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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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Shankaraiah N, Sengupta S, Menon GI. Orientational correlations in fluids with quenched disorder. J Chem Phys 2019; 151:124501. [PMID: 31575199 DOI: 10.1063/1.5116734] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Snapshots of colloidal particles moving on disordered two-dimensional substrates can be used to extract equal-time many-body correlations in their positions. To understand the systematics of these correlations, we perform Monte Carlo simulations of a two-dimensional model fluid placed in a quenched disordered background. We use configurations generated from these simulations to compute translational and orientational two-point correlations at equal time, concentrating on correlations in local orientational order as a function of density and disorder strength. We calculate both the disorder averaged version of conventional two-point correlation functions for orientational order, as well as the disorder averaged version of a novel correlation function of time-averaged disorder-induced inhomogeneities in local orientation analogous to the Edwards-Anderson correlation function in spin systems. We demonstrate that these correlations can exhibit interesting nonmonotonic behavior in proximity to the underlying fluid-solid transition and suggest that this prediction should be experimentally accessible.
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Affiliation(s)
- N Shankaraiah
- TIFR Centre for Interdisciplinary Sciences, 36/p Gopanpally, Hyderabad 500107, India
| | - Surajit Sengupta
- TIFR Centre for Interdisciplinary Sciences, 36/p Gopanpally, Hyderabad 500107, India
| | - Gautam I Menon
- The Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600113, India
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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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Chen W, Zhao SL, Holovko M, Chen XS, Dong W. Scaled Particle Theory for Multicomponent Hard Sphere Fluids Confined in Random Porous Media. J Phys Chem B 2016; 120:5491-504. [PMID: 27294670 DOI: 10.1021/acs.jpcb.6b02957] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The formulation of scaled particle theory (SPT) is presented for a quite general model of fluids confined in a random porous media, i.e., a multicomponent hard sphere (HS) fluid in a multicomponent hard sphere or a multicomponent overlapping hard sphere (OHS) matrix. The analytical expressions for pressure, Helmholtz free energy, and chemical potential are derived. The thermodynamic consistency of the proposed theory is established. Moreover, we show that there is an isomorphism between the SPT for a multicomponent system and that for a one-component system. Results from grand canonical ensemble Monte Carlo simulations are also presented for a binary HS mixture in a one-component HS or a one-component OHS matrix. The accuracy of various variants derived from the basic SPT formulation is appraised against the simulation results. Scaled particle theory, initially formulated for a bulk HS fluid, has not only provided an analytical tool for calculating thermodynamic properties of HS fluid but also helped to gain very useful insight for elaborating other theoretical approaches such as the fundamental measure theory (FMT). We expect that the general SPT for multicomponent systems developed in this work can contribute to the study of confined fluids in a similar way.
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Affiliation(s)
- W Chen
- 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.,Computer Network Information Center, Chinese Academy of Sciences , P.O. Box 349, 100190 Beijing, China
| | - S L Zhao
- State Key Laboratory of Chemical Engineering, East China University of Science and Technology , 130 Meilong Road, 200237 Shanghai, China
| | - M Holovko
- Institute for Condensed Matter Physics, National Academy of Sciences , 1 Svientsitskii Street, 79011 Lviv, Ukraine
| | - X S Chen
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences , P.O. Box 2735, 100190 Beijing, 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.,State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences , P.O. Box 2735, 100190 Beijing, China
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Jadrich RB, Schweizer KS. Directing colloidal assembly and a metal-insulator transition using a quench-disordered porous rod template. PHYSICAL REVIEW LETTERS 2014; 113:208302. [PMID: 25432057 DOI: 10.1103/physrevlett.113.208302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 06/04/2023]
Abstract
Replica and effective-medium theory methods are employed to elucidate how to massively reconfigure a colloidal assembly to achieve globally homogeneous, strongly clustered, and percolated equilibrium states of high electrical conductivity at low physical volume fractions. A key idea is to employ a quench-disordered, large-mesh rigid-rod network as a templating internal field. By exploiting bulk phase separation frustration and the tunable competing processes of colloid adsorption on the low-dimensional network and fluctuation-driven colloid clustering in the pore spaces, two distinct spatial organizations of greatly enhanced particle contacts can be achieved. As a result, a continuous, but very abrupt, transition from an insulating to metallic-like state can be realized via a small change of either the colloid-template or colloid-colloid attraction strength. The approach is generalizable to more complicated template or colloidal architectures.
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Affiliation(s)
- Ryan B Jadrich
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA and Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
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Chen W. Phase separation of binary nonadditive hard sphere fluid mixture confined in random porous media. J Chem Phys 2013; 139:154712. [PMID: 24160538 DOI: 10.1063/1.4825178] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
I analyze the fluid-fluid phase separation of nonadditive hard sphere fluid mixture absorbed in random porous media. An equation of state is derived by using the perturbation theory to this complex system with quenched disorders. The results of this theory are in good agreement with those obtained from semi-grand canonical ensemble Monte Carlo simulations. The contact value of the fluid-fluid radial distribution functions of the reference which is the key point of the perturbation process is derived as well, the comparison against Monte Carlo simulations shows that it has an excellent accuracy.
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Affiliation(s)
- W Chen
- Department of Applied Physics, Aalto University, School of Science, P.O. Box 14100, FI-00076 Aalto, Finland
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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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Tarjus G, Rosinberg ML, Kierlik E, Tissier M. Hierarchical reference theory of critical fluids in disordered porous media. Mol Phys 2011. [DOI: 10.1080/00268976.2011.620024] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Krakoviack V. Mode-coupling theory predictions for the dynamical transitions of partly pinned fluid systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:050501. [PMID: 22181359 DOI: 10.1103/physreve.84.050501] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2011] [Indexed: 05/31/2023]
Abstract
The predictions of the mode-coupling theory (MCT) for the dynamical arrest scenarios in a partly pinned (PP) fluid system are reported. The corresponding dynamical phase diagram is found to be very similar to that of a related quenched-annealed (QA) system. The only significant qualitative difference lies in the shape of the diffusion-localization lines at high matrix densities, with a reentry phenomenon for the PP system but not for the QA model, in full agreement with recent computer simulation results. This finding clearly lends support to the predictive power of the MCT for fluid-matrix systems. In addition, the predictions of the MCT are shown to be in stark contrast with those of the random first-order transition theory. The PP systems are thus confirmed as very promising models for differentiating tests of theories of the glass transition.
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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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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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Patsahan T, Holovko M, Dong W. Fluids in porous media. III. Scaled particle theory. J Chem Phys 2011; 134:074503. [PMID: 21341855 DOI: 10.1063/1.3532546] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Based on a new and consistent formulation of scaled particle theory for a fluid confined in random porous media, a series of new approximations are proposed and one of them gives equations of state with excellent accuracy for a hard sphere fluid adsorbed in a hard sphere or an overlapping hard sphere matrix. Although the initial motivation was to remedy a flaw in a previous formulation of the scaled particle theory for a confined fluid, the new formulation is not a trivial and straightforward correction of the previous one. A few conceptual and significant modifications have to be introduced for developing the present formulation.
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Affiliation(s)
- T Patsahan
- Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, Lyon, France
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15
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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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16
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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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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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Chen W, Dong W, Holovko M, Chen XS. Comment on “A Highly Accurate and Analytic Equation of State for a Hard Sphere Fluid in Random Porous Media”. J Phys Chem B 2009; 114:1225. [DOI: 10.1021/jp9106603] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- W. Chen
- Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France, Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China, and Institute for Condensed Matter Physics, National Academy of Sciences, 1 Svientsitskii Street, 79011 Lviv, Ukraine
| | - W. Dong
- Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France, Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China, and Institute for Condensed Matter Physics, National Academy of Sciences, 1 Svientsitskii Street, 79011 Lviv, Ukraine
| | - M. Holovko
- Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France, Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China, and Institute for Condensed Matter Physics, National Academy of Sciences, 1 Svientsitskii Street, 79011 Lviv, Ukraine
| | - X. S. Chen
- Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France, Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China, and Institute for Condensed Matter Physics, National Academy of Sciences, 1 Svientsitskii Street, 79011 Lviv, Ukraine
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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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BRYK PAWEL, PIZIO OREST, SOKOLOWSKI STEFAN. A hard sphere fluid in equilibrium with microporous membranes. Inhomogeneous replica Ornstein—Zernike equations and grand canonical Monte Carlo simulations. Mol Phys 2009. [DOI: 10.1080/00268979809483163] [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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Krakoviack V. Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:061501. [PMID: 19658507 DOI: 10.1103/physreve.79.061501] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2009] [Revised: 03/18/2009] [Indexed: 05/28/2023]
Abstract
A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its equations, such as the previous ones, reflect the interplay between confinement-induced relaxation phenomena and glassy dynamics through the presence of two contributions in the slow part of the memory kernel, which are linear and quadratic in the density correlation functions, respectively. From numerical solutions for two simple models with pure hard-core interactions, it is shown that two different scenarios result for the diffusion-localization transition depending on the strength of the confinement. For weak confinement, this transition is discontinuous and coincides with the ideal glass transition, such as in one-component bulk systems, while, for strong confinement, it is continuous and occurs before the collective dynamics gets nonergodic. In the latter case, the glass transition manifests itself as a secondary transition, which can be either continuous or discontinuous, in the already arrested single-particle dynamics. The main features of the anomalous dynamics found in the vicinity of all these transitions are reviewed and illustrated with detailed computations.
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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 7, France
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Holovko M, Dong W. A Highly Accurate and Analytic Equation of State for a Hard Sphere Fluid in Random Porous Media. J Phys Chem B 2009; 113:6360-5. [DOI: 10.1021/jp809706n] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- M. Holovko
- Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46, Allée d’Italie, 69364 Lyon Cedex 07, France
| | - W. Dong
- Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46, Allée d’Italie, 69364 Lyon Cedex 07, France
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23
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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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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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Salinas JF, Dominguez H. Studies of diffusion coefficients in disordered porous matrices confined in a slit-pore. Mol Phys 2007. [DOI: 10.1080/00268970701367956] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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27
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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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28
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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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29
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Detcheverry F, Kierlik E, Rosinberg ML, Tarjus G. Gas adsorption and desorption in silica aerogels: a theoretical study of scattering properties. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:041511. [PMID: 16711813 DOI: 10.1103/physreve.73.041511] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Indexed: 05/09/2023]
Abstract
We present a numerical study of the structural correlations associated with gas adsorption and desorption in silica aerogels in order to provide a theoretical interpretation of scattering experiments. Following our earlier work, we use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis. We focus on the differences between the adsorption and desorption mechanisms and their signature in the fluid-fluid and gel-fluid structure factors as a function of temperature. At low temperature, but still in the regime where the isotherms are continuous, we find that the adsorbed fluid density, during both filling and draining, is correlated over distances that may be much larger than the gel correlation length. In particular, extended fractal correlations may occur during desorption, indicating the existence of a ramified cluster of vapor filled cavities. This also induces an important increase of the scattering intensity at small wave vectors. The similarity and differences with the scattering of fluids in other porous solids such as Vycor are discussed.
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Affiliation(s)
- F Detcheverry
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
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30
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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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31
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Krakoviack V. Liquid-glass transition of a fluid confined in a disordered porous matrix: a mode-coupling theory. PHYSICAL REVIEW LETTERS 2005; 94:065703. [PMID: 15783750 DOI: 10.1103/physrevlett.94.065703] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2004] [Indexed: 05/13/2023]
Abstract
We derive an extension of the mode-coupling theory for the liquid-glass transition to a class of models of confined fluids, where the fluid particles evolve in a disordered array of interaction sites. We find that the corresponding equations are similar to those describing the bulk, implying that the methods of investigation which were developed there are directly transferable to this new domain of application. We then compute the dynamical phase diagram of a simple model system and show that new and nontrivial transition scenarios, including reentrant glass transitions and higher-order singularities, can be predicted from the proposed theory.
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Affiliation(s)
- V Krakoviack
- Laboratoire de Chimie, Ecole Normale Supérieure de Lyon, 46, Allée d'Italie, 69364 Lyon Cedex 07, France
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32
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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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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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RIVERA MARGARITA, DOMINGUEZ HECTOR. Pore matrices prepared at supercritical temperature by computer simulations: matrix characterization and studies of diffusion coefficients of adsorbed fluids. Mol Phys 2003. [DOI: 10.1080/00268970310001606812] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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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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HANSEN JEANPIERRE, LYNDEN-BELL RUTH. Dominique Levesque. Mol Phys 2003. [DOI: 10.1080/0026897031000094515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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37
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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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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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DOMINGUEZ HECTOR, RIVERA MARGARITA. Studies of porosity and diffusion coefficient in porous matrices by computer simulations. Mol Phys 2002. [DOI: 10.1080/00268970210164437] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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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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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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42
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Rżysko W, Sokołowski S, Pizio O. Theory of adsorption in a polydisperse templated porous material: Hard sphere systems. J Chem Phys 2002. [DOI: 10.1063/1.1450556] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Kovalenko A, Hirata F. A replica reference interaction site model theory for a polar molecular liquid sorbed in a disordered microporous material with polar chemical groups. J Chem Phys 2001. [DOI: 10.1063/1.1409954] [Citation(s) in RCA: 33] [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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44
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Abstract
Adsorption at various interfaces has concerned scientists since the beginning of this century. This phenomenon underlies a number of extremely important processes of utilitarian significance. The technological, environmental and biological importance of adsorption can never be in doubt. Its practical applications in industry and environmental protection are of paramount importance. The adsorption of substrates is the first stage in many catalytic processes. The methods for separation of mixtures on a laboratory and on an industrial scale are increasingly based on utilising the change in concentration of components at the interface. Moreover, such vital problems as purification of water, sewages, air and soil are involved here too. On the other hand, many areas in which technological innovation has covered adsorption phenomena have been expanded more through art and craft than through science. A basic understanding of the scientific principles is far behind; in part because the study of interfaces requires extremely careful experimentation if meaningful and reproducible results are to be obtained. In recent years, however, considerable effort has been increasingly directed toward closing the gap between theory and practice. Crucial progress in theoretical description of the adsorption has been achieved, mainly through the development of new theoretical approaches formulated on a molecular level, by means of computer simulation methods and owing to new techniques which examine surface layers or interfacial regions. Moreover, during the last 15 years new classes of solid adsorbents have been developed, such as activated carbon fibres and carbon molecular sieves, fullerenes and heterofullerenes, microporous glasses and nanoporous--both carbonaceous and inorganic--materials. Nanostructured solids are very popular in science and technology and have gained extreme interest due to their sorption, catalytic, magnetic, optical and thermal properties. Although the development of adsorption up to the 1918s has been following rather a zig-zag path, this arm of surface science is now generally considered to have become a well-defined branch of physical science representing an intrinsically interdisciplinary area between chemistry, physics, biology and engineering. This review presents in brief the history of adsorption and highlights the progress in theoretical description of the phenomenon under consideration. The paper deals with the above problems critically, showing the development of adsorption, presenting some of the latest important results and giving a source of up-to-date literature on it. Moreover, in this paper the most important aspects are overviewed referring to today's trends and visions in application of adsorption science in industry, environmental protection and in environmental analysis. The relationship between development of adsorption theory and adsorption practice is pointed out. Current understanding and perspectives pertaining to applications of adsorption phenomena on laboratory and on industrial scale as well as environmental protection are discussed and illustrated by means of a few spectacular examples.
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Affiliation(s)
- A Dabrowski
- Faculty of Chemistry, M. Curie-Skłodowska University, 20031 Lublin, Poland.
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45
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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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46
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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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47
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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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48
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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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49
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Hribar B, Vlachy V, Pizio O. Structural and Thermodynamic Properties of Electrolyte Solutions in Hard-Sphere Confinement: Predictions of the Replica Integral Equation Theory. J Phys Chem B 2000. [DOI: 10.1021/jp994324p] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Barbara Hribar
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana 1001, Slovenia Instituto de Química de la UNAM, Circuito Exterior, Coyoacán 04510, México, D.F
| | - Vojko Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana 1001, Slovenia Instituto de Química de la UNAM, Circuito Exterior, Coyoacán 04510, México, D.F
| | - Orest Pizio
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana 1001, Slovenia Instituto de Química de la UNAM, Circuito Exterior, Coyoacán 04510, México, D.F
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50
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Zhang L, Van Tassel PR. Theory and simulation of adsorption in a templated porous material: Hard sphere systems. J Chem Phys 2000. [DOI: 10.1063/1.480874] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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