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

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

2002-10-25

arxiv.org/abs/cond-mat/0210575v1

Physics

Condensed Matter

Statistical Mechanics

AMSTeX, 27 pages + 4 figures

Scientific paper

10.1103/PhysRevE.67.016115

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.

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