Ziff-Gulari-Barshad model with CO desorption: An Ising-like nonequilibrium critical point.
01 Feb 1993-Physical Review E (Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics)-Vol. 47, Iss: 2, pp 948-952
About: This article is published in Physical Review E.The article was published on 1993-02-01. It has received 49 citations till now. The article focuses on the topics: Tricritical point & Critical point (thermodynamics).
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TL;DR: In this article, a review of the first-order kinetic phase transition with bistability and chemical waves is presented, where the authors mainly focus on the first order kinetic phase transitions connected with bistsability and resulting in chemical waves.
190 citations
TL;DR: In this paper, the authors summarize some of the recent work based on discrete models for irreversible surface reactions and discuss the fundamental aspects of nonequilibrium kinetics, and show through specific examples that explicit Monte Carlo simulations can transcend traditional approaches based on rate-equation methods, in particular those invoking the mean-field approximation.
Abstract: Numerical simulations based on the Monte Carlo method offer a powerful approach for detailed studies of complex reaction sequences, such as those associated with heterogeneous catalysis. In this article, we summarize some of the recent work based on discrete models for irreversible surface reactions. Particular emphasis is placed on kinetic phase transition, bistability, and oscillatory (nonstationary) reactions. In addition to discussing some of the fundamental aspects of nonequilibrium kinetics, we show through specific examples that explicit Monte Carlo simulations can transcend traditional approaches based on rate-equation methods, in particular those invoking the mean-field approximation. This is particularly the case when local correlations and fluctuations among the reactants are important.
102 citations
TL;DR: In this article, a realistic molecular-level description of catalytic reactions on single-crystal metal surfaces can be provided by stochastic multisite lattice-gas (msLG) models.
65 citations
TL;DR: An efficient analysis of surface reactions on single‐crystal substrates which involve highly mobile adspecies is provided by a ‘‘hybrid treatment’’ which is applied here to the monomer–dimer surface reaction model in the case of coexisting immobile dimer adspecies and highly mobile monomer adspecies.
Abstract: For surface reactions on single‐crystal substrates which involve highly mobile adspecies, there is a vast separation in natural time and length scales. Adspecies hop rates can be many orders of magnitude larger than rates for other processes. Strong spatial correlations or ordering can exist on the atomic scale, while spatial pattern formation occurs on a macroscopic scale due to high diffusivity. An efficient analysis of such systems is provided by a ‘‘hybrid treatment’’ which we apply here to the monomer–dimer surface reaction model in the case of coexisting immobile dimer adspecies and highly mobile monomer adspecies. Specifically, we combine a mean‐field treatment of the ‘‘randomized’’ mobile adspecies, and a lattice‐gas description of the immobile adspecies. Monte Carlo simulations then reveal bistability and ‘‘critical’’ bifurcation phenomena, while precisely accounting for the influence of correlations in the immobile adspecies distribution. A corresponding analysis of the evolution of macroscopic ...
54 citations
TL;DR: An atomistic lattice-gas model for the catalytic oxidation of CO on single-crystal Pd(100) surfaces under ultrahigh vacuum conditions is developed andKinetic Monte Carlo simulations of this reaction model are performed to predict temperature-programmed reaction spectra, as well as steady-state bifurcation behavior.
Abstract: We have developed an atomistic lattice-gas model for the catalytic oxidation of CO on single-crystal Pd(100) surfaces under ultrahigh vacuum conditions. This model necessarily incorporates an detailed description of adlayer ordering and adsorption-desorption kinetics both for CO on Pd(100), and for oxygen on Pd(100). Relevant energetic parameters are determined by comparing model predictions with experiment, together with some guidance from density functional theory calculations. The latter also facilitates description of the interaction and reaction of adsorbed CO and oxygen. Kinetic Monte Carlo simulations of this reaction model are performed to predict temperature-programed reaction spectra, as well as steady-state bifurcation behavior.
52 citations
References
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TL;DR: The renormalization group theory has been applied to a variety of dynamic critical phenomena, such as the phase separation of a symmetric binary fluid as mentioned in this paper, and it has been shown that it can explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions.
Abstract: An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.
4,980 citations
TL;DR: In this paper, a specific form for the equation of state of a fluid near its critical point is proposed, where a function Φ(x, y) is introduced, with x a measure of the temperature and y of the density.
Abstract: A specific form is proposed for the equation of state of a fluid near its critical point. A function Φ(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an equation of state of van der Waals type (``classical'' fluids) are characterized by Φ being a constant. It is suggested that in a real fluid Φ(x, y) is a homogeneous function of x and y, with a positive degree of homogeneity (Sec. 2). This leads to a nonclassical compressibility, the behavior of which is determined by the degree of homogeneity of Φ (Sec. 3). A previously derived relation connecting the degree of the critical isotherm, the degree of the coexistence curve, and the compressibility index, again follows, this time without the restrictive assumption of effective isochore linearity (Sec. 4). The locus in the temperature—density plane of the points of inflection in the pressure—density isotherms, as determined experimentally by Habgood and Schneider, is accounted for (Sec. 5). It is shown that if a certain combination of the compressibility and coexistence curve indices is an integer, then the constant‐volume specific heat on the critical isochore has a logarithmic singularity at the critical temperature with, in general, a superimposed finite discontinuity (Sec. 6).
1,015 citations
TL;DR: In this paper, an irreversible kinetic surface-reaction model based on the reaction of carbon monoxide and oxygen on a catalyst surface was presented, and it was found by computer simulation that the adsorbed molecules on the surface undergo both first-and second-order kinetic phase transitions.
Abstract: An irreversible kinetic surface-reaction model, based upon the reaction of carbon monoxide and oxygen on a catalyst surface, is presented. It is found by computer simulation that the adsorbed molecules on the surface undergo both first- and second-order kinetic phase transitions. These transitions correspond to the "poisoning" phenomenon seen on catalysts. Interesting transient and periodic behavior is also seen.
784 citations
TL;DR: In this paper, the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external field were investigated theoretically and via computer simulation on a periodic 30 × 30 square lattice with attractive nearest neighbor interactions.
Abstract: We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is to bias jumps in the field direction and thus produce a current carrying steady state. Simulations on a periodic 30 × 30 square lattice with attractive nearest-neighbor interactions suggest a nonequilibrium phase transition from a disordered phase to an ordered one, similar to the para-to-ferromagnetic transition in equilibriumE=0. At low temperatures and largeE the system segregates into two phases with an interface oriented parallel to the field. The critical temperature is larger than the equilibrium Onsager value atE=0 and increases with the field. For repulsive interactions the usual equilibrium phase transition (ordering on sublattices) is suppressed. We report on conductivity, bulk diffusivity, structure function, etc. in the steady state over a wide range of temperature and electric field. We also present rigorous proofs of the Kubo formula for bulk diffusivity and electrical conductivity and show the positivity of the entropy production for a general class of stochastic lattice gases in a uniform electric field.
418 citations
TL;DR: In this article, the stationary nonequilibrium states of a lattice gas of interacting particles subject to an external field were investigated, where the dynamics of the system were given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction of the external field.
Abstract: We investigated the stationary nonequilibrium states of a lattice gas of interacting particles subject to an external field $\stackrel{\ensuremath{\rightarrow}}{E}$. The dynamics of the system are given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction of $\stackrel{\ensuremath{\rightarrow}}{E}$. This system is often used to model fast ionic conductors. Using computer simulations of a two-dimensional lattice with nearest-neighbor interactions we studied the dependence of the structure function, current, etc., on temperature and $\stackrel{\ensuremath{\rightarrow}}{E}$. We found evidence for a transition line in the temperature-field plane at which the system develops (anisotropic) long-range order. $\stackrel{\ensuremath{\rightarrow}}{E}$ enhances the transition for attractive interactions and represses it for repulsive ones.
297 citations