Finite-size 'poisoning' in heterogeneous catalysis

Abstract

The dynamics of a monomer-monomer and a monomer-dimer surface catalytic reaction is investigated. From the mean-field solution, finite systems eventually 'poison' at an exponential rate to a fully occupied, non-reactive state. For the monomer-monomer process, this poisoning is driven by concentration fluctuations of a diffusive nature, leading to poisoning times which vary as a power of the linear system size L. A comparison of the Monte Carlo simulations with the mean-field result suggests that the upper critical dimension for the monomer-monomer model is d, = 2. For the monomer-dimer process, there is an effective potential that needs to be surmounted by fluctuations, leading to poisoning times which grow at least as fast as eL. This gives rise to an apparent reactive steady state. Heterogeneous catalysis is a fundamental kinetic process in which the rate of a chemical reaction is enhanced by the presence of suitable catalyst material ( 13. A typical example is where reactants adsorb on a catalytic surface which then promotes the bonding of reactants. Once a reaction occurs, the reaction product desorbs, thereby allowing for continued operation of the system. This type of catalytic reaction underlies a host of technological processes and a substantial fraction of all chemical production ( 11. It has only been very recently, however, that investigations of microscopic models have begun to identify the general principles underlying the dynamical behaviour of heterogeneous catalysis. Ziff et a1 (2) introduced a simple lattice model which appears to describe various features of the surface catalytic reaction of carbon monoxide (monomers, which adsorb onto a single lattice site) and oxygen (which are deposited as dimers and disassociate upon adsorption). Depending on the relative deposition rate of the monomers and dimers, there may be 'poisoning', where the surface eventually becomes covered by only one species, or there may be an apparent reactive steady state. Novel kinetic phase transitions demarcate these two possibilities. This intriguing behaviour has stimulated further work on this and a simpler monomer-monomer process to be defined below (3-71. Our goal, in this letter, is to show that the mean-field solution, together with numerical simulations of very small systems, provide a rather complete description of the dynamics of idealised surface catalytic reactions. For the monomer-monomer process, we show that the final state of a finite system is always poisoned and that poisoning is approached at an exponential rate in mean-field theory. These facts are actually quite difficult to establish in numerical simulations of large systems (5).