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Li Z, Turner J, Snurr RQ. Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores. Commun Chem 2023; 6:90. [PMID: 37156883 PMCID: PMC10167368 DOI: 10.1038/s42004-023-00889-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2022] [Accepted: 04/19/2023] [Indexed: 05/10/2023] Open
Abstract
Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.
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Affiliation(s)
- Zhao Li
- Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA
| | - Jake Turner
- Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA
| | - Randall Q Snurr
- Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA.
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2
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Stadik A, Kahl G. Deformable hard particles confined in a disordered porous matrix. J Chem Phys 2021; 155:244507. [PMID: 34972368 DOI: 10.1063/5.0068680] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
With suitably designed Monte Carlo simulations, we have investigated the properties of mobile, impenetrable, yet deformable particles that are immersed into a porous matrix, the latter one realized by a frozen configuration of spherical particles. By virtue of a model put forward by Batista and Miller [Phys. Rev. Lett. 105, 088305 (2010)], the fluid particles can change in their surroundings, formed by other fluid particles or the matrix particles, their shape within the class of ellipsoids of revolution; such a change in shape is related to a change in energy, which is fed into suitably defined selection rules in the deformation "moves" of the Monte Carlo simulations. This concept represents a simple yet powerful model of realistic, deformable molecules with complex internal structures (such as dendrimers or polymers). For the evaluation of the properties of the system, we have used the well-known quenched-annealed protocol (with its characteristic double average prescription) and have analyzed the simulation data in terms of static properties (the radial distribution function and aspect ratio distribution of the ellipsoids) and dynamic features (notably the mean squared displacement). Our data provide evidence that the degree of deformability of the fluid particles has a distinct impact on the aforementioned properties of the system.
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Affiliation(s)
- Alexander Stadik
- Institute for Theoretical Physics and Center for Computational Materials Science (CMS), Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
| | - Gerhard Kahl
- Institute for Theoretical Physics and Center for Computational Materials Science (CMS), Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
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3
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Naincy Attri, Sudhir K. Singh. Estimation of Pore Critical Temperature of Nanoconfined Alkanes Using Vapour-Liquid Interfacial Free Energy. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2021. [DOI: 10.1134/s1990793121090037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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4
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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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5
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Qiao CZ, Zhao SL, Liu HL, Dong W. Connect the Thermodynamics of Bulk and Confined Fluids: Confinement-Adsorption Scaling. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:3840-3847. [PMID: 30691262 DOI: 10.1021/acs.langmuir.8b03126] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A fluid (a gas or a liquid) adsorbed in a porous material can behave very differently from its bulk counterpart. The advent of various synthesized materials with nanopores and their wide applications have provided strong impetus for studying fluids in confinement because our current understanding is still incomplete. From a large number of Monte Carlo simulations, we found a scaling relation that allows for connecting some thermodynamic properties (chemical potential, free energy per particle, and grand potential per particle) of a confined fluid to the bulk ones. Upon rescaling the adsorbed fluid density, the adsorption isotherms for many different confining environments collapse to the corresponding bulk curve. We also reveal the intimate connection of the reported scaling relation to Gibbs theory of inhomogeneous fluids and morphological thermodynamics. The advance in our understanding of confined fluids, gained from this study, also opens attractive perspectives for circumventing experimental difficulty for directly measuring some fluid thermodynamic properties in nanoporous 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
| | | | | | - 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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6
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Hvozd TV, Kalyuzhnyi YV, Cummings PT. Phase Equilibria of Polydisperse Square-Well Chain Fluid Confined in Random Porous Media: TPT of Wertheim and Scaled Particle Theory. J Phys Chem B 2018; 122:5458-5465. [PMID: 29656640 DOI: 10.1021/acs.jpcb.7b11741] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Extension of Wertheim's thermodynamic perturbation theory and its combination with scaled particle theory is proposed and applied to study the liquid-gas phase behavior of polydisperse hard-sphere square-well chain fluid confined in the random porous media. Thermodynamic properties of the reference system, represented by the hard-sphere square-well fluid in the matrix, are calculated using corresponding extension of the second-order Barker-Henderson perturbation theory. We study effects of polydispersity and confinement on the phase behavior of the system. While polydispersity causes increase of the region of phase coexistence due to the critical temperature increase, confinement decreases the values of both critical temperature and critical density making the region of phase coexistence smaller. This effect is enhanced with the increase of the size ratio of the fluid and matrix particles. The increase of the average chain length at fixed values of polydispersity and matrix density shifts the critical point to a higher temperature and a slightly lower density.
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Affiliation(s)
- Taras V Hvozd
- Institute for Condensed Matter Physics , National Academy of Sciences of Ukraine , 1 Svientsitskii St. , Lviv 79011 , Ukraine
| | - Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics , National Academy of Sciences of Ukraine , 1 Svientsitskii St. , Lviv 79011 , Ukraine
| | - Peter T Cummings
- Department of Chemical and Biochemical Engineering , Vanderbilt University , Nashville , Tennessee 37235-1604 , United States
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7
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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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8
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KOVALENKO ANDRIY, HIRATA FUMIO. TOWARDS A MOLECULAR THEORY FOR THE VAN DER WAALS–MAXWELL DESCRIPTION OF FLUID PHASE TRANSITIONS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000282] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We briefly review developments of theories for phase transitions of molecular fluids and mixtures, from semi-phenomenological approaches providing equations of state with adjustable parameters to first-principles microscopic methods qualitatively correct for a variety of molecular models with realistic interaction potentials. We further present the generalization of the van der Waals–Maxwell description of fluid phase diagrams to account for chemical specificities of polar molecular fluids, such as hydrogen bonding. Our theory uses the reference interaction site model (RISM) integral equation approach complemented with the new closure we have proposed (KH approximation), successful over a wide range of density from gas to liquid. The RISM/KH theory is applied to the known three-site models of water, methanol, and hydrogen fluoride. It qualitatively reproduces their vapor-liquid phase diagrams and the structure in the gas as well as liquid phases, including hydrogen bonding. Furthermore, phase transitions of water and methanol sorbed in nanoporous carbon aerogel are described by means of the replica generalization of the RISM approach we have developed. The changes as compared to the bulk fluids are in agreement with simulations and experiment. The RISM/KH theory is promising for description of phase transitions in various associating fluids, in particular, electrolyte as well as non-electrolyte solutions and ionic liquids.
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Affiliation(s)
- ANDRIY KOVALENKO
- Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan
| | - FUMIO HIRATA
- Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan
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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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10
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Kurzidim J, Coslovich D, Kahl G. Dynamic arrest of colloids in porous environments: disentangling crowding and confinement. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:234122. [PMID: 21613709 DOI: 10.1088/0953-8984/23/23/234122] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Using numerical simulations we study the slow dynamics of a colloidal hard-sphere fluid adsorbed in a matrix of disordered hard-sphere obstacles. We calculate separately the contributions to the single-particle dynamic correlation functions due to free and trapped particles. The separation is based on a Delaunay tessellation to partition the space accessible to the centres of fluid particles into percolating and disconnected voids. We find that the trapping of particles into disconnected voids of the matrix is responsible for the appearance of a nonzero long-time plateau in the single-particle intermediate scattering functions of the full fluid. The subdiffusive exponent z, obtained from the logarithmic derivative of the mean squared displacement, is essentially unaffected by the motion of trapped particles: close to the percolation transition, we determined z approximately = 0.5 for both the full fluid and the particles moving in the percolating void. Notably, the same value of z is found in single-file diffusion and is also predicted by mode-coupling theory along the diffusion-localization line. We also reveal subtle effects of dynamic heterogeneity in both the free and the trapped component of the fluid particles, and discuss microscopic mechanisms that contribute to this phenomenon.
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Affiliation(s)
- Jan Kurzidim
- Institut für Theoretische Physik and Center for Computational Materials Science, Technische Universität Wien, Wien, Austria.
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11
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Kurzidim J, Kahl G. Accessible volume in quenched-annealed mixtures of hard spheres: a geometric decomposition. Mol Phys 2011. [DOI: 10.1080/00268976.2011.556579] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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12
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Schwanzer DF, Coslovich D, Kurzidim J, Kahl G. Effects of porous confinement on the structural properties of the Gaussian core model. Mol Phys 2010. [DOI: 10.1080/00268970902845321] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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13
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Krakoviack V. Statistical mechanics of homogeneous partly pinned fluid systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061501. [PMID: 21230672 DOI: 10.1103/physreve.82.061501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2010] [Indexed: 05/30/2023]
Abstract
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.
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Affiliation(s)
- Vincent Krakoviack
- Laboratoire de Chimie, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France
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14
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Kurzidim J, Coslovich D, Kahl G. Impact of random obstacles on the dynamics of a dense colloidal fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041505. [PMID: 21230280 DOI: 10.1103/physreve.82.041505] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2010] [Indexed: 05/30/2023]
Abstract
Using molecular dynamics simulations we study the slow dynamics of a colloidal fluid annealed within a matrix of obstacles quenched from an equilibrated colloidal fluid. We choose all particles to be of the same size and to interact as hard spheres, thus retaining all features of the porous confinement while limiting the control parameters to the packing fraction of the matrix, φ(m), and that of the fluid, φ(f). We conduct detailed investigations on several dynamic properties, including the tagged-particle and collective intermediate scattering functions, the mean-squared displacement, and the van Hove function. We show the confining obstacles to profoundly impact the relaxation pattern of various quantifiers pertinent to the fluid. Varying the type of quantifier (tagged-particle or collective) as well as φ(m) and φ(f), we unveil both discontinuous and continuous arrest scenarios. Furthermore, we discover subdiffusive behavior and demonstrate its close connection to the matrix structure. Our findings partly confirm the various predictions of a recent extension of mode-coupling theory to the quenched-annealed protocol.
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Affiliation(s)
- Jan Kurzidim
- Institut für Theoretische Physik and CMS, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
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15
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Zheng F, Chen G, Zhang X, Wang W. A Monte Carlo study of crowding effects on the self-assembly of amphiphilic molecules. J Chem Phys 2009; 130:204701. [PMID: 19485469 DOI: 10.1063/1.3133950] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, lattice Monte Carlo was used to study the effects of crowding on the self-assembly of surfactants. Simulation results show that crowding strongly shifts the critical micelle concentration (CMC) of surfactants from the bulk value. Two effects originated from crowding are found to govern the CMC shift: one is the depletion effect by crowding agents and the other is the available volume for micelle formation. The depletion effects inevitably result in the enrichment of surfactants in crowding-free regions and cause the decrease in CMC. On the other hand, the appearance of crowding agents decreases the available volume for micelle formation, which reduces the conformational entropy and impedes the micelle formation. Three factors, including the radius of crowding agents, the arrangement of crowding agents, and the volume fraction of crowding agents, are considered in this work to study the crowding effects. The trends of CMC shifts are interpreted from the competition between the depletion effects and the available volume for micelle formation.
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Affiliation(s)
- Fengxian Zheng
- Division of Molecular and Materials Simulation, Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, China
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16
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ZHANG LINGHUI, VAN TASSEL PAULR. Configurational effects of templating on the adsorption isotherms of templated porous materials. Mol Phys 2009. [DOI: 10.1080/00268970009483357] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- LINGHUI ZHANG
- a Department of Chemical Engineering and Materials Science , Wayne State University , 5050 Anthony Wayne Drive, Detroit , MI , 48202 , USA
| | - PAUL R. VAN TASSEL
- a Department of Chemical Engineering and Materials Science , Wayne State University , 5050 Anthony Wayne Drive, Detroit , MI , 48202 , USA
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17
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KIERLIK E, ROSINBERG ML, TARJUS G, PITARD E. Mean-spherical approximation for a lattice model of a fluid in a disordered matrix. Mol Phys 2009. [DOI: 10.1080/00268979809483166] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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18
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Zhou S, Solana JR. Progress in the Perturbation Approach in Fluid and Fluid-Related Theories. Chem Rev 2009; 109:2829-58. [DOI: 10.1021/cr900094p] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Shiqi Zhou
- State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China, and School of Physics Science and Technology, Central South University, Changsha, Hunan 410083, China
| | - J. R. Solana
- Applied Physics Department, University of Cantabria, 39005 Santander, Spain
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19
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Kumar AN, Singh JK. The effects of interaction range, porosity and molecular association on the phase equilibrium of a fluid confined in a disordered porous media. Mol Phys 2008. [DOI: 10.1080/00268970802418963] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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20
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Talbot J, Tarjus G, Viot P. Exactly solvable model of reversible adsorption on a disordered substrate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:051106. [PMID: 18233622 DOI: 10.1103/physreve.76.051106] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2007] [Indexed: 05/25/2023]
Abstract
We consider the reversible adsorption of particles (monomers with exclusion nearest-neighbor sites) on a one-dimensional lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this one-dimensional system to the pure system where all sites are available for adsorption, we show that when the activity goes to infinity, there exists a mapping between this model and the pure system at the same density. By examining the susceptibilities, we demonstrate that there is no mapping at finite activity. However, when the site density is small or moderate, the mapping exists up to second order in site density. We also propose and evaluate approximate approaches that may be applied to systems where no analytic result is known.
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Affiliation(s)
- J Talbot
- Department of Chemistry and Biochemistry, Duquesne University, Pittsburgh, Pennsylvania 15282-1530, USA
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21
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22
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Krakoviack V. Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:031503. [PMID: 17500702 DOI: 10.1103/physreve.75.031503] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2006] [Revised: 01/09/2007] [Indexed: 05/15/2023]
Abstract
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical framework, except for a linear contribution to the memory kernel which adds to the usual quadratic term. The coupling coefficients involve structural quantities which are specific of fluids evolving in random environments and have expressions which are consistent with those found in related problems. Numerical solutions for two simple models with pure hard core interactions lead to the prediction of a variety of glass transition scenarios, which are either continuous or discontinuous and include the possibility of higher-order singularities and glass-glass transitions. The main features of the dynamics in the two most generic cases are reviewed and illustrated with detailed computations. Moreover, a reentry phenomenon is predicted in the low fluid-high matrix density regime and is interpreted as the signature of a de-correlation mechanism by fluid-fluid collisions competing with the localization effect of the solid matrix.
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Affiliation(s)
- V Krakoviack
- Laboratoire de Chimie, UMR CNRS 5182, Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon cedex 07, France
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23
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Abstract
The liquid-liquid phase behavior of binary mixtures in random pores is investigated with non-additive hard spheres using both ROZ (Replica Ornstein-Zernike) integral equations and cavity biased grand canonical Monte Carlo simulations. The critical densities of the coexistence phase envelopes are determined as function of the non-additivity parameter Delta, varying from Delta = 0.2, 0.4, 0.6, up to 0.8. The matrix is made of quenched hard spheres. Its porosity is varied to ascertain the effects of confinement, with packing densities rho(0) ranging from 0.1, 0.3, to 0.5. To obtain fiduciary results from ROZ, we use the accurate ZSEP closure relation proposed earlier with and without thermodynamic consistency. The ZSEP closure is known to enforce the zero-separation theorems via special adjustable parameters in the bridge function. Two versions of this closure are used to assess their accuracies (vis-à-vis the Monte Carlo data): first ZSEP-T, namely, the ZSEP closure with added thermodynamic consistency (the Gibbs-Duhem relation); and second purely ZSEP without adding thermodynamic consistency. It is found that both closures give correct qualitative trend, with errors of ZSEP falling within 8-9%, while ZSEP-T, being more accurate, to within 1-2%. As non-additivity is increased, both versions become more accurate. The critical density rho(c) is found to decrease with decreasing porosity. In addition, rho(c) also decreases with increasing Delta, in a non-monotone fashion.
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Affiliation(s)
- Giuseppe Pellicane
- Dipartimento di Fisica, Università di Messina, Contrada Papardo, 98166 Messina (Me), Italy.
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24
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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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25
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Sarkisov L, Van Tassel PR. Replica Ornstein-Zernike theory of adsorption in a templated porous material: Interaction site systems. J Chem Phys 2005; 123:164706. [PMID: 16268721 DOI: 10.1063/1.2049247] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular templating offers the possibility of porous materials whose selectivity rivals the molecular recognition observed in nature. The design of templated materials requires a molecular understanding of the templating effect on the material structure and performance. We present here a theoretical description of adsorption in a model templated porous material. Our model material is a quenched, equilibrated mixture of template and matrix molecular species where the template component has been subsequently removed. We propose a set of site-site [i.e., reference interaction site model (RISM)] replica Ornstein-Zernike equations relating the correlation functions of template, matrix, and adsorbing fluid molecules. To test this approach, we focus here on systems interacting via hard-sphere site-site potentials and employ a Percus-Yevick closure. We consider chain and cluster species composed of up to five spheres and observe a range of effects associated with template structure, including higher affinity toward, and enhanced templating by, compact cluster molecules. We assess these effects by grand canonical Monte Carlo simulation and discuss their implication to the design of templated molecular recognition materials.
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Affiliation(s)
- Lev Sarkisov
- Department of Chemical Engineering, Yale University, New Haven, Connecticut 06520-8286, USA
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Tompsett GA, Krogh L, Griffin DW, Conner WC. Hysteresis and scanning behavior of mesoporous molecular sieves. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2005; 21:8214-25. [PMID: 16114924 DOI: 10.1021/la050068y] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Sorption hysteresis is a widely studied phenomenon whose predicted behavior is well documented and researched. On the other hand, there is much less known about the region that lies between sorption isotherms, believed to be a metastable region. Scanning curves are a way of understanding the mechanism of hysteresis and a tool for hysteresis model validation. Scanning curves were produced for mesoporous materials: SBA-15 and MCM-41 for N(2) sorption at 77 K and Ar sorption at 87 K. A limited set of different scanning behaviors is identified. Like most hysteresis theories, it was found that a single model for scanning behavior cannot be extended to all materials under the same or different experimental conditions. Two behaviors are consistent with recent theories and simulations; however, several are not. The implications as to the characterization of pore dimensions and structure are discussed.
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Affiliation(s)
- G A Tompsett
- Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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27
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De Grandis V, Gallo P, Rovere M. Computer simulation of the phase diagram for a fluid confined in a fractal and disordered porous material. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:061505. [PMID: 15697372 DOI: 10.1103/physreve.70.061505] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2004] [Indexed: 05/24/2023]
Abstract
We present a grand canonical Monte Carlo simulation study of the phase diagram of a Lennard-Jones fluid adsorbed in a fractal and highly porous aerogel. The gel environment is generated from an off-lattice diffusion limited cluster-cluster aggregation process. Simulations have been performed with the multicanonical ensemble sampling technique. The biased sampling function has been obtained by histogram reweighting calculations. Comparing the confined and the bulk system liquid-vapor coexistence curves we observe a decrease of both the critical temperature and density in qualitative agreement with experiments and other Monte Carlo studies on Lennard-Jones fluids confined in random matrices of spheres. At variance with these numerical studies we do not observe upon confinement a peak on the liquid side of the coexistence curve associated with a liquid-liquid phase coexistence. In our case only a shouldering of the coexistence curve appears upon confinement. This shoulder can be associated with high density fluctuations in the liquid phase. The coexisting vapor and liquid phases in our system show a high degree of spatial disorder and inhomogeneity.
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Affiliation(s)
- V De Grandis
- Dipartimento di Fisica, Università "Roma Tre", INFM, Via della Vasca Navale 84, 00146 Roma, Italy
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28
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Duda Y, Pizio O, Sokolowski S. Nonadditive Binary Hard Sphere Mixture in Disordered Hard Sphere Matrices: Integral Equations and Computer Simulation. J Phys Chem B 2004. [DOI: 10.1021/jp040340x] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Y. Duda
- Instituto Mexicano de Petroleo, Mexico D.F., Mexico, Institute of Condensed Matter Physics, National Academy of Sciences, Lviv, Ukraine, Instituto de Quimica de la UNAM, Coyoacan 04510, Mexico, D.F., and Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, Lublin, Poland
| | - O. Pizio
- Instituto Mexicano de Petroleo, Mexico D.F., Mexico, Institute of Condensed Matter Physics, National Academy of Sciences, Lviv, Ukraine, Instituto de Quimica de la UNAM, Coyoacan 04510, Mexico, D.F., and Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, Lublin, Poland
| | - S. Sokolowski
- Instituto Mexicano de Petroleo, Mexico D.F., Mexico, Institute of Condensed Matter Physics, National Academy of Sciences, Lviv, Ukraine, Instituto de Quimica de la UNAM, Coyoacan 04510, Mexico, D.F., and Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, Lublin, Poland
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29
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Spöler C, Klapp SHL. Vapor-liquid transitions of dipolar fluids in disordered porous media: Performance of angle-averaged potentials. J Chem Phys 2004; 121:9623-9. [PMID: 15538884 DOI: 10.1063/1.1804151] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Using replica integral equations in the reference hypernetted-chain (RHNC) approximation we calculate vapor-liquid spinodals, chemical potentials, and compressibilities of fluids with angle-averaged dipolar interactions adsorbed to various disordered porous media. Comparison with previous RHNC results for systems with true angle-dependent Stockmayer (dipolar plus Lennard-Jones) interactions indicate that, for a dilute hard sphere matrix, the angle-averaged fluid-fluid (ff) potential is a reasonable alternative for reduced fluid dipole moments m( *2)=mu(2)/(epsilon(0)sigma(3))< or =2.0. This range is comparable to that estimated in bulk fluids, for which RHNC results are presented as well. Finally, results for weakly polar matrices suggest that angle-averaged fluid-matrix (fm) interactions can reproduce main features observed for true dipolar (fm) interactions such as the shift of the vapor-liquid spinodals towards lower temperatures and higher densities. However, the effective attraction induced by dipolar (fm) interaction is underestimated rather than overestimated as in the case of angle-averaged ff interactions.
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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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30
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Chang R, Jagannathan K, Yethiraj A. Diffusion of hard sphere fluids in disordered media: a molecular dynamics simulation study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:051101. [PMID: 15244802 DOI: 10.1103/physreve.69.051101] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2004] [Indexed: 05/24/2023]
Abstract
Molecular dynamic simulations are reported for the static and dynamic properties of hard sphere fluids in matrices (or media) composed of quenched hard spheres. The effect of fluid and matrix density, matrix structure, and fluid to matrix sphere size ratio on the static and dynamic properties is studied using discontinuous molecular dynamics. The matrix density has a stronger effect on the self-diffusion coefficient than the fluid density, especially at high matrix densities where the geometric constraints due to the quenched spheres are significant. When the ratio of the size of the fluid spheres to that of the matrix spheres is equal to or greater than one, the diffusion increases as the fluid density is increased, at constant total volume fraction. This trend is however reversed if the ratio is smaller than one. Different methods of generating the matrix have a very strong effect on the dynamic properties even though the static correlations are similar. An analysis of the single-chain structure factor of the particle trajectories shows a change in the particle diffusive behavior at different time scales, suggestive of a hopping mechanism, although normal diffusion is recovered at long times. At high matrix densities, there is considerable heterogeneity in the diffusion of the fluid particles. The simulations demonstrate that the correlations in the matrix play a significant role on the diffusion of fluid spheres. For example, the diffusion constant in matrices constructed by different methods can be an order of magnitude different even though the pair correlation functions are almost identical.
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Affiliation(s)
- Rakwoo Chang
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA
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31
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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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32
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Brovchenko I, Geiger A, Oleinikova A. Water in nanopores. I. Coexistence curves from Gibbs ensemble Monte Carlo simulations. J Chem Phys 2004; 120:1958-72. [PMID: 15268330 DOI: 10.1063/1.1631919] [Citation(s) in RCA: 106] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Coexistence curves of water in cylindrical and slitlike nanopores of different size and water-substrate interaction strength were simulated in the Gibbs ensemble. The two-phase coexistence regions cover a wide range of pore filling level and temperature, including ambient temperature. Five different kinds of two-phase coexistence are observed. A single liquid-vapor coexistence is observed in hydrophobic and moderately hydrophilic pores. Surface transitions split from the main liquid-vapor coexistence region, when the water-substrate interaction becomes comparable or stronger than the water-water pair interaction. In this case prewetting, one and two layering transitions were observed. The critical temperature of the first layering transition decreases with strengthening water-substrate interaction towards the critical temperature expected for two-dimensional systems and is not sensitive to the variation of pore size and shape. Liquid-vapor phase transition in a pore with a wall which is already covered with two water layers is most typical for hydrophilic pores. The critical temperature of this transition is very sensitive to the pore size, in contrast to the liquid-vapor critical temperature in hydrophobic pores. The observed rich phase behavior of water in pores evidences that the knowledge of coexistence curves is of crucial importance for the analysis of experimental results and a prerequiste of meaningful simulations.
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Affiliation(s)
- I Brovchenko
- Physikalische Chemie, Universitat Dortmund, D-44221 Dortmund, Germany
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33
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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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34
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Sokolovskii RO, Cates ME, Sokolovska TG. Model fluid in a porous medium: results for a Bethe lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:026124. [PMID: 14525066 DOI: 10.1103/physreve.68.026124] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2003] [Indexed: 11/07/2022]
Abstract
We consider a lattice gas with quenched impurities or "quenched-annealed binary mixture" on the Bethe lattice. The quenched part represents a porous matrix in which the (annealed) lattice gas resides. This model features the three main factors of fluids in random porous media: wetting, randomness, and confinement. The recursive character of the Bethe lattice enables an exact treatment, whose key ingredient is an integral equation yielding the one-particle effective field distribution. Our analysis shows that this distribution consists of two essentially different parts. The first one is a continuous spectrum and corresponds to the macroscopic volume accessible to the fluid, the second is discrete and comes from finite closed cavities in the porous medium. Those closed cavities are in equilibrium with the bulk fluid within the grand canonical ensemble we use, but are inaccessible in real experimental situations. Fortunately, we are able to isolate their contributions. Separation of the discrete spectrum facilitates also the numerical solution of the main equation. The numerical calculations show that the continuous spectrum becomes more and more rough as the temperature decreases, and this limits the accuracy of the solution at low temperatures.
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Affiliation(s)
- R O Sokolovskii
- School of Physics, JCMB Kings Buildings, University of Edinburgh, United Kingdom
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35
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Fernaud MJ, Lomba E, Martı́n C, Levesque D, Weis JJ. Study of dipolar fluid inclusions in charged random matrices. J Chem Phys 2003. [DOI: 10.1063/1.1576377] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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FERNAUD MJ, LOMBA E, WEIS JJ, LEVESQUE D. Computer simulation and replica Ornstein—Zernike integral equation studies of a hard-sphere dipolar fluid adsorbed into disordered porous media. Mol Phys 2003. [DOI: 10.1080/0026897031000092274] [Citation(s) in RCA: 5] [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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37
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Application of association theory to liquid/vapor coexistence in a simple fluid adsorbed on porous media. J Mol Liq 2003. [DOI: 10.1016/s0167-7322(03)00058-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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38
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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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39
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Douglas Frink LJ, Salinger AG. Rapid analysis of phase behavior with density functional theory. II. Capillary condensation in disordered porous media. J Chem Phys 2003. [DOI: 10.1063/1.1558314] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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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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41
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Tovbin Y, Yeremich D. Phase diagrams of simple fluids in porous globular adsorbents. Colloids Surf A Physicochem Eng Asp 2002. [DOI: 10.1016/s0927-7757(02)00052-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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42
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RESZKO-ZYGMUNT JOANNA, PATRYKIEJEW ANDRZEJ, SOKOŁOWSKI STEFAN, SOKOŁOWSKA ZOFIA. Phase coexistence and interface structure of a two-component Lennard-Jones fluid in porous media: application of Born—Green—Yvon equation. Mol Phys 2002. [DOI: 10.1080/00268970210126600] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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43
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Brennan JK, Dong W. Phase transitions of one-component fluids adsorbed in random porous media: Monte Carlo simulations. J Chem Phys 2002. [DOI: 10.1063/1.1469614] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Sarkisov L, Monson PA. Lattice model of adsorption in disordered porous materials: mean-field density functional theory and Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:011202. [PMID: 11800685 DOI: 10.1103/physreve.65.011202] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2000] [Revised: 06/18/2001] [Indexed: 05/23/2023]
Abstract
We present mean-field density functional theory calculations and Monte Carlo simulations for a lattice model of a fluid confined in a disordered porous material. The model is obtained by a coarse graining of an off-lattice model of adsorption of simple molecules in silica xerogels. In some of our calculations a model of a porous glass is also considered. The lattice models exhibit behavior that is qualitatively similar to that of their off-lattice counterparts but the computations required are much more tractable and this makes it feasible to investigate the effects of porous material microstructure at longer length scales. We focus on exploring in detail the behavior in the adsorption/desorption hysteresis region for these models. In agreement with recent results for a model that uses a random distribution of solid sites on the lattice [Kierlik et al., Phys. Rev. Lett. 87, 055701 (2001)] we show that the disorder of the solid matrix induces multiple metastable states within the hysteresis region, which are evident in both the mean-field theory calculations and the Monte Carlo simulations. These multiple metastable states can be connected by scanning curves that are very similar to those seen in experimental studies of adsorption hysteresis. The results from mean-field theory predict that while there is hysteresis in the adsorption/desorption isotherms it is not possible to locate a condition of phase equilibrium that satisfies thermodynamic consistency. A wider significance of these results is discussed.
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Affiliation(s)
- L Sarkisov
- Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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45
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Zhang L, Cheng S, Van Tassel PR. Effect of templated quenched disorder on fluid phase equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:042101. [PMID: 11690064 DOI: 10.1103/physreve.64.042101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2001] [Indexed: 05/23/2023]
Abstract
Templating offers a means to direct the structure of quenched disorder. We show here that changes in phase equilibrium due to the presence of quenched disorder can themselves be altered by templating. We calculate the phase diagram of a fluid in a collection of template-directed, quenched particles by solving a set of replica Ornstein-Zernike equations within the mean spherical approximation and show templating to enhance phase behavior, that is, shift the phase envelope upward from its location for a nontemplated system of identical available volume. This enhancement is due to an augmented number of fluid-fluid interactions.
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Affiliation(s)
- L Zhang
- Department of Chemical Engineering and Materials Science, Wayne State University, Detroit, Michigan 48202, USA
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46
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Schöll-Paschinger E, Levesque D, Weis JJ, Kahl G. Phase diagram of a symmetric binary fluid in a porous matrix. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:011502. [PMID: 11461257 DOI: 10.1103/physreve.64.011502] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2000] [Revised: 11/27/2000] [Indexed: 05/23/2023]
Abstract
The phase behavior of a binary symmetric fluid in thermal equilibrium with a porous matrix has been studied with the optimized random phase approximation and grand canonical Monte Carlo simulations. Depending on the matrix properties and the matrix-fluid and fluid-fluid interactions we find three types of phase diagram characterized by a tricritical point, a tricritical point with a triple point, or a critical end point. Small changes in the properties of the matrix or in the interactions are demonstrated to lead to drastic modifications of the phase diagram of the fluid, in qualitative agreement with observations in experimental studies. We show, in particular, that the change between the different types of phase diagram is triggered not only by the fluid-fluid interactions (internal parameters) but also by the properties of the matrix and of the matrix-fluid potentials (external parameters).
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Affiliation(s)
- E Schöll-Paschinger
- Institut für Theoretische Physik and Center for Computational Materials Science, TU Wien, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
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47
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Hribar B, Vlachy V, Pizio O. Equilibrium Properties of a Model Electrolyte Adsorbed in Quenched Disordered Charged Media: the ROZ Theory and GCMC Simulations. J Phys Chem B 2001. [DOI: 10.1021/jp010346b] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Barbara Hribar
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana 1001, Slovenia, and Department for Modeling of Physico-Chemical Processes, Maria Curie-Sklodowska University, 200-31 Lublin, Poland
| | - Vojko Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana 1001, Slovenia, and Department for Modeling of Physico-Chemical Processes, Maria Curie-Sklodowska University, 200-31 Lublin, Poland
| | - Orest Pizio
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana 1001, Slovenia, and Department for Modeling of Physico-Chemical Processes, Maria Curie-Sklodowska University, 200-31 Lublin, Poland
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48
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Cheng S, Van Tassel PR. Theory and simulation of the available volume for adsorption in a chain molecule templated porous material. J Chem Phys 2001. [DOI: 10.1063/1.1350442] [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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49
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Sarkisov L, Monson PA. Computer simulations of phase equilibrium for a fluid confined in a disordered porous structure. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:7231-7234. [PMID: 11088427 DOI: 10.1103/physreve.61.7231] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2000] [Indexed: 05/23/2023]
Abstract
We present calculations of the phase diagrams of a Lennard-Jones 12-6 fluid confined in a disordered porous structure made up of a dispersion of spherical particles, following up on an earlier work on the same system. In particular we present additional calculations using more realizations of the matrix and we investigate the applicability of the Gibbs-Duhem integration method to the calculation of phase equilibrium in these systems. The essential picture of disordered and inhomogeneous coexisting vapor and liquid phases, which emerged in the earlier work, is confirmed by the new calculations. However, a second phase transition associated with the wetting of the porous material by the fluid is found to be more sensitive to variations of the matrix realization. While for the present model this transition appears for particular realizations of the matrix, it does not seem to survive averaging over realizations.
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Affiliation(s)
- L Sarkisov
- Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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50
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Paschinger E, Kahl G. Structure and thermodynamic properties of a binary liquid in a porous matrix: the formalism. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:5330-5338. [PMID: 11031581 DOI: 10.1103/physreve.61.5330] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2000] [Indexed: 05/23/2023]
Abstract
Using the replica trick we derive a formalism to describe the structure and the thermodynamic properties of a binary liquid in equilibrium with a porous medium. We present the replica Ornstein-Zernike equations for the general case of a k-component liquid inside a porous matrix; besides the usual liquid-state closure relations, we consider in particular the optimized random phase approximation (ORPA) restricting ourselves at present to hard-core potentials exclusively. We present furthermore several thermodynamic relations: the Gibbs-Duhem equation, the compressibility, and the viral equation. Within the framework of the ORPA (mean spherical approximation), closed expressions for the perturbation contribution to the free energy and the chemical potentials can be presented. Finally, we offer suggestions for numerical implementations.
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Affiliation(s)
- E Paschinger
- Institut fur Theoretische Physik, TU Wien, Austria
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