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

Abstract

The diffusion of small molecules in disordered media has been studied by employing kinetic Monte Carlo (KMC) simulations and the time-dependent effective medium approximation (EMA). The simulations were conducted in a cubic lattice, to the bonds of which were assigned rate constants governing the elementary jump events, according to a prescribed probability distribution function. Different distributions with a variance ranging from a very small value, representative of a homogeneous medium, to a very large value, representative of a highly disordered, heterogeneous medium, were studied. It was found that the variance of the distribution of rate constants has a profound effect on the diffusion process, giving rise to an anomalous, non-Fickian 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-based calculations are in excellent quantitative agreement with the simulation findings, particularly for distributions of not too high variance. Simulations were also performed on spatially correlated lattices, consisting of domains within each of which the rate constants assume similar values. Spatial correlations were found to strongly influence the diffusion process at short time scales, prolonging the duration of the anomalous regime; at long time scales, however, spatially correlated lattices are characterized by the same diffusivity as uncorrelated ones with the same rate constant distribution.