On the Temperature Dependence of Cooperative Relaxation Properties in Glass-Forming Liquids

TLDR

Bestul and Chang previously derived Tg/T2 ratios of similar magnitude from calorimetric data. The authors present a molecular‑kinetic theory linking the temperature dependence of glass‑forming liquid relaxation to the size of cooperatively rearranging regions. The theory expresses the region size in terms of configurational entropy, and its application to viscosity data allows evaluation of Tg/T2 ratios and hindrance‑free energies for fifteen substances. The theory reproduces the empirical WLF equation, predicts hindrance‑free energies consistent with molecular interactions, and finds Tg/T2 ≈ 1.30 ± 8.4 % across diverse materials.

Abstract

A molecular-kinetic theory, which explains the temperature dependence of relaxation behavior in glass-forming liquids in terms of the temperature variation of the size of the cooperatively rearranging region, is presented. The size of this cooperatively rearranging region is shown to be determined by configuration restrictions in these glass-forming liquids and is expressed in terms of their configurational entropy. The result of the theory is a relation practically coinciding with the empirical WLF equation. Application of the theory to viscosimetric experiments permits evaluation of the ratio of the kinetic glass temperature Tg (derived from usual ``quasistatic'' experiments) to the equilibrium second-order transition temperature T2 (indicated by either statistical-mechanical theory or extrapolations of experimental data) as well as the hindrance-free energy per molecule. These parameters have been evaluated for fifteen substances, the experimental data for which were available. Hindrance-free energies were found to be of the magnitude to be expected from consideration of molecular interaction energies. The values of Tg/T2 thus obtained for these fifteen widely differing materials were found to be nearly the same, i.e., 1.30±8.4%. Values for Tg/T2 of nearly the same magnitude were derived by Bestul and Chang from calorimetric data.