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Pospíšil M, Malijevský A. Phase behavior of fluids in undulated nanopores. Phys Rev E 2022; 106:024801. [PMID: 36109889 DOI: 10.1103/physreve.106.024801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 07/20/2022] [Indexed: 06/15/2023]
Abstract
The geometry of walls forming a narrow pore may qualitatively affect the phase behavior of the confined fluid. Specifically, the nature of condensation in nanopores formed of sinusoidally shaped walls (with amplitude A and period P) is governed by the wall mean separation L as follows. For L>L_{t}, where L_{t} increases with A, the pores exhibit standard capillary condensation similar to planar slits. In contrast, for L<L_{t}, the condensation occurs in two steps, such that the fluid first condenses locally via bridging transition connecting adjacent crests of the walls, before it condenses globally. For the marginal value of L=L_{t}, all the three phases (gaslike, bridge, and liquidlike) may coexist. We show that the locations of the phase transitions can be described using geometric arguments leading to modified Kelvin equations. However, for completely wet walls, to which we focus on, the phase boundaries are shifted significantly due to the presence of wetting layers. In order to take this into account, mesoscopic corrections to the macroscopic theory are proposed. The resulting predictions are shown to be in a very good agreement with a density-functional theory even for molecularly narrow pores. The limits of stability of the bridge phase, controlled by the pore geometry, is also discussed in some detail.
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Affiliation(s)
- Martin Pospíšil
- Department of Physical Chemistry, University of Chemical Technology Prague, Praha 6, 166 28, Czech Republic and The Czech Academy of Sciences, Institute of Chemical Process Fundamentals, Department of Molecular Modelling, 165 02 Prague, Czech Republic
| | - Alexandr Malijevský
- Department of Physical Chemistry, University of Chemical Technology Prague, Praha 6, 166 28, Czech Republic and The Czech Academy of Sciences, Institute of Chemical Process Fundamentals, Department of Molecular Modelling, 165 02 Prague, Czech Republic
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Láska M, Parry AO, Malijevský A. Three-Phase Fluid Coexistence in Heterogenous Slits. PHYSICAL REVIEW LETTERS 2020; 124:115701. [PMID: 32242718 DOI: 10.1103/physrevlett.124.115701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Revised: 02/19/2020] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, where evaporated, locally condensed, and globally condensed states all coexist are possible depending on the value of the aspect ratio a=L/H, where H is the stripe width and L the wall separation. In particular, for a capillary made from completely dry walls patterned with completely wet stripes the condition for the triple point occurs when the aspect ratio takes its maximum possible value 8/π. These predictions are tested using a fully microscopic classical density functional theory and shown to be remarkably accurate even for molecularly narrow slits. The qualitative differences with local and global condensation in heterogeneous cylindrical pores are also highlighted.
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Affiliation(s)
- Martin Láska
- Department of Physical Chemistry, University of Chemical Technology Prague, Praha 6, 166 28, Czech Republic and Department of Molecular and Mesoscopic Modelling, ICPF of the Czech Academy Sciences, Prague, Czech Republic
| | - Andrew O Parry
- Department of Mathematics, Imperial College London, London SW7 2BZ, United Kingdom
| | - Alexandr Malijevský
- Department of Physical Chemistry, University of Chemical Technology Prague, Praha 6, 166 28, Czech Republic and Department of Molecular and Mesoscopic Modelling, ICPF of the Czech Academy Sciences, Prague, Czech Republic
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Puibasset J, Kierlik E, Tarjus G. Influence of system size on the properties of a fluid adsorbed in a nanopore: Physical manifestations and methodological consequences. J Chem Phys 2014; 141:044716. [PMID: 25084946 DOI: 10.1063/1.4891359] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Hysteresis and discontinuities in the isotherms of a fluid adsorbed in a nanopore in general hamper the determination of equilibrium thermodynamic properties, even in computer simulations. A way around this has been to consider both a reservoir of small size and a pore of small extent in order to restrict the fluctuations of density and approach a classical van der Waals loop. We assess this suggestion by thoroughly studying through Monte Carlo simulations and density functional theory the influence of system size on the equilibrium configurations of the adsorbed fluid and on the resulting isotherms. We stress the importance of pore-symmetry-breaking states that even for modest pore sizes lead to discontinuous isotherms and we discuss the physical relevance of these states and the methodological consequences for computing thermodynamic quantities.
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Affiliation(s)
- Joël Puibasset
- CRMD, CNRS FRE 3520, Université d'Orléans, 1b rue de la Férollerie, 45071 Orléans Cedex 02, France
| | - Edouard Kierlik
- LPTMC, CNRS UMR 7600, Université Pierre et Marie Curie, boîte 121, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Gilles Tarjus
- LPTMC, CNRS UMR 7600, Université Pierre et Marie Curie, boîte 121, 4 place Jussieu, 75252 Paris Cedex 05, France
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Rodriguez J, Elola MD, Laria D. Confined Polar Mixtures within Cylindrical Nanocavities. J Phys Chem B 2010; 114:7900-8. [DOI: 10.1021/jp101836b] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Javier Rodriguez
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, (1429) Buenos Aires, Argentina, ECyT, UNSAM, Martín de Irigoyen 3100, (1650) San Martín, Provincia de Buenos Aires, Argentina, and Departamento de Química Inorgánica, Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, (1428) Buenos Aires, Argentina
| | - M. Dolores Elola
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, (1429) Buenos Aires, Argentina, ECyT, UNSAM, Martín de Irigoyen 3100, (1650) San Martín, Provincia de Buenos Aires, Argentina, and Departamento de Química Inorgánica, Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, (1428) Buenos Aires, Argentina
| | - Daniel Laria
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, (1429) Buenos Aires, Argentina, ECyT, UNSAM, Martín de Irigoyen 3100, (1650) San Martín, Provincia de Buenos Aires, Argentina, and Departamento de Química Inorgánica, Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, (1428) Buenos Aires, Argentina
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Ruckenstein E, Berim GO. Symmetry breaking in confined fluids. Adv Colloid Interface Sci 2010; 154:56-76. [PMID: 20170894 DOI: 10.1016/j.cis.2010.01.008] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2009] [Accepted: 01/20/2010] [Indexed: 11/16/2022]
Abstract
The recent progress in the theoretical investigation of the symmetry breaking (the existence of a stable state of a system, in which the symmetry is lower than the symmetry of the system itself) for classical and quantum fluids is reviewed. The emphasis is on the conditions which cause symmetry breaking in the density distribution for one component fluids and binary mixtures confined in a closed nanoslit between identical solid walls. The existing studies have revealed that two kinds of symmetry breaking can occur in such systems. First, a one-dimensional symmetry breaking occurs only in the direction normal to the walls as a fluid density profile asymmetric with respect of the middle of the slit and uniform in any direction parallel to the walls. Second, a two-dimensional symmetry breaking occurs in the fluid density distribution which is nonuniform in one of the directions parallel to the walls and asymmetrical in the direction normal to the walls. It manifests through liquid bumps and bridges in the fluid density distribution. For one component fluids, conditions of existence of symmetry breaking are provided in terms of the average fluid density, strength of fluid-solid interactions, distance at which the solid wall generates a hard core repulsion, and temperature. In the case of binary mixtures, the occurrence of symmetry breaking also depends on the composition of the confined mixtures.
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Affiliation(s)
- Eli Ruckenstein
- Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, New York 14260, USA.
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Affiliation(s)
- Javier Rodriguez
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, 1429, Buenos Aires, Argentina, ECyT, UNSAM, Martín de Irigoyen 3100, 1650, San Martín, Provincia de Buenos Aires, Argentina, and Departamento de Química Inorgánica, Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428, Buenos Aires, Argentina
| | - M. Dolores Elola
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, 1429, Buenos Aires, Argentina, ECyT, UNSAM, Martín de Irigoyen 3100, 1650, San Martín, Provincia de Buenos Aires, Argentina, and Departamento de Química Inorgánica, Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428, Buenos Aires, Argentina
| | - Daniel Laria
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, 1429, Buenos Aires, Argentina, ECyT, UNSAM, Martín de Irigoyen 3100, 1650, San Martín, Provincia de Buenos Aires, Argentina, and Departamento de Química Inorgánica, Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428, Buenos Aires, Argentina
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Puibasset J. Monte-Carlo multiscale simulation study of argon adsorption/desorption hysteresis in mesoporous heterogeneous tubular pores like MCM-41 or oxidized porous silicon. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2009; 25:903-911. [PMID: 19063620 DOI: 10.1021/la802474c] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
In a recent paper [J. Chem. Phys. 2007, 127, 154701] a multiscale approach was introduced which allowed calculation of adsorption/desorption hysteresis for fluid confined in a single mesoporous, heterogeneous tubular pore. The main interest in using such an approach is that it allows one to reconcile a molecular simulation approach generally limited to the nanometer scale (atomistic description of the confined fluid and pore roughness) with the much larger scale (micrometer) relevant to understand the complexity of adsorption/desorption hysteresis (the numerous metastable states in the hysteresis loop are a consequence of the large-scale disorder in the porous material). In this paper, this multiscale approach is used to study adsorption phenomena in mesoporous models made of a collection of disordered, noninterconnected tubular pores, as MCM-41 or porous silicon. A double distribution is introduced: one to characterize the disorder in a given pore, and the other to characterize the disorder between the pores. We consider two distribution shapes: Gaussian and uniform truncated and two cases of pores open at one or both ends. These models are expected to cover a wide variety of real materials made of independent pores, as MCM-41 and oxidized porous silicon. A large variety of hysteresis shapes is obtained, ranging from almost parallel adsorption/desorption branches typical of MCM-41 adsorption to triangular hysteresis typical of porous silicon. The structure of the metastable states inside the hysteresis (scanning adsorption/desorption curves) is also examined. The results are expected to be useful to experimentalists who want to infer pore structure and level of disorder from experimental adsorption/desorption experiments.
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Affiliation(s)
- Joël Puibasset
- Centre de Recherche sur la Matiere Divisee, CNRS-Universite d'Orleans, 1b rue de la Ferollerie, 45071 Orleans, Cedex 02, France.
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Berim GO, Ruckenstein E. Symmetry breaking in binary mixtures in closed nanoslits. J Chem Phys 2008; 128:134713. [PMID: 18397100 DOI: 10.1063/1.2904880] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The symmetry breaking (SB) of the fluid density distribution (FDD) in closed nanoslits between two identical parallel solid walls described by Berim and Ruckenstein [J. Chem. Phys. 128, 024704 (2008)] for a single component fluid is examined for binary mixtures on the basis of a nonlocal canonical ensemble density functional theory. As in Monte Carlo simulations, the periodicity of the FDD in one of the lateral (parallel to the wall surfaces) directions, denoted as the x direction, was assumed. In the other lateral direction, y direction, the FDD was considered to be uniform. The molecules of the two components have different diameters and their Lennard-Jones interaction potentials have different energy parameters. It was found that depending on the average fluid density in the slit and mixture composition, SB can occur for both or none of the components but never for only one of them. In the direction perpendicular to the walls (h direction), the FDDs of both components can be asymmetrical about the middle plane between walls. In the x direction, the SB occurs as bumps and bridges enriched in one of the components, whereas the composition of the mixture between them is enriched in the other component. The dependence of the SB states on the length Lx of the FDD period at fixed average densities of the two components was examined for Lx in the range from 10 to 120 molecular diameters of the smaller size component. It was shown that for large Lx, the stable state of the system corresponds to a bridge. Because the free energy of that state decreases monotonically with increasing Lx, one can conclude that the real period is very large (infinite) and that a single bridge exists in the slit.
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Affiliation(s)
- Gersh O Berim
- Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, New York 14260, USA
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Puibasset J. Influence of surface chemical heterogeneities on adsorption/desorption hysteresis and coexistence diagram of metastable states within cylindrical pores. J Chem Phys 2006; 125:074707. [PMID: 16942364 DOI: 10.1063/1.2229193] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Grand canonical Monte Carlo simulations are performed to determine the adsorption/desorption isotherms at different temperatures of a Lennard-Jones fluid confined within a simple model of cylindrical pores presenting chemical heterogeneities. A complex hysteresis loop is observed, showing hysteresis subloops (scanning curves). This is shown to be consistent with the existence of several metastable states (local minima in the system free energy). A recent extension to the Gibbs ensemble technique is then used to calculate the complete coexistence diagram of these local minima.
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Affiliation(s)
- Joël Puibasset
- Centre de Recherche sur la Matière Divisée, CNRS, Université d'Orléans, 1b rue de la Férollerie, 45071 Orléans, Cedex 02, France.
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