Williams-Landel-Ferry rate-temperature equivalence

Since the G of non-crystalline polymers is associated with an energy dissipation of the polymer, it is analysed in terms of the Williams-Landel-Ferry rate-temperature equivalence. To investigate the reinforcing effect of NR to SBRl in the present study, the rate-temperature equivalence was applied to the G of SBRl and the NR/SBRl blend, assuming that the energy dissipation was... 

Fig. 3.4. With a multi-frequency measurement, frequencies beyond the measurable range of the DMA can be achieved by using the superposition method. Employing the Williams-Landel-Ferry (WLF) equation, and with a treatment of the data, designated as the method of reduced variables or time-temperature superposition (TTS) it is possible to overcome the difficulty of extrapolating limited laboratory tests at shorter times to longer-term, more real world conditions. The underlying bases for TTS are that the processes involved in molecular relaxation or rearrangements in viscoelastic materials occur at accelerated rates at higher temperatures and that there is a direct equivalency between time (the frequency of the measurement) and temperature.

According to Williams-Landel-Ferry (WLF) principle longer time is equivalent to higher temperature. Thus at higher rates the modulus is shifted to the direction of lower temperature and vice versa [210]. 

In fact, the same increase in joint strength that is obtained with a simple viscoelastic adhesive on increasing the rate of debonding, can be achieved by a suitable reduction in test temperature. This is referred to as the principle of rate-temperature equivalence. For amorphous glass-forming liquids above their glass transition temperature Tg, Williams, Landel, and Ferry (WLF) proposed a universal relationship for the ratio of corresponding test rates at temperatures Tand Tgi ... 

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