Alexander Tarasenko

Surface diffusion of particles adsorbed on a lattice with two non-equivalent sites

Abstract We investigate the surface diffusion in a system of particles adsorbed on a lattice with two non-equivalent sites, whose number in the unit cell and adsorption energy are different. When the adsorption energies are comparable, the adparticle diffusion proceeds by uncorrelated adparticle jumps. In the opposite case, the adparticle migration proceeds by pairs of consecutive jumps. The contributions to the surface diffusion of these jump sequences depend considerably on the adparticle surface coverage and the relation between the adsorption energies.

Diffusion of particles adsorbed on a triangular lattice: pairwise and three-particle interactions

Abstract In the present paper, the influence of both pairwise and three-particle interactions on the mobility of adsorbed particles diffusing on a lattice with triangular symmetry has been studied. Two different techniques has been used for describing the surface diffusion phenomenon. On one hand, explicit expressions for the chemical and jump diffusion coefficients have been calculated by using real-space renormalization group (RSRG) approach. A number of the RSRG transformations with blocks of different sizes and symmetries have been investigated. In particular, it has been shown that the precision of the method depends strongly not only on the number of sites in the RSRG blocks but also on their composition and structure. On the other hand, numerical simulations by using the Monte Carlo scheme has been used to simulate the process of particle migration. Using both methods, adsorption isotherms for different temperatures and the coverage dependencies for the thermodynamic factor and the chemical diffusion coefficient have been calculated. The behavior of the above mentioned quantities has been compared when the adparticles interact via only either pairwise or three-particle interactions. Despite the fact that both methods constitute very different approaches, the correspondence of numerical data with analytical results is surprisingly good. Therefore, it can be concluded that the RSRG method can be successfully applied for lattice gas systems to characterize the thermodynamic and kinetic properties of strongly interacting adsorbates.

Adsorption and diffusion in a square lattice gas with strong attraction between particles : The real-space renormalization group approach

A two-dimensional lattice gas with an attractive nearest neighbor (NN) pairwise lateral interaction on a lattice of square symmetry and its equivalent two-dimensional Ising spin model have been investigated by using the real-space renormalization group (RSRG) approach with blocks of different sizes and symmetries. We have calculated (a) adsorption isotherms for different temperatures and (b) the spontaneous magnetization for the Ising spin ferromagnet. The RSRG data are compared with the well-known exact expression. The coincidence between the exact and RSRG data is rather good. It is shown that the precision of the RSRG method strongly depends not only on the number of sites in the block but also on its symmetry.In addition, we have calculated the coverage dependences of the pair correlation function for nearest neighbor adparticles, the isothermal susceptibility and the chemical adparticle diffusion coefficient at different temperatures. Furthermore, we have calculated the critical behavior of the mean square adparticle density fluctuations and of the chemical diffusion coefficient. The critical exponent is close to the value obtained by other methods. The RSRG data have been compared with results from Monte Carlo simulations. The coincidence is very good and, therefore, we conclude that the RSRG method can be applied at least for the systems discussed here to investigate the thermodynamic and kinetic properties of interacting adsorbates.

Diffusion of Particles Adsorbed on a Reconstructive Surface

The influence of surface reconstruction on diffusion of adsorbed particles is investigated in the framework of simple two-position symmetrical model. Exact expressions for the free energy and diffusion coefficient are obtained neglecting the lateral interaction between the adsorbed particles. The critical behavior of the system is described by an anisotropic Ising spin model. The coverage dependencies of the chemical diffusion coefficient are calculated for different temperatures and interaction parameters. The dependencies show clearly the strong influence of the phase transitions, occurring in the system, on the particle migration. The chemical diffusion coefficient turns to zero at the critical points of the system.

Finite-size scaling of kinetic quantities

In this contribution we analyze the finite-size scaling behavior of the tracer and jump surface diffusion coefficients, Dt and Dj, in the vicinity of a second order phase transition. For this purpose, we use a two-dimensional lattice gas model of repulsively interacting particles on a square lattice. For all lattice sizes L studied, the temperature dependences of Dt and Dj at half coverage are smooth functions, having an inflexion point at the critical temperature. Their derivatives, ∂Dt/∂(1/kBT) and ∂Dj/∂(1/kBT), exhibit cusp-like maxima which (a) are sharply pronounced and (b) converge to Tc for large lattice sizes. The finite-size behavior of Dt and Dj can be described by critical exponents σt=0.665±0.003 and σj=0.585±0.003.

Diffusion of Particles Adsorbed on a Patchwise Surface

The diffusion of particles adsorbed on a patchwise surface with two non-equivalentsites is investigated in the framework of the lattice-gas model. The coverage dependencies of thecenter-of-mass and Fickian diffusion coefficients are calculated for some representative valuesof the lateral interaction. We propose the analytical expressions for the diffusion coefficients.We compare the theoretical dependencies with the numerical data obtained by the kineticMonte Carlo simulations. The good coincidence of the data obtained by the two quite differentmethods corroborates strongly the approach developed to describe the particle migration onsuch complex, heterogeneous lattices.

Study of Diffusion in a One-Dimensional Lattice-Gas Model of Zeolites: The Analytical Approach and Kinetic Monte Carlo Simulations

The diffusion of molecules adsorbed in a one-dimensional channel with side pockets is investigated in the framework of a one-dimensional lattice-gas model. The model can describe the molecules migration in some type of zeolites. We obtained the exact expression for the free energy of this model. Using the local equilibrium approximation we derived the analytical expressions for the diffusion coefficients. The concentration dependencies of the center-of-mass and Fickian diffusion coefficients are calculated for some representative values of the lateral interactions between molecules. The theoretical dependencies are compared with the numerical data obtained by the kinetic Monte Carlo simulations. The data obtained by the two completely different methods coincide amazingly well in the whole concentration and wide interaction regions.

The Kinetic Monte Carlo Simulations of the Self-Diffusivity in Zeolites

The diffusion of guest molecules in zeolites is investigated in the framework of a onedimensionallattice-gas model with two non-equivalent sites. The concentration dependenciesof the tracer and center-of-mass diffusion coefficients are calculated for some representative valuesof the lateral interaction between the guest molecules. Using simple ideas about moleculesdiffusion we propose analytical expressions for the diffusion coefficients. We compare the theoreticaldependencies with the numerical data obtained by the kinetic Monte Carlo simulations.A very good coincidence of the data obtained by the two quite independent different methodscorroborates strongly the validity of the proposed approach.

Diffusion of Particles Adsorbed on a Dynamically Disordered Reconstructive Surface

We have considered the diffusion of particles in a dynamically disordered medium in the framework of a simple lattice-gas model of a reconstructive surface. Using kinetic Monte Carlo simulations we have investigated the diffusion of particles over the host lattice with moving atoms. The dynamic lattice reconstruction increases substantially the particle diffusion coefficient and changes its activation energy.

Diffusion of Particles on a Fluctuating Surface

Using kinetic Monte Carlo simulations, we have investigated within the framework of a simple lattice–gas diffusion model, the diffusion of particles adsorbed onto a lattice with moving surface atoms. Dynamic surface reconstruction was found to substantially increase the particle diffusion coefficient and change the activation energy.