Unstable and Oscillatory Behaviour in Heterogeneous Catalysis

Wicke, E.; Kummann, P.; Keil, Werner; Schiefler, Jan

doi:10.1002/bbpc.19800840405

Cited by 126 publications

(25 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The two saturated phases meet the reactive phase at a bicritical point [16] at a critical value of r = r c . In the case of r = 1, the reactive region no longer exists [18,19] and the only transition line is the first-order discontinuous line between the saturated phases. Another model in which the adsorption repulsion is not symmetric (only A's feel the repulsion) has been studied [17], and its critical behavior was found to be in the DP universality class.…”

Section: The Modelmentioning

confidence: 99%

Mean-field analysis and Monte Carlo study of an interacting two-species reaction model

1997

View full text Add to dashboard Cite

We study the phase diagram and critical behavior of an interacting one dimensional two species monomer-monomer catalytic surface reaction model with a reactive phase as well as two equivalent adsorbing phase where one of the species saturates the system. A mean field analysis including correlations up to triplets of sites fails to reproduce the phase diagram found by Monte Carlo simulations. The three phases coexist at a bicritical point whose critical behavior is described by the even branching annihilating random walk universality class. This work confirms the hypothesis that the conservation modulo 2 of the domain walls under the dynamics at the bicritical point is the essential feature in producing critical behavior different from directed percolation. The interfacial fluctuations show the same universal behavior seen at the bicritical point in a three-species model, supporting the conjecture that these fluctuations are a new universal characteristic of the model. 05.70.Ln, 82.20.Mj, 82.65.Jv, 64.60.Kw

show abstract

Section: The Modelmentioning

confidence: 99%

Mean-field analysis and Monte Carlo study of an interacting two-species reaction model

1997

View full text Add to dashboard Cite

show abstract

“…This research area continues to be [31][32][33] of particular interest because of its diverse applications in pharmaceuticals, separation devices, microelectronics, magnetics, catalysts, etc. The first MC simulation of surface kinetics appeared in Wicke et al [34]. However, it was the work of Ziff and co-workers [35] in 1986 that 'ignited' mainly the physics community in investigating non-equilibrium phase transitions using the MC method.…”

Section: Introductionmentioning

confidence: 98%

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

Chatterjee

Vlachos

2007

J Computer-Aided Mater Des

416

400

View full text Add to dashboard Cite

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ -leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ -leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption-desorption, surface diffusion, and phase transitions.

show abstract

“…In modeling heterogeneous catalysis [1], the monomermonomer surface reaction model plays an important role, at least from the theoretical point of view since an appealing simplicity of this model allows one to examine several issues analytically. In particular, investigations of the monomer-monomer model clarified the role of fluctuations [2][3][4][5][6][7][8], interfacial roughening [9], diffusion of the adsorbants [10], and surface disorder [11]. In the simplest situation (no diffusion, no disorder, etc.…”

mentioning

confidence: 99%

Exact results for kinetics of catalytic reactions

1996

View full text Add to dashboard Cite

The kinetics of an irreversible catalytic reaction on a substrate of arbitrary dimension is examined. In the limit of infinitesimal reaction rate (reaction-controlled limit), we solve the dimer-dimer surface reaction model (or voter model) exactly in arbitrary dimension D. The density of reactive interfaces is found to exhibit a power law decay for D < 2 and a slow logarithmic decay in two dimensions. We discuss the relevance of these results for the monomer-monomer surface reaction model. PACS numbers: 05.40.+j, 68.10.Jy, 82.20.Mj In modeling heterogeneous catalysis [1], the monomermonomer surface reaction model plays an important role, at least from the theoretical point of view since an appealing simplicity of this model allows one to examine several issues analytically. In particular, investigations of the monomer-monomer model clarified the role of fluctuations [2][3][4][5][6][7][8], interfacial roughening [9], diffusion of the adsorbants [10], and surface disorder [11]. In the simplest situation (no diffusion, no disorder, etc.), it was found that single-species clusters grow with time when the dimensionality D of the substrate is sufficiently small, D ≤ 2. However, the details of the coarsening like the decay rate of the density of reactive interfaces remain uncertain in two dimensions, -simulations [5,12,13] revealed a very slow decay which could be logarithmic or power law with a small exponent. In this paper, we clarify these questions by computing analytically kinetic characteristics of an idealized version of the monomer-monomer model, the voter model. We then expand these results and perform numerical simulations for the full model.The monomer-monomer surface reaction process can be schematically represented by the following kinetic steps:A and B particles impinge upon a surface, with respective rates k A and k B , and adsorb onto vacant sites V to form a monolayer of adsorbed particles, A V and B V . Nearest-neighbor pairs of dissimilar adsorbed particles, A V B V , react and desorb with rate k r , leaving behind two vacancies. For k A = k B , the adsorption imbalance leads to the quick saturation of the surface by the majority species. For k A = k B and for dimensions D ≤ 2, there is a fluctuation-induced coarsening of the surface into growing A and B adsorbed islands. This nontrivial case of equal adsorption rates will be considered in the following. Furthermore, in theoretical analysis we will restrict ourselves to the reaction-controlled limit, k r ≪ k A = k B , which was found to provide qualitatively the same behavior as the general case [4,6] but more amenable to theoretical treatment. In the reaction-controlled limit, the substrate quickly becomes completely covered and then stays covered forever, since in units of the typical, i.e. adsorption, time interval unoccupied sites are refilled instantaneously. The kinetics of the monomer-monomer surface reaction model is conveniently described by a mapping onto the Ising model with mixed zero-temperature voter dynamics and infinite-temperature...

show abstract

Unstable and Oscillatory Behaviour in Heterogeneous Catalysis

Cited by 126 publications

References 21 publications

Mean-field analysis and Monte Carlo study of an interacting two-species reaction model

Mean-field analysis and Monte Carlo study of an interacting two-species reaction model

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

Exact results for kinetics of catalytic reactions

Contact Info

Product

Resources

About