Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution

TL;DR

This paper provides an exact solution for the equilibrium properties of a one-dimensional catalytic chain with randomly placed catalytic segments, analyzing how these affect particle density and pressure in reactive and inert regions.

Contribution

It introduces an exact analytical approach for the disorder-averaged pressure, density, and compressibility in a catalytic chain with random segment placement, covering both annealed and quenched disorder.

Findings

Exact disorder-averaged pressure per site calculated

Asymptotic formulas for particle density derived

Compressibility behavior characterized

Abstract

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) in which some segments (placed at random, with mean concentration $p$) possess special, catalytic properties. Annihilation reaction takes place, as soon as any two $A$ particles land onto two vacant sites at the extremities of the catalytic segment, or when any $A$ particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another $A$ particle. Non-catalytic segments are inert with respect to reaction and here two adsorbed $A$ particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-average pressure per site. Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.