Ruhland Polymer Processing

Polymer Processing:

„Engineering activities concerned with operations

carried out on polymeric materials to enhance their utility“

Prof. Dr. Klaus Ruhland

Z. Tadmor, C. G. Gogos, Principles of Polymer Processing, Wiley-Interscience

T. A. Osswald, Polymer Processing Fundamentals, Hanser Verlag

M. D. Lechner, K. Hehrke, E. H. Nordmeier, Makromolekulare Chemie, Birkhäuser Verlag

B. Tieke, Makromolekulare Chemie, VCH Verlag

M. Brahm, Polymerchemie kompakt, Hirzel Verlag

J. Hoinkis, E. Lindner, Chemie für Ingenieure, Wiley-VCH Verlag

Monomer Polymer compound Plastic final productpoly-reaction adding/mixing shaping

Thermal and mechanical impact

compoundingsynthesis

Polymer Recycling

Processing of Polymers

1. Introduction to Polymers

2. Thermal behaviour3. Mechanical behaviour

4. Extrusion5. Mixing

6. Injection molding

7. Secondary Shaping8. Other Important Polymer Processes

(Calendering, Coating, Foaming)

Historical Evolution of Polymer Processing

taken from „principles of polymer processing“

Monomer: Smallest molecule(s), a polymer can be synthesized from

Polyreaction: Chemical transformation in which monomers are transformed into polymers

Repeat unit: Smallest entity, with which the stoichiometry of a polymer can be described,

just by multiplication (sometimes inconsistent: PE).

Oligomer: (oligos – some, meros – part) Molecule consisting of several repeat units. If one

repeat unit is added, the property under focus changes measurably.

Polymer: (polys – much, meros – part) Molecule consisting of manyrepeat units. If one repeat unit is added, the property under focus does not change.

Degree of polymerization: Pn = Mpolymer/Mrepeat unit

Polymer compound: a mixture of polymers composed of the same repeat unit, but with different

degree of polymerization.

Polymer blend: a mixture of polymer compounds, in which the different compounds are

composed of different repeat units.

Co-Polymer: Polymer consisting of more than one type of repeat unit

Additives: External non-polymer materials, added to the polymer compound to improve its

properties

Plastics = Polymer compound or blend + Additive(s)

Polymer processing: engineering activity concerned with operations carried out on

polymeric materials to enhance their utility.

Introduction into Polymer Chemistry: Definition of some terms

Classification of Monomers

Bifunctional acyclic:

Terephthalic acid

Adipinic acid

Phosgene

Glycole

Bisphenol A

Hexamethylene diamine

Hexamethylene diisocyanate

Monofunctional cyclic:

ε-Caprolactame

Laurin lactone

Ethylene oxide

Cyclooctene

Monofunctional acyclic

(multiple bond):

Ethylene

Styrene

Tetrafluor ethylene

Vinyl chloride

Methyl metacrylate

(butadiene)

(isoprene)

COOHHOOC

HOOC

COOH

Cl

O

Cl

HO

OH

HO OH

NH2

H2N

NCO

OCN

O

NH

O

O

O

H

H

H

H

HH

H

F

F

F

F

H

Cl

H

H

CH3

COOCH3

H

H

Classification of Polyreactions

Polyreaction

monofunctional monomerbifunctional monomer

Chain-growth reaction:growing chain reacts only with monomer

step-growth reaction:all components in the system react simultaneously

Poly-condensation

Poly-addition

Poly-recombination

Poly-elimination

Poly-merization

anionic radical cationic insertion group-transfer

Averaged degree of polymerization in dependence of the conversion:

a) step-growth reaction

b) chain-growth reaction without chain termination reaction (living polymerization)

c) chain-growth reation with chain termination raction

Structure of Polymers

repeat unit

polymer (intra-chain)

polymer compound (inter-chain)

Isomerism in Chemistry

Isomerism(same stoichiometry, different structure)

stereo isomers(same type of bonds, different orientation)

constitution isomers(different types of bonds)

configurational isomers(superimposition only with bond cleavage)

conformational isomers(superimposition by rotation about bond)

syn-periplanar

syn-clinal

anti-clinal

anti-periplanar

polymerizationisomers

(CH2)5 (CH2)6

sequenceisomers

chiral isomers

enantiomers(mirror images)

diastereomers

A

B DC

A

BDC

RR

R

RR R

R

R

geometric isomers


repeat unit



Structure of Polymer Compounds (repeat unit)

H H

H H

n

conformationalisomers PE

H

H RR

HHR

H HR

HHH

R

H

R

HHR

H

H

R

HH

H H

H CH3

n

configurationisomers PP

H H

H CH3

n

H H

H3C H

n

n

geometricisomers IR n

(

)n

n

constitutionisomers BR n

n

1,4-BR 1,2-BR


repeat unit



Structure of Polymer Compounds (polymer I)

H H

H H

n

conformationalisomers PE

H

R

H

R

HH

H

R HR

HH

R

H HR

HH

R

H

H

R

HHH

H

R

R

HH H

R

H

R

HH

H

H RR

HH

α

L0

L = n L0 sin(α/2)

<r2>0 = n L0

2 (1-cos(α))

(1+cos(α))

(1+cos(β))

(1-cos(β))

α: bond angleβ: averaged torsional angle

σ: empirical steric factor

<r2>0 = n L0

2 (1-cos(α))

(1+cos(α))σ2

σ(PE) = 1.85

σ(PS)at = 2.2σ(PMMA)at = 1.9σ(PMMA)i = 2.2

σ(PMMA)syn = 1.9σ(PP)a = 1.7σ(PP)i = 1.6σ(PP)syn = 1.8

i: isotacticat: aticticsyn: syndiotactic

coiling takes relaxation timeRandom coil

Structure of Polymer Compounds (polymer II)

H H

H CH3

n

configurationisomers PP

H H

H CH3

n

H H

H3C H

n

isotactic

syndiotactic

atacitc

hem-isotactic

block-isotactic

Tm = 176 °C

Tm = 165 °C

Tm = 120-176 °C

Tm: melting temperature

Structure of Polymer Compounds (polymer III)

n

constitutionisomers PP

n n

CH3CH3

CH3

head to head tail to tail

Structure of Polymer Compounds (polymer IV)

constitutionisomers

n n nPE

HDPE ρ = 0.94-0.96 g/mLTg = 127-135 °C

LLDPE ρ = 0.93-0.94 g/mLTg = 123 °C

LDPE ρ = 0.91-0.93 g/mLTg = 105-115 °C

Tg: Glas temperature


repeat unit



Structure of Polymer Compounds (polymer compound)

Polymerization „isomers“

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 100 200 300 400 500 600 700 800

degree of polymerization

Mo

lecu

lar

Weig

ht

Mn

Mw Mn

Mw= 2 -

1

Pn

Most probable distribution (Schulz/Flory)

Mn = Σ ni Mi / Σ ni

Mw = Σ ni Mi2 / Σ ni Mi

σ2 = Σ ni (Mi-Mn)2 / Σ ni = Mn (Mw - Mn) σ: standard deviation of distribution

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 100 200 300 400 500 600 700 800

degree of polymerization

Mole

cula

r w

eig

ht

Poisson distribution (living polymerization)

Mn

Mw= 1 +

1

Pn

Mn Mw

Thermal behaviour of polymers

Thermal Behaviour of Polymer compounds

Tm Tc

melt

Tg

dQ

dt

Tg

Viscous solid

solid (amorphous or semicristalline)

Tc

Viscous solid

Tm

meltViscous solid/semicrystalline

Viscous solid/semicrystalline

∆Hm

∆Hcrys

amorphous orsemicrystalline

solid

viscoussemicrystalline

solid

melt depolymerizationdecomposition

glass transition partial crystallization melting depolymerization

endo-therm

exo-therm

Tcrys

S R

∆T = 0

Q

QS

dQ

dt= const.

QR

Differential Scanning Calorimetry


Tg: torsional rotation in the amorphous regions becomes excessable• no phase transition• heat capacity Cp increases (entropic effect, rather enthalpic)• density of polymer decreases above Tg (larger free volume)• value is dependent on the heating/cooling rateTg

0: Tg measured with cooling rate of 10-5 °C/s

V0: mass-filled volume in the Polymer

Vf: empty volume in the polymer

V


Tg(P) = Tg0 - K P-1

For linear chains Tg increases with increasing degree of polymerization


Tg decreases with increasing amount of added plasticizer

The plasticizer serves as a poor solvent for the polymer compound

xW: molar fraction of added plasticizer


In statistical co-polymers Tg can be settled between Tg1 and Tg2 of the two

homo-polymers by the molar composition of the co-polymer

TgPAN: 60 °C

TgBR: -60 °C

Tgco-polymer: xAN Tg

PAN + (1-xAN) TgBR

xAN: molar fraction of acrylonitrile in the co-polymer


In homo-polymers there exists a relation between Tg and Tm:

Tg ≈ ⅔ Tm


Increment calculation of Tg0:

Tg0 = Σ Yi/ Σ Mi

184,272000Ph-S-Ph

180,284000Ph-CO-Ph

108,137400O-Ph-O

5920000O-CO-NH

6020000O-CO-O

82,922000CCl2

48,519400CHCl

3212400CHF

90,136100CH(Ph)

96,241300CH(cyclohexyl)

56,119900CH(iPr)

288000CH(CH3)

142700CH2

[g/mol][g K/mol]

Mi

Yi

Structure unit i

• Polar substituents increase Tg

• sterically flexible substituents increase Tg

• cross-linking increases Tg

• large energy barriers for torsional rotation

increase Tg

188cis-1,4-BR

373PS

323Nylon 66

424PEK

250PP

360PVC

Tg

0 [K]Polymer

Crystallinity in Polymer compounds

Molten polymer compound Solid state (semi-crystalline) Solid state (fiber, oriented)

Diffractogram of a

semicrystalline

polymer compound

amorphous semi-crystalline semi-crystalline

oriented

Chain length: 10-5 m

Interactions between polymer molecules:

•Van der Waals

•Dipole/Dipole

•Hydrogen bonds

•No chemical bonds (crosslinking)

Crystallinity depends on prior thermo-mechanical treatment of the polymer compound

Fib

er

direction


Tm is dependent on the heating and cooling rate, because the

reorientation of the polymer chains takes time.

Tm0 is defined as that temperature when Tm = Tcrys and Pn = ∞

It holds: Tcrys ≤ Tm ≤ Tm0


Tm


1/Tm(P) = 1/Tm0 + (2 R/∆Hm) P-1

PE

For linear polymer chains the end groups serve as „impurities“

lowering the melting point.


Tm


Increment calculation of Tm0:

Tm0 = Σ Yi/ Σ Mi

Tm = ∆Hm/∆Sm

• Polarizable substituents increase Tm (∆H)

• Polar substituents increase Tm (∆H)

• Opportunity for hydrogen bonds increases Tm (∆H)

• Uniformity increases Tm (∆H, ∆S)

• Rigidity in the back bone increases Tm (∆S)

1518000NH

1613500O

48,527500CHCl

3217400CHF

90,148000CH(Ph)

56,135300CH(iPr)

2813000CH(CH3)

146000CH2

[g/mol][g K/mol]

Mi

Yi

Structure unit i

450PS

459PP

415PEK

Tm

0 [K]Polymer meltViscous solid/semicrystalline

Tm


Depolymerization:

COOMe COOMe COOMe

Tc = 60°C

COOMe COOMe COOMe

∆Hp, ∆Sp

Tc = ∆Hp/∆Sp

Since ∆Sp is negative, ∆Hp must be exothermic for a polymerization,

to be thermodynamically feasable (∆Gp<0).As a consequence there exists a temperature Tc (ceiling temperature),

starting from which depolymerization is thermodynamically favored for

entropic reasons.

melt

Tc

Cross-linking in Polymer compounds

EPDM

S8 S1.6 H2S + S5.4

hot vulcanisation

Chemical bonding between the polymer molecules

1,4-BR

Thermoplast Elastoplast Elastomer ThermosetFluidoplast

viscous solid

fluid

no glass transitionTgTgTg

fluid

no melt transition

Viscous solid

TmTm

solid (amorphous or semicristalline)

solid(cristalline block domains)

solid solid

no melt transition

meltmelt

elastomer elastomer solid

solidelastomer

TF

TCTCTC

TF: fluid temperature, Tg: glass temperature, Tm: melt temperature, Tc:ceiling temperature, TD: decomposition temperature

TD TD

no melt transition

Chain fixation increases

Tem

peratu

rein

creases

Room

temp.

fluidoplast/thermoplastlow gas permeabilityisobutenepolyisobutylenePIB

fluidoplast/elastomerlow temperature elastomerdimethylchlorosilanepolydimethylsilanePDMS

duroplasturea, formaldehydeUrea/formaldehyde resinUF

duroplastmelamin, formaldeyhdemelamin/formaldehyde resinMF

thermoplast/fiberprecursor to carbon fibersacrylic nitrilePolyacrylnitrilePAN

duroplastmotor housings, telephonesphenol, formaldehydephenol/formaldehyde-resin, BakelitePF

thermoplastClothes1,6-adipodiamine, adipinic acidpolyamide 66PA 66

thermoplastFormaldehydePolyoxomethylenePOM

thermoplasttoys, garden equipmentacrylnitrile, butadiene, styreneacrylnitrile, butadiene, styreneABS

thermoplastCDs, DVDs, unbreakable bottlesbisphenol A, phosgenepolycarbonate, MakrolonPC

thermoplastDiversevinylchloridepolyvinyl chloridePVC

elastomer after vulcanisationtires and tubesisopreneisoprene rubber, natural rubberIR

elastomer after vulcanisationsolvent-resistent rubber, glovesacrylic nitrile, butadienenitrile/butadiene rubberNBR

elastomer after vulcanisationtires and tubesbutadienebutadiene rubberBR

styrene, acrylic nitrilestyrene/acrylnitrile co-polymerSAN

thermoplastbottles, clothesglycole, phthalic acidpolyethyleneterephthalatePET

thermoplastbullet-proved jacketsphthalic acid chloride, phthalic aminepoly(para-phenylene-amide), KevlarPPTA

thermoplast/duroplasthigh-temperature resistencetetrafluoroethenepoly(tretafluoroethene)PTFE

thermoplastLenses, „plexi glass“methyl metacrylatepoly(methylmetacrylate)PMMA

thermoplast/elastoplastheat-resistentpropenepolypropylenePP

thermoplastfoilsethene, 1-octadecenelinear low-density-polyethyleneLLDPE

thermoplasttransport containeretheneHigh-density-polyethyleneHDPE

thermoplastfoilsetheneLow-densitiy-polyethyleneLDPE

elastomeraging-resistentethene, propene, 1,5-hexadieneethylene/propylene/diene-monomersEPDM

elastomer after vulcanisationtires and tubesstyrene, butadienestyrene/butadiene rubberSBR

thermal classificationapplicationmonomer(s)nameabbriv.

Some important polymers

styrene

butadiene ethene propene 1,5-hexadiene

1-octadecene

COOMemethyl-metacrylate

FF

F F

tetrafluoroethene

COClClOC phthalic acid chloride

COOHHOOC phthalic acid

NH2H2N phthalic amine

HOOH

glycole

CNacrylic nitril

isoprene

Cl

vinyl chloride

OHHO

Bisphenol-A

Cl

O

Cl

phosgene

O

HH

formaldehyde

N

N

N

NH2

NH2H2N

melamin

H2N NH2

O

urea

isobutylene

Me Si

Cl

Cl

Me

dimethylsilylchloride

Some important monomers

Some important polymers

PE (polyethylene)

COOMe COOMe COOMe COOMe COOMe COOMe COOMe

PP (polypropylene)

PMMA (polymethylmetacrylate)

PTFE (polytetrafluorethylene)

F F

F F

F F

F F

F F

F F

F F

F F

F F

F F

F F

O

HN

O

NH

HNO

PPTA (poly(para-phenylene-amide)

O

O

O

O

O

O

O

O

PET (polyethyleneterephthalate)

O

O

O OO

O

Makrolon

O O O O O O O O O O

POM (poly-oxymethylene)

OSi

OSi

OSi

OSi

OSi

OSi

OSi

OSi

OSi

PDMS (polydimethylsiloxan)

PIB (polyisobutylene)

Economic importance

90%

Plastics-

production in

dependence of

time

Further Modification of Polymer Compounds

Polymer Compound

chemical modificationphysical modification

-polymer-analogousreactions

-chemical blowing

mixing

Additives:-Plastizers-Flame retardants-Stabilizers-Fillers-Blowing agents

other Polymers:Polymer blends

shaping

post-reactor phase

preperation forprocessing

processing phase

Additives

Plasticizers Stabilizers Fillers Antistaticagents

Blowingagents

thermal light mechanic active inactive

flameretardant

heat

atmosphere

oxygen moisture

FibersUV-absorbers

Anti-oxidants

hydro-phobics

Lead-organyls

extenders:fill volume lower the price

color pigmentsanti-shrinkingself-healing

-act as "poor solvent" forthe polymer-decrease the operatingtemperature for shaping

absorbe heat by de-composing into less-reactive products

internal extinguishers:Al(OH)3 H2OXBrn n BrXPn "PO"coating

Mechanical behaviour of polymers

Mechanical Behaviour of Polymer compounds

(energy-elastic) (visco-elastic) (viscous)

solid liquidthermoplast

Newton-Modell:

σ = ηdεdt

Hook-Modell:

σ = E ε

Voigt-Modell:

ε = ε1 = ε2

σ = σ1 + σ2

Maxwell-Modell:

σ = σ1 = σ2ε = ε1 + ε2

0

0,2

0,4

0,6

0,8

1

1,2

0 50 100 150 200 250 300 350 400 450

time

ten

sio

n σσ σσ solid

thermoplast

liquid

0

0,2

0,4

0,6

0,8

1

1,2

0 50 100 150 200 250 300 350 400 450

time

elo

ng

ati

on

εε εε

solid

thermoplast

liquid

0

0,2

0,4

0,6

0,8

1

1,2

0 50 100 150 200 250 300 350 400 450

time

ten

sio

n σσ σσ solid

thermoplast

liquid

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 50 100 150 200 250 300 350 400 450

time

elo

ng

ati

on

εε εε

solid

thermoplast

liquid

Elastomere

σ

α

L0

L = n L0 sin(α/2)

Reforming driving force:multiple microstates of random coil

(solely entropic!)

Mechanical Behaviour of Polymer compoundsT

ensi

on σ

Rel. Elongation ε

oriented

(a)

(b)(c)

(d)

(e)

Stabilization of polymer compounds towards tension by orienting streching

Tg Tm

Mechanical Behaviour of Polymer compounds

elastomer

melt

Log(E

/(N

m-2

))

elastomer

HookVoigt-

Maxwell

Newton-

like ?!

elongation in %

Non-Newtonian behaviour in polymeric melts

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2

0 2 4 6 8 10 12 14 16 18 20

shear rate dεεεε/dt

vis

co

sit

y ηη ηη

Newtonian behaviour

Polymer compound

shear rate ε

relaxation rate 1/λ

Deborah number De =chain relaxation time

processing time=

λtP

= λ ε

De << 1 De = 1 De >> 1

σ = ηdεdt

= η εNewtonian:

σ = ηdεdt

= η ε

Polymer:

σ = η(ε) ε = m(T) ε n, 0 < n < 1

for De << 1

for De ≈ 1 m(T) = m0 e-a (T-T0)

Shear thinning effect!

Non-Newtonian behaviour in polymeric melts

L

R

p1

p2

∆p = p1 - p2

flow Q

Newtonian flow field: Polymer compound flow field:

vz(r) =∆p

4 L η R2 - r

2vz(r) =

∆p

4 L mR

1+1/n - r

1+1/n1

1 + 1/n

1/n

σ = ηdεdt

= η ε σ = η(ε) ε = m ε n, 0 < n < 1

-1774600

-1574600

-1374600

-1174600

-974600

-774600

-574600

-374600

-174600-1333 -833 -333 167 667 1167

radius r

vz(

r)

-738000

-638000

-538000

-438000

-338000

-238000

-138000

-38000-848 -648 -448 -248 -48 152 352 552 752

radius r

vz(

r)

Reduction during extrusion Swell during extrusion

Q =π R4

8 L η∆P Q =

π R3

1/n +3 ∆P

2 m L

1/nR 1/n

vz(r)

Hagen-Poisseuille

Classification of Polymer Processing

Classification of Polymer Processing

1. Die forming (fiber, film, sheet, tube, wire)

2. Calendering and coating (knife, roll)

3. Mold coating (powder, rotation)

4. Molding and casting (injection, transfer, react. inj.)

5. Strech shaping (thermoforming, blowmolding)

continuous

cyclic

The Extruder

The Navier-Stokes equation (incompressible fluids)

dv

dtρ = P + η ∆v + ρ g

acceleration of fluid

externalpressure

internalpressure

gravitationalpressure

The velocity field of an extruder

x

y

zux

y/h

0

uz 0

x/W

= P + η ∆v

externalpressure

internalpressure

0

The Extruder

Brinkmann number:

Br =

=

Viscous dissipation

Heat transport

η V02

k (Ta - Tb)

Solid bed profile

The Extruder

The die design

Rules of thumb:• avoid thick sections

• minimize the number of hollow sections

• generate profiles with constant wall thickniss.

The Extruder

The coat hanger die (films, sheets, foils)

W

xα

R

extrudate extrudate

R(x) =(3 + s)/π * h

2n+1 (W-x)

n

2n (s + 2)

n * sin(α)

1/(3n + 1)

for uniform flow in the land

(s = 1/n)

(shear thinning effect)

diebarrel with screw

Characteristic curve of an extruder

die shape

m.

∆p

open

discharge

closed

discharge

N, H

2 N, H.. N: screw rate

H: channel depth of screw

.N, 2 H.

Non-Newtonian flow

Newtonian flow

m = ∆Pk

m = k' ∆P1/n

∆ps ∆pd

m.

HWDB

Ls LD

RD

Characteristic curve of an extruder

die shape

Mixing of polymers

Compatibility of polymers

16666666666LDPE

1

LDPE

16665666666HDPE

1666666666PP

161563266PVC

15665666POM

1161144PMMA

162256PC

16645PA

1166ABS

166SAN

16HIPS

1PS

HDPEPPPVCPOMPMMAPCPAABSSANHIPSPS

1 = very compatible, 6 = incompatible

Hildebrand-parameters

∆Hmix = Vges x1 x2 (δ1 - δ2)2

Two polymers mix with each other if ∆δ ≤ 0.1(cal cm-3)½

(J cm-3)0.5

Polyethylene 15,8-17,1

Polystyrene 16,8-18,8

Poly(methylmetacrylate) 16,0-16,6

Polypropylene 17,4-19,0

Poly(vinylchloride) 19,2-22,1

Nylon 66 25,8-29,1

Polyacrylonitrile 25,6-31,5

Poly(propylenoxid) 15,4-20,3

δ2 = ρ Σ Fi/Mi

structure unit Fi Mi

-CH3 303 15

-CH2- 269 14

C(quart) 65,5 12

-CH(CH3)- 479 28

-C(CH3)2- 672 42

-CH=CH- 497 26

-OH 462 17

-O- 235 16

-CO- 538 28

-COOH 1000 45

-COO- 668 44

Mixing of polymers

Mixing mechanisms

Distributive mixing Dispersive mixing

Distributive mixing

Dispersive mixing

notmixed

well-mixeddispersively and

distributivelymixing = tension + reorientation

Mixing of polymers

distributive dispersive

Mixing of polymers

Flow number: λ =

Capillary number: Ca = Deviatoric stress

Surface tension=

τ Rσs

γγ + ω

..

Mixing devices

Injection molding

Injection molding

A

B

C

D

A

B

C‘/C

D

C‘

A

BC‘C

5. S

crew

back

(ch

eck

valv

eopen)

Injection molding

Injection blow molding

Extrusion blow moldingParison programming

by die-temperature as function of t

by die opening as function of t

by screw rate as function of t

Film blowing

Biaxial stretching!

Film blowing

Blow-up ratio:

BR =

draw ration:

DR =

ratio of film thickness:

h0/hf = DR BR

Rf

R0

vf

v0

Rotational molding

Thermoforming

plug-

assisted

vacuum

Calendering

The velocity field of a calender

R

h0 h1

x

y

h0 h1h-1

h2h2

N

vx(y) = 2 πNR + y2 - h2

h12

1 -h1

h

h1

h

23

2

h = h0 + R - √R2 - x2

dP

dx= η

d2vx

dy2

Calendering

n: viscosity-power-law index

Ribbing in roll coating

Ca = η N

σsN: roll rate

Fiber-spinning

Fiber-spinning

Take-up

Final take-up

Heater:Stretching/molecularorientation

Extruder

Spinneret

Fiber-spinning

Fiber-spinning

DR = vz/v0 De = 3(n-1)/2 (m/G) (v0/L)

viscosity η = m ε(n-1).

Thermosets/Reactive molding

Thermosets/Reactive molding

curing byheatmixinglightmoisture

hv

Welding

thermal friction

Ruhland Polymer Processing

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