Kinetic phase diagrams for the monomer–dimer surface reaction: Unification of mean-field and lattice–gas behavior

Abstract

We provide a unified discussion of kinetic phase transitions for mean-field and lattice–gas treatments of the monomer–dimer surface reaction. For high surface mobilities, kinetics is typically well described by mean-field rate equations. These reveal bistability over a range of monomer adsorption rates which diminishes with increasing nonreactive monomer desorption rate d, and vanishes at some critical d=dc. Relative stability in the bistable region is determined from the behavior of chemical waves corresponding to the displacement of one stable state by the other. Their evolution is determined via appropriate reaction–diffusion equations. Conventional diffusion terms are modified here to reflect the influence of the presence of one species on diffusion of the other. We determine equistability (i.e., discontinuous transition) points for d≤dc, and thus construct a kinetic phase diagram including a spinodal line. For lower surface mobilities, analysis of lattice–gas models reveals qualitatively analogous behavior. The key difference is that for lower mobilities, spontaneous fluctuations are effective in automatically selecting the most stable state, i.e., in reducing metastability, and thus producing discontinuous transitions.