Influence of phase transition on pattern formation during catalytic reactions

We investigate the influence of the order of surface phase transitions on pattern formation during chemical reaction on mono-crystal catalysts. We use a model consisting of two partial differential equations, one of which describes the dynamics of the surface state with the help of a Ginzburg–Landau potential. Second- or first-order transitions are described by decreasing or increasing the relative value of the third-order coefficient of the potential. We concentrate on the stability of spiral patterns, and determine the region of the diagram where plane waves, asymptotic solutions of the spiral arms far from the core, are Benjamin–Feir unstable. The results indicate that spiral patterns are much more abundant when the transition is of second order, which is corroborated by the numerical integration of the equations of motion. Results also find support on the experiments, which show a rich pattern selection for the CO oxidation on Pt(1 1 0), but fail to detect the same behavior when the surface is Pt(1 0 0).