Irreversible phase transitions in a surface-reaction model with diffusion- and adsorption-limited reactions.

Abstract

A model is proposed and studied for the heterogeneously catalyzed monomer-monomer reaction of the type A+B\ensuremath{\rightarrow}AB. In two dimensions, the active sites (AS's) of the catalyst belong to a (fractal) incipient percolation cluster, while the remaining surface, i.e., the inactive sites (IS's), is reaction passive. B adsorption is only allowed on AS's while IS's are embedded on a (fully) A-covered state. A monomers can diffuse from IS to AS and reaction takes place when A and B monomers are adsorbed on a pair of nearest-neighbor AS's. The model has a single parameter, namely, the adsorption probability of B monomers (${\mathit{p}}_{\mathit{B}}$). Starting from an empty configuration of AS's, two points ${\mathit{p}}_{\mathit{B}1}$ and ${\mathit{p}}_{\mathit{B}2}$ are found such that for ${\mathit{p}}_{\mathit{B}}$\ensuremath{\le}${\mathit{p}}_{\mathit{B}1}$ (${\mathit{p}}_{\mathit{B}}$\ensuremath{\ge}${\mathit{p}}_{\mathit{B}2}$) the fractal cluster of AS's becomes poisoned by A (B) monomers. For ${\mathit{p}}_{\mathit{B}1}$${\mathit{p}}_{\mathit{B}}$${\mathit{p}}_{\mathit{B}2}$ the reaction reaches a stationary regime with AB production. So, both ${\mathit{p}}_{\mathit{B}1}$\ensuremath{\simeq}0.2075\ifmmode\pm\else\textpm\fi{}0.0025 and ${\mathit{p}}_{\mathit{B}2}$\ensuremath{\simeq}0.3600\ifmmode\pm\else\textpm\fi{}0.0025 are critical points at which second-order irreversible phase transitions take place. The dynamic critical behavior of the reaction is also studied and the obtained critical exponents strongly suggest that the model does not belong to the Reggeon-field-theory universality class, in contrast to rather well-established conjectures.