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

Lattice Monte Carlo methods are widely used to study diffusion problems suc h as the random walk of a probe particle among fixed obstacles. However, th e diffusion coefficient D found with such methods generally depends on the type of lattice used. In order to obtain experimentally relevant results, o ne often needs to consider the continuum limit, i.e., the limit where the s ize of the lattice parameter is infinitely small compared to the size of bo th the probe particle and the obstacles. A numerical procedure to reach thi s limit for a single particle diffusing between quenched impenetrable obsta cles is presented. As an example, the case of a system of periodic spherica l obstacles is treated and a general relation between the diffusion coeffic ient D, the total obstructed volume f, and the dimensionality d of the prob lem is proposed. (C) 2000 American Institute of Physics. [S0021-9606(00)504 44-9].