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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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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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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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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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Lomba E, Weis JJ. A computational study of electrolyte adsorption in a simple model for intercalated clays. J Chem Phys 2010; 132:104705. [PMID: 20232982 DOI: 10.1063/1.3357351] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A pillared interlayered clay is represented by a two-dimensional quenched charged disordered medium, in which the pillar configuration is produced by the quench of a two-dimensional electrolyte and the subsequent removal of the anions (that act as a template). The cation charge is counterbalanced by a neutralizing background that is an ideal representation of the layer's negative charge in the experimental system. In this paper we investigate the adsorption of electrolyte particles in this charged disordered medium resorting both to the use of the replica Ornstein-Zernike equation in the hypernetted chain approximation and grand canonical Monte Carlo simulations. The theoretical approach qualitatively reproduces the simulated behavior of the adsorbed fluids. Theoretical estimates of the material porosities obtained for various types of pillar distributions are in good agreement with the simulation. We investigate the influence of the matrix on correlation functions and adsorption isotherms.
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Affiliation(s)
- E Lomba
- Instituto de Química-Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain.
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Zhao SL, Dong W, Liu QH. Fluids in porous media. II. A new model of templated matrices. J Chem Phys 2007; 127:144701. [DOI: 10.1063/1.2756835] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abstract
The morphology of many porous materials is spongelike. Despite the abundance of such materials, simple models which allow for a theoretical description of these materials are still lacking. Here, we propose a hard sponge model which is made by digging spherical cavities in a solid continuum. We found an analytical expression for describing the interaction potential between fluid particles and the spongelike porous matrix. The diagrammatic expansions of different correlation functions are derived as well as that of grand potential. We derived also the Ornstein-Zernike (OZ) equations for this model. In contrast to Madden-Glandt model of random porous media [W. G. Madden and E. D. Glandt, J. Stat. Phys. 51, 537 (1988)], the OZ equations for a fluid confined in our hard sponge model have some similarity to the OZ equations of a three-component fluid mixture. We show also how the replica method can be extended to study our sponge model and that the same OZ equations can be derived also from the extended replica method.
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Affiliation(s)
- S L Zhao
- School of Theoretical Physics and School of Material Science and Engineering, Hunan University, Changsha, 410082, China
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Puibasset J. Generalized isobaric–isothermal ensemble: application to capillary condensation and cavitation in heterogeneous nanopores. Mol Phys 2006. [DOI: 10.1080/00268970600938485] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Lafuente L, Cuesta JA. First-principles derivation of density-functional formalism for quenched-annealed systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041502. [PMID: 17155060 DOI: 10.1103/physreve.74.041502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2006] [Indexed: 05/12/2023]
Abstract
We derive from first principles (without resorting to the replica trick) a density-functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid. When the matrix is created as a quenched configuration of another fluid, the functional can be regarded as depending on the density profile of the matrix fluid as well. In this situation, the replica Ornstein-Zernike equations which do not contain the blocking parts of the correlations can be obtained as functional identities in this formalism, provided the second derivative of this functional is interpreted as the connected part of the direct correlation function. The blocking correlations are totally absent from QA-DFT, but nevertheless the thermodynamics can be entirely obtained from the functional. We apply the formalism to obtain the exact functional for an ideal fluid in an arbitrary matrix, and discuss possible approximations for nonideal fluids.
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Affiliation(s)
- Luis Lafuente
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain.
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