Measurement of the Frequency Dependence of Relaxation

Purpose

Since the glass transition is frequency dependent, information on relaxation behavior can also be obtained by means of isothermal measurements in which the frequency is varied (frequency sweep). The frequency dependence of the modulus is discussed in this section. 

Sample

Unfilled SBR elastomer vulcanized with 2 phr sulfur

Conditions

Measuring cell: DMA/SDTA861^e with the 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 –10 °C in the frequency range 1 mHz to 1 kHz. Maximum force amplitude 5 N; maximum displacement amplitude 10 Pm; offset control zero. 

Interpretation

In an isothermal measurement, the modulus changes with the frequency. In the relaxation range, the storage modulus changes stepwise. At high frequencies it is larger than at low frequencies. At high frequencies, the measurement frequency is higher than that of the corresponding cooperative rearrangements. This means that the stress is applied rapidly in comparison with cooperative rearrangements. The sample therefore appears hard and has a large storage modulus. At low frequencies, the molecular rearrangements are able to react to the external stress. The sample appears soft and has a low storage modulus. 

In the relaxation range a peak occurs in the loss modulus. In the sample measured the frequency at the peak maximum was 54 Hz. The shape of the peak in the loss modulus corresponds to a distribution of relaxation times. A broad peak means a broad distribution of the relaxation times and therefore a larger difference in the possibilities for cooperative rearrangements, which can be caused by a complex intermolecular or intramolecular structure. In the relaxation range, the loss factor, tan g, also exhibits a peak whose maximum is at lower frequencies. In the example measured this was at 0.32 Hz. Another source of data for the estimation of the relaxation behavior is the curve shape. If the material measured exhibits a distinct relaxation range, then the sides of the peaks of G", tan g and J" in log-log presentation should be straight lines. If deviations from the expected behavior occur, as in the example considered at about 10 Hz, then this is a very sensitive indication of other frequency-dependent processes. Possible reasons for this are other relaxation processes due to internal surfaces (e.g. through phase separation) or complex molecular structure (e.g. the formation of molecular networks). 

Conclusions

The measurement of the frequency dependence of the mechanical quantities under isothermal conditions is a very sensitive method for the investigation of relaxation behavior. Besides the relaxation intensity and the frequency range of the relaxation, the width and curve shape are also important values from which one can draw conclusions about molecular and supermolecular structures or their changes. Because the relaxation range is wide, for interpretation purposes, experiments should cover the largest possible frequency range.

Since many technological processes and material applications involve dynamic stress over a wide frequency range, measurements of the type described above can also be useful for material or product optimization or for failure analysis. A dynamic measurement should as far as possible be performed in the frequency range in which the material is actually stressed because the behavior at other frequencies can be quite different and extrapolation does not always ensure satisfactory results.

_{Measurement of the Frequency dependence of Relaxation | Thermal Analysis Handbook No.HB423 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 1}