Simulations of Surfaces

Pinilla et al. studied the structure and dynamics of [MMIM]Q confined between two parallel solid walls [146], this was the first simulation of an ionic-hquid/solid interface. Simulations were performed at various interwall distances. Mass and charge density along the confinement axis revealed a structure of foyers parallel to the walls and a corresponding oscillatory profile of electrostatic potential. In particular, the potential drop between a point inside the sohd wall and the center of the liquid slab was —0.5 V. Orientational correlation functions indicated that, at the interface, cations orient tilted with respect to the surface but that such orientational order is lost thereafter. A rather singular result vras that the ionic diffusion under confinement was faster than in the bulk, at least for the non orrugated walls used in the modd. 

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Complementing these very well established approaches for the study of any scientific field, namely experiments and analytical theory, very recently, computer simulations have become a powerful tool for the study of a great variety of processes occurring in nature in general [4-6], as well as surface chemical reactions in particular [7]. Within this context, the aim of this chapter is not only to offer a critical overview of recent progress in the area of computer simulations of surface reaction processes, but also to provide an outlook of promising trends in most of the treated topics. 

Within this context, the following sections are devoted to the description of the state of the art in the modeling and simulation of surface chemical reactions of simple systems using Monte Carlo techniques. 

Toffoli and Margolus [tofF86] point out that what appears on the macroscopic scale is a good simulation of surface tension, in which the boundaries behave as though they are stretched membranes exerting a pull proportional to their curvature. Vichniac adds that the behavior of such twisted majority rules actually simulates the Allen-Cahn equation of surface tension rather accurately ... 

The main idea of a lattice model is to assume that atomic or molecular entities constituting the system occupy well-defined lattice sites in space. This method is sometimes employed in simulations with the grand canonical ensemble for the simulation of surface electrochemical proceses. The Hamiltonians H of the lattice gas for one and two adsorbed species from which the ttansition probabilities 11 can be calculated have been discussed by Brown et al. (1999). We discuss in some detail MC lattice model simulations applied to the electrochemical double layer and electrochemical formation and growth two-dimensional phases not addressed in the latter review. MC lattice models have also been applied recently to the study the electrox-idation of CO on metals and alloys (Koper et al., 1999), but for reasons of space we do not discuss this topic here. 

Abstract. We present preliminary results of 3D hydrodynamical simulations of surface convection in red giants stars. We investigate the main differences between static ID and 3D time-dependent model stellar atmospheres of red giants for a range of metallicities between solar and [Fe/H] = —3 focusing in particular on the impact of 3D spectral line formation on the derivation of stellar abundances. 

Blum, A. E., and A. C. Lasaga (1987), "Monte Carlo Simulations of Surface Reaction Rate Laws", in W. Stumm, Ed., Aquatic Surface Chemistry, pp. 255-292. 

Wehrli, B. (1989), "Monte Carlo Simulations of Surface Morphologies During Mineral Dissolution", J. Coll. Int. Sd. 132, 230-242. 

M. Dumitrescu, C. Cobianu, D. Lungu, D. Dascalu, A. Pascu, S. Kolev, and A. van den Berg. Thermal simulation of surface micromachinedpolysUicon hotplates oflowpower consumption . Sensors and Actuators A76 (1999), 51-56. 

Note also that the choice of what the move X- X from one phase space point to the next means microscopically depends on the type of problem that one wishes to study e.g., for a simulation of surface difiusion in the framework of the lattice gas model (see section 4.2), this move may mean a hop of a randomly chosen adatom to a randomly chosen nearest neighbor site (and W = 0 it this latter site is already taken). 

For the simulation of surface relaxation, KMC has two advantages over Metropolis. Firstly, since an atom moves at every iteration regardless of temperature, lower temperatures can be studied. Secondly, the dynamic (vs. thermodynamic) nature of the algorithm yields a proper time step, whereas is debated whether or not Metropolis does so . 

A.P.J. Jansen. An introduction to Monte Carlo simulations of surface reactions. http //arXiv.org/, paperno. cond-mat/0303028, 2003. 

J.P.L. Segers, Algorithms for the Simulation of Surface Processes , Ph.D. thesis, Eindhoven University of Technology, 1999. 

The results obtained for the stochastic model show that surface reactions are well-suited for a description in terms of the master equations. Since this infinite set of equations cannot be solved analytically, numerical methods must be used for solving it. In previous Sections we have studied the catalytic oxidation of CO over a metal surface with the help of a similar stochastic model. The results are in good agreement with MC and CA simulations. In this Section we have introduced a much more complex system which takes into account the state of catalyst sites and the diffusion of H atoms. Due to this complicated model, MC and in some respect CA simulations cannot be used to study this system in detail because of the tremendous amount of required computer time. However, the stochastic ansatz permits to study very complex systems including the distribution of special surface sites and correlated initial conditions for the surface and the coverages of particles. This model can be easily extended to more realistic models by introducing more aspects of the reaction mechanism. Moreover, other systems can be represented by this ansatz. Therefore, this stochastic model represents an elegant alternative to the simulation of surface reaction systems via MC or CA simulations. 

The observed almost universal value of the surface fractal dimension ds 2.6 of furnace blacks can be traced back to the conditions of disordered surface growth during carbon black processing. It compares very well to the results evaluated within the an-isotropic KPZ-model as well as numerical simulations of surface growth found for random deposition with surface relaxation. This is demonstrated in some detail in [18]. 

Blum A. E. and Lasaga A. C. (1987) Monte Carlo simulations of surface reaction rate laws. In Aquatic Surface Chemistry Chemical Processes at the Particle-water Interface (ed. W. Stumm). Wiley, New York, pp. 255-291. 

W. A, Steele, Computer Simulation of Surface Diffusion in Adsorbed Phases, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, ed. W. Rudzinski, W. A. Steele and G. Zgrablich (Elsevier, Amsterdam, 1996), 451-486. 

R. M. Nieminen and A. P. J. Jansen, Monte Carlo Simulations of Surface Reactions, Appl. Catal. A General, 160 (1997) 99. 

The aim of this chapter is to provide the reader with an overview of the potential of modern computational chemistry in studying catalytic and electro-catalytic reactions. This will take us from state-of-the-art electronic structure calculations of metal-adsorbate interactions, through (ab initio) molecular dynamics simulations of solvent effects in electrode reactions, to lattice-gas-based Monte Carlo simulations of surface reactions taking place on catalyst surfaces. Rather than extensively discussing all the different types of studies that have been carried out, we focus on what we believe to be a few representative examples. We also point out the more general theory principles to be drawn from these studies, as well as refer to some of the relevant experimental literature that supports these conclusions. Examples are primarily taken from our own work other recent review papers, mainly focused on gas-phase catalysis, can be found in [1-3]. 

The most extensive simulation of surface excess properties, and the first study to determine a directly, was that of Broughton and Gilmer, who looked at the fee (100), (110), and (111) surfaces of a Lennard-Jones crystal-melt system. They determined the surface free energy by calculating the reversible work necessary to cleave the solid and liquid phases and to join the two systems to form a liquid-solid interface. They found the results... 

Kang, H.C., Weinberg, W.H. Monte Carlo simulations of surface-rate processes. Acc. Chem. Res. 1992, 25, 253-9. 

In order to establish the quantitative criterion we have carried out computer simulation of surface coverage by the modifier molecules in the case of random distribution. The following model assumptions have been used in computations ... 

Thus, for one of the analyzed above combinations of electrostatic models and sets of experimental data (diffuse layer + Csoban) the 2-pK model was superior over the ]-pK model in simulation of surface charging curves. For other combinations 1-pK model produced fits nearly equally good as (or better than) the 2-pK model. 

Blum, A.E., and A.C lisaga. 11 1988. Monte Carlo simulations of surface reaction rate laws, p. 255-292. In W.E.Sumn Cntn (ed.) Aquatic surface chemistry. John Wiley Sons, New York. 

Rustad, J.R., Wasserman, E., and Fehny, A.R., Molecular modeling of the surface charging of hematite. 11. Optimal proton distribution and simulation of surface charge versus pH relationships. Surf. Sci., 424, 28, 1999. 

SIMULATIONS OF SURFACE-ASSISTED FREE-RADICAL PROCESS... 

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