SURFACE DIFFUSIVITIES AND REACTION-RATE CONSTANTS - MAKING A QUANTITATIVE EXPERIMENTAL CONNECTION

For diffusion-controlled reactions in three dimensions, continuum mech anics provides a quantitative relation between the steady-state reacti on rate constant k and the diffusion coefficient D. However, this appr oach fails in two dimensions, where no steady-state solution exists on an infinite domain. Using both Monte Carlo methods and analytical tec hniques, we show that previous attempts to circumvent this problem fai l under real laboratory conditions, where fractional coverages often e xceed 10(-3). Instead, we have developed a rigorous and general relati on between k and D for all coverages on a square lattice for the react ion A + A --> A(2). For short times or high coverages, the relation k = pi D/gamma holds exactly where gamma denotes the two-dimensional pac king fraction. For lower coverages, however, k depends on time in both constant-coverage (adsorption allowed) and transient-coverage (adsorp tion forbidden) regimes. In both cases, k decreases in response to the evolution of nonrandom adsorbate configurations on the surface. These results indicate that diffusion-limited surface reactions may be iden tified unambiguously in the laboratory and also provide a quantitative link between diffusion parameters and experimentally determined recom bination rate parameters. Practical experimental methods highlighting such effects are outlined. (C) 1996 American Institute of Physics.