Binary Reactive Adsorbate on a Random Catalytic Substrate

TL;DR

This paper investigates the equilibrium behavior of a binary reactive monomer mixture on a random catalytic substrate, mapping it to a classical spin model to analyze phase diagrams and effects of catalytic bond density.

Contribution

It introduces a novel mapping of a reactive monomer mixture with catalytic bonds onto a classical spin model, enabling mean-field analysis of phase behavior.

Findings

Phase diagram depends on catalytic bond density q.

Reveals conditions for phase separation and ordering.

Shows impact of catalytic bond randomness on system behavior.

Abstract

We study the equilibrium properties of a model for a binary mixture of catalytically-reactive monomers adsorbed on a two-dimensional substrate decorated by randomly placed catalytic bonds. The interacting $A$ and $B$ monomer species undergo continuous exchanges with particle reservoirs and react ($A + B \to \emptyset$) as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For the case of annealed disorder in the placement of the catalytic bonds this model can be mapped onto a classical spin model with spin values $S = -1,0,+1$, with effective couplings dependent on the temperature and on the mean density $q$ of catalytic bonds. This allows us to exploit the mean-field theory developed for the latter to determine the phase diagram as a function of $q$ in the (symmetric) case in which the chemical potentials of the particle reservoirs, as well as the $A-A$ and $B-B$ interactions are equal.