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van Westen T, Gross J. Double-Hard-Sphere perturbation theory: a perturbation theory that is less dependent on the value of the hard-sphere diameter. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2059410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart, Germany
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van Westen T, Hammer M, Hafskjold B, Aasen A, Gross J, Wilhelmsen Ø. Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid. J Chem Phys 2022; 156:104504. [DOI: 10.1063/5.0082690] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.
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Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Morten Hammer
- Department of Gas Technology, SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Bjørn Hafskjold
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Ailo Aasen
- Department of Gas Technology, SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Øivind Wilhelmsen
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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van Westen T, Gross J. Accurate thermodynamics of simple fluids and chain fluids based on first-order perturbation theory and second virial coefficients: uv-theory. J Chem Phys 2021; 155:244501. [PMID: 34972377 DOI: 10.1063/5.0073572] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a simplification of our recently proposed uf-theory for describing the thermodynamics of simple fluids and fluids comprising short chain molecules. In its original form, the uf-theory interpolates the Helmholtz energy between a first-order f-expansion and first-order u-expansion as (effective) lower and upper bounds. We here replace the f-bound by a new, tighter (effective) lower bound. The resulting equation of state interpolates between a first-order u-expansion at high densities and another first-order u-expansion that is modified to recover the exact second virial coefficient at low densities. The theory merely requires the Helmholtz energy of the reference fluid, the first-order u-perturbation term, and the total perturbation contribution to the second virial coefficient as input. The revised theory-referred to as uv-theory-is thus simpler than the uf-theory but leads to similar accuracy, as we show for fluids with intermolecular pair interactions governed by a Mie potential. The uv-theory is thereby easier to extend to fluid mixtures and provides more flexibility in extending the model to non-spherical or chain-like molecules. The usefulness of the uv-theory for developing equation-of-state models of non-spherical molecules is here exemplified by developing an equation of state for Lennard-Jones dimers.
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Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
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van Westen T, Gross J. Accurate first-order perturbation theory for fluids: uf-theory. J Chem Phys 2021; 154:041102. [PMID: 33514104 DOI: 10.1063/5.0031545] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We propose a new first-order perturbation theory that provides a near-quantitative description of the thermodynamics of simple fluids. The theory is based on the ansatz that the Helmholtz free energy is bounded below by a first-order Mayer-f expansion. Together with the rigorous upper bound provided by a first-order u-expansion, this brackets the actual free energy between an upper and (effective) lower bound that can both be calculated based on first-order perturbation theory. This is of great practical use. Here, the two bounds are combined into an interpolation scheme for the free energy. The scheme exploits the fact that a first-order Mayer-f perturbation theory is exact in the low-density limit, whereas the accuracy of a first-order u-expansion grows when density increases. This allows an interpolation between the lower "f"-bound at low densities and the upper "u" bound at higher liquid-like densities. The resulting theory is particularly well behaved. Using a density-dependent interpolating function of only two adjustable parameters, we obtain a very accurate representation of the full fluid-phase behavior of a Lennard-Jones fluid. The interpolating function is transferable to other intermolecular potential types, which is here shown for the Mie m-6 family of fluids. The extension to mixtures is simple and accurate without requiring any dependence of the interpolating function on the composition of the mixture.
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Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
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van Westen T, Gross J. A critical evaluation of perturbation theories by Monte Carlo simulation of the first four perturbation terms in a Helmholtz energy expansion for the Lennard-Jones fluid. J Chem Phys 2017; 147:014503. [DOI: 10.1063/1.4991008] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
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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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Affiliation(s)
- Udai P. Singh
- a Department of Chemistry , Boston College , Chestnut Hill , Massachusetts , 02167 , U.S.A
- b Department of Physics , Raja Harpal Singh Degree College , Singramau , Jaunpur , 222175 , India
| | - Udayan Mohanty
- a Department of Chemistry , Boston College , Chestnut Hill , Massachusetts , 02167 , U.S.A
| | - Suresh K. Sinha
- c Department of Physics , L. S. College, Bihar University , Muzaffarpur , 842001 , India
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Andersen HC, Chandler D, Weeks JD. Roles of Repulsive and Attractive Forces in Liquids : The Equilibrium Theory of Classical Fluids. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470142530.ch2] [Citation(s) in RCA: 212] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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JACKSON GEORGE. John Adair Barker 24 March 1925–27 October 1995. Mol Phys 1998. [DOI: 10.1080/00268979809483200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Madden WG, Fitts DD, Smith WR. Perturbation theory for the radial distribution functions of dipolar and quadrupolar hard-sphere fluids. Mol Phys 1978. [DOI: 10.1080/00268977800100751] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Perturbation theory and the radial distribution function of fluids with nonspherical potentials. Chem Phys Lett 1975. [DOI: 10.1016/0009-2614(75)87013-8] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Moffat MJ, Kozak JJ. Analysis of the Barker‐Henderson local‐compressibility approximation. II. Comparison with other theories of liquids. J Chem Phys 1973. [DOI: 10.1063/1.1679341] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Smith WR, Henderson D, Barker JA. Approximate Evaluation of the Second‐Order Term in the Perturbation Theory of Fluids. J Chem Phys 1970. [DOI: 10.1063/1.1674017] [Citation(s) in RCA: 65] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Henderson D, Barker JA. Perturbation Theory and the Equation of State of Mixtures of Hard Spheres. J Chem Phys 1968. [DOI: 10.1063/1.1670610] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Barker JA, Henderson D. Perturbation Theory and Equation of State for Fluids: The Square‐Well Potential. J Chem Phys 1967. [DOI: 10.1063/1.1712308] [Citation(s) in RCA: 911] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Nosanow LH. Statistical Mechanics of Multicomponent Systems: Perturbation Theory. J Chem Phys 1959. [DOI: 10.1063/1.1730245] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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