2 5 O ct 2 00 2 Adsorption of Reactive Particles on a Random Catalytic Chain : An Exact Solution

We study equilibrium properties of a catalytically-activated annihilation A + A → 0 reaction taking place on a one-dimensional chain of length N (N → ∞) 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.