Surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions

Kinetic modelling of heterogeneous catalytic systems

The importance of heterogeneous catalysis in modern life is evidenced by the fact that numerous products and technologies routinely used nowadays involve catalysts in their synthesis or function. The discovery of catalytic materials is, however, a non-trivial procedure, requiring tedious trial-and-error experimentation. First-principles-based kinetic modelling methods have recently emerged as a promising way to understand catalytic function and aid in materials discovery. In particular, kinetic Monte Carlo (KMC) simulation is increasingly becoming more popular, as it can integrate several sources of complexity encountered in catalytic systems, and has already been used to successfully unravel the underlying physics of several systems of interest. After a short discussion of the different scales involved in catalysis, we summarize the theory behind KMC simulation, and present the latest KMC computational implementations in the field. Early achievements that transformed the way we think about catalysts are subsequently reviewed in connection to latest studies of realistic systems, in an attempt to highlight how the field has evolved over the last few decades. Present challenges and future directions and opportunities in computational catalysis are finally discussed.

Catalytic reduction of NO with NH3 on a Pt(100) surface: Monte Carlo simulations

We propose a surface reaction model for NO reduction with NH3 on a Pt(100) single crystal catalyst surface and we explore it by carrying out Monte Carlo simulations. Our model includes experimentally observed realistic features such as adsorbate-induced surface phase transition, structure-dependent sticking coefficients and reactivity, desorption probabilities, and surface diffusion of adsorbed species. We discuss similarities found while comparing the available experimental data and our model as reactant ratio and temperature vary. Simulations qualitatively reproduce the kinetic oscillations observed in reaction rates and surface coverages. Also, the essential role of the adsorbate-induced phase transition regarding the appearance of kinetic oscillations is discussed.

Kinetic phase transition in A2 + B2 -->2AB reaction system

Three lattice gas models for A2 + B2 -->2AB reaction system are studied by Monte Carlo simulation in two-dimensional triangular lattice surface. When both A2 and B2 adsorb and dissociate on the catalytic surface in the random dimer-filling mechanism or in the end-on dimer-filling mechanism, there is no reactive window in the reaction system and just a discontinuous phase transition appears from a "B+vacancy" poisoned state to an "A+vacancy" poisoned state. However, a reactive window appears when one of the two dimers, A2, dissociates in the random dimer-filling mechanism but another dimer, B2, is in the end-on dimer-filling mechanism and the system exhibits a discontinuous phase transition from the active reaction state to a B+ vacancy poisoned state and a continuous phase transition to an "A+vacancy" poisoned state. Furthermore, we show that the critical behavior of the continuous phase transition with infinitely many absorbing states belongs to the robust directed percolation universality class.

Perturbation of period-2 oscillations in catalytic reactions accompanied by surface restructuring

We present Monte Carlo simulations illustrating the effect of periodic forcing on period-2 oscillations related to the interplay of catalytic reaction and surface restructuring. The oscillations are found to be fairly stable if the external frequency equals the main internal frequency. In contrast, perturbations with other frequencies may easily change the type of oscillation. In particular, perturbations with double frequency convert period-2 oscillations into period-1 oscillations with the imposed frequency.

Spontaneous formation of dynamical patterns with fractal fronts in the cyclic lattice Lotka-Volterra model

Dynamical patterns, in the form of consecutive moving stripes or rings, are shown to develop spontaneously in the cyclic lattice Lotka-Volterra model, when realized on square lattice, at the reaction limited regime. Each stripe consists of different particles (species) and the borderlines between consecutive stripes are fractal. The interface width w between the different species scales as w(L,t) approximately L(alpha)f(t/L(z)), where L is the linear size of the interface, t is the time, and alpha and z are the static and dynamical critical exponents, respectively. The critical exponents were computed as alpha=0.49+/-0.03 and z=1.53+/-0.13 and the propagating fronts show dynamical characteristics similar to those of the Eden growth models.

Effect of inert species in gas phase on oscillatory dynamics of oxidation system of CO on Pt(100)

We present a Monte Carlo simulation for the global oscillation of the CO catalytic oxidation system in the presence of inert species in gas phase, which can adsorb and desorb on the catalytic surface but cannot react with other species. It is found that the impurity has a dramatic effect on the oscillatory dynamics, although it does not involve in the reaction of CO oxidation. The simulation results show that with an increase in the fraction of impurity in gas phase, the periodic oscillation may change into an irregular oscillation and even can be inhibited completely. However, as the desorption rate of the impurity is increased, the regular oscillation will be recovered again.

Oscillatory reactive dynamics on surfaces: a lattice limit cycle model

Complex reactive dynamics on low-dimensional lattices is studied using mean-field models and Monte Carlo simulations. A lattice-compatible reactive scheme that gives rise to limit cycle behavior is constructed, involving a quadrimolecular reaction step and bimolecular adsorption and desorption steps. The resulting lattice limit cycle model is dissipative and, in the mean-field limit, exhibits sustained oscillations of the species concentrations for a wide range of parameter values. Lattice Monte Carlo simulations of the lattice limit cycle model show locally the emergence of sustained oscillations of the species concentrations. Random fluctuations of the concentrations, clustering between homologous species, and competition between the various clusters/species cause the in-phase oscillations of neighboring sites. Distant regions oscillate out of phase and spatial correlations decay exponentially with the distance. The amplitude and period of the local oscillations depend on the system parameters.

Comment on "Monte Carlo simulations for a Lotka-type model with reactant diffusion and interactions"

Discussing the effect of adsorbate-adsorbate lateral interactions on the kinetics of heterogeneous catalytic reactions, Zvejnieks and Kuzovkov [Phys. Rev. E 63, 051104 (2001)] conclude that in the case of adsorbed particles the Metropolis Monte Carlo dynamics is meaningless and propose to use their own dynamics, which is equivalent to the Glauber dynamics. In this Comment, I show that these and other conclusions and prescriptions by Zvejnieks and Kuzovkov are not in line with the general principles of simulations of rate processes in adsorbed overlayers.

Reply to "comment on 'Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions' "

We reply to the Comment by Zhdanov [preceding paper, Phys. Rev. E 65, blacksquare, square, filled (2002)] on our recent paper [G. Zvejnieks and V. N. Kuzovkov, Phys. Rev. E 63, 051104 (2001)]. We demonstrate that our quite different viewpoints result, in fact, entirely from nonunique definitions of the master equation, which has nothing to do with neglecting important physical principles, as Zhdanov claims.

Fractal properties of the lattice Lotka-Volterra model

The lattice Lotka-Volterra (LLV) model is studied using mean-field analysis and Monte Carlo simulations. While the mean-field phase portrait consists of a center surrounded by an infinity of closed trajectories, when the process is restricted to a two-dimensional (2D) square lattice, local inhomogeneities/fluctuations appear. Spontaneous local clustering is observed on lattice and homogeneous initial distributions turn into clustered structures. Reactions take place only at the interfaces between different species and the borders adopt locally fractal structure. Intercluster surface reactions are responsible for the formation of local fluctuations of the species concentrations. The box-counting fractal dimension of the LLV dynamics on a 2D support is found to depend on the reaction constants while the upper bound of fractality determines the size of the local oscillators. Lacunarity analysis is used to determine the degree of clustering of homologous species. Besides the spontaneous clustering that takes place on a regular 2D lattice, the effects of fractal supports on the dynamics of the LLV are studied. For supports of dimensionality D(s)<2 the lattice can, for certain domains of the reaction constants, adopt a poisoned state where only one of the species survives. By appropriately selecting the fractal dimension of the substrate, it is possible to direct the system into a poisoned or oscillatory steady state at will.

Coupled catalytic oscillators: Beyond the mass-action law

We present Monte Carlo simulations of the reaction kinetics corresponding to two coupled catalytic oscillators in the case when oscillations result from the interplay between the reaction steps and adsorbate-induced surface restructuring. The model used is aimed to mimic oscillations on a single nm catalyst particle with two kinds of facets or on two catalyst particles on a support. Specifically, we treat the NO reduction by H(2) on a composite catalyst containing two catalytically active Pt(100) parts connected by an inactive link. The catalyst is represented by a rectangular fragment of a square lattice. The left- and right-hand parts of the lattice mimic Pt(100). With an appropriate choice of the model parameters, these sublattices play a role of catalytic oscillators. The central catalytically inactive sublattice is considered to be able only to adsorb NO reversibly and can be viewed as a Pt(111) facet or a support. The interplay of the reactions running on the catalytically active areas occurs via NO diffusion over the boundaries between the sublattices. Using this model, we show that the coupling of the catalytically active sublattices may synchronize nearly harmonic oscillations observed on these sublattices and also may result in the appearance of aperiodic partly synchronized oscillations. The spatio-temporal patterns corresponding to these regimes are nontrivial. In particular, the model predicts that, due to phase separation, the reaction may be accompanied by the formation of narrow NO-covered zones on the left and right sublattices near the boundaries between these sublattices and the central sublattice. Such patterns cannot be obtained by using the conventional mean-field reaction-diffusion equations based on the mass-action law. The experimental opportunities to observe the predicted phenomena are briefly discussed. (c) 2001 American Institute of Physics.

Reactive dynamics on two-dimensional supports: Monte Carlo simulations and mean-field theory

Monte Carlo simulations and mean-field models are used for the study of nonequilibrium reactions taking place on the surface of a catalyst. The model represents the catalytic reduction of NO with H2 on a Pt surface. Both Monte Carlo simulations and mean-field results predict the existence of a critical surface in the parameter space where the catalyst remains active for long times. Outside this critical region the catalyst remains active for finite times only. A discrete version of the mean-field model is proposed that takes into account the discrete, two-dimensional nature of the catalyst. For homogeneous initial conditions this improved model provides better quantitative agreement with the Monte Carlo results.

Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions

The standard Lotka-type model, which was introduced for the first time by Mai et al. [J. Phys. A 30, 4171 (1997)] for a simplified description of autocatalytic surface reactions, is generalized here for a case of mobile and energetically interacting reactants. The mathematical formalism is proposed for determining the dependence of transition rates on the interaction energy (and temperature) for the general mathematical model, and the Lotka-type model, in particular. By means of Monte Carlo computer simulations, we have studied the impact of diffusion (with and without energetic interactions between reactants) on oscillatory properties of the A+B-->2B reaction. The diffusion leads to a desynchronization of oscillations and a subsequent decrease of oscillation amplitude. The energetic interaction between reactants has a dual effect depending on the type of mobile reactants. In the limiting case of mobile reactants B the repulsion results in a decrease of amplitudes. However, these amplitudes increase if reactants A are mobile and repulse each other. A simplified interpretation of the obtained results is given.

Comment on "surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions"

In a recent article Zhdanov studied the oscillating NO+H2 reaction on the Pt(100) single-crystal surface [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)]. We have scrutinized his model and found fundamental errors in the chemical modeling, in the modeling of the surface reconstruction and in the simulation procedure itself.

Reply to "Comment on 'Surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions' "

In my numeration, the criticism of my simulations of kinetic oscillations in NO reduction by H2 on Pt(100) [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)] by Kuzovkov, Kortlüke, and von Niessen [preceding paper, Phys. Rev. 63, 023101 (2001)] contains 19 comments. I show that four comments are irrelevant. The other 15 comments are wrong, because they either contradict the basic principles of the theory of phase transitions, Monte Carlo simulations, and catalytic chemistry or ignore numerous experimental data on adsorbate-induced restructuring of the Pt(100) surface.

Simulation of enzymatic cellular reactions complicated by phase separation

We present two-dimensional Monte Carlo simulations of enzymatic cellular reaction occurring via the Michaelis-Menten scheme in the case of attractive interactions between the reaction products. The model employed predicts phase separation in the cell provided that the reaction is relatively fast. The shape of the corresponding patterns varies from a few separate islands to a large patch located in the center of the cell. The fluctuations of the reaction rate during such regimes are found to be much higher than those predicted by the Poissonian distribution.

Surface restructuring and kinetic oscillations in heterogeneous catalytic reactions

We extend our earlier Monte Carlo simulations of isothermal kinetic oscillations in the NO-H(2)/Pt(100) system [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)]. The analysis, based on a lattice-gas model describing surface restructuring in terms of the statistical theory of first-order phase transitions, is primarily focused on adsorbate-diffusion-mediated synchronization of oscillations. The conventional condition for synchronization, (D tau)(1/2)>L (D is the diffusion coefficient, tau the oscillation period, and L the lattice size), is proved to considerably underestimate the role of surface diffusion. Due to the formation of mesoscopic islands, well developed oscillations are found to be possible in the cases when the left part of this condition is much lower than the right part.