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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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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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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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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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Zhao S, Liu Y, Chen X, Lu Y, Liu H, Hu Y. Unified Framework of Multiscale Density Functional Theories and Its Recent Applications. MESOSCALE MODELING IN CHEMICAL ENGINEERING PART II 2015. [DOI: 10.1016/bs.ache.2015.10.001] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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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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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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