Ziff Gulari Barshad Research Articles

Surface diffusion effects on the system and the film properties of a Ziff–Gulari–Barshad type growth model

Surface diffusion stands as a fundamental process influencing the dynamics and thermodynamics of surface reactions, playing a pivotal role in the behavior of heterogeneous catalysis and thin film growth. To enhance our understanding, we extend the Ziff-Gulari-Barshad (ZGB) growth model by incorporating the diffusion of reactants involved in film formation. Initially, in the realm of heterogeneous catalysis, we compare our findings with an extended ZGB model that accounts for reactant diffusion. We analyze the shift in phase transition positions, induced by diffusion, in comparison to the original ZGB model. Subsequently, we integrate the film growth aspect. Across all examined cases, diffusion fails to adequately preserve the dynamic features of the extended ZGB model, resulting in poisonous states. Our conclusion underscores the dual impact of diffusion: firstly, it diminishes the film growth rate relative to the diffusionless scenario, and secondly, its effective influence on the final film height is evident only when considering hops in different layers. This assertion is validated through computations where diffusion with hops in different layers is either permitted or prohibited.

Insights into the effect of growth on the Ziff–Gulari–Barshad model and the film properties

We perform kinetic Monte Carlo computations with a modified Ziff–Gulari–Barshad (ZGB) model which considers the growth of a film. We show that the growth of the film significantly affects the conclusions that can be drawn from the ZGB model, even if the main mechanism, the surface reaction, remains the same. We compare the results of the growth model to the original ZGB and the phase transitions disappears; they are replaced by a smooth transition from 0 to full coverage. The latter observations qualitatively agree with experimental measurements for the CO2 formation. However, in the growth model the surface is always poisoned to a particular coverage values due to the local height differences of the lattice sites. Finally, a potential mechanism based only on surface phenomena which can lead to the decrement of the growth rate even if the amount of the precursor increases is explored.

Phase diagrams of the Ziff-Gulari-Barshad model on random networks.

In this study, we revisited the Ziff-Gulari-Barshad (ZGB) model in order to study the behavior of its phase diagram when two well-known random networks play the role of the catalytic surfaces: the random geometric graph and the Erdös-Rényi network. The connectivity and, therefore, the average number of neighbors of the nodes of these networks can vary according to their control parameters, the neighborhood radius α, and the linking probability p, respectively. In addition, the catalytic reactions of the ZGB model are governed by the parameter y, the adsorption rate of carbon monoxide molecules on the catalytic surface. So, to study the phase diagrams of the model on both random networks, we carried out extensive steady-state Monte Carlo simulations in the space parameters (y, α) and (y, p) and showed that the continuous phase transition is greatly affected by the topological features of the networks while the discontinuous one remains present in the diagram throughout the interval of study.

Highly detailed computational study of a surface reaction model with diffusion: Four algorithms analyzed via time-dependent and steady-state Monte Carlo simulations

In this work, we present an extensive computational study on the Ziff–Gulari–Barshad (ZGB) model extended in order to include the spatial diffusion of oxygen atoms and carbon monoxide molecules, both adsorbed on the surface. In our approach, we consider two different protocols to implement the diffusion of the atoms/molecules and two different ways to combine the diffusion and adsorption processes resulting in four different algorithms. The influence of the diffusion on the continuous and discontinuous phase transitions of the model is analyzed through two very well established methods: the time-dependent Monte Carlo simulations and the steady-state Monte Carlo simulations. We also use an optimization method based on a concept known as coefficient of determination to construct color maps and obtain the phase transitions when the parameters of the model vary. This method was proposed recently to locate nonequilibrium second-order phase transitions and has been successfully used in both systems: with defined Hamiltonian and with absorbing states. The results obtained via time-dependent Monte Carlo simulation along with the coefficient of determination are corroborated by traditional steady-state Monte Carlo simulations also performed for the four algorithms. Finally, we analyze the finite-size effects on the results, as well as, the influence of the number of runs on the reliability of our estimates.

Alternative method to characterize continuous and discontinuous phase transitions in surface reaction models

In this paper we revisited the Ziff-Gulari-Barshad model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We use a method proposed recently to locate the nonequilibrium second-order phase transitions and that has been successfully used in systems with defined Hamiltonians and with absorbing states. This method, which is based on optimization of the coefficient of determination of the order parameter, was able to characterize the continuous phase transition of the model, as well as its upper spinodal point, a pseudocritical point located near the discontinuous phase transition. The static critical exponents β,ν_{∥}, and ν_{⊥}, as well as the dynamic critical exponents θ and z for the continuous transition point, were also estimated and are in excellent agreement with results found in literature.

Dynamical critical behavior of the Ziff–Gulari–Barshad model with quenched impurities

The simplest model to explain the CO oxidation in some catalytic processes is the Ziff–Gulari–Barshad (ZGB) model. It predicts a continuous phase transition between an active phase and an absorbing phase composed of O atoms. By employing Monte Carlo simulations we investigate the dynamical critical behavior of the model as a function of the concentration of fixed impurities over the catalytic surface. By means of an epidemic analysis we calculate the critical exponents related to the survival probability Ps(t), the number of empty sites nv(t), and the mean square displacement R2(t). We show that the critical exponents depend on the concentration of impurities over the lattice, even for small values of this quantity. We also show that the exponents do not belong to the Directed Percolation universality class and are in agreement with the Harris criterion since the quenched impurities behave as a weak disorder in the system.

A model for the catalytic oxidation of CO that includes CO desorption and diffusion, O repulsion, and impurities in the gas phase

We present kinetic Monte Carlo simulations exploring the nonequilibrium phase diagram of a modified Ziff–Gulari–Barshad (ZGB) dynamic lattice-gas model for the catalytic oxidation of carbon monoxide (CO) on a surface. The modified model includes the simultaneous presence of contaminants in the gas phase, CO desorption, CO diffusion, and strong repulsion between adsorbed oxygen (O) atoms; all of which have been observed in experimental systems. We find that the strong O–O repulsion produces higher reaction rates, albeit in a reduced reactive pressure window. In systems with impurities, the CO2 production rate is greatly reduced, but this effect is mitigated by CO desorption and diffusion. CO desorption has the effect of widening the reactive pressure window, while CO diffusion has the effect of increasing the reaction rate. In some parameter regimes the presence of impurities destroys the discontinuous transition between the reactive and high CO coverage phases.

Monte Carlo simulations of the critical properties of a Ziff-Gulari-Barshad model of catalytic CO oxidation with long-range reactivity.

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 240×240 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 β/ν. The observed behavior is consistent with that of the 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.

Fluctuations and Universality in a Catalysis Model with Long-range Reactivity

The critical properties of the Ziff-Gulari-Barshad (ZGB) model with the addition of long-range reactivity [C. H. Chan and P. A. Rikvold, Phys. Rev. E 91, 012103 (2015)] are further investigated. The scaling behaviors of the order parameter, susceptibility, and correlation length provide additional evidence that the universality class of the ZGB system changes from the two-dimensional Ising class to the mean-field class with the addition of even a weak long-range reactivity mechanism.

Kinetic Monte Carlo Simulation of the oscillatory catalytic CO oxidation using a modified Ziff-Gulari-Barshad model

The oxidation of CO on Pt-group metal surfaces has attracted widespread attention since a long time due to its interesting oscillatory kinetics and spatiotemporal behavior. The use of STM in conjunction with other experimental data has confirmed the validity of the surface reconstruction (SR) model under low pressure and the more recent surface oxide (SO) model which is possible under sub-atmospheric pressure conditions [1]. In the SR model the surface is periodically reconstructed below a certain low critical CO-coverage and this reconstruction is lifted above a second, higher critical CO-coverage. Alternatively the SO model proposes periodic switching between a low-reactivity metallic surface and a high-reactivity oxide surface. Here we present an overview of our recent kinetic Monte Carlo (KMC) simulation studies on the oscillatory kinetics of surface catalyzed CO oxidation. Different modifications of the lattice gas Ziff-Gulari-Barshad (ZGB) model have been utilized or proposed for this purpose. First we present the effect of desorption on the ZGB reactive to poisoned irreversible phase transition in the SR model. Next we discuss our recent research on KMC simulation of the SO model. The ZGB framework is utilized to propose a new model incorporating not only the standard Langmuir-Hinshelwood (LH) mechanism, but also introducing the Mars-van Krevelen (MvK) mechanism for the surface oxide phase [5]. Phase diagrams, which are plots between long time averages of various oscillating quantities against the normalized CO pressure, show two or three transitions depending on the CO coverage critical threshold (CT) value beyond which all adsorbed oxygen atoms are converted to surface oxide.

Effects of inert species in the gas phase in a model for the catalytic oxidation of CO

We study by kinetic Monte Carlo simulations the catalytic oxidation of carbon monoxide on a surface in the presence of contaminants in the gas phase. The process is simulated by a Ziff-Gulari-Barshad (ZGB) model that has been modified to include the effect of the contaminants and to eliminate an unphysical oxygen poisoned phase at very low CO partial pressures. The impurities can adsorb and desorb on the surface but otherwise remain inert. We find that if the impurities cannot desorb, no matter how small their proportion in the gas mixture, the reactive window and discontinuous transition to a CO poisoned phase at high CO pressures that characterize the original ZGB model disappear. The coverages become continuous, and once the surface has reached a steady state there is no production of CO(2). This is quite different from the behavior of systems in which the surface presents a fixed percentage of impurities. When the contaminants are allowed to desorb, the reactive phase appears again for CO pressures below a value that depends on the proportion of contaminants in the gas and on their desorption rate.

First-Order Phase Transition in a Modified Ziff-Gulari-Barshad Model with Self-oscillating Reactant Coverages

Using kinetic Monte Carlo simulations, we study the effect of oscillatory kinetics due to surface reconstructions on Ziff-Gulari-Barshad (ZGB) model discontinuous phase transition. To investigate the transition, we do extensive finite size scaling analysis. It is found that the discontinuous transition still exists. On inclusion of desorption in the model, the order-parameter probability distribution broadens but remains bimodal. That is, the first-order phase transition becomes weaker with increase in desorption rate.

Ziff–Gulari–Barshad model with CO desorption under oscillating reactant pressure

We study the Ziff–Gulari–Barshad (ZGB) model subjected to periodic variation of reactant pressure, without desorption as well as at different desorption rates. Keeping the time period of oscillation fixed at a small value, Monte Carlo simulations are carried out at different amplitudes. With increase in the amplitude of oscillation, a transition occurs from the reactive state to the (partially) poisoned state. The reactant pressure oscillation is periodic cosine and symmetric about the ZGB discontinuous phase transition. Even for the model with no desorption, the numerical data for the fourth-order cumulant and the finite size scaling analysis suggest that the system does not undergo any phase transition but only a smooth crossover from the reactive to the poisoned state.

Effect of CO desorption and coadsorption with O on the phase diagram of a Ziff–Gulari–Barshad model for the catalytic oxidation of CO

We study the effect of coadsorption of CO and O on a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O --> CO(2) on a catalytic surface. Coadsorption of CO at a surface site already occupied by an O is introduced by an Eley-Rideal-type mechanism that occurs with probability p, 0 < or = p < or = 1. We find that besides the well-known effect of eliminating the second-order phase transition between the reactive state and an O-poisoned state, the coadsorption step has a profound effect on the transition between the reactive state and the CO-poisoned state. The coexistence curve between these two states terminates at a critical value k(c) of the desorption rate k, which now depends on p. Our Monte Carlo simulations and finite-size scaling analysis indicate that k(c) decreases with increasing values of p. For p = 1, there appears to be a sharp phase transition between the two states only for k at (or near) zero.

Effect of the Eley–Rideal step on catalytic oxidation of CO under periodic external pressure

The effect of periodic variation of external pressure on the catalytic oxidation of CO is simulated for a modified Ziff–Gulari–Barshad (ZGB) model including the Eley–Rideal (ER) step. The external CO partial pressure is periodically varied between its values in reactive and CO poisoned states. The results show different amplitudes of such perturbation significantly influence the CO 2 production rate. Latter also changes with the period of such oscillations, especially for perturbations with larger amplitudes. However, for a given period there is a critical value of the amplitude above which, the catalyst surface becomes irreversibly poisoned.

Fractal pattern formation in the Ziff–Gulari–Barshad model

The dynamics of the Ziff–Gulari–Barshad (ZGB) model is studied on three differenttwo-dimensional (2D) lattices: square (sq) lattice, hexagonal-honeycomb (hex-hon) latticeand purely hexagonal (hex) lattice. The effects of the support geometry on the steady stateand the dynamics are assessed. In all 2D lattice geometries the ZGB model is shown toexhibit non-equilibrium phase transitions of the first and second order, but thecritical values of the kinetic parameters depend crucially on the substrate geometry.Clustering and island formation are observed in all ranges of parameters, but the clustersare fractal only outside the active catalytic region. The fractal dimensions depend on thekinetic parameters.

Response of a model of CO oxidation with CO desorption and diffusion to a periodic external CO pressure

We present a study of the dynamical behavior of a Ziff–Gulari–Barshad model with CO desorption and lateral diffusion. Depending on the values of the desorption and diffusion parameters, the system presents a discontinuous phase transition between low and high CO coverage phases. We calculate several points on the coexistence curve between these phases. Inclusion of the diffusion term produces a significant increase in the CO 2 production rate. We further applied a square-wave periodic pressure variation of the partial CO pressure with parameters that can be tuned to modify the catalytic activity. Contrary to the diffusion-free case, this driven system does not present a further enhancement of the catalytic activity, beyond the increase induced by the diffusion under constant CO pressure.

Spatiotemporal oscillations and clustering in the Ziff-Gulari-Barshad model with surface reconstruction

We study the dynamics of the Ziff-Gulari-Barshad (ZGB) model on square (sq) and hexagonal-honeycomb (hex) lattices and when surface restructuring is introduced. We show that the ZGB model exhibits nonequilibrium phase transitions on the hex lattice similar to the ones already observed on the sq lattice, but the critical values of the kinetic parameters depend crucially on the substrate type. If surface reconstruction (sq<-->hex) is assumed for high lattice coverage of one of the reactive species then persistent spatiotemporal oscillations and clustering of homologous species are observed for kinetic parameter values 0.348<k1<0.393.

NUMERICAL STUDY OF THE FIRST ORDER IRREVERSIBLE PHASE TRANSITION IN THE ZIFF–GULARI–BARSHAD MODEL

The Ziff–Gulari–Barshad model [ZGB; Phys. Rev. Lett.56, 2553 (1986)] is a lattice gas adsorption–reaction model that qualitatively reproduces some relevant features of the oxidation of carbon monoxide on single crystal surfaces. We study the first order irreversible critical behavior of this model by means of two different types of simulation techniques, namely constant coverage simulations and epidemic analysis. Constant coverage simulations allow us to investigate in detail hysteretic and finite size effects within the coexistence region. The position of the coexistence point is accurately determined by introducing a small perturbation into the constant coverage method. Extensive epidemic simulations reveal the absence of power law behavior in the dynamic behavior at coexistence, in contrast to previous claims.

Monte Carlo simulations of the short time dynamics of a first-order irreversible phase transition

The ZGB model (Ziff–Gulari–Barshad, Phys. Rev. Lett. 56 (1986) 2553) for the catalytic oxidation of carbon monoxide has a single parameter given by the normalized partial pressure of CO molecules ( P CO). For P CO⩾ P CO Coex≃0.52583 the surface of the catalyst becomes irreversibly covered by CO molecules and the system cannot escape from this state. However, for P CO slightly below P CO Coex the system reaches an active stationary state. So, just at P CO Coex a sharp first-order irreversible phase transition is observed. It is shown that a study of the short time dynamics of the ZGB model allows to obtain a fairly accurate evaluation of the upper spinodal point given by P CO Usp≃0.52675(5). This figure is in excellent agreement with extensive simulations performed using the constant coverage ensemble.