Temperature Dependence of the Relaxation Spectrum
Purpose
An isothermal frequency-dependent measurement of mechanical relaxation behavior is also known as mechanical relaxation spectroscopy if the frequency range investigated is sufficiently large. The experiment shows the extent to which the relaxation spectrum depends on temperature.
Sample
Unfilled and uncross-linked SBR
Conditions
Measuring cell: DMA/SDTA861e with the shear sample holder
Sample preparation: The SBR 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 in the frequency range 100 mHz to 1 kHz under isothermal conditions at different temperatures between –50 °C and 100 °C. Maximum force amplitude 5 N; maximum displacement amplitude 10 Pm; offset control zero.
Shear storage modulus in the observed frequency window from 0.1 to 1000 Hz, measured at temperatures between –50 °C and 100 °C.
Interpretation
In a frequency-dependent measurement at sufficiently low temperatures (47 °C), the storage modulus is relatively large (700 MPa) and practically independent of the frequency. With increasing the temperature, the storage modulus decreases at low frequencies until the step of the relaxation range shifts across the measurement range. At –10 °C practically the entire step can be measured in the frequency range used. With further temperature increase, the relaxation range is shifted to higher frequencies so that at about 40 °C in the measured frequency range only the almost frequency-independent rubbery plateau with a storage modulus of about 7 MPa is measured. On further temperature increase, especially at low frequencies, the storage modulus decreases. The material then begins to flow.
Conclusions
The relaxation range is shifted to higher frequencies at higher temperature. In a frequency sweep experiment, the sample is measured at constant temperature in an experimentally accessible frequency window. If such an experiment is performed at two temperatures, T1 and T2 (where T1<T2), the behavior measured at T2in the frequency window is the same as that which would be measured at T1 at lower frequencies. The relaxation range can therefore be shifted across the frequency window by varying the temperature.
In other words, in such measurements the curves at lower temperatures correspond to those at the reference temperature and higher frequencies, and the curves at higher temperatures to those at the reference temperature and lower frequencies. At temperatures below the reference temperature, the same relaxation behavior is measured as at lower frequencies. It is thought that there is a general equivalence between the frequency (time) and temperature behavior of amorphous polymers close to the glass transition temperature - a polymer that has rubbery characteristics under certain conditions can behave as a glass if the temperature is reduced or the time scale of the observation is decreased. Since the frequency-dependence is directly related to a corresponding time-dependence, the relationship is usually referred to as the time-temperature superposition principle.
The relationship between temperature and frequency is described by the VogelFulcher equation or the WLF equation (Section 3.4.2. The frequency dependence of the glass transition).
Comments
The time-temperature superposition principle is only valid for so-called rheologically simple materials. These include amorphous materials in which molecular interactions are not affected by internal surfaces (e.g. phase separation with blends or crystallization), structure formation, fillers or chemical reactions, and in which different relaxation ranges do not overlap.
Temperature Dependence of the Relaxation Spectrum | Thermal Analysis Handbook No.HB424 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 1