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Polymer Rheology

P Sunthar

Department of Chemical EngineeringIndian Institute of Technology, Bombay

Mumbai 400076, [email protected]

05 Jan 2010
http://localhost/var/www/apps/conversion/tmp/scratch_2/[email protected]://find/http://localhost/var/www/apps/conversion/tmp/scratch_2/[email protected]


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Introduction Phenomenology Modelling

Outline of the Lecture

1 Introduction

2 Phenomenology

3 Modelling

P Sunthar (IIT Bombay) Polymer Rheology ComFlu 2009 2 / 44
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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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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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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).


d h l d ll f l d l h l
http://find/


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Chemical Nature

Long chain monomers joined by chemical bonds

Large molecular weights: 1000 to 109

Linear or branchedNatural (DNA, Proteins) or Synthetic

Linear

Branched


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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Physical Nature

Linearity of large portions: L dFlexibility: Not rigid long rods

Is NOT: Suspension ofpolystyrene beads


I t d ti Ph l M d lli N t f P l i Li id P l Rh l
http://find/http://goback/


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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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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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Role of Temperature







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Role of Temperature







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Role of Temperature









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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


http://find/


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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

Complex mechanical response and microstructureP Sunthar (IIT Bombay) Polymer Rheology ComFlu 2009 14 / 44

Introduction Phenomenology Modelling Visual Linear Nonlinear
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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


http://www.youtube.com/watch?v=npZzlgKjs0Ihttp://www.youtube.com/watch?v=npZzlgKjs0Ihttp://www.youtube.com/watch?v=npZzlgKjs0Ihttp://www.youtube.com/watch?v=npZzlgKjs0Ihttp://video/weissenberg-effect.mpeghttp://video/weissenberg-effect.mpeghttp://find/


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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


http://www.youtube.com/watch?v=KcNWLIpv8ghttp://www.youtube.com/watch?v=KcNWLIpv8ghttp://www.youtube.com/watch?v=KcNWLIpv8ghttp://www.youtube.com/watch?v=KcNWLIpv8ghttp://video/die-swell.mpeghttp://find/http://goback/


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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


http://www.youtube.com/watch?v=aY7xiGQ-7iwhttp://www.youtube.com/watch?v=aY7xiGQ-7iwhttp://www.youtube.com/watch?v=aY7xiGQ-7iwhttp://www.youtube.com/watch?v=aY7xiGQ-7iwhttp://video/tubeless-syphon.mpeghttp://video/tubeless-syphon.mpeghttp://find/


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Drop Formation

Jet and Drop breakup

Elongational flow

Dilute PEO solutionElongational stresses holdagainst surface tension andgravity driven breakup

Satellite drop



T b l D R d i
http://images/peo-water-drop.htmlhttp://find/


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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



C i Fl
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Contraction Flow

Sudden contraction low Re Flow

Elongational flow

Lip-vortices

Corner Vortices

Newtonian

Polymeric



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



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)



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



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



Rheological Tests
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Rheological Tests

Oscillatory

Controlled StressControlled Strain

Stress RelaxationAfter step strainAfter cessation of shear flow

Creep (Constant stress applied)



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

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SemiDilute

Entangled

Dilute

log c

log

sp0

c

c



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



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



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



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



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



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



Extensional Viscosity


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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



Trouton Ratio
http://find/


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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

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Introduction Phenomenology Modelling Solution Viscosity Normal Stresses Extensional Viscosity

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1 Introduction

2 Phenomenology

3 ModellingBasicsShear ThinningNormal Stresses




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



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



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



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



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



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



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.



Extensional Viscosity in Melts
http://find/


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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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