Lattice-gas study of the kinetics of the catalytic NO-CO reaction on rhodium surfaces. II. The effect of nitrogen surface islands A Markov chain model for spatially distributed autocatalytic systems with a quadratic reaction rate is considered. An approximate solution for the local probability distribution is obtained in the form of a perturbation expansion for the regimes where diffusion is relatively fast. Using this approximate distribution, properties of the chemical wave fronts found in these autocatalytic systems are studied, and deviations of the minimum propagation velocity and the concentration profile from deterministic predictions are analyzed. A comparison with numerical results from lattice-gas automaton simulations is also provided.
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles on a lattice. The parameter γ, the ratio of characteristic time scales of reaction and diffusion, is used to gauge the relative contributions of these two processes to the overall dynamics. For the case of relatively fast diffusion, i.e. γ ≪ 1, an approximate solution to the Markov chain in the form of a perturbation expansion in powers of γ is derived. Kinetic equations for the average concentrations that follow from the solution differ from the mass-action law and contain memory terms. For a reaction-diffusion system with Willamowski-Rössler reaction mechanism, we further derive the following two results: a) in the limit of γ → 0, these memory terms vanish and the mass-action law is recovered; b) the memory kernel is found to assume a simple exponential form. A comparison with numerical results from lattice gas automaton simulations is also carried out. 05.40.+j, 82.40.Bj, 82.20.Fd
The electronic properties of polydithioquinone, a hypothetical C 4 S 2 carbon-sulfur polymer related to both tetrathiotetracene and thiothiophthene, are examined using approximate molecular orbital calculations. We focus on a curious pattern of sulfur-sulfur bonding interactions suggested by the band structure calculations, a pattern observed in thiothiophthenes and other molecular analogues of our polymer. The π system of each C 4 S 2 repeat unit contains eight electrons, consistent with a thiothiophthene-like rather than localized polydithioquinone valence structure. A pairing distortion in the carbon sublattice is implied; furthermore, the half-filled sulfur σ bands suggest that the sulfur sublattice is also likely to undergo distortions. Restricting our consideration to those distortions that retain planarity of the polymer, we find deformations of the carbon backbone considerably less favorable energetically than those of the sulfur sublattice. Four nicely bond-localized isomers result from the distortions of both carbon and sulfur sublattices; these all are found to be low bandgap semiconductors. We also examine helical distortions and find a stable isomer with an approximately 10-fold helical axis.
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