A thermodynamic treatment of the glass transition

TL;DR

This paper develops a thermodynamic framework for the glass transition, linking anharmonic interatomic potentials to thermal expansion and heat capacity behaviors in undercooled liquids and glasses.

Contribution

It introduces a model connecting inherent structure energy, volume expansion, and the Prigogine-Defay ratio, providing a unified thermodynamic description of the glass transition.

Findings

Thermal expansion follows a 1/T^2 dependence due to inherent structure energy.

Prigogine-Defay ratio is predicted to be one in the model.

Experimental deviations explained by structural volume changes without energy variation.

Abstract

In undercooled liquids, the anharmonicity of the interatomic potentials causes a volume increase of the inherent structures with increasing energy content. In most glass formers, this increase is stronger than the vibrational Gr\"uneisen volume expansion and dominates the thermal expansion of the liquid phase. For a gaussian distribution of inherent states in energy, the generic case, this implies a 1/T-squared temperature dependence of the additional thermal expansion and the additional heat capacity at zero pressure. The corresponding compressibility contribution has the Prigogine-Defay ratio one. In experiment, one finds a higher Prigogine-Defay ratio, explainable in terms of structural volume changes without any energy change. These should always exist, though their influence becomes weak in close-packing systems, at the crossover to soft matter.