Reaction Kinetics on Fractal and Euclidean Structures with Energetic Disorder: Random Walk Simulations

Abstract

A Monte Carlo approach is used to treat diffusion-limited reaction kinetics in microscopically heterogeneous media with energetic disorder. Simulations performed on the Cyber 205 supercomputer for the elementary reaction A + A → A show that the rate law is well described in terms of the microscopic exploration space of a single random walker, that is, by the number of distinct sites visited, S. This provides a scaling approach for moving from single walker simulations to reacting random walker simu­lations over a broad range of times and reduced temperatures. In the asymptotic limit of long times, single walker simulations for exponential, Gaussian and uniform distributions of energetic disorder on the Sierpinski gasket appear to follow a simple power law, S(t) ∝ tf. Simulations of re­acting random walkers show that the density, ρ, is fairly well described by the relation: p−1 ∝S(t) as t → ∞.