On the Use of Generalized 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) equations, as well as the semiempirical equations 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 mathematically common expansion of lnη into a Taylor series in a small temperature parameter near the glass transition temperature, provided that the temperature range satisfies approximately (T − Tg)/Tg ≲ 0.1–0.15). The applicability of the principle of corresponding states for glasses of similar composition follows from this expansion. A new two-parameter equation in the form of a second-degree polynomial is proposed for ln(η) in the glass transition region. This equation contains physically significant parameters and adequately describes the available experimental data for individual glass-forming substances. The temperature range over which the proposed series expansion up to the third (quadratic in the small parameter) term is valid can be determined only experimentally, because the coefficients of the series depend on the nature of the glass. For the specific experimental data we used, the sharp temperature dependence of the viscosity in the glass transition region makes the quadratic polynomial applicable over almost the entire temperature range studied.