First-Order Phase Transition in the Framework of the Cell Fluid Model: Regions of Chemical Potential Variation and the Corresponding Densities
DOI:
https://doi.org/10.15407/ujpe67.1.54Keywords:
cell fluid model, chemical potential, density, equation of state, binodalAbstract
A microscopic description is given for the behavior of the fluid system in an immediate vicinity of its critical point, where theoretical and experimental researches are difficult to carry out. For the temperatures T < TC, the regions of chemical potential and density variations are singled out and analyzed. The equation of state of the cell fluid model in terms of temperature-chemical potential is written using the Heaviside functions. This equation is also given in terms of the temperature and density variables. As a result of the study of the relationship between the density and the chemical potential, an equation for the binodal curve is obtained in a narrow neighborhood of the critical point.
References
C.-L. Lee, G. Stell, J.S. Høye. A simple SCOZA for simple fluids. J. Mol. Liq. 112, 13 (2004).
https://doi.org/10.1016/j.molliq.2003.11.004
C.E. Bertrand, J.F. Nicoll, M.A. Anisimov. Comparison of complete scaling and a field-theoretic treatment of asymmetric fluid criticality. Phys. Rev. E 85, 031131 (2012).
https://doi.org/10.1103/PhysRevE.85.031131
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
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
T.J. Yoon, Y.-W. Lee. Current theoretical opinions and perspectives on the fundamental description of supercritical fluids. J. Supercrit. Fluids 134, 21 (2018).
https://doi.org/10.1016/j.supflu.2017.11.022
L.F. Vega. Perspectives on molecular modeling of supercritical fluids: From equations of state to molecular simulations. Recent advances, remaining challenges and opportunities. J. Supercrit. Fluids 134, 41 (2018).
https://doi.org/10.1016/j.supflu.2017.12.025
A. Oleinikova, L. Bulavin, V. Pipich. Critical anomaly of shear viscosity in a mixture with an ionic impurity. Chem. Phys. Lett. 278, 121 (1997).
https://doi.org/10.1016/S0009-2614(97)00945-7
S. Pittois, B. Van Roie, C. Glorieux, J. Thoen. Thermal conductivity, thermal effusivity, and specific heat capacity near the lower critical point of the binary liquid mixture n-butoxyethanol-water. J.Chem. Phys. 121, 1866 (2004).
https://doi.org/10.1063/1.1765652
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
I.V. Pylyuk. Fluid critical behavior at liquid-gas phase transition: Analytic method for microscopic description. J. Mol. Liq. 310, 112933 (2020).
https://doi.org/10.1016/j.molliq.2020.112933
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
M.P. Kozlovskii, O.A. Dobush, I.V. Pylyuk. Using a cell fluid model for the 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.V. Pylyuk, O.A. Dobush. Equation of state of a cell fluid model with allowance for Gaussian fluctuations of the order parameter. Ukr. J. Phys. 65, 1080 (2020).
https://doi.org/10.15407/ujpe65.12.1080
I.R. Yukhnovskii. Phase Transitions of the Second Order. Collective Variables Method (World Scientific, 1987).
J.K. Singh, J. Adhikari, S.K. Kwak. Vapor-liquid phase coexistence curves for Morse fluids. Fluid Phase Equilib. 248, 1 (2006).
https://doi.org/10.1016/j.fluid.2006.07.010
E.M. Apfelbaum. The calculation of vapor-liquid coexistence curve of Morse fluid: Application to iron. J. Chem. Phys. 134, 194506 (2011).
https://doi.org/10.1063/1.3590201
Y. Zhou, M. Karplus, K.D. Ball, R.S. Berry. The distance fluctuation criterion for melting: Comparison of squarewell and Morse potential models for clusters and homopolymers. J. Chem. Phys. 116, 2323 (2002).
https://doi.org/10.1063/1.1426419
X. Xu, C. Cheng, I.H. Chowdhury. Molecular dynamics study of phase change mechanisms during femtosecond laser ablation. J. Heat Transfer 126, 727 (2004).
https://doi.org/10.1115/1.1797011
I. Last, Y. Levy, J. Jortner. Beyond the Rayleigh instability limit for multicharged finite systems: From fission to Coulomb explosion. Proc. Natl. Acad, Sci. USA 99, 9107 (2002).
https://doi.org/10.1073/pnas.142253999
J.P.K. Doye, D.J. Wales. The structure and stability of atomic liquids: From clusters to bulk. Science 271, 484 (1996).
https://doi.org/10.1126/science.271.5248.484
J.P.K. Doye, R.H. Leary, M. Locatelli, F. Schoen. Global optimization of Morse clusters by potential energy transformations. INFORMS J. Comput. 16, 371 (2004).
https://doi.org/10.1287/ijoc.1040.0084
A. Tekin, M. Yurtsever. Molecular dynamics simulation of phase transitions in binary LJ clusters. Turk. J. Chem. 26, 627 (2002).
C.-I. Chou, C.-L. Ho, B. Hu, H. Lee. Morse-type Frenkel-Kontorova model. Phys. Rev. E 57, 2747 (1998).
https://doi.org/10.1103/PhysRevE.57.2747
A. Strachan, T. Cagin, W.A. Goddard, III. Phase diagram of MgO from density-functional theory and moleculardynamics simulations. Phys. Rev. B 60, 15084 (1999).
https://doi.org/10.1103/PhysRevB.60.15084
T.-C. Lim. Approximate relationships between the Generalized Morse and the Extended-Rydberg potential energy functions. Acta Chim. Slov. 52, 149 (2005).
A. Del Sol Mesa, C. Quesne, Yu.F. Smirnov. Generalized Morse potential: Symmetry and satellite potentials. J. Phys. A 31, 321 (1998).
https://doi.org/10.1088/0305-4470/31/1/028
P.M. Morse, E.C.G. Stueckelberg. Diatomic molecules according to the wave mechanics I: Electronic levels of the hydrogen molecular ion. Phys. Rev. 33, 932 (1929).
https://doi.org/10.1103/PhysRev.33.932
A.S. Leal, C. Gouvea dos Santos, C.M. Quintella, H.H.R. Schor. A theoretical model for the scattering of I2 molecule from a perfluoropolyeter liquid surface. J. Braz. Chem. Soc. 10, 359 (1999).
https://doi.org/10.1590/S0103-50531999000500004
V. Constantoudis, C.A. Nicolaides. Stabilization and relative phase effects in a dichromatically driven diatomic Morse molecule: Interpretation based on nonlinear classical dynamics. J. Chem. Phys. 122, 084118 (2005).
https://doi.org/10.1063/1.1854631
A.I. Milchev, A.A. Milchev. Wetting behavior of nanodroplets: The limits of Young's rule validity. Europhys. Lett. 56, 695 (2001).
https://doi.org/10.1209/epl/i2001-00576-1
D. Osorio-Gonzalez, M. Mayorga, J. Orozco, L. RomeroSalazar. Entropy and thermalization of particles in liquids. J. Chem. Phys. 118, 6989 (2003).
https://doi.org/10.1063/1.1560933
P. Shah, C. Chakravarty. Instantaneous normal mode analysis of Morse liquids. J. Chem. Phys. 116, 10825 (2002).
https://doi.org/10.1063/1.1479714
H. Okumura, F. Yonezawa. Liquid-vapor coexistence curves of several interatomic model potentials. J. Chem. Phys. 113, 9162 (2000).
https://doi.org/10.1063/1.1320828
T.-C. Lim. The relationship between Lennard-Jones (12-6) and Morse potential functions. Z. Naturforsch. 58a, 615 (2003).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
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. Duration.
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. Loyalty.
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.