### Time-Temperature Superposition (TTS) Using DMA Acknowledgments

```Time-Temperature Superposition (TTS) Using DMA
Mohammed Alzayer, Chris Clay, Xinhang Shen
Mat E 453, Department of Materials Engineering, Iowa State University, Ames, IA 50011
Introduction
Dynamic Mechanical Analysis (DMA) is a
method that gives useful information on the
viscoelastic properties of polymers. Most
materials have a combination of elastic
(Hookean) and viscous (Newtonian) behaviors
and hence exhibit a phase lag between an
applied sinusoidal stress and the strain.
[1]This results in the material having a
complex modulus which accounts for both
behaviors. Rheological measurements are
utilized to
generate master curves that
describe the viscoelastic behavior of a
material. Temperature superposition (TTS) is a
procedure in which a storage modulus versus
frequency master curve is created by making
measurements at varying temperatures and a
range of frequencies and multiplying the
frequencies by a shift factor to shift the curves
left or right in the horizontal axis. [1]
Testing Procedures
The polymer investigated in this lab is
bisphenol E cyanate ester (BECy) which has a
glass transition temperature of 270 °C
(reference temperature).
Sample preparation: Width
and thickness of BECy sample
measured by caliper.
Clamped the sample in DMA
Sample
800 to obtain a height of 10mm.
Screen cover placed over the
sample.
Software programming:
software was used.
Tested Temperatures: 260,
270, 280, 290, and 300 ºC
Frequency Range: 1-100 Hz, Fig 1. Sample in
11 points per temperature.
DMA 800
Force Track: 125%.
Results
 The shift factors were calculated from the raw
frequency data, not from the log(frequency)
data. The log of the shifted frequencies was
then taken and plotted.
 The shift factor listed for 290 ºC  270 ºC in
Table 1 is actually the shift factor for 280 ºC
270 ºC multiplied by the shift factor for
290 ºC 280 ºC.
Conclusions
 By testing at different temperatures, a master
curve for reference 270 ºC could be
generated quickly.
 The shifting was done to 270 ºC because that
is where the glass transition of BECy is
known to be.
 The glass transition temperature can be
Fig 2. Modulus versus frequency at varying temperatures. Fig 3. Log-log graph of modulus versus frequency.
observed by the differences of slopes of the
high
temperature
and
low
temperature
Table 1. Shift Factors used to generate TTS plot
curves.
Shift in Temperature
Shift Factor
 At higher temperatures, the storage modulus
260 °C  270 °C
21
was lower, which agrees with expectations.
 TTS shifting could also be used to generate a
270 °C  270 °C
1
master curve for loss modulus
and
viscoelastic phase lag at 270 ºC
280 °C  270 °C
0.1899
 The TTS shifting was good, but not perfect.
290 °C  270 °C
0.0753
 To obtain better results, a smaller difference
in temperatures could be used.
300 °C  270 °C
0.1899
 TTS shifting is not an exact method, as lines
can overlap in multiple places and a choice of
where to calculate shift factor must be made.
 The shift factors could have been taken from
the log(frequency) data, which would result in
different shift factors even from the same
data.
Acknowledgments
This laboratory report utilized data from an
actual laboratory performed by a previous Mat E
453 class at Iowa State University.
References
Fig 4. Log-log graph of modulus versus frequency after TTS shifting
[1].Mendoza, J. D. Lab 9: Dynamic Mechanical Analysis, Iowa
State University
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