David M. Ackerman

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

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. Disciplines Astrophysics and Astronomy | Biological and Chemical Physics | Mathematics | Physics Comments Reprinted (adapted) with permission from Chemical Reviews 115 (2015): 5979,doi:10.1021/cr500453t . Copyright 2015 American Chemical Society. Authors Da-Jiang Liu, Andrés Garcia, Jing Wang, David M. Ackerman, Chi-Jen Wang, and James W. Evans This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/176 Kinetic Monte Carlo Simulation of Statistical Mechanical Models and Coarse-Grained Mesoscale Descriptions of Catalytic Reaction− Diffusion Processes: 1D Nanoporous and 2D Surface Systems Da-Jiang Liu,† Andres Garcia,†,‡ Jing Wang,†,§ David M. Ackerman,† Chi-Jen Wang,†,§,# and James W. Evans*,†,‡,§ †Ames LaboratoryUSDOE, Division of Chemical and Biological Sciences, ‡Department of Physics & Astronomy, and Department of Mathematics, Iowa State University, Ames, Iowa 50011, United States

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

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

Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport.

Boundary Conditions for Burton–Cabrera–Frank Type Step-Flow Models: Coarse-Graining of Discrete 2D Deposition-Diffusion Equations

We analyze discrete two-dimensional (2D) deposition-diffusion equations for the density of adatoms deposited at a periodic array of adsorption sites on a vicinal crystalline surface with kinked steps. Our analysis provides insight into the appropriate boundary conditions (BC) at steps for a coarse-grained Burton–Cabrera–Frank (BCF) type treatment involving continuum 2D deposition-diffusion equations. Such a BCF type treatment should describe step flow on vicinal surfaces under nonequilibrium growth conditions. We focus on cases where there is no additional activation barrier inhibiting to attachment at steps beyond that for terrace diffusion. Then, the classical BCF treatment simply imposes a Dirichlet BC equating the limiting value of the terrace adatom density to its equilibrium value at the step edge. Our analysis replaces this BC with one incorporating finite kinetic coefficients,

Tracer Counterpermeation Analysis of Diffusivity in Finite-length Nanopores with and without Single-file Dynamics

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A finite element approach to self-consistent field theory calculations of multiblock polymers

, measuring inhibited diffusion-limited attachment at kinks. We determine the dependence of

A real-time phenotyping framework using machine learning for plant stress severity rating in soybean

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

We perform a tracer counterpermeation (TCP) analysis for a stochastic model of diffusive transport through a narrow linear pore where passing of species within the pore is inhibited or even excluded (single-file diffusion). TCP involves differently labeled but otherwise identical particles from two decoupled infinite reservoirs adsorbing into opposite ends of the pore, and desorbing from either end. In addition to transient behavior, we assess steady-state concentration profiles, spatial correlations, particle number fluctuations, and diffusion fluxes through the pore. From the profiles and fluxes, we determine a generalized tracer diffusion coefficient D_{tr}(x), at various positions x within the pore. D_{tr}(x) has a plateau value in the pore center scaling inversely with the pore length, but it is enhanced near the pore openings. The latter feature reflects the effect of fluctuations in adsorption and desorption, and it is also associated with a nontrivial scaling of the concentration profiles near the pore openings.

Generalized Hydrodynamic Treatment of the Interplay between Restricted Transport and Catalytic Reactions in Nanoporous Materials

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.