From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations

Abstract

Atomistic lattice-gas models for surface reactions can accurately describe spatial correlations and ordering in chemisorbed layers due to adspecies interactions or due to limited mobility of some adspecies. The primary challenge in such modeling is to describe spatiotemporal behavior in the physically relevant "hydrodynamic" regime of rapid diffusion of (at least some) reactant adspecies. For such models, we discuss the development of exact reaction-diffusion equations (RDEs) describing mesoscale spatialpattern formation in surface reactions. Formulation and implementation of these RDEs requires detailed analysis of chemical diffusion in mixed reactant adlayers, as well as development of novel hybrid and parallel simulation techniques. Disciplines Mathematics | Physics CommentsThe following article appeared in Chaos 12, 1 (2002) Atomistic lattice-gas models for surface reactions can accurately describe spatial correlations and ordering in chemisorbed layers due to adspecies interactions or due to limited mobility of some adspecies. The primary challenge in such modeling is to describe spatiotemporal behavior in the physically relevant ''hydrodynamic'' regime of rapid diffusion of ͑at least some͒ reactant adspecies. For such models, we discuss the development of exact reaction-diffusion equations ͑RDEs͒ describing mesoscale spatial pattern formation in surface reactions. Local adsorption, desorption, and reaction processes occurring in surface reactions, when combined with surface diffusion, produce a diverse variety of spatiotemporal pattern formation. A key feature of these systems is that both the hysteresis often observed in the reaction kinetics, and the characteristic length of spatial patterns on the order of m, are controlled by the very rapid surface diffusion of at least some reactant adspecies. Many aspects of these phenomena have been successfully elucidated via mean-field reaction-diffusion equation modeling, in which the effects of adlayer ordering are neglected or treated approximately. A more fundamental approach is presented here based on atomistic lattice-gas "LG… models. One could attempt direct simulation of atomistic LG models, but this approach is complicated by the large separation of time and length scales "due to adspecies hop rates many orders of magnitude above other rates…. Thus, we have developed another more appropriate strategy to ''exactly'' connect-the-length-scales from these atomistic LG models to the mesoscale pattern formation. Specifically, we treat directly this ''hydrodynamic'' regime of large hop rates utilizing special simulation models and procedures, coupled with a correct description of chemical diffusion in mixed reactant adlayers. This leads to development of exact reaction-diffusion equations for the hydrodynamic regime. In this report, we pay particular attention to recent developments in the description of chemical diffusion, which has a complicated tensorial nature since the presence of one adspecies can interfere with the diffusion of coadsorbed adspecies.

Polymer length distributions for catalytic polymerization within mesoporous materials: Non-Markovian behavior associated with partial extrusion

“…[16][17][18][19][20] The key feature of these KMC simulations is that processes are implemented with probabilities proportional to their rates.…”

Fluctuations and bistability in a “hybrid” atomistic model for CO oxidation on nanofacets: An effective potential analysis

“…However, the actual behavior of CO oxidation is rather different, although still complex: certainly there are nontrivial spatial correlations ͑e.g., in the oxygen adlayer due to strong NN repulsions and due to limited mobility͒ which cannot be described by MF treatments, but the rapid mobility of adsorbed CO ensures the existence of MF type bistability rather than equilibrium Ising-type discontinuous transitions. 17,18 The latter observation has prompted development of ''hybrid'' models for CO oxidation which incorporate nontrivial spatial correlations in the oxygen adlayer using a lattice-gas treatment, but which also account for bistability induced by rapid CO mobility via a MF treatment of CO. [17][18][19][20][21] These type of hybrid atomistic models raise interesting new questions for the analysis of fluctuation-induced transitions in ͑small͒ finite systems. Despite the incorporation of nontrivial spatial correlations, is behavior analogous to traditional mean-field stochastic reaction models, or is it fundamentally different ͑e.g., as in equilibrium Ising systems͒?…”

Chemical diffusion of CO in mixed CO+O adlayers and reaction-front propagation in CO oxidation on Pd(100)

“…Input to these RDEs requires description of both the reaction kinetics and transport properties for generally nonequilibrium nonsteady states distributed across the front. 10,14,19 These states are described below as "front states." The standard strategy to analyze the above RDEs is to adopt a mean-field form for the reaction kinetics terms ͑which then just depend on coverages͒ assuming a "wellstirred" spatially randomized reactant adlayer, and to assume a simple Fick's law expression for J CO =−D CO ٌ CO with constant D CO .…”

“…An alternative and practical approach potentially allowing precise analysis of the exact RDEs is to implement a heterogeneous multiscale modeling strategy. 20 Specifically, using our heterogeneous coupled lattice-gas ͑HCLG͒ approach, 10,14,19,21 one can perform parallel simulations of an atomistic latticegas model for the reaction, where individual simulations correspond to distinct macroscopic points distributed across the spatial pattern. We simultaneously extract from these simulations a precise characterization of both the local reaction kinetics and transport coefficients for chemical diffusion, and use the latter to suitably couple the parallel simulations to describe mesoscale surface diffusion.…”

“…Despite this fact, there has been little consideration of chemical diffusion in mixed adlayers, which are of relevance to these surface reaction systems. The primary exceptions are some analyses for LG models of ideal mixed adlayers ͑i.e., noninteracting adlayers except for exclusion of double-site occupancy͒ where both species are mobile, [10][11][12] and of stochastic mesoscale mean-field models 13 and simplistic LG models, [14][15][16][17] where one species is mobile and the other͑s͒ are immobile. In the latter case, one must effectively consider a percolative-type transport problem.…”