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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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Mausbach P, Fingerhut R, Vrabec J. Structure and dynamics of the Lennard-Jones fcc-solid focusing on melting precursors. J Chem Phys 2020; 153:104506. [PMID: 32933290 DOI: 10.1063/5.0015371] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Lennard-Jones potential is taken as a basis to study the structure and dynamics of the face centered cubic (fcc) solid along an isochore from low temperatures up to the solid/fluid transition. The Z method is applied to estimate the melting point. Molecular dynamics simulations are used to calculate the pair distribution function, numbers of nearest neighbors, and the translational order parameter, analyzing the weakening of the fcc-symmetry due to emerging premelting effects. A range of dynamic properties, such as the mean-squared displacement, non-Gaussian parameter, Debye-Waller factor, and vibrational density of states, is considered for the analysis of the solid state. All of these parameters clearly show that bulk mobility is activated at about 2/3 of the melting temperature, known as the Tammann temperature. This indicates that vibrational motion of atoms is not maintained exclusively in the entire stable solid state and that collective atomic motion constitutes a precursor of the melting process.
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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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Stephan S, Deiters UK. Characteristic Curves of the Lennard-Jones Fluid. INTERNATIONAL JOURNAL OF THERMOPHYSICS 2020; 41:147. [PMID: 32863513 PMCID: PMC7441092 DOI: 10.1007/s10765-020-02721-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 07/25/2020] [Indexed: 05/25/2023]
Abstract
Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown's characteristic curves and characteristic state points. Brown's characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.
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Affiliation(s)
- Simon Stephan
- Laboratory of Engineering Thermodynamics (LTD), TU Kaiserslautern, Erwin-Schrödinger-Straße 44, 67663 Kaiserslautern, Germany
| | - Ulrich K. Deiters
- Institute of Physical Chemistry, University of Cologne, Greinstraße 4-6, 50939 Cologne, Germany
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Apfelbaum EM, Vorob'ev VS. The Line of the Unit Compressibility Factor (Zeno-Line) for Crystal States. J Phys Chem B 2020; 124:5021-5027. [PMID: 32437611 DOI: 10.1021/acs.jpcb.0c02749] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We study the behavior of the line of the unit compressibility factor (Zeno-line) in crystalline states. We used the Lennard-Jones system, experimental P-V-T data for a number of substances, and the Debye model. We found that, contrary to the case of the liquid states, the Zeno-line in a crystal is not a straight line at the density-temperature plane. However, the corresponding pressure-temperature dependence appears to be quasi-linear. As a result, this line in the solid state can be defined by the only one point where the Zeno-line crosses the melting curve.
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Affiliation(s)
- E M Apfelbaum
- Joint Institute for High Temperatures of Russian Academy of Sciences, Izhorskaya Street, 13, Building 2, Moscow 125412, Russia
| | - V S Vorob'ev
- Joint Institute for High Temperatures of Russian Academy of Sciences, Izhorskaya Street, 13, Building 2, Moscow 125412, Russia
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Stephan S, Thol M, Vrabec J, Hasse H. Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment. J Chem Inf Model 2019; 59:4248-4265. [DOI: 10.1021/acs.jcim.9b00620] [Citation(s) in RCA: 55] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Simon Stephan
- Laboratory of Engineering Thermodynamics (LTD), TU Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Monika Thol
- Thermodynamics, Ruhr University Bochum, 44801 Bochum, Germany
| | - Jadran Vrabec
- Thermodynamics and Process Engineering, TU Berlin, 10587 Berlin, Germany
| | - Hans Hasse
- Laboratory of Engineering Thermodynamics (LTD), TU Kaiserslautern, 67663 Kaiserslautern, Germany
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Schultz AJ, Kofke DA. Comprehensive high-precision high-accuracy equation of state and coexistence properties for classical Lennard-Jones crystals and low-temperature fluid phases. J Chem Phys 2018; 149:204508. [DOI: 10.1063/1.5053714] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Andrew J. Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
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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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