Bifurcation analysis of the three-variable model for the NO+CO reaction on Pt surfaces

Abstract

Under isothermal conditions at low pressure (10−6 mbar range), the NO+CO reaction exhibits oscillatory behavior on a Pt(100) surface. Based on the results of in situ low-energy electron diffraction (LEED) measurements which showed that the 1×1⇄hex phase transition is not essential for producing oscillations, a three-variable model of coupled differential equations was developed which instead relies solely on the autocatalysis provided by the stoichiometry of the individual reaction steps. This model has been analyzed with the help of bifurcation theory using realistic values for the constants in the equations. The results demonstrate that the model reproduces, quite well, the existence range for oscillations on Pt(100). Two oscillatory regions exist with a large one located above the stoichiometry ratio pNO: pCO=1 and a very small one which is found just below pNO: pCO=1. Only the former one has a counterpart in the experiment. At low temperature two isolated branches of the reaction exist which merge at higher T in a transcritical bifurcation thus creating a peculiar hysteresis loop in the shape of a mushroom. Bifurcation analysis has also been applied to investigate the role of the internal parameters, e.g., the role of the constants in the differential equations. The most critical constants were those which control the dissociation of NO and, therefore, are decisive whether ignition or extinction in the reaction takes place. The high degree of qualitative and quantitative agreement which could be achieved with the three-variable model demonstrates that the model provides a reasonable description of the experiments.