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Láska M, Parry AO, Malijevský A. Breaking Cassie's Law for Condensation in a Nanopatterned Slit. PHYSICAL REVIEW LETTERS 2021; 126:125701. [PMID: 33834816 DOI: 10.1103/physrevlett.126.125701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Revised: 02/10/2021] [Accepted: 03/01/2021] [Indexed: 06/12/2023]
Abstract
We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls, each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations. These are characterised by different contact angles due to interfacial pinning, with one larger and one smaller than the Cassie angle. We determine the triple point and predict two types of dispersion force induced Derjaguin-like corrections due to mesoscopic volume reduction and the singular free-energy contribution from nanodroplets and bubbles. We test these predictions using a fully microscopic density functional model which confirms their validity even for molecularly narrow slits. Analogous mesoscopic corrections are also predicted for two-dimensional systems arising from thermally induced interfacial wandering.
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Affiliation(s)
- Martin Láska
- 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
| | - 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 The Czech Academy of Sciences, Institute of Chemical Process Fundamentals, Department of Molecular Modelling, 165 02 Prague, Czech Republic
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2
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Wójtowicz A, Napiórkowski M. Phase diagrams and solvation forces of a uniaxial ferromagnet in a slit--the double-parabola approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:485007. [PMID: 24200538 DOI: 10.1088/0953-8984/25/48/485007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We obtain the phase diagrams of a uniaxial ferromagnet enclosed in a slit and analyse the properties of the solvation forces acting between the slit walls. Our analysis is based on the mean-field theory applied to the double-parabola Hamiltonian for a uniaxial ferromagnet in a slit, which allows us to derive several results in analytic form. In particular, the Kelvin law and the law describing the influence of the slit width on the position of the delocalization transition as compared to the wetting transition are derived and the corresponding critical exponent is evaluated. The influence of the thermodynamic state of the system on the properties of the solvation forces, in particular their discontinuous behaviour at coexistence lines, is discussed.
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Affiliation(s)
- Adam Wójtowicz
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, 00-681 Warszawa, Hoża 69, Poland
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Rascón C, Parry AO, Nürnberg R, Pozzato A, Tormen M, Bruschi L, Mistura G. The order of condensation in capillary grooves. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:192101. [PMID: 23611878 DOI: 10.1088/0953-8984/25/19/192101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We consider capillary condensation in a deep groove of width L. The transition occurs at a pressure p(co)(L) described, for large widths, by the Kelvin equation p(sat) - p(co)(L) = 2σ cosθ/L, where θ is the contact angle at the side walls and σ is the surface tension. The order of the transition is determined by the contact angle of the capped end θcap; it is continuous if the liquid completely wets the cap, and first-order otherwise. When the transition is first-order, corner menisci at the bottom of the capillary lead to a pronounced metastability, determined by a complementary Kelvin equation Δp(L) = 2σ sinθcap/L. On approaching the wetting temperature of the capillary cap, the corner menisci merge and a single meniscus unbinds from the bottom of the groove. Finite-size scaling shifts, crossover behaviour and critical singularities are determined at mean-field level and beyond. Numerical and experimental results showing the continuous nature of condensation for θcap = 0 and the influence of corner menisci on adsorption isotherms are presented.
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Affiliation(s)
- Carlos Rascón
- GISC, Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain.
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4
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Zubaszewska M, Gendiar A, Drzewiński A. Capillary condensation in a square geometry with surface fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:062104. [PMID: 23367989 DOI: 10.1103/physreve.86.062104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2012] [Indexed: 06/01/2023]
Abstract
We study the influence of wetting on capillary condensation for a simple fluid in a square geometry with surface fields, where the reference system is an infinitely long slit. The corner transfer matrix renormalization group method has been extended to study a two-dimensional Ising model confined in an L × L geometry with equal surface fields. Our results have confirmed that in both geometries the coexistence line shift is governed by the same scaling powers, but their prefactors are different.
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Affiliation(s)
- M Zubaszewska
- Institute of Physics, University of Zielona Góra, ulica Prof Z Szafrana 4a, 65-516 Zielona Góra, Poland
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Brovchenko I, Oleinikova A. Effect of Pore Size on the Condensation/Evaporation Transition of Confined Water in Equilibrium with Saturated Bulk Water. J Phys Chem B 2011; 115:9990-10000. [DOI: 10.1021/jp112052f] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Ivan Brovchenko
- Physical Chemistry, Dortmund University of Technology, Otto-Hahn-Strasse 6, Dortmund, D-44227, Germany
| | - Alla Oleinikova
- Physical Chemistry, Dortmund University of Technology, Otto-Hahn-Strasse 6, Dortmund, D-44227, Germany
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Dantchev D, Rudnick J, Barmatz M. Finite-size effects on the behavior of the susceptibility in van der Waals films bounded by strongly absorbing substrates. Phys Rev E 2007; 75:011121. [PMID: 17358124 DOI: 10.1103/physreve.75.011121] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2006] [Indexed: 11/07/2022]
Abstract
We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slablike system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of 3He and 4He films in the vicinity of their respective liquid-vapor critical points.
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Affiliation(s)
- Daniel Dantchev
- Institute of Mechanics-BAS, Academic Georgy Bonchev St. Building 4, 1113 Sofia, Bulgaria
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Roth R, Kroll KM. Capillary evaporation in pores. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:6517-6530. [PMID: 21690851 DOI: 10.1088/0953-8984/18/28/007] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We combine a density functional theory (DFT) treatment of capillary evaporation in a cylindrical pore with the morphometric approach in order to study the formation and breaking of bubbles in a hydrophobically lined part of a cone. The morphometric approach, in which the grand potential of a system is described in four geometrical terms with corresponding thermodynamical coefficients, allows extrapolation or scaling from macroscopic system sizes to nanoscales. Since only a small number of fluid particles are involved in bubble formation, it is a pseudo phase transition, and the system is subjected to fluctuations between states with and without a bubble. Fluctuations are not included in a DFT treatment, which makes it possible to explore both states of the system in great detail, in contrast to computer simulations, in which averages might be obscured by fluctuations.
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Affiliation(s)
- R Roth
- Max-Planck Institut für Metallforschung, Heisenbergstraße 3, D-70589 Stuttgart, Germany. Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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Vink RLC, Binder K, Horbach J. Critical behavior of a colloid-polymer mixture confined between walls. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056118. [PMID: 16803009 DOI: 10.1103/physreve.73.056118] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2006] [Indexed: 05/10/2023]
Abstract
We investigate the influence of confinement on phase separation in colloid-polymer mixtures. To describe the particle interactions, the colloid-polymer model of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] is used. Grand canonical Monte Carlo simulations are then applied to this model confined between two parallel hard walls, separated by a distance D = 5 colloid diameters. We focus on the critical regime of the phase separation and look for signs of crossover from three-dimensional (3D) Ising to two-dimensional (2D) Ising universality. To extract the critical behavior, finite size scaling techniques are used, including the recently proposed algorithm of Kim et al [Phys. Rev. Lett. 91, 065701 (2003)]. Our results point to "effective" critical exponents that differ profoundly from 3D Ising values, and that are already very close to 2D Ising values. In particular, we observe that the critical exponent of the order parameter in the confined system is smaller than in 3D bulk, yielding a "flatter" binodal. Our results also show an increase in the critical colloid packing fraction in the confined system with respect to the bulk. The latter seems consistent with theoretical expectations, although subtleties due to singularities in the critical behavior of the coexistence diameter cannot be ruled out.
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Affiliation(s)
- R L C Vink
- Institut Theoretische Physik II, Heinrich Heine Universität, Düsseldorf, Germany
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Borówko M, Bucior K, Sokołowski S, Staszewski T. Adsorption of fluids in slitlike pores containing a small amount of mobile ions. J Colloid Interface Sci 2005; 291:223-8. [PMID: 15964009 DOI: 10.1016/j.jcis.2005.04.080] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2005] [Revised: 04/21/2005] [Accepted: 04/23/2005] [Indexed: 11/26/2022]
Abstract
We apply density functional theory to investigate changes in the phase behavior of a fluid caused by the presence of mobile ions inside the pore. The approach has been based on the fundamental measure density functional theory and on the theory of nonuniform electrolytes developed recently by O. Pizio, A. Patrykiejew, S. Sokołowski [J. Chem. Phys. 121 (2005) 11,957]. We have evaluated capillary condensation phase diagrams for pores of different widths and for different concentrations of confined ions. The calculations have demonstrated that the presence of ions leads to lowering the critical temperature and to an increase of the value of the chemical potential at the capillary condensation point.
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Affiliation(s)
- M Borówko
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, UMCS, 20031 Lublin, Poland
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Reister E, Müller M, Kumar SK. Equilibrium Phase Behavior of Polybutadiene/Polyisoprene Films: Binodals and Spinodals. Macromolecules 2005. [DOI: 10.1021/ma0473465] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ellen Reister
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Marcus Müller
- Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706-1390
| | - Sanat K. Kumar
- Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180
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Bryk P, Pizio O, Sokolowski S. Capillary condensation of short-chain molecules. J Chem Phys 2005; 122:194904. [PMID: 16161614 DOI: 10.1063/1.1898484] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A density-functional study of capillary condensation of fluids of short-chain molecules confined to slitlike pores is presented. The molecules are modeled as freely jointed tangent spherical segments with a hard core and with short-range attractive interaction between all the segments. We investigate how the critical parameters of capillary condensation of the fluid change when the pore width decreases and eventually becomes smaller than the nominal linear dimension of the single-chain molecule. We find that the dependence of critical parameters for a fluid of dimers and of tetramers on pore width is similar to that of the monomer fluid. On the other hand, for a fluid of chains consisting of a larger number of segments we observe an inversion effect. Namely, the critical temperature of capillary condensation decreases with increasing pore width for a certain interval of values of the pore width. This anomalous behavior is also influenced by the interaction between molecules and pore walls. We attribute this behavior to the effect of conformational changes of molecules upon confinement.
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Affiliation(s)
- Paweł Bryk
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, 20-031 Lublin, Poland.
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Drzewiński A, Szota K. Corrections to the Kelvin equation for long-range boundary fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:056110. [PMID: 16089605 DOI: 10.1103/physreve.71.056110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2005] [Indexed: 05/03/2023]
Abstract
The properties of a simple fluid, or Ising magnet, confined in an L x infinity geometry, are studied by means of numerical density-matrix renormalization-group techniques. Whereas the particle-particle interactions are short ranged, the wall-particle interactions can be long ranged. Using a few complementary criteria the wetting transition line has been found for boundary fields with different ranges (including a marginal case) and its scaling form has been analyzed. A main goal was to analyze the influence of wetting on the scaling of the Kelvin equation, focusing on the leading correction term. We have found that at complete wetting the larger the range of the boundary fields, the smaller the region of anomalous corrections of type 1/L(4/3).
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Affiliation(s)
- Andrzej Drzewiński
- Czestochowa University of Technology, Institute of Mathematics and Computer Science, ul.Dabrowskiego 73, 42-200 Czestochowa, Poland
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Maciołek A, Drzewiński A, Evans R. Near-critical confined fluids and Ising films: density-matrix renormalization-group study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:056137. [PMID: 11736044 DOI: 10.1103/physreve.64.056137] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2001] [Indexed: 05/23/2023]
Abstract
Two-dimensional Ising strips subject to identical surface fields h(1)=h(2) > or =0 are studied for temperatures above and below the bulk critical temperature T(c) and a range of bulk fields h by means of the density-matrix renormalization-group method. In the case of nonvanishing surface fields, the near-critical behavior of the solvation force f(solv), total adsorption Gamma, inverse longitudinal correlation length xi(parallel)( -1) and specific heat C(H) is strongly influenced by the (pseudo) capillary condensation that occurs below T(c). We obtain scaling functions of f(solv), Gamma, and xi(parallel)(-1). C(H) exhibits a weakly rounded singularity on crossing the pseudocoexistence line. We contrast these results with those for the case of free boundaries where, for temperatures slightly below T(c), f(solv) and C(H) exhibit a sharp extremum away from h=0. Our results have direct repercussions for the properties of near-critical Ising films in three dimensions and we argue that the long-ranged solvation (Casimir) force in confined fluids should be more attractive in the neighborhood of the capillary critical point than exactly at the bulk critical point.
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Affiliation(s)
- A Maciołek
- Institute of Physical Chemistry, Polish Academy of Sciences, Department III, Kasprzaka 44/52, PL-01-224 Warsaw, Poland
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Dillmann O, Janke W, Müller M, Binder K. A Monte Carlo test of the Fisher–Nakanishi–Scaling theory for the capillary condensation critical point. J Chem Phys 2001. [DOI: 10.1063/1.1350574] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Drzewiński A, Maciołek A, Evans R. Influence of capillary condensation on the near-critical solvation force. PHYSICAL REVIEW LETTERS 2000; 85:3079-3082. [PMID: 11019271 DOI: 10.1103/physrevlett.85.3079] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2000] [Indexed: 05/23/2023]
Abstract
We argue that in a fluid, or magnet, confined by adsorbing walls which favor liquid, or the (+) phase, the solvation (Casimir) force in the vicinity of the critical point is strongly influenced by capillary condensation which occurs below the bulk critical temperature T(c). At T slightly below and above T(c), a small bulk field h<0, which favors gas, or the (-) phase, leads to residual condensation and a solvation force which is much more attractive (at the same large wall separation) than that found exactly at the critical point. Our predictions are supported by results obtained from density-matrix renormalization-group calculations in a two-dimensional Ising strip subject to identical surface fields.
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Affiliation(s)
- A Drzewiński
- Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, Wrocław 2, Poland
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Drzewinski A. Coexistence of excited states in confined ising systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:4378-4381. [PMID: 11088967 DOI: 10.1103/physreve.62.4378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2000] [Indexed: 05/23/2023]
Abstract
Using the density-matrix renormalization-group method we study the two-dimensional Ising model in an infinite strip geometry with free-boundary conditions. The renormalization scheme enables us to consider systems of width up to 300 (lattice spacings) and study the influence of the bulk magnetic field on correlation function structure for all temperatures. From our numerical results we have determined the crossover line for the correlation length related to the coexistence of the excited states. A detailed scaling study of this line is performed. Our numerical results support and further specify previous conclusions reached by Abraham, Parry, and Upton based on the bubble model of correlations.
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Affiliation(s)
- A Drzewinski
- Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wroclaw 2, Poland
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Albano EV, Binder K, Paul W. Capillary condensation in the two-dimensional lattice gas: A Monte Carlo test of fluctuation corrections to the Kelvin equation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/30/10/009] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Müller M, Binder K. Wetting and Capillary Condensation in Symmetric Polymer Blends: A Comparison between Monte Carlo Simulations and Self-Consistent Field Calculations. Macromolecules 1998. [DOI: 10.1021/ma980052x] [Citation(s) in RCA: 72] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Müller
- Institut für Physik, WA 331, Johannes Gutenberg Universität, D-55099 Mainz, Germany
| | - K. Binder
- Institut für Physik, WA 331, Johannes Gutenberg Universität, D-55099 Mainz, Germany
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Parry AO, Evans R. Finite-size-scaling derivation of the Widom critical-exponent relation for surface tension. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:5282-5283. [PMID: 9908756 DOI: 10.1103/physreva.46.5282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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