Equation of State of a Cell Fluid Model with Allowance for Gaussian Fluctuations of the Order Parameter


  • I.V. Pylyuk Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
  • O.A. Dobush Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine




cell fluid model, equation of state, grand partition function, Morse potential, zero-mode approximation


The paper is devoted to the development of a microscopic description of the critical behavior of a cell fluid model with allowance for the contributions from collective variables with nonzero values of the wave vector. The mathematical description is performed in the supercritical temperature range (T > Tc) in the case of a modified Morse potential with additional repulsive interaction. The method, developed here for constructing the equation of state of the system by using the Gaussian distribution of the order parameter fluctuations, is valid beyond an immediate vicinity of the critical point for wide ranges of the density and temperature. The pressure of the system as a function of the chemical potential and density is plotted for various fixed values of the relative temperature, both with and without considering the above-mentioned contributions. Compared with the results of the zero-mode approximation, the insignificant role of these contributions is indicated for temperatures T > Tc. At T < Tc, they are more significant.


L.A. Bulavin, V. Kopylchuk, V. Garamus, M. Avdeev, L. Almasy, A. Hohryakov. SANS studies of critical phenomena in ternary mixtures. Appl. Phys. A: Materials Sci. and Proc. 74, s546 (2002). https://doi.org/10.1007/s003390201545

Y.B. Melnichenko, G.D. Wignall, D.R. Cole, H. Frielinghaus, L.A. Bulavin. Liquid-gas critical phenomena under confinement: Small-angle neutron scattering studies of CO2 in aerogel. J. Mol. Liq. 120, 7 (2005). https://doi.org/10.1016/j.molliq.2004.07.070

A.V. Chalyi, L.A. Bulavin, V.F. Chekhun, K.A. Chalyy, L.M. Chernenko, A.M. Vasilev, E.V. Zaitseva, G.V. Khrapijchyk, A.V. Siverin, M.V. Kovalenko. Universality classes and critical phenomena in confined liquid systems. Condens. Matter Phys. 16, 23008 (2013). https://doi.org/10.5488/CMP.16.23008

M.V. Ushcats, L.A. Bulavin, V.M. Sysoev, V.Y. Bardik, A.N. Alekseev. Statistical theory of condensation - Advances and challenges, J. Mol. Liq. 224, 694 (2016). https://doi.org/10.1016/j.molliq.2016.09.100

J.-P. Hansen, I.R. McDonald. Theory of Simple Liquids: With Applications to Soft Matter (Academic Press, 2013). https://doi.org/10.1016/B978-0-12-387032-2.00012-X

A.R.H. Goodwin, J.V. Sengers, C.J. Peters. Applied Thermodynamics of Fluids (Royal Society of Chemistry, 2010). https://doi.org/10.1039/9781849730983

M.A. Anisimov. Critical Phenomena in Liquids and Liquid Crystals (Gordon and Breach, 1991).

L.A. Bulavin. Critical Properties of Liquids (АСМI, 2002) (in Ukrainian).

J.V. Sengers, J.M.H. Levelt Sengers. Thermodynamic behavior of fluids near the critical point. Ann. Rev. Phys. Chem. 37, 189 (1986). https://doi.org/10.1146/annurev.pc.37.100186.001201

M.A. Anisimov, J.V. Sengers. Critical region. In: Equations of State for Fluids and Fluid Mixtures. Edited by J.V. Sengers, R.F. Kayser, C.J. Peters, H.J. White, jr. (Elsevier, 2000), pp. 381-434. https://doi.org/10.1016/S1874-5644(00)80022-3

D.Yu. Zalepugin, N.А. Tilkunova, I.V. Chernyshova, V.S. Polyakov. Development of technologies based on supercritical fluids. Supercritical Fluids: Theory and Practice 1, 27 (2006) (in Russian).

Y. Kozitsky, M. Kozlovskii, O. Dobush. Phase transitions in a continuum Curie-Weiss system: A quantitative analysis. In: Modern Problems of Molecular Physics. Edited by L.A. Bulavin, A.V. Chalyi (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 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

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.P. Kozlovskii, O.A. Dobush. Phase behavior of a cell fluid model with modified Morse potential. Ukr. J. Phys. 65, 428 (2020). https://doi.org/10.15407/ujpe65.5.428

R.C. Lincoln, K.M. Koliwad, P.B. Ghate. 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 Equilib. 248, 1 (2006). https://doi.org/10.1016/j.fluid.2006.07.010

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.P. Kozlovskii, I.V. Pylyuk, O.O. Prytula. Critical behaviour of a three-dimensional one-component magnet in strong and weak external fields at T > Tc. Physica A 369, 562 (2006). https://doi.org/10.1016/j.physa.2006.02.016

M.P. Kozlovskii, I.V. Pylyuk, Z.E. Usatenko. Method of calculating the critical temperature of three-dimensional Ising-like system using the non-Gaussian distribution. Phys. Stat. Sol. (b) 197, 465 (1996). https://doi.org/10.1002/pssb.2221970221

M.P. Kozlovskii, R.V. Romanik. Influence of an external field on the critical behavior of the 3D Ising-like model. J. Mol. Liq. 167, 14 (2012). https://doi.org/10.1016/j.molliq.2011.12.003

M.P. Kozlovskii. Free energy of 3D Ising-like system near the phase transition point. Condens. Matter Phys. 12, 151 (2009). https://doi.org/10.5488/CMP.12.2.151

M.P. Kozlovskii, I.V. Pylyuk. Entropy and specific heat of the 3D Ising model as functions of temperature and microscopic parameters of the system. Phys. Stat. Sol. (b) 183, 243 (1994). https://doi.org/10.1002/pssb.2221830119

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




How to Cite

Pylyuk, I., & Dobush, O. (2020). Equation of State of a Cell Fluid Model with Allowance for Gaussian Fluctuations of the Order Parameter. Ukrainian Journal of Physics, 65(12), 1080. https://doi.org/10.15407/ujpe65.12.1080



Physics of liquids and liquid systems, biophysics and medical physics