Model For CO Oxidation Research Articles

Crossover Between Mean-Field and Ising Critical Behavior in a Lattice-Gas Reaction-Diffusion Model

Lattice-gas models for CO oxidation can exhibit a discontinuous nonequilibrium transition between reactive and inactive states, which disappears above a critical CO-desorption rate. Using finite-size-scaling analysis, we demonstrate a crossover from Ising to mean-field behavior at the critical point, with increasing surface mobility of adsorbed CO or with decreasing system size. This behavior is elucidated by analogy with that of equilibrium Ising-type systems with long-range interactions.

A Model for the CO Oxidation Reaction over a Catalyst Surface with Microscopic Nonuniformities

A modified lattice gas model for heterogeneous CO oxidation is proposed that takes into account microscopic nonuniformities of the catalyst surface. It is shown that, in contrast to the conventional model that assumes that the surface is uniform, according to the modified model the surface is not poisoned with the O2 phase when the concentration of nonuniformities is high. The mechanism considered in this paper may partly explain the behavior of the reaction system in the region of low CO concentrations.

Critical behavior in an atomistic model for a bistable surface reaction: CO oxidation with rapid CO diffusion.

We analyze critical behavior associated with the loss of bistability for an atomistic model for CO oxidation on surfaces in the limit of infinite diffusion of CO. The model includes infinite nearest-neighbor repulsions between adsorbed immobile O. We use a "hybrid" treatment incorporating a lattice-gas description of the O adlayer, but tracking just the number of adsorbed CO (which are randomly distributed on non-O sites). The critical exponents obtained from a finite-size-scaling analysis on LxL site surfaces with periodic boundary conditions show that the "hybrid" reaction model belongs to the mean-field universality class, despite strong spatial correlations in the O adlayer. We also quantify finite-size effects in the global bifurcation diagram, revealing a significant shift of the bistable region with decreasing system size. Our study elucidates fluctuation effects observed in experiments of CO oxidation on the nanoscale facets of metal-field emitter tips.

The structure of higher defective ZnO[formula omitted

The surface structure of clean and defective ZnO(101̄0) have been studied using ab initio plane wave density functional theory. Two models of surface defects have been examined; an oxygen vacancy within the surface Zn–O dimer and an oxygen vacancy in the second layer of the material. Previous models of CO oxidation on this surface have invoked the formation of isolated second layer defects. In the current study we show that the formation of such a defect costs 1.01 eV more energy than the formation of a vacancy within the dimer bond and hence models of catalytic activity that invoke the formation of isolated second layer defects need to be re-examined.

Oscillation-Generating Mechanisms in Stochastic and Deterministic Models of a Catalytic Reaction

The article examines consistent mathematical micro- and macro-level models of CO oxidation on platinum-group metals. New mechanisms responsible for the excitation of oscillations are studied in detail by simulation. Micro-level oscillations may arise in parameter-space regions where the corresponding macro model has a limiting cycle, a bistability, or a unique stable steady-state solution. In the latter case, necessary conditions for the excitation of oscillations include fluctuations in the concentration of adsorbed particles, which are characteristic of micro models of small-volume systems, and a special arrangement of the macro-model trajectories on the phase plane producing sensitivity to small perturbations or excitability of the medium.

Spiral concentration waves in the Monte Carlo model of CO oxidation over Pd(1 1 0) caused by synchronisation via CO ads diffusion between separate parts of catalytic surface

The role of adsorbed CO diffusion as a synchronisation factor between the separate oscillating surfaces in CO oxidation reaction has been examined by means of Monte Carlo model. As a result of the chosen simulation strategy the spiral waves of adsorbed species on the palladium surface (imagined as a set of independent Pd(1 1 0) planes) have been observed. The dependence of the results on the details of the simulation experiment as well as on the size of the lattice representing the catalytic surface has been studied.

Fluctuations and bistability in a “hybrid” atomistic model for CO oxidation on nanofacets: An effective potential analysis

We analyze fluctuations in a “hybrid” atomistic model mimicking CO oxidation on nanoscale facets of metal(100) catalyst surfaces. The model incorporates a mean-field-like treatment of infinitely mobile CO, and a lattice-gas treatment of the superlattice ordering of immobile O. For an infinite system, it exhibits an Ising-type order–disorder transition for O, together with mean-field-like bistability disappearing at a cusp bifurcation. For finite systems, we use kinetic Monte Carlo simulation to study the probability distribution for the population of adsorbed species, from which bistability can be observed, together with fluctuation-induced transitions between the two stable states. An effective potential picture emerges from our analyses that can be used to quantify both the system size dependence of fluctuations and the transition rates. Thus, our hybrid atomistic model displays fluctuation behavior analogous to traditional mean-field models. This qualitative behavior can be understood by approximate treatments of population dynamics using master equations and Fokker–Planck equations. A generalized model with finite mobility of CO is also analyzed for comparison with the hybrid model. In contrast, it exhibits fluctuation behavior akin to equilibrium systems with Ising-type first-order transitions.

Electrooxidation of small organic molecules on mesoporous precious metal catalysts I: CO and methanol on platinum

Nanostructured platinum prepared by the chemical reduction of hexachloroplatinic acid dissolved in aqueous domains of the liquid crystalline phases of oligoethylene oxide surfactants has been examined as an innovative model electrocatalyst. Owing to its high specific surface area and periodic mesoporous nanostructure, electrooxidation of both carbon monoxide and methanol has been investigated using cyclic voltammetry and chronoamperometry as a probe of the electrocatalytic properties of this material. The oxidation of CO adsorbed on the new type of platinum is determined by the rate of an adsorption and nucleation-growth controlled phase transformation occurring inside the CO adlayer. This mechanism appears to be different from the traditional Langmuir–Hinshelwood model for CO oxidation. The methanol electrooxidation reaction appears to proceed mainly through a direct pathway with CO 2 as the final product and the potentiostatic current attains a steady-state value even at low potentials (<0.5 V). These results are very important since the nanostructured platinum shows a much lower poisoning rate at potentials relevant to fuel cell operation. Enhanced electrocatalytic durability to the methanol oxidation reaction is obtained on this new type of platinum in comparison to one high surface area platinum from Johnson–Matthey plc.

The influence of concentration-dependent diffusivities on wave stability

Investigations on the onset of wave instability in excitable reaction–diffusion media have mainly focused on the effects of reaction kinetics and the relative diffusivity of activator and inhibitor. In this study, we characterize wave stability in a medium in which a diffusion coefficient depends on the local concentration of a reagent. Calculations with a simple CO oxidation model illustrate that the sensitivity of the diffusion coefficient to the concentration can behave like a dynamical parameter to induce transitions between “backfiring” and “regular” propagating pulses. The transition is due to the influence of the variable diffusion process on the refractory zone of wave activity.

Pattern formation in models of fixed-bed reactors

This work reviews and compares spatiotemporal patterns in three models of adiabatic fixed catalytic beds for reactions with oscillatory kinetics: homogeneous and heterogeneous models, which are studied using generic first-order kinetics, and a detailed model of CO oxidation in the monolithic reactor. These three models describe reactors with one, two or all three phases (fluid-, solid- and adsorbed-phases), respectively. Pattern selection is based on the oscillatory or bistable nature of the kinetics and on the nature of fronts. The heterogenous and detailed models may exhibit local bistability while the homogeneous model does not admit this property: a simple conversion between the parameters of the homogeneous and heterogeneous models is suggested. The spatiotemporal patterns in the reactor can be predicted from the sequence of phase planes spanned by the reactor. Stationary or oscillatory front solutions, oscillatory states that sweep the whole surface or excitation fronts may be realized in the homogeneous and heterogeneous models. The detailed model of the converter may exhibit oscillatory motion, which may be periodic or chaotic, in which typically a hot domain enters the reactor exit and moves quickly upstream; the following extinction occurs almost simultaneously due to strong coupling by convection.

Stochastic model of CO oxidation on platinum surfaces and deterministic limit

We present a general model for the oxidation of CO on low-index platinum single crystal surfaces. In order to take fluctuations into account, it is first formulated in terms of stochastic birth–death processes. A corresponding deterministic limit for large particle numbers can be derived rigorously. The dynamical behavior of the reaction kinetics is investigated by means of a numerical bifurcation analysis of the deterministic limit and stochastic simulations. The computed bifurcation diagrams for Pt(110) and Pt(100) are in qualitative and reasonable quantitative agreement with experimental results. For Pt(110), several types of noise-induced oscillations are obtained.

Fluctuations and critical phenomena in catalytic CO oxidation on nanoscale Pt facets

Local fluctuations and fluctuation-induced transitions in catalytic CO oxidation are studied with field electron microscopy on the (112) facets of a [100]-oriented Pt field emitter tip. The reaction is investigated in the bistable range close to the cusp point (critical point) that terminates the bistability range in ${p}_{\mathrm{CO}},$ T-parameter space. The amplitude and the spatial coherence of the fluctuations increase on approaching the critical point. The fluctuations are spatially well correlated on each flat (112) facet, but their correlation decays rapidly across stepped regions that terminate the flat facets. On smaller (112) facets, an onset of fluctuation-induced transitions is observed earlier (i.e., further away from the critical point) than for larger (112) facets. The behavior of the reaction system near the cusp point appears to be similar to that of an equilibrium system near the critical point. The observed fluctuations are mimicked in a simple reaction model for CO oxidation on surfaces that incorporates both rapid diffusion of adsorbed CO, and superlattice ordering of adsorbed immobile oxygen. The steady states of the model exhibit a cusp bifurcation, from a regime of bistability to one of monostability. The fluctuations increase near this cusp point, as in experiment. This behavior is analyzed via kinetic Monte Carlo simulations and analytic procedures, focusing on the consequences for fluctuation-induced transitions.

Toward the study of catalytic reactions under industrial conditions: a contaminated CO oxidation model

Recent trends in surface chemistry are trying to bridge the gap between ideal ultrahigh vacuum (UHV) studies and results of catalytic reactions under industrial conditions. These conditions are mainly characterized by a heterogeneous active phase, high pressure and the presence of contaminant species. In the present work we address the last of these three factors. More precisely we study the effects of a contaminating species, whose only action is adsorption and desorption being otherwise inert, on the kinetics of CO oxidation on transition metals. We introduce a suitably modified Ziff–Gulari–Barshad model, a contaminated ZGB model, and obtain by Monte Carlo simulations the behavior of the steady state of the system for different CO and contaminant concentrations. We find that the reaction window shrinks with increasing contaminant concentration until it disappears at a critical value. Moreover, we find that the classical lower bound ZGB irreversible phase transition is unaffected while the upper bound first order transition transforms continuously into a second order one with increasing contaminant concentration, as revealed by the behavior of critical exponents.

Surface diffusion in mixed overlayers with superlattice ordering: Percolative transport around obstacles and along domain boundaries

To elucidate surface diffusion in the presence of a coadsorbate with superlattice ordering, we consider particle hopping on a square lattice with some fraction, θB, of quenched blocking sites arranged with checkerboard or c(2×2) ordering. Behavior for low θB corresponds to diffusion around isolated obstacles, and can be described by exact density expansions. Behavior for high θB corresponds to percolative diffusion along (or sometimes away from) domain boundaries. The connectivity of these domain boundaries is closely related to the existence of symmetry breaking [i.e., long-range c(2×2) order] in the distribution of blocking sites. In some cases, symmetry breaking induces critical behavior for diffusive transport which is fundamentally different from that for the conventional “ant in the labyrinth” problem. Our results apply to recently developed models for CO oxidation, where CO(ads) diffuses rapidly through coadsorbed relatively immobile c(2×2)-O(ads). The characterization of CO diffusion in these systems is key to describing spatial pattern formation.

Spatiotemporal chaos and nonequilibrium transitions in a model excitable medium

We present a detailed study of the statistical steady states of a model for CO oxidation on Pt(110) proposed by Bar and co-workers. We show that the stability diagram of this model depends sensitively on the boundary conditions. We elucidate several novel properties of a state with meandering spirals (M) briefly mentioned by Bar and co-workers. (1) We show that, with periodic boundary conditions, M is the state MP, a binary mixture displaying a coexistence of quasiperiodically rotating spirals and chaotically moving pointlike defects. We show that the transition from MP to the turbulent state T1 is continuous; the transition line marks the locus where the two phases cease to be distinct. (2) With Neumann boundary conditions M is the state MN, a single quasiperiodically rotating spiral. We show that the MN-T1 transition is discontinuous or first order. We also characterize the transitions from MP and MN to the state S, which has quasiperiodically rotating spirals. We also propose qualitative mechanisms for these transitions.

Symmetry-breaking and percolation transitions in a surface reaction model with superlattice ordering

A symmetry-breaking order-disorder transition of the Ising type is found in a nonequilibrium surface reaction model for CO oxidation incorporating superlattice ordering of adsorbed oxygen. We relate this transition to the percolation of superlattice domains of oxygen, and discuss the consequences for chemical diffusion of coadsorbed CO. The latter constitutes a new type of problem involving transport in disordered media.

Modeling and analysis of spatiotemporal oscillatory patterns during CO oxidation in the catalytic converter

In spite of numerous reports of kinetic instabilities during CO oxidation on supported noble-metal catalysts, previous models of the catalytic converter typically employed explicit rate-expressions. Such oscillatory motions or bistable behavior occur at low temperatures and should affect the converter cold-start performance. In this work we incorporate an oscillatory elementary-step kinetic model of CO oxidation into the converter model and analyze its behavior. The kinetic model was suggested by Sales et al. (1982 Surface Science, 114, 381–394) and we modify the suggested parameters to assure that the steady-state rate is monotonically increasing with temperature. We draw typical bifurcation maps, in the temperature vs. P CO plane, for the isothermal kinetic model, for the catalyst surface (the lumped problem) and for the whole reactor and analyze the various boundaries by means of phase plane analysis. The domain of oscillations in the catalyst problem is quite similar to that in the converter and is bound by Hopf and global-saddle-node bifurcations. The converter may exhibit either a stable steady behavior or an oscillatory motion. In typical oscillations, which may be periodic or chaotic, a hot domain enters the reactor exit and moves quickly upstream; the following extinction occurs almost simultaneously due to strong coupling by convection. New avenues of cold-starting the converter, which is an excitable system, by means of periodic local perturbations upstream that send fronts propagating downstream are also suggested. The analysis shows, however, that this approach is not advantageous due to the slow relaxation of the surface activity during CO oxidation.

CO-oxidation model with superlattice ordering of adsorbed oxygen. I. Steady-state bifurcations

We analyze a model for CO oxidation on surfaces which incorporates both rapid diffusion of adsorbed CO, and superlattice ordering of adsorbed immobile oxygen on a square lattice of adsorption sites. The superlattice ordering derives from an “eight-site adsorption rule,” wherein diatomic oxygen adsorbs dissociatively on diagonally adjacent empty sites, provided that none of the six additional neighboring sites are occupied by oxygen. A “hybrid” formalism is applied to implement the model. Highly mobile adsorbed CO is assumed randomly distributed on sites not occupied by oxygen (which is justified if one neglects CO–CO and CO–O adspecies interactions), and is thus treated within a mean-field framework. In contrast, the distribution of immobile adsorbed oxygen is treated within a lattice–gas framework. Exact master equations are presented for the model, together with some exact relationships for the coverages and reaction rate. A precise description of steady-state bifurcation behavior is provided utilizing both conventional and “constant-coverage ensemble” Monte Carlo simulations. This behavior is compared with predictions of a suitable analytic pair approximation derived from the master equations. The model exhibits the expected bistability, i.e., coexistence of highly reactive and relatively inactive states, which disappears at a cusp bifurcation. In addition, we show that the oxygen superlattice ordering produces a symmetry-breaking transition, and associated coarsening phenomena, not present in conventional Ziff–Gulari–Barshad-type reaction models.

Monte Carlo simulations of a surface reaction model showing spatio-temporal pattern formations and oscillations

Results of dynamic Monte Carlo simulations of a model for CO oxidation on a reconstructing Pt(100) surface are presented. A comparison is made between simulations that explicitly include surface diffusion of adsorbed CO and simulations without diffusion. Oscillatory behavior as well as spatio-temporal pattern formation are studied as a function of system size. In the absence of diffusion the amplitude of kinetic oscillations decreases with grid size and oscillations are not stable. Spatio-temporal patterns appear, as expected for an excitable medium. Such patterns become stabilized by structural substrate defects. The length scale of the patterns is in the order of 10–100 nm, the temporal period of the oscillations is around 200 seconds. Inclusion of diffusion stabilizes and synchronizes oscillations. Spatio-temporal features now appear with larger spatial dimensions.

Monte Carlo and Cellular Automata Modeling of CO Oxidation on a Catalytic Surface Including the Eley−Rideal Step and CO Diffusion

We present the results of cellular automaton and Monte Carlo simulations for the case of CO oxidation on a catalytic surface with simultaneous adsorption, reaction, and diffusion, including the Eley-Rideal step in the reaction mechanism. The results show that the carbon monoxide diffusion on the catalytic surface does not alter the qualitative nature of phase transitions. Also for any given adsorption to diffusion ratio the cellular automaton predicts slightly lower values of the phase transition point. The automaton has considerable speed advantage and corroborates the Monte Carlo simulation results.