Reaction-diffusion fronts and the butterfly set.

A single-species reaction-diffusion model is used for studying the coexistence of multiple stable steady states. In these systems, one can define a potential-like functional that contains the stability properties of the states, and the essentials of the motion of wave fronts in one- and two-dimensional space. Using a quintic polynomial for the reaction term and taking advantage of the well-known butterfly bifurcation, we analyze the different scenarios involving the competition of two and three stable steady states, based on equipotential curves and points in parameter space. The predicted behaviors, including a front splitting instability, are contrasted to numerical integrations of reaction fronts in two dimensions.

Permethylated Disila[2]metallocenophanes of Group 14 and 15 Elements.

Permethylated disila[2]metallocenophanes of silicon, germanium, tin, lead, 2 a-d, (tetrelocenophanes) and antimony, 3 a,b, (pnictogenocenophanes) are described. In the case of antimony, a chloro-substituted stibonocenophane, 3 a, as well as cationic stibonocenophanium tetrachloroaluminate and tetraphenylborate salts, 3 b[X] (X=[AlCl4 ], [BPh4 ]), were synthesized. These represent the first examples of metallocenophanes of any Group 15 element. All compounds were studied in solution and in the solid state. Without exception the ansa-bridge exerts a strong influence on the bending angle of the two Cp-ligands. For disila[2]plumbocenophane, 2 d, its reactivity towards Group 15 halides was probed. Treatment of disila[2]plumbocenophane, 2 d, with two equivalents of phosphorus(III) chloride or arsenic(III) chloride, results in a ring-opening reaction and gives the bis(dihalopnictogenyl)-substituted products, 4 a,b.

Competing ternary surface reaction CO + O2 + H2 on Ir(111).

The CO oxidation on platinum-group metals under ultra-high-vacuum conditions is one of the most studied surface reactions. However, the presence of disturbing species and competing reactions are often neglected. One of the most interesting additional gases to be treated is hydrogen, due to its importance in technical applications and its inevitability under vacuum conditions. Adding hydrogen to the reaction of CO and O2 leads to more adsorbed species and competing reaction steps towards water formation. In this study, a model for approaching the competing surface reactions CO+O 2 + H2 is presented and discussed. Using the framework of bifurcation theory, we show how the steady states of the extended system correspond to a swallowtail catastrophe set with a tristable regime within the swallowtail. We explore numerically the possibility of reaching all stable states and illustrate the experimental challenges such a system could pose. Lastly, an approximative first-principle approach to diffusion illustrates how up to three stable states balance each other while forming heterogeneous patterns.