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Dynamic Mechanical AnalysisBasic Theory & Applications Training

TA Instruments – Waters LLC


Course Outline

• Basic Theories of Dynamic Mechanical Analysis

• DMA Instrumentation and Clamps

• Introduction to DMA Experiments

Dynamic tests

Transient tests

• DMA Applications and Data Interpretation

• Troubleshooting Experimental Issues

• Time-Temperature Superposition (TTS)


Basic Theories of

Dynamic Mechanical Analysis


DMA Definitions

• What is a DMA? Dynamic Mechanical Analyzer/ Dynamic Mechanical Analysis

• What does a DMA do? A DMA measures the mechanical/rheological properties of a material as a function of time, frequency, temperature, stress and strain

• What are the typical samples a DMA can handle? Thermal plastic and thermosets Elastomers/ rubbers Gels Foams More….


How Does a DMA Work?

• Apply a force or a deformation to a sample, then measure sample’s response, which will be a deformation or a force.

• All mechanical parameters (stress, strain, modulus, stiffness et al) are calculated from these 2 raw signals

Length

Area

Force

Deformation

Stress (Pa) = Force(N)Area(m2)

Strain = Deformation (m)

Length (m)

Modulus (Pa) = Stress (Pa)

Strain


What Does a DMA Measure?

• DMA measures the viscoelastic properties (stiffness and damping) of a material as a function of time and temperature. These are reported as

Modulus (E and G) / Compliance (J)

Damping factor (tan d)

Transition temperatures (e.g. Tg)


Newton’s Law of Viscosity

• For a purely Viscous Liquid, Stress is proportional to Strain Rate dε/dt

•The slope of stress over strain rate is the viscosity of the material

σ = η* dε/dt

Str

ess

Strain Rate

η


Hooke’s Law of Elasticity

• For a purely Elastic Solid, Stress and Strain have a constant proportionality

• The slope of stress over strain is the Young’s modulus of the material

σ = E*ε

Str

ess

Strain

E


Viscoelasticity Defined

Range of Material Behavior

Ideal Liquid ----- Most Materials ----- Ideal SolidPurely Viscous ----- Viscoelastic ----- Purely Elastic

Viscoelasticity: Having both viscous and elastic properties

• Most of the materials in the world have both elastic and viscous behavior. Therefore, they are viscoelastic


How to Describe 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


Mechanical Property Becomes Time Dependent

•In tensile testing of viscoelastic materials, the rate of extension will give different results

the stress depends on both the strain, and the strain rate

σ = E*ε + η*dε/dt

Stre

ss, σ

Strain, ε


Time-Dependent Viscoelastic Behavior

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

Long deformation time: pitch behaves like a highly viscous liquid

9th drop fell July 2013

Short deformation time: pitch behaves like a solid


Time-Dependent Viscoelastic Behavior

T is short [< 1 sec] T is long [>2 hours]

Deborah Number [De] = /


Viscoelasticity, Deborah Number

•Old Testament Prophetess who said (Judges 5:5):"The Mountains ‘Flowed’ before the Lord"

•Everything Flows if you wait long enough!

•Deborah Number, De - The ratio of a characteristic relaxation time of a material () to a characteristic time of the relevant deformation process ().

De =


Deborah Number

• Hookean elastic solid - τ is infinite• Newtonian Viscous Liquid - τ is zero• Polymer melts processing - τ may be a few seconds

High De Solid-like behaviorLow De Liquid-like behavior

IMPLICATION: Material can appear solid-like because1) it has a very long characteristic relaxation time or2) the relevant deformation process is very fast


Dynamic Mechanical Testing

Deformation

Response

Phase angle d

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

The material response (strain or stress) is measured.

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


Phase Angles

Purely Elastic Response(Hookean Solid)

Purely Viscous Response(Newtonian Liquid)

Viscoelastic Response(Most materials)


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

Phase angle d

Complex Stress, *

Strain,

* = ' + i"

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

The material functions can be described in terms of complex variables having both real and imaginary parts. Thus, using the relationship:

Complex number: 𝑥 + 𝑖𝑦 = 𝑥 + 𝑦

Dynamic Stress: Complex, Elastic, & Viscous Stress


DMA Viscoelastic Parameters

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

The Viscous (loss) Modulus:The ability of the material to dissipate energy. Energy lost as heat.

The Modulus: Measure of materials overall resistance to deformation.

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


Storage and Loss of a Viscoelastic Material

Rubber Ball

Tennis Ball X

STORAGE

LOSSX

Phase angle d

E*

E'

E"Dynamic measurement represented as a vector


Viscoelastic Spectrum for a Typical Amorphous Polymer

Terminal Region

Rubbery PlateauRegion

TransitionRegion

Glassy Region

Loss Modulus (E" or G")Storage Modulus (E' or G')

Very hard and rigid solid

Stiff to Soft rubber

Viscoelastic liquid

Temperature


DMA Results Can Correlate To…..

Stress

Strain

Stiffness

Damping factor

Transition temperatures

Modulus (E, G) / Compliance (J)

Stress

Strain

Stiffness

Damping factor



Processing ConditionsProcessing Conditions

Stress

Strain

Stiffness

Damping factor



Processing Conditions


DMA Instrumentationand Clamps


DMAs from TA Instruments

RSA G2 Discovery DMA850 Q800


DMAs from TA Instruments

Motor Applies Force (Stress)

Displacement SensorMeasures

deformation (Strain)

SampleForce Rebalance Transducer (FRT)

Measures Force (Stress)

Actuator Applies deformation

(Strain)

Sample

Fixed

Combined Motor & TransducerSeparate Motor & Transducer

RSA G2 DMA850 and Q800


RSA G2: Schematic Dual Head Design

Transducer

Motor

Upper Geometry MountLower Geometry Mount


DMA850: Schematic


DMA850 and Q800: Humidity Option


DMA Specifications

RSA G2 DMA850 Q800

Max Force 35 N 18 N 18 N

Min Force 0.0005 N 0.0001 N 0.0001 N

Displacement Resolution

1 nm 0.1 nm 1 nm

Frequency Range 2 x 10-6 to 100 Hz 1 x 10-4 to 200 Hz 1 x 10-2 to 200 Hz

Dynamic Deformation Range

± 5 x 10-5 to 1.5 mm ± 5 x 10-6 to 10 mm ± 5 x 10-4 to 10 mm

Temperature range -150 to 600°C -150 to 600°C -150 to 600°C

Isothermal Stability ± 0.1 ± 0.1 ± 0.1

Heating Rate 0.1oC to 60oC/min 0.1oC to 20oC/min 0.1oC to 20oC/min

Cooling Rate 0.1oC to 60oC/min 0.1oC to 10oC/min 0.1oC to 10oC/min


DMA Mode on DHR and ARES-G2

Force Rebalance Transducer (FRT)

(Measures Stress)

For the ARES-G2, the bottom Actuator remains

locked during DMA function

Sample

Servo control on Null position

(Strain)

Strain control & dynamic test only

ARES G2 and DHR DMA Mode


Specifications of the DHR-DMA and the ARES-G2 DMA

DHR – DMA mode

ARES-G2 DMA mode

Motor Control FRT FRT

Minimum Force (N) Oscillation 0.1 0.001

Maximum Axial Force (N) 50 20

Minimum Displacement (m) Oscillation 1.0 0.5

Maximum Displacement (m) Oscillation 100 50

Displacement Resolution (nm) 10 10

Axial Frequency Range (Hz) 1 x 10-5 to 16 1 x 10-5 to 16

• Dynamic test only


Clamps for DMA850 and Q800

S/D Cantilever Film/Fiber Tension 3-Point Bending Compression

Shear Sandwich Submersible Tension Submersible Bending Submersible Compression


Clamps for RSA G2

Film/Fiber Tension

Compression

3-Point Bending

S/D Cantilever

Shear Sandwich

Contact Lens


RSA G2 Immersion Clamps

• Immersion clamp kit offers 3 geometries with temperature control from -10 to 200 C in the FCO.

Tension Compression 3 Point Bending

Tension: Up to 25 mm long, 12.5 mm wide and 1.5 mm thick.Compression: 15 mm in diameter; maximum sample thickness is 10 mm.Three Point Bending: includes interchangeable spans for lengths of 10, 15, and 20 mm. Maximum sample width is 12.5 mm and maximum thickness is 5 mm.


What Samples Can DMA Measure?

• By changing the clamp, we can test a range of different materials: solid bars, elastomers, soft foams, thin films and fibers

Solid Polymers

Elastomers

Films

Foams Composites

Fibers

Polymer Melts

Gels


Deformation of Solids and the Modulus

•All materials change in shape, volume, or both under the influence of an applied stress.

•The Modulus measures the resistance to deformation of a material when an external force is applied.Modulus = Stress/Strain

•We can define three kinds of Moduli for a materialYoung’s Modulus (Modulus of Elasticity) EShear Modulus (Modulus of Rigidity) GBulk Modulus B


The Three Deformation Modes and Moduli

ShearModulus

BulkModulus

Young’s Modulus

E =

gG = hyd

DV/VoB =

Where Dashed lines indicate initial stressed state = uniaxial tensile or compressive stress = shear stresshyd = hydrostatic tensile or compressive stress = normal straing = shear strainDV/Vo = fractional volume expansion or contraction


Relationship Between Moduli and Poisson’s Ratio for Elastic Isotropic Materials

• Elastic Isotropic materials are materials in which properties at a point are the same in all directions. Some examples of isotropic materials are unorientedamorphous polymers and annealed glasses [1].

• If any of the two elastic constants of a homogenous (in which properties do not vary from point to point) isotropic material, the other two may be calculated [2].

1. Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, p. 1.

2. Hayden, H. W., Moffatt, W.G., and Wulff, J., The structure and Properties of Materials, Volume III, Mechanical Behavior,John Wiley & Sons, Inc, New York, 1965, p.26.

E = 2G(1 + n) = 3B(1 + 2n)


Poisson's Ratio - The Fourth Elastic Constant

• Poison's ratio, n, is the ratio of transverse to axial strain

l0zlz

z

z

ly

-y

2ly - l0y

2 =

z

2lz - l0z

2 =

n = - y

z

Poisson’s Ratiol0y


Poisson’s Ratio

•If the volume of the specimen remains constant when deformed, n = 0.5.

•Examples of constant volume materials are liquids and ideal rubbers.

•In general, there is an increase in volume given by DV/Vo = (1 - 2n)where DV = increase in initial volume Vo caused by straining the sample.


Comparison of Moduli and Poisson’s Ratio

Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991p. 275ISBN 0 7514 0134 X

Material E (GPa) n G (GPa)

Steel 220 0.28 85.9

Copper 120 0.35 44.4

Glass 60 0.23 24.4

Granite 30 0.30 15.5

Polystyrene 34 0.33 12.8

Polyethylene 24 0.38 8.7

Natural Rubber 0.02 0.49 0.0067


Testing Solids on a Rheometer

Torsion (rotational) and DMA (axial) geometries allow solid samples to be characterized in a temperature controlled environment.

Rectangular and cylindrical torsion

3-point bending Cantilever Tension

Shear Modulus: G’, G”, G* Young’s Modulus: E’, E”, E*

E = 2G(1 + ν) ν : Poisson’s ratio

Parallel plate


How DMA Calculate Modulus?

DMA850 and Q800 RSA G2

Stiffness (K) = Force / Displacement

Modulus (E) = Stress / Strain

GF: Geometry factor. Clamp dependentCan be found in online help manual

Stress = Force x K

Strain = Displacement x KnModulus (E) = K x GF

K:Stress constantKn :Strain constantClamp dependentCan be found in online help manual

GF = KKn


Choose the Correct Clamp for Testing

Sample Dimension Films and fibers: tension clamps Bars and cylinders: bending clamps O-rings and tablets: compression and/or shear

Deformation Mode: E [tension, compression and bending] G [shear]

Sample Stiffness: Machine range fixed: 100 - 10, 000,000 N/m. Stiffness of

sample related to its dimensions [L, w, t]. Stiffness may limit sample size to below clamp maximum.


DMA: Dual Cantilever Clamp

Highly damped materials can be measured Best mode for evaluating the cure of supported materials

Sample

Stationary Clamp

Movable clamp


Geometry Factor - Dual Cantilever Clamp

Modulus = Stiffness × Geometry Factor

If length/thickness > 10, Poisson’s Ratio term is dropped


Operating Range of the Dual Cantilever Clamp

16 mm long10 mm wide4 mm thick

35 mm long12.5 mm wide3.2 mm thick



10 510 210 110 0

Geometry Factor (1/mm)10 3 10 4

10 -1

10 4

10 5

10 6

10 7

10 8

10 9

10 10

10 13

10 12

10 11

10 3

Mo

du

lus

(P

a)


DC


DMA: Single Cantilever Clamp

Best general purpose mode (thermoplastics) Preferred mode over dual cantilever for most neat

thermoplastics (unreinforced), except elastomers Clamping torque is important

Sample

Stationary Clamp

Movable clamp


Geometry Factor - Single Cantilever Clamp




Operating Range of the Single Cantilever Clamp

17.5 mm long12.5 mm wide3.2 mm thick



10 510 210 110 0


10 -1

10 4

10 5

10 6

10 7

10 8

10 9

10 10

10 13

10 12

10 11

10 3


DMA: 3 Point Bend Clamp

Best mode for measuring medium to high modulus materials Conforms with ASTM standard test method for bending Purest deformation mode since clamping effects are eliminated

Moveable Clamp Force

Sample

Stationary Fulcrum


Geometry Factor - 3 Point Bending Clamp




Operating Range of the 3 Point Bending Clamp



50 mm long12.5 mm wide

1 mm thick

10 510 210 110 0


10 4

10 5

10 6

10 7

10 8

10 9

10 10

10 13

10 12

10 11

Mo

du

lus

(P

a)


DMA: Film and Fiber Tension Clamp

Best mode for evaluation of thin films and fibers bundle or single filaments

Small samples of high modulus materials can be measured TMA-like constant force and force ramp measurements

aka. mini-tensile tester Force track and constant force control

Movable clamp

Sample(film, fiber, or thin sheet)

StationaryClamp


Operating Range of the Film/Fiber Tension Clamp

Geometry Factor (1/mm)

10 mm long5 mm long

0.2 mm long

20 mm long4 mm wide

0.1 mm thick20 mm long0.1 mm diameter

10 -1 10 010 1 10 2 10 4

10 310 5

10 4

10 5

10 6

10 7

10 8

10 9

10 10

10 11

10 12

10 13

Mo

du

lus

(P

a)



DMA: Compression Clamp

Good mode for low to medium modulus materials(gels,elastomers)

Materials must provide restoring force(support necessary static load)

Options for expansion & penetration measurements Typically shear component is significant

Stationary Clamp

Sample

Movable Clamp


Operating Range of the Compression Clamp

10 -110 010 -210 -310 -4

10 4

10 5

10 6

10 7

10 8

10 9

10 10

10 3

10 2

10 1


Mo

du

lus

(P

a)

1 mm thick40 mm diameter





DMA: Shear Sandwich Clamp

Square sample configuration provides pure shear deformation Provides Shear Moduli: G*, G', G" & G(t) Good for evaluating highly damped soft solids such as gels and

adhesives & elastomers > Tg Can be used for high viscosity melts and resins

MovableClamp

StationaryClamp

Sample


Operating Range of the Shear Sandwich Clamp

each piece2 mm thick

10 mm square

each piece4 mm thick

5 mm square

10 -110 010 -210 -3

10 4

10 5

10 6

10 7

10 8

10 9

10 10

10 3

10 2

10 1


Mo

du

lus

(P

a)



Changing Sample Stiffness

Clamp Type To Increase Stiffness… To Decrease Stiffness… Tension Film Decrease length or increase

width. If possible increase thickness.

Increase length or decrease width. If possible decrease thickness.

Tension Fiber Decrease length or increase diameter if possible.

Increase length or decrease diameter if possible.

Dual/Single Cantilever Decrease length or increase width. If possible increase thickness. Note: L/T 10

Increase length or decrease width,, If possible decrease thickness. Note: L/T 10

Three Point Bending Decrease length or increase width. If possible increase thickness.

Increase length or decrease width. If possible decrease thickness.

Compression – circular sample

Decrease thickness or Increase diameter.

Increase thickness or decrease diameter.

Shear Sandwich Decrease thickness or Increase length and width.

Increase thickness or decrease length and width.


DMA Clamping Guide

Sample Clamp Sample Dimensions

High modulus metals or composites

3-point BendDual Cantilever

Single CantileverL/T> 10 if possible

Unreinforced thermoplastics or thermosets

Single Cantilever L/T >10 if possible

Brittle solid (ceramics) 3-point BendDual Cantilever

L/T>10 if possible

Elastomers Dual CantileverSingle CantileverShear SandwichTension

L/T>20 for T<TgL/T>10 for T<Tg(only for T> Tg)T<2 mm W<5 mm

Films/Fibers Tension L 10-20 mmT<2 mm

Supported Systems 8 mm Dual Cantilever minimize sample, put foil on clamps


Available DMA Experiments

(1) Dynamic Tests


Dynamic (Oscillatory) Testing

Available oscillatory test modes

•Strain (stress) Sweep

•Time Sweep

•Frequency Sweep

•Temperature Ramp

•Temperature Step (Sweep) (TTS)

•Others


Some Clamps Require Offset (static) Force!

Clamps with offset force:Tension FilmTension: Fiber3-Point BendCompressionPenetration

Force/Time Curves

OFA

0A

A = Oscillatory force amplitudeOF = Offset force (static force)

Clamps without offset force:Single CantileverDual CantileverShear Sandwich


Offset (Static) Force

Static force [General] Used in tensioning clamps to prevent sample buckling [tension], or loss of

contact with the probe [compression] during the test. Static force must exceed dynamic force at all times during experiment

Applied before dynamic oscillation to automatically measure sample lengthConstant Force

Applies same static force throughout experiment Can be used with highly crystalline or cross-linked materials

to measure displacement at constant force for quant. expansionForce Track

Applies Static Force in Proportion to Sample Modulus. Used in "Tensioning" Clamps to reduce stretching as specimen weakens

Ratio of static to dynamic force: Static Force = (Force Track %/100) x (Stiffness x Amplitude) where stiffness = Force applied to sample/amplitude of deformation

Values from 125-150% work well for most samples


Offset Force on DMA850

Constant static force Force track


Offset Force on Q800



Offset Force on RSA G2



Temperature Ramp with Force Track

•Static Force tracks Dynamic Force throughout Temperature Ramp


Choosing Force Track Parameters

Clamp Type Static Force Force Track Tension Film 0.01 N 120 to 150% Tension Fiber 0.001 N 120% Compression 0.001 to 0.01 N 125%

Three Point Bending Thermoplastic Sample

1 N 125 to 150%

Three Point Bending Stiff Thermoset Sample

1 N 150 to 200% Can use constant static

force

Initial static force before testing

Note: Constant (or static) force can be used as long as static force > dynamic force through out the entire experiment.


Dynamic Strain (Stress) Sweep

• The material response to increasing deformation amplitude is monitored at a constant frequency and temperature. Time

Deformation

USES• Identify Linear Viscoelastic Region• Resilience/elasticity


Dynamic Strain Sweep: Material Response

gc = Critical Strain

ConstantSlope

Results depend on strainLinear viscoelastic regionResults independent of strain


Programming Strain Sweep on DMA850


Programming Strain Sweep on Q800

Mode: DMA Multi-Strain


Programming Strain Sweep on RSA G2


Dynamic Time Sweep

Time

Deformation • The material response is monitored at a constant frequency, amplitude and temperature.

USES• Curing studies• Fatigue tests• Stability against thermal degradation


Epoxy Curing on Glass Braid

Instrument: DMA850Clamp: Dual cantileverSample: Epoxy coated on glass braidDynamic time sweepTemperature: 35°CFrequency: 1 HzAmplitude: 10 m


Programming Time Sweep or Fatigue on DMA850

• Time sweep example • Fatigue example


Programming Time Sweep on Q800

Mode: DMA Multi-Frequency-Strain


Programming Time Sweep or Fatigue on RSA G2

• Time sweep example • Fatigue example


Frequency Sweep

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

Time

Deformation

USES• Quick comparison on modulus and elasticity on

solids• Study polymer melt processing (shear sandwich).• Estimate long term properties with extended

frequency (time) range using TTS


Happy & Unhappy Balls

10-1 100 101102

105

106

107

108

10-2

10-1

100

Freq [rad/s]

E

' ()

[d

yn/c

m²]

tan

_de

lta (

) [ ]

Unhappy ball

Happy ball

Modulus is the sametan d is very different

Happy & Unhappy Balls


Frequency Sweep: Material Response

Terminal Region


TransitionRegion

Glassy Region

12

Storage Modulus (E' or G')Loss Modulus (E" or G")

log Frequency (rad/s or Hz)


Programming Frequency Sweep on DMA850


Programming Frequency Sweep on Q800

Mode: DMA Multi-Frequency-Strain


Programming Frequency Sweep on RSA G2


Dynamic Temperature Ramp

• A linear heating rate is applied. The material response is monitored at a constant frequency and constant amplitude of deformation. Data is taken at user defined time intervals. Time

Data Acquisition Interval

m = ramp rate

Recommend ramp rate for polymer testing: 1-5˚C/min.


Temperature Step & Hold- Single /Multi-Frequency

• A step and hold temperature profile is applied. The material response is monitored at one, or over a range of frequencies, at constant amplitude of deformation

Time

Soak Time

Step Size

OscillatoryMeasurement

Time

Step Size OscillatoryMeasurement

Soak Time


Temperature Profile on Amorphous Polymers

Temperature

Terminal Region


TransitionRegion

Glassy Region

Loss Modulus (E" or G")

Storage Modulus (E' or G')

DMA Applications Range


Temp Ramp on Polycarbonate

Clamp: single cantileverTemperature:ambient to 180°CHeating rate: 3°C/minFrequency: 1 HzAmplitude: 20 m

PC sample

p/n: 982165.903

• Available from TA for Instrument verification


Programming Temp Ramp/Sweep on DMA850

• Temp Ramp Example • Temp Sweep Example

Note: Measurement can be done with single or multiple frequencies


Programming Temp Ramp/Step on Q800

Mode: DMA Multi-Frequency-Strain• Temp Ramp Example • Temp Sweep Example



Programming Temp Ramp/Sweep on RSA G2

• Temp Ramp Example • Temp Sweep Example



Experimental Considerations

• Sample Deformation Mode Stiffness (sample size and shape) Clamp Type (sample size and shape)

• Static Force/Force Track

• Amplitude (single/multiple)

• Frequency (Single/multiple)

• Heating Rate/Temperature Program


Selecting Appropriate Amplitude and Force

• Strain considerationMust be within the linear region

• Force considerationMaximum - 18 N on Q800, DMA850Maximum - 35 N on RSA G2

• Yielding /Creep If the force is too high the specimen may deform irreversiblyMust consider behavior at all temperatures and frequencies

• NoiseHigher amplitude = lower noise (generally) Trade off against yielding/creep behavior


Frequencies

• Single Frequency In a temperature ramp the most commonly used frequency is

between 1 to 10 Hz (6.28 or 63 rad/sec)• Multiple Frequencies For an ambient test the commonly used frequency range is

from 0.1 – 10Hz. Frequency sweeps at multiple temperatures for Time-

Temperature Superpositioning (TTS) Run from high to low frequencies for faster initial data

acquisition (for DMA850 and Q800 users)• Data Collection Rate Lower frequencies take longer time - control experimentMore frequencies = longer experiment


Temperature Program

• Temp ramp Commonly used heating rate: 1-5°C/min

Larger samples have more thermal lag

Use slower ramp rates for lower frequencies and frequency sweeps because these take more time

• Temp sweep No thermal lag but time consuming

Commonly used for TTS testing, typical temp step: 5-10°C

• Multiple temp steps Commonly used to mimic certain application temperature profile


Available DMA Experiments

(2) Transient Tests


Transient Testing

Available transient test modes

•Creep-Recovery

•Stress Relaxation

•Iso-strain Temperature Ramp

•Iso-force Temperature Ramp

•Stress-Strain Rate Tests


Creep Recovery Experiment

• A stress is applied to sample instantaneously at t1 and held constant for a specific period of time. The strain is monitored as a function of time (g(t) or (t)).

• The stress is reduced to zero at t2 and the strain is monitored as a function of time(g(tor(t

Stre

ss

timet1 t2



Response of Classical Extremes

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

time

time time

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

t2t1

t1 t2t2t1


Creep Recovery: Response of Viscoelastic Material

Creep > 0

timet 1

t2

/

Strain rate decreases with time in the creep

zone, until finally reaching a steady state.

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)

/

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.


UnrecoverableStrain

Creep Recovery: Response of Viscoelastic Material



time

Recovery ZoneCreep Zone

Less Elastic

More Elastic

Creep > 0 Recovery = 0 (after steady state)

/

t1 t2


Creep Recovery : Creep and Recoverable Compliance


J(t)

1/

time

Creep Zone

J r(t)

time

Recovery Zone

Creep Compliance Recoverable Compliance

Where gu = Strain at unloadingg(t) = time dependent

recoverable strain

Je = Equilibrium recoverable compliance

more elastic

Je

Creep experiments report the material property Compliance which is in a sense the inverse of Modulus


Creep-Recovery Test on PET Film

Stress: 5MPa

Instrument: Q800Clamp: TensionTemperature: 75°CStress: 5MPa

p/n: 984309.901


Creep: Material Response

Terminal Region


TransitionRegion

Glassy Region

log time


Programming Creep Recovery on a DMA850


Programming Creep Recovery on a Q800


Programming Creep Recovery on a RSA-G2

• A pre-test is required to obtain sample information for the feedback loop• Stress Control Pre-test: frequency sweep within LVR


Programming Creep Recovery on a RSA-G2

Creep Recovery

• Stress: needs to be in the linear region• Creep time: until it reaches steady state• Recovery time: until the compliance and strain reach plateau


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).St

rain

0time



Response of Classical Extremestime0

time0

stress for t>0is constant

time0

stress for t>0 is 0

Hookean Solid Newtonian Fluid



Response of ViscoElastic 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, E(t)

E(t) = (t)/g

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

time0


Stress Relaxation: Material Response

Terminal Region


TransitionRegion

Glassy Region

log time


Stress Relaxation Happy and Unhappy Balls

Happy ball has an infinite relaxation time


Programming Stress Relaxation on a DMA850


Programming Stress Relaxation on a Q800


Programming Stress Relaxation on a RSA-G2


Iso-strain/Iso-stress Temperature Ramp

Temperature

Time

Data Acquisition Interval

m = ramp rate

• The strain or stress is held at a constant value and a linear heating rate is applied.

• Valuable for assessing mechanical behavior under conditions of confined or fixed load (stress) or deformation (strain).

• Example: Measure sample shrinkage (length shrinkage or shrinking force)


Iso-Strain Temp Ramp: Measure Shrinking Force

Strain = 0.05%

Sample is held at a constant length; shrinkage force is measured

X


Iso-Force Temp Ramp: Measure Length Shrinkage

Hold force at 0.05NTemperature : ambient to 120˚CRamp rate: 3˚C/min

X

Sample is held at a constant force; shrinkage is measured


Iso-Strain/Iso-Stress on a DMA850

• DMA Iso-strain• Hold strain constant and

measure sample shrinking force

• DMA Iso-stress• Hold stress constant and measure

sample dimension change


Iso-Strain/Iso-Stress on a Q800



• DMA Control force• Hold force constant and measure



Iso-Strain/Iso-Stress on a RSA G2



• DMA Iso-force• Hold stress constant and measure



Stress-Strain Testing

time

Linear rate

HenckyRate

Axial Test: Strain Rate Controlled• Sample is deformed under a

constant linear strain rate,

Hencky strain rate, force, or

stress for generating more

traditional stress-strain curves.

• Measure sample’s Young’s

modulus, yield stress, strain

hardening effect and sample

fracture

time

Linear rate


Polysaccharide Film Stress-Strain Test

time

Linear rate

Geometry: TensionTemperature: 37°CRate: 10 m/s

Strain hardening


Strain/Stress Ramp on a DMA850

Stress RampStrain Ramp


Strain/Stress Ramp on a Q800

• DMA strain rate mode• Strain ramp• Displacement ramp

• DMA control force mode• Force ramp


Strain Ramp on a RSA G2

• Linear strain rate • Hencky strain rate


DMA Applications and Data Interpretation


The DMA Results Can Correlate To…

DMA Results:

E, G, JTan d

Tg, Tb, Tg

Molecular structures• MW and MWD• Branching• Crystallinity• Crosslinking• Phase• Relaxation

Product properties• Transition

temperatures (Tg, Tb, Tg)

• Environmental resistance

• Impact strength• Long term

behavior, aging• Adhesion

Processing:• Heat history• Residual stress• Shear or orientation• Temperature• Fillers


Most Common DMA Test – Temp Ramp

• The most Common DMA measurement is a dynamic temperature ramp

• The test results report modulus (E*, E’, E”), damping factor (Tan d) and transition temperatures (Tg)

• Provide information to polymer’s structure-property relationship


What is Glass Transition (Tg)?

•A transition over a range of temperature from a glassy state to a rubber state in an amorphous material

•Mechanical: Below the Glass Transition, the material is in a brittle, glassy state, with a modulus of 109 PaAbove the Glass Transition, the material becomes soft and flexible, and the modulus decreases two to three decades

•Molecular: Below the Glass Transition, polymer chains are locked in place, without sufficient energy to overcome the barrier for rotational or translational motion. At temperatures above the Glass Transition, there is molecular mobility, and chains can slide past each other


How to Define Tg in DMA?

Onset of E’ Peak of E” Peak of Tan d


Secondary Transitions

Turi,Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 487.

Glass Transition (Tg) Cooperative motion among a large number of chain segments,

including those from neighboring polymer chains

Secondary Transitions (Tb, Tg) Local Main-Chain Motion – intra-molecular rotational motion of

main chain segments four to six atoms in length Side group motion with some cooperative motion from the main

chain Internal motion within a side group without interference from side

group. Motion of, or within, a small molecule or diluent dissolved in the

polymer (eg. plasticizer.)


Primary and Secondary Transitions in PC

Instrument: DMA850Temperature:-150°C to 180°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 15 m


Primary and Secondary Transitions in PET

Instrument: RSA G2Temperature:-150°C to 110°CHeating rate: 5°C/minFrequency: 1HzStrain: 0.1%


What Will Affect Tg and Modulus?

• Heating rate Thermal lag

• Test frequency

• Polymer structures Rigid polymer chain shows higher Tg (e.g. PS)

Flexible polymer chain shows lower Tg (e.g. PE)

Crystallization

Degree of crosslinking


The Effect of Test Frequency on Tg

• The glass transition is a kinetic transition. It is therefore influenced strongly by the frequency of the test. The Tg is a molecular relaxation that involves cooperative segmental motion.

• Because the RATE of segmental motion depends on temperature, as the frequency increases, the relaxations associated with the Tg can only happen at higher temperatures.

• In general, increasing the frequency will Increase the Tg

Decrease the intensity of tan d or loss modulus Broaden the peak Decrease the slope of the storage modulus curve in the region of

the transition.

Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 529.


PET Film: Effect of Frequency on Tg

• PET film tested at 0.1 Hz, 1Hz and 10 Hz


Chemical Composition of Polymers

•Polymers are long chains of repeating units (monomers)

•The chemical composition determines mechanical properties, and the temperature where transitions occur

Polyethylene Tg : -128° C Polypropylene Tg: -20° C

Polystyrene Tg: 100 ° C

“Introduction to Polymer Viscoelasticity,” 2nd Edition. Aklonis, John J; MacKnight, William J. Wiley-Interscience


Effect of Crystallinity in Polymer

“The major effect of the crystallite in a sample is to act as a crosslink in the polymer matrix. This makes the polymer behave as though it was a crosslinked network, but as the crystallite anchoring points are thermally labile, they disintegrate as the temperature approaches the melting temperature, and the material undergoes a progressive change in structure until beyond Tm, when it is molten”

Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991p. 330-332. ISBN 0 7514 0134 X

Random Chain100% Amorphous

Fringed MicellCrystalline


Effect of Crystallinity on Tg

• Crystalline Polymers - multiphase systems - can be thought of as being made up of an amorphous phase containing dispersed crystalline units.

• Simple Picture of Two Phase System - crystalline phase acts to restrain mobility of neighboring amorphous regions

• General Case for Semi-crystalline PolymersIncreasing Crystallinity will: increase the glass transition temperature decrease the intensity of the glass transition peak broaden the transition temperature range

Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 518.


Effect of Crystallinity on Modulus

0% Crystallinity (100% Amorphous)

25%

40%

65%

M.P.

Temperature

Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991p. 330-332. ISBN 0 7514 0134 X

• Crystallinity mostly affects the sample at Tg <T < Tm,

• Below Tg the effect on the modulus is small

• The modulus at T > Tg of a semi-crystalline polymer is directly proportional to the degree of crystallinity

• Remains independent of temperature if the amount of crystalline order remains unchanged

Increase Tg


Polymer Crosslinking

• Linear polymers can be chemically or physically joined at points to other chains along their length to create a crosslinkedstructure

• Chemically crosslinked systems are typically known as thermosetting polymers because the crosslinking agent is heat activated.

• Thermosetting polymers never molten

Ward, I.M., Hadley, D.W., An Introduction to the Mechanical Properties of Solid Polymers, John Wiley & Sons Ltd., New York, 1993


Effect of Crosslinking on Tg

Increasing Crosslinking

Higher Density

Less Free Volume

Restricted molecular motion

More Energy needed

Higher Glass Transition Temperature

Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991 p.262 ISBN 0 7514 0134 X

For low values of crosslink density, Tg can be found to increase linearly with the

number of crosslinks.

For high crosslink density, the Tg is broad and not well

defined.


Effect of Crosslinking

120

160

300

1500

9000

30,000

M = MW betweencrosslinks

c

Temperature

Increase Tg


Amorphous, Crystalline and Crosslinked Polymers

Amorphous

Crystalline

Crosslinked

increasecrystallinity

increasecrosslinkingM

odu

lus

(E o

r G

)

Temperature


Polymer Cold Crystallization (PET)

• Modulus (E’) increase due to cold crystallization

What happened here?


PET: Heat-Cool-Heat Test

In second heat: • Tg shifted to higher temperature • Transition becomes much broader and weaker• Rubbery plateau modulus increased more than one decade

Before test

After test


Anisotropic Materials

• Anisotropic materials have different properties in different directions. fibers, wood, fiber-filled composites oriented amorphous polymers, injection molded

specimens crystalline polymers in which the crystalline phase is not

randomly oriented

• Show different moduli at different measurement direction

Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, pp. 39-40.


Anisotropic Material

Notes:Frequency = 1 HzAmplitude = 40 micronsForce Track = 150%Ramp Rate = 3°C/min.

10

100

1000

10000

1.0E5

Los

s M

od

ulu

s (M

Pa

)

10

100

1000

10000

1.0E5

Sto

rag

e M

odu

lus

(MP

a)

20 40 60 80 100 120 140 160 180 200

Temperature (°C)

––––––– Fibers Parallel to Length– – – – Fibers Perpindicular to length

Universal V2.6D TA Instruments

Storage Modulus

Loss Modulus

A B

length

A

BA

B

• Polyester/Glass Fiber Reinforced Composite


Anisotropic Material

104.55°C

96.82°C

Notes:Frequency = 1 HzAmplitude = 40 micronsForce Track = 150%Ramp Rate = 3°C/min.

0.02

0.04

0.06

0.08

0.10

0.12

Ta

n D

elta

25 50 75 100 125 150 175 200

Temperature (°C)

––––––– Fibers Parallel to Length– – – – Fibers Perpindicular to Length


A B

length

A

B

• Polyester/Glass Fiber Reinforced Composite


Oriented Polymer: Shrink Wrap

•“Shrink Wrap” is widely used in packaging to conveniently label irregularly shaped containers

•When this kind of biaxially oriented film is heated, it turns to shrink and returns to lower energy random-coil state.

•PET-based LabelZ-direction

X-direction

•RSA G2: 5˚ C per minute, 1 HzZ

X


PET Film Measured at X and Z Direction

Z

X


Len

gth

(m

m)

Iso-force Temp Ramp: measure shrinkage

Hold force at 0.05NTemperature : ambient to 120˚CRamp rate: 3˚C/min

Z

X

z

x


Str

ess

(

kPa

) Iso-strain Temp Ramp: measure shrinking force

Strain = 0.05%Temperature : ambient to 120˚CRamp rate: 3˚C/min

Z

X

z

x


Blending of Amorphous Polymers

• Blending polymers with different glass transition temperatures and modulus will create new materials that may show better physical properties

• If the polymers blended are completely compatible then the blend behaves like an ordinary amorphous polymer with a single transition region and an intermediate glass transition temperature.

• If the polymers are incompatible, then the blend will show separate glass transitions


Polymer Blend – Miscible Case

Temperature (°C)

l–––––– Polymer Ap – – – Polymer Blend: A + B–––– Polymer B

Ela

stic

Mod

ulu

s

100%Polymer B

Polymer BlendA + B

100 % Polymer A

Aerospace Coating


l l l l l l l l l ll

l

l

l

l

l

l

lp p p p p p p

p

p

p

pp

p

p

p

p

89.77°C

76.19°C

46.46°C

-0.5

0.0

0.5

1.0

1.5

Tan

Del

ta

-25 0 25 50 75 100 125

Temperature (°C)

l–––––– Polymer Ap – – – Polymer Blend: A + B–––– ∙ Polymer B


100 % Polymer A

100%Polymer B

Polymer BlendA + B

Polymer Blend – Miscible Case

Aerospace Coating


Polymer Blend - Immiscible Case

• Acrylonitrile-Butadiene-Styrene (ABS) is a polymer blend

Tg of “B”

Tg of “S”


Using Glass Transition to Evaluate Blending

• Investigating manufacturing blend uniformity


Effect of Filler on Modulus

20

60% mica

40% mica

60% asbestos

40% asbestos

20% mica

20% asbestos

20% calcium carbonate

polystyrene control

Nielson, L. E., Wall, R. A., and Richmond, P. G., Soc. Plastics Eng. J., 11, 22 (1966)

40 60 80 100 120 140 160

Temperature (°C)

Sto

rag

e M

od

ulu

s (E

’)


Effect of Aging on Elastomer O Rings


Effect of Aging on Tg of PVC Roofing Membrane

l l ll

l

l

l

l

l

l

l

ll

l

l

l

l

l

l

p p pp

p

p

p

p

p

p

p

p

p

p

p

p

p

p

10.44°C

Initial 90 days

12.82°C

150 days

14.91°C

0.0

0.1

0.2

0.3

0.4

Tan

Delta

-100 -75 -50 -25 0 25 50

Temperature (°C)

l PVC - Initial Conditionp PVC - Aged for 90 days PVC Aged for 150 days



Effect of Plasticizer

• Plasticizers are generally low molecular weight organic additives which are used to soften rigid polymers

• Typically added to a polymer for two reasons:1. To lower the Tg to make a rigid polymer become soft 2. To make the polymer easier to process

• Plasticizers act as lubricant in polymer chains

• Therefore plasticizers will have the effect of:1. Lowering the Tg and broadening tan d peak2. Lowering the moduli (E’ and E”)


Effect of Plasticizer on Vinyl Flooring

Higher % Plasticizer


Humidity Influence: Nylon Film


O-rings: Stress Relaxation

• Squeeze the O-ring to a certain strain. Hold it constant, then measure how long it takes for the force to relax


Creep Tests on Packaging Bags

l

l

l l l l l l l l

p

p

p p p p p p p p

0

20000

40000

60000

80000

100000

120000

Cre

ep

Co

mp

lianc

e (

µm

^2/N

)

0 1 2 3 4 5 6 7 8 9 10

Time (min)

l Poor Performancep Good Performance Excellent Performance

Universal V2.1A TA Instruments

• Apply a load force, then measure how much the bag is stretched


Memory Foam: Multi-Step Creep RecoveryS

tra

in

(%

)

Stre

ss

(Pa

)


Troubleshooting

Experimental Issues


Factors That Influence Measurement Results

Geometry• Clamp• Sample size• Sample loading• Sample integrity

Check list• Clamp calibrations• Proper loading

torque/force• Sample uniformity

and thermal stability• Bad contact or

sample bending and twisting

Test Parameters

Check list• Loading force• Proper force track• Equilibration time• Heating rates• Amplitude• Frequency

Primary measurements• Force• Displacement• Temperature

Check list• Instrument

calibrations• Thermocouple

position


Instrument and Clamp

• Periodically calibrate the instrument following the online help manual

• Perform clamp calibration every time when attaching a new clamp on the instrument

http://www.youtube.com/user/TATechTips

• Perform confidence verification check using polycarbonate provided by TA Instruments

p/n: 982165.903


DMA850 Flow Chart of Calibration Procedures

• Follow the online help manual

• The stability verification is performed at installation

• Instrument calibration includes 2 steps: force and phase

• Clamp calibration: perform when newly attached.


Q800 Flow Chart of Calibration Procedures

Clamp

Position

Instrument

MassZero Compliance

ElectronicsForceDynamic

BalanceWeight

Select ClampClamp MassCompliance

0.005 steel0.010 steel0.020 steel0.030 steelThick steel

Analyze data

• Instrument calibration includes 3 steps: Electronics, Force, and Dynamic

• Position calibration: calibrate the absolute position of the drive shaft. Perform this calibration when DMA is moved, reset, or powered down.

• Clamp calibration: perform when newly attached.


RSA G2 Flow Chart of Calibration Procedures

• Follow the online help manual

• Instrument calibration: force and phase angle check

• Clamp calibration: mass (perform when newly attached)


DMA Confidence Check - Polycarbonate

• Load Polycarbonate (L 17.5, w 12.85, t 1.6mm)• Use Single Cantilever Clamp 20-30 micrometer amplitude 1 Hz frequency

• Storage Modulus at Room TemperatureE' = 2.35 GPa (2350 MPa) +/- 5%

• Tan Delta at Room TemperatureTan d < 0.01

• Transition TemperatureTan d peak between 155-160°C @ 1Hz, 3-5°C/minE" peak will be about 5°C lower

p/n: 982165.903


Sample Preparation

•DMA measurement results are highly depending on the quality of sample preparation

• Sample flatness and uniformity have big influence to the accuracy of the test results


E’ Increase in a Strain Sweep

l ll

l ll

ll

ll l l ll

p

p

p

p

p

p

p

p

p

p

p

p

pp

0.01

0.1

1

10

[

] D

ynam

ic F

orc

e (

N)

p

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

[

] S

tora

ge

Mo

dulu

s (M

Pa

)l

0.1 1 10 100 1000

Amplitude (µm)

Instrument: DMA Q800 V21.3 Build 96


Why does E’ increase with increasing amplitude?How to verify linear viscoelastic region?

Instrument: Q800Clamp: 3-p bendingTemperature: ambientAmplitude: 1-500 mFrequency: 1Hz


E’ Increase in a Strain Sweep

l ll

l ll

ll

ll l l ll

p

p

p

p

p

p

p

p

p

p

p

p

pp

0.01

0.1

1

10

[

] D

ynam

ic F

orc

e (

N)

p

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

[

] Sto

rag

e M

odu

lus

(MP

a)

l

0.1 1 10 100 1000

Amplitude (µm) Universal V4.5A TA Instruments

The sample is not flat and not in full contact with the clamp face.Solutions: (1) Prepare a flat sample

(2) Increase force track or increase static force


E’ Increase in a Temp Ramp

• The E’ of a material should not increase with temperature unless it is crystalized or crosslinked

Instrument: DMA850Clamp: tensionTemperature:0°C to 180°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m


Noisy Modulus After Tg

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

Lo

ss M

od

ulu

s (M

Pa

)

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

Sto

rage

Mo

dul

us (

MP

a)

-100 -50 0 50 100 150

Temperature (°C) Universal V4.5A TA Instruments

What is the problem with this data collected after Tg?

What’s wrong here?

Instrument: Q800Clamp: tensionTemperature:-100°C to 150°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m


Noisy Modulus After Tg

Sample stiffness is below the instrument spec. (100N/m)Solution: Increase the sample stiffness (wider, thicker, shorter)

78.71°C39.76N/m

0.1

1

10

100

1000

10000

1.0E5

Stif

fne

ss (

N/m

)

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

Lo

ss M

od

ulu

s (M

Pa)

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

Sto

rag

e M

odu

lus

(MP

a)

-100 -50 0 50 100 150

Temperature (°C)

Instrument: DMA Q800 V21.2 Build 88


Instrument: Q800Clamp: tensionTemperature:-100°C to 150°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m


Sample Sagging

• Sample sagging after Tg

• Solution: use cantilever clamp instead of 3-p bending

Instrument: RSA G2Clamp: 3-p bendingTemperature:50°C to 180°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m


Compression Testing on Foam/Rubber

Question: How to measure correct modulus?Answer: (1) Prepare regular sample

(2) Apply appropriate static force

(1) Poor contact

(2) Appropriate

(3) Over squeezed


Time-Temperature Superposition (TTS)


Time and Temperature Relationship

(E" or G")(E' or G')

(E" or G")

(E' or G')

log Frequency Temperature

• Linear viscoelastic properties are both time and temperature dependent

• Some materials show a time dependence that is proportional to the temperature dependence Decreasing temperature has the same effect on viscoelastic

properties as increasing the frequency, and vice versa• For such materials, changes in temperature can be used to “re-scale”

time, and predict behavior over time scales not easily measured


Time Temperature Superpositioning Benefits

• TTS applies to materials that are thermo-rheological simple. When all relaxation times have the same temperature dependence

•TTS can be used to extend the frequency beyond the instrument’s range. Frequency is correlate to time and shear

• Creep or Stress Relaxation TTS can predict behavior over longer times that cannot be practically measured


TTS Limitations

• TTS works with polymers that are thermo-rheological simple

• TTS does not work if:

Sample is partially crystalized, crosslinked, or highly filled

Sample change properties (e.g. crystalize, melt, cure, decompose) within temperature of interest

Polymer contains multiple phases: composite or blends

Liquid samples with multiple components

• TTS has been used as empirical rules to predict sample properties over long time scales


Guidelines for TTS

• Decide first on the Reference Temperature: T0. What is the use temperature?

• If you want to obtain information at higher frequencies or shorter times, you will need to conduct frequency (stress relaxation or creep) scans at temperatures lower than T0.

• If you want to obtain information at lower frequencies or longer times, you will need to test at temperatures higher than T0.

• Good idea to scan material over temperature range at single frequency to get an idea of modulus-temperature and transition behavior.


Sto

rag

e m

od

ulu

s

(P

a)

Reference T

TTS Shifting

• Generating frequency sweep data at different temperature steps• Select your reference temperature (e.g. 155°C)


Sto

rag

e m

od

ulu

s

(P

a)

TTS Shifting

aT=150

• Low temperature data shift to higher frequencies

Reference T


Sto

rag

e m

od

ulu

s

(P

a)

TTS Shifting

aT=145

Reference T



Sto

rag

e m

od

ulu

s

(P

a)

TTS Shifting

aT=140

Reference T



Sto

rag

e m

od

ulu

s

(P

a)

TTS Shifting

aT=160

Reference T

• High temperature data shift to lower frequencies


Sto

rag

e m

od

ulu

s

(P

a)

TTS Shifting

aT=165

Reference T



Sto

rag

e m

od

ulu

s

(P

a)

TTS Shifting

aT=170

Reference T



Sto

rag

e m

od

ulu

s

(P

a)

TTS Shifting

aT=175

Reference T



Master Curve from TTS ShiftingS

tora

ge

mo

dul

us

(

Pa

)

• TTS Master Curve using 155°C as reference

Each frequency sweep test

range


WLF and Arrhenius Equations

• Master Curves can be generated using shift factors derived from the Williams, Landel, Ferry (WLF) model

log aT= -c1(T-T0)/(c2+(T-T0))

aT = temperature shift factor T0 = reference temperaturec1 & c2 = constants from curve fitting

Generally, c1=17.44 & c2=51.6 when T0 = Tg

• The Arrhenius model works better if T > Tg+100°C; or T < Tg and polymer is not elastomeric temperature range is small, then c1 & c2 cannot be calculated precisely

ln aT = (Ea/R)(1/T-1/T0)

aT = temperature shift factor Ea = Apparent activation energyT0 = reference temperature R = gas constant


Shift Factors aT vs. Temperature

WLF model

• Shift factors fitted with WLF model


Lo

ss m

odu

lus

(

Pa

)

Cole-Cole Plot to Validate TTS

• The Cole-Cole plot and van Gurp-Palmen plot are commonly used to validate the application of Time-Temperature Superposition (TTS).


Pha

se a

ngle

(

°)

van Gurp-Palmen Plot to Validate TTS

• The Cole-Cole plot and van Gurp-Palmen plot are commonly used to validate the application of Time-Temperature Superposition (TTS).


References for TTS

1) Ward, I.M. and Hadley, D.W., "Mechanical Properties of Solid Polymers", Wiley, 1993, Chapter 6.

2) Ferry, J.D., "Viscoelastic Properties of Polymers", Wiley, 1970, Chapter 11.

3) Plazek, D.J., "Oh, Thermorheological Simplicity, wherefore art thou?" Journal of Rheology, vol 40, 1996, p987.

4) Lesueur, D., Gerard, J-F., Claudy, P., Letoffe, J-M. and Planche, D., "A structure related model to describe asphalt linear viscoelasticity", Journal of Rheology, vol 40, 1996, p813.


Setting up TTS procedure on DMA850


Setting up TTS procedure on Q800

Amplitude within the linear region


Setting up TTS procedure on RSA G2


Getting Started Manuals


Trios Online Help Manual


From www.tainstruments.com click on Videos, Support or Training

Select Videos for TA Tech Tips, Webinars and Quick Start Courses

Instructional Videos

See also: https://www.youtube.com/user/TATechTips


Instructional Video Resources

Quickstart e-Training Courses


Need DMA HELP?!?

• Check the manuals, help and error help.• Contact the TA Instruments Rheology Hotline

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