Influence of temperature and elastic properties on some polymer relaxations

The temperature dependence of the apparent activation energy for polymer relaxations is significantly different above and below the crossover temperature typical of each relaxation. We propose a phenomenological alternative to the empirical VTF law often used to explain this behavior. Below the crossover temperature of a given relaxation, the Eyring equation applies resulting in constant activation enthalpy and entropy. They are linearly related, which explains the compensation law. Above the crossover temperature, the free activation energy is composed of two terms, one thermal and one volumic. The thermal contribution appears to be related to the energy of cohesion of the polymer. The activation volume under atmospheric pressure depends on the activation entropy and on the ratio of the thermal expansion coefficient over compressibility. It is shown that the activation volume and the heterogeneity length associated to the boson peak are related assuming a prolate-shaped activation volume.