Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain

Abstract

We present an exact solution describing equilibrium properties of the catalytically-activated A + A \to 0 reaction taking place on a one-dimensional lattice, where some of the sites possess special "catalytic" properties. The A particles undergo continuous exchanges with the vapor phase; two neighboring adsorbed As react when at least one of them resides on a catalytic site (CS). We consider three situations for the CS distribution: regular, annealed random and quenched random. For all three CS distribution types, we derive exact results for the disorder-averaged pressure and present exact asymptotic expressions for the particles' mean density. The model studied here furnishes another example of a 1D Ising-type system with random multi-site interactions which admits an exact solution.

arXiv comment7 pages, 3 Figures, appearing in Europhysics Letters

References in corpus (2)

• Soluble two-species diffusion-limited Models in arbitrary dimensions
• Influence of auto-organization and fluctuation effects on the kinetics of a monomer-monomer catalytic scheme

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