Surface restructuring and kinetic oscillations in heterogeneous catalytic reactions

Synchronization of stochastic oscillations due to long-range diffusion

We investigate the effect of long-range diffusive mixing on stochastic processes taking place on low-dimensional catalytic supports. As a working example, the cyclic lattice Lotka-Volterra (LLV) model is used which is conservative at the mean-field level and demonstrates fractal patterns and local oscillations when realized on low-dimensional lattice supports. We show that the local oscillations are synchronized when a weak, long-range, diffusive process is added to LLV and global oscillations of limit cycle type emerge. This phenomenon is demonstrated as a nonequilibrium phase transition and takes place when the mixing-to-reaction rate p (order parameter) is above a critical point p_{c} . The value of the critical point is shown to depend on the kinetic parameters. The global oscillations in this case emerge as a result of phase synchronization between local oscillations on sublattices.

Pattern formation during the oxidation of CO on Pt{100}: a mesoscopic model

Constantly changing irregular patterns of carbon monoxide (CO) and oxygen are seen during CO oxidation on platinum crystals in the [100] orientation. Ours is the first reaction-diffusion model to reproduce this pattern formation on physically feasible length and time scales, faithfully incorporating the available experimental data. Numerical simulations show patterns made up of CO and oxygen fronts moving at similar speeds to those seen in experiments.

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.

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.

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.

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.

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.

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.