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

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.

arXiv commentAMSTeX, 27 pages + 4 figures

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Cited by in corpus (9)

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• Survival Probability of a Ballistic Tracer Particle in the Presence of Diffusing Traps
• Catalytic reactions with bulk-mediated excursions: Mixing fails to restore chemical equilibrium
• Random Geometric Series
• Equilibrium Properties of A Monomer-Monomer Catalytic Reaction on A One-Dimensional Chain
• Binary Reactive Adsorbate on a Random Catalytic Substrate
• Equilibrium properties of two-species reactive lattice gases on random catalytic chains
• An exactly solvable model of reversible adsorption on a disordered substrate
• Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices