Phase Behavior of a Cell Fluid Model with Modified Morse Potential
Keywords:cell fluid model, coexistence curve, collective variables, equation of state, first-order phase transition
The present article gives a theoretical description of a first-order phase transition in the cell fluid model with a modified Morse potential and an additional repulsive interaction. In the framework of the grand canonical ensemble, the equation of state of the system in terms of chemical potential–temperature and terms of density–temperature is calculated for a wide range of the density and temperature. The behavior of the chemical potential as a function of the temperature and density is investigated. The maximum and minimum admissible values of the chemical potential, which approach each other with decreasing the temperature, are exhibited. The existence of a liquid-gas phase transition in a limited temperature range below the critical Tc is established.
A.J. Schultz, D.A. Kofke. Vapor-phase metastability and condensation via the virial equation of state with extrapolated coefficients. Fluid Phase Equilibria 409, 12 (2016). https://doi.org/10.1016/j.fluid.2015.09.016
A.J. Masters. Virial expansions. J. Phys.: Condens. Matter 20, 283102 (2008). https://doi.org/10.1088/0953-8984/20/28/283102
M.V. Ushcats. Modified Lennard-Jones model: Virial coefficients to the 7th order. J. Chem. Phys. 140, 234309 (2014). https://doi.org/10.1063/1.4882896
D. Pini, G. Stell, N.B. Wilding. A liquid-state theory that remains successful in the critical region. Mol. Phys. 95, 483 (1998). https://doi.org/10.1080/00268979809483183
C.-L. Lee, G. Stell, J. Hoye. A simple SCOZA for simple fluids. J. Mol. Liq. 112, 13 (2004). https://doi.org/10.1016/j.molliq.2003.11.004
Y. Kozitsky, M. Kozlovskii, O. Dobush. Phase transitions in a continuum Curie-Weiss system: A quantitative analysis. In: Modern Problems of Molecular Physics (Springer, 2018), pp. 229-251. https://doi.org/10.1007/978-3-319-61109-9_11
M.P. Kozlovskii, O.A. Dobush. Phase transition in a cell fluid model. Condens. Matter Phys. 20, 23501 (2017). https://doi.org/10.5488/CMP.20.23501
M.P. Kozlovskii, O.A. Dobush, I.V. Pylyuk. Using a fluid cell model for description of a phase transition in simple liquid alkali metals. Ukr. J. Phys. 62, 865 (2017). https://doi.org/10.15407/ujpe62.10.0865
I. Yukhnovskii, V. Kolomiets, I. Idzyk. Liquid-gas phase transition at and below the critical point. Condens. Matter Phys. 16, 23604 (2013). https://doi.org/10.5488/CMP.16.23604
I.R. Yukhnovskii. The phase transition of the first order in the critical region of the gas-liquid system. Condens. Matter Phys. 17, 43001 (2014). https://doi.org/10.5488/CMP.17.43001
M.P. Kozlovskii, I.V. Pylyuk, O.A. Dobush. The equation of state of a cell fluid model in the supercritical region. Condens. Matter Phys. 21, 43502 (2018). https://doi.org/10.5488/CMP.21.43502
M. Kozlovskii, O. Dobush. Representation of the grand partition function of the cell model: The state equation in the mean-field approximation. J. Mol. Liq. 215, 58 (2016). https://doi.org/10.1016/j.molliq.2015.12.018
R.C. Lincoln, K.M. Koliwad. Morse-potential evaluation of second- and third-order elastic constants of some cubic metals. Phys. Rev. 157, 463 (1967). https://doi.org/10.1103/PhysRev.157.463
J.K. Singh, J. Adhikari, S.K. Kwak. Vapor-liquid phase coexistence curves for Morse fluids. Fluid Phase Equilibria 248, 1 (2006). https://doi.org/10.1016/j.fluid.2006.07.010
I.R. Yukhnovskii, M.P. Kozlovskii, I.V. Pylyuk. Thermodynamics of three-dimensional Ising-like systems in the higher non-Gaussian approximation: Calculational method and dependence on microscopic parameters. Phys. Rev. B 66, 134410 (2002). https://doi.org/10.1103/PhysRevB.66.134410
M.V. Fedoryuk. Asymptotic methods in analysis. In: Analysis I: Integral Representations and Asymptotic Methods. Edited by M.A. Evgrafov, R.V. Gamkrelidze (Springer, 1989). https://doi.org/10.1007/978-3-642-61310-4_2
A. Parola, L. Reatto. Recent developments of the hierarchical reference theory of fluids and its relation to the renormalization group. Mol. Phys. 110, 2859 (2012). https://doi.org/10.1080/00268976.2012.666573
J.-M. Caillol. Non-perturbative renormalization group for simple fluids. Mol. Phys. 104, 1931 (2006). https://doi.org/10.1080/00268970600740774
I.R. Yukhnovskii. Phase space of collective variables and the Zubarev transition function. Theor. Math. Phys. 194, 224 (2018). https://doi.org/10.1134/S0040577918020022
A. Oleinikova, L. Bulavin, V. Pipich. Critical anomaly of shear viscosity in a mixture with an ionic impurity. Chem. Phys. Let. 278, 121 (1997). https://doi.org/10.1016/S0009-2614(97)00945-7
G. Brunner. Near critical and supercritical water. Part I. Hydrolytic and hydrothermal processes. J. Supercrit. Fluids 47, 373 (2009). https://doi.org/10.1016/j.supflu.2008.09.002
G. Brunner. Near and supercritical water. Part II: Oxidative processes. J. Supercrit. Fluids 47, 382 (2009). https://doi.org/10.1016/j.supflu.2008.09.001
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.