A thermodynamic description of the glass state and its application to glass transition

Abstract

Many properties of solids, such as the glass state, hysteresis, and memory effects, are commonly treated as nonequilibrium phenomena, which involve many conceptual difficulties. However, few studies have addressed the problem of understanding equilibrium itself. Equilibrium is commonly assessed based on the assumption that its thermodynamic state should be determined solely by temperature and pressure. However, this assumption must be fundamentally reappraised from the beginning through a rigorous definition of equilibrium because no rigorous proof for this assumption exists. Previous work showed that for solids, the equilibrium positions of all constituent atoms of the solid are state variables (i.e., thermodynamic coordinates, or "TCs"). In this study, this conclusion is further elaborated starting from the principles of solid-state physics. The internal variables such as the fictive temperature qualify as TCs on this ground, if suitably treated. This theory is applied to glass materials, for which many challenges remain. Results show that first, the glass state is an equilibrium state. Accordingly, the properties of a glass can be solely described by the present positions of the atom, irrespective of their previous history, which is consistent with the definition of a state in the thermodynamic context. Second, the glass transition, although a nonequilibrium phenomenon, is well described using TCs if the thermal part of the energy is be assumed to be well separated from the structural part. The only dynamic parameter involved in this approach is the relaxation time, which is uniquely determined using the present values of the TCs. Therefore, complicated functions describing the past history, which are widely used in the glass literature, are unnecessary. This implies that the activation energy for the structural relaxation strongly depends on TCs. This finding provides a reasonable understanding of the large deviations from the Arrhenius law, which often occur in glasses. The unrealistic values of the activation energy and of the pre-exponential factor of the relaxation time can be resolved on this basis. The theory is particularly suitable for experiments that do not involve hypothetical quantities such as the effective temperature or hypothetical models such as the ideal glass model; therefore, all quantities are measurable.