Kramers theory and vibrational entropy in the compensation law for polyethylene relaxations

It is well known that there is a compensation law between the change of enthalpy and the pre-exponential factor of the Arrhenius equation for the α, β, and γ relaxations of polyethylene (PE). We have already suggested that the relaxations can be described by the Eyring equation. The limits of that approach are briefly discussed and a modified Kramers equation seems to be more acceptable from a theoretical stand point. Contrarily to Kramers and following Eyring, we propose to include a term similar to a vibrational entropy in order to explain the compensation law between the apparent activation energy and the log of the pre-exponential term. The influence of the damping or friction parameter associated with Kramers theory is then discussed. It also seems possible to combine the proposed equation with the multi excitations entropy theory. Future work is suggested.