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We study the early stages of self-assembly of elementary building blocks of nanophase materials, considering explicitly their structure and the symmetry and the dimensionality of the reaction space. Previous work [Kozak et al., J. Chem. Phys. 134, 154701 (2007)] focused on characterizing self-assembly on small square-planar templates. Here we consider larger lattices of square-planar symmetry having N = 255 sites, and both hexagonal and triangular lattices of N = 256 sites. Furthermore, to assess the consequences of a depletion zone above a basal layer (λ = 1), we study self-assembly on an augmented diffusion space defined by λ = 2 and λ = 5 stacked layers having the same characteristics as the basal plane. The effective decrease in the efficiency of self-assembly of individual nanophase units when the diffusion space is expanded, by increasing the template size and/or by enlarging the depletion zone, is then quantified. The results obtained reinforce our earlier conclusion that the most significant factor influencing the kinetics of formation of a final self-assembled unit is the number of reaction pathways from one or more precursor states. We draw attention to the relevance of these results to zeolite synthesis and reactions within pillared clays. [ABSTRACT FROM AUTHOR]

A minimal model for the NO + H[SUB2] reaction on a Pt emitter tip is proposed, with emphasis placed on surface explosions observed in field ion microscopy experiments. The model is first studied in the mean-field approximation, where it is shown to exhibit bistability and associated explosive phenomena. Using kinetic Monte Carlo simulations, irreversible phase transitions, fluctuation-induced dynamics and reaction front propagation are observed, which are not predicted by the mean-field approach. This comparative study allows to shed some light on the origins of the surface explosions, and to investigate the influence of the discrete nature of the support on the dynamics. [ABSTRACT FROM AUTHOR]

Studies the Schlogl-1 and Schlogl-2 models in a spatially extended systems with the aid of a probabilistic cellular automation emulating chemical dynamics in a dispersed medium. Deviation of the steady-state behavior from the deterministic value for Schlogl-1 model; Bifurcations for Schlog1-2 model found under the conditions of intensive stirring and low rate constants.

The chlorite–thiosulfate reaction provides us with an example of isothermal chemical reaction giving rise to explosive-like behavior in batch condition. Experimental results show that this phenomenon is characterized by high sensitivity, reflected in particular by the fact that reaction times occur randomly despite the care taken to prepare initially the system in identical states. In the present paper a reaction scheme reproducing explosive dynamics analogous to the experimental data is proposed and the effects of fluctuations of different origins on the reaction time are examined. As it turns out, both internal and external fluctuations induce a significant broadening of the probability distribution of explosion times as well as an asymmetry in its shape. The effect of random initial conditions is also analyzed and shown to affect deeply the explosive behavior. [ABSTRACT FROM AUTHOR]

Montroll’s approach to diffusion-controlled annihilation reactions recently generalized by the present authors to account for the simultaneous displacement of two walkers, is extended by including more complex kinetic schemes and many-body effects. The mean walklength to reaction and the spatial organization of the reactants in a finite planar lattice is evaluated analytically and by Monte Carlo simulations in two representative schemes involving, respectively, a single autocatalytic reaction and an autocatalytic reaction coupled to isomerization. While in the first scheme the results are in qualitative (though not quantitative) accord with mean-field predictions, marked qualitative differences with mean-field behavior are found in the second scheme. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Numerically-exact values of the mean walk length before first encounter for reactants diffusing on a lattice are calculated by generalizing a Markovian method introduced previously. The approach developed is illustrated by presenting results for two random walkers diffusing simultaneously on a square-planar lattice; the results obtained are compared with those calculated assuming one of the reactant partners is stationary. In almost all cases, it is found that the former process is the more efficient. Analytic arguments are presented and Monte Carlo studies are carried out to support the results obtained. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]