Chapter 9: Rheological and Mechanical Properties of Polymers

AE 447: Polymer Technology, Dr. Cattaleeya Pattamaprom

Fundamentals of Rheology Seminarby

Dr. Abel Gaspar-Rosas

TA Instruments – Waters, Inc.

April, 2004

Thailand

Adapted from the workshop on

Outline

1. Rheology – Introduction

2. Elasticity, Viscosity and Viscoelasticity

3. Rheology tests• Steady-state flow

• Stress Relaxation

• Creep Recovery

• Oscillatory Tests– Dynamic Frequency sweep

– Dynamic Temperature ramp

4. Molecular Properties vs. Rheology of Polymers

5. Mechanical Testing

Definition of Rheology

• Rheology is the science of deformation and flow of matter.

รี�โอโลยี� (Rheology): ศาสตร์�ของร์โอโลยี เป็�นศาสตร์�ที่�กล�าวถึ�งสมบั�ต�การ์ไหลหร์ อการ์เสยีร์!ป็ ร์โอโลยีของพอล�เมอร์�ส�วนใหญ่�ม�กกล�าวถึ�งค่�าโมดู!ล�ส และค่�าค่วามหน ดู

Simple Shear Deformation and Shear Flow

= FA

y0

x(t)

1 d x(t)y0 d t

Strain, =

x(t)y0

Strain Rate, = . Vy0

Shear Modulus, G =

V

y

x

Az

Shear Deformation

Viscosity, =.

. = t

Range of Rheological Material Behavior

Rheology: The study of deformation and flow of matter.

Range of material behaviorSolid Like ---------Liquid Like

Ideal Solid-------------Ideal Fluid

Classical Extremes

Viscous liquidElastic solid

Viscoelastic

Classical Extremes: Elastic Solid

1678: Robert Hooks develops his “True Theory of Elasticity”

“The power of any spring is in the same proportion with the tension thereof.”

Hooke’s Law: = G or (Stress = G x Strain)

where G is the RIGIDITY MODULUS

.

G is constant

Classical Extremes: Viscosity

1687: Isaac Newton addresses liquids and steady simple shearing flow in his “Principia”

“The resistance which arises from the lack of slipperiness of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another.”

Newton’s Law: = is constant

whereis the Coefficient of Viscosity

Response for Classical Extremes

Purely ElasticResponse

Hookean Solid = G

Purely ViscousResponse

Newtonian Liquid =

For the classical extremes cases, what only matters are the values of stress, strain and strain rate. The response is independent of the loading.

Spring Dashpot

OverviewOverviewabout the different rheological material behaviorabout the different rheological material behaviorilustrated by the use of…ilustrated by the use of…

IdealIdeal viscousviscous

Oil, SolventOil, Solvent

NewtonNewton‘‘s laws law

[Pas] viscosity shear [Pa] stress shear

[1/s] rate shear

IdealIdeal elasticelastic

Glass, SteelGlass, Steel

HookeHooke‘‘s laws law

[Pa] G modulus shear

viscoelasticviscoelasticfluid / solidfluid / solid

Coatings, Food, Cosmetics,Coatings, Food, Cosmetics,PolymersPolymers

Apparent Yield Point, Apparent Yield Point, Thixotropy, Thixotropy, ……

Physica Messtechnik Gmbh Vor dem lauch 6, 70567 Stuttgart, Germany Internet:http://www.physica .de

Viscoelasticity Defined

Range of Material BehaviorSolid Like ---------- Liquid Like

Ideal Solid ----- Most Materials ----- Ideal FluidPurely Elastic ----- Viscoelastic ----- Purely Viscous

Viscoelasticity: Having both viscous and elastic properties

Realistic polymer material

- Materials are in between Elastic solid and Newtonian liquid called “viscoelastic”

- Some energy stored, some dissipated.

- Some time independent, some time dependent.

A typical viscoelastic effect is tackiness (with long strings) which is not occuring with purely viscous liquid (example: water),or purely elastic solid (example: stone)

Physica Messtechnik Gmbh Vor dem lauch 6, 70567 Stuttgart, Germany Internet:http://www.physica .de

Viscoelastic FluidsViscoelastic Fluids

Viscoelastic behavior, illustrated by use of a dashpot and a springViscoelastic behavior, illustrated by use of a dashpot and a spring

at restat rest

under shearunder shear

PolymersPolymers

Macromolecules are entangled

and have spherical shapes

high viscosity

Macromolecules are deformed and disentangled

low viscosity

Physica Messtechnik Gmbh Vor dem lauch 6, 70567 Stuttgart, Germany Internet:http://www.physica .de

Newtonian and Non-Newtonian Behavior of Fluids

Newtonian Region Independent of

Non-Newtonian Region

= f()

1.0001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000

shear rate (1/s)

1.000E5

10000

(P

a.s)

1.000E5

1.000

10.00

100.0

1000

10000

(P

a)

Shear thinningPseudo-plastic

Zero-shear viscosity (o)

Elastic Modulus vs. Temp.

Area 1: Viscous state: Area 2: Rubbery stateArea 3: Leathery stateArea 4: Glassy state

E = stress = F/A = strain = dL/LE = elastic modulus

E

Temp

brittle

leathery

rubbery

viscous

4

3

2

1

Linear and Non-Linear Stress-Strain Behavior of Solids

Non-Linear Region

G = f()Linear Region G is constant

G

1000.00.010000 0.10000 1.0000 10.000 100.00% strain

1000

1.000

10.00

100.0

G' (

Pa

)

100.0

0.01000

os

c. s

tres

s (

Pa

)

Viscosity and Viscoelasticity

Viscosity: Definition

Viscosity is . . . . synonymous with internal friction. resistance to flow.

Variables that Affect Viscosity –for polymer

• Shear Rate - Molecular Weight

• Time of Shearing

• Temperature

• Pressure

• Surface Tension

Characteristic Diagrams for Newtonian Fluids,

Pa

s or Pa

Pa.

ss

Ideal Yield Stress(Bingham Yield)

Viscosity: Temperature dependence

100.020.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

temperature (Deg C)

10000

10.00

100.0

1000

visc

osi

ty (

Pa.

s)

Summary of Types of Flow

Shea

r St

ress

,

Newtonian

Shear Rate,

Bingham Plastic(shear-thinning w/yield stress)

Shear Thickening (Dilatent)

y

Shear Thinning (Pseudoplastic)

Bingham (Newtonian w/yield stress)

• NewtonianNewtonianIdeal viscous (e.g.: oil, solvent)Ideal viscous (e.g.: oil, solvent)

• Shear thinningShear thinning(e.g.: typical food, cosmetics, coatings, polymers, …) (e.g.: typical food, cosmetics, coatings, polymers, …)

• Shear ThickeningShear ThickeningShear thickening (e.g.: PVC plastisol & paper coatings under high Shear thickening (e.g.: PVC plastisol & paper coatings under high shear cond.)shear cond.)

Viscosity vs. Shear RateViscosity vs. Shear RateResult:Result: Rheological material behaviourRheological material behaviourShear stress & viscosity as a function of the shear rateShear stress & viscosity as a function of the shear rate

Newtonian and Non-Newtonian Behavior of Fluids

Newtonian Region Independent of

Non-Newtonian Region

= f()

1.0001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000

shear rate (1/s)

1.000E5

10000

(P

a.s)

1.000E5

1.000

10.00

100.0

1000

10000

(P

a)

Idealized Flow Curve - Polymers

1.001.00E-5 1.00E-4 1.00E-3 0.0100 0.100

shear rate (1/s)

10.00 100.00 1000.00 1.00E4 1.00E5

log

Molecular Structure Compression Molding Extrusion Blow and Injection Molding

0 = Zero Shear Viscosity0 = K x MW3.4

Measure in Flow Mode onAR1000/AR500

Extend Range with Oscillation

& Cox-Merz

Extend Range with Time-

TemperatureSuperposition (TTS)

& Cox-Merz

First Newtonian Plateau

Second Newtonian Plateau

Power Law Region

Comparison of Newtonian & Shear Thinning Samples

10001.000E-6 1.000E-4 0.01000 1.000 10.00 100.0

shear rate (1/s)

10000

1.000E-3

0.01000

0.1000

1.000

10.00

100.0

1000

visc

osi

ty (

Pa

.s)

Xanthan/GellanFructose Soln.

Standard oil A

Standard oil B

Non-Newtonian, Time Dependent Fluids

ThixotropyA decrease in apparent viscosity with time under

constant shear rate or shear stress, followed by a gradual recovery, when the stress or shear rate is removed.

RheopexyAn increase in apparent viscosity with time under

constant shear rate or shear stress, followed by a gradual recovery when the stress or shear rate is removed. Also called Anti-thixotropy or negative thixotropy.

Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., 1989. ISBN 0-444-87469-0

Non-Newtonian, Time Dependent Fluids

time

Vis

cosi

ty

Thixotropic

Rheopectic

Shear Rate = Constant

Time-Dependent Viscoelastic Behavior:Solid and Liquid Properties of "Silly Putty"

T is short [< 1s] T is long [24 hours]

Deborah Number [De] = /

Storage and Loss of Viscoelastic Material

SUPER BALL

TENNISBALLX

STORAGE

LOSS

Rheology Tests

Some Types of Rheometers• Typical Rheometer: Low shear rate/Oscillatory

• Capillary Rheometer: High shear rate

Geometries: Geometries: Typical RheometerTypical Rheometer

Max. 3°Max. 3°

Delta < 1.2Delta < 1.2

0.25mm < gap < 2mm0.25mm < gap < 2mm

Max. 3°Max. 3°

Delta < 1.2Delta < 1.2

Ref.: Physica

Rheology:Choosing Tests and Conditions

A series of logarithmic stress steps allowed to reach steady state, each one giving a single viscosity data point:

Shear ThinningRegion

Shear Rate, 1/s

Vis

cosi

ty

Shear Rate

Time

(d dt)

1. Stepped Ramp or Steady-Shear Flow

Polyethylene Rheology @ 150 C

10.001.000E-4 1.00E-3 0.01000 0.1000 1.000

shear rate (1/s)

1000000

1000

10000

100000

viscosity (P

a.s)

HDPE

LDPE

LLDPE

Typical steady shear flow experiment

Idealized Full Flow Curve - Polymers

1.001.00E-5 1.00E-4 1.00E-3 0.0100 0.100

shear rate (1/s)

10.00 100.00 1000.00 1.00E4 1.00E5

log

Molecular Structure Compression Molding Extrusion Blow and Injection Molding

0 = Zero Shear Viscosity0 = K x MWc 3.4

Measure in Flow Mode onAR1000/AR500

Extend Range with Oscillation

& Cox-Merz

Extend Range with Time-

TemperatureSuperposition (TTS)

& Cox-Merz

First Newtonian Plateau

Second Newtonian Plateau

Power Law Region

At very high shear rate Melt fracture

Higher Shear Rate

2. Stress Relaxation Experiment

Strain is applied to sample instantaneously (in principle) and held constant with time.Stress is monitored as a function of time (t).

Str

ain

time0

Stress Relaxation Experiment

Response of Classical Extremes

time0

time0

stress for t>0is constant

time0

stress for t>0 is 0

Str

ess

Str

ess

Str

ain

Hookean Solid Newtonian Fluid

Stress Relaxation Experiment (cont’d)

Response of Material

For small deformations (strains within the linear region) the ratio of stress to strain is a function of time only.

This function is a material property known as the STRESS RELAXATION MODULUS, G(t)

G(t) = (t)/

Stress decreases with timestarting at some high value and decreasing to zero. S

tres

s

time0

3. Creep Recovery Experiment

Stress is applied to sample instantaneously, t1, and held constant for a specific period of time. The strain is monitored as a function of time (t).The stress is reduced to zero, t2, and the strain is monitored as a function of timet.

Str

ess

timet1 t2

Creep Recovery Experiment

Response of Classical Extremes

– Stain for t>t1 is constant– Strain for t >t2 is 0

time

Str

ain

time

Str

ain

time

– Stain rate for t>t1 is constant– Strain for t>t1 increase with time– Strain rate for t >t2 is 0

t2

Str

ess

t1

t1 t2t2t1

Creep Recovery Experiment:Response of Viscoelastic Material

Reference: Mark, J., et.al., Physical Properties of Polymers ,American Chemical Society, 1984, p. 102.

Creep 0

timet 1 t2

RecoverableStrain

Recovery = 0 (after steady state)

/

Str

ain

Strain rate decreases with time in the creep

zone, until finally reaching a steady state.

In the recovery zone, the viscoelastic fluid recoils, eventually reaching a equilibrium at some small total strain relative to the strain at unloading.

4.Oscillatory Testing of Polymers

(Dynamic Mechanical Tests)

Dynamic Mechanical Testing

Deformation

Response

Phase angle

An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample.

The material response (strain or stress) is measured.

The phase angle , or phase shift, between the deformation and response is measured.

Dynamic Mechanical Testing Viscoelastic Material Response

Phase angle 0° < < 90°

Stress

Strain

DMA Viscoelastic Parameters:The Complex, Elastic, & Viscous Stress

The stress in a dynamic experiment is referred to as the complex stress *

Phase angle

Complex Stress, *

Strain, * = ' + i"

DMA Viscoelastic Parameters

The Elastic (Storage) Modulus: Measure of elasticity of material. The ability of the material to store energy.

G' = (stress*/strain)cos

G" = (stress*/strain)sinThe Viscous (loss) Modulus: The ability of the material to dissipate energy. Energy lost as heat.

The Complex Modulus: Measure of materials overall resistance to deformation.

G* = Stress*/StrainG* = G′ + iG″

Tan = G"/G'

Tan Delta: Measure of material damping - such as vibration or sound damping.

Storage and Loss of Viscoelastic Material

SUPER BALL

TENNISBALLX

STORAGE

LOSS

4.1 Frequency Sweep

The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude (stress or strain) and temperature. S

tres

s or

Str

ain

Time

Deformation

USESViscosity Information - Zero Shear , shear thinningElasticity (reversible deformation) in materials MW & MWD differences Polymer Melts and Polymer solutions.Finding Yield in gelled dispersionsHigh and Low Rate (short and long time) modulus properties.Extend time or frequency range with TTS

Frequency Sweep: Material Response

Terminal Region

Rubbery PlateauRegion

TransitionRegion

Glassy Region

12

Storage Modulus (E' or G')

Loss Modulus (E" or G")

log Frequency (rad/s or Hz)

log

G'a

nd G

"

Typical Oscillatory Data

100.01.000E-5 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00frequency (Hz)

1.000E6

0.01000

0.1000

1.000

10.00

100.0

1000

10000

1.000E5

G' (

Pa

)

1.000E6

0.01000

0.1000

1.000

10.00

100.0

1000

10000

1.000E5

G'' (P

a)

1.000E5

100.0

1000

10000

|n*|

(P

a.s

)

PDMS

PDMS Extended frequency sweep-0001o, Frequency sweep step

G’

G”

Time-Dependent Viscoelastic Behavior:Solid and Liquid Properties of "Silly Putty"

T is short [< 1s] T is long [24 hours]

Deborah Number [De] = /

Dynamic Moduli of a Polymer Melt vs. Frequency

10001.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0

ang. frequency (rad/sec)

1000000

0.1000

1.000

10.00

100.0

1000

10000

100000

G' (

Pa)

1000000

0.1000

1.000

10.00

100.0

1000

10000

100000

G''

(Pa)

1.00E7

100.0

1000

10000

100000

1000000

* (

Pa

.s)

G"

G'

*

PDMS at 20°C

Polyethylene Rheology @ 150 C

10.001.000E-4 1.00E-3 0.01000 0.1000 1.000

shear rate (1/s)

1000000

1000

10000

100000

viscosity (P

a.s)

HDPE

LDPE

LLDPE

Typical steady shear flow experiment

Cox-Merz Rule

10001.000E-5 1.000E-3 0.1000 10.00

shear rate (1/s)

100000

100.0

1000

10000

visc

osity

(P

a.s)

PDMS.05F-Flow stepPDMS.08F-Flow step

Dynamic data gives highshear rates unattainable in flow

Creep or Steady shear FlowDynamicFrequencySweep

.

Polydimethylsiloxane

4.2 Dynamic Temperature Ramp: Material Response

Temperature

Terminal Region

Rubbery PlateauRegion

TransitionRegion

Glassy Region

Loss Modulus (E" or G")

Storage Modulus (E' or G')log

E' (

G')

and

E"

(G")

Time – Temp Superposition: can be used for shifting “moduluse” in creep test (E(t)), relaxation test (G(t)), dynamic oscillatory test ( G’, G”)

t 1/f “ Time scale (or frequency) of stress applies and temperature has a similar influent on mechanical properties.! “

short time low temp.( high f )

= /G long time high temp. ( low f )

works because t and T affect the relaxation time of polymer in same way < Relaxation time determines mechanical properties

Time – Temp Superposition:

Relationship betweenRelationship between

Molecular Properties Molecular Properties and Rheology and Rheology of of

PolymersPolymers

Effect of Molecular Properties on Rheology

Molecular Structure•MW & MWD•Chain Branching and Cross-linking•Interaction of Fillers with Matrix Polymer•Single or Multi-Phase Structure

Viscoelastic PropertiesAs a function of::•Strain Rate(frequency)•Strain Amplitude•Temperature

Processability & Product Performance

Molecular Structure - Effect of Molecular Weight

Rubbery PlateauRegion

TransitionRegion

Glassy Region

log

E' (

G')

Temperature

MW has practically no effect on the modulus below Tg

LowMW

Med.MW

HighMW

Effect of Molecular Weight on Viscosity and Elasticity

MWc

log MW

log

o 3.4

log MW

log

J eo

MWc’

Ref. Graessley, Physical Properties of Polymers, ACS, c 1984.

MWc = critical MW

Zero Shear Viscosity o

Sensitive to molecular weight, MW

For low MW (no entanglements) o

is proportional to MW

For MW > Critical MW, o is proportional to MW3.4.

Effect of Molecular Weightlo

g

log

0

Increasing MW

0 =K x MW3.4

Effect of Molecular Weight Distribution on 0

Narrow MWD

Broad MWD

Log Shear Rate (1/s)

Lo

g V

isco

sity

(P

a.s)

A Polymer with a broad MWD exhibits non-Newtonian flow at a lower rate of shear than a polymer with the same 0 but has a narrow MWD

IV.8 : Mechanical Tests Tensile – Compression Test < stress – strain behavior >

F(t) A0 L(t) ( A = cross-section area ) if A = A 0 engineering stress A = A (t) true stress F(t) Derive จากการ์ใช้+L(t) (True Length ) แที่นL0

Normal Stress

Stress = Force F / A ( normal stress)

Strain = 0

0

L L

L

(engineering )

true = ln ( 1 + eng ) ( true strain)

Force FShear stress =

surface area

xUShear strain =

y

u x = ร์ะยีะที่างที่�เค่ล �อนที่�ไป็ในแนวแกนX

Shear Stress

x

y

yU

xU F A x

y x

y

Stress – strain curve for a normally brittle polymer under tension and compression

Elastic modulus : slope of stress – strain curve at origin ( indicator of stiffness )

Strength : stress at fracture (normally strength tension < strength compression)

Elongation at break : strain at fracture ถึ+ามค่�ามาก ductile

น+อยี brittle

Toughness : area under stress–strain curve [ = ] energy/unit volume desirable material stiff, strong, ductile, and tough

Note Test can be performed in tension, compression, flexure, or torsion.

30

Stress (psi * 103)

Strain ( % )

compression

fracture

tension

fracture eng

true

Compressive strength

Tensile strength

Ultimate strength

Plastic deformation

Elongation at yield

Yield stress

strain

stress

Physical Testing