J. J. Luque

Monte Carlo simulation of a surface reaction model with local interaction

Influence of the interaction between nearest‐neighbor adatoms in a reaction of catalyzed oxidation of carbon monoxide has been studied by Monte Carlo simulation. The transition probabilities are chosen in the Arrhenius form, and the activation energy is divided into two additive terms, corresponding to the action of the substrate and to the interaction between nearest adatoms, respectively. When the interaction makes desorption easier or hinders adsorption the behavior is similar: Three steady state regimes or phases were observed; in the first phase, the surface is poisoned by oxygen; in the second phase there is a reactive steady state in which carbon dioxide is continuously produced, and in the third phase, the surface is poisoned by carbon monoxide. The transition from the O‐poisoned phase to the reactive phase is continuous, or second order, and the transition from the reaction to the CO‐poisoned phase is first order. The same occurs when the interaction is not considered. The interaction makes the s...

Kinetic model for desorption of paired adatoms

By employing an extension of the Glauber–Ising model, the kinetics of the desorption of paired adatoms from a linear chain is studied. Three competitive mechanisms for changing a state of the system are allowed, namely desorption from or readsorption onto the chain or migration of the adatoms from site to site on the chain. The transition probabilities depend on an external field, on the interaction between nearest neighbors, and on three proper rate constants characterizing desorption, readsorption, and migration processes. An infinite set of coupled kinetic equations is obtained from the master equation. In order to compute the adsorption degree ϑ and the fraction of adjacent adatom pairs η, a ’’closure’’ approximation is taken. The steady‐state solution is in agreement with the exact result of the equilibrium statistical mechanics. We find that relaxation far from equilibrium is, in general, not describable by a single exponential. The relaxation is slower when mobility does not exist than when adatoms...

Influence of the interaction on oscillatory behavior in a surface reaction model

Bistability and oscillations of temperature and concentrations are observed in a kinetic model, based on the oxidation of carbon monoxide on a solid surface. The macroscopic kinetic equations, which govern the reaction, are obtained by applying a closure approximation of mean-field type. With the aim of studying how the interaction affects the oscillatory behavior in the reaction, we have explicitly considered the interaction between nearest-neighbor adsorbed species, CO–CO, CO–O, and O–O. Interactions favoring CO2 production are analyzed.

Fractal structure in adsorbates in a catalysed reaction on a surface

The influence of interaction and lattice coordination number on the reactivity and structure of adsorbed particles on a surface has been analysed for a reaction of a monomer and a dimer that dissociates, both of which are adsorbed on a surface and react. For the case without interaction there is a narrow range for a control parameter in which reaction is effective. Depending on the interaction, this range can grow very large, spanning almost all the range of the control parameter or, on the contrary, the reaction can disappear. Aggregates of adsorbed particles with fractal structure have been observed. Fractal dimension has been determined for different values of a control parameter for square and triangular lattices.

Temperature programmed desorption by dimers from a surface

The desorption by dimers from a surface is studied. Migration on the lattice and interaction between neighboring adatoms can exist. Starting from a master equation with transition probabilities in the Arrhenius form, a set of kinetic equations is obtained. For a square lattice, when lateral interaction is repulsive and surface mobility operates, rate desorption curves first exhibit a maximum, next a shoulder, and finally a long tail. For the linear chain and all the other cases of the square lattice these curves show only a maximum.

Multistability of steady states in competitive adsorption of two species

Competitive adsorption of two species on a linear chain is considered. The adsorption–desorption probabilities are chosen in the Arrhenius form and it is assumed that the activation energies are partially due to interaction between nearest neighboring adatoms. Multistability can occur for an attractive interaction greater than a critical value, depending on the values of other parameters, and the least critical value corresponding to an interaction energy of ≂0.3 kcal mol−1 for room temperature. Up to seven steady states can result, three being stable. The relaxation times tend to infinitum at the critical points and the exponent α, where τJ→Jcritical∼(Jcritical−J)−α and J being a parameter gauging the strength of the interaction, has been determined for a number of cases. The analysis has been extended to two‐dimensional lattices and similar results have been obtained, although Jcritical is less than that for the linear chain. Next a dimerization reaction between adatoms has been considered jointly with ...

MULTIFRACTAL ANALYSIS OF ADSORBATE IN A CATALYZED SURFACE REACTION

The use of multifractals in heterogeneous chemistry has proven useful in the characterization of some complex phenomena. This paper proposes a multifractal analysis in order to study the distribution of adsorbed particles for a reaction of a monomer and a dimer that dissociates, both of which are adsorbed on a surface and react. For a range of a control parameter, there is a steady reactive window that changes when adsorbate-adsorbate lateral interaction is considered. τ(q) and f(α) for different values of control parameter and interactions are calculated, studying distribution of adsorbed particles in relation to multifractal properties.

One-dimensional time-dependent Ising model in ramdom magnetic fields

The relaxation to equilibrium of a spin chain in a random magnetic field H is investigated; periodic, patchwise and purely random distributions are studied. To close the set of kinetic equations, the Bragg-Williams approximation (BWA) and a triplet closure approximation (TCA) are applied, and stationary solutions show agreement with those obtained from equilibrium statistical mechanics. However, BWA and TCA time-dependent solutions exhibit differences which are not only quantitative but qualitative for certain values of the coupling constant J. The TCA is applied to analyze the relaxation far from equilibrium and the relaxation function of magnetization departs from a single exponential and significant differences exist between both cases J > 0 and J < 0. For the antiferromagnetic coupling constant, the relaxation function of the magnetization first decays quickly, then becomes negative, passes through a minimum and tends to equilibrium slowly. On the other hand, differences are significant for various distributions of H, especially in the antiferromagnetic case.

TRANSIENT ORDERED STATES IN A MODEL REACTION ON A SURFACE WITH ACTIVE SITES

A model for the monomer–monomer surface reaction of the type A + B → AB, with diffusion of A and B monomers on a surface and reaction only on active sites randomly distributed on the surface, has been proposed and studied. For a critical point where both adsorption probabilities are the same, a seemingly reactive steady state transforms itself into a poisoned state. In this transient state, the production of AB molecules, in relation to the density of active sites, is considered and an inert-reactive irreversible phase transition is observed. The critical values of the density of active sites, where the irreversible phase transition occurs, is obtained in the limit L → ∞ by means of a finite-size scaling analysis. The critical exponents that dominate the correlation length of clusters, as well as the production of AB molecules at criticality, are determined.