Effect of defect structures on chemically active surfaces: A continuum approach

A continuum approach is used to analyze the effect of defect structures on chemically active surfaces. The model comprises a linear diffusion equation with adsorption and desorption in which the defect structures are represented by nonlinear localized-reaction terms. The issue of multiple steady states and stability is treated, and a novel procedure is outlined that uses conformal mapping to derive stability criteria for these localized-reaction diffusion equations. This conformal mapping procedure also provides insight into how the various physical processes affect the stability of the system. A class of reactive-trapping models is considered in which defects are assumed to act as sinks of material that ultimately desorbs as a chemical product. Other features included in the model are nonlinear enhanced reactivity with concentration, and saturation effects. The continuum assumption is tested by direct comparison with a discrete reactive-trapping model and found to be a remarkably good approximation, even when the number of interdefect sites is as low as 20. We investigate the effect of relative defect locations on the balance between the desorptive processes that take place on the surface. The effect of defect locations on desorption is analyzed by considering symmetry-breaking perturbations to the defects in a periodic lattice. Two regimes of desorption are identified depending on the level of adsorption on the surface and the defect spacing. (i) Competitive: Defects that are moved closer by the perturbation compete for material, which reduces the trapping efficiency of the defect lattice and increases the bulk desorption rate; by considering the bulk desorption rate to be a function of the defect locations, we conclude that the situation of equally spaced defects is a local minimum of this function. (ii) Cooperative: Defects that are moved closer by perturbation in this regime act cooperatively to reduce the saturation level locally, which enhances the trapping efficiency of the defect lattice and reduces the bulk desorption rate. In this complex environment of competing physical effects it would be difficult to determine the dominant process without the analysis presented here. In order to determine whether these phenomena persist when the defects undergo finite random perturbations, we solve the continuum equations numerically using the boundary-element technique. The phenomena identified by the small perturbation case do persist when finite defect variations are considered.