A hybrid stochastic-deterministic algorithm for lattice-gas models of catalytic reactions and the computation of TPD spectra

Abstract

We present a hybrid numerical approach for modeling surface reactions in the framework of a lattice-gas model with lateral interactions between adsorbed particles. A hybrid multiscale algorithm, which we refer to as Quasi-Equilibrium Kinetic Monte Carlo (QE-KMC), comprises traditional Metropolis Monte Carlo (MMC) simulations of equilibrium systems and standard numerical methods for deterministic ordinary differential equations (ODEs). The functional dependence of these ODEs on the macroscopic state variables (adsorbate coverages) is not explicitly known, but their right-hand sides can be evaluated “on the fly” with prescribed accuracy by means of the MMC simulations. At the time scale of these ODEs it is assumed that an equilibrium statistical distribution of adsorbed particles on an infinite lattice is attained at every moment in time due to infinitely fast surface diffusion. QE-KMC and conventional KMC simulations are used to study the temperature-programmed desorption (TPD) spectra of adsorbed particles. We critically discuss results of previous studies that applied Monte Carlo simulations to describe the TPD spectra in the case of fast adsorbate diffusion and strong lateral interactions. We show that the quasi-equilibrium TPD spectra can be quickly and accurately estimated by the QE-KMC algorithm, while the KMC simulations require much more extensive computational resources to obtain the same results.