Monte Carlo Simulations of the Critical Properties of a Ziff-Gulari-Barshad model of Catalytic CO Oxidation with Long-range Reactivity

Abstract

The Ziff-Gulari-Barshad (ZGB) model, a simplified description of the oxidation of carbon monoxide (CO) on a catalyst surface, is widely used to study properties of nonequilibrium phase transitions. In particular, it exhibits a nonequilibrium, discontinuous transition between a reactive and a CO poisoned phase. If one allows a nonzero rate of CO desorption ($k$), the line of phase transitions terminates at a critical point ($k_c$). In this work, instead of restricting the CO and atomic oxygen (O) to react to form carbon dioxide (CO${}_2$) only when they are adsorbed in close proximity, we consider a modified model that includes an adjustable probability for adsorbed CO and O atoms located far apart on the lattice to react. We employ large-scale Monte Carlo simulations for system sizes up to 240$\times$240 lattice sites, using the crossing of fourth-order cumulants to study the critical properties of this system. We find that the nonequilibrium critical point changes from the two-dimensional Ising universality class to the mean-field universality class upon introducing even a weak long-range reactivity mechanism. This conclusion is supported by measurements of cumulant fixed-point values, cluster percolation probabilities, correlation-length finite-size scaling properties, and the critical exponent ratio $\beta /\nu$. The observed behavior is consistent with that of the \emph{equilibrium} Ising ferromagnet with additional weak long-range interactions [T. Nakada, P. A. Rikvold, T. Mori, M. Nishino, and S. Miyashita, Phys. Rev. B 84, 054433 (2011)]. The large system sizes and the use of fourth-order cumulants also enable determination with improved accuracy of the critical point of the original ZGB model with CO desorption.

arXiv comment26 pages, 10 figures

References in corpus (20)

• A fast Monte Carlo algorithm for site or bond percolation
• Realization of the mean-field universality class in spin-crossover materials
• CO oxidation on Pd(100) at technologically relevant pressure conditions: A first-principles kinetic Monte Carlo study
• Medium-range interactions and crossover to classical critical behavior
• Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model
• Nonmonotonical crossover of the effective susceptibility exponent
• Crossover scaling in two dimensions
• Response of a catalytic reaction to periodic variation of the CO pressure: Increased CO_2 production and dynamic phase transition
• Decay of metastable phases in a model for the catalytic oxidation of CO
• Asymptotic forms and scaling properties of the relaxation time near threshold points in spinodal-type dynamical phase transitions
• Scaling properties of the relaxation time near the mean-field spinodal
• Threshold Phenomena under Photo Excitation of Spin-crossover Materials with Cooperativity due to Elastic Interactions
• Critical temperature and correlation length of an elastic interaction model for spin-crossover materials
• Crossover between a Short-range and a Long-range Ising model
• Catalytic CO Oxidation on Nanoscale Pt Facets: Effect of Inter-Facet CO Diffusion on Bifurcation and Fluctuation Behavior
• Effects of inert species in the gas phase in a model for the catalytic oxidation of CO
• Model for the catalytic oxidation of CO, including gas-phase impurities and CO desorption
• Effect of CO desorption and coadsorption with O on the phase diagram of a Ziff-Gulari-Barshad model for the catalytic oxidation of CO
• Crossover between mean-field and Ising critical behavior in a lattice-gas reaction-diffusion model
• Response of a Model of CO Oxidation with CO Desorption and Diffusion to a Periodic External CO Pressure

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• Multicritical Bifurcation and First-order Phase Transitions in a Three-dimensional Blume-Capel Antiferromagnet
• Highly detailed computational study of a surface reaction model with diffusion: four algorithms analyzed via time-dependent and steady-state Monte Carlo simulations
• Fluctuations and universality in a catalysis model with long-range reactivity