Mean field treatment of heterogeneous steady state kinetics

Abstract

We propose a method to quickly compute steady state populations of species undergoing a set of chemical reactions whose rate constants are heterogeneous. Using an average environment in place of an explicit nearest neighbor configuration, we obtain a set of equations describing a single fluctuating active site in the presence of an averaged bath. We apply this Mean Field Steady State (MFSS) method to a model of H 2 production on a disordered surface for which the activation energy for the reaction varies from site to site. The MFSS populations quantitatively reproduce the KMC results across the range of rate parameters considered.

Heterogeneous Pair Approximation of Methanol Oxidation on TiO2 Reveals Two Reaction Pathways

“…The mean-field steady state (MFSS) method can be obtained by setting the left hand side of the HMF equations to zero and solving to obtain the steady state probabilities. 30,31 Notice that terms of the form, k BA→Y X [B] , appear in the equations. These are not the same as k BA→Y X [B] .…”

“…In this paper, we propose a novel method to simulate the chemical kinetics of methanol oxidation on TiO 2 . Combining the intuitions of the mean-field steady state (MFSS) method 30,31 and the pair approximation (PA), [32][33][34][35] we take representative pairs of sites and place them in a self-consistent bath of the average pairwise correlation. Then, we pre-average over the static disorder in one site of each pair, which gives a considerable reduction in the computational costs.…”

Machine learning dynamic correlation in chemical kinetics

“…SI). Assuming Markovian processes and an a priori knowledge of the rate constants, CME gives an exact treatment of both static disorder (site-to-site variations that are reflected in the rate constants, k Ψ→Φ ) 43,44 and dynamic correlation (segregation and self-organization of reactants that manifest on the explicit lattice configurations, Ψ). 45,46 In the present investigation, we assume no static disorder and consider dynamic correlation only.…”

Machine Learning Dynamic Correlation in Chemical Kinetics

“…where k Ψ→Φ is a sum of the elementary rate constants, if any, that would take a lattice in configuration Ψ to configuration Φ. Assuming Markovian processes and an a priori knowledge of the rate constants, CME gives an exact treatment of both static disorder (site-to-site variations that are reflected in the rate constants, k Ψ→Φ ) 57,58 and dynamic correlation (segregation and self-organization of reactants that manifest on the explicit lattice configurations, Ψ). 52,53 Unfortunately, the dimensionality of CME scales as S L , where S is the number of species and L is the number of sites on the lattice, making CME intractable in many systems of practical relevance.…”