Diffusion of small molecules in disordered media: study of the effect of kinetic and spatial heterogeneities

The diffusion of small molecules in disordered media has been studied by em ploying kinetic Monte Carlo (KMC) simulations and the time-dependent effect ive medium approximation (EMA). The simulations were conducted in a cubic l attice, to the bonds of which were assigned rate constants governing the el ementary jump events, according to a prescribed probability distribution fu nction. Different distributions with a variance ranging from a very small v alue, representative of a homogeneous medium, to a very large value, repres entative of a highly disordered, heterogeneous medium, were studied. It was found that the variance of the distribution of rate constants has a profou nd effect on the diffusion process, giving rise to an anomalous, non-Fickia n regime at short time scales. The higher the variance of the distribution, the longer the duration of the anomalous regime and the smaller the value of the diffusion coefficient in the long-time, Fickian regime. The EMA-base d calculations are in excellent quantitative agreement with the simulation findings, particularly for distributions of not too high variance. Simulati ons were also performed on spatially correlated lattices, consisting of dom ains within each of which the rate constants assume similar values. Spatial correlations were found to strongly influence the diffusion process at sho rt time scales, prolonging the duration of the anomalous regime; at long ti me scales, however, spatially correlated lattices are characterized by the same diffusivity as uncorrelated ones with the same rate constant distribut ion. (C) 2001 Elsevier Science Ltd. All rights reserved.