The Frequency Dependence of the Glass Transition - METTLER TOLEDO

The Frequency Dependence of the Glass Transition

Purpose

To show how the mechanical modulus changes at the glass transition when measured at different frequencies. 

 

Sample

Unvulcanized unfilled SBR (VSL5025-0)

 

Conditions

Measuring cell: DMA/SDTA861 with the shear sample holder 

Sample Preparation: The material was pressed to a 1-mm thick film. Cylinders of 4-mm diameter were punched out and mounted in the shear sample holder with 10% predeformation.

DMA measurement: The measurement was performed at 1, 10, 100 and 1000 Hz and a heating rate of 2 K/min. Maximum force amplitude 5 N; maximum displacement amplitude 10 Pm; offset control zero

 

Interpretation

The glass transition is a kinetic phenomenon that is observed in amorphous or semicrystalline materials. It has its origins in the molecular mobility of cooperative units. With increasing temperature, the frequency of the cooperative rearrangements increases. At low temperatures the frequency of these rearrangements is much lower than the measurement frequencies used. In this case the sample is hard and the storage modulus is therefore large. At higher temperatures the frequency of the cooperative rearrangements is much greater than the measurement frequency. The material is then soft and has a low storage modulus. In the temperature range in which the measurement frequency corresponds to about the frequency of the cooperative rearrangements, a step is observed in the storage modulus. In this case part of the mechanical energy is dissipated. It is converted to heat. This is why the step in the storage modulus is accompanied by a peak in the loss modulus. The relationship between the glass transition and the frequency of the molecular movement is again reflected in the frequency dependence of the measured transition. Such frequency-dependent effects that are accompanied by a step in the storage modulus and a maximum in energy dissipation are also known as relaxation. The glass transition is therefore a region in which relaxation of the cooperative rearrangements occurs.

 

Evaluation

To investigate the temperature and frequency dependence of the glass transition (relaxation), the maximum temperature of the G" peak at different measurement frequencies can be evaluated. Normally the logarithm of the frequency is plotted against the reciprocal temperature (in Kelvin):

Since the measurement frequency corresponds to about the average frequency of the cooperative rearrangements, the curve can be looked on as the activation diagram of the relaxation process. Cooperative relaxation processes, such as the glass transition always exhibit a curve of the type shown in this diagram, which is described by the Vogel-Fulcher equation: 

Here fo is the upper frequency limit, Tv the Vogel temperature and B a curvature parameter. The WLF equation of Williams, Landel and Ferry is also often used to describe the temperature dependence:

Here Tr is any reference temperature, f is the reference frequency assigned to Tr and C1 and C2 are the WLF constants. Of course here the WLF constants depend on the choice of the reference values. Both equations are equivalent to one another. 

 

Conclusion

The glass transition is frequency dependent. At higher frequencies it shifts to higher temperatures. The measuring frequency is of the same order as the actual frequency of the cooperative rearrangements. Because of the nonlinear relationship between the frequency and the transition temperature, a broader transition is measured at higher frequencies than at lower frequencies. When reporting glass transition temperatures determined by DMA, it is essential to specify the experimental conditions and the frequency used.

The frequency dependence of the glass trasnsition | Thermal Analysis Handbook No.HB421 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 1