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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
Theory Oscillation example How to set up experimentsRheology AdvantageTA Orchestrator
How to analyze the dataRheology AdvantageTA Orchestrator
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
Temperature200180160140
0.0
Arrhenius or WLF
17
TTS, Briefly
Oscillation Example
a T
Temperature200180160140
0.0
Arrhenius or WLF(temperature dependence of
VE properties)
Agenda - TTS
Theory Oscillation example How to set up experimentsRheology AdvantageTA Orchestrator
How to analyze the dataRheology AdvantageTA Orchestrator
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
Setting up Experiments for TTS
Using Rheology Advantage
Using TA Orchestrator
19
Setting up Experiments for TTS
Using Rheology Advantage
Using TA Orchestrator
20
Enter Experimental Parameters
Edit Test Parameters
Strain in LVR
21
Agenda - TTS
Theory Oscillation example How to set up experimentsRheology AdvantageTA Orchestrator
How to analyze the dataRheology AdvantageTA Orchestrator
Shifting Curves with Analysis Software
Using Rheology Advantage
Using TA Orchestrator
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
TTS Toolbar Explained
23
Shift
Allows user to select variable to shift and then shifts the curves to the reference temperature
TTS Toolbar Explained
Reset shift factors
Reset the shifts factors so that curves are unshifted
TTS Toolbar Explained
24
Manual Adjustments
Reset the shifts factors so that curves are unshifted
TTS Toolbar Explained
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.
TTS Toolbar Explained
25
0.1 to 100 rad/s
26
Begin TTS Session
Set Reference Temp
27
28
29
Shift
30
Select a temp
31
32
Click curve with mouse
33
Drag manually
34
35
36
37
38
39
40
41
42
Generate Mastercurve
43
44
45
46
Shifting Curves with Analysis Software
Using Rheology Advantage
Using TA Orchestrator
47
48
49
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
55
56
After shifting to fit
57
After shifting to fit
58
MasterCurve @ 180C
Original Data
59
60
MasterCurve @ 140C
Original Data