The order parameter model of liquids and glasses with applications to dielectric relaxation

Abstract

The order parameter model is generalized to describe systems whose equilibrium states depend on other intensive variables, e.g., electric field E, in addition to temperature T and pressure P. The set of order parameters required to specify the state of a liquid or glass is shown to form an abstract Euclidean vector space in the vicinity of a particular equilibrium state. The results of relaxational experiments are then connected with geometric relations in this space of order parameters. Thermodynamic stability requires that certain angles in this space have real values. This leads to thermodynamic stability conditions (TSC’s), which include the well known Prigogine–Defay condition for systems with intensive variables T and P and analogs of it for systems with other sets of intensive variables. The order parameter model is applied to dielectric relaxation, and its predictions are tested against available data. It is shown that the addition of E as an intensive variable requires at least one more order parameter to specify the state of the system than the number needed when T and P are the only intensive variables.