Curie–Weiss Cell Fluid Model: Fitting to Experimental Critical-Point Data
DOI:
https://doi.org/10.15407/ujpe71.11.878Keywords:
cell fluid model, Curie–Weiss interaction, experimental data, critical point, triple pointAbstract
We examine how the Curie–Weiss cell fluid model can be quantitatively related to real fluids by determining its microscopic parameters from experimental critical-point data for water, carbon dioxide, and three polyol ester lubricants (POE5, POE7, and POE9). The microscopic parameters of the model are determined from the experimental values of the critical temperature and critical density: the global attraction coupling constant is fixed by the critical temperature, and the cell volume by the critical density. The critical pressure then follows as an independent model prediction, deviating from experimental values by 10–41% across the studied substances. Varying the ratio of local repulsion to global attraction f = J₂/J₁ over a wide range has only a weak effect on this deviation. For f ≥ 1, the model’s critical compressibility factor lies within a narrow range Zc ≈ 0.382–0.386, remaining close to the mean-field van der Waals value Zc = 3/8 = 0.375 and consistently overestimating experimental values. The best agreement with experiment is obtained for the polyol ester lubricants and improves along the POE5–POE7–POE9 series with increasing molar mass, suggesting that multiple-occupancy cell fluid models are well suited to systems of large molecules, particularly soft-matter systems with bounded interaction potentials. We further show that generalizing the model by introducing a temperature- and phase-dependent effective attraction allows it to describe a triple point and to reproduce the broad range of critical-to-triple temperature ratios Tc/Ttr characteristic of real fluids.
References
1. D.C. Johnston. Advances in Thermodynamics of the van der Waals Fluid (Morgan & Claypool Publishers, 2014). [ISBN: 978-1-627-05532-1]
https://doi.org/10.1088/978-1-627-05532-1
2. N. Goldenfeld. Lectures on Phase Transitions and the Renormalization Group (Taylor & Francis Group, 2018).
https://doi.org/10.1201/9780429493492
3. M.E. Fisher. Renormalization group theory: Its basis and formulation in statistical physics. Rev. Mod. Phys. 70, 653 (1998).
https://doi.org/10.1103/RevModPhys.70.653
4. D. Frenkel, B. Smit. Understanding Molecular Simulation: From Algorithms to Applications, 3rd ed. (Academic Press, 2023) [ISBN: 9780323902922].
https://doi.org/10.1016/B978-0-32-390292-2.00011-8
5. M.P. Allen, D.J. Tildesley. Computer Simulation of Liquids, 2nd ed. (Oxford University Press, 2017) [ISBN: 9780198803195].
https://doi.org/10.1093/oso/9780198803195.001.0001
6. K. Binder, D.W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction, 6th ed. (Springer, 2019) [ISBN: 978-3-030-10758-1].
https://doi.org/10.1007/978-3-030-10758-1
7. E.H. Stanley. Introduction to Phase Transitions and Critical Phenomena (Clarendon, 1971) [ISBN: 9780195053166].
8. J.P. Hansen, I.R. McDonald. Theory of Simple Liquids: with Applications to Soft Matter, 4th ed. (Academic Press, 2013) [ISBN: 9780123870339].
https://doi.org/10.1016/B978-0-12-387032-2.00012-X
9. Yu. 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 International Publishing, 2018) [ISBN: 978-3-319-61109-9].
https://doi.org/10.1007/978-3-319-61109-9_11
10. Yu.V. Kozitsky, M.P. Kozlovskii, O.A. Dobush. A phase transition in a Curie-Weiss system with binary interactions. Condens. Matter Phys. 23, 23502 (2020).
https://doi.org/10.5488/CMP.23.23502
11. M.P. Kozlovskii, O.A. Dobush. Phase behavior of a cell model with Curie-Weiss interaction. J. Mol. Liq. 353, 118843 (2022).
https://doi.org/10.1016/j.molliq.2022.118843
12. I.V. Pylyuk, O.A. Dobush, M.P. Kozlovskii, R.V. Romanik, M.A. Shpot. Influence of attractive parts of interaction potentials on critical point parameters. Ukr. J. Phys. 70, 787 (2025).
https://doi.org/10.15407/ujpe70.11.787
13. O.A. Dobush, M.P. Kozlovskii, I.V. Pylyuk, Yu.O. Plevachuk. Influence of microscopic parameters on phase behavior of a cell model with Curie-Weiss interaction. Physica A 681, 131133 (2026).
https://doi.org/10.1016/j.physa.2025.131133
14. O.A. Dobush, M.A. Shpot. A new special function related to a discrete Gauss-Poisson distribution and some physics of the cell model with Curie-Weiss interactions. arXiv:2412.05428 (2024).
15. O.A. Dobush, M.P. Kozlovskii, I.V. Pylyuk, R.V. Romanik, M.A. Shpot. The cell fluid model with Curie-Weiss interactions: special cases and analytical results. Eur. Phys. J. B 99, 124 (2026).
https://doi.org/10.1140/epjb/s10051-026-01235-x
16. M.P. Kozlovskii, O.A. Dobush, I.V. Pylyuk, R.V. Romanik, M.A. Shpot. Triple point in a cell fluid model with effective temperature-dependent attraction. Physica A 692, 131510 (2026).
https://doi.org/10.1016/j.physa.2026.131510
17. M.P. Kozlovskii, O.A. 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
18. 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
19. 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
20. 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
21. I.V. Pylyuk, M.P. Kozlovskii, R.V. Romanik. Microscopic description of the liquid-gas coexistence curve for Morse fluids in the immediate vicinity of the critical point. Fluid Phase Equilib. 600, 114551 (2026).
https://doi.org/10.1016/j.fluid.2025.114551
22. L.A. Bulavin, Y.G. Rudnikov, A.V. Chalyi. Thermodynamic anomalies of water near its singular temperature of 42 °C. J. Mol. Liq. 389, 122849 (2023).
https://doi.org/10.1016/j.molliq.2023.122849
23. L.A. Bulavin, Y.G. Rudnikov, A.V. Chalyi. Special temperatures of water in the region of its physical anomalies. J. Mol. Liq. 435, 128135 (2025).
https://doi.org/10.1016/j.molliq.2025.128135
24. D. Ruelle. Superstable interactions in classical statistical mechanics. Commun. Math. Phys. 18, 127 (1970).
https://doi.org/10.1007/BF01646091
25. R.V. Romanik, O.A. Dobush, M.P. Kozlovskii, I.V. Pylyuk, M.A. Shpot. A multiple occupancy cell fluid model with competing attraction and repulsion interactions. J. Stat. Phys. 193 (2026).
https://doi.org/10.1007/s10955-026-03568-4
26. R. Span, W. Wagner. A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 25, 1509 (1996).
https://doi.org/10.1063/1.555991
27. R. Span, W. Wagner. Equations of state for technical applications. III. Results for polar fluids. Int. J. Thermophys. 24, 111 (2003).
https://doi.org/10.1023/A:1022362231796
28. D.W. Green, M.Z. Southard. Perry's Chemical Engineers' Handbook, 9th ed. (McGraw-Hill Education, 2019) [ISBN: 9780071834087].
29. E.W. Lemmon, I.H. Bell, M.L. Huber, M.O. McLinden. Thermophysical properties of fluid systems. In: NIST Chemistry WebBook, NIST Standard Reference Database Number 69. Edited by P.J. Linstrom, W.G. Mallard (National Institute of Standards and Technology, 2025), retrieved September 7, 2026.
30. National Institute of Standards and Technology. miniREFPROP - version 10.0 (2020), accessed September 7, 2026.
31. I.H. Bell, J. Wronski, S. Quoilin, V. Lemort. Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library CoolProp. Ind. Eng. Chem. Res. 53, 2498 (2014).
https://doi.org/10.1021/ie4033999
32. T.J. Bruno, T.J. Fortin, M.L. Huber, A. Laesecke, E.W. Lemmon, E. Mansfield, M.O. McLinden, S.L. Outcalt, R.A. Perkins, K.N. Urness, J.A. Widegren. Thermophysical Properties of Polyol Ester Lubricants. NIST Interagency/Internal Report (NISTIR) 8263 (National Institute of Standards and Technology, 2019).
https://doi.org/10.6028/NIST.IR.8263
33. I.C. Sanchez, R.H. Lacombe. An elementary molecular theory of classical fluids. Pure fluids. J. Phys. Chem. 80, 2352 (1976).
https://doi.org/10.1021/j100562a008
34. W. Wagner, A. Pruß. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387 (2002).
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