1
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Ouyang XY, Ye QJ, Li XZ. Complex phase diagram and supercritical matter. Phys Rev E 2024; 109:024118. [PMID: 38491632 DOI: 10.1103/physreve.109.024118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 01/11/2024] [Indexed: 03/18/2024]
Abstract
The supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquidlike and gaslike, however, suggest "supercritical boundaries." Here we provide a mathematical description of these phenomena by revisiting the Yang-Lee theory and introducing a complex phase diagram, specifically a four-dimensional (4D) one with complex T and p. While the traditional 2D phase diagram with real temperature T and pressure p values (the physical plane) lacks Lee-Yang (LY) zeros beyond the critical point, preventing the occurrence of criticality, the off-plane zeros in this 4D scenario still induce critical anomalies in various physical properties. This relationship is evidenced by the correlation between the Widom line and LY edges in van der Waals, 2D Ising model, and water. The diverged supercritical boundaries manifest the high-dimensional feature of the phase diagram: e.g., when LY zeros of complex T or p are projected onto the physical plane, boundaries defined by isobaric heat capacity C_{p} or isothermal compression coefficient K_{T} emanates. These results demonstrate the incipient phase transition nature of the supercritical matter.
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Affiliation(s)
- Xiao-Yu Ouyang
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Qi-Jun Ye
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Xin-Zheng Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, People's Republic of China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, People's Republic of China
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2
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Fomin YD. Boiling line and near-critical maxima of propane-nitrogen mixtures. Phys Rev E 2022; 106:064102. [PMID: 36671079 DOI: 10.1103/physreve.106.064102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Accepted: 11/09/2022] [Indexed: 06/17/2023]
Abstract
It is well known that some thermodynamic quantities demonstrate maxima in the vicinity of a critical point. The lines of these maxima in the density-temperature or pressure-temperature planes are called "Widom lines." The behavior of Widom lines of one-component fluids has already been well studied in a number of papers by different authors. However, up to now the understanding of Widom lines in binary mixtures is still lacking. In this paper we study the boiling curve and the near-critical maxima of mixtures of nitrogen and propane by means of molecular dynamics simulation. We calculate the boiling curves and estimate the critical temperatures in a set of concentrations from pure nitrogen to pure propane. The influence of the composition of the mixture on the Widom lines of the system is evaluated. We find that the mixture of propane and nitrogen behaves as a type I mixture in the van Konynenburg-Scott classification, i.e., when the concentration is changed, the critical point and the corresponding Widom lines continuously shift in the density-temperature plane.
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Affiliation(s)
- Yu D Fomin
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow 108840, Russia
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3
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Widom line of supercritical CO2 calculated by equations of state and molecular dynamics simulation. J CO2 UTIL 2022. [DOI: 10.1016/j.jcou.2022.102075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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4
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Apfelbaum EM. The Line of Ideal Isothermal Compressibility. J Phys Chem B 2022; 126:2912-2920. [PMID: 35389650 DOI: 10.1021/acs.jpcb.2c01247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We have considered the line along which the values of the isothermal compressibility of a system are the same as they would be for an ideal gas. It was called the κT line. Various substances and models have been studied with the use of the multi-parameter equations of states, implemented in REFPROP (Lemmon, E. W.; Bell, I. H.; Huber, M. L.; McLinden, M. O. NIST standard reference database 23: Reference fluid thermodynamic and transport properties-REFPROP, version 10.0 (National Institute of Standards and Technology, 2018)), and numerical simulations, respectively. It is shown that in the reduced variables, all κT lines can be described by the same relation following from the van der Waals equation. This similarity appears to be valid even for the systems with non-straight Zeno lines. Deviations within ∼5% are observed only near the binodals.
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Affiliation(s)
- E M Apfelbaum
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya Street 13 Bldg. 2, Moscow 125412, Russia
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5
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Pruteanu CG, Kirsz M, Ackland GJ. Frenkel Line in Nitrogen Terminates at the Triple Point. J Phys Chem Lett 2021; 12:11609-11615. [PMID: 34812632 DOI: 10.1021/acs.jpclett.1c03206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Recent studies on supercritical nitrogen revealed clear changes in structural markers and dynamical properties when the coordination number approaches its maximum value. The line in P and T space where these changes occur is referred to as the Frenkel line. Here, we qualitatively reproduce such changes in the supercritical regime using the popular "optimized potential for liquid simulation" (OPLS) classical force field for molecular dynamics. Unfortunately, at 160 K, OPLS nitrogen predicts sublimation rather than producing a liquid phase; therefore, we developed our own force field to achieve quantitative agreement with experimental data. We confirm the asymptotic behavior of the coordination number on crossing the Frenkel line and note an associated change in the diffusion constant, consistent with the non-rigid to rigid liquid-like character of the "transition". The simulations allow us to track the Frenkel line to subcritical temperatures and demonstrate that it terminates at the triple point. This establishes the experimentally measurable changes, which could unequivocally determine the Frenkel line in other systems.
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Affiliation(s)
- Ciprian G Pruteanu
- Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Marcin Kirsz
- Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Graeme J Ackland
- Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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6
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7
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Ghandili A, Moeini V. A new analytical modeling for the determination of thermodynamic quantities of refrigerants. AIChE J 2020. [DOI: 10.1002/aic.16293] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Ali Ghandili
- Department of Scientific and Industrial ResearchWest Azerbaijan Standard Administration Urmia Iran
| | - Vahid Moeini
- Department of ChemistryPayame Noor University Tehran Iran
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8
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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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9
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Wang L, Yang C, Dove MT, Brazhkin VV, Trachenko K. Thermodynamic heterogeneity and crossover in the supercritical state of matter. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:225401. [PMID: 30808013 DOI: 10.1088/1361-648x/ab0ab1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A hallmark of a thermodynamic phase transition is the qualitative change of system thermodynamic properties such as energy and heat capacity. On the other hand, no phase transition is thought to operate in the supercritical state of matter and, for this reason, it was believed that supercritical thermodynamic properties vary smoothly and without any qualitative changes. Here, we perform extensive molecular dynamics simulations in a wide temperature range and find that a deeply supercritical state is thermodynamically heterogeneous, as witnessed by different temperature dependence of energy, heat capacity and its derivatives at low and high temperature. The evidence comes from three different methods of analysis, two of which are model-independent. We propose a new definition of the relative width of the thermodynamic crossover and calculate it to be in the fairly narrow relative range of 13%-20%. On the basis of our results, we relate the crossover to the supercritical Frenkel line.
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Affiliation(s)
- L Wang
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom
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10
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Takemoto A, Kinugawa K. Quantumness and state boundaries hidden in supercritical helium-4: A path integral centroid molecular dynamics study. J Chem Phys 2018; 149:204504. [DOI: 10.1063/1.5053988] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ayumi Takemoto
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
| | - Kenichi Kinugawa
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
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11
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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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12
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Brazhkin VV, Prescher C, Fomin YD, Tsiok EN, Lyapin AG, Ryzhov VN, Prakapenka VB, Stefanski J, Trachenko K, Sapelkin A. Comment on “Behavior of Supercritical Fluids across the ‘Frenkel Line’”. J Phys Chem B 2018; 122:6124-6128. [DOI: 10.1021/acs.jpcb.7b11359] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- V. V. Brazhkin
- Institute for High Pressure Physics, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - C. Prescher
- Institut für Geologie und Mineralogie, Universität zu Köln, Cologne 50939, Germany
| | - Yu. D. Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - E. N. Tsiok
- Institute for High Pressure Physics, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - A. G. Lyapin
- Institute for High Pressure Physics, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - V. N. Ryzhov
- Institute for High Pressure Physics, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - V. B. Prakapenka
- Consortium for Advanced Radiation Sources, University of Chicago, Chicago, Illinois 60637, United States
| | - J. Stefanski
- Institut für Geologie und Mineralogie, Universität zu Köln, Cologne 50939, Germany
| | - K. Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - A. Sapelkin
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
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13
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Fomin YD, Ryzhov VN, Tsiok EN, Proctor JE, Prescher C, Prakapenka VB, Trachenko K, Brazhkin VV. Dynamics, thermodynamics and structure of liquids and supercritical fluids: crossover at the Frenkel line. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:134003. [PMID: 29443011 DOI: 10.1088/1361-648x/aaaf39] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We review recent work aimed at understanding dynamical and thermodynamic properties of liquids and supercritical fluids. The focus of our discussion is on solid-like transverse collective modes, whose evolution in the supercritical fluids enables one to discuss the main properties of the Frenkel line separating rigid liquid-like and non-rigid gas-like supercritical states. We subsequently present recent experimental evidence of the Frenkel line showing that structural and dynamical crossovers are seen at a pressure and temperature corresponding to the line as predicted by theory and modelling. Finally, we link dynamical and thermodynamic properties of liquids and supercritical fluids by the new calculation of liquid energy governed by the evolution of solid-like transverse modes. The disappearance of those modes at high temperature results in the observed decrease of heat capacity.
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Affiliation(s)
- Yu D Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia
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14
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Lamorgese A, Ambrosini W, Mauri R. Widom line prediction by the Soave–Redlich–Kwong and Peng–Robinson equations of state. J Supercrit Fluids 2018. [DOI: 10.1016/j.supflu.2017.07.031] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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15
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Raman AS, Li H, Chiew YC. Widom line, dynamical crossover, and percolation transition of supercritical oxygen via molecular dynamics simulations. J Chem Phys 2018; 148:014502. [PMID: 29306275 DOI: 10.1063/1.5002699] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Supercritical oxygen, a cryogenic fluid, is widely used as an oxidizer in jet propulsion systems and is therefore of paramount importance in gaining physical insights into processes such as transcritical and supercritical vaporization. It is well established in the scientific literature that the supercritical state is not homogeneous but, in fact, can be demarcated into regions with liquid-like and vapor-like properties, separated by the "Widom line." In this study, we identified the Widom line for oxygen, constituted by the loci of the extrema of thermodynamic response functions (heat capacity, volumetric thermal expansion coefficient, and isothermal compressibility) in the supercritical region, via atomistic molecular dynamics simulations. We found that the Widom lines derived from these response functions all coincide near the critical point until about 25 bars and 15-20 K, beyond which the isothermal compressibility line begins to deviate. We also obtained the crossover from liquid-like to vapor-like behavior of the translational diffusion coefficient, shear viscosity, and rotational relaxation time of supercritical oxygen. While the crossover of the translational diffusion coefficient and shear viscosity coincided with the Widom lines, the rotational relaxation time showed a crossover that was largely independent of the Widom line. Further, we characterized the clustering behavior and percolation transition of supercritical oxygen molecules, identified the percolation threshold based on the fractal dimension of the largest cluster and the probability of finding a cluster that spans the system in all three dimensions, and found that the locus of the percolation threshold also coincided with the isothermal compressibility Widom line. It is therefore clear that supercritical oxygen is far more complex than originally perceived and that the Widom line, dynamical crossovers, and percolation transitions serve as useful routes to better our understanding of the supercritical state.
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Affiliation(s)
- Abhinav S Raman
- Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Huiyong Li
- Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Y C Chiew
- Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08854, USA
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16
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Desgranges C, Anderson PW, Delhommelle J. Classical and quantum many-body effects on the critical properties and thermodynamic regularities of silicon. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:045401. [PMID: 27875329 DOI: 10.1088/1361-648x/29/4/045401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using molecular simulation, we determine the critical properties of Si as well as the loci for several remarkable thermodynamic contours spanning the supercritical region of the phase diagram. We consider a classical three-body potential as well as a quantum (tight-binding) many-body model, and determine the loci for the ideality contours, including the Zeno line and the H line of ideal enthalpy. The two strategies (classical or quantum) lead to strongly asymmetric binodals and to critical properties in good agreement with each other. The Zeno and H lines are found to remain linear over a wide temperature interval, despite the changes in electronic structure undergone by the fluid along these contours. We also show that the classical and quantum model yield markedly different results for the parameters defining the H line, the exponents for the power-laws underlying the line of minima for the isothermal enthalpy and for the density required to achieve ideal behavior, most notably for the enthalpy.
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Affiliation(s)
- C Desgranges
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, ND 58202, USA
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18
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Urbic T. Liquid-liquid critical point in a simple analytical model of water. Phys Rev E 2016; 94:042126. [PMID: 27841542 DOI: 10.1103/physreve.94.042126] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2016] [Indexed: 11/07/2022]
Abstract
A statistical model for a simple three-dimensional Mercedes-Benz model of water was used to study phase diagrams. This model on a simple level describes the thermal and volumetric properties of waterlike molecules. A molecule is presented as a soft sphere with four directions in which hydrogen bonds can be formed. Two neighboring waters can interact through a van der Waals interaction or an orientation-dependent hydrogen-bonding interaction. For pure water, we explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility and found that the volumetric and thermal properties follow the same trends with temperature as in real water and are in good general agreement with Monte Carlo simulations. The model exhibits also two critical points for liquid-gas transition and transition between low-density and high-density fluid. Coexistence curves and a Widom line for the maximum and minimum in thermal expansion coefficient divides the phase space of the model into three parts: in one part we have gas region, in the second a high-density liquid, and the third region contains low-density liquid.
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Affiliation(s)
- Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, 1000 Lubljana, Slovenia
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19
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Desgranges C, Delhommelle J. Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. V. Impact of an electric field on the thermodynamic properties and ideality contours of water. J Chem Phys 2016; 145:184504. [DOI: 10.1063/1.4967336] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
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20
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Fomin YD, Ryzhov VN, Tsiok EN, Brazhkin VV, Trachenko K. Crossover of collective modes and positive sound dispersion in supercritical state. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:43LT01. [PMID: 27603524 DOI: 10.1088/0953-8984/28/43/43lt01] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Supercritical state has been viewed as an intermediate state between gases and liquids with largely unknown physical properties. Here, we address the important ability of supercritical fluids to sustain collective excitations. We directly study propagating modes on the basis of correlation functions calculated in molecular dynamics simulations and find that the supercritical system sustains propagating solid-like transverse modes below the Frenkel line but not above where there is one longitudinal mode only. Important thermodynamic implications of this finding are discussed. We directly detect positive sound dispersion (PSD) below the Frenkel line where transverse modes are operative and quantitatively explain its magnitude on the basis of transverse and longitudinal velocities. PSD disappears above the Frenkel line which therefore demarcates the supercritical phase diagram into two areas where PSD does and does not operate.
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Affiliation(s)
- Yu D Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow, Russia
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21
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Brazhkin VV, Ryzhov VN. Erratum: "Van der Waals supercritical fluid: Exact formulas for special lines" [J. Chem. Phys. 135, 084503 (2011)]. J Chem Phys 2016; 145:059901. [PMID: 27497581 DOI: 10.1063/1.4960613] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- V V Brazhkin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow Region 142190, Russia and Moscow Institute of Physics and Technology, Moscow State University, Dolgoprudny, Moscow Region 141700, Russia
| | - V N Ryzhov
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow Region 142190, Russia and Moscow Institute of Physics and Technology, Moscow State University, Dolgoprudny, Moscow Region 141700, Russia
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Desgranges C, Huber L, Delhommelle J. Impact of Friedel oscillations on vapor-liquid equilibria and supercritical properties in two and three dimensions. Phys Rev E 2016; 94:012612. [PMID: 27575184 DOI: 10.1103/physreve.94.012612] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Indexed: 11/07/2022]
Abstract
We determine the impact of the Friedel oscillations on the phase behavior, critical properties, and thermodynamic contours in films [two dimensions (2D)] and bulk phases [three dimensions (3D)]. Using expanded Wang-Landau simulations, we calculate the grand-canonical partition function and, in turn, the thermodynamic properties of systems modeled with a linear combination of the Lennard-Jones and Dzugutov potentials, weighted by a parameter X (0<X<1). Varying X allows us to control the height of the first Friedel oscillation and to provide a complete characterization of the effect of the metal-like character in the potential on the thermodynamic properties over a wide range of conditions. For 3D systems, we are able to show that the critical parameters exhibit a linear dependence on X and that the loci for the thermodynamic state points, for which the system shows the same compressibility factor or enthalpy as an ideal gas, are two straight lines spanning the subcritical and supercritical regions of the phase diagram for all X values. Reducing the dimensionality to 2D results in a loss of impact of the Friedel oscillation on the critical properties, as evidenced by the virtually constant critical density across the range of X values. Furthermore, our results establish that the straightness of the two ideality lines is retained in 2D and is independent from the height of the first Friedel oscillation in the potential.
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Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, University of North Dakota, Grand Forks, North Dakota 58202, USA
| | - Landon Huber
- Department of Chemistry, University of North Dakota, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, University of North Dakota, Grand Forks, North Dakota 58202, USA
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24
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Trachenko K, Brazhkin VV. Collective modes and thermodynamics of the liquid state. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:016502. [PMID: 26696098 DOI: 10.1088/0034-4885/79/1/016502] [Citation(s) in RCA: 97] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system with a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.
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Affiliation(s)
- K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, UK
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25
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Abstract
Dynamical crossover in water is studied by means of computer simulation. The crossover temperature is calculated from the behavior of velocity autocorrelation functions. The results are compared with experimental data. It is shown that the qualitative behavior of the dynamical crossover line is similar to the melting curve behavior. Importantly, the crossover line belongs to experimentally achievable (P, T) region which stimulates the experimental investigation in this field.
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26
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Trachenko K, Brazhkin VV. Reply to "Comment on 'Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants' ". PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:036102. [PMID: 25871254 DOI: 10.1103/physreve.91.036102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2015] [Indexed: 06/04/2023]
Abstract
We have recently proposed the dynamic transition of molecular hydrogen in gas giants around 10 GPa based on the recent understanding of a supercritical state related to the Frenkel line. In the preceding Comment, Bryk makes several remarks with regard to the Frenkel line and its relationship to the speed of sound. We disagree with this discussion and respond to it in this Reply.
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Affiliation(s)
- K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - V V Brazhkin
- Institute for High Pressure Physics, RAS, 142190 Troitsk, Moscow, Russia
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27
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Fomin YD, Ryzhov VN, Tsiok EN, Brazhkin VV. Thermodynamic properties of supercritical carbon dioxide: Widom and Frenkel lines. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022111. [PMID: 25768462 DOI: 10.1103/physreve.91.022111] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2014] [Indexed: 06/04/2023]
Abstract
Supercritical fluids are widely used in a number of important technological applications, yet the theoretical progress in the field has been rather moderate. Fairly recently, a new understanding of the liquidlike and gaslike properties of supercritical fluids has come to the fore, particularly with the advent of the Widom and Frenkel lines that aim to demarcate different physical properties on the phase diagram. Here, we report the results of a computational study of supercritical carbon dioxide, one of the most important fluids in the chemical industry. We study the response functions of CO_{2} in the supercritical state and calculate the locations of their maxima (Widom lines). We also report the preliminary calculations of the Frenkel line, the line of crossover of microscopic dynamics of particles. Our insights are relevant to physical processes in the atmosphere of Venus and its evolution.
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Affiliation(s)
- Yu D Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow, Russia and Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia
| | - V N Ryzhov
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow, Russia and Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia
| | - E N Tsiok
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow, Russia
| | - V V Brazhkin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow, Russia
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28
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Gallo P, Corradini D, Rovere M. Widom line and dynamical crossovers as routes to understand supercritical water. Nat Commun 2014; 5:5806. [DOI: 10.1038/ncomms6806] [Citation(s) in RCA: 92] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2014] [Accepted: 11/10/2014] [Indexed: 11/09/2022] Open
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29
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Dudalov DE, Fomin YD, Tsiok EN, Ryzhov VN. How dimensionality changes the anomalous behavior and melting scenario of a core-softened potential system? SOFT MATTER 2014; 10:4966-4976. [PMID: 24888366 DOI: 10.1039/c4sm00124a] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present a computer simulation study of the phase diagram and anomalous behavior of two-dimensional (2D) and three-dimensional (3D) classical particles repelling each other through an isotropic core-softened potential. As in the analogous three-dimensional case, in 2D a reentrant-melting transition occurs upon compression under not too high pressure, along with a spectrum of thermodynamic and dynamic anomalies in the fluid phase. However, in two dimensions the order of the region of anomalous diffusion and the region of structural anomaly is inverted in comparison with the 3D case, where there exists a water-like sequence of anomalies, and has a silica-like sequence. In the low density part of the 2D phase diagram, melting is a continuous two-stage transition, with an intermediate hexatic phase. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario for this melting transition. On the other hand, at high density part of the phase diagram one first-order transition takes place.
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Affiliation(s)
- D E Dudalov
- Institute for High Pressure Physics RAS, 142190 Kaluzhskoe shosse, 14, Troitsk, Moscow, Russia.
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30
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Brazhkin VV, Fomin YD, Ryzhov VN, Tareyeva EE, Tsiok EN. True Widom line for a square-well system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042136. [PMID: 24827221 DOI: 10.1103/physreve.89.042136] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2014] [Indexed: 06/03/2023]
Abstract
In the present paper we propose a van der Waals-like model that allows a purely analytical study of fluid properties including the equation of state, phase behavior, and supercritical fluctuations. We take a square-well system as an example and calculate its liquid-gas transition line and supercritical fluctuations. Employing this model allows us to calculate not only the thermodynamic response functions (isothermal compressibility βT, isobaric heat capacity CP, density fluctuations ζT, and thermal expansion coefficient αT), but also the correlation length in the fluid ξ. It is shown that the bunch of extrema widens rapidly upon departure from the critical point. It seems that the Widom line defined in this way cannot be considered as a real boundary that divides the supercritical region into gaslike and liquidlike regions. As it has been shown recently, a dynamic line on the phase diagram in the supercritical region, namely, the Frenkel line, can be used for this purpose.
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Affiliation(s)
- V V Brazhkin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia
| | - Yu D Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia
| | - V N Ryzhov
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia
| | - E E Tareyeva
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia
| | - E N Tsiok
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia
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31
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Apfelbaum EM, Vorob’ev VS. Regarding the Universality of Some Consequences of the van der Waals Equation in the Supercritical Domain. J Phys Chem B 2013; 117:7750-5. [DOI: 10.1021/jp404146h] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- E. M. Apfelbaum
- Joint Institute for High Temperatures of Russian Academy of Science, Izhorskaya 13, Building
2, Moscow 125412, Russia
| | - V. S. Vorob’ev
- Joint Institute for High Temperatures of Russian Academy of Science, Izhorskaya 13, Building
2, Moscow 125412, Russia
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32
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Fomin YD, Tsiok EN, Ryzhov VN. Silicalike sequence of anomalies in core-softened systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042122. [PMID: 23679387 DOI: 10.1103/physreve.87.042122] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2013] [Indexed: 06/02/2023]
Abstract
We present a simulation study of density, structural, and diffusion anomalies in a core-softened system, a remarkable model liquid that exhibits anomalous properties seen in tetrahedral liquids such as silica and water. It is widely believed that core-softened potentials demonstrate waterlike sequence of anomalies. Here, we show that the order of the region of anomalous diffusion and the regions of density and structural anomalies are inverted with increasing depth of the attractive part of the potential and have silicalike sequence. We also show that the Widom line slope is negative as in water.
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Affiliation(s)
- Yu D Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia
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33
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Gorelli FA, Bryk T, Krisch M, Ruocco G, Santoro M, Scopigno T. Dynamics and Thermodynamics beyond the critical point. Sci Rep 2013; 3:1203. [PMID: 23383373 PMCID: PMC3563038 DOI: 10.1038/srep01203] [Citation(s) in RCA: 63] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2012] [Accepted: 01/03/2013] [Indexed: 11/08/2022] Open
Abstract
Sudden changes in the dynamical properties of a supercritical fluid model have been found as a function of pressure and temperature (T/T(c) = 2-5 and P/P(c) = 10-10(3)), striving with the notion of a single phase beyond the critical point established by thermodynamics. The sound propagation in the Terahertz frequency region reveals a sharp dynamic crossover between the gas like and the liquid like regimes along several isotherms, which involves, at sufficiently low densities, the interplay between purely acoustic waves and heat waves. Such a crossover allows one to determine a dynamic line in the phase diagram which exhibits a very tight correlation with a number of thermodynamic observables, showing that the supercritical state is remarkably more complex than thought so far.
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Affiliation(s)
- F. A. Gorelli
- IPCF-CNR, UOS Roma, I-00185 Roma, Italy
- LENS, European Laboratory for Non Linear Spectroscopy, I-50019 Sesto Fiorentino, Italy
| | - T. Bryk
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine
- National Polytechnic University of Lviv, UA-79013 Lviv, Ukraine
| | - M. Krisch
- European Synchrotron Research Facility, Grenoble, France
| | - G. Ruocco
- IPCF-CNR, UOS Roma, I-00185 Roma, Italy
- Dipartimento di Fisica, Università di Roma “La Sapienza”, Roma, Italy
| | - M. Santoro
- IFAC-CNR, I-50019 Sesto Fiorentino, Italy
| | - T. Scopigno
- IPCF-CNR, UOS Roma, I-00185 Roma, Italy
- Dipartimento di Fisica, Università di Roma “La Sapienza”, Roma, Italy
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34
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Imre A, Deiters U, Kraska T, Tiselj I. The pseudocritical regions for supercritical water. NUCLEAR ENGINEERING AND DESIGN 2012. [DOI: 10.1016/j.nucengdes.2012.07.007] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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35
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Gallo P, Rovere M. Mode coupling and fragile to strong transition in supercooled TIP4P water. J Chem Phys 2012; 137:164503. [DOI: 10.1063/1.4759262] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Han S, Yu CC. Widom line and noise-power spectral analysis of a supercritical fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051201. [PMID: 23004739 DOI: 10.1103/physreve.85.051201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2011] [Indexed: 06/01/2023]
Abstract
We have performed extensive molecular dynamics simulations to study noise-power spectra of density and potential energy fluctuations of a Lennard-Jones model of a fluid in the supercritical region. Emanating from the liquid-vapor critical point, there is a locus of isobaric specific heat maxima, called the Widom line, which is often regarded as an extension of the liquid-vapor coexistence line. Our simulation results show that the noise-power spectrum of the density fluctuations on the Widom line of the liquid-vapor transition exhibits three distinct 1/f^{γ} behaviors with exponents γ=0, 1.2, and 2, depending on the frequency f. We find that the intermediate frequency region with an exponent γ∼ 1 appears as the temperature approaches the Widom temperature from above or below. On the other hand, we do not find three distinct regions of 1/f^{γ} in the power spectrum of the potential energy fluctuations on the Widom line. Furthermore, we find that the power spectra of both the density and potential energy fluctuations at low frequency have a maximum on the Widom line, suggesting that the noise power can provide an alternative signature of the Widom line.
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Affiliation(s)
- Sungho Han
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
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37
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May HO, Mausbach P. Riemannian geometry study of vapor-liquid phase equilibria and supercritical behavior of the Lennard-Jones fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031201. [PMID: 22587083 DOI: 10.1103/physreve.85.031201] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2011] [Indexed: 05/31/2023]
Abstract
The behavior of thermodynamic response functions and the thermodynamic scalar curvature in the supercritical region have been studied for a Lennard-Jones fluid based on a revised modified Benedict-Webb-Rubin equation of state. Response function extrema are sometimes used to estimate the Widom line, which is characterized by the maxima of the correlation lengths. We calculated the Widom line for the Lennard-Jones fluid without using any response function extrema. Since the volume of the correlation length is proportional to the Riemannian thermodynamic scalar curvature, the locus of the Widom line follows the slope of maximum curvature. We show that the slope of the Widom line follows the slope of the isobaric heat capacity maximum only in the close vicinity of the critical point and that, therefore, the use of response function extrema in this context is problematic. Furthermore, we constructed the vapor-liquid coexistence line for the Lennard-Jones fluid using the fact that the correlation length, and therefore the thermodynamic scalar curvature, must be equal in the two coexisting phases. We compared the resulting phase envelope with those from simulation data where multiple histogram reweighting was used and found striking agreement between the two methods.
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