Heterogeneous catalytic reaction on a 2×2 lattice

We study a model proposed by Fichthorn, Gulari and Ziff for the kinetics of a generic heterogeneous catalytic reaction, A+B→AB. This reaction includes the steps of adsorption and desorption of reactants A and B, surface reaction through the Langmuir–Hinshelwood mechanism, and desorption of product AB. We solve the model exactly and without any restriction on a 2×2 lattice.

Despite the reduced number of sites employed, the solution shows some of the general features observed by simulating the mechanism on a large N×N lattice.

The rate of reaction depends on the rate of desorption of reactants with a maximum at a value similar to those found by performing heavy simulations. Also, on a 2×2 lattice, we have coverage of fluctuations of reactants as a function of their rate of desorption, as found on large N×N lattices.