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Rheology and
Polymer Characterization
Asst Prof Anongnat [email protected]
20 Sep 2010
http://pioneer.netserv.chula.ac.th/~sanongn1/course.html
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Fundamentals:
• Why Rheology ?
• Fundamental Rheology Concepts and Parameters
• Fundamental Rheometry Concepts
• Viscosity, Viscoelasticiy and the Storage Modulus
• The Linear Viscoelastic Region (LVR)
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AGENDA
• Why Rheology ?
• Fundamental Rheology Concepts and Parameters
• Fundamental Rheometry Concepts
• Viscosity, Viscoelasticiy and the Storage Modulus
• The Linear Viscoelastic Region (LVR)
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A Rheological Paradox
Sometimes it does ____ Sometimes it doesn’t ____
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BECAUSE …
If a material is pumped, sprayed, extended, extruded, molded, coated, mixed, chewed, swallowed, rubbed, transported, stored, heated, cooled, aged …
RHEOLOGY is important ….!!
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AGENDA
• Why Rheology ?
• Fundamental Rheology Concepts and Parameters
• Fundamental Rheometry Concepts
• Viscosity, Viscoelasticiy and the Storage Modulus
• The Linear Viscoelastic Region (LVR)
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“παντα ρει” (everything flows … )
- Heraclito de Samos (500 A.C.)
Time Scale in Rheology
Deborah Number De = λ / texpJudges 5:5
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Definition of Rheology
Rheology is the science of
____?____ and ____?___ of matter under controlled testing conditions .
• flow• deformation
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Definition of Rheology
Rheology is the science of deformationand flow of matter under controlledtesting conditions .
• Flow is a special case of deformation• Deformation is a special case of flow
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Simple Shear Deformation and Shear Flow
τ = FA
y0
x(t)
θ
Vy0
1 d x(t)y0d t
Strain, γ =x(t)y0
Strain Rate, γ = .
Shear Modulus, G = τγ
V
y
xA
z
Shear Deformation
Viscosity, η =τγ.
γ. = ∆γ∆t
=
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Range of Rheological Material Behavior
Rheology: The study of deformation and flow of matter at specified conditions.
Range of material behaviorSolid Like --------- Liquid Like
(Ideal Solid ------------- Ideal Fluid)
Classical Extremes
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Classical Extremes: Elasticity
1678: Robert Hooke develops his “True Theory of Elasticity”
“The power of any spring is in the same proportion with the tension thereof.”
Hooke’s Law: τ = G γ or (Stress = G x Strain)
where G is the RIGIDITY MODULUS
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Linear and Non-Linear Stress-Strain Behavior of Solids
Non-Linear RegionG = f(γ)
Linear RegionG is constant
σ
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
osc.
str
ess
(Pa)
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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: τ = ηγ
where η is the Coefficient of Viscosity
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Newtonian and Non-Newtonian Behavior of Fluids
γ
τ
η
Newtonian Regionη Independent of γ
Non-Newtonian Regionη = f(γ)
1.0001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000
shear rate (1/s)
1.000E5
10000
η (P
a.s)
1.000E5
1.000
10.00
100.0
1000
10000
τ(P
a)
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PARAMETERS for Rheological PropertiesClassical Extremes
Ideal Solid -- [External Force] -- Ideal Fluid
STEEL WATERStrong Structure Weak StructureRigidity FluidityDeformation FlowRetains/recovers form Losses form Stores Energy Dissipates Energy
(Purely Elastic – R. Hooke, 1678) [Energy] (Purely Viscous – I. Newton, 1687)ELASTICITY VISCOSITYStorage Modulus Loss Modulus
REAL BehaviorApparent Solid [Energy + time] Apparent Fluid
- viscoelastic materials -
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Types of non-Newtonian fluids
• Deformation rate dependent viscosity• Yield Stress (plasticity)• Elasticity• Thixotropy• Transient behaviour
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Dilatancy (shear thickening)Plastic and Pseudoplastic (shear thinning)
Stress-strain rate curve
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apparent viscosity as a function of time
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AGENDA
• Why Rheology ?
• Fundamental Rheology Concepts and Parameters
• Fundamental Rheometry Concepts
• Viscosity, Viscoelasticiy and the Storage Modulus
• The Linear Viscoelastic Region (LVR)
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Viscometer vs. Rheometer
• Viscometer: instrument that measures the viscosity of a fluid over a limited shear rate range
• Rheometer: instrument that measures:• Viscosity over a wide range of shear rates, and…• Viscoelasticity of fluids, semi-solids and solids
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Frame of Reference…
• Recognize that a rheometer is a highly sensitive device used to quantify viscoelastic properties of the molecular structure of materials.
• A rheometer can not always mimic the conditions of a process, application or use.
• Rheometers determine apparent properties under a wide range of testing conditions.
– The apparent behavior can be used as a “finger print” or “benchmark” of the material.
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Constitutive Relations
ModulusStrainStress
=
Viscosity=rateShear
Stress
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Measuring Systems - Geometries
ParallelPlates
Cone andPlate
ConcentricCylinders
Rectangular Torsion
Very Low to Medium Viscosity
Very Low to High
Viscosity
Low Viscosity to soft Solids Soft to Rigid
Solids
Decane Water Steel
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AGENDA
• Why Rheology ?
• Fundamental Rheology Concepts and Parameters
• Fundamental Rheometry Concepts
• Viscosity, Viscoelasticiy and the Storage Modulus
• The Linear Viscoelastic Region (LVR)
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Dynamic Testing
Deformation
Response
Phase angle δ
An oscillatory (sinusoidal) deformation (stress or strain)is applied to a sample.
The material response (strain or stress) is measured.
The phase angle δ, or phase shift, between the deformation and response is measured.
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Dynamic Viscoelastic Material Response
Phase angle 0° < δ < 90°
Stress
Strain
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Viscoelastic Parameters
The Elastic (Storage) Modulus:Measure of elasticity of material. The ability of the material to store energy.
G' = (stress*/strain)cosӨ
G" = (stress*/strain)sinӨThe 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 σ= G"/G'Tan Delta:Measure of material damping - such as vibration or sound damping.
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Dynamic Time Sweep (Time Ramp)
Stre
ss o
r Stra
in
Time
DeformationThe material response is monitored at a constant frequency, amplitude and temperature.
USESTime dependent ThixotropyCure StudiesStability against thermal degradationSolvent evaporation/drying
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AGENDA
• Why Rheology ?
• Fundamental Rheology Concepts and Parameters
• Fundamental Rheometry Concepts
• Viscosity, Viscoelasticiy and the Storage Modulus
• The Linear Viscoelastic Region (LVR)
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Dynamic Stress or Strain Sweep(Torque Ramp)
The material response to increasing deformation amplitude (stress or strain) is monitored at a constant frequency and temperature.
Stre
ss o
r Stra
in
Time
Deformation
USESIdentify Linear Viscoelastic RegionStrength of dispersion structure - settling stabilityResilience
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Dynamic Strain Sweep: Material Response
Non-Linear RegionG = f(γ)Linear Region
G is constant
σ
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
osc.
stre
ss (P
a)
Critical Strain γc
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Frequency Sweep
The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude (stress or strain) and temperature.S
tress
or S
train
Time
Deformation
USESViscosity Information - Zero Shear η, shear thinningElasticity (reversible deformation) in materialsMW & 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
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Time Sweep on Latex
225.00
25.00 50.00 75.00 100.0 125.0 150.0 175.0 200.0
time (s)
100.0
0
20.00
40.00
60.00
80.00
G' (
Pa)
Structural Recovery after Preshear
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Dynamic Strain Sweep: Material Response
Non-Linear RegionG = f(γ)Linear Region
G is constant
σ
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
osc.
stre
ss (P
a)
Critical Strain γc
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Oscillation Model Fitting for Classic Polymer Data [Polyacrylamide Soln.]
10000.01000 0.1000 1.000 10.00 100.0ang. frequency (rad/sec)
1000
1.000E-4
1.000E-3
0.01000
0.1000
1.000
10.00
100.0
G' (
Pa)
1000
1.000E-4
1.000E-3
0.01000
0.1000
1.000
10.00
100.0
G'' (Pa)
100.0
0.1000
1.000
10.00
n' (Pa.s)
TA InstrumentsPolyacrylamideSolution 20 C
4 ElementMaxwell Fit
Straight LineFit to TerminalRegion of Data
Slope = 1.96
Slope = 0.97
G'
G" n'
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Defining Shear Rate Ranges
Bearings, engines103 to 107Lubrication
Atomization, spray drying105 to 106Spraying
Paper manufacture104 to 106High-speed coating
Skin creams, lotions104 to 105Rubbing
Painting103 to 104Brushing
Pumping liquids, blood flow100 to 103Pipe Flow
Liquids manufacturing101 to 103Mixing and stirring
Confectionery, paints101 to 102Dip coating
Foods101 to 102Chewing and Swallowing
Polymers, foods100 to 102Extruders
Toilet bleaches, paints, coatings10-1 to 101Draining off surfaces under gravity
Paints, Printing inks10-2 to 10-1Leveling due to surface tension
Medicines, Paints, Salad Dressing10-6 to 10-3Sedimentation of fine powders in liquids
ExamplesShear Rate Range
Situation
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Stress Relaxation Experiment
Response of Classical Extremes
time0
time0
stress for t>0is constant
time0
stress for t>0 is 0
Stre
ss
Str e
s s
Str a
in
Hookean Solid Newtonian Fluid
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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) = s(t)/γ
Stress decreases with timestarting at some high value and decreasing to zero. S
tress
time0
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Creep Recovery Experiment
Response of Classical Extremes
– Stain for t>t1 is constant– Strain for t >t2 is 0
time
Stra
in
time
Stra
in
time
– Stain rate for t>t1 is constant– Strain for t>t1 increase with time– Strain rate for t >t2 is 0
t2S
tress
t1
t1 t2 t2t1
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Creep Recovery Experiment:Response of Viscoelastic Material
Reference: Mark, J., et.al., Physical Properties of Polymers ,American Chemical Society, 1984, p. 102.
Creep t1> 0
timet 1 t2
RecoverableStrain
Recovery t 2= 0 (after steady state)
σ/η
Stra
in
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.
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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
visc
osity
(Pa.
s)
HDPE
LDPE
LLDPE
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Polydimethylsiloxane - Cox-Merz Data
10001.000E-5 1.000E-3 0.1000 10.00shear rate (1/s)
100000
100.0
1000
10000
visc
osity
(Pa.
s)
PDMS.05F-Flow stepPDMS.08F-Flow step
Dynamic data gives highshear rates unattainable in flow
Creep or Equilibrium FlowDynamicFrequencySweep
η (γ) = η∗ (ω).
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Dynamic Temperature Ramp or Step and Hold: Material Response
Temperature
Terminal RegionRubbery PlateauRegion
TransitionRegion
Glassy Region
Loss Modulus (E" or G")
Storage Modulus (E' or G')log
E' (
G')
and
E" (G
")
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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
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Effect of Heating Rate on Temperature of Cold Crystallization in PET
Heating RateAfter QuenchCooling
Tg
melt
Crystallization [kinetic event]
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PET Bottle Resin – Cold CrystallizationTemperature Ramp at 3°C/min.Frequency = 1 HzStrain = 0.025%
G’
G”
tan δ
β- transition-56.62°C
α- transitionTg = 88.0°C
250.0-200.0 -150.0 -100.0 -50.0 0 50.0 100.0 150.0 200.0temperature (Deg C)
1.000E10
1.000E6
1.000E7
1.000E8
1.000E9
G' (
Pa)
1.000E10
1.000E6
1.000E7
1.000E8
1.000E9
G'' (Pa)
0.4000
0
0.05000
0.1000
0.1500
0.2000
0.2500
0.3000
0.3500
tan(
delta
)
ColdCrystallization
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PET Bottle Resin – Before and After DMA Scan
PET After Temperature Ramp Scan
(Cold Crystallization)
Pressed PET Bottle Resin
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PET Bottle Resin - Repeat Run After Cold Crystallization
250.0-200.0 -150.0 -100.0 -50.0 0 50.0 100.0 150.0 200.0temperature (Deg C)
1.000E10
10000
1.000E5
1.000E6
1.000E7
1.000E8
1.000E9
G' (
Pa)
1.000E10
10000
1.000E5
1.000E6
1.000E7
1.000E8
1.000E9
G'' (P
a)2.250
0
0.2500
0.5000
0.7500
1.000
1.250
1.500
1.750
2.000
tan(
delta
)
Temperature Ramp at 3°C/min.Frequency = 1 HzStrain = 0.025%G’
G”
tan δ
α- transitionTg = 103°C
MeltTm = 240°C
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PET Bottle Resin - Comparison of G’
250.0-150.0 -100.0 -50.0 0 50.0 100.0 150.0 200.0temperature (Deg C)
1.000E10
1.000E6
1.000E7
1.000E8
1.000E9
G' (
Pa)
Temperature Ramp at 3°C/min.Frequency = 1 HzStrain = 0.025%
ColdCrystallization
Repeat Run After Cold Crystallization
Initial Scan on Pressed Resin
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Temperature
Hea
t Flo
w
GlassTransition
Crystallization
Melting
Cross-Linking(Cure)
Oxidation or
Decomposition
BECAUSE …Typical DSC Transitions
Describe Thermal Transitions of the Materials Structure
Quantitative Description of Consistency (structure) ?
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• Thermal Analysis describes thermal transitions
NEED to quantify ...
• Physical Properties of Structure • Strength or weakness of the Structure
and because …
Rheology can do these; therefore, it is much more informative tool
BECAUSE …
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Shear
Flexure
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Tension
Compression
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Creep
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Stress relaxation
Creep
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Stress relaxation
Constant stressing rate
Creep
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Stress relaxation
Constant stressing rate
Creep
Constant straining rate
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Acknowledgements
Abel Gaspar-Rosas, Ph.D. TA Instruments – Waters, IncFor graphs and figures