Exact Results for Kinetics of Catalytic Reactions

TL;DR

This paper provides exact solutions for the kinetics of irreversible catalytic reactions across different dimensions, revealing distinct decay behaviors and their implications for surface reaction models.

Contribution

It offers the first exact solutions for the dimer-dimer surface reaction model in arbitrary dimensions, especially in the reaction-controlled limit.

Findings

Reactive interface density decays as a power law for D<2

Logarithmic decay observed in two dimensions

Results are relevant for monomer-monomer surface reactions

Abstract

The kinetics of an irreversible catalytic reaction on substrate of arbitrary dimension is examined. In the limit of infinitesimal reaction rate (reaction-controlled limit), we solve the dimer-dimer surface reaction model (or voter model) exactly in arbitrary dimension $D$. The density of reactive interfaces is found to exhibit a power law decay for $D<2$ and a slow logarithmic decay in two dimensions. We discuss the relevance of these results for the monomer-monomer surface reaction model.