Dependence of the diffusion coefficient on the energy distribution of random barriers.

Abstract

We study hopping transport of particles in the presence of randomly distributed energy barriers for diffusion. Exponential, Gaussian, and uniform distributions of barrier heights on square and simple-cubic lattices are investigated to uncover the influence of the form and width of the distributions. The temperature dependence of the characteristic time separating the initial regime of anomalous diffusion from the long-time normal diffusion is of Arrhenius form with an effective activation energy determined by the percolation threshold of the corresponding lattice. Our analytic results, derived within the framework of effective medium approximation, show that the asymptotic diffusion coefficient does not depend on the degree of disorder on a square lattice whereas on a cubic lattice it does. These predictions are confirmed by numerical simulations. The temperature dependence of the diffusion coefficient is also determined by the coordination number z of the lattice for ``static'' barrier disorder. On a square lattice it is of Arrhenius form and for z\ensuremath{\ne}4 it deviates from it with increasing degree of disorder. It is always non-Arrhenian in the case of dynamically changing disorder.