Mean-field hierarchical equations for some A+BC catalytic reaction models

Abstract

A mean-field study of the (A+BC→AC+12B2) system is developed from hierarchical equations, considering mechanisms that include dissociation, reaction with finite rates, desorption, and diffusion of the adsorbed species. The phase diagrams are compared to Monte Carlo simulations.

Lattice-gas study of the kinetics of catalytic conversion of NO–CO mixtures on rhodium surfaces

“…1,2 The catalytic reduction of NO to N 2 on rhodium has been heavily investigated both experimentally [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and theoretically [22][23][24][25][26][27][28][29][30][31][32][33][34][35] for many years. The key steps of this reaction have long been thought to be the breaking of the N-O bond in NO upon chemisorption on the metal and the subsequent recombination of surface nitrogen atoms to form N 2 .…”

Theory of theNO+COsurface-reaction model

“…(Various aspects of incomplete dissociation are considered in Refs. [15][16][17].) As noted above, reactions are assumed to occur instantaneously: nearest-neighbor CO-O and N-N pairs cannot reside on the lattice.…”

“…Truncated at the 1-site level, the hierarchy of equations governing the cluster probabilities yields a reasonable estimate for y 2 on the triangular lattice [8,9], but places the continuous transition at y 1 = 0. Cortés et al derived a pair approximation for the NO+CO model including CO-desorption, using finite reaction rates [17]. Kortlüke, Kuzovkov and von Niessen (KKN) derived a very accurate prediction for y 1 on the triangular lattice using a two-site cluster approximation [18].…”

Dynamic Monte Carlo Simulation of the NO + CO Reaction on Rh(111)

“…The catalytic reduction of NO by CO (and other reducing agents) promoted by transition metals has received a great deal of attention in connection with its relevance to problems of pollution control in the atmosphere. − To date, rhodium has proven to be the best catalyst for this reduction . Extensive experimental investigations using model surfaces have also shown that Rh(111), the expected predominant facet in metal nanoclusters dispersed on catalyst supports, is especially adept for the promotion of this reaction. − Consequently, much theoretical modeling has been performed to attempt to understand its kinetics. − In spite of the extensive past work in this area, however, renewed interest has emerged in the past few years because of new molecular-level information about the reaction mechanism derived from new experimental and theoretical reports.…”

“…Theoretical studies on the kinetics of the NO + CO surface reaction have so far focused mainly on establishing the precise conditions under which a reactive state can be sustained, that is, on calculating steady-state phase diagrams and characterizing the window of parameters under which the reaction operates. This window is usually limited by two kinetic phase transitions, so much emphasis has been placed on identifying how such a phase diagram is affected by different assumptions in the molecular mechanism. − ,− In view of the complexity of the reaction, lattice-gas models and Monte Carlo simulations have been the main techniques used for these studies. The theoretical work has followed the evolution of experimental findings and has evolved from early studies based on classical reaction schemes 13-16,18,27-29 to more recent calculations that progressively incorporate new molecular-beam experimental findings. ,− …”