Surface site diffusion and reaction on molecular "organizates" and colloidal catalysts: A geometrical perspective

We study surface-mediated, diffusion-controlled reactive processes on particles whose overall geometry is homeomorphic to a sphere. Rather than assuming that a coreactant can diffuse freely over the surface of the particle to a target site (reaction center), we consider the case where the coreactant can migrate only among N - 1 satellite sites that are networked to the reaction site by means of a number of pathways or reaction channels. Five distinct lattice topologies are considered and we study the reaction efficiency both for the case where the satellite sites are passive and for the case where reaction may occur with finite probability at these sites. The results obtained for this class of surface problems are compared with those obtained by assuming that the reaction-diffusion process takes place on a planar, two-dimensional surface (lattice). The applicability of our results to surface-mediated processes on "organizates" (cells, vesicles, micelles) and on colloidally dispersed catalyst particles is brought out in the Introduction, and the correspondence between the lattice-based, Markovian approach developed here and Fickian models of surface diffusion, particularly with regard to the exponentiality of the decay, is discussed in the concluding section.