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Mausbach P, Fingerhut R, Vrabec J. Thermodynamic metric geometry and the Fisher-Widom line of simple fluids. Phys Rev E 2022; 106:034136. [PMID: 36266912 DOI: 10.1103/physreve.106.034136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 07/12/2022] [Indexed: 06/16/2023]
Abstract
Two boundary lines are frequently discussed in the literature, separating state regions dominated by repulsion or attraction. The Fisher-Widom line indicates where the longest-range decay of the total pair correlation function crosses from monotonic to exponentially damped oscillatory. In the context of thermodynamic metric geometry, such a transition exists where the Ricci curvature scalar vanishes, R=0. To establish a possible relation between these two lines, R is worked out for four simple fluids. The truncated and shifted Lennard-Jones, a colloid-like and the square-well potential are analyzed to investigate the influence of the repulsive nature on the location of the R=0 line. For the longer-ranged Lennard-Jones potential, the influence of the cutoff radius on the R=0 line is studied. The results are compared with literature data on the Fisher-Widom line. Since such data are rare for the longer-ranged Lennard-Jones potential, dedicated simulations are carried out to determine the number of zeros of the total correlation function, which may provide approximate information about the position of the Fisher-Widom line. An increase of the repulsive strength toward hard sphere interaction leads to the disappearance of the R=0 line in the fluid phase. A rising attraction range results in the nonexistence of the Fisher-Widom line, while it has little effect on the R=0 line as long as it is present in the fluid state.
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Affiliation(s)
- Peter Mausbach
- Plant and Process Engineering, Technical University of Cologne, 50678 Cologne, Germany
| | - Robin Fingerhut
- Thermodynamics and Process Engineering, Technical University of Berlin, 10587 Berlin, Germany
| | - Jadran Vrabec
- Thermodynamics and Process Engineering, Technical University of Berlin, 10587 Berlin, Germany
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Zerón I, Torres-Arenas J, de Jesús E, Ramírez B, Benavides A. Discrete potential fluids in the supercritical region. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.111518] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Mausbach P, May HO, Ruppeiner G. Thermodynamic metric geometry of the two-state ST2 model for supercooled water. J Chem Phys 2019. [DOI: 10.1063/1.5101075] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Schienbein P, Marx D. Investigation concerning the uniqueness of separatrix lines separating liquidlike from gaslike regimes deep in the supercritical phase of water with a focus on Widom line concepts. Phys Rev E 2018; 98:022104. [PMID: 30253513 DOI: 10.1103/physreve.98.022104] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2018] [Indexed: 06/08/2023]
Abstract
The supercritical phase of fluids has long been known to feature significantly different liquidlike and gaslike regimes. However, it is textbook knowledge that the supercritical state is a homogeneous fluid phase where properties change continuously. Nevertheless, there has been an increasing amount of evidence published that suggests that there might exist a unique line that rigorously separates different regimes in supercritical phases, particularly in the case of water. Here, we use the quasiexact IAPWS95 equation of state to rigorously assess the macroscopic thermodynamic properties of supercritical water without invoking any water model or related approximations. We focus on how these properties change deep in the supercritical phase, in particular if they allow one to introduce a unique "thermodynamic separatrix." Our rigorous thermodynamic analysis, which relies exclusively on accurate experimental data, makes clear that there is no unique separatrix in real supercritical water-such as the recently much-invoked "Widom line." A comparison to the van der Waals equation of state reproduces qualitatively all our findings for real water, thereby suggesting that our analysis should be transferable to other fluids and critical points. Topological analysis of the H-bond network structure of supercritical water, as obtained from molecular-dynamics simulations using a standard water model, demonstrates that also the percolation line does not provide a meaningful separatrix to rigorously distinguish liquidlike from gaslike regimes.
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Affiliation(s)
- Philipp Schienbein
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
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Mausbach P, Köster A, Vrabec J. Liquid state isomorphism, Rosenfeld-Tarazona temperature scaling, and Riemannian thermodynamic geometry. Phys Rev E 2018; 97:052149. [PMID: 29906919 DOI: 10.1103/physreve.97.052149] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Indexed: 11/07/2022]
Abstract
Aspects of isomorph theory, Rosenfeld-Tarazona temperature scaling, and thermodynamic geometry are comparatively discussed on the basis of the Lennard-Jones potential. The first two approaches approximate the high-density fluid state well when the repulsive interparticle interactions become dominant, which is typically the case close to the freezing line. However, previous studies of Rosenfeld-Tarazona scaling for the isochoric heat capacity and its relation to isomorph theory reveal deviations for the temperature dependence. It turns out that a definition of a state region in which repulsive interactions dominate is required for achieving consistent results. The Riemannian thermodynamic scalar curvature R allows for such a classification, indicating predominantly repulsive interactions by R>0. An analysis of the isomorphic character of the freezing line and the validity of Rosenfeld-Tarazona temperature scaling show that these approaches are consistent only in a small state region.
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Affiliation(s)
| | - Andreas Köster
- Thermodynamics and Energy Technology, University of Paderborn, 33098 Paderborn, Germany
| | - Jadran Vrabec
- Thermodynamics and Energy Technology, University of Paderborn, 33098 Paderborn, Germany
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Pieprzyk S, Brańka AC, Maćkowiak S, Heyes DM. Comprehensive representation of the Lennard-Jones equation of state based on molecular dynamics simulation data. J Chem Phys 2018; 148:114505. [DOI: 10.1063/1.5021560] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- S. Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - A. C. Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - Sz. Maćkowiak
- Institute of Physics, Poznań University of Technology, Piotrowo 3, 60-965 Poznań, Poland
| | - D. M. Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
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Brańka AC, Pieprzyk S, Heyes DM. Thermodynamic curvature of soft-sphere fluids and solids. Phys Rev E 2018; 97:022119. [PMID: 29548097 DOI: 10.1103/physreve.97.022119] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2017] [Indexed: 06/08/2023]
Abstract
The influence of the strength of repulsion between particles on the thermodynamic curvature scalar R for the fluid and solid states is investigated for particles interacting with the inverse power (r^{-n}) potential, where r is the pair separation and 1/n is the softness. Exact results are obtained for R in certain limiting cases, and the R behavior determined for the systems in the fluid and solid phases. It is found that in such systems the thermodynamic curvature can be positive for very soft particles, negative for steeply repulsive (or large n) particles across almost the entire density range, and can change sign between negative and positive at a certain density. The relationship between R and the form of the interaction potential is more complex than previously suggested, and it may be that R is an indicator of the relative importance of energy and entropy contributions to the thermodynamic properties of the system.
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Affiliation(s)
- A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - S Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
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Ruppeiner G, Dyjack N, McAloon A, Stoops J. Solid-like features in dense vapors near the fluid critical point. J Chem Phys 2017; 146:224501. [DOI: 10.1063/1.4984915] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- George Ruppeiner
- Division of Natural Sciences, New College of Florida, 5800 Bay Shore Road, Sarasota, Florida 34243, USA
| | - Nathan Dyjack
- Center for Genes, Environment & Health, National Jewish Health, 1400 S Jackson St., Denver, Colorado 80206, USA
| | - Abigail McAloon
- Oak Hill School, 86397 Eldon Schafer Dr, Eugene, Oregon 97405, USA
| | - Jerry Stoops
- Division of Natural Sciences, New College of Florida, 5800 Bay Shore Road, Sarasota, Florida 34243, USA
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Mohammadzadeh H, Adli F, Nouri S. Perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. Phys Rev E 2017; 94:062118. [PMID: 28085371 DOI: 10.1103/physreve.94.062118] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2016] [Indexed: 11/07/2022]
Abstract
We investigate perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. We show that the intrinsic statistical interaction of nonextensive Bose (Fermi) gas is attractive (repulsive) similar to the extensive case but the value of thermodynamic curvature is changed by a nonextensive parameter. In contrary to the extensive ideal classical gas, the nonextensive one may be divided to two different regimes. According to the deviation parameter of the system to the nonextensive case, one can find a special value of fugacity, z^{*}, where the sign of thermodynamic curvature is changed. Therefore, we argue that the nonextensive parameter induces an attractive (repulsive) statistical interaction for z<z^{*} (z>z^{*}) for an ideal classical gas. Also, according to the singular point of thermodynamic curvature, we consider the condensation of nonextensive Boson gas.
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Affiliation(s)
- Hosein Mohammadzadeh
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| | - Fereshteh Adli
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| | - Sahereh Nouri
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
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Mausbach P, Köster A, Rutkai G, Thol M, Vrabec J. Comparative study of the Grüneisen parameter for 28 pure fluids. J Chem Phys 2016; 144:244505. [DOI: 10.1063/1.4954282] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Corradini D, Rovere M, Gallo P. The Widom line and dynamical crossover in supercritical water: Popular water models versus experiments. J Chem Phys 2015; 143:114502. [DOI: 10.1063/1.4930542] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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