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Abstract

The traditional approach followed for mathematically modeling physico-chemical processes on catalytic surfaces involves the choice of an infinitesimal surface area on the catalyst and formulation of mass balances involving adsorbate surface concentrations. Such a strategy is inadequate when the catalytic surface itself changes dynamically with respect to adsorbate-dependent surface arrangement of its catalytic atoms (and hence) its characteristic kinetics. A rigorous mathematical framework to model such processes is presented. The basic postulates of the theory are the availability of (1) a length scale over which the local infinitesimal area is of one surface type of another and (2) a time scale in which changes in fractional coverage occurring on the length scale in (1) are deterministically describable by continuous variables. A combination of probability and area-averaging is used to arrive at a deterministic set of partial differential equations for surface concentrations. The resulting equations include reaction and surface diffusion, and new terms such as dilution/augmentation of surface concentration of species brought about by phase transformation. Such terms are significant in predicting the nonlinear behavior of the system and in extracting the kinetics of surface reactions from dynamic data. An application of the theoretical framework to CO oxidation on Pt(100) is demonstrated and dilution/augmentation terms were identified in the purely temporal model. These terms are shown to be significantly important by simulation.