Non-Debye relaxation and the glass transition

Abstract

A review of some long-standing problems, as well as some new theoretical results regarding non-Debye relaxation and the glass transition is given. The question of whether a phase transition below (or above) the glass transition temperature, T g, exists is considered. The result that the glass transition temperature and jumps in the dynamic heat capacity and volume expansion coefficient can be calculated if the relevant frequency-dependent linear response functions are known makes the question of the origin of non-Debye relaxation even more important. In effective medium theories, certainly valid at high temperatures, non-Debye relaxation is apparently due to dynamic effects of interactions. At lower temperatures, energy disorder is larger compared with kT, and percolation-based theories may be more appropriate. The question as to the actual magnitude of disorder in energies cannot be conclusively resolved at this time. Certainly, it has been shown that systems exist in which non-Debye relaxation is due exclusively to disorder but, in many systems, an important component of the energy disorder is a manifestation of the influence of topological disorder on interactions. Thus, in these systems, an increase in the magnitude of dynamic interactions relative to kT accompanies the increase in the disorder. The question as to whether universal properties imply universality in the mechanism of non-Debye relaxation is explored in some depth. The present article reaches the tentative conclusion that the relative importance of ‘disorder’ and ‘interactions’ may be dependent on the type of glass considered, and possibly even on specific systems. Certainly, the relative importance of dynamic interaction effects increases as the frequency of an applied ‘force’ is reduced. If their respective influences ‘crossover’ in importance at some finite frequency, ω ∗, the relevant question is whether ω ∗ is above, at, or below the relaxation peak frequency, ω ∗. If universality exists, it relates to the role of disorder, but such a conclusion would require that ω ∗ ≤ α c always, the generality of which has not been established.