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 good conducting (type 1) and the other poor conducting (type 2), distributed at random. The two types of sites are assigned different waiting times ($\tau_{1}$ for type 1 and $\tau_{2}$ for type 2) . We assume that at intervals of time $\tau_{r}$, the site distribution changes. The effect of this rearrangement on the diffusion coefficient is studied with varying $\tau_{r}$. We study this effect for different ratios of dwell times of the two types of sites (R) and also for different fractions (X) of the less conducting sites. An empirical relation for D($\tau_{1}$ ,$\tau_{2}$,$\tau_{r}$,X) is suggested. We have employed the well model and considered diffusion controlled by sites, 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 upto 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 low conducting sites, and R is the ratio of the dwell times for the two types of sites. Further for $\tau_{r}$ > 250$\tau$ ($\tau$ 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.