Random walk and diffusion of hard spherical particles in quenched systems: Reaching the continuum limit on a lattice

Abstract

Lattice Monte Carlo methods are widely used to study diffusion problems such as the random walk of a probe particle among fixed obstacles. However, the diffusion coefficient D found with such methods generally depends on the type of lattice used. In order to obtain experimentally relevant results, one often needs to consider the continuum limit, i.e., the limit where the size of the lattice parameter is infinitely small compared to the size of both the probe particle and the obstacles. A numerical procedure to reach this limit for a single particle diffusing between quenched impenetrable obstacles is presented. As an example, the case of a system of periodic spherical obstacles is treated and a general relation between the diffusion coefficient D, the total obstructed volume f, and the dimensionality d of the problem is proposed.