Kinetic Monte Carlo Simulation of Statistical Mechanical Models and Coarse-Grained Mesoscale Descriptions of Catalytic Reaction–Diffusion Processes: 1D Nanoporous and 2D Surface Systems

Abstract

Traditional mean-field rate equations of chemical kinetics for spatially uniform systems1−3 and the corresponding reaction−diffusion equations describing spatial heterogeneity4−6 have proved immensely useful in elucidating catalytic processes. However, it is well-recognized that standard mean-field rate expressions neglect spatial correlations in the reactant and/or product distribution. It is less well appreciated that the standard treatment of diffusion is generally applicable only at low concentrations and in unrestricted environments.

Tracer counterpermeation analysis of diffusivity in finite-length nanopores with and without single-file dynamics

“…Separate equations can be obtained for the two-cell pair probabilities appearing in the flux terms which couple to triple-cell probabilities, etc. Two-cell spatial correlations control the flux, and we find that these are significant for small P ex [19,20]. Despite the last observation, it is instructive to consider mean-field (MF) type factorization approximations to the above equations.…”

“…Finally, we also note that adding equations for B j and R j yields classic discrete diffusion equations for d/dt X j = −∇J X (j > j + 1) where J X (j > j + 1) = − h∇ X j exploiting an exact cancellation of pair probability terms [19,27]. For the initial value problem considered in this study, at t = 0 for all j , we set X j = X 0 the external reservoir concentration, and thus these quantities do not change in time.…”

“…As an aside, we also note that recently a different strategy was introduced to analyze generalized tracer diffusivity in these above types of systems based on tracking of a tagged walker [19,20]. The tagged walker starts at a specified location x inside the porous system of finite width and wanders among a prescribed density of untagged particles.…”

“…Perhaps closer to the TCP scenario are finite or semi-infinite lattice-gas reaction-diffusion systems with SFD or less restrictive inhibited passing. In these systems, reaction induces subtle positive clustering correlations [19,25].…”

Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure

“…37 Thus, we expect a discontinuous CO-poisoning transition in our current reaction model for d = 2 with very low or zero d O2 provided that one sufficiently reduces d CO . 38 Since we operate in the reaction-limited rather than adsorption-limited regime (with k = 0.01) with negligible desorption, reaction creates rare empty site pairs which are filled by CO with rate 2p CO or with O 2 at rate p O2 /2. Thus, adsorption balance requires that the transition occurs at around p CO /p O2 = 1 /4.…”