Critical Temperature Determination for Simple Fluids: an Analytical Approach Based on Collective Variables Method

Authors

  • I.R. Yukhnovskii Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine https://orcid.org/0000-0002-4834-3948
  • R.V. Romanic Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe69.9.671

Keywords:

simple fluids, collective variables, critical temperature

Abstract

An explicit equation for the liquid-vapor critical temperature of simple fluids is derived within an analytic approach – the method of collective variables with a reference system. This equation is applied to calculate the critical temperature values for several hard-core van der Waals fluids. The study also examines how the critical temperature depends on parameters of the interaction. Specifically, it is observed that, as the range of attractive interaction decreases, the critical temperature decreases as well.

References

I.R. Yukhnovskii, M.F. Holovko. Statistical Theory of Classical Equilibrium Systems (Naukova dumka, 1980) [in Russian].

I.R. Yukhnovskii. The functional of the grand partition function for the investigation of the liquid-gas critical point. Physica A 168, 999 (1990).

https://doi.org/10.1016/0378-4371(90)90268-W

I.R. Yukhnovskii. Phase transitions in a vicinity of the vapor-liquid critical point. Ukr. J. Phys. 10, 33 (2015) [in Ukrainian].

J.P. Hansen, I.R. McDonald. Theory of Simple Liquids: With Applications to Soft Matter (Academic Press, 2013) [ISBN: 9780123870339].

https://doi.org/10.1016/B978-0-12-387032-2.00012-X

I.I. Adamenko, L.A. Bulavin. Physics of Liquids and Liquid Systems (ASMI, 2006) [in Ukrainian] [ISBN: 966-7653-32-3].

I.R. Yukhnovskii, I.M. Idzyk, V.O. Kolomiets. Investigation of a homogeneous many-particle system in the vicinity of the critical point. J. Stat. Phys. 80, 405 (1995).

https://doi.org/10.1007/BF02178366

I.R. Yukhnovskii, R.V. Romanik. Grand partition function functional for simple fluids. J. Phys. Stud. 28, 2602-1 (2024).

https://doi.org/10.30970/jps.28.2602

I.R. Yukhnovskii, R.V. Romanik. Grand Partition Function Functional for Simple Fluids (Preprint ICMP-23-01E, 2023).

https://doi.org/10.30970/jps.28.2602

I.R. Yukhnovskii, M.P. Kozlovskii, I.V. Pylyuk. Microscopic Theory of Phase Transitions in the Three-Dimensional Systems (Eurosvit, 2001) [in Ukrainian] [ISBN: 966-7343-26-X].

M.P. Kozlovskii. Influence of an External Field on the Critical Behavior of Three-Dimensional Systems (Halytskyi drukar, 2012) [in Ukrainian] [ISBN: 978-966-970-442-7].

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

V.L. Kulinskii. Simple geometrical interpretation of the linear character for the zeno-line and the rectilinear diameter. J. Phys. Chem. B 114, 2852 (2010).

https://doi.org/10.1021/jp911897k

L.A. Bulavin, V.L. Kulinskii. Generalized principle of corresponding states and the scale invariant mean-field approach. J. Chem. Phys. 133, 134101 (2010).

https://doi.org/10.1063/1.3496468

I.R. Yukhnovskii. Solution of the three-dimensional Ising model for description of the second-order phase transition. Riv. Nuovo Cimento 12, 1 (1989).

https://doi.org/10.1007/BF02740597

M.P. Kozlovskii. Recurrence relations for the threedimensional Ising-like model in the external field. Condens. Matter Phys. 8, 473 (2005).

https://doi.org/10.5488/CMP.8.3.473

J.-M. Caillol, O.V. Patsahan, I.M. Mryglod. The collective variables representation of simple fluids from the point of view of statistical field theory. Condens. Matter Phys. 8, 665 (2005).

https://doi.org/10.5488/CMP.8.4.665

J.-M. Caillol, O.V. Patsahan, I.M. Mryglod. Statistical field theory for simple fluids: The collective variables representation. Physica A 368, 326 (2006).

https://doi.org/10.1016/j.physa.2005.11.010

N.F. Carnahan, K.E. Starling. Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635 (1969).

https://doi.org/10.1063/1.1672048

J.D. Weeks, D. Chandler, H.C. Andersen. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 54, 5237 (1971).

https://doi.org/10.1063/1.1674820

J. Krejci, I. Nezbeda. The critical temperature and properties of real gas from low order perturbed virial expansions. Fluid Phase Equilib. 314, 156 (2012).

https://doi.org/10.1016/j.fluid.2011.10.005

E.B. El Mendoub, J.-F. Wax, N. Jakse. Evolution of the liquid-vapor coexistence of the hard-core Yukawa fluid as a function of the interaction range. J. Chem. Phys. 132, 164503 (2010).

https://doi.org/10.1063/1.3385894

I.R. Yukhnovskii, O.V. Patsahan. Grand canonical distribution for multicomponent system in the collective variables method. J. Stat. Phys. 81, 647 (1995).

https://doi.org/10.1007/BF02179251

I.V. Pylyuk, M.P. Kozlovskii, O.A. Dobush. Analytic calculation of the critical temperature and estimation of the critical region size for a fluid model. Ukr. J. Phys. 68, 601 (2023).

https://doi.org/10.15407/ujpe68.9.601

I.V. Pylyuk, M.P. Kozlovskii, O.A. Dobush, M.V. Dufanets. Morse fluids in the immediate vicinity of the critical point: calculation of thermodynamic coefficients. J. Mol. Liq. 385, 122322 (2023).

https://doi.org/10.1016/j.molliq.2023.122322

G.M. Sowers, S.I. Sandler. Equations of state from generalized perturbation theory. Part 1. The hard-core LennardJones fluid. Fluid Phase Equilib. 63, 1 (1991).

https://doi.org/10.1016/0378-3812(91)80017-P

A. Diez, J. Largo, J.R. Solana. Excess energy and equation of state of fluids with hard-core potential models from a second-order Monte Carlo perturbation theory. Fluid Phase Equilib. 298, 262 (2010).

https://doi.org/10.1016/j.fluid.2010.08.003

F.W. Olver, D.W. Lozier, R. Boisvert, C.W. Clark. The NIST Handbook of Mathematical Functions (Cambridge University, 2010) [ISBN: 978-0521140638].

Published

2024-10-16

How to Cite

Yukhnovskii, I., & Romanic, R. (2024). Critical Temperature Determination for Simple Fluids: an Analytical Approach Based on Collective Variables Method. Ukrainian Journal of Physics, 69(9), 671. https://doi.org/10.15407/ujpe69.9.671

Issue

Section

Physics of liquids and liquid systems, biophysics and medical physics