1. Chapter 9: Rheological and Mechanical Properties of Polymers
AE 447: Polymer Technology, Dr. Cattaleeya Pattamaprom

2. Fundamentals of Rheology Seminar
Adapted from the workshop on
Fundamentals of Rheology Seminar by
Dr. Abel Gaspar-Rosas
TA Instruments – Waters, Inc.
April, 2004
Thailand

3. Outline Rheology – Introduction
Elasticity, Viscosity and Viscoelasticity
Rheology tests
Steady-state flow
Stress Relaxation
Creep Recovery
Oscillatory Tests
Dynamic Frequency sweep
Dynamic Temperature ramp
Molecular Properties vs. Rheology of Polymers
Mechanical Testing

4. Definition of Rheology
Rheology is the science of deformation and flow of matter.
รีโอโลยี (Rheology): ศาสตร์ของรีโอโลยี เป็นศาสตร์ที่กล่าวถึงสมบัติการไหลหรือการเสียรูป รีโอโลยีของพอลิเมอร์ส่วนใหญ่มักกล่าวถึงค่าโมดูลัส และค่าความหนืด

5. Simple Shear Deformation and Shear Flow
Strain, g =
x(t) y0
x(t) F A t = V V y0
1 d x(t)
y0 d t y0
Strain Rate, g = . q y A
Viscosity, h = t g . z x t g g . = Dg Dt
Shear Modulus, G =

6. Range of Rheological Material Behavior
Rheology: The study of deformation and flow of matter.
Range of material behavior
Solid Like Liquid Like
Ideal Solid Ideal Fluid
Classical Extremes
Viscous liquid
Elastic solid
Viscoelastic

7. 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: t = G  or (Stress = G x Strain)
where G is the RIGIDITY MODULUS .
G is constant

8. 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: t =   is constant
whereis the Coefficient of Viscosity

9. Response for Classical Extremes
Spring
Dashpot
Purely Viscous
Response
Newtonian Liquid
t = 
Purely Elastic
Response
Hookean Solid
t = G
For the classical extremes cases, what only matters are the values of stress, strain and strain rate.
The response is independent of the loading.
use mechanical models as analogies for ideal solid and liquid responses

10. Coatings, Food, Cosmetics, Polymers
Overview about the different rheological material behavior ilustrated by the use of…
viscoelastic fluid / solid
Ideal viscous
Oil, Solvent
Newton‘s law
Ideal elastic
Glass, Steel
Hooke‘s law
Apparent Yield Point,
Thixotropy, …
Coatings, Food, Cosmetics, Polymers
Physica Messtechnik Gmbh Vor dem lauch 6, Stuttgart, Germany Internet: .de

11. Viscoelasticity Defined
Range of Material Behavior
Solid Like Liquid Like
Ideal Solid Most Materials Ideal Fluid
Purely Elastic Viscoelastic Purely Viscous
Viscoelasticity: Having both viscous
and elastic properties

12. 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, Stuttgart, Germany Internet: .de

13. Viscoelastic Fluids Polymers
Viscoelastic behavior, illustrated by use of a dashpot and a spring
Polymers
Macromolecules are deformed and disentangled
low viscosity
at rest
Macromolecules are entangled
and have spherical shapes
high viscosity
under shear
Physica Messtechnik Gmbh Vor dem lauch 6, Stuttgart, Germany Internet: .de

14. Newtonian and Non-Newtonian Behavior of Fluids
Region
 = f()
1.000E5
1.000E5
Newtonian Region
 Independent of 
10000
Zero-shear viscosity (o)
1000 
t (Pa)
h (Pa.s)
100.0
Shear thinning
Pseudo-plastic t
10.00
10000
1.000
1.000E-5
1.000E-4
1.000E-3 
0.1000
1.000
shear rate (1/s)

15. Elastic Modulus vs. Temp.
brittle
leathery
rubbery
viscous 4 3 2 1
Area 1: Viscous state:
Area 2: Rubbery state
Area 3: Leathery state
Area 4: Glassy state
= stress = F/A
= strain = dL/L
E = elastic modulus

16. Linear and Non-Linear Stress-Strain Behavior of Solids
1000
100.0
Linear Region
G is constant
Non-Linear Region
G = f()
100.0 G
G' (Pa)
osc. stress (Pa)
10.00 s
1.000
1.0000
10.000
100.00
1000.0
% strain

17. Viscosity and Viscoelasticity

18. Viscosity is . . . . Viscosity: Definition
synonymous with internal friction.
resistance to flow.
Variables that Affect Viscosity –for polymer
Shear Rate - Molecular Weight
Time of Shearing
Temperature
Pressure
Surface Tension

19. Characteristic Diagrams for Newtonian Fluids
Ideal Yield Stress
(Bingham Yield)
Pa.s
t, Pa
s or t, Pa
s

20. Viscosity: Temperature dependence
If we plot on a log scale you can se that 80°C results a two decade change in viscosity! Clearly temperature control is VERY important

21. Shear Thickening (Dilatent)
Summary of Types of Flow
Bingham (Newtonian w/yield stress)
Bingham Plastic
(shear-thinning w/yield stress)
Shear Stress, t
Shear Thinning (Pseudoplastic)
Newtonian t y
Shear Thickening (Dilatent)
These rheograms depict non-Newtonian fluids
Shear thinning [pseudoplastic] and shear thickening [dilatant] can be classed as power law fluids stress = rate ^n where n is not = 1. The names in parentheses are no longer in common usage and may be misleading.
Other fluids exhibit an apparent yield stress, in that they have a non-zero y intercept
Yield stress implies an infinite viscosity below that stress, which is physically unlikely; even polycrstalline metals flow over centuries
Shear Rate, g

22. Viscosity vs. Shear Rate Result: Rheological material behaviour Shear stress & viscosity as a function of the shear rate
Newtonian Ideal viscous (e.g.: oil, solvent)
Shear thinning (e.g.: typical food, cosmetics, coatings, polymers, …)
Shear Thickening Shear thickening (e.g.: PVC plastisol & paper coatings under high shear cond.)

23. Newtonian and Non-Newtonian Behavior of Fluids
Region
 = f()
1.000E5
1.000E5
Newtonian Region
 Independent of 
10000
1000 
t (Pa)
h (Pa.s)
100.0 t
10.00
10000
1.000
1.000E-5
1.000E-4
1.000E-3 
0.1000
1.000
shear rate (1/s)

24. Idealized Flow Curve - Polymers
Power Law Region
First Newtonian Plateau
h0 = Zero Shear Viscosity
h0 = K x MW3.4
Extend Range
with Time-
Temperature
Superposition (TTS)
& Cox-Merz
log h
Measure in Flow Mode on
AR1000/AR500
Extend Range
with Oscillation
& Cox-Merz
Second Newtonian Plateau
Molecular Structure
Compression Molding
Extrusion
Blow and Injection Molding
1.00E-5
1.00E-4
1.00E-3
0.0100
0.100
1.00
10.00
100.00
1.00E4
1.00E5
shear rate (1/s)

25. Comparison of Newtonian & Shear Thinning Samples
10000
Standard oil A
1000
100.0
viscosity (Pa.s)
10.00
Xanthan/Gellan
Fructose Soln.
1.000
0.1000
This slide illustrates the importance of shear thinning in a fluid ["Orbitz"]. The two standard oils are at the extremes of viscosity. The fluid can exist at both these extremes depending on the shear rate.
Thus at rest the fluid is stiffer than plasticine, but at moderate shear rates it is as fluid as milk
This kind of behavior allows for easy dispensing and handling, but robust structure and thus stability in its container
Standard oil B
1.000E-3
1.000E-6
1.000E-4
1.000
10.00
100.0
1000
shear rate (1/s)

26. Non-Newtonian, Time Dependent Fluids
Thixotropy
A 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.
Rheopexy
An 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., ISBN

27. Non-Newtonian, Time Dependent Fluids
Rheopectic
Viscosity
Shear Rate = Constant
Thixotropic
time

28. Time-Dependent Viscoelastic Behavior:
Solid and Liquid Properties of "Silly Putty"
T is short [< 1s]
T is long [24 hours]
Deborah Number [De] = / 

29. Storage and Loss of Viscoelastic Material
SUPER BALL
LOSS
TENNIS
BALL X
STORAGE

30. Rheology Tests

31. Some Types of Rheometers
Typical Rheometer:
Low shear rate/Oscillatory
Capillary Rheometer:
High shear rate

32. Rheology:Choosing Tests and Conditions
Geometries: Typical Rheometer
Max. 3°
Max. 3°
Delta < 1.2
Delta < 1.2
0.25mm < gap < 2mm
Ref.: Physica

33. 1. Stepped Ramp or Steady-Shear Flow
A series of logarithmic stress steps allowed to reach steady state, each one giving a single viscosity data point:
Shear Rate
Time
h = s / g/ (d
dt)
Shear Thinning
Region
Viscosity
This shows how and equilibrium flow curve is constructed from many stress steps. Each step is allowed to reach equilibrium, before a viscosity calculation is made.
The inset box shows a step reaching steady state [shear rate approaching a constant]and from the shear rate asymptote and the known stress the viscosity is derived
Lower stress steps are performed as creep tests, see later sections
Shear Rate, 1/s

34. HDPE LLDPE LDPE Typical steady shear flow experiment
Polyethylene 150 C
HDPE
LDPE
LLDPE
100000
viscosity (Pa.s)
10000
PE can be divided into 3 categories based on long and short chain branching: HDPE has no branching and is much more visous, being processed at higher temps., LDPE is highly branched with long and short chain branches, resulting in a lower overall viscosity.
In between in LLDPE with some short chain branching.
The graph shows a family of 9 resins with varying degrees of branching etc.
1000
1.000E-4
0.1000
1.000
10.00
1.00E-3
shear rate (1/s)

35. Idealized Full Flow Curve - Polymers
Power Law Region
First Newtonian Plateau
h0 = Zero Shear Viscosity
h0 = K x MWc 3.4
Extend Range
with Time-
Temperature
Superposition (TTS)
& Cox-Merz
log h
Measure in Flow Mode on
AR1000/AR500
Extend Range
with Oscillation
& Cox-Merz
Second Newtonian Plateau
Molecular Structure
Compression Molding
Extrusion
Blow and Injection Molding
1.00E-5
1.00E-4
1.00E-3
0.0100
0.100
1.00
10.00
100.00
1.00E4
1.00E5
shear rate (1/s)

36. At very high shear rate  Melt fracture
Higher Shear Rate

37. 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).
Strain
time

38. Response of Classical Extremes
Stress Relaxation Experiment
Deformation
Strain
time
Response of Classical Extremes
Elastic
Viscous
Hookean Solid
Newtonian Fluid
Stress
stress for t>0 is 0
stress for t>0
is constant
Stress
time
time

39. Stress Relaxation Experiment (cont’d)
Response of Material
Visco
elastic
Stress decreases with time
starting at some high value
and decreasing to zero.
Stress
time
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)/

40. 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 timet.
Stress t1 t2
time

41. Response of Classical Extremes
Creep Recovery Experiment
Deformation
Stress t1
time t2
Response of Classical Extremes
Elastic
Viscous
Stain rate for t>t1 is constant
Strain for t>t1 increase with time
Strain rate for t >t2 is 0
Stain for t>t1 is constant
Strain for t >t2 is 0
Strain
Strain
time t1
time t2 t1 t2

42. Creep Recovery Experiment: Response of Viscoelastic Material
Recovery  = 0 (after steady state)
/
Recoverable
Strain
Strain t t 1 2
time
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.
Reference: Mark, J., et.al.,
Physical Properties of Polymers
,American Chemical Society, 1984, p. 102.

43. 4.Oscillatory Testing of Polymers (Dynamic Mechanical Tests)

44. Dynamic Mechanical Testing
Deformation
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.
Response
Phase angle d

45. Dynamic Mechanical Testing Viscoelastic Material Response
Phase angle 0° < d < 90°
Stress
Strain

46. DMA Viscoelastic Parameters: The Complex, Elastic, & Viscous Stress
The stress in a dynamic experiment is referred to as the complex stress t*
Phase angle d
Strain, g
t* = t' + it"
Complex Stress, t*

47. DMA Viscoelastic Parameters
The Complex Modulus: Measure of materials overall resistance to deformation.
G* = Stress*/Strain
G* = G′ + iG″
The Elastic (Storage) Modulus: Measure of elasticity of material. The ability of the material to store energy.
G' = (stress*/strain)cos
The Viscous (loss) Modulus:
The ability of the material to dissipate energy. Energy lost as heat.
G" = (stress*/strain)sin
Tan Delta:
Measure of material damping - such as vibration or sound damping.
Tan = G"/G'

48. Storage and Loss of Viscoelastic Material
SUPER BALL
LOSS
TENNIS
BALL X
STORAGE

49. 4.1 Frequency Sweep Deformation Time Stress or Strain
The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude (stress or strain) and temperature.
Stress or Strain
Time
USES
Viscosity Information - Zero Shear h, shear thinning
Elasticity (reversible deformation) in materials
MW & MWD differences Polymer Melts and Polymer solutions.
Finding Yield in gelled dispersions
High and Low Rate (short and long time) modulus properties.
Extend time or frequency range with TTS

50. Frequency Sweep: Material Response
Transition
Region
Rubbery Plateau
Region
Terminal Region
Glassy Region
log G'and G" 1 2
Storage Modulus (E' or G')
Loss Modulus (E" or G")
log Frequency (rad/s or Hz)

51. Typical Oscillatory DataG” G’
Curve of a frequency sweep used to talk about oscillation modes; talk about other ways to run the experiment like time sweeps, temp sweeps; ability to do in both controlled strain and stress mode and advantage of each
the waveform and why that is important(and unique to us)

52. Time-Dependent Viscoelastic Behavior:
Solid and Liquid Properties of "Silly Putty"
T is short [< 1s]
T is long [24 hours]
Deborah Number [De] = / 

53. Dynamic Moduli of a Polymer Melt vs. Frequency
1.00E7
PDMS at 20°C
100000
100000
10000
10000 h*
100000
G' (Pa)
1000
1000
G'' (Pa)
h* (Pa.s)
100.0
100.0
10000
G"
10.00
10.00
1000
1.000
1.000 G'
100.0
0.1000
0.1000
1.000E-4
1.000E-3
0.1000
1.000
10.00
100.0
1000
ang. frequency (rad/sec)

54. HDPE LLDPE LDPE Typical steady shear flow experiment
Polyethylene 150 C
HDPE
LDPE
LLDPE
100000
viscosity (Pa.s)
10000
PE can be divided into 3 categories based on long and short chain branching: HDPE has no branching and is much more visous, being processed at higher temps., LDPE is highly branched with long and short chain branches, resulting in a lower overall viscosity.
In between in LLDPE with some short chain branching.
The graph shows a family of 9 resins with varying degrees of branching etc.
1000
1.000E-4
0.1000
1.000
10.00
1.00E-3
shear rate (1/s)

55. Cox-Merz Rule . h (g) = h*(w) Polydimethylsiloxane
Creep or Steady shear Flow
Dynamic Frequency Sweep .
h (g) =
h*(w)
Cox-Merz data for PDMS
software allows the plotting of oscillation data [rad/s] and flow data as shear rate
"shear rates" up to max freq in rad/s can thus be achieved without artifact 250 CSL, 628 AR, 1000 WB
This technique allows medium to high shear measurements to be made without edge instability
Is an empirical test - it either works or it doesn't
Dynamic data gives high
shear rates unattainable in flow

56. 4.2 Dynamic Temperature Ramp: Material Response
Glassy Region
Transition
Region
Rubbery Plateau
Region
Terminal Region
log E' (G') and E" (G")
Loss Modulus (E" or G")
Storage Modulus (E' or G')
Temperature

57. Time – Temp Superposition:
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

58. Relationship between Molecular Properties and Rheology of Polymers

59. 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 Properties
As a function of::
Strain Rate(frequency)
Strain Amplitude
Temperature
Processability & Product Performance

60. Molecular Structure - Effect of Molecular Weight
Glassy Region
Rubbery Plateau
Region
Transition
Region
MW has practically no effect on the modulus below Tg
log E' (G')
High MW
Med. MW
Low MW
Temperature

61. Effect of Molecular Weight on Viscosity and Elasticity
MWc = critical MW
MWc’
3.4
log o
MWc
log Je o
log MW
log MW
Ref. Graessley, Physical Properties of Polymers,
ACS, c 1984.

62. Sensitive to molecular weight, 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.

63. Effect of Molecular Weight
h0 =K x MW3.4 h0
Increasing MW
log h
log g

64. Effect of Molecular Weight Distribution on h0
A Polymer with a broad MWD exhibits non-Newtonian flow at a lower rate of shear than a polymer with the same h0 but has a narrow MWD
Narrow MWD
Log Viscosity (Pa.s)
Broad MWD
Log Shear Rate (1/s)

66. x x y y

67. Compressive strength
Tensile strength

69. Physical Testing