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Kalyuzhnyi YV, Patsahan T, Holovko M, Cummings PT. Phase behavior of patchy colloids confined in patchy porous media. NANOSCALE 2024; 16:4668-4677. [PMID: 38305436 DOI: 10.1039/d3nr02866f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
A simple model for functionalized disordered porous media is proposed and the effects of confinement on self-association, percolation and phase behavior of a fluid of patchy particles are studied. The media are formed by randomly distributed hard-sphere obstacles fixed in space and decorated by a certain number of off-center square-well sites. The properties of the fluid of patchy particles, represented by the fluid of hard spheres each bearing a set of the off-center square-well sites, are studied using an appropriate combination of the scaled particle theory for the porous media, Wertheim's thermodynamic perturbation theory, and Flory-Stockmayer theory. To assess the accuracy of the theory a set of computer simulations have been performed. In general, predictions of the theory appeared to be in good agreement with the computer simulation results. Confinement and competition between the formation of bonds connecting the fluid particles, and connecting fluid particles and obstacles of the matrix, gave rise to a re-entrant phase behavior with three critical points and two separate regions of the liquid-gas phase coexistence.
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Affiliation(s)
- Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
| | - Taras Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
- Lviv Polytechnic National University, 12 S. Bandera Street, UA-79013 Lviv, Ukraine
| | - Myroslav Holovko
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
| | - Peter T Cummings
- School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
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Dong W. Nanoscale thermodynamics needs the concept of a disjoining chemical potential. Nat Commun 2023; 14:1824. [PMID: 37005406 PMCID: PMC10067931 DOI: 10.1038/s41467-023-36970-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 02/21/2023] [Indexed: 04/04/2023] Open
Abstract
Disjoining pressure was discovered by Derjaguin in 1930's, which describes the difference between the pressure of a strongly confined fluid and the corresponding one in a bulk phase. It has been revealed recently that the disjoining pressure is at the origin of distinct differential and integral surface tensions for strongly confined fluids. Here we show how the twin concept, disjoining chemical potential, arises in a reminiscent way although it comes out eighty years later. This twin concept advances our understanding of nanoscale thermodynamics. Ensemble-dependence (or environment-dependence) is one hallmark of thermodynamics of small systems. We show that integral surface tension is ensemble-dependent while differential surface tension is not. Moreover, two generalized Gibbs-Duhem equations involving integral surface tensions are derived, as well as two additional adsorption equations relating surface tensions to adsorption-induced strains. All the results obtained in this work further evidence that an approach alternative of Hill's nanothermodynamics is possible, by extending Gibbs surface thermodynamics instead of resorting to Hill's replica trick. Moreover, we find a compression-expansion hysteresis without any underlying phase transition.
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Affiliation(s)
- W Dong
- Laboratoire de Chimie, CNRS, UMR 5182, Ecole Normale Supérieure de Lyon, 46, Allée d'Italie, 69364, Lyon, Cedex 07, France.
- State Key Laboratory of Chem/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, 410082, Changsha, China.
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Hvozd T, Kalyuzhnyi YV, Vlachy V. Behaviour of the model antibody fluid constrained by rigid spherical obstacles: Effects of the obstacle-antibody attraction. SOFT MATTER 2022; 18:9108-9117. [PMID: 36426679 DOI: 10.1039/d2sm01258h] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
This study investigates the behaviour of a fluid of monoclonal antibodies (mAbs) when trapped in a confinement represented by rigid spherical obstacles that attract antibodies. The antibody molecule is depicted as an assembly of seven hard spheres (7-bead model), organized to resemble a Y-shaped object. The model antibody has two Fab and one Fc domains located in the corners of letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pairs of interactions are effective. The confinement is formed by the randomly distributed hard-spheres fixed in space. The spherical obstacles, besides the size exclusion, interact with beads of the antibody molecules via the Yukawa attractive potential. We applied the combination of the scaled particle theory, replica Ornstein-Zernike equations, Wertheim's thermodynamic perturbation approach and the Flory-Stockmayer theory to calculate: (i) the phase diagram of the liquid-liquid phase separation and the percolation threshold, (ii) the cluster size distributions, and (iii) the second virial coefficient of the protein fluid distributed among the obstacles. All these quantities were calculated as functions of the strength of the attraction between the monoclonal antibodies, and the monoclonal antibodies and obstacles. The conclusion is that while the hard-sphere obstacles decrease the critical density and the critical temperature of the mAbs fluid, the effect of the protein-obstacle attraction is more complex. Adding an attractive potential to the obstacle-mAbs interaction first increases the wideness of the T*-ρ envelope. However, with the further increase of the obstacle-mAbs attraction intensity, we observe reversal of the effect, the T*-ρ curves become narrower. At some point, depending on the obstacle-mAbs interaction, the situation is observed where two different temperatures have the same fluid density (re-entry point). In all the cases shown here the critical point decreases below the value for the neat fluid, but the behaviour with respect to an increase of the strength of the obstacle-mAbs attraction is not monotonic. Yet another interesting phenomenon, known in the literature as an approach toward the "empty liquid" state, is observed. The stability of the "protein droplets", formed by the liquid-liquid phase separation, depends on their local environment and temperature.
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Affiliation(s)
- Taras Hvozd
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskoho 1, Lviv, Ukraine.
| | - Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskoho 1, Lviv, Ukraine.
| | - Vojko Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Večna pot 113, SI-1000 Ljubljana, Slovenia.
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4
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Qiao C, Zhao S, Dong W. Augmented scaled particle theory for a hard disk fluid. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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5
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Hvozd TV, Kalyuzhnyi YV, Vlachy V, Cummings PT. Empty liquid state and re-entrant phase behavior of the patchy colloids confined in porous media. J Chem Phys 2022; 156:161102. [DOI: 10.1063/5.0088716] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Patchy colloids with three and four equivalent patches, confined in an attractive random porous medium, undergo re-entrant gas–liquid phase separation with the liquid phase density approaching zero at low temperatures. The (bonding) colloid–colloid interaction causes the liquid–gas phase separation, which is modulated by the presence of the randomly distributed hard-sphere obstacles, attracting the colloids via Yukawa potential. Due to this interaction, a layer of mutually bonded colloids around the obstacles is formed. The network becomes nonuniform, with colloid particles locally centered on the obstacles. Features described in this article may open possibilities to produce equilibrium gels with predefined nonuniform distribution of particles and indicate how complicated the phase behavior of biological macromolecules in a crowded environment may be.
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Affiliation(s)
- T. V. Hvozd
- Institute for Condensed Matter Physics, Svientsitskoho 1, 79011 Lviv, Ukraine
| | - Yu. V. Kalyuzhnyi
- Institute for Condensed Matter Physics, Svientsitskoho 1, 79011 Lviv, Ukraine
| | - V. Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Večna pot 113, Ljubljana, Slovenia
| | - P. T. Cummings
- Department of Chemical and Biochemical Engineering, Vanderbilt University, Nashville, Tennessee 37235-1604, USA
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Thermodynamics of interfaces extended to nanoscales by introducing integral and differential surface tensions. Proc Natl Acad Sci U S A 2021; 118:2019873118. [PMID: 33452136 DOI: 10.1073/pnas.2019873118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
As a system shrinks down in size, more and more molecules are found in its surface region, so surface contribution becomes a large or even a dominant part of its thermodynamic potentials. Surface tension is a venerable scientific concept; Gibbs defined it as the excess of grand potential of an inhomogeneous system with respect to its bulk value per interface area [J. W. Gibbs, "The Collected Works" in Thermodynamics (1928), Vol. 1]. The mechanical definition expresses it in terms of pressure tensor. So far, it has been believed the two definitions always give the same result. We show that the equivalence can break down for fluids confined in narrow pores. New concepts of integral and differential surface tensions, along with integral and differential adsorptions, need to be introduced for extending Gibbs thermodynamics of interfaces. We derived two generalized Gibbs adsorption equations. These concepts are indispensable for an adequate description of nanoscale systems. We also find a relation between integral surface tension and Derjaguin's disjoining pressure. This lays down the basis for measuring integral and differential surface tensions from disjoining pressure by using an atomic force microscope.
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Hvozd T, Kalyuzhnyi YV, Vlachy V. Aggregation, liquid-liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles. SOFT MATTER 2020; 16:8432-8443. [PMID: 32812624 DOI: 10.1039/d0sm01014f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This study is concerned with the behaviour of proteins within confinement created by hard-sphere obstacles. An individual antibody molecule is depicted as an assembly of seven hard spheres, organized to resemble a Y-shaped (on average) antibody (7-bead model) protein. For comparison with other studies we, in one case, model the protein as a hard sphere decorated by three short-range attractive sites. The antibody has two Fab and one Fc domains located in the corners of the letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pair interactions are possible. The confinement is formed by the randomly distributed hard-sphere obstacles fixed in space. Aside from size exclusion, the obstacles do not interact with antibodies, but they affect the protein-protein correlation. We used a combination of the scaled-particle theory, Wertheim's thermodynamic perturbation theory and the Flory-Stockmayer theory to calculate: (i) the second virial coefficient of the protein fluid, (ii) the percolation threshold, (iii) cluster size distributions, and (iv) the liquid-liquid phase separation as a function of the strength of the various pair interactions of the protein and the model parameters, such as protein concentration and the packing fraction of obstacles. The conclusion is that hard-sphere obstacles strongly decrease the critical density and also, but to a much lesser extent, the critical temperature. Also, the confinement enhances clustering, making the percolating region broader. The effect depends on the model parameters, such as the packing fraction of obstacles η0, the inter-site interaction strength εIJ, and the ratio between the size of the obstacle σ0 and the size of one bead of the model antibody σhs; the value of this ratio is varied here from 2 to 5. Interestingly, at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), and the slope depends on the observation temperature, but then at higher values of η0 it increases. The calculated values of the second virial coefficient also depend on the size of the obstacles.
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Affiliation(s)
- Taras Hvozd
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskoho 1, Lviv, Ukraine.
| | - Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskoho 1, Lviv, Ukraine. and Faculty of Science, J. E. Purkinje University, 400 96 Ústí nad Labem, Czech Republic
| | - Vojko Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Večna pot 113, SI-1000 Ljubljana, Slovenia.
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Nelson A, Kalyuzhnyi Y, Patsahan T, McCabe C. Liquid-vapor phase equilibrium of a simple liquid confined in a random porous media: Second-order Barker-Henderson perturbation theory and scaled particle theory. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2019.112348] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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9
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Affiliation(s)
- C. Z. Qiao
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, 130 Meilong Road, 200237 Shanghai, China
- 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
- State Key Laboratory of Chemical Engineering and School 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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10
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Qiao CZ, Zhao SL, Liu HL, Dong W. Connect the Thermodynamics of Bulk and Confined Fluids: Confinement-Adsorption Scaling. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:3840-3847. [PMID: 30691262 DOI: 10.1021/acs.langmuir.8b03126] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A fluid (a gas or a liquid) adsorbed in a porous material can behave very differently from its bulk counterpart. The advent of various synthesized materials with nanopores and their wide applications have provided strong impetus for studying fluids in confinement because our current understanding is still incomplete. From a large number of Monte Carlo simulations, we found a scaling relation that allows for connecting some thermodynamic properties (chemical potential, free energy per particle, and grand potential per particle) of a confined fluid to the bulk ones. Upon rescaling the adsorbed fluid density, the adsorption isotherms for many different confining environments collapse to the corresponding bulk curve. We also reveal the intimate connection of the reported scaling relation to Gibbs theory of inhomogeneous fluids and morphological thermodynamics. The advance in our understanding of confined fluids, gained from this study, also opens attractive perspectives for circumventing experimental difficulty for directly measuring some fluid thermodynamic properties in nanoporous materials.
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Affiliation(s)
- C Z Qiao
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Chimie, UMR 5182 , 46, Allée d'Italie , 69364 Lyon Cedex 07 , France
| | | | | | - W Dong
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Chimie, UMR 5182 , 46, Allée d'Italie , 69364 Lyon Cedex 07 , France
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11
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Patsahan O, Patsahan T, Holovko M. Vapour-liquid critical parameters of a 2:1 primitive model of ionic fluids confined in disordered porous media. J Mol Liq 2018. [DOI: 10.1016/j.molliq.2017.12.033] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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12
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Hvozd M, Patsahan T, Holovko M. Isotropic-Nematic Transition and Demixing Behavior in Binary Mixtures of Hard Spheres and Hard Spherocylinders Confined in a Disordered Porous Medium: Scaled Particle Theory. J Phys Chem B 2018; 122:5534-5546. [PMID: 29385800 DOI: 10.1021/acs.jpcb.7b11834] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory, the analytical expressions of the free energy, the pressure, and the chemical potentials of HS and HSC have been derived. The improvement of obtained results is considered by introducing the Carnahan-Starling-like and Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic transition are calculated from the bifurcation analysis of the integral equation for the orientation singlet distribution function and from the conditions of thermodynamic equilibrium. Both the approaches correctly predict the isotropic-nematic transition at low concentrations of hard spheres. However, the thermodynamic approach provides more accurate results and is able to describe the demixing phenomena in the isotropic and nematic phases. The effects of porous medium on the isotropic-nematic phase transition and demixing behavior in a binary HS/HSC mixture are discussed.
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Affiliation(s)
- M Hvozd
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine , 1 Svientsitskii Street , 79011 Lviv , Ukraine
| | - T Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine , 1 Svientsitskii Street , 79011 Lviv , Ukraine
| | - M Holovko
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine , 1 Svientsitskii Street , 79011 Lviv , Ukraine
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13
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Hvozd TV, Kalyuzhnyi YV, Cummings PT. Phase Equilibria of Polydisperse Square-Well Chain Fluid Confined in Random Porous Media: TPT of Wertheim and Scaled Particle Theory. J Phys Chem B 2018; 122:5458-5465. [PMID: 29656640 DOI: 10.1021/acs.jpcb.7b11741] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Extension of Wertheim's thermodynamic perturbation theory and its combination with scaled particle theory is proposed and applied to study the liquid-gas phase behavior of polydisperse hard-sphere square-well chain fluid confined in the random porous media. Thermodynamic properties of the reference system, represented by the hard-sphere square-well fluid in the matrix, are calculated using corresponding extension of the second-order Barker-Henderson perturbation theory. We study effects of polydispersity and confinement on the phase behavior of the system. While polydispersity causes increase of the region of phase coexistence due to the critical temperature increase, confinement decreases the values of both critical temperature and critical density making the region of phase coexistence smaller. This effect is enhanced with the increase of the size ratio of the fluid and matrix particles. The increase of the average chain length at fixed values of polydispersity and matrix density shifts the critical point to a higher temperature and a slightly lower density.
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Affiliation(s)
- Taras V Hvozd
- Institute for Condensed Matter Physics , National Academy of Sciences of Ukraine , 1 Svientsitskii St. , Lviv 79011 , Ukraine
| | - Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics , National Academy of Sciences of Ukraine , 1 Svientsitskii St. , Lviv 79011 , Ukraine
| | - Peter T Cummings
- Department of Chemical and Biochemical Engineering , Vanderbilt University , Nashville , Tennessee 37235-1604 , United States
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14
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Patsahan OV, Patsahan TM, Holovko MF. Vapor-liquid phase behavior of a size-asymmetric model of ionic fluids confined in a disordered matrix: The collective-variables-based approach. Phys Rev E 2018; 97:022109. [PMID: 29548228 DOI: 10.1103/physreve.97.022109] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Indexed: 11/07/2022]
Abstract
We develop a theory based on the method of collective variables to study the vapor-liquid equilibrium of asymmetric ionic fluids confined in a disordered porous matrix. The approach allows us to formulate the perturbation theory using an extension of the scaled particle theory for a description of a reference system presented as a two-component hard-sphere fluid confined in a hard-sphere matrix. Treating an ionic fluid as a size- and charge-asymmetric primitive model (PM) we derive an explicit expression for the relevant chemical potential of a confined ionic system which takes into account the third-order correlations between ions. Using this expression, the phase diagrams for a size-asymmetric PM are calculated for different matrix porosities as well as for different sizes of matrix and fluid particles. It is observed that general trends of the coexistence curves with the matrix porosity are similar to those of simple fluids under disordered confinement, i.e., the coexistence region gets narrower with a decrease of porosity and, simultaneously, the reduced critical temperature T_{c}^{*} and the critical density ρ_{i,c}^{*} become lower. At the same time, our results suggest that an increase in size asymmetry of oppositely charged ions considerably affects the vapor-liquid diagrams leading to a faster decrease of T_{c}^{*} and ρ_{i,c}^{*} and even to a disappearance of the phase transition, especially for the case of small matrix particles.
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Affiliation(s)
- O V Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine
| | - T M Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine
| | - M F Holovko
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine
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15
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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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16
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Holovko M, Patsahan T, Patsahan O. Application of the ionic association concept to the study of the phase behaviour of size-asymmetric ionic fluids in disordered porous media. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.11.030] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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17
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Hvozd TV, Kalyuzhnyi YV. Two- and three-phase equilibria of polydisperse Yukawa hard-sphere fluids confined in random porous media: high temperature approximation and scaled particle theory. SOFT MATTER 2017; 13:1405-1412. [PMID: 28120982 DOI: 10.1039/c6sm02613c] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We have studied the phase behavior of polydisperse Yukawa hard-sphere fluid confined in random porous media using extension and combination of high temperature approximation and scaled particle theory. The porous media are represented by the matrix of randomly placed hard-sphere obstacles. Due to the confinement, polydispersity effects are substantially enhanced. At an intermediate degree of fluid polydispersity and low density of the matrix, we observe two-phase coexistence with two critical points, and cloud and shadow curves forming closed loops of ellipsoidal shape. With the increase of the matrix density and the constant degree of polydispersity, these two critical points merge and disappear, and at lower temperatures the system fractionates into three coexisting phases. A similar phase behavior was observed in the absence of the porous media caused, however, by the increase of the polydispersity.
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Affiliation(s)
- Taras V Hvozd
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine - 1 Svientsitskii St., Lviv, Ukraine 79011.
| | - Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine - 1 Svientsitskii St., Lviv, Ukraine 79011.
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18
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Holovko M, Patsahan T, Patsahan O. Effects of disordered porous media on the vapour-liquid phase equilibrium in ionic fluids: application of the association concept. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.10.045] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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19
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Holovko MF, Patsahan O, Patsahan T. Vapour-liquid phase diagram for an ionic fluid in a random porous medium. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:414003. [PMID: 27548356 DOI: 10.1088/0953-8984/28/41/414003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the vapour-liquid phase behaviour of an ionic fluid confined in a random porous matrix formed by uncharged hard sphere particles. The ionic fluid is modelled as an equimolar binary mixture of oppositely charged equisized hard spheres, the so-called restricted primitive model (RPM). Considering the matrix-fluid system as a partly-quenched model, we develop a theoretical approach which combines the method of collective variables with the extension of the scaled-particle theory (SPT) for a hard-sphere fluid confined in a disordered hard-sphere matrix. The approach allows us to formulate the perturbation theory using the SPT for the description of the thermodynamics of the reference system. The phase diagrams of the RPM in matrices of different porosities and for different size ratios of matrix and fluid particles are calculated in the random-phase approximation and also when the effects of higher-order correlations between ions are taken into account. Both approximations correctly reproduce the basic effects of porous media on the vapour-liquid phase diagram, i.e. with a decrease of porosity the critical point shifts towards lower fluid densities and lower temperatures and the coexistence region gets narrower. For the fixed matrix porosity, both the critical temperature and the critical density increase with an increase of size of matrix particles and tend to the critical values of the bulk RPM.
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Affiliation(s)
- M F Holovko
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine
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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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Patsahan T, Holovko M, Dong W. Erratum: “Fluids in porous media. III. Scaled particle theory” [J. Chem. Phys. 134, 074503 (2011)]. J Chem Phys 2016; 144:099903. [DOI: 10.1063/1.4943572] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kalyuzhnyi YV, Holovko M, Patsahan T, Cummings PT. Phase Behavior and Percolation Properties of the Patchy Colloidal Fluids in the Random Porous Media. J Phys Chem Lett 2014; 5:4260-4264. [PMID: 26273972 DOI: 10.1021/jz502135f] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The lack of a simple analytical description of the hard-sphere fluid in a matrix with hard-core obstacles is limiting progress in the development of thermodynamic perturbation theories for the fluid in random porous media. We propose a simple and highly accurate analytical scheme, which allows us to calculate thermodynamic and percolation properties of a network-forming fluid confined in the random porous media, represented by the hard-sphere fluid and overlapping hard-sphere matrices, respectively. Our scheme is based on the combination of scaled-particle theory, Wertheim's thermodynamic perturbation theory for associating fluids and extension of the Flory-Stockmayer theory for percolation. The liquid-gas phase diagram and percolation threshold line for several versions of the patchy colloidal fluid model confined in a random porous media are calculated and discussed. The method presented enables calculation of the thermodynamic and percolation properties of a large variety of polymerizing and network-forming fluids confined in random porous media.
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Affiliation(s)
- Y V Kalyuzhnyi
- †Institute for Condensed Matter Physics, Svientsitskoho 1, 79011 Lviv, Ukraine
| | - M Holovko
- †Institute for Condensed Matter Physics, Svientsitskoho 1, 79011 Lviv, Ukraine
| | - T Patsahan
- †Institute for Condensed Matter Physics, Svientsitskoho 1, 79011 Lviv, Ukraine
| | - P T Cummings
- ‡Department of Chemical and Biochemical Engineering, Vanderbilt University, Nashville, Tennessee 37235-1604, United States
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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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Abstract
The scaled particle theory (SPT) is applied to describe thermodynamic properties of a hard sphere (HS) fluid in random porous media. To this purpose, we extended the SPT2 approach, which has been developed previously. The analytical expressions for the chemical potential of an HS fluid in HS and overlapping hard sphere (OPH) matrices, sponge matrix, and hard convex body (HCB) matrix are obtained and analyzed. A series of new approximations for SPT2 are proposed. The grand canonical Monte Carlo (GGMC) simulations are performed to verify an accuracy of the SPT2 approach combined with the new approximations. A possibility of mapping between thermodynamic properties of an HS fluid in random porous media of different types is discussed. It is shown that thermodynamic properties of a fluid in the different matrices tend to be equal if the probe particle porosities and the specific surface pore areas of considered matrices are identical. The obtained results for an HS fluid in random porous media as reference systems are used to extend the van der Waals equation of state to the case of a simple fluid in random porous media. It is observed that a decrease of matrix porosity leads to lowering of the critical temperature and the critical density of a confined fluid, while an increase of a size of matrix particles causes an increase of these critical parameters.
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Löwen H, Allahyarov E, Ivlev A, Morfill GE. Heterogeneous crystallization in colloids and complex plasmas: the role of binary mobilities. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:284125. [PMID: 22738924 DOI: 10.1088/0953-8984/24/28/284125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Both charged colloidal suspensions and complex (dusty) plasmas represent classical many-body strongly coupled Coulomb systems. Here we discuss their basic properties and focus on their heterogeneous crystallization from an undercooled melt. In particular, a model with different mobilities is proposed which is realizable in binary mixtures of charged particles. Within this binary-mobility model, the crystallization behaviour near a structured wall is explored by Brownian dynamics computer simulations. As a result, the propagation velocity of the crystal-fluid interface is a nonmonotonic function of the mobility ratio (if expressed in terms of an averaged mobility).
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Affiliation(s)
- H Löwen
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
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