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Lai KC, Pleasant TJ, García A, Evans JW. Generalized hydrodynamic analysis of transport through a finite open nanopore for two-component single-file systems. Phys Rev E 2020; 101:062103. [PMID: 32688593 DOI: 10.1103/physreve.101.062103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2020] [Accepted: 04/28/2020] [Indexed: 11/07/2022]
Abstract
Single-file diffusion (SFD) in finite open nanopores is characterized by nonzero spatially varying tracer diffusion coefficients within a generalized hydrodynamic description. This contrasts with infinite SFD systems where tracer diffusivity vanishes. In standard tracer counterpermeation (TCP) analysis, two reservoirs, each containing a different species, are connected to opposite ends of a finite pore. We implement an extended TCP analysis to allow the two reservoirs to contain slightly different mixtures of the two species. Then, determination of diffusion fluxes through the pore allows extraction of diffusion coefficients for near-constant partial concentrations of the two species. This analysis is applied for a lattice-gas model describing two-component SFD through a finite linear pore represented by a one-dimensional array of cells. Two types of particles, A and B, can hop only to adjacent empty cells with generally different rates, h_{A} and h_{B}. Particles are noninteracting other than exclusion of multiple cell occupancy. Results reveal generalized hydrodynamic tracer diffusion coefficients which adopt small values inversely proportional to pore length in the pore center, but which are strongly enhanced near pore openings.
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Affiliation(s)
- King C Lai
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA
| | - Tyler J Pleasant
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
| | - Andrés García
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
| | - James W Evans
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA.,Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
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2
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Jin W, van Ommen JR, Kleijn CR. Moving reaction fronts in fractal nanoparticle agglomerates. Chem Eng Sci 2019. [DOI: 10.1016/j.ces.2019.05.027] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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García A, Slowing II, Evans JW. Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica. J Chem Phys 2018; 149:024101. [DOI: 10.1063/1.5037618] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andres García
- Division of Chemical and Biological Sciences, Ames Laboratory USDOE, Iowa State University, Ames, Iowa 50010, USA
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50010, USA
| | - Igor I. Slowing
- Division of Chemical and Biological Sciences, Ames Laboratory USDOE, Iowa State University, Ames, Iowa 50010, USA
- Department of Chemistry, Iowa State University, Ames, Iowa 50010, USA
| | - James W. Evans
- Division of Chemical and Biological Sciences, Ames Laboratory USDOE, Iowa State University, Ames, Iowa 50010, USA
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50010, USA
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Ackerman DM, Evans JW. Tracer counterpermeation analysis of diffusivity in finite-length nanopores with and without single-file dynamics. Phys Rev E 2017; 95:012132. [PMID: 28208315 DOI: 10.1103/physreve.95.012132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2016] [Indexed: 11/07/2022]
Abstract
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.
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Affiliation(s)
- David M Ackerman
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Mechanical Engineering, Iowa State University, Ames, Iowa 50011, USA
| | - James W Evans
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Physics & Astronomy and Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
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García A, Evans JW. Catalytic conversion in nanoporous materials: Concentration oscillations and spatial correlations due to inhibited transport and intermolecular interactions. J Chem Phys 2016; 145:174705. [PMID: 27825244 DOI: 10.1063/1.4966543] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
We show that steady-state catalytic conversion in nanoporous materials can occur in a quasi-counter-diffusion mode with the reactant (product) concentration strongly decaying (growing) into the pore, but also with oscillations in the total concentration. These oscillations reflect the response of the fluid to the transition from an extended to a confined environment near the pore opening. We focus on the regime of strongly inhibited transport in narrow pores corresponding to single-file diffusion. Here, limited penetration of the reactant into the pores and the associated low reaction yield is impacted by strong spatial correlations induced by both reaction (non-equilibrium correlations) and also by intermolecular interactions (thermodynamic correlations). We develop a generalized hydrodynamic formulation to effectively describe inhibited transport accounting for the effect of these correlations, and incorporate this description of transport into appropriate reaction-diffusion equations. These equations accurately describe both shorter-range concentration oscillations near the pore opening and the longer-range mesoscale variation of concentration profiles in the pore (and thus also describe reaction yield). Success of the analytic theory is validated by comparison with a precise kinetic Monte Carlo simulation of an appropriate molecular-level stochastic reaction-diffusion model. This work elucidates unconventional chemical kinetics in interacting confined systems.
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Affiliation(s)
- Andrés García
- Division of Chemical & Biological Sciences, Ames Laboratory-U.S. Department of Energy and Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA
| | - James W Evans
- Division of Chemical & Biological Sciences, Ames Laboratory-U.S. Department of Energy and Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA
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García A, Wang J, Windus TL, Sadow AD, Evans JW. Catalytic conversion reactions in nanoporous systems with concentration-dependent selectivity: Statistical mechanical modeling. Phys Rev E 2016; 93:052137. [PMID: 27300859 DOI: 10.1103/physreve.93.052137] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2016] [Indexed: 11/07/2022]
Abstract
Statistical mechanical modeling is developed to describe a catalytic conversion reaction A→B^{c} or B^{t} with concentration-dependent selectivity of the products, B^{c} or B^{t}, where reaction occurs inside catalytic particles traversed by narrow linear nanopores. The associated restricted diffusive transport, which in the extreme case is described by single-file diffusion, naturally induces strong concentration gradients. Furthermore, by comparing kinetic Monte Carlo simulation results with analytic treatments, selectivity is shown to be impacted by strong spatial correlations induced by restricted diffusivity in the presence of reaction and also by a subtle clustering of reactants, A.
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Affiliation(s)
- Andrés García
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA
| | - Jing Wang
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
| | - Theresa L Windus
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
| | - Aaron D Sadow
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
| | - James W Evans
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA.,Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
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Liu DJ, Garcia A, Wang J, Ackerman DM, Wang CJ, Evans JW. Kinetic Monte Carlo Simulation of Statistical Mechanical Models and Coarse-Grained Mesoscale Descriptions of Catalytic Reaction–Diffusion Processes: 1D Nanoporous and 2D Surface Systems. Chem Rev 2015; 115:5979-6050. [DOI: 10.1021/cr500453t] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Da-Jiang Liu
- 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
| | - Andres Garcia
- 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
| | - Jing Wang
- 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
| | - David M. Ackerman
- 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
| | - Chi-Jen Wang
- 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
| | - 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
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Liu DJ, Evans JW. Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure. J Chem Phys 2015; 142:134703. [DOI: 10.1063/1.4916380] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - James W. Evans
- Ames Laboratory USDOE, Ames, Iowa 50011, USA
- Departments of Physics & Astronomy and Mathematics, Iowa State University, Ames, Iowa 50011, USA
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Wang CJ, Ackerman DM, Slowing II, Evans JW. Langevin and fOkker-Planck analyses of inhibited molecular passing processes controlling transport and reactivity in nanoporous materials. PHYSICAL REVIEW LETTERS 2014; 113:038301. [PMID: 25083666 DOI: 10.1103/physrevlett.113.038301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2014] [Indexed: 06/03/2023]
Abstract
Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P ∼ (R-R(c))(σ), where passing is sterically blocked for R≤R(c), with σ below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules.
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Affiliation(s)
- Chi-Jen Wang
- Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA and Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
| | - David M Ackerman
- Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - Igor I Slowing
- Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA and Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
| | - James W Evans
- Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
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Leibovich N, Barkai E. Everlasting effect of initial conditions on single-file diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032107. [PMID: 24125214 DOI: 10.1103/physreve.88.032107] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2013] [Indexed: 06/02/2023]
Abstract
We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one-dimensional channel (a single-file model). In particular, we examine the influence of initial conditions on the dynamics of the tagged particle. We compare two initial conditions: equal distances between particles and uniform density distribution. The effect is shown by the differences of mean-square-displacement and correlation function for the two ensembles of initial conditions. We discuss the violation of Einstein relation, and its dependence on the initial condition, and the difference between time and ensemble averaging. More specifically, using the Jepsen line, we will discuss how transport coefficients, like diffusivity, depend on the initial state. Our work shows that initial conditions determine the long time limit of the dynamics, and in this sense the system never forgets its initial state in complete contrast with thermal systems (i.e., a closed system that attains equilibrium independent of the initial state).
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Affiliation(s)
- N Leibovich
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
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Wang J, Ackerman DM, Lin VSY, Pruski M, Evans JW. Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling. J Chem Phys 2013; 138:134705. [DOI: 10.1063/1.4798463] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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