Quantitative model of super-Arrhenian behavior in glass forming materials

Abstract

The key feature of glass forming liquids is the super-Arrhenian temperature dependence of the mobility, where the mobility can increase by ten orders of magnitude or more as the temperature is decreased if crystallization does not intervene. A fundamental description of the super-Arrhenian behavior has been developed; specifically, the logarithm of the relaxation time is a linear function of $1/{\overline{U}}_{x}$, where ${\overline{U}}_{x}$ is the independently determined excess molar internal energy and $B$ is a material constant. This one-parameter mobility model quantitatively describes data for 21 glass forming materials, which are all the materials where there are sufficient experimental data for analysis. The effect of pressure on the $loga$ mobility is also described using the same ${\overline{U}}_{x}(T,p)$ function determined from the difference between the liquid and crystalline internal energies. It is also shown that $B$ is well correlated with the heat of fusion. The prediction of the $B/{\overline{U}}_{x}$ model is compared to the Adam and Gibbs $1/T{\overline{S}}_{x}$ model, where the $B/{\overline{U}}_{x}$ model is significantly better in unifying the full complement of mobility data. The implications of the $B/{\overline{U}}_{x}$ model for the development of a fundamental description of glass are discussed.