On the Use of Generalised Coordinates to Describe the Temperature Dependence of Viscosity and Relaxation Time in the Glass Transition Region

It is shown that the empirical Williams-Landel-Ferry (WLF) and Vogel-Fulcher-Tammann (VFT) formulas, as well as the semiempirical formulas of other researchers, for the viscosity η in the glass transition region are, in fact, hyperbolic functions of temperature with corresponding relationships between their parameters. The hyperbolic dependence can be derived from the universal expansion of ln(η) into a Taylor series in a small temperature parameter near the glass transition temperature. The applicability of the principle of corresponding states follows from this expansion. A new two-parameter formula in the form of a second-degree polynomial is proposed for ln(η) in the glass transition region. This formula contains physically significant parameters and adequately describes the available experimental data for individual glass-forming substances.