the form

cos u ¼ 1þ bðgC�gLVÞ;where gC is the critical surface energy andgLV is the interfacial energy between theliquid and air saturated with liquid vapour.(See Surface energy.)

348j 6 Zisman Plot

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