1
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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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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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3
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Chen Z, Wang H, Su NQ, Duan S, Shen T, Xu X. Beyond Mean-Field Microkinetics: Toward Accurate and Efficient Theoretical Modeling in Heterogeneous Catalysis. ACS Catal 2018. [DOI: 10.1021/acscatal.8b00943] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Zheng Chen
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai, Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - He Wang
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai, Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai, Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Sai Duan
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai, Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Tonghao Shen
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai, Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai, Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
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4
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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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5
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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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6
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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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7
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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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8
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Chatterjee S, Harish R, Schütz G. Strong Reactivity Enhancement through Molecular Traffic Control in Zeolites. CHEM-ING-TECH 2013. [DOI: 10.1002/cite.201300030] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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9
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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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10
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Ackerman DM, Wang J, Evans JW. Generalized hydrodynamic treatment of the interplay between restricted transport and catalytic reactions in nanoporous materials. PHYSICAL REVIEW LETTERS 2012; 108:228301. [PMID: 23003660 DOI: 10.1103/physrevlett.108.228301] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2012] [Indexed: 06/01/2023]
Abstract
Behavior of catalytic reactions in narrow pores is controlled by a delicate interplay between fluctuations in adsorption-desorption at pore openings, restricted diffusion, and reaction. This behavior is captured by a generalized hydrodynamic formulation of appropriate reaction-diffusion equations (RDE). These RDE incorporate an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The RDE elucidate the nonexponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth.
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Affiliation(s)
- David M Ackerman
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
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11
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Liu DJ, Wang J, Ackerman DM, Slowing II, Pruski M, Chen HT, Lin VSY, Evans JW. Interplay between Anomalous Transport and Catalytic Reaction Kinetics in Single-File Nanoporous Systems. ACS Catal 2011. [DOI: 10.1021/cs200115c] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Da-Jiang Liu
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
| | - Jing Wang
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
| | - David M. Ackerman
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
| | - Igor I. Slowing
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
| | - Marek Pruski
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
| | - Hung-Ting Chen
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
| | - Victor S.-Y. Lin
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
| | - James W. Evans
- Ames Laboratory−USDOE, and ‡Departments of Mathematics, §Chemistry, and ∥Physics & Astronomy, Iowa State University, Ames Iowa 50011, United States
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12
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Ackerman DM, Wang J, Wendel JH, Liu DJ, Pruski M, Evans JW. Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior. J Chem Phys 2011; 134:114107. [PMID: 21428607 DOI: 10.1063/1.3563638] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
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.
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Affiliation(s)
- David M Ackerman
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
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13
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Liu DJ, Chen HT, Lin VSY, Evans JW. Polymer length distributions for catalytic polymerization within mesoporous materials: non-Markovian behavior associated with partial extrusion. J Chem Phys 2010; 132:154102. [PMID: 20423163 DOI: 10.1063/1.3361663] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We analyze a model for polymerization at catalytic sites distributed within parallel linear pores of a mesoporous material. Polymerization occurs primarily by reaction of monomers diffusing into the pores with the ends of polymers near the pore openings. Monomers and polymers undergo single-file diffusion within the pores. Model behavior, including the polymer length distribution, is determined by kinetic Monte Carlo simulation of a suitable atomistic-level lattice model. While the polymers remain within the pore, their length distribution during growth can be described qualitatively by a Markovian rate equation treatment. However, once they become partially extruded, the distribution is shown to exhibit non-Markovian scaling behavior. This feature is attributed to the long-tail in the "return-time distribution" for the protruding end of the partially extruded polymer to return to the pore, such return being necessary for further reaction and growth. The detailed form of the scaled length distribution is elucidated by application of continuous-time random walk theory.
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Affiliation(s)
- Da-Jiang Liu
- Ames Laboratory (USDOE), Iowa State University, Ames, Iowa 50011, USA
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14
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Liu DJ, Chen HT, Lin VSY, Evans JW. Statistical mechanical modeling of catalytic polymerization within surface-functionalized mesoporous materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:011801. [PMID: 19658720 DOI: 10.1103/physreve.80.011801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2009] [Revised: 05/06/2009] [Indexed: 05/28/2023]
Abstract
A discrete lattice model is developed to describe diffusion-mediated polymerization occurring within mesopores, where reaction is enhanced at catalytic sites distributed within the interior of the pores. Diffusive transport of monomers and polymers is one-dimensional, diffusion coefficients for the latter decreasing with polymer length. Kinetic Monte Carlo simulation is utilized to analyze model behavior focusing on a "clogging" regime, where the amount of polymer within the pores grows. We characterize the evolution of the overall and mean length of polymers, the mean number of polymers, as well as the polymer spatial and length distributions.
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Affiliation(s)
- Da-Jiang Liu
- Ames Laboratory-U.S. DOE, Department of Chemistry, Iowa State University Ames, Iowa 50011, USA
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15
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Sheintuch M, Efremenko I. Analysis of a carbon membrane reactor: from atomistic simulations of single-file diffusion to reactor design. Chem Eng Sci 2004. [DOI: 10.1016/j.ces.2004.09.016] [Citation(s) in RCA: 4] [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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16
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Nedea SV, Jansen APJ, Lukkien JJ, Hilbers PAJ. Infinitely fast diffusion in single-file systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046707. [PMID: 12786529 DOI: 10.1103/physreve.67.046707] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2002] [Indexed: 05/24/2023]
Abstract
We have used dynamic Monte Carlo(DMC) methods and analytical techniques to analyze single-file systems for which diffusion is infinitely fast. We have simplified the master equation removing the fast reactions, and we have introduced a DMC algorithm for infinitely fast diffusion. The DMC method for fast diffusion give similar results as the standard DMC with high diffusion rates. We have investigated the influence of characteristic parameters, such as pipe length, adsorption, desorption, and conversion rate constants on the steady-state properties of single-file systems with a reaction, looking at cases when all the sites are reactive and when only some of them are reactive. We find that the effect of fast diffusion on single-file properties of the system is absent even when diffusion is infinitely fast. Diffusion is not important in these systems. Smaller systems are less reactive and the occupancy profiles for infinitely long systems show an exponential behavior.
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Affiliation(s)
- S V Nedea
- Department of Mathematics and Computer Science, Technical University of Eindhoven, PO Box 513, 5600 MB Eindhoven, The Netherlands.
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Jansen APJ, Nedea SV, Lukkien JJ. Analytical results for the reactivity of a single-file system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:036104. [PMID: 12689129 DOI: 10.1103/physreve.67.036104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2002] [Indexed: 05/24/2023]
Abstract
We derive analytical expressions for the reactivity of a single-file system with fast diffusion and particles entering and leaving the system at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of particles entering and leaving the system. For large systems, the number of unconverted particles decreases exponentially with distance from the open end.
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Affiliation(s)
- A P J Jansen
- Department of Chemical Engineering, ST/SKA Schuit Institute of Catalysis, Eindhoven University of Technology, P.O. Box 513, The Netherlands.
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