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Polymer Rheology
P Sunthar
Department of Chemical EngineeringIndian Institute of Technology, Bombay
Mumbai 400076, [email protected]
05 Jan 2010
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Introduction Phenomenology Modelling
Outline of the Lecture
1 Introduction
2 Phenomenology
3 Modelling
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Outline of this Section
1 IntroductionNature of Polymeric LiquidsPolymer Rheology
2 Phenomenology
3 Modelling
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Questions to Ask for a New Phenomena
Fundamental Questions
What makes the phenomena different ?
How to represent in terms of a mathematical model ?
Are there distinct laws or rules for the behaviour ?
Are there other known phenomena that obey similar laws ?
What role has this played in the current state of theuniverse ?
Application oriented questions
Can it be employed for betterment of quality of life?
Consequences to processes that manipulate the material ?
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Polymeric Liquids
Definition
Liquids that contain Polymers
Liquids: Materials that flow
Simple Liquids
Definition: Material that does not support shear stress atrest
Complex fluids
Liquid (viscous) and Solid (elastic) like behaviourDynamic properties are not thermodynamic constantsEg: Viscosity = f(), = f(t).
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d h l d ll f l d l h l
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Chemical Nature
Long chain monomers joined by chemical bonds
Large molecular weights: 1000 to 109
Linear or branchedNatural (DNA, Proteins) or Synthetic
Linear
Branched
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I t d ti Ph l M d lli N t f P l i Li id P l Rh l
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Physical Nature
Linearity of large portions: L dFlexibility: Not rigid long rods
Is NOT: Suspension ofpolystyrene beads
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
States of Polymeric Liquids
Polymer Melts
T> Tg. Eg HDPE
ConcentratedSolution
Semi-dilute solution
Dilute Solution, Eg:Polystyrene incyclohexane
Polymer Melt
Semi-DiluteSolution
Concentrated
Solution
Dilute Solution
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Role of Temperature
Noodle SoupWhat is the difference between apolymeric liquid to us and a hugebowl of noodles to a Giant?
Noodles are linear, Soup is like asolvent.
Difference Random lineartranslating motion
Noodles is a zero temperature(Frozen) system
Polymeric liquid is a finitetemperature system
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Role of Temperature
Noodle SoupWhat is the difference between apolymeric liquid to us and a hugebowl of noodles to a Giant?
Noodles are linear, Soup is like asolvent.
Difference Random lineartranslating motion
Noodles is a zero temperature(Frozen) system
Polymeric liquid is a finitetemperature system
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Role of Temperature
Noodle SoupWhat is the difference between apolymeric liquid to us and a hugebowl of noodles to a Giant?
Noodles are linear, Soup is like asolvent.
Difference Random lineartranslating motion
Noodles is a zero temperature(Frozen) system
Polymeric liquid is a finitetemperature system
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Introduction Phenomenology Modelling Nature of Polymeric Liquids Polymer Rheology
Role of Temperature
Noodle SoupWhat is the difference between apolymeric liquid to us and a hugebowl of noodles to a Giant?
Noodles are linear, Soup is like asolvent.
Difference Random lineartranslating motion
Noodles is a zero temperature(Frozen) system
Polymeric liquid is a finitetemperature system
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gy g y q y gy
Need for Study of Polymeric Liquids
Polymer Processing
Reactors and MixersExtrusion MouldingFilmsFibre Spinning
Consumer Products
ShampooPastesPrinting InksPaintsLamination and Coating
Food Additives
GumsGlycerine
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gy g y q y gy
Nobel in Physics
Pierre-Gilles de Gennes \d-zhen\19322007
Nobel in Physics: 1991
Nobel for generalising theory of phase
transitions to polymers and liquidcrystals.
Scaling Theory in Polymeric liquids
Reptation in Polymer Melts
Coil-stretch transitions in Extensionalflows
Polymer induced Turbulent dragreduction
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Polymer Rheology
Industrial Flows are Complex
GeometryPolydisperse and Multi-component
Understand Response to Simple flows (Viscometric)
Shear
ElongationalUnderstand Response of Simple Materials (reproducible)
Single or two component systemsMonodisperse molecular weightDilute Systems
Melts (Pure polymer)
Rheology
Science of Deformation and Flow
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Polymer Rheology
Industrial Flows are Complex
GeometryPolydisperse and Multi-component
Understand Response to Simple flows (Viscometric)
Shear
ElongationalUnderstand Response of Simple Materials (reproducible)
Single or two component systemsMonodisperse molecular weightDilute Systems
Melts (Pure polymer)
Rheology
Science of Deformation and Flow
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Rheology Core: Viscosity and Elasticity
What is Deformation?
Relative displacements withinmaterialMeasured by Deformation(Strain): Resisted by Elasticity
G =xy
What is Flow?
Continuous Relative motion
Measured by rate ofDeformation (Strain rate): Resisted by viscosity
=xy
Deformation
Flow
Shear
Elongation
Elongation
Shear
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Polymers, Soft Matter, Complex Fluids
Liquid Viscosity Modulus
(Pa.s) G (Pa)Water 103 109
An Oil 0.1 108
A polymer solution 1 10
A polymer melt 105
104
A glass > 1015 > 1010
Soft Materials
Elasticity has Entropic Origin (Not Energetic origin as forsolids)G proportional to kBTtimes number concentration offlexible unitsPhysical feel of softness, intermediate G
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Outline of this Section
1 Introduction
2 Phenomenology
Visual PhenomenaLinear viscoelasticityNonlinear Phenomena
3 Modelling
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Weissenberg Rod Climbing Effect
Rod rotating in a polymericliquid
Fluid climbs the rod
Common fluids that show
Gum solutionsBatter (with egg white)
Due to Normal stress differences
psidot, Youtube:npZzlgKjs0I
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Extrudate or Die Swell
POLYOXTM
(PEO, PEG) SolutionEjected from a syringe
Significant increased diameterupon exit
Also known as Barus EffectNewtonian fluids diameter doesnot change significantly
Due to Normal stress differences
psidot, Youtube:KcNWLIpv8g
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Tubeless Syphon
Elongational flowStresses hold up against gravityand surface tension
After initial pouring (suction) afree-surface syphon ismaintained.
Also known as Fano Flow
psidot, Youtube:aY7xiGQ-7iw
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Drop Formation
Jet and Drop breakup
Elongational flow
Dilute PEO solutionElongational stresses holdagainst surface tension andgravity driven breakup
Satellite drop
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T b l D R d i
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Turbulent Drag Reduction
Small amounts of polymers (ppm) to water
Fluid drag in pipelines reduced significantlyTransportation of liquids.2
Firefighting: Farther throw
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C i Fl
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Contraction Flow
Sudden contraction low Re Flow
Elongational flow
Lip-vortices
Corner Vortices
Newtonian
Polymeric
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R l ti Ti
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Relaxation Times
Observable microscopic time scale,
Simple liquids 1015 secTime for large scale changes in polymer configurations
Microseconds to minutes
Similar order of macroscopic observation period andprocessing rates
Configurations altered by thermal energy
Elasticity
is an Elastic time scale
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Di i l N b
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Dimensionless Numbers
Macroscopic time scales
Kinematic (rate of deformation)time scale
for shear flows for extensional flows
Dynamic time scale, tdTime to traverse a geometry orsectionPulsatile flowMay not be known apriori
Weissenberg NumberFor Viscometric flows(with kinematictimescale)
Wi = or (1)
Deborah Number
For complex flows (with
dynamic timescale)
De =
td(2)
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M l l W i ht D d f R l ti Ti
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Molecular Weight Dependence of Relaxation Time
Large scale motion depends on M
Scaling dependence for a class of liquids
Class Scaling
Dilute solution in poor solvent M1.0Dilute solution in -conditions M1.5Dilute solution in good solvent M1.8Semi dilute solution chain
M2
Entangled Melts rep M3.4
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Linear Response
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Linear Response
Response to small imposed deformation
Linearity means additive responseLinearity of Response inViscous propertiesElastic properties
Linear Viscoelastic Properties
Mainly Polymer physics
Liquid Viscosity Relaxation time Modulus (Pa.s) (s) G (Pa)
Water 103 1012 109
An Oil 0.1 109 108
A polymer solution 1 0.1 10A polymer melt 105 10 104
A glass > 1015 105 > 1010
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Rheological Tests
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Rheological Tests
Oscillatory
Controlled StressControlled Strain
Stress RelaxationAfter step strainAfter cessation of shear flow
Creep (Constant stress applied)
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Zero shear rate viscosity
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Zero-shear rate viscosity
Linear response (
0)
Micro-structural information
Dilute: c < c
Intrinsic Viscosity (inverseconcentration)
[]0 lim0
[] lim0
limc0
sc s
[]0 M
Semi-dilute: c < c < c
sp0 = 0 sEntangled: c > c
1
2
14/3
SemiDilute
Entangled
Dilute
log c
log
sp0
c
c
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Small Amplitude Oscillatory Tests
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Small Amplitude Oscillatory Tests
G: Elastic Modulus; G: Viscous
Rubbery/PlateauGlassy
Viscous Transition to Flow
log()
log(G
)
log
(G
)
1
G
G
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Plateau Modulus with Molecular Weight
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Plateau Modulus with Molecular Weight
Increased M
IncreasedEntanglements
Rubber like network
Entanglements are likecross-links
Crosslinked Polymer
Entangled Melt
Unentangled Melt
log()
log(G
)
G0N
log()
log(G
)
M
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Characteristic Relaxation Time
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Characteristic Relaxation Time
Low Frequency response always Viscous
G
> G
Wait long enough, even Mountains will flow!
Low frequency scaling for all polymeric liquids (Maxwellmodel)
G G22
G 0 Cross over frequency or Characteristic relaxation time
=
G
G
Zero-shear rate viscosity estimate
0 G
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Stress Relaxation
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Stress Relaxation
Small step strain is linearResponse G(t) = xy/
G(t) Fourier Transform G()Small t large : ElasticLarge t small : Viscous (flow)0 = Area under the G(t) curve
0 G(0)for exponentially decaying tail:expt/
Reptation
Rouse
t
G(t)
G0N
e
rep
Reptation
RouseMonomer
log t
log
G(t)
G0N
0 e
rep
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Shear Thinning
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Shear Thinning
Decrease in viscosity upon shear
More pronounced inconcentrated solutions thandilute
Intermediate shear rates: PowerLaw Fluid
Worm-like Micelles LivingPolymers abrupt changes
Cylindrical micelles
Breaking and formingLarge shear rates most aresmall fragments
2
2
5 1
4
0Dilute Solution
Concentrated solution
Wormlike Micelle
log
log
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Normal Stresses
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Normal Stresses
Simple liquids: Normal stress isthe pressure
Complex fluids: Microstructureleads to flow induced anisotropy
Normal Stresses:
N1 = xx yyN2 = yy zz
Shear thinning for 1 = N1/2N2 is usually 0 for polymericliquids
log
log
,
N1
N1
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Extensional Viscosity
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Extensional Viscosity
Stretching and Compressing flowfield
Contraction flowStagnation pointsSpinning of fibres
Break up of jets to dropsBlow moulding
Elongational viscosity E
Experiments: Transient (not
Steady) +
E Tensile StressGrowth Coefficient
Strain ( t) hardening
log t
log
+ E
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Trouton Ratio
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Ratio of extensional to shearviscosity
TR =E()
(3 )Newtonian Liquids: TR = 3
Solutions
Branched Melts
Linear Melts
log , log
log
logE
E
3
3
100
1000
Melts
Inelastic liquid
Dilute Solution
log , log
logTR
1/2
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Outline of this Section
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1 Introduction
2 Phenomenology
3 ModellingBasicsShear ThinningNormal Stresses
Extensional Viscosity
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Dilute Solution and Colloidal Suspensions
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p
Spherical particles only on the
averageLike Porous particles (fluid canpass through)
Suspension viscosity (Einstein)
= s (1 + 2.5 )
Dilute polymer solution
= s1 + U
R
UR = 1.66 Zimm theory
UR 1.5 Molecular simulationsand Experiments
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Tube Model
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Chains cannot cross each other
Entanglement is like a crosslinkMotion between entanglements
Pervaded volume: Tube [SamEdwards, 1967]
Primitive path
Melt
Entanglement
Tube
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Reptation and other Relaxation Times
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p
Smallest time 0: Monomer
relaxationIntermediate e: Rouserelaxation betweenentanglements
Largest rep
: Reptation orrelaxation along the lengthof the tube [P G de Gennes,1971]
Diffusion time of polymer
is reptation time
Monomer
Rouse
Reptation
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Relaxation Modulus and Reptation
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Relaxation after step strain
Initial monomer relaxation 0
Plateau region, relaxationbetween entaglements
eTerminal region, reptation rep
Viscosity related to reptation time
0
rep G(0)
Reptation
Rouse
t
G(t)
G0N
e
rep
Reptation
RouseMonomer
log t
log
G(t)
G0N
0 e
rep
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Shear Thinning in Melts
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Entangled state (rubber like) high viscosity
Entanglements are constraints for motion
Shear flow releases some constraints
High shear rate chains align along flow
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Understanding Normal Stress Difference
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Anisotropy in microstructureEquilibrium: spherical pervadedvolume
Shear Flow: Stretch and Tumble
Shear pervaded volume: inclinedellipsoidal
Restoring force in normal planesare different
Normal stress difference
Shear
Equilibrium
yy
xx
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Extensional Viscosity in Dilute Solutions
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Equilibrium: Spherical pervaded
volumeSmall extension rates < 0.5,small deformation
Large extension rates: stretchingof chain, larger stress
Equilibrium
Small Extn.
LargeExtn.
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Extensional Viscosity in Melts
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Reptation
Entanglements and Confining
tubeTube orientation
Rouse time: Chain Stretching
Reptation Orientation Stretching
Fully
Stre
tched
log
log
E
1rep
1e
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