On the Reactions A+A+...+A->0 at a One-Dimensional Periodic Lattice of Catalytic Centers: Exact Solution

TL;DR

This paper provides an exact solution for the kinetics of a diffusion-controlled multi-particle reaction on a one-dimensional periodic lattice of catalytic centers, revealing that at large times the reaction probability is independent of catalyst density.

Contribution

It offers a rigorous proof that, asymptotically, the reaction probability does not depend on the spacing of catalytic sites in a one-dimensional lattice.

Findings

Reaction probability W(t) becomes independent of lattice period at large times.

The asymptotic behavior is the same for dense and sparse catalytic arrangements.

Exact solution within the Smoluchowski approximation is provided.

Abstract

The kinetics of the diffusion-controlled chemical reactions A+A+...+A->0 that occur at catalytic centers periodically arranged along a straight line is considered. Modes of the behavior of reaction probability W(t) were studied at different times and different densities of the catalyst. Within the Smoluchowski approximation, it was rigorously proved that at large times the function W(t) is independent of the lattice period. This means that, in the given asymptotic mode, the probability of the reaction on a lattice with a catalyst placed in each lattice site is the same as on a lattice with a catalyst placed in sparse sites.