What happens to Tg with increasing pressure?

1
What happens to Tg with increasing pressure?
2
Bar 1 atm 100 kPa
Why?
3
A Demonstration of Polymer Viscoelasticity
Poly(ethylene oxide) in water
4
Memory of Previous State
Poly(styrene) Tg 100 C
5
Chapter 5. Viscoelasticity

• Is silly putty a solid or a liquid?
• Why do some injection molded parts warp?
• What is the source of the die swell phenomena
  that is often observed in extrusion processing?
• Expansion of a jet
• of an 8 wt solution of
• polyisobutylene in decalin
• Under what circumstances am I justified in
  ignoring viscoelastic effects?

6
What is Rheology?

• Rheology is the science of flow and deformation
  of matter

Rheology Concepts, Methods, Applications, A.Y.
Malkin and A.I. Isayev ChemTec Publishing, 2006
7
(No Transcript)
8
Temperature Strain Rate
9
(No Transcript)
10
Time dependent processes Viscoelasticity

• The response of polymeric liquids, such as melts
  and solutions, to an imposed stress may resemble
  the behavior of a solid or a liquid, depending on
  the situation.

11
(No Transcript)
12
(No Transcript)
13
Network of Entanglements
There is a direct analogy between chemical
crosslinks in rubbers and physical crosslinks
that are created by the entanglements.
The physical entanglements can support stress
(for short periods up to a time tT), creating a
transient network.
14
Entanglement Molecular Weights, Me, for Various
Polymers
Me (g/mole)
Poly(ethylene) 1,250 Poly(butadiene) 1,700 Pol
y(vinyl acetate) 6,900 Poly(dimethyl
siloxane) 8,100 Poly(styrene) 19,000
15
Pitch drop experiment

• Started in 1927 by University of Queensland
  Professor Thomas Parnell.
• A drop of pitch falls every 9 years

Pitch drop experiment apparatus
Pitch can be shattered by a hammer
16
Viscoelasticity and Stress Relaxation

• Whereas steady-shear measurements probe material
  responses under a steady-state condition, creep
  and stress relaxation monitor material responses
  as a function of time.
• Stress relaxation studies the effect of a
  step-change in strain on stress.

17
Physical Meaning of the Relaxation Time
time
18
Introduction to Viscoelasticity
All viscous liquids deform continuously under the
influence of an applied stress They exhibit
viscous behavior. Solids deform under an applied
stress, but soon reach a position of equilibrium,
in which further deformation ceases. If the
stress is removed they recover their original
shape They exhibit elastic behavior. Viscoelast
ic fluids can exhibit both viscosity and
elasticity, depending on the conditions.
Viscous fluid
Viscoelastic fluid
Elastic solid

• Polymers display VISCOELASTIC properties

19
Static Testing of Rubber Vulcanizates

• Static tensile tests measure retractive stress at
  a constant elongation (strain) rate.
• Both strain rate and temperature influence the
  result

Note that at common static test conditions,
vulcanized elastomers store energy efficiently,
with little loss of inputted energy.
20
Dynamic Testing of Rubber Vulcanizates Resilience
Resilience tests reflect the ability of an
elastomeric compound to store and return energy
at a given frequency and temperature.

• Change of rebound
• resilience (h/ho) with
• temperature T for
• 1. cis-poly(isoprene)
• 2. poly(isobutylene)
• 3. poly(chloroprene)
• 4. poly(methyl methacrylate).

21
Hooke and Newton

• It is difficult to predict the creep and stress
  relaxation for polymeric materials.
• It is easier to predict the behaviour of
  polymeric materials with the assumption ? it
  behaves as linear viscoelastic behaviour.
• Deformation of polymeric materials can be divided
  to two components
• Elastic component Hookes law
• Viscous component Newtons law
• Deformation of polymeric materials ? combination
  of Hookes law and Newtons law.

22
Hookes law Newtons Law

• The behaviour of linear elastic were given by
  Hookes law

or

• The behaviour of linear viscous were given by
  Newtons Law

• E Elastic modulus
• s Stress
• e strain
• de/dt strain rate
• ds/dt stress rate
• ?? viscosity

This equation only applicable at low strain
23
Viscoelasticity and Stress Relaxation
Stress relaxation can be measured by shearing the
polymer melt in a viscometer (for example
cone-and-plate or parallel plate). If the
rotation is suddenly stopped, ie. g0, the
measured stress will not fall to zero
instantaneously, but will decay in an exponential
manner.
.

• Relaxation is slower for Polymer B than for
  Polymer A, as a result of greater elasticity.
• These differences may arise from polymer
  microstructure (molecular weight, branching).

24
STRESS RELAXATION
CREEP
Constant strain is applied ? the stress relaxes
as function of time
Constant stress is applied ? the strain relaxes
as function of time
25
Time-dependent behavior of Polymers
The response of polymeric liquids, such as melts
and solutions, to an imposed stress may under
certain conditions resemble the behavior of a
solid or a liquid, depending on the
situation. Reiner used the biblical expression
that mountains flowed in front of God to define
the DEBORAH number
26
metal
elastomer
Viscous liquid
27
Static Modulus of Amorphous PS
Polystyrene
Stress applied at x and removed at y
28
Stress Relaxation Test
Strain
Elastic
Viscoelastic
Stress
Stress
Stress
Viscous fluid
Viscous fluid
Viscous fluid
0
Time, t
29
Stress relaxation

• Stress relaxation after a step strain go is the
  fundamental way in which we define the relaxation
  modulus

• Go (or GNo) is the plateau modulus

where Me is the average mol. weight between
entanglements

• G(t) is defined for shear flow. We can also
  define a relaxation modulus for extension

30
Stress relaxation of an uncrosslinked melt
Mc critical molecular weight above which
entanglements exist
3.24
31
(No Transcript)
32
Network of Entanglements
There is a direct analogy between chemical
crosslinks in rubbers and physical crosslinks
that are created by the entanglements.
The physical entanglements can support stress
(for short periods up to a time tT), creating a
transient network.
33
Relaxation Modulus for Polymer Melts
Elastic
tT terminal relaxation time
Viscous flow
34
Viscosity of Polymer Melts
ho
Extrapolation to low shear rates gives us a value
of the zero-shear-rate viscosity, ho.
Shear thinning behaviour
Poly(butylene terephthalate) at 285 ºC
For comparison h for water is 10-3 Pa s at room
temperature.
35
Rheology and Entanglements.
The elastic properties of linear thermo-plastic
polymers are due to chain entanglements.
Entanglements will only occur above a critical
molecular weight. When plotting melt viscosity
?o against molecular weight we see a change of
slope from 1 to 3.45 at the critical entanglement
molecular weight.
36
Scaling of Viscosity ho N3.4
h tTGP
ho N3.4 N0 N3.4
Universal behaviour for linear polymer melts
Applies for higher N NgtNC
Why?
G.Strobl, The Physics of Polymers, p. 221
37
(No Transcript)
38
Application of Theory Electrophoresis
From Giant Molecules
39
(No Transcript)
40
Mechanical Model

• Methods that used to predict the behaviour of
  visco-elasticity.
• They consist of a combination of between elastic
  behaviour and viscous behaviour.
• Two basic elements that been used in this model
• Elastic spring with modulus which follows Hookes
  law
• Viscous dashpots with viscosity h which follows
  Newtons law.
• The models are used to explain the phenomena
  creep and stress relaxation of polymers involved
  with different combination of this two basic
  elements.

41
Dynamic Viscosity (dashpot)
Shear stress

• Lack of slipperiness
• Resistance to flow
• Interlayer friction

SI Unit Pascal-second
Shear rate
1 centi-Poise milli Pascal-second
42
stress
stress input
Strain in dashpot
dashpot
43

• Maxwell model
• In series
• Viscous strain remains after load removal.

stress input
Model
Strain Response
Maxwell model
44

• Kelvin or Voigt model
• In parallel
• Nonlinear increase in strain with time
• Strain decreases with time after load removal
  because of the action of the spring (and dashpot).

stress input
Model
Strain Response
Voigt model
45

• Typical Viscosities (Pa.s)

Asphalt Binder --------------- Polymer Melt
----------------- Molasses ----------------------
Liquid Honey ----------------- Glycerol
----------------------- Olive Oil
----------------------- Water --------------------
------ Acetic Acid --------------------
100,000 1,000 100 10 1 0.01 0.001 0.00001
Courtesy TA Instruments
46
Shear stress
Non Newtonian Fluids
Shear rate
47
The Theory of Viscoelasticity

• The liquid behavior can be simply represented by
  the Newtonian model. We can represent the
  Newtonian behavior by using a dashpot
  mechanical analog

The simplest elastic solid model is the Hookean
model, which we can represent by the spring
mechanical analog.
????stress?
????strain?
????viscosity
G???modulus
48
Maxwell Model

• Lets create a VISCOELASTIC material
• At least two components are needed, one to
  characterize elastic and the other viscous
  behavior. One such model is the Maxwell model

????stress?
????strain?
????viscosity
G???modulus
49
Maxwell Model

• Lets try to deform the Maxwell element

????stress?
????strain?
????viscosity
G???modulus
50
Maxwell solid line Experiment circles
Maxwell model too primitive
51
Maxwell Model
The deformation rate of the Maxwell model is
equal to the sum of the individual deformation
rates
l is the relaxation time
If the mechanical model is suddenly extended to a
position and held there (gconst., g0)
.
Exponential decay in stresses
????stress?
????strain?
????viscosity
G???modulus
52
Examples of Viscoelastic Materials

• Mattress, Pillow

• Tissue, skin

53
Elastic
Viscous

• The common mechanical model that use to explain
  the viscoelastic phenomena are
• Maxwell
• Spring and dashpot ? align in series
• Voigt
• Spring and dashpot ? align in parallel
• Standard linear solid
• One Maxwell model and one spring ? align in
  parallel.

54
Measurements of Shear Viscosity

• Melt Flow Index
• Capillary Rheometer
• Coaxial Cylinder Viscometer (Couette)
• Cone and Plate Viscometer (Weissenberg
  rheogoniometer)
• Disk-Plate (or parallel plate) viscometer

55
Weissenberg Effect
56
Dough Climbing Weissenberg Effect
Other effects Barus Kaye
57
Courtesy Dr. Osvaldo Campanella
58

• Dynamic Mechanical Testing
• Response for Classical Extremes

Purely Viscous Response (Newtonian Liquid)
Purely Elastic Response (Hookean Solid)
? 90
? 0
Stress
Stress
Strain
Strain
Courtesy TA Instruments
59

• Dynamic Mechanical Testing Viscoelastic Material
  Response

Phase angle 0 lt d lt 90
Strain
Stress
Courtesy TA Instruments
60

• DMA Viscoelastic Parameters
• The Complex, Elastic, Viscous Stress

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

• The complex stress can be separated into two
  components
• 1) An elastic stress in phase with the strain.
  ?' ?cos??
• ??????' is the degree to which material behaves
  like an elastic solid.
• 2) A viscous stress in phase with the strain
  rate. ?" ?sin?
• ??????" is the degree to which material behaves
  like an ideal liquid.

Phase angle d
? ?' i?"
Complex Stress, ?
Courtesy TA Instruments
Strain, ?
61

• 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'
Courtesy TA Instruments
62

• DMA Viscoelastic Parameters Damping, tan ?

G
G"
Dynamic measurement represented as a vector It
can be seen here that G (G2 G2)1/2
Phase angle ?
G'

• The tangent of the phase angle is the ratio of
  the loss modulus to the storage modulus.

tan ? G"/G'

• "TAN DELTA" (tan ?)?is a measure of the damping
  ability of the material.

Courtesy TA Instruments
63

• 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)
Courtesy TA Instruments
64
Viscoelasticity in Uncrosslinked, Amorphous
Polymers
Logarithmic plots of G and G against angular
frequency for uncrosslinked poly(n-octyl
methacrylate) at 100C (above Tg), molecular
weight 3.6x106.
65
Dynamic Characteristics of Rubber Compounds

• Why do E and E vary with frequency and
  temperature?
• The extent to which a polymer chains can
  store/dissipate energy depends on the rate at
  which the chain can alter its conformation and
  its entanglements relative to the frequency of
  the load.
• Terminal Zone
• Period of oscillation is so long that chains can
  snake through their entanglement constraints and
  completely rearrange their conformations
• Plateau Zone
• Strain is accommodated by entropic changes to
  polymer segments between entanglements, providing
  good elastic response
• Transition Zone
• The period of oscillation is becoming too short
  to allow for complete rearrangement of chain
  conformation. Enough mobility is present for
  substantial friction between chain segments.
• Glassy Zone
• No configurational rearrangements occur within
  the period of oscillation. Stress response to a
  given strain is high (glass-like solid) and tand
  is on the order of 0.1

66

• Dynamic Temperature Ramp or Step and Hold
  Material Response

Glassy Region
Transition Region
Rubbery Plateau Region
Terminal Region
Log G' and G"
1
2
Courtesy TA Instruments
Temperature
67
One more time Dynamic (Oscillatory) Testing

• In the general case when the sample is deformed
  sinusoidally, as a response the stress will also
  oscillate sinusoidally at the same frequency, but
  in general will be shifted by a phase angle d
  with respect to the strain wave. The phase angle
  will depend on the nature of the material
  (viscous, elastic or viscoelastic)

• Input

• Response

where 0ltdlt90
????stress?
????strain?
????viscosity
G???modulus
3.29
68
One more time Dynamic (Oscillatory) Testing

• By using trigonometry

(3-1)
In-phase component of the stress, representing
solid-like behavior
Out-of-phase component of the stress,
representing liquid-like behavior
Lets define
where
3.30
69
Physical Meaning of G, G
Equation (3-1) becomes
We can also define the loss tangent

• For solid-like response

• For liquid-like response

G???storage modulus
G???loss modulus
70
Typical Oscillatory Data
G???storage modulus
G???loss modulus

• Rubbers Viscoelastic solid response
• G gt G over the whole range of frequencies

71
Typical Oscillatory Data
G???storage modulus
G???loss modulus

• Polymeric liquids (solutions or melts)
  Viscoelastic liquid response
• G gt G at low frequencies
• Response becomes solid-like at high frequencies
• G shows a plateau modulus and decreases with w-2
  in the limit of low frequency (terminal region)
• G decreases with w-1 in the limit of low
  frequency

72
Typical Oscillatory Data

• For Rubbers Viscoelastic solid response
• G gt G over the whole range of frequencies
• For polymeric liquids (solutions or melts)
  Viscoelastic liquid response
• GgtG at low frequencies
• Response becomes solid-like at high frequencies
• G shows a plateau modulus and decreases with w-2
  in the limit of low frequency (terminal region)
• G decreases with w-1 in the limit of low
  frequency

73
(No Transcript)
74

• Sample is strained (pulled, ?) rapidly to
  pre-determined strain (?)
• Stress required to maintain this strain over time
  is measured at constant T
• Stress decreases with time due to molecular
  relaxation processes
• Relaxation modulus defined as
• Er(t) also a function of temperature

Er(t) ?(t)/e0
75
(No Transcript)
76
(No Transcript)