Kinetic Monte Carlo simulations of the partial oxidation of methanol on oxygen-covered Cu(1 1 0)

The partial oxidation of methanol to formaldehyde on oxygen-precovered Cu(1 1 0) has been studied using kinetic Monte Carlo simulations. The rates entering the simulation have been derived from density functional theory calculations within the generalized gradient approximation using transition state theory. We demonstrate that kinetic Monte Carlo simulations are a powerful tool to elucidate the microscopic details of the reaction kinetics on surfaces. Furthermore, the comparison of calculated and measured temperature programmed desorption rates allows a genuine assessment of the calculated barrier heights. We find that some of the calculated barriers and adsorption energies have to be adjusted by up to 0.5 eV in order to reproduce the measured desorption spectra. Possible reasons for the discrepancies between experiment and theory are discussed.     

Monte Carlo simulations of oscillations, chaos and pattern formation in heterogeneous catalytic reactions

Experimental studies employing surface science methods indicate that kinetic oscillations, chaos, and pattern formation in heterogeneous catalytic reactions often result from the interplay of rapid chemical reaction steps and relatively slow complementary processes such as oxide formation or adsorbate-induced surface restructuring. In general, the latter processes should be analysed in terms of theory of phase transitions. Therefore, the conventional mean-field reaction–diffusion equations widely used to describe oscillations in homogeneous reactions are strictly speaking not applicable. Under such circumstances, application of the Monte Carlo method becomes almost inevitable. In this review, we discuss the advantages and limitations of employing this technique and show what can be achieved in this way. Attention is focused on Monte Carlo simulations of CO oxidation on (1 0 0) and (1 1 0) single-crystal Pt and polycrystal Pt, Pd and Ir surfaces and of NO reduction by CO and H₂ on Pt(1 0 0). CO oxidation on supported nanometre-sized catalyst particles and NO reduction on composite catalysts are also discussed. The results show that with current computer facilities the MC technique has become an effective tool for analysing temporal oscillations and pattern formation on the nanometre scale in catalytic reactions occurring on both single crystals and supported particles.     

Impact of surface science on the understanding of kinetics of heterogeneous catalytic reactions

The kinetics of chemical reactions in gas and liquid phases are usually described by employing the conventional mass-action law equations. The laws governing the kinetics of heterogeneous catalytic reactions are as a rule much more complex due to adsorbate–adsorbate lateral interactions, surface heterogeneity, spontaneous and adsorbate-induced changes in a surface, and/or limited mobility of reactants. The importance of these factors was recognized by the heterogeneous catalysis community far before the surface-science era. Only with the development of surface science, however, has it become possible to study in detail the non-ideality of rate processes on solid surfaces. In the present paper, we survey the main conceptual results currently available in this field and illustrate the impact of surface science on its development. Specifically, we outline the approaches used to describe elementary reaction steps and the whole reaction kinetics near and far from equilibrium, including such topics as kinetic phase transitions, pattern formation, kinetic oscillations and chaos, and pressure- and structure-gap problems. All these phenomena and problems are demonstrated to provide promising opportunities for further experimental and theoretical studies.     

A kinetic Monte Carlo/UBI-QEP model of O2 adsorption on fcc (1 1 1) metal surfaces

The previously developed kinetic Monte Carlo model of molecular oxygen adsorption on fcc (1 0 0) metal surfaces has been extended to fcc (1 1 1) surfaces. The model treats uniformly all elementary steps of the process—O₂ adsorption, dissociation, recombination, desorption, and atomic oxygen hopping—at various coverages and temperatures. The model employs the unity bond index—quadratic exponential potential (UBI-QEP) formalism to calculate coverage-dependent energetics (atomic and molecular binding energies and activation barriers of elementary steps) and a Metropolis-type algorithm including the Arrhenius-type reaction rates to calculate coverage- and temperature-dependent features, particularly the adsorbate distribution over the surface. Optimal values of non-energetic model parameters (the spatial constraint, a travel distance of “hot” atoms, attempt frequencies of elementary steps) have been chosen. Proper modifications of the fcc (1 0 0) model have been made to reflect structural differences in the fcc (1 1 1) surface, in particular the presence of two different hollow sites (fcc and hcp). Detailed simulations were performed for molecular oxygen adsorption on Ni(1 1 1). We found that at very low coverages, only O₂ adsorption and dissociation were effective, while O₂ desorption and O₂ and O diffusion practically did not occur. At a certain O + O₂ coverage, the O₂ dissociation becomes the fastest process with a rate one-two orders of magnitude higher than adsorption. Dissociation continuously slows down due to an increase in the activation energy of dissociation and due to the exhaustion of free sites. The binding energies of both molecular and atomic oxygen decrease with coverage, and this leads to greater mobility of atomic oxygen and more pronounced desorption of molecular oxygen. Saturation is observed when the number of adsorbed molecules becomes approximately equal to the number of desorbed molecules. Simulated coverage dependences of the sticking probability and of the atomic binding energy are in reasonable agreement with experimental data. From comparison with the results of the previous work, it appears that the binding energy profiles for Ni(1 1 1) and Ni(1 0 0) have similar shapes, although at any coverage the absolute values of the oxygen binding energy are higher for the (1 0 0) surface. For metals other than Ni, particularly Pt, the model projections were found to be too parameter-dependent and therefore less certain. In such cases further model developments are needed, and we briefly comment on this situation.     

Transient yielding of CO2 over oxidized ruthenium surfaces: Monte Carlo simulations

We develop Monte Carlo simulations to study the catalytic oxidation of CO over a surface of ruthenium. The catalyst is exposed to a continuous flux of CO molecules and its surface is pre-covered with an amount of oxygen atoms. Recent experiments performed on this system [R. Blume, W. Christen, H. Niehus, J. Phys. Chem. B 110 (2006) 13912] have shown that three different reaction mechanisms can account for the experimental results. Two of them are based on the Langmuir-Hinshelwood mechanism, where CO molecules are adsorbed at oxygen-free defect sites before reactions take place. The third one proceeds via the Eley-Rideal mechanism, which is almost time independent, and reactions occur at non-defect sites. In our model, we consider a semi-infinite cubic lattice to mimic the surface of the catalyst and oxygen atoms are incorporated into the layers below the surface. A fraction of defects is created at the topmost layer and at the first subsurface layer. Oxygen atoms can diffuse over the surface as well as between adjacent layers of the system. We also assumed a temperature dependent reaction rate that is related to the residence time of CO at the surface. Comparisons are made between the CO₂ yielding at defect-rich and smooth surfaces as a function of temperature.     

Molecular origins of surface poisoning during CO oxidation over RuO2(1 1 0)

Metal oxides are of interest as environmental oxidation catalysts, but practical applications are often limited by poorly understood surface poisoning processes. RuO₂ is active for CO oxidation under UHV conditions but is deactivated by some surface poisoning processes at ambient pressures. In this work, we report kinetic models of surface poisoning during CO oxidation over RuO₂(1 1 0), based on data obtained from plane-wave, supercell DFT calculations. While a surface carbonate is stable at low O₂ pressures and high CO₂ exposures, it is not stable under catalytic conditions. A surface bicarbonate is more stable and deactivates the RuO₂ surface over a wide range of CO and oxygen pressures in the presence of trace amounts of water.     

The virtual chemistry lab for reactions at surfaces: Is it possible? Will it be useful?

Ab initio total-energy calculations based on electronic structure theory have tremendously enlarged our knowledge about the geometrical and electronic structure of clean and adsorbate-covered low-index surfaces and reactions on these surfaces. In technological applications, however, extended flat surfaces are very rarely used. Hence the applicability of the theoretical results for the technological surfaces are indeed questionable. In this review I will reflect on the question whether ab initio calculations of reactions at surfaces can contribute to the development of, e.g., better catalysts. Simulations alone will not be able to lead to new products but it will be demonstrated that they can contribute enormously to the development process. Thus the virtual chemistry lab is indeed possible and helpful.     

Computer simulations of the Stranski-Krastanov growth of heteroepitaxial films with elastic anisotropy

A three-dimensional finite element method is developed to simulate the surface morphological evolution during the Stranski-Krastanov heteroepitaxial growth. In the formulation, the surface evolves through surface diffusion driven by the gradient of the surface chemical potential, which includes the elastic strain energy, elastic anisotropy and surface energy. Surface condensation rate is assumed to depend on the difference between the surface chemical potential and the chemical potential of the vapor phase. Our simulations reveal that the self-assembly of quantum dots are strongly dependent on the variation of growth rate and elastic anisotropy strength. With appropriate choice of growth rate and elastic anisotropy strength, a relatively more uniform and regular quantum dot array can be obtained.     

Monte Carlo simulations for the slow relaxation of crumpled surfaces

In this paper we study crumpled surfaces through Monte Carlo Simulations. A crumpled surface is represented by a cluster of spins pointing up; spins pointing down represent the air both inside and around the surface. We follow the time dynamics of this fractal structure and we show that it presents a stretched exponential behaviour.     

Simulated reaction dynamics of F atoms on partially fluorinated Si(100) surfaces

We have investigated the influence of translational excitation on the reactivity of atomic fluorine with the Si(100) surface via molecular dynamics simulations using a first-principles-derived interaction potential. Surface reactivity is contrasted for both clean and partially fluorinated surfaces with the results of previous simulations of F₂ molecules impinging on Si(100) surfaces, indicating many similarities between the dynamics of F atoms and F₂ molecules. Mechanisms for the reaction are proposed based on reactivity trends and scattered product energy and angular distributions, including evidence for the existence of a precursor-mediated adsorption pathway for low incident energy F atoms on partially fluorinated surfaces.     

A Monte Carlo study of the thermal properties of Cu3Au low index surfaces

The thermal dependencies of composition and order of the (111), (100) and (110) Cu₃Au surfaces are studied at the atomic scale by means of Monte Carlo simulations in the “transmutational” ensemble at constant volume. The question addressed is the extent to which such simulations carried on with a model N-body potential designed on the basis of bulk energetic and mechanical properties allow predictions consistent with experimental observations of the surface. Although the currently available experimental data still leave unanswered questions, many of them allow for comparison with modelling. Qualitative agreement is found for temperature dependencies of both surface composition and order, and the simulation results are discussed in detail. Some clear discrepancies are found as well, in particular (but not only) in the case of the (110) surface and its first neighbouring layer. Although the origin of such differences is not yet clear, it is suggested that they may serve to assess and to improve the model in the light of quantitative surface studies.     

Non-equilibrium effects in profile spreading on stepped surfaces

We study non-equilibrium effects in spreading and collective diffusion of adatoms on stepped surfaces through Monte Carlo simulations of a lattice-gas model. The spreading density profiles are analyzed by the Boltzmann-Matano method to determine the temporal behavior of the effective collective diffusion coefficients. We find that the presence of steps induces considerable non-equilibrium effects in diffusion. For spreading along the steps, we find that these deviations can be explained by the slow approach of the different adparticle concentrations on terraces and at step edges towards equilibrium. For spreading across the steps, however, we find no such dependence, indicating the breakdown of the linear response theory at early times.     

A microkinetic model of the methanol oxidation over silver

A simple microkinetic model for the oxidation of methanol on silver based on surface science studies at UHV and low temperatures has been formulated. The reaction mechanism is a simple Langmuir-Hinshelwood mechanism, with one type of active oxygen and one route to formaldehyde and carbon dioxide, respectively. The model explains observed reaction orders, selectivity, apparent activation enthalpies and the choice of industrial reaction conditions. More interesting the model disproves the notion that the mechanism deduced from surface science in UHV cannot be responsible for formaldehyde synthesis at industrial steady-state conditions. The present work therefore seriously questions the prevailing models of formaldehyde synthesis in the literature. One of the reasons for this controversy is that many of the models in the literature are derived from transient experiments exhibiting dynamic effects that are not present at steady state under industrial conditions.     

Stochastic aspects of pattern formation during the catalytic oxidation of CO on Pd(111) surfaces

We present experimental results on rare transitions between two states due to intrinsic noise between two states in a bistable surface reaction, namely the catalytic oxidation of CO on Pd(111) surfaces. The mean time scales involved are typically of order 10⁴ s and the probability distribution shows two peaks over a large part of the bistable regime of this surface reaction. We use measurements of the resulting CO₂ rate as well as photoelectron emission microscopy (PEEM) to characterize these rare transitions. From our dynamic data we can extract probability distributions for the CO₂ rate. We use x-t plots from PEEM measurements to describe the transitions, which are-as we demonstrate-characterized by one wall moving through the field of view in PEEM measurements. The resulting probability distributions for the CO₂ rate are shown to depend strongly on the value, Y, of the CO fraction in the reactant flux inside the bistable regime. We find that the probability distribution is strongly asymmetric indicating that the two basins of attraction are rather different in depth and width. This is also concluded from the PEEM measurements, which show in one case a rather sharp and narrow domain wall going one way, while it is rather wide and diffuse for the motion in the opposite direction. To have two basins of attraction in the bistable regime, which are rather different in nature is reminiscent of other bistable systems such as, for example, optical bistability, although the time scales involved in the present system are entirely different.     

Adatom lifetime in film growth at solid surfaces in the framework of the Johnson–Mehl–Avrami–Kolmogorov model

On the basis of the quasi-static approximation and for simultaneous nucleation the adatom lifetime, τ, during film growth at solid surfaces has been computed by Monte Carlo (MC) simulation. The quantity DN₀τ, N₀ and D being respectively the cluster density and the adatom diffusion coefficient, is found to depend upon the portion of surface covered by clusters and, very weakly, on N₀. Moreover, a stochastic approach based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory has been developed to obtain the analytical expression of the MC curve. The collision factor of the mean island has been calculated and compared with those previously obtained from the uniform depletion approximation and the lattice approximation.     

Desorption induced by hot electrons: wave packet calculation of CO on Cu surfaces

A quantum mechanical photodesorption model, valid for metallic substrates and sub-picosecond laser pulses, is presented. It takes into consideration the photodesorption coordinate and models the metal hot-electron mediated desorption by a three electronic states: an ionic state of the adsorbate and two effective states representing the continuum of the metal. This multiple-state picture allows the sharing of the flow of energy injected by the laser between the adsorbate and the substrate. For the first time, the present modeling introduces the hot electrons of the metal through an optical potential based on the kinetic model developed earlier by the authors. This potential, and the resulting desorption yield, depend on the laser fluence. For CO on Cu(1 0 0) or Cu(1 1 1), the results are in fair agreement with the experimental findings.     

Local bond breaking via STM-induced excitations: the role of temperature

We discuss the influence of temperature on local bond breaking through multiple vibrational excitations induced by inelastic tunneling in the STM. We focus on hydrogen desorption from the H---Si(111) and H---Si(100) systems, but the results are general. The substrate temperature affects the desorption yield in two important ways: first, lowering the temperature increases the H---Si vibrational energy relaxation time, resulting in a higher effective adsorbate temperature and an increased desorption yield. Second, lowering the substrate temperature decreases the dephasing rate of the H---Si modes (manifested by a decrease of the infrared absorption linewidth), which then reduces the rate of incoherent (Förster) vibrational energy transfer away from the Stark-shifted H---Si mode under the tip. This increases the localization of the vibrational energy and enhances the probability for multiple vibrational excitation and desorption. Finally, we discuss the possible implications of our findings on the mechanism of MOS device degradation by hot electrons.     

Surface diffusion and concentration polarization on oxide-supported metal electrocatalyst particles

A common assumption for solid oxide fuel cells (SOFCs) is that the hydrogen-oxygen reaction that produces the electrical current is strictly localized at the triple phase boundary (TPB) between the metal catalyst particle, the zirconia support, and the gas atmosphere. Detailed analysis of oxygen spillover onto the catalyst surface indicates that the reactive area simply spreads over the surface as needed to support the current, leading to TPB widths of several hundred Angstroms. Lower adspecies surface diffusivities (due to catalyst crystallography), lower reactant partial pressures (due to electrode design), and higher current demands, generally shift the peak turnover number (TON) for H₂O generation away from the TPB in practical SOFCs with cermet anodes. The diffusivity-coverage relationship (repulsive, neutral, or attractive adspecies interactions) affects the location of the TON peak on the catalyst surface in a non-monotonic manner, indicating that care should be taken when applying research data to models of practical SOFCs. The most detailed surface diffusion model investigated in this work indicates that the catalytic process is limited by oxygen surface diffusion on the metal particle.