nanoDMA® of PMMA at Elevated TemperatureTemperature and Frequency Dependence in PMMA

Figure 1. 3-D log plot of reduced storage modulus vs. temperature and frequency from averaged 10-300 Hz frequency sweep indents performed at a range of temperatures on PMMA.

APPLICATION NOTE

By: Jeffrey SchirerRichard Nay

Michelle Dickinson, Ph.D.Hysitron, Inc.

IntroductionMethods to accurately measure and analyze time-dependent mechanical material properties over a range of non-ambient temperatures at the nanoscale are essential in characterizing and predicting material performance in realistic working conditions. Standard macroscale material characterization techniques involve large sampling sizes, which are not suitable for nanoscale structures such as thin films. This study shows a new technique that is fully capable of both precisely modeling working conditions and accurately measuring material properties at the nanoscale, which are sensitive to changing environment. One common material that exhibits time-dependent properties sensitive to changing temperatures is polymethyl methacrylate (PMMA).

ProcedureTo find time- and temperature-dependent mechanical properties of PMMA, a Hysitron TI 900 TriboIndenter® equipped with nanoDMA and a heating/cooling stage was used to perform dynamic and quasistatic nanoindentation on a standard PMMA sample. 10-300 Hz frequency sweep indents were run at a range of temperatures (24˚C-128˚C), which enabled the glass transition temperature (Tg) of the material to be identified. In addition, quasistatic nanoindentation tests were run at the same temperature range to further extend the frequency range (to a relatively low frequency) of the results.

To ensure accuracy in the measured data, a thermocouple was placed on the sample surface to determine when the sample had been heated uniformly. PMMA samples obtained from

a commercial supplier were affixed to the heating/cooling stage using mechanical clips.

Frequency sweeps and load-controlled quasistatic indents were performed with a Berkovich diamond tip. With these tests the mechanical properties of PMMA as functions of both frequency and temperature could be determined. Quasistatic loads were adjusted to achieve contact depths of 500-600 nm and dynamic loads were adjusted to achieve dynamic displacement amplitudes of 1 nm to aid repeatability in results. TriboAnalysis™, an advanced data analysis and reporting package powered by OriginPro®, was used to quickly analyze and clearly present the data.

Results and DiscussionReduced storage modulus and tan delta vs. temperature and frequency results are plotted in Figures 1 and 2, respectively. These plots show a continuous data spectrum from which trends can be easily observed.

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One clear trend in Figure 1 is the sharp change in reduced storage modulus across the 90˚C isotherm, which corresponds to the approximate Tg of PMMA. Another observable trend shown in Figure 1 is the rise in reduced storage modulus as temperature decreases and as frequency increases; this result is desirable as the material property response to a temperature decrease is expected to be analogous to the material property response to a frequency increase.

Similarly, figure 2 shows a sharp change in tan delta across the 90˚C isotherm, which corresponds to the approximate Tg of PMMA. Force vs. displacement curves of representative quasistatic indents performed at varying temperatures are shown in Figure 3 to highlight the wide range of quasistatic

Figure 4. Plot showing correlation of dynamic and quasistatic test results for PMMA sample tested at different temperatures.

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loads required to maintain a 500-600 nm contact depth for indents at all test temperatures.

The quasistatic nanoindentation data agrees well with the dynamic data. One expected PMMA material property response to a decrease in frequency is a decrease in calculated reduced complex modulus. Since a frequency of less than 1 Hz can be assigned to all quasistatic tests, one would expect to see lower quasistatic reduced modulus values than those reduced complex modulus values found by higher frequency nanoDMA indents at similar temperatures. This expected result was produced and is shown in Figure 4.

ConclusionThe Hysitron TI 900 TriboIndenter was successful in obtaining accurate and reliable time- and temperature-dependent mechanical property data on PMMA. This material exhibits time-dependent properties sensitive to changing temperature, over a broad range of temperatures and frequencies using nanoDMA in combination with the heating/cooling stage. TriboAnalysis performed quick data analysis and produced a clear presentation of the data in an organized format. Using such a combination of Hysitron’s technology allows users to obtain and present accurate material property data for both viscoelastic and temperature-sensitive samples.

Figure 3. Force vs. displacement curves for quasistatic load-controlled indents on PMMA at varying temperatures with quasistatic loads specified to achieve contact depths of 500-600 nm.

Figure 2. 3-D plot of tan delta vs. temperature and frequency from averaged 10-300 Hz frequency sweep indents performed at varying temperatures on PMMA.

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