Kinetics of catalysis with surface disorder

We study the effects of generalised surface disorder on the monomer-monomer model of heterogeneous catalysis, where disorder is implemented by allowing different adsorption rates for each lattice site. By mapping the system in the reaction-controlled limit onto a kinetic Ising model, we derive the rate equations for the one and two-spin correlation functions. There is good agreement between these equations and numerical simulations. We then study the inclusion of desorption of monomers from the substrate, first by both species and then by just one, and find exact time-dependent solutions for the one-spin correlation functions.Comment: LaTex, 19 pages, 1 figure included, requires epsf.st

Voting and Catalytic Processes with Inhomogeneities

We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many ``competing'' inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a nontrivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system, the strength of the inhomogeneities and their separating distances. In fact, in arbitrary dimensions, we obtain an exact (yet formal) expression of the order parameters (magnetization and concentration of adsorbed particles) in the presence of an arbitrary number $n$ of inhomogeneities (``zealots'' in the voter language) and formal similarities with {\it suitable electrostatic systems} are pointed out. In the nontrivial cases $n=1, 2$, we explicitly compute the static and long-time properties of the order parameters and therefore capture the generic features of the systems. When $n>2$, the problems are studied through numerical simulations. In one spatial dimension, we also compute the expressions of the stationary order parameters in the completely disordered case, where $n$ is arbitrary large. Particular attention is paid to the spatial dependence of the stationary order parameters and formal connections with electrostatics.Comment: 17 pages, 6 figures, revtex4 2-column format. Original title ("Are Voting and Catalytic Processes Electrostatic Problems ?") changed upon editorial request. Minor typos corrected. Published in Physical Review

Interactions Mediated by Surface States: From Pairs and Trios to Adchains and Ordered Overlayers

Since metallic surface states on (111) noble metals are free-electron like, their propagators can be evaluated analytically. Since they are well-screened, one can use simple tight-binding formalism to study their effects. The needed phase shifts can be extracted from experiment. Hence, one can now make quantitative predictions of these slowly-decaying, oscillatory indirect interactions. For the (isotropic!) pair interactions (which decay as the inverse square of adatom-adatom separation), remarkable agreement has been obtained with experiments by two groups. We have extended the formalism to consider the full indirect ("triple") interaction of 3 adsorbates, which is the sum of the 3 constituent pair interactions plus the non-pairwise "trio" contribution, which tends to decay with the 5/2 power of perimeter. Here, we concentrate on interactions due to ordered overlayers and to linear defects, relating the latter to the interactions of (nx1) ordered overlayers and to the constituent pair interactions. We compare with experimental studies of interactions of adatoms with adchains and of consequent 1D motion of adatoms trapped between two such parallel chains. We discuss implications for step-step interactions (on vicinal surfaces), with attention to the modification of the surface state itself for small terrace widths.Comment: 4 pages, Proceedings of 14th International Conference on Crystal Growth, Grenoble, France, 9-13 August 2004; to be published in J. Crystal Growth (2005

Catalytic CO Oxidation on Nanoscale Pt Facets: Effect of Inter-Facet CO Diffusion on Bifurcation and Fluctuation Behavior

We present lattice-gas modeling of the steady-state behavior in CO oxidation on the facets of nanoscale metal clusters, with coupling via inter-facet CO diffusion. The model incorporates the key aspects of reaction process, such as rapid CO mobility within each facet, and strong nearest-neighbor repulsion between adsorbed O. The former justifies our use a "hybrid" simulation approach treating the CO coverage as a mean-field parameter. For an isolated facet, there is one bistable region where the system can exist in either a reactive state (with high oxygen coverage) or a (nearly CO-poisoned) inactive state. Diffusion between two facets is shown to induce complex multistability in the steady states of the system. The bifurcation diagram exhibits two regions with bistabilities due to the difference between adsorption properties of the facets. We explore the role of enhanced fluctuations in the proximity of a cusp bifurcation point associated with one facet in producing transitions between stable states on that facet, as well as their influence on fluctuations on the other facet. The results are expected to shed more light on the reaction kinetics for supported catalysts.Comment: 22 pages, RevTeX, to appear in Phys. Rev. E, 6 figures (eps format) are available at http://www.physik.tu-muenchen.de/~natali

Induced Charge-Density Oscillations at Metal Surfaces

Induced charge-density (ICD) oscillations at the Cu(111) surface caused by an external impurity are studied within linear response theory. The calculation takes into account such properties of the Cu(111) surface electronic structure as an energy gap for three-dimensional (3D) bulk electrons and a $s-p_z$ surface state that forms two-dimensional (2D) electron system. It is demonstrated that the coexistence of these 2D and 3D electron systems has profound impact on the ICD in the surface region. In the case of a static impurity the characteristic ICD oscillations with the $1/\rho^2$ decay as a function of lateral distance, $\rho$, are established in both electron systems. For the impurity with a periodically time-varying potential, the novel dominant ICD oscillations which fall off like $\sim1/\rho$ are predicted.Comment: 11 pages, 5 figure

Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems

An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors time clocks current in a global sense. Boundary conflicts are rigorously solved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of the serial method, which confirms the statistical validity of the method. We have assessed the parallel efficiency of the method and find that our algorithm scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations

Heterogeneous Catalysis on a Disordered Surface

We introduce a simple model of heterogeneous catalysis on a disordered surface which consists of two types of randomly distributed sites with different adsorption rates. Disorder can create a reactive steady state in situations where the same model on a homogeneous surface exhibits trivial kinetics with no steady state. A rich variety of kinetic behaviors occur for the adsorbate concentrations and catalytic reaction rate as a function of model parameters.Comment: 4 pages, gzipped PostScript fil

Implication of the overlap representation for modelling generalized parton distributions

Based on a field theoretically inspired model of light-cone wave functions, we derive valence-like generalized parton distributions and their double distributions from the wave function overlap in the parton number conserved s-channel. The parton number changing contributions in the t-channel are restored from duality. In our construction constraints of positivity and polynomiality are simultaneously satisfied and it also implies a model dependent relation between generalized parton distributions and transverse momentum dependent parton distribution functions. The model predicts that the t-behavior of resulting hadronic amplitudes depends on the Bjorken variable x_Bj. We also propose an improved ansatz for double distributions that embeds this property.Comment: 15 pages, 8 eps figure

Influence of auto-organization and fluctuation effects on the kinetics of a monomer-monomer catalytic scheme

We study analytically kinetics of an elementary bimolecular reaction scheme of the Langmuir-Hinshelwood type taking place on a d-dimensional catalytic substrate. We propose a general approach which takes into account explicitly the influence of spatial correlations on the time evolution of particles mean densities and allows for the analytical analysis. In terms of this approach we recover some of known results concerning the time evolution of particles mean densities and establish several new ones.Comment: Latex, 25 pages, one figure, submitted to J. Chem. Phy

Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size--the scaled second moment of the magnetisation distribution--belies the full extent of these finite-size effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401