Mesoscopic Pattern Formation In Catalytic Processes By An Extension Of The Mean Field Approach

For some years it has been known that a number of catalytic reactions, under specified steady operating conditions, exhibit oscillations, in the rate of product formation. These are often related to beautiful spatiotemporal patterns, including targets and spirals, on the metal surface.These examples of self-organizational phenomena have attracted considerable interest, because they are proving to be theoretically amenable.Here we review different approximations to model heterogeneous surface chemical reactions, which exhibit oscillatory behavior.A focal point is the use of a detailed knowledge of the dynamics of surface structural phase transition for modeling kinetic oscillations, which represent a severe test of our understanding of chemical processes at surfaces.Advantages and disadvantages of the Monte Carlo approach are presented to model heterogeneous oscillatory chemical reactions, with special emphasis if a Monte Carlo method is going to be applied to study the time evolution of a surface chemical reaction, as there should be a linear relationship between the time unit called the Monte Carlo step (MCS) and actual time. We conclude that special care must be taken when two or more processes are included in a simulation, because now overall MCS should be compatible with every individual process.The mean field approach (MFA) takes into account only reaction processes and completely neglects spatial correlation and fluctuations. Therefore, this approach is not adequate for describing the rich variety of spatial patterns that are experimentally observed. On the other hand, Monte Carlo approaches are severely limited by computational capabilities. To overcome MFA limitations we propose to extend the earlier work of King and coworkers [J. Chem. Phys.100, 14417 (1996)], which did not include spatial dependence, by adding diffusion processes and gas global coupling to the coupled reaction equations.The extended MFA can now be used as a new tool for the analysis of pattern formation in surface chemistry.