Theory of relaxation in viscous liquids and glasses

Publisher Website
Google Scholar
Abstract
A theory of relaxation (the time-dependent change of macroscopic properties) of nonpolymeric viscous liquids and glasses is presented. The fluid is described by a set of quasiequilibrium structures, and a master equation gives the transitions among these structures. Any structural change is presumed to require a cooperative rearrangement involving many atoms, and this rearrangement entails a fluctuation to a high-energy transition state. The structure of the fluid varies from point to point, and the rate of this transformation depends crucially on the local structure. The resulting kinetic equation describes very well the main features of observed relaxation—namely, the broad distribution of relaxation times and the nonlinearity (in ΔT) of relaxation following a temperature jump ΔT, where the apparent activation energy for relaxation depends on time. The kinetic equation is solved exactly, and the resulting solution is exhibited for a particular set of the parameters. The resulting relaxation function for energy relaxation goes as e−t1/4, except at the very shortest times. (The precise exponent— 1/4 in this case—will depend on the parameters used in the particular calculation.) A detailed comparison with other theories is made, and suggestions of how the theory can be used to develop a phenomenological model of relaxation of glass are given.