Fundementals of Polymer Rheology CUICAR 2016...Angular Frequency (rad/sec) 0.1 1 10 0.01 0.1 1 10...

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Fundamentals of Polymer Rheology

Sarah Cotts

TA Instruments

Rubber Testing Seminar

CUICAR, Greenville SC


Rheology: An Introduction

= Viscosity

= Modulus

Rheology: The study of stress-deformation relationships

Rheology: The study of stress-deformation relationships

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Shear Flow in Parallel Plates

= !ΩΩΩΩ

= !θθθθ

" = #

$%!MStress (σσσσ)

Strain (γγγγ)

Strain rate ()

r = plate radiush = distance between platesM = torque (µN.m)θ = Angular motor deflection (radians)Ω= Motor angular velocity (rad/s)


Open Boundary Rotational Rheometer

Controlled Strain

ARES G2

Applied Strain or Rotation

Measured Torque(Stress)

Direct Drive Motor

Transducer

Sample

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Closed Die Cavity Rheometer

Applied Strain or Rotation

Measured Torque(Stress)

Direct Drive Motor

Transducer

RPA Elite

Controlled Strain


Viscoelasticity

•Viscoelasticity: Having both Viscous and Elastic properties.

•Elastic Behavior: Stress is dependent on Strain

Hooke’s Law of Elasticity: Modulus = Stress/Strain

•Viscous Behavior: Stress is dependent on Strain Rate

Newton’s Law of Viscosity: Viscosity = Stress/ Strain Rate

•Viscoelastic materials cannot be fully understood using only one of these relationships. Oscillation measurements are able to measure stress as a function of both strain and strain rate.

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Hooke’s Law of Elasticity

•For an Elastic Solid, Stress and Strain have a constant proportionality σ = E*ε

• If the material follows Hooke’s Law, the deformation will be reversible when the stress is removed

The modulus of a Hookean solid will not show any time dependence- the stress depends on the strain, but not the strain rate


Newton’s Law of Viscosity

•For a Viscous Liquid, Stress is proportional to Strain Rate dε/dt by a coefficient of Viscosity η

σ = η* dε/dt

•The deformation of a liquid is non-reversible

Str

ess

Strain Rate

η

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Viscoelastic Behavior

σ = E*ε + η*dε/dt

Kelvin-Voigt Model (Creep) Maxwell Model (Stress Relaxation)

Viscoelastic Materials: Force

depends on both Deformation and

Rate of Deformation and vice versa.

L1

L2


Time-Dependent Viscoelastic Behavior

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

Deborah Number [De] = τ/T

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Pitch Drop Experiment

Long deformation time: pitch behaves like a highly viscous liquid

9th drop fell July 2013

Short deformation time: pitch behaves like a solid

http://www.theatlantic.com/technology/archive/2013/07/the-3-most-exciting-words-in-science-right-now-the-pitch-dropped/277919/

Started in 1927 by Thomas Parnell in Queensland, Australia


Silly Putties have different characteristic relaxation times

Dynamic (oscillatory) testing can measure time-dependent viscoelastic properties more accurately and efficiently by varying frequency (deformation time)

Time-Dependent Viscoelastic Behavior

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Frequency Sweep- Time Dependent Viscoelastic Properties

Frequency of modulus crossover correlates with Relaxation Time


Storage and Loss of a Viscoelastic Material

RUBBER BALL

TENNISBALL X

STORAGE

(G’)

LOSS

(G”)X

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Oscillation Testing

• The motor applies an oscillating deformation to the sample at a set Amplitude and Frequency.

Amplitude: Degree of Arc, or % Strain

Frequency: Hz (cycles per second) or CPM (cycles per minute)

• The torque transducer measures the response of the sample.

Amplitude: Torque (S*), or Stress

• The phase lag between the deformation and the torque is used to determine the Elastic and Viscous response.

Deformation

Torque, S*

Phase Angle δ


Oscillation Testing

In a purely Elastic material, Stress is in phase with the Strain

Viscoelastic material

In a purely Viscous material, Stress

is out of phase with the Strain

Phase angle= 0° Phase angle= 90°

0˚ < Phase angle< 90°

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Oscillation Testing- Lissajous-Bowditch Plots

Elastic Material Viscoelastic material Viscous Material

Strain StrainStrain

Str

ess Str

ess

Str

ess

Raw oscillation data can also be plotted as stress vs. strain. An elliptical shape represents a viscoelastic response.


Oscillation Testing

The Phase Angle can be used to separate the stress signal into the elastic and viscous components

G’: Storage Modulus

Measure of elasticity, or the ability to store energy

G’ = (Stress/Strain)*cos(δ)

G”: Loss Modulus

Measure of viscosity, or the ability to lose energy

G” = (Stress/Strain)*sin(δ)

Tan Delta

Measure of dampening properties

Tan (δ) = G”/G’

G*: Complex Modulus

Measure of resistance to deformation

G*= Stress/Strain

η*: Complex Viscosity

Measure of resistance to flow

η* = Stress/Strain RateStorage Modulus

Loss

Mo

du

lus

δ

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PDMS Frequency Sweep Comparison Overlay


Frequency Sweeps on Solids

10-1 100 101 102105106107108

10-210-1100

Freq [rad/s] E' () [dyn/cm²] tan_delta () [ ]Unhappy ball Happy ball

Modulus is the same

tan δ is very different

Happy & Unhappy Balls

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Applications of Polymer Rheology


Apart from chemical nature, tacticity and microstructure, polymers have 3 major characteristics which affect processability

1. Average molecular weight2. Molecular weight distribution3. Branching (Type and architecture)

Polymer Characteristics

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Long Chain Branching: Improving Processability

• Long Chain Branching (LCB) provides Shear Thinning, Strain Hardening and Melt Strength

• Very effective only one per 10000C needed.

• Difficult to fully characterize length of branches, number per chain and distribution.


Common Characterization Techniques

Chromatography (SEC) NMR

FTIR

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Influence of Molecular Weight on G’ and G”

The G’ and G” curves are shifted to lower frequency (longer time) with increasing molecular weight.

10-4

10-3

10-2

10-1

100

101

102

103

104

105

101

102

103

104

105

106

Mod

ulu

s G

', G

'' [P

a]

SBR Mw [g/mol]

G' 130 000

G'' 130 000

G' 430 000

G'' 430 000

G' 230 000

G'' 230 000

Freq ω [rad/s]


Influence of MW on Viscosity

The zero shear viscosity increases with increasing molecular weight.

TTS is applied to obtain the extended frequency range.

The high frequency behavior (slope -1) is independent of the molecular weight

10-4

10-3

10-2

10-1

100

101

102

103

104

105

102

103

104

105

106

107

100000

105

106

Slope 3.08 +/- 0.39

Zero Shear Viscosity

Ze

ro S

he

ar

Vis

co

sity ηo [

Pa

s]

Molecilar weight Mw [Daltons]

Vis

co

sity

η*

[Pa

s]

Frequency ω aT [rad/s]

SBR Mw [g/mol]

130 000

230 000

320 000

430 000

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Materials Evaluated: Polyolefin Elastomers

L. J. Effler,et.al., DuPont Dow Elastomers, Freeport, TX, Presented at Society of Plastics Engineers 2005 ANTEC Boston, MA

POE Co-Monomer Density (g/cm3) Long Chain Branching

EB-1 Butene 0.901 High

EB-2 Butene 0.870 Medium

EB-3 Butene 0.870 High

EO-1 Octene 0.870 Medium

• The level of Long Chain Branching (LCB) is difficult to directly measure in POEs

Amount and length of short chain branching interferes with NMR

• Characterize differences in LCB using rheology


Conventional Rheology of Polyolefin Elastomers

1,000

10,000

100,000

1,000,000

0.01 0.1 1 10 100 1000

αααα ωωωω (rad/s)

(bT/ αα αα

T) ηη ηη

(P

ois

e)


EB-1: High LCBEB-2: Med LCBEB-3: High LCBEO-1: Med LCB

Vis

co

sit

y (

po

ise

)

Angular Frequency (rad/sec)

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Conventional Rheology of Polyolefin Elastomers



Ta

n D

elt

a

Angular Frequency (rad/sec)

0.1

1

10

0.01 0.1 1 10 100 1000

αααα ωωωω (rad/s)


Extensional Viscosity of Polyolefin Elastomers

0

500000

1000000

1500000

2000000

2500000

3000000

0 2 4 6 8 10 12 14 16 18 20

Time (s)

ηη ηηe (

Po

ise

)

1-s 1.0=ε& 190 °C



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Linear Viscoelasticity

In the Linear Viscoelastic Region, the Stress

signal is a sine wave, and meaningful

rheology measurements can be made.



At higher strains, stress

becomes non-sinusoidal.

Modulus is an approximation.

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Non-Linear Viscoelasticity- Higher Harmonics

SAOS

LAOS

τ(t) = τ1 sin(ω1t+ϕ1) + τ3 sin(3ω1t+ϕ3) + τ5 sin(5ω1t+ϕ5) + ...

= τn

sin(nω1+ϕn)

γ(t) = γ0 sin(ωt)

τ(t) = τ0 sin(ωt+δ)

γ(t) = γ0 sin(ωt)

Σn=1

odd

∞

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Non-Linear Viscoelasticity- Higher Harmonics

=

+ +

Sample Response

Fundamental 3rd Harmonic 5th Harmonic


Large Amplitude Oscillatory Shear (LAOS)

0.0π 0.5π 1.0π 1.5π 2.0π

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1200

PIB, ω=0.1 Hz, γ0=1000%, T=140°C

τ [P

a]

t×ω [Pa]

γ [%

]

-1200 -600 0 600 1200-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

PIB, ω=0.1 Hz, γ0=1000%, T=140°C

τ [P

a]

γ [%]

“The potential of large amplitude oscillatory shear to gain an insight into the long-chain branching structure of polymers”

ACS Meeting 2008, Florian J. Stadler, Sunil Dhole, Adrien Leygue, Christian Bailly – Université Catholique de Louvain (UCL)

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Large Amplitude Oscillatory Shear (LAOS)

-300000

-200000

-100000

0

100000

200000

300000

-8 -6 -4 -2 0 2 4 6 8

Sh

ea

r s

tre

ss

(P

a)

Strain rate (s-1)

Branched

Linear

5% Branched in Linear




Long Chain Branching Index



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Long Chain Branching

-10 -5 0 5 100

Shear rate (s-1)

-75000

-50000

-25000

0

25000

50000

75000

Shear stress (Pa)

High visc. PP

Low visc. PP

95% Low visc. PP+5% high visc. PP

50% Low visc. PP+50% high visc. PP

Secondary loops

not affected by

AMW and MWD

•Secondary loops can be associated

with linear polymer architecture

•There has to be a mathematical

condition to account for loops


Lissajous-Bowditch Plots

Ewoldt, R.H; McKinley, G. H. “On secondary loops in LAOS via self-intersection of Lissajous-Bowditch Curves.” Rheologica Acta 49, no 2. February 12th, 2010. 213-219.

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Rheological characterization of EPDMs

ML(1+4) at 125 C

Burhin, Henri G. Polymer Process Consult


Rheological characterization of EPDMs


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LAOS testing of EPDMs



Long Chain Branching Index- EPDMs


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Dynamic Mechanical Analysis

•Is DMA Rheology, or Thermal Analysis?

•Oscillation measurements- E’, E”, Tan Delta

•Characterize viscoelastic materials as a function of time, temperature, stress and strain.


Glass Transition of PSA measured by DMA

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Effect of Crosslinking

120

160

300

1500

9000

30,000

M = MW between

crosslinksc

Temperature


Effect of Aging on Elastomer O Rings

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Conclusions

•Closed-Die RPA rheometer can match the viscoelastic measurements of the ARES

•Rheological measurements within the linear visocelasticregion can be used to compare MW for non-branched polymers

•Effects of branching are seen in linear, small-amplitude rheology measurements, especially at low frequency

•Large Amplitude Oscillatory Shear (LAOS) clearly differentiates linear and branched polymers.

•DMA measurements also show differences in viscoelastic properties. These can indicate differences in chemistry or molecular structure, but also relate to bulk properties.


Thank You

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Fundementals of Polymer Rheology CUICAR 2016...Angular Frequency (rad/sec) 0.1 1 10 0.01 0.1 1 10...

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