Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate

Abstract

We present an \textit{exactly solvable} model of a monomer-monomer $A+B\to \varnothing$ reaction on a 2D inhomogeneous, catalytic substrate and study the equilibrium properties of the two-species adsorbate. The substrate contains randomly placed catalytic bonds of mean density $q$ which connect neighboring adsorption sites. The interacting $A$ and $B$ (monomer) species undergo continuous exchanges with corresponding adjacent gaseous reservoirs. A reaction $A+B\to \varnothing$ takes place instantaneously if $A$ and $B$ particles occupy adsorption sites connected by a catalytic bond. We find that for the case of \textit{annealed} disorder in the placement of the catalytic bonds the reaction model under study can be mapped onto the general spin $S=1$ (GS1) model. Here we concentrate on a particular case in which the model reduces to an exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys. Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986)) and derive an exact expression for the disorder-averaged equilibrium pressure of the two-species adsorbate. We show that at equal partial vapor pressures of the $A$ and $B$ species this system exhibits a second-order phase transition which reflects a spontaneous symmetry breaking with large fluctuations and progressive coverage of the entire substrate by either one of the species.

4 pages, 2 figures, submitted to Phys. Rev. Lett

References in corpus (4)

• Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution
• Single-Species Reactions on a Random Catalytic Chain
• Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain
• Equilibrium Properties of A Monomer-Monomer Catalytic Reaction on A One-Dimensional Chain

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