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Nelson A, Kalyuzhnyi Y, Patsahan T, McCabe C. Liquid-vapor phase equilibrium of a simple liquid confined in a random porous media: Second-order Barker-Henderson perturbation theory and scaled particle theory. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2019.112348] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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2
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Qiao CZ, Zhao SL, Liu HL, Dong W. Fluids in porous media. IV. Quench effect on chemical potential. J Chem Phys 2017. [PMID: 28641429 DOI: 10.1063/1.4984773] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
It appears to be a common sense to measure the crowdedness of a fluid system by the densities of the species constituting it. In the present work, we show that this ceases to be valid for confined fluids under some conditions. A quite thorough investigation is made for a hard sphere (HS) fluid adsorbed in a hard sphere matrix (a quench-annealed system) and its corresponding equilibrium binary mixture. When fluid particles are larger than matrix particles, the quench-annealed system can appear much more crowded than its corresponding equilibrium binary mixture, i.e., having a much higher fluid chemical potential, even when the density of each species is strictly the same in both systems, respectively. We believe that the insight gained from this study should be useful for the design of functionalized porous materials.
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Affiliation(s)
- C Z Qiao
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Chimie, UMR 5182, 46, Allée d'Italie, 69364 Lyon Cedex 07, France
| | - S L Zhao
- School of Chemical Engineering and State Key Laboratory of Chemical Engineering, East China University of Science and Technology, 130 Meilong Road, 200237 Shanghai, China
| | - H L Liu
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, 130 Meilong Road, 200237 Shanghai, China
| | - W Dong
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Chimie, UMR 5182, 46, Allée d'Italie, 69364 Lyon Cedex 07, France
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3
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The scientific life of Vojko Vlachy. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.11.073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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4
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Lomba E, Bores C, Sánchez-Gil V, Noya EG. A three dimensional integral equation approach for fluids under confinement: Argon in zeolites. J Chem Phys 2015; 143:164703. [PMID: 26520539 DOI: 10.1063/1.4934230] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we explore the ability of an inhomogeneous integral equation approach to provide a full three dimensional description of simple fluids under conditions of confinement in porous media. Explicitly, we will consider the case of argon adsorbed into silicalite-1, silicalite-2, and an all-silica analogue of faujasite, with a porous structure composed of linear (and zig-zag in the case of silicalite-1) channels of 5-8 Å diameter. The equation is based on the three dimensional Ornstein-Zernike approximation proposed by Beglov and Roux [J. Chem. Phys. 103, 360 (1995)] in combination with the use of an approximate fluid-fluid direct correlation function furnished by the replica Ornstein-Zernike equation with a hypernetted chain closure. Comparison with the results of grand canonical Monte Carlo/molecular dynamics simulations evidences that the theory provides an accurate description for the three dimensional density distribution of the adsorbed fluid, both at the level of density profiles and bidimensional density maps across representative sections of the porous material. In the case of very tight confinement (silicalite-1 and silicalite-2), solutions at low temperatures could not be found due to convergence difficulties, but for faujasite, which presents substantially larger channels, temperatures as low as 77 K are accessible to the integral equation. The overall results indicate that the theoretical approximation can be an excellent tool to characterize the microscopic adsorption behavior of porous materials.
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Affiliation(s)
- Enrique Lomba
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - Cecilia Bores
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - Vicente Sánchez-Gil
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - Eva G Noya
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
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Lomba E, Bores C, Kahl G. Explicit spatial description of fluid inclusions in porous matrices in terms of an inhomogeneous integral equation. J Chem Phys 2014; 141:164704. [DOI: 10.1063/1.4898713] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Enrique Lomba
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - Cecilia Bores
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - Gerhard Kahl
- Institut für Theoretische Physik, Technische Universität Wien and Center for Computational Materials Science (CMS), Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
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6
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Jardat M, Hribar-Lee B, Dahirel V, Vlachy V. Self-diffusion and activity coefficients of ions in charged disordered media. J Chem Phys 2012; 137:114507. [DOI: 10.1063/1.4752111] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lukšič M, Hribar-Lee B, Tochimani SB, Pizio O. Solvent primitive model for electrolyte solutions in disordered porous matrices of charged species. Replica Ornstein-Zernike theory and grand canonical Monte Carlo simulations. Mol Phys 2012. [DOI: 10.1080/00268976.2011.631057] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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Lomba E, Weis JJ. A computational study of electrolyte adsorption in a simple model for intercalated clays. J Chem Phys 2010; 132:104705. [PMID: 20232982 DOI: 10.1063/1.3357351] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A pillared interlayered clay is represented by a two-dimensional quenched charged disordered medium, in which the pillar configuration is produced by the quench of a two-dimensional electrolyte and the subsequent removal of the anions (that act as a template). The cation charge is counterbalanced by a neutralizing background that is an ideal representation of the layer's negative charge in the experimental system. In this paper we investigate the adsorption of electrolyte particles in this charged disordered medium resorting both to the use of the replica Ornstein-Zernike equation in the hypernetted chain approximation and grand canonical Monte Carlo simulations. The theoretical approach qualitatively reproduces the simulated behavior of the adsorbed fluids. Theoretical estimates of the material porosities obtained for various types of pillar distributions are in good agreement with the simulation. We investigate the influence of the matrix on correlation functions and adsorption isotherms.
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Affiliation(s)
- E Lomba
- Instituto de Química-Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain.
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Jardat M, Hribar-Lee B, Vlachy V. Self-diffusion coefficients of ions in the presence of charged obstacles. Phys Chem Chem Phys 2008; 10:449-57. [DOI: 10.1039/b711814g] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Zhao SL, Dong W, Liu QH. Fluids in porous media. II. A new model of templated matrices. J Chem Phys 2007; 127:144701. [DOI: 10.1063/1.2756835] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Luksic M, Hribar-Lee B, Vlachy V. Electrolyte exclusion from charged adsorbent: replica Ornstein-Zernike theory and simulations. J Phys Chem B 2007; 111:5966-75. [PMID: 17488109 DOI: 10.1021/jp065685p] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.
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Affiliation(s)
- Miha Luksic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Askerceva 5, Ljubljana, Slovenia
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Zhang X, Cao D, Wang W. A stepwise approximation for modeling of the wall–fluid potential of a mesoscopic pore. J Colloid Interface Sci 2007; 308:49-52. [PMID: 17257611 DOI: 10.1016/j.jcis.2006.12.042] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2006] [Revised: 12/04/2006] [Accepted: 12/14/2006] [Indexed: 10/23/2022]
Abstract
A common computational method for the characterization of porous materials is to calculate the adsorption isotherm of fluids in the materials from the pre-assumed wall-fluid potential. If the wall-fluid potential is unknown, the common computational method becomes invalid. In a realistic experiment, however, it is common to know the experimental adsorption isotherm of nitrogen and not to know the wall-fluid potential. Here we propose a stepwise approximation for modeling wall-fluid potential under conditions where only the adsorption isotherm of nitrogen is measured experimentally. Based on the modeled wall-fluid potential, we can characterize the porous materials and predict the adsorption of other adsorbates on the materials. It is expected that the approach would provide a powerful means for the characterization of novel materials under conditions where only the experimental adsorption isotherm is available.
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Affiliation(s)
- Xianren Zhang
- Division of Molecular and Materials Simulation, Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, People's Republic of China
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Abstract
The morphology of many porous materials is spongelike. Despite the abundance of such materials, simple models which allow for a theoretical description of these materials are still lacking. Here, we propose a hard sponge model which is made by digging spherical cavities in a solid continuum. We found an analytical expression for describing the interaction potential between fluid particles and the spongelike porous matrix. The diagrammatic expansions of different correlation functions are derived as well as that of grand potential. We derived also the Ornstein-Zernike (OZ) equations for this model. In contrast to Madden-Glandt model of random porous media [W. G. Madden and E. D. Glandt, J. Stat. Phys. 51, 537 (1988)], the OZ equations for a fluid confined in our hard sponge model have some similarity to the OZ equations of a three-component fluid mixture. We show also how the replica method can be extended to study our sponge model and that the same OZ equations can be derived also from the extended replica method.
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Affiliation(s)
- S L Zhao
- School of Theoretical Physics and School of Material Science and Engineering, Hunan University, Changsha, 410082, China
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Spöler C, Klapp SHL. Integral equation study of a Stockmayer fluid adsorbed in polar disordered matrices. J Chem Phys 2004; 120:6734-43. [PMID: 15267567 DOI: 10.1063/1.1665633] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on replica integral equations in the (reference) hypernetted chain approximation we investigate the structural features and phase properties of a dipolar Stockmayer fluid confined to a disordered dipolar matrix. The integral equations are applied to the homogeneous high-temperature phase where the system is globally isotropic. At low densities we find the influence of dipolar interactions between fluid (f) and matrix (m) particles to be surprisingly similar to the previously investigated effect of attractive isotropic (fm) interactions: the critical temperature of the vapor-liquid transition decreases with increasing (fm) coupling, while the critical density increases. The anisotropic nature of the dipolar (fm) interactions turns out to play a more dominant role at high fluid densities where we observe a pronounced sensitivity in the dielectric constant and a strong degree of local orientational ordering of the fluid particles along the local fields generated by the matrix. Moreover, an instability of the dielectric constant, which is a precursor of ferroelectric ordering occurring both in bulk Stockmayer fluids and in fluids in nonpolar matrices, is observed only for very small dipolar (fm) couplings.
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Affiliation(s)
- C Spöler
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekretariat TC7, Technische Universität Berlin, Strasse des 17. Juni 124, D-10623 Berlin, Germany
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Vitalis* A, Baker NA, McCammon‡ JA. ISIM: A Program for Grand Canonical Monte Carlo Simulations of the Ionic Environment of Biomolecules. MOLECULAR SIMULATION 2004. [DOI: 10.1080/08927020310001597862] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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17
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Vlachy V, Dominguez H, Pizio O. Temperature Effects in Adsorption of a Primitive Model Electrolyte in Disordered Quenched Media: Predictions of the Replica OZ/HNC Approximation. J Phys Chem B 2003. [DOI: 10.1021/jp035166b] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- V. Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Aškerčeva 5, 1000 Ljubljana, Slovenia, and Instituto de Quımica de la UNAM, Circuito Exterior, Coyoacán 04510, México D.F
| | - H. Dominguez
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Aškerčeva 5, 1000 Ljubljana, Slovenia, and Instituto de Quımica de la UNAM, Circuito Exterior, Coyoacán 04510, México D.F
| | - O. Pizio
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Aškerčeva 5, 1000 Ljubljana, Slovenia, and Instituto de Quımica de la UNAM, Circuito Exterior, Coyoacán 04510, México D.F
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Spöler C, Klapp SHL. Phase behavior of Stockmayer fluids confined to a nonpolar porous material. J Chem Phys 2003. [DOI: 10.1063/1.1539047] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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HRIBAR B, VLACHY V, PIZIO O. Chemical potential of electrolytes adsorbed in porous media with charged obstacles: application of the continuum replica methodology. Mol Phys 2002. [DOI: 10.1080/00268970210130272] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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