Simple models for heterogeneous catalysis: Phase transition-like behavior in nonequilibrium systems

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Abstract
A simple model for heterogeneous catalysis, recently introduced by Ziff, Gulari, and Barshad (ZGB), has been explored using computer simulation. This is a nonequilibrium model which exhibits phase transition-like behavior. The only parameter in this model (Y) sets the ratio with which two reactive species (A and B2) are fed to the surface (lattice). On the square lattice, ZGB found a range of values of this parameter for which steady states with nonzero A and B concentrations occur. Outside of this range, the surface becomes completely covered with A or B sites. The range of Y values corresponding to steady state with nonzero A and B concentrations is bounded by two ‘‘critical’’ values Y1 and Y2. For values of Y close to but above Y1 we have obtained approximate values for the exponents which describe the dependence of the steady-state densities of A and B sites on (Y−Y1). These exponents both seem to have the same value independent of lattice details. We have extended the work of ZGB to the hexagonal lattice, one-dimensional lattice, and narrow strips. The results obtained for the hexagonal lattice are qualitatively similar to those obtained for the square lattice. For the 1D lattice and strips with a width of 2 lattice units, steady states with nonzero A and B site concentrations are not found. For widths of 3 or more lattice units, such steady states are found and the range of the relative probability parameter over which this behavior occurs grows steadily with increasing strip width. We have also obtained new results for the more simple C+D product reaction. Here C and D occupy single lattice sites and react immediately if they are nearest neighbors.