Theory of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">NO</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">CO</mml:mi></mml:math>surface-reaction model

Dickman, Adriana Gomes; Grandi, B. C. S.; Figueiredo, W.; Dickman, Ronald

doi:10.1103/physreve.59.6361

Cited by 44 publications

(29 citation statements)

References 29 publications

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“…Using Monte Carlo simulations they found that this surface model presents the main features of the pure CO-O 2 system, which contains an active phase where the carbon dioxide molecules are produced continuously. After the appearance of this article, an avalanche of other papers concerning the reaction catalytic surfaces also have appeared in the literature [4][5][6][7][8][9][10][11][12][13][14][15]. In general, these papers are related with the own ZGB model or they are extensions of the same, concerning the various aspects of the experimental observations of these phenomena.…”

Section: Introductionmentioning

confidence: 99%

Dimer Production in a Poisoned Catalytic Model

Schmidt

Santos

2001

phys. stat. sol. (a)

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We studied a catalytic reaction model among three monomers on a square lattice using Monte Carlo simulations. Our model consists in the introduction of an irreversible adsorption step to the well known Ziff, Gulari, and Barshad model. In this step, the third monomer blocks one site on the catalytic surface. Besides, we also allow for the diffusion of the monomers on the surface. This model does not present a phase transition, because the steady states are always poisoned for any value of the adsorption rate of the monomers. However, we have determined the total dimer production rate and the mean lifetime of the catalytic surface as a function of the adsorption rate of the monomers. We have seen that the total production of dimers and the mean lifetime exhibit a maximum value in different values of the adsorption rates of the monomers. This result is independent of the diffusion rate. However, we also noted that the production rate of dimers decreases and the mean lifetime increases when the diffusion process is dominant.

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Section: Introductionmentioning

confidence: 99%

Dimer Production in a Poisoned Catalytic Model

Schmidt

Santos

2001

phys. stat. sol. (a)

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“…To calculate the transition probabilities we proceed in a manner similar to that used in the site mean-field approximation, but now they are more involved. Examples of the application of this pair approximation can be found in the references [34] and [35]. In particular, in the appendix B of the reference [34], a detailed description of the method used here is given, with emphasis to the N O + CO reaction model.…”

Section: B Pair Approximationmentioning

confidence: 99%

“…Examples of the application of this pair approximation can be found in the references [34] and [35]. In particular, in the appendix B of the reference [34], a detailed description of the method used here is given, with emphasis to the N O + CO reaction model. The reaction probability Π AA was defined as being the probability of an arriving A monomer to react with anyone of its nearest neighbor A on the lattice, in the presence of the B monomers.…”

Section: B Pair Approximationmentioning

confidence: 99%

Catalysis with competitive reactions: static and dynamical critical behavior

Costa

Figueiredo²

2003

Braz. J. Phys.

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We studied in this work a competitive reaction model between monomers on a catalyst. The catalyst is represented by hypercubic lattices in d = 1, 2 and 3 dimensions. The model is described by the following reactions: A + A → A2 and A + B → AB, where A and B are two monomers that arrive at the surface with probabilities y A and y B , respectively. The model is studied in the adsorption controlled limit where the reaction rate is infinitely larger than the adsorption rate. We employ site and pair mean-field approximations as well as static and dynamical Monte Carlo simulations. We show that, for all d, the model exhibits a continuous phase transition between an active steady state and a B-absorbing state, when the parameter y A is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis near the critical point are used to determine the static critical exponents β, ν ⊥ and the dynamical critical exponents ν || , δ, η and z. The results found for this competitive reaction model are in accordance with the conjecture of Grassberger, which states that any system undergoing a continuous phase transition from an active steady state to a single absorbing state, exhibits the same critical behavior of the directed percolation universality class. I IntroductionIn the course of the last decade the statistical mechanics community has made great progress in the study of nonequilibrium phenomena. Until now, we do not have a complete theory accounting for the nonequilibrium systems. The fundamental concept of a Gibbsian distribution of states in equilibrium has no counterpart in the nonequilibrium situation. This happens because many of these systems do not present even an hamiltonian function and, if it is possible to define an hamiltonian, the detailed balance would be violated.Examples of recent problems on nonequilibrium processes include markets [1, 2], rain precipitation [3], sandpiles [4] and conserved contact process [5]. There is also a great interest in modeling interface growth [6,7], traffic flow [8], temperature dependent catalytic reactions [9], etc. Nonequilibrium magnetic systems, with a well defined hamiltonian, have been also studied in the context of nonequilibrium processes [10,11] as well.For the equilibrium systems we can induce phase transitions by changing some external parameters. Usually, the temperature is the selected control parameter to study phase transitions between equilibrium states. In the case of continuous phase transitions, at the critical point, long range correlations are established inside the system and a set of critical exponents can be defined to describe the critical behavior of some thermodynamic properties. The renormalization group theory [12] is a well known theory that allows the calculation of these critical exponents.We can also consider external constraints for the nonequilibrium systems that can drive the dynamical behavior of the system. The nature of the external parameter depends on the nature of the system. For instance, in an epidemic mode...

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“…On the other hand, very recently an elaborated mean-field theory of the YK model has been developed up to the pair-approximation level [138] that yields a very accurate estimation of the coexistence point, namely P 2CO = 0.363.…”

Section: The Catalytic Reaction Between Nitrogen Monoxide and Carbon mentioning

confidence: 99%

“…The reactions given by equations (31) and (32) are assumed to be instantaneous (infinity reaction rate limit) while the limiting steps are the adsorption events given by equations (29) and (30 [134,135,136,137,138,139].…”

Section: The Catalytic Reaction Between Nitrogen Monoxide and Carbon mentioning

confidence: 99%

Critical behaviour of irreversible reaction systems

Loscar

Albano

2003

Rep. Prog. Phys.

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An introductory review on the critical behaviour of some irreversible reaction systems is presented. The study of these systems has attracted great attention during the last decades due to, on the one hand, the rich and complex underlying physics, and, on the other, their relevance to numerous technological applications in heterogeneous catalysis, corrosion and coating, development of microelectronic devices, etc. The review focuses on recent advances in the understanding of irreversible phase transitions (IPTs), providing a survey of the theoretical development in the field during the last decade, as well as a detailed discussion of relevant numerical simulations. The Langevin formulation for the treatment of second-order IPTs is discussed. Different Monte Carlo (MC) approaches are also presented in detail and the finite-size-scaling analysis of second-order IPTs is described. Special attention is devoted to the description of the recent progress in the study of first-order IPTs observed upon catalytic oxidation of carbon monoxide and the reduction of nitrogen monoxide, using lattice gas reaction models. Only brief comments are given on other reactions such as the oxidation of hydrogen, ammonia synthesis. Also, a discussion of relevant experiments is presented and measurements are compared with the numerical results. Furthermore, promising areas for further research and open questions are also addressed.

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Theory of theNO+COsurface-reaction model

Cited by 44 publications

References 29 publications

Dimer Production in a Poisoned Catalytic Model

Dimer Production in a Poisoned Catalytic Model

Catalysis with competitive reactions: static and dynamical critical behavior

Critical behaviour of irreversible reaction systems

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