Equilibrium Properties of A Monomer-Monomer Catalytic Reaction on A One-Dimensional Chain

TL;DR

This paper analytically investigates the equilibrium behavior of a one-dimensional lattice-gas model for a catalytic A+B→0 reaction, deriving exact expressions for pressure, densities, and compressibilities in contact with particle reservoirs.

Contribution

It provides the first exact analytical solution for the equilibrium properties of a one-dimensional catalytic reaction model with adsorption and desorption.

Findings

Derived exact expression for pressure as a function of chemical potentials.

Obtained explicit formulas for mean particle densities.

Calculated compressibilities of the adsorbed species.

Abstract

We study the equilibrium properties of a lattice-gas model of an $A + B \to 0$ catalytic reaction on a one-dimensional chain in contact with a reservoir for the particles. The particles of species $A$ and $B$ are in thermal contact with their vapor phases acting as reservoirs, i.e., they may adsorb onto empty lattice sites and may desorb from the lattice. If adsorbed $A$ and $B$ particles appear at neighboring lattice sites they instantaneously react and both desorb. For this model of a catalytic reaction in the adsorption-controlled limit, we derive analytically the expression of the pressure and present exact results for the mean densities of particles and for the compressibilities of the adsorbate as function of the chemical potentials of the two species.