CO oxidation on thin Pt crystals: Temperature slaving and the derivation of lumped models

We review the Langmuir-Hinshelwood model for the heterogeneous catalytic oxidation of carbon monoxide on thin (approximate to3000 Angstrom) platinum catalysts. Our ultimate goal is to model observed thermo-mechano-chemical oscillations on a thin Pt (110) crystal under low pressure/vacuum conditions. Here we consider only the thermochemical aspects. We supplement the reaction-diffusion model of chemical kinetics by a heat balance equation for the catalyst surface, derived from the energetics of the reaction, adsorption, and desorption processes, and including radiation and conduction to the supporting environment. From the resulting distributed system a four-dimensional lumped ordinary differential equation is derived, which we study via dynamical systems theory, making use of time scale separation, and deriving reduced two-dimensional models. We show that key types of dynamics of the isothermal reaction persist, including multiple equilibria and periodic oscillations, but with the varying catalyst temperature "slaved" to the chemistry. We show how the stability of the periodic orbit branch changes as the catalyst's area and thickness change, we verify that the lumped models capture the dominant dynamics of the distributed system, and we outline the major differences. (C) 2003 American Institute of Physics.