Interplay between Anomalous Transport and Catalytic Reaction Kinetics in Single-File Nanoporous Systems

Abstract

Functionalized nanoporous materials have broad utility for catalysis applications. However, the kinetics of catalytic reaction processes in these systems can be strongly impacted by the anomalous transport. The most extreme case corresponds to single-file diffusion for narrow pores in which species cannot pass each other. For conversion reactions with a single-file constraint, traditional mean-field-type reaction-diffusion equations fail to capture the initial evolution of concentration profiles, and they cannot describe the scaling behavior of steady-state reactivity. Hydrodynamic reaction-diffusion equations accounting for the single-file aspects of chemical diffusion can describe such initial evolution, but additional refinements are needed to incorporate fluctuation effects controlling, for example, steady-state reactivity localized near pore openings. For polymerization reactions with a single-file constraint, initial behavior depends strongly on system details such as catalytic site loading and reaction rate. However, long-time behavior often involves the formation of a dominant large polymer near each end of the pore, initially within the pore but subsequently partly extruding. In this partial extrusion regime, the kinetics is governed by the special features of the random walk describing the motion of the end of the partly extruded polymer, noting that this extruded end must return within the pore for further growth.

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

“…As noted in previous studies, catalytic activity is also strongly dependent on the propensity for passing of reactants and products within the pores. 9,14,15,21 Our generalized hydrodynamic formulation of reaction-diffusion phenomena provides an efficient tool to explore behavior over a broad phase-space of model parameters. This approach can reliably capture the complex interplay between reaction and restricted transport which results in subtle spatial correlations and fluctuations of reactants and products within the pore.…”

“…20 To account for the finite length of pores, we have considered a refinement of the DH choice where F tr ∼ 1/L for SFD when P ex = 0. 21 This modified choice was motivated by analyses of transport through channels across membranes of finite width. 22 near pore openings, and thus underestimates the overall reactivity.…”

“…22 near pore openings, and thus underestimates the overall reactivity. 21 To address the shortcomings of the MF and DH approaches described above, we will utilize a GH treatment 23 which incorporates a position-dependent F tr (x = na) = F tr (GH). This F tr (x = na) is enhanced near pore openings above the deterministic hydrodynamic value of F tr (DH).…”

Conversion Reactions in Surface-Functionalized Mesoporous Materials: Effect of Restricted Transport and Catalytic Site Distribution

“…Passing of A with other A (or B with B) is not significant. Several previous analyses exist for the case of single-file diffusion [8][9][10][11][12][13][14][15] revealing that reactivity is strongly localized near the pore openings in this case of no-passing [9]. A perception exists that a simple mean-field (MF) type treatment of chemical diffusion (see below) is adequate [11].…”

“…This feature motivated our development of an alternative "hydrodynamic" description of chemical diffusion which effectively captures the single-file constraint [13]. However, this formulation did not incorporate finite-size or fluctuation effects, so additional refinement was necessary to achieve quantitative predictive capability [14,15]. We also note that an effective alternative for precise characterization of model behavior is Kinetic Monte Carlo (KMC) simulation.…”