Isobaric thermal behavior of glasses during uniform cooling and heating: Dependence of the characteristic temperatures on the relative contributions of temperature and structure to the rate of recovery. II. A one-parameter model approach

Isobaric variations of the characteristic temperatures T_g and T_max, obtained on uniform cooling and heating of glasses, are investigated in terms of their dependence on the relevant experimental variables, using a single retardation time model. The corresponding partial derivatives of T_g and T_max are derived as functions of the partition parameter x (ranging between zero and unity), which determines the relative contributions of temperature and structure to the retardation time. It is shown that the variation of T_g with the cooling rate is independent of x. In contrast, T_max critically depends on x, and its value as well as those of its three partial derivatives are linear functions of x^?1. The variations of T_max are analyzed in terms of a set of reduced variables, leading to simple reduction rules between any two of the experimental variables when the third is kept invariant. The reduction rules are further substantiated by investigating the behavior of glasses in two-step thermal cycles, which result in a unique set of inter-relationships between any pair of the partial derivatives of T_max, whatever the value of x. The results are discussed in terms of their relevance to the behavior of real glasses.