Fractal Aspects of Heterogeneous Chemical Reactions

Abstract

Heterogeneous reactions in which the rate is limited by the motion on the heterogeneous substrate differ significantly in their kinetics from diffusion-limited homogeneous reactions. We test a conjecture that combines the exploration space concept of the classical collision- rate-theory with the newly discovered paradigm of Brownian motion on low-dimensional (fractal-like) structures. We define a reduced time, which replaces real time in the classical rate equations. The reduced- time relations are tested by computer simulations, effectively proving the simple connection between a single-particle Brownian motion on a fractal structure and the dynamics of an ensemble of reacting Brownian particles. The real-time kinetic relations are governed by the random walk exponents, e.g. the effective spectral dimension which characterizes the time dependence of the number-of-distinct-sites-visited on a low-dimensional structure.