Theoretical modeling of spatiotemporal self-organization in a surface catalyzed reaction exhibiting bistable kinetics

A two-variable Langmuir–Hinshelwood mechanism for isothermal CO oxidation on a catalytically active surface is presented. It shows bistability stemming from 2 cusp bifurcations, which can be obtained analytically for low pressure. Inclusion of CO diffusion on the surface leads to a system of partial differential equations, which exhibits nucleation and front propagation phenomena in the bistable region. While the line of equistability could with good accuracy be solved for analytically, the front velocities and critical radii for nucleation had to be determined numerically (using the method of heteroclinic orbits). Throughout the calculations the kinetics and rate constants for the CO oxidation on Pt(111) are used. Here the model can be reduced by adiabatic elimination of one variable (namely oxygen coverage) allowing a comparison to the exactly solved one-variable Schlögl model. Possible implications for future experimental work are briefly discussed.