V. Pereyra

Monte Carlo study of dimer adsorption at monolayer on square lattices

The localized monolayer adsorption of interacting homonuclear dimers (AA) on square lattices is studied using a lattice-gas model. The effect of lateral interactions on the behavior of different thermodynamic quantities is considered. Phase diagrams (i.e. critical temperature versus coverage) are calculated using Monte Carlo simulation and finite-size scaling for both attractive and repulsive nearest-neighbors lateral interactions. Of special interest is the repulsive case where different ordered structures are observed, confirming the results given by Phares et al. [J. Phys. A: Math. Gen. 26 (1993) 6847] based upon exact transfer-matrix method for dimers on a semi-infinite square lattice.

Mechanistic study of surface processes on adsorbents: I. Statistical description of adsorptive surfaces

Abstract A dual description based on a network of “sites” and “bonds” is developed for the characterization of the adsorptive energy of a heterogeneous surface. This description is more complete than previous ones based on only one of those elements. The joint site-bond energy distribution is determined through a correlation function in such a way that the maximum degree of randomness is attained in the network. The degree of randomness is limited by the “Construction Principle”: according to this, the adsorptive energy at a site must be deeper than that of any bond connected to that site. This correlation function contains valuable information about the topology of the energy surface, which plays an important role in adsorption equilibrium and dynamics.

The diffusion-controlled annihilation reaction in random adsorptive fields

The kinetics of the A+A to 0 reaction on a correlated heterogeneous one-dimensional chain is studied. As a novel result it is found that the temporal behaviour of the density of A particles depends on the energetic topography of the surface when A particles are initially located preferentially on the more energetic sites, as happens in the case of thermodynamical equilibrium for the absorbate.

Study of adsorption of binary mixtures on disordered substrates

The adsorption of binary mixtures on solid heterogeneous substrates is studied by Monte Carlo simulation in the framework of the lattice gas model. The energy of the surface has been modeled by considering two kind of adsorption sites, deep and shallow traps, forming square homogeneous patches of different sizes; these adsorption domains have been distributed either at random or in chessboard-like lattice to obtain simple heterogeneous topographies. The adsorption process has been monitored through total and partial isotherms and differential heats of adsorption corresponding to both species of the mixture, for different values of the parameters involved in the model (lateral interactions, energy gap between deep and shallow patches) and different topographies. A rich variety of behaviors is found and analyzed in the context of the lattice gas theory.

Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals.

In this Brief Report, the convergence of the 1t and Wang-Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two, and higher dimensions. The efficiency and accuracy of both algorithms are determined by the dynamical behavior of the errors between the exact and the calculated values of the integral. It is observed that the time dependence of the error calculated with the 1t algorithm varies as N;{-12} [with N the number of Monte Carlo (MC) trials], in quantitative agreement with the simple sampling Monte Carlo method. In contrast, the error calculated with the Wang-Landau algorithm saturates in time, evidencing the nonconvergence of this method. The sources of error for both methods are also determined.

Diffusion of interacting lattice gases on heterogeneous surfaces with simple topographies

Collective diffusion coefficients are studied for heterogeneous bivariate trap surfaces with different topographies. The topography is shown to affect strongly the coverage dependence and Arrhenius behavior of diffusion coefficients. The fluctuation and Kubo-Green methods are in strong disagreement, which is attributed to the failure of the former when the probe size is of the order of the applicable scale length for the lattice gas.

Surface diffusion of dimers: I repulsive interactions

We analyze the diffusion process of rigid homonuclear dimers (AA) adsorbed on a simple cubic (sc(100)) surface. The coverage dependence of the collective diffusion coefficient is obtained by means of Monte Carlo simulations in the framework of the Kubo-Green formalism. Different microscopic diffusion mechanisms are introduced and their influence in the collective motion have been investigated. Repulsive adsorbate-adsorbate interaction, JAA, is considered in order to analyze the influence of such parameter on the diffusion process. The behavior of the diffusion coefficient in the critical region is studied, where several ordered adsorbate structures appear depending on the values of JAA.

Collective diffusion on strongly correlated heterogeneous surfaces

Abstract Collective diffusion coefficients are studied for heterogeneous bivariate surfaces with two different topographies, namely the random patches and the chessboard-like ordered distributions. The topography is shown to affect strongly the coverage dependence of the transport coefficients. Various diffusion quantities like the chemical D , jump D J and tracer D ∗ diffusion coefficients are analyzed by means of Monte Carlo simulations in the framework of the fluctuation and the Kubo–Green theory. The behavior of diffusion coefficients in small patches is mainly affected by the mobility of the particles in the border vacancies, and a simple law is obtained for the ratio D (1)/ D (0). For large patches the behavior is dominated by the mobility of particles in the central vacancies. In the limit of very large patches the diffusion coefficients become independent of the energetic topography.

Temperature behavior of tracer diffusion on heterogeneous surfaces

The behavior of a tagged particle on a generalized heterogeneous surface is studied by Monte Carlo simulation. Using the dual site-bond model (SBM), the energetic properties of the heterogeneous substrates can be appropriately described through the site and bond energy distributions and the overlapping degree between them. The effect of the adsorptive energy topography on the tracer diffusion coefficient, as well as on the time behavior of the mean-square displacement of the adparticle, are analyzed for different temperatures and energy correlation degrees. The short-time behavior of tracer diffusion is highly sensitive to the surface energy structure. The possibility of using tracer diffusion analysis for a better characterization of the energetic topography of heterogeneous surfaces is discussed.

Adsorption-induced surface reconstruction: predictions of a simple model

Surface reconstruction can be a spontaneous or adsorbate-induced phenomenon. The effect of chemisorption is the extensive restructuring of the substrate to form a completely new surface structure. Such a phase transition can be explained qualitatively by employing statistical models like the lattice-gas model. In this work we analyze in detail the two-position model introduced by Myshlyavtsev and Zhdanov [A.V. Myshlyavtsev, V.P. Zhdanov, J. Chem. Phys. 92 (1990) 3909]. The model is a simplified latticegas version of the HW(001) system, which presents a c(2 × 2) ordered structure below the critical temperature Tc. The phase diagram of the real system is reproduced only at low coverage (θ < 0.4). The phase diagram is obtained by the mean-field approximation as well as by Monte Carlo simulations through finite-size scaling techniques. Different kinds of situations can be observed depending on the characteristics of the metal-metal (J), adsorbate-adsorbate (ϵ) and metal-adsorbate (λ) interactions.