Effect of disorder on diffusion and viscosity in condensed systems

Abstract

A simple theoretical model describing the influence of disorder on transport properties (viscosity, diffusion coefficients, etc.) in undercooled melts and crystals is suggested. The basic assumption is that structural disarray results in a random probability distribution of energy barriers for diffusion characterized by dispersion σ around some mean value 〈 E〉. It is shown that the effect of σ on the mean jump frequency 〈 v(E)〉 may lead to corrections of many order of magnitude as compared to the hopping frequency calculated traditionally in terms of the average activation energy 〈 E〉 only. The temperature course of 〈 v(E)〉 is then examined making use of the relation between σ and the entropy of the system S. Thus an analytical formula is obtained which properly describes molecular transport in both the crystalline and the amorphous state. Even in a simplified form, η= η 0 exp( β/ T α ), it reproduces well the existing data on temperature variation of viscosity η (or self-diffusion) in glassforming melts. In another aspect - in terms of the percolation theory - the model describes the diffusion of a foreign particle in a rigid host structure and yields also a qualitative estimate of the variation of the percolation threshold E p with the degree of amorphisation σ.