Monomer-dimer Surface Reaction Research Articles

Correlated noise induced non-equilibrium phase transition in surface catalytic reaction model

In recent years, with the development of chemical study of complex systems, such as surface catalytic system, etc. the research of nonlinear dynamics problem of complex system has received much attention. These systems have high-degree complexity, and they are inevitably affected by intrinsic and extrinsic fluctuations (noise) and time delay. The combination of noise and time delay is ubiquitous in nature, and often changes fundamentally dynamical behavior of the system, and thus making the system produce more richer and complex dynamical behaviors. At present, in the theoretical studies of the nonlinear dynamic properties, the macroeconomic deterministic or stochastic dynamic equation is adopted most, and the time delay factor, especially the influences of combination of noise and time delay on complex system are rarely taken into account. Thus, the study of the character, mechanism and application has important realistic significance and scientific value. In this paper, we first introduce the Dimer-Monomer reaction model (DM model), where various dimer adsorption mechanisms in catalyst surface, namely, the local and random adsorption surface catalytic reaction models are considered. Then we use the stochastic delayed theory involved in this paper and its extension, including the analytical approximation and numerical simulation of complex systems under the action of noise and time delay. In this paper, we consider the effects of noise and time-delayed feedback in the surface catalytic reaction model, and construct a delayed monomer-dimer surface reaction model including correlated noise. According to the Langevin equation, applying small delay approximation, we obtain the delayed Fokker-Planck equation for calculating characteristic parameters of the non-equilibrium phase transition behavior (the extreme of the steady state probability distribution), analyzing the effect mechanism of noise and its correlation with the non-equilibrium phase transition. The MD model exhibits the first- and second-order phase transition, namely, the reactive window between first- and second-order phase transition. The MD models for various dimer adsorption mechanisms (namely, local and random adsorption models) are discussed. The results are indicated as follows. (1) The external noise and correlation between two noise signals cause the reactive window width to contract. (2) The influence of the internal noise on the behavior of non-equilibrium dynamical phase transition depends on the noise correlation, i.e., when the two noise signals are negatively correlated, the internal noise causes the reactive window width to expand. However when the two noise signals are positively correlated, the internal noise causes the reactive window width to contract. (3) The noise-caused changes of reaction window have important scientific significance in the first- and second-order phase transition of the MD surface reaction model.

Stochastic delayed monomer-dimer surface reaction model with various dimer adsorption

In this paper, we study the impacts of noise and time delay in the monomer-dimer (MD) surface reaction model by using theoretical analysis. The MD models for various dimer adsorption mechanisms (namely, local and random adsorption models), which exhibit the first- and second-order phase transitions (PTs), are analyzed. By comparison with two various dimer adsorption, it is found that the qualitative predictions of the well-known first- and second-order PTs are better for the random adsorption model than that for the local adsorption model. The validity of approximate analytic results is checked by numerical simulations.

Structural effects in the kinetic behavior of the monomer–dimer surface reaction over nondeterministic fractal surfaces

A study is made of the segregation effect of adsorbed species related to the inner structure of two bidimensional adsorbent fractals, the incipient percolation cluster (IPC) and the backbone of the IPC, and their connection with the rate-determining step of the kinetic mechanism of the monomer–dimer (MD) surface reaction on those fractals. Production, R AB , is proportional to the concentration of A in the gas phase y A and to the fraction of vacant superficial sites x E ( R AB = y A x E ), and it is shown that adsorption of the monomer is the rate-controlling step of the reaction mechanism.

Effect of the coordination of the superficial site in the monomer–dimer reaction on a disordered substrate

Using Monte Carlo simulation experiments, a study is made of the effect of the superficial coordination number in a square lattice of sites for the monomer–dimer surface reaction (Ziff, Gulari and Barshad model) in the case of disordered substrates showing geometric heterogeneity of the sites, such as the percolation clusters. An analysis is made of the change in character of the phase transitions and in the size of the reactive window in the phase diagram, and the results were also compared with mean field theoretical calculations for disordered systems.

Monte Carlo and mean field theory studies of the effect of the next nearest neighbour sites of a square lattice on the monomer–dimer surface reaction

A study was made of the monomer–dimer surface processes on a square lattice of sites that include, in addition to the four nearest neighbours (nn) to the surface site, the next nearest neighbours sites (nnn), using Monte Carlo computer simulation techniques and a hierarchical mean field theory. Of particular interest were the factors that affect the window width of the process.

Hydrodynamic limits for the monomer-dimer surface reaction: Chemical diffusion, wave propagation, and equistability

For finite adspecies mobility, the lattice-gas monomer-dimer (A+B{sub 2}) surface reaction model exhibits a discontinuous transition from a stable reactive steady state to a stable A-poisoned steady state, as the impingement rate P{sub A} for A increases above a critical value P{sup {asterisk}}. The reactive (poisoned) state is metastable for P{sub A} just above (below) P{sup {asterisk}}. Increasing the surface mobility of A enhances metastability, leading to bistability in the limit of high mobility. In the bistable region, the more stable state displaces the less stable one separated from it by a planar interface, with P{sup {asterisk}} becoming the equistability point for the two states. This hydrodynamic regime can be described by reaction-diffusion equations (RDE{close_quote}s). However, for finite reaction rates, mixed adlayers of A and B are formed, resulting in a coverage-dependent and tensorial nature to chemical diffusion (even in the absence of interactions beyond site blocking). For equal mobility of adsorbed A and B, and finite reaction rate, the prediction for P{sup {asterisk}} from such RDE{close_quote}s, incorporating the appropriate description of chemical diffusion, is shown to coincide with that from kinetic Monte Carlo simulations for the lattice-gas model in the regime of high mobility. Behavior for this special casemore » is compared with that for various other prescriptions of mobility, for both finite and infinite reaction rates. {copyright} {ital 1998} {ital The American Physical Society}« less

Oscillatory dynamics in a heterogeneous surface reaction: Breakdown of the mean-field approximation.

Hierarchical mean-field rate equations and lattice-gas simulations were developed to elucidate the effects of the breakdown of the mean-field approximation for a model heterogeneous chemical oscillator that represents a simple extension of the well-known monomer-dimer surface reaction model. The bifurcation structure of the reaction kinetics depends sensitively on the details of surface transport processes, and the oscillatory behavior exhibited by the site approximation rate equations is not generally robust with respect to spatial correlations. \textcopyright{} 1996 The American Physical Society.

Hybrid treatment of spatio-temporal behavior in surface reactions with coexisting immobile and highly mobile reactants

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 spatial inhomogeneities is achieved through parallel simulation of the distributed macroscopic points with distinct correlated states and adspecies coverages. These simulations are appropriately coupled to describe diffusive mass transport of the mobile adspecies. In this way, we examine for this model the propagation and structure of chemical waves, corresponding to interface between bistable reactive states, and thereby determine the relative stability of these states.

Monomer-dimer surface-reaction model: Influence of the dimer adsorption mechanism.

We consider the monomer-dimer surface reaction without surface diffusion for various dimer adsorption mechanisms, described below. After a dimer impinges ``end on'' at an empty site, its bottom atom remains there while its top atom searches N\ensuremath{\ge}1 sites, either in a local neighborhood (N-local models), or randomly located on the surface (N-random models), to find a second empty site. If one is found, the dimer can then adsorb dissociatively. The N-local models have a reactive window of finite width in the relative impingement rates, bordered by poisoning transitions, whereas the N-random models exhibit true bistability. As N increases, the reactivity is either strictly or effectively confined to relative impingement rates close to the stoichiometric ratio. We precisely analyze the limiting behavior as N\ensuremath{\rightarrow}\ensuremath{\infty}.

The influence of the ?hot?-dimer adsorption mechanism on the kinetics of a monomer-dimer surface reaction

“Hot” dimers are molecules which after adsorption dissociate and each of the remaining “hot” monomers fly apart up to a maximum distance R from the original adsorption site. The influence of the “hot”-dimer adsorption mechanism on relevant aspects of the bimolecular catalyzed reaction of the type A − (1/2)B2(“hot”) → AB is studied by means of the Monte-Carlo simulation technique. The temporal evolution of both the reactant's coverages as well as the rate of AB-production is evaluated and discussed. Due to the enhanced probability of “hot” species for encounters with other adsorbed particles, the rate of AB-production becomes faster when increasing R. This behavior may be relevant in the dynamic of some catalyzed reactions such as for example the oxidation of carbon monoxide on transition metal surfaces, i.e. A≡CO, B2≡O2, and AB≡CO2. Also the sticking coefficient of “hot” dimers and the average distance traveled by the “hot” monomers are evaluated and discussed.

Kinetics of the monomer-monomer surface reaction model

The two-dimensional monomer-monomer ([ital AB]) surface reaction model without diffusion is considered for infinitesimal, finite, and infinite reaction rates [ital k]. For equal reactant adsorption rates, in all cases, simulations reveal the same form of slow poisoning, associated with clustering of reactants. This behavior is also the same as that found in simulations of the two-dimensional [ital voter] [ital model] studied in interacting-particle systems theory. The voter model can also be obtained from the dimer-dimer or monomer-dimer surface reaction models with infinitesimal reaction rate. We provide a detailed elucidation of the slow poisoning kinetics via an analytic treatment for the [ital k]=0[sup +] [ital AB] reaction and the voter models. This analysis is extended to incorporate the effects of place-exchange diffusion which slows, but does not prevent poisoning. We also show that the [ital k]=0[sup +] [ital AB] reaction with no diffusion is equivalent to the voter model with diffusion at rate 1/2. Identical behavior of the monomer-monomer reaction and the voter model is also found in an epidemic'' analysis, where one considers the evolution of a surface poisoned by one species, except for a small patch. Finally, we apply our findings to elucidate the behavior of the monomer-dimer surfacemore » reaction model for small reaction rates.« less

The influence of lateral interactions on the critical behavior of a dimer–monomer surface reaction model

The ZGB model [Ziff et al., Phys. Rev. Lett. 56, 2553 (1986)] for a monomer–dimer surface reaction process of the type A+(1/2)B2→AB, exhibits two irreversible phase transitions (IPT) from a stationary regime with AB production for p1A≤pA≤p2A, to poisoned states with B (A)-species for pA≤p1A (pA≥p2A), respectively, where pA is the mole fraction of A-species in the gas phase and piA (i=1, 2) are critical points. A generalization of the ZGB model in order to account for both attractive and repulsive interactions between the reactants is presented and discussed. It is found that in most cases the first order IPT at p2A becomes of second order and the critical points are shifted. For some particular choices of the interactions energies it is found that the second order IPT at p1A becomes of first order. Also, a first order IPT from the reactive state to a effectively poisoned regime where A-species are adsorbed forming a c(2×2) metastable structure is obtained.

Kinetic phase diagrams for the monomer–dimer surface reaction: Unification of mean-field and lattice–gas behavior

We provide a unified discussion of kinetic phase transitions for mean-field and lattice–gas treatments of the monomer–dimer surface reaction. For high surface mobilities, kinetics is typically well described by mean-field rate equations. These reveal bistability over a range of monomer adsorption rates which diminishes with increasing nonreactive monomer desorption rate d, and vanishes at some critical d=dc. Relative stability in the bistable region is determined from the behavior of chemical waves corresponding to the displacement of one stable state by the other. Their evolution is determined via appropriate reaction–diffusion equations. Conventional diffusion terms are modified here to reflect the influence of the presence of one species on diffusion of the other. We determine equistability (i.e., discontinuous transition) points for d≤dc, and thus construct a kinetic phase diagram including a spinodal line. For lower surface mobilities, analysis of lattice–gas models reveals qualitatively analogous behavior. The key difference is that for lower mobilities, spontaneous fluctuations are effective in automatically selecting the most stable state, i.e., in reducing metastability, and thus producing discontinuous transitions.