Saturation transition in a monomer-monomer model of heterogeneous catalysis

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Abstract
We discuss the kinetics of an irreversible monomer-monomer model of heterogeneous catalysis. In this model, two reactive species, A and B, adsorb ir- reversibly onto single sites of a catalytic substrate; subsequently nearest-neighbour adsorbed AB pairs can bond to form a reaction product which desorbs from the substrate. The kinetics of this process is investigated in a mean-field approximation, where the catalytic substrate is considered to be an N-site complete graph. Two fun- damental limits are identified: (a) the adsorption-controlled limit, where the reaction on the surface occurs quickly, so that the overall process is IimiCed by the adsorption rate, and (b) the reaction-controlled limit, where adsorption occurs readily so that the overall reaction is limited by the conversion of unlike neighbouring monomers to an AB pair. By analysing the master equation for the probability density of coverage, we determine the rate at which the catalyst becomes 'saturated', i.e. completely cov- ered by only one species. We show that the saturation time is proportional to N, and we also derive the probability distribution for the substrate coverage. Numerical sim- ulations are performed on lattice substrates of finite spatial dimensionality d to test the range of validity of the mean-field approach. We find good agreement between simulations and mean-field theory for d = 2 and 3, but not for d = 1, suggesting that d = 2 is a critical dimensionality for the monomer-monomer process.

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