rheo user training 3-tts

1Rheology Training CourseSection III

Time-Temperature Superposition(TTS)

TA Instruments User MeetingSan Antonio, TX February 4, 2004

Agenda - TTS

Theory Oscillation example How to set up experimentsRheology AdvantageTA Orchestrator

How to analyze the dataRheology AdvantageTA Orchestrator

2Agenda - TTS



Time & Temperature Effects

Rheological behavior of viscoelastic materials vary with both time and temperature

To fully understand a materials properties we need short time (high frequency) and long time (low frequency) data

Easier said than done Changes that occur in less than 1 second are hard

to measureChanges that occur over days or weeks are

inconvenient to measure

3The Answer Observations that time and temperature of

time-dependent processes have equivalent effects on rheological properties

Principal effect of changing temperature is to rescale time:Temperature changes shift the viscoelastic functions

along the modulus, and time (or frequency) scales without changing the shape

Can create a master curve from a series of curves collected at different temperatures

This procedure is referred to as Time-Temperature Superposition (TTS)

Time-Temperature Superposition (TTS) An empirical method for polymersAccording to the Merriam-Webster Dictionary;

empirical means that something is based on observation or experience i.e. it either works or it doesnt

Based on the observation that viscoelastic data [G-G, G(t), J(t)] seem to have some overlaying characteristics, if the curves can be shifted along a time/frequency axis.The processes involved in molecular relaxations or

rearrangements occur at accelerated rates at higher temperaturesA direct equivalency exists between time (frequency

of measurement) and Temperature

4What Materials can TTS be Applied to?

Can be applied to amorphous, non modified polymers

Material must be thermo-rheological simple Thermo-rheological simple materialOne in which all relaxations times shift with

the same shift factor aT

TTS Benefits

Data over a range of temperatures with a modest frequency range can predict behavior over a wider frequency range than practical to determine experimentallyLow frequencies can take days or weeks to collect

dataUltra high frequencies cannot be measured by

existing instruments Can be used to gauge long-time properties

(using stress-relaxation or creep) in a more reasonable experimental time

5WLF Equation Master Curves can be generated using shift

factors derived from the Williams, Landel, Ferry (WLF) equation

logaT= -c1(T-T0)/c2+(T-T0)aT = temperature shift factorT0 = reference temperaturec1 & c2 = constants from curve fitting Generally, c1=17.44 & c2=51.6 when

T0=Tg

When not to Use TTS If any crystallinity is present, especially if any

melting occurs in the temperature range of interest The structure changes with temperatureCross linking, decomposition, etc, occurring

Material is a block copolymer (TTS may work within a limited temperature range)

Material is a composite of different polymers Viscoelastic mechanisms other than configurational

changes of the polymer backbone occure.g., side-group motions, especially near the Tg

6When not to use the WLF Equation Sometimes you shouldnt use the WLF equation (even

if it appears to work) If T>Tg+100 If T

7TTS, Briefly

Oscillation Example

G

frequency

200

TTS, Briefly

Oscillation Example

G

frequency

200

Higher frequencies experimentally

inaccessible

8TTS, Briefly

Oscillation Example

G

frequency

200

180

160

140

TTS, Briefly

Oscillation Example

200

180

160

140

G

frequency

9TTS, Briefly

Oscillation Example

200

180

160

140G

frequency

TTS, Briefly

Oscillation Example

200

180

160

140

G

frequency

10

TTS, Briefly

Oscillation Example

200

180

160

140G

frequency

TTS, Briefly

Oscillation Example

200

180

160

140

G

frequency

11

TTS, Briefly

Oscillation Example

200

180

160

140G

frequency

TTS, Briefly

Oscillation Example

200

180

160

140

G

frequency

12

TTS, Briefly

Oscillation Example

200

180

160

140G

frequency

TTS, Briefly

Oscillation Example

200

180

160

140

G

frequency

13

TTS, Briefly

Oscillation Example

200

180

160

140G

frequency

TTS, Briefly

Oscillation Example

200

180

160

140

G

frequency

14

TTS, Briefly

Oscillation Example

G

frequency

Master-curve at 200

TTS, Briefly

Oscillation Example

G

frequency

200

180

160

140

aT=180

15

TTS, Briefly

Oscillation Example

G

frequency

200

180

160

140

aT=160

TTS, Briefly

Oscillation Example

G

frequency

200

180

160

140 aT=140

16

TTS, Briefly

Oscillation Example

a T

Temperature200180160140

0.0

TTS, Briefly

Oscillation Example

a T


0.0

Arrhenius or WLF

17

TTS, Briefly

Oscillation Example

a T


0.0

Arrhenius or WLF(temperature dependence of

VE properties)

Agenda - TTS



18

Setting up Experiments for TTS

What data can be shifted?Data collected at multiple temperatures from

the following types of experiments: Dynamic Frequency sweeps Creep Stress Relaxation

Well concentrate on Dynamic Frequency sweeps for this presentation


Using Rheology Advantage

Using TA Orchestrator

19




20

Enter Experimental Parameters

Edit Test Parameters

Strain in LVR

21

Agenda - TTS



Shifting Curves with Analysis Software



22

Begin TTS Session

Starts the TTS session on current file(s)

TTS Toolbar Explained

Select reference temperature

Used to select the reference temperature before shifting


23

Shift

Allows user to select variable to shift and then shifts the curves to the reference temperature


Reset shift factors

Reset the shifts factors so that curves are unshifted


24

Manual Adjustments

Reset the shifts factors so that curves are unshifted


Generate Mastercurve

Creates a new file in file-list that is the mastercurve at a temperature, which may or may not be the reference temperature.


25

0.1 to 100 rad/s

26

Begin TTS Session

Set Reference Temp

29

Shift

30

Select a temp

32

Click curve with mouse

33

Drag manually

42

Generate Mastercurve

46

Shifting Curves with Analysis Software



50

Reference Curve set at 180C

Choose all except original curve

51

Overlay Curve Shift Factor Curve

Both horizontal & vertical shift factors shown on plot

Clear this axis to eliminate vertical shift factor from

plot

52

Horizontal shift factor only is now shown

53

Shifted Curves

54

Fit to WLF equation

56

After shifting to fit

57

After shifting to fit

58

MasterCurve @ 180C

Original Data

60

MasterCurve @ 140C

Original Data

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