Comparison of Different Possibilities for Evaluating the Glass Transition

Purpose

As has already been shown in Section 3.4.1, DMA can be used to measure curves such as the modulus, loss factor or compliance. Depending on which curve is evaluated, different values of the glass transition temperature are obtained. These values will be compared in the following section. 

Sample

Unfilled SBR vulcanized with 8 phr sulfur

Conditions

Measuring cell: DMA/SDTA861e with shear sample holder 

Sample preparation: Cylinders of 5-mm diameter were punched out from a 1.2-mm thick film 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. 

Evaluation

The results obtained from the DMA measurements are the modulus, G' and G", the compliance, J' and J", and the loss factor, tan g. The curves of G", J" and tan g as a function of temperature each show a peak in relaxation regions such as the glass transition region. The corresponding measurement curves measured at different frequencies are displayed in the above diagram. It can be seen that the peaks are shifted to higher temperatures at higher frequencies. Furthermore, one notices that the peaks of different curves measured at the same frequency do not appear at the same temperature. One way to define the mechanical glass transition temperature is to use the maximum temperature of the appropriate peak. This gives at least three glass transition temperatures from one measurement frequency - the transition temperature determined from the modulus is the lowest, and that from the compliance the highest. The activation curves can also be constructed from the corresponding measurement data:

For comparison purposes, the diagram also shows the value of the glass transition temperature that was obtained from a DSC measurement at a heating rate of 10 K/min (after cooling at 10 K/min). It can be seen that the characteristic temperatures obtained from the compliance and loss factor curves are higher than that of the glass transition temperature measured by DSC. The temperatures determined from the modulus agree with the DSC result at about 10 Hz. This result cannot, however, be generalized because the relative temperature range and the increase of the curves in the activation energy diagram are characteristic of the material. All the rules that describe the relationship between the mechanical glass transition temperatures and the DSC results are in fact rules of thumb and should be applied with caution. 

Interpretation

It has been shown that the compliance curve in the activation energy diagram is at higher temperatures than that of the modulus. If one considers the processes at the same temperature, then the characteristic frequency of the relaxation process of the modulus is greater than that of the compliance. If σ*(f) is the frequency-dependent mechanical stress in the sample and ε*(f) the frequency-dependent strain, then the relationship between the two quantities is given by the material functions G*(f,T) and J*(f,T) as follows: 

The modulus therefore describes the response of the sample to a given deformation and the compliance the corresponding response to a given stress. The first process is also known as stress relaxation and the second as retardation. A plausibility explanation of the differences between the relaxation and the retardation is given by the following.

With stress relaxation, the deformation is given. The stress therefore relaxes with given sample dimensions. In addition, relatively short-range cooperative rearrangements are necessary

In the case of retardation, the sample dimensions change with given stress. For a change in shape, long-distance cooperative rearrangements are necessary. These, however, take longer to occur than rearrangements with stress relaxation involving smaller regions. 

The different rearrangement times are inversely proportional to the frequencies at which the corresponding peaks are measured. The characteristic lengths involved in these rearrangements are of the order of 10 nm. The curve of the loss factor in the activation energy diagram lies between that of the modulus and the compliance. This quantity cannot be directly assigned to a physical process. For practical reasons, however, it is often used for the characterization of materials because it is not influenced by errors due to changes of geometry during the measurement or in sample preparation.

Conclusion

The glass transition is not only frequency dependent but also depends on the quantity that is evaluated. These facts must always be taken into account when reporting and discussing the characteristic values of the glass transition. 

^{Comparison of Different Possibilities for Evaluating the Glass Transition | Thermal Analysis Handbook No.HB422 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 1}