Generalization of the Williams–Landel–Ferry equation

Based on the model of Gibbs–Di Marzio we write the logarithmic shift factor without explicit knowledge of the form for the entropy, an expression which enables us to write a generalization of the Williams–Landel–Ferry equation. Comparison with the empirical relation of Williams–Landel–Ferry and use of the fact that the model exhibits the existence of a isoentropic temperature T0 for which the configurational entropy of the system vanishes, leads to a value of the isoentropic temperature for which the configurational entropy of the system vanishes. The form for the specific heat proposed by Dowell and Di Marzio based on the lattice model of Gibbs–Di Marzio for the glass transition of polymeric substances, has been used by García-Colín et al. to find the molar configurational entropy (MCE) of glass. Knowledge of the form of the MCE, allows us to find an expression for the critical configurational entropy (Sc*) and a form for the potential energy hindering the cooperative rearrangement per monomer segment (Δμ).