Diffusion on a rearranging lattice

Abstract

In this paper we present a computer simulation of a random walk (RW) for diffusion on a rearranging lattice. The lattice consists of two types of sites - one highly conducting (type 1) and the other poorly conducting (type 2), distributed at random. The two types of site are assigned different waiting times (τ₁ for type 1 and τ₂ for type 2). We assume that at intervals of time the site distribution changes. The effect of this rearrangement on the diffusion coefficient is studied with varying τ_r. We study this effect for different ratios of dwell time of the two types of site (R) and also for different fractions (X) of the less conducting sites. An empirical relation for D(τ₁, τ₂, τ_r, X) is suggested. We have employed the well model and considered diffusion controlled by sties, rather than bonds. So our approach is different from the dynamic bond percolation model, which studies these aspects. Our results show that the diffusion coefficient D may change by a factor of up to 3 (approximately) for rapid rearrangement, and there is a considerable effect of varying X and R on the range of variation of D, where X is the fraction of poorly conducting sites, and R is the ratio of the dwell times for types of site. Further for τ_r > 250τ (τ is the time unit for the random walk) the effect of rearrangement becomes negligible. The results may be useful for studying diffusion and conduction of ion conducting polymers.