Publishing House “Akademperiodyka”

National Academy of Sciences of Ukraine

Books Scientific monographs Ukrainian scientific book in a foreign language

Statistical Theory of Classical Equilibrium Systems

Authors:

IHOR YUKHNOVSKII (1925-2024)
Professor of Physics (1967), Full member of the National Academy of Sciences of Ukraine (1982), an outstanding Ukrainian scientist, theoretical physicist, a renowned expert in the field of statistical physics, theory of electrolyte solutions, quantum statistical physics, theory of phase transitions and critical phenomena. Leader of the modern Lyiv school of statistical physics, founder and long-time director of the Institute for Condensed Matter Physics of the NAS of Ukraine, which today bears his name.

 

 

 

 

 

 

MYROSLAV HOLOVKO (1943) Professor of Physics (1985) the Corresponding Member of National Academy of Sciences of Ukraine
a prominent Ukrainian, scientist, theoretical physicist, who made significant contributions to the statistical theory of simple and complex liquids, electrolytes and associating molecular systems.
His pioneering studies have greatly advanced the understanding of molecular association, the phase behaviour of fluids in bulk,
in porous media and at interfaces. He is well-known for his fundamental role in shaping modern statistical physics of liquids and solutions.

 

 

 

 

 

 

 

Reviewers:
W. EBELING, Yu. KALYUZHNYI, Yu. SLYUSARENKO

Year: 2025
Pages: 444
ISBN: 978-966-360-558-6
Publication Language:  English
Publisher: PH “Akademperiodyka”
Place Published: Kyiv

The monograph, first published by Naukova Dumka in 1980, provides a systematic presentation of the statistical theory of classical equilibrium systems.
It is among the first works devoted to the microscopic theory of the liquid state and may be regarded as an advanced textbook. A broad class of systems representing gases, liquids, and solutions is analyzed from a unified standpoint. The theory describes interacting particles in an extended phase space that includes both individual coordinates and collective variables characterizing density fluctuations. The ion-molecular approach developed for electrolyte solutions treats interactions between ions and solvent molecules on an equal basis, revealing fundamentally different mechanisms of electrostatic screening.

Spatially inhomogeneous systems are examined in detail as well

REFERENCE:

  1. P.-G. de Gennes, Soft matter: more than words, Soft Matter 1, (2005) 16-16, https://doi.org/10.1039/B419223K
  2. P.-G. de Gennes, Soft matter (nobel lecture), Reviews of Modern Physics 64, no. 3, (1993) 645-648, https://doi.org/10.1103/RevModPhys.64.645
  3. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, Elsevier, Amsterdam, 4th edn., 2013.
  4. J. R. Solana, Perturbation Theories for the Thermodynamic Properties of Fluids and Solids, CRC Press, Boca Raton, 2013. https://doi.org/10.1201/b13960
  5. C. G. Gray and K. E. Gubbins, Theory of Molecular Fluids, Volume 1: Fundamentals, Oxford University Press, New York, 1984. https://doi.org/10.1093/oso/9780198556022.001.0001
  6. C. G. Gray, K. E. Gubbins, and C. G. Joslin, Theory of Molecular Fluids, Volume 2: Applications, Oxford University Press, Oxford, 2011. https://doi.org/10.1093/acprof:oso/9780198556213.001.0001
  7. J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity, Clarendon Press, Oxford, 1982.
  8. F. Hirata, Molecular Theory of Fluctuations in Life Phenomena, Springer, Cham, 2025. https://doi.org/10.1007/978-981-96-3364-7
  9. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford University Press, Oxford, 2nd edn., 2017. https://doi.org/10.1093/oso/9780198803195.001.0001
  10. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, Elsevier Science, Amsterdam, 3rd edn., 2023.
  11. M. S. Wertheim, Fluids with highly directional attractive forces. I. Statistical thermodynamics, J. Stat. Phys. 35, no. 1, (1984) 19-34, https://doi.org/10.1007/BF01017362
  12. M. S. Wertheim, Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations, Journal of Statistical Physics 35, (1984) 35-47, https://doi.org/10.1007/BF01017363
  13. M. S. Wertheim, Fluids with highly directional attractive forces. III. Multiple attraction sites, J. Stat. Phys. 42, no. 3-4, (1986) 459-476, https://doi.org/10.1007/BF01127721
  14. M. S. Wertheim, Fluids with highly directional attractive forces. IV. Equilibrium polymerization, J. Statist. Phys. 42, no. 3-4, (1986) 477-492, https://doi.org/10.1007/BF01127722
  15. I. Z. Fisher, Statistical Theory of Liquids, University of Chicago Press, Chicago, 1964.
  16. S. A. Rice and P. Gray, The Statistical Mechanics of Simple Liquids: An Introduction to the Theory of Equilibrium and Non-equilibrium Phenomena, Interscience Publishers, 1965.
  17. C. A. Croxton, Liquid State Physics: A Statistical Introduction, Cambridge University Press, Cambridge, 1974. https://doi.org/10.1017/CBO9780511753480
  18. G. Temperley, I. R. McDonald, and E. W. Montroll (eds.), Physics of Simple Liquids, North-Holland Publishing Company, Amsterdam, 1970.
  19. K. Singer (ed.), Statistical Mechanics, vol. 1 of Specialist Periodical Report, Royal Society of Chemistry, London, 1973.
  20. K. Singer (ed.), Statistical Mechanics, vol. 2 of Specialist Periodical Report, Royal Society of Chemistry, London, 1975.
  21. B. J. Berne (ed.), Statistical Mechanics. Part A: Equilibrium Techniques, Plenum Press, New York, 1977. https://doi.org/10.1007/978-1-4684-2553-6
  1. D. N. Zubarev, Calculation of the configuration integral for a system of particles with Coulomb interaction, Dokl. Akad. Nauk SSSR 95, no. 4, (1954) 757-760, (in Russian).
  2. I. R. Yukhnovskii, Application of collective variables and consideration of shortrange forces in the theory of systems of charged particles, Zh. Eksp. Teor. Fiz. 34, no. 2, (1958) 379-389, (in Russian).
  3. H. C. Andersen and D. Chandler, Mode expansion in equilibrium statistical mechanics. I. General theory and application to the classical electron gas, J. Chem. Phys. 53, no. 2, (1970) 547-554, https://doi.org/10.1063/1.1674024
  4. H. C. Andersen and D. Chandler, Mode expansion in equilibrium statistical mechanics. III. Optimized convergence and application to ionic solution theory, J. Chem. Phys. 55, no. 4, (1971) 1497-1504, https://doi.org/10.1063/1.1676270
  5. H. C. Andersen and D. Chandler, Optimized cluster expansions for classical fluids. I. General theory and variational formulation of the mean spherical model and hard sphere Percus-Yevick equations, J. Chem. Phys. 57, no. 5, (1972) 1918- 1929, https://doi.org/10.1063/1.1678512
  6. H. C. Andersen, D. Chandler, and J. D. Weeks, Roles of repulsive and attractive forces in liquids: The optimized random phase approximation, J. Chem. Phys. 56, no. 8, (1972) 3812-3823, https://doi.org/10.1063/1.1677784
  7. H. C. Andersen, D. Chandler, and J. D. Weeks, Optimized cluster expansions for classical fluids. III. Applications to ionic solutions and simple liquids, J. Chem. Phys. 57, no. 7, (1972) 2626-2631, https://doi.org/10.1063/1.1678641
  8. H. C. Andersen, J. D. Weeks, and D. Chandler, Relationship between the hardsphere fluid and fluids with realistic repulsive forces, Phys. Rev. A 4, no. 4, (1971) 1597-1607, https://doi.org/10.1103/PhysRevA.4.1597
  9. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, John Wiley & Sons, New York, 1975.
  10. N. N. Bogoliubov, Problems of a dynamical theory in statistical physics, in: Selected Works in Three Volumes, (ed.) Y. A. Mitropolskii, vol. 2, pp. 99-196, Naukova Dumka, Kyiv, 1970, (in Russian)
  11. N. N. Bogolubov, Problems of a dynamical theory in statistical physics, in: Selected works. Pt. 1. Dynamical theory, (eds.) N. N. Bogolubov and A. M. Kurbatov, pp. 1-206, Gordon and Breach, New York, N.Y, 1990.
  12. A. F. Skryshevsky, Structural Analysis of Liquids: X-ray, Neutron, and Electron Diffraction, Vysshaya Shkola, Moscow, 1971, (in Russian).
  13. I. R. Yukhnovskii, Some questions on the current state of the theory of equilibrium systems of charged particles, Ukr. Fiz. Zh. 14, no. 5, (1969) 705-719, (in Russian).
  14. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, John Wiley & Sons, New York, 1954.
  15. R. G. Gordon and Y. S. Kim, Theory for the forces between closed-shell atoms and molecules, J. Chem. Phys. 56, no. 6, (1972) 3122-3133, https://doi.org/10.1063/1.1677649
  16. Y.S. Kim and R.G. Gordon, Ion-ion interaction potentials and their application to the theory of alkali halide and alkaline earth dihalide molecules, J. Chem. Phys. 60, no. 11 (1974) 4332-4344. https://doi.org/10.1063/1.1680908
  17. D. Pines, Elementary Excitations in Solids, W. A. Benjamin, Inc., New York, 1963.
  18. E. A. Mason and T. H. Spurling, The Virial Equation of State, Pergamon Press, Oxford, 1969.
  19. J. E. Mayer and M. Goeppert Mayer, Statistical Mechanics, John Wiley & Sons, New York, 1940.
  1. D. Ruelle, Statistical Mechanics: Rigorous Results, World Scientific Publishing / Imperial College Press, Singapore, 1999. https://doi.org/10.1142/4090
  2. K. Huang, Statistical Mechanics, John Wiley & Sons, New York, 2nd edn., 1987. 43. T. Morita and K. Hiroike, A new approach to the theory of classical fluids. I, Prog. Theor. Phys. 23, no. 6, (1960) 1003-1027, https://doi.org/10.1143/PTP.23.1003
  3. J. M. J. van Leeuwen, J. Groeneveld, and J. de Boer, New method for the calculation of the pair correlation function, Physica 25, no. 9, (1959) 792-808, https://doi.org/10.1016/0031-8914(59)90004-7
  4. J. Frenkel, Kinetic Theory of Liquids, Oxford University Press, Oxford, 1946. 46. L. L. Lee, Correlation functions of classical fluids. III. The method of partition function variation applied to the chemical potential: Cases of PY and HNC2, J. Chem. Phys. 60, no. 4, (1974) 1197-1207, https://doi.org/10.1063/1.1681182
  5. M. S. Wertheim, Integral equations in the theory of classical fluids, J. Math. Phys. 8, no. 4, (1967) 927-938, https://doi.org/10.1063/1.1705301
  6. L. Verlet, On the theory of classical fluids-III, Physica 30, no. 1, (1964) 95-104, https://doi.org/10.1016/0031-8914(64)90204-6
  7. R. J. Baxter, Direct correlation functions and their derivatives with respect to particle density, J. Chem. Phys. 41, no. 2, (1964) 553-558, https://doi.org/10.1063/1.1725907
  8. L. Blum, Mean spherical model for a mixture of charged spheres and hard dipoles, Chem. Phys. Lett. 26, no. 2, (1974) 200-202, https://doi.org/10.1016/0009-2614(74)85396-0
  9. V. M. Zamalin, G. E. Norman, and V. S. Filinov, The Monte Carlo Method in Statistical Thermodynamics, Nauka, Moscow, 1977, (in Russian).
  10. A. N. Lagarkov and V. M. Sergeev, The molecular dynamics method in statistical physics, Physics-Uspekhi 21, no. 8, (1978) 566-588, https://doi.org/10.1070/PU1978v021n08ABEH005644
  11. M. E. Tuckerman, Statistical mechanics: theory and molecular simulation, Oxford university press, 2023. https://doi.org/10.1093/oso/9780198825562.001.0001
  12. D. Bohm, General theory of collective coordinates, in: The many body problem- Le probl’eme ‘а N corps (Les Houches 1958), (eds.) C. Dewitt and P. Nozieres, pp. 401-516, Methuen, London, 1959.
  13. D. ter Haar, Elements of Statistical Mechanics, Butterworth-Heinemann, Oxford, 3rd edn., 1995.
  14. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, Volume 1: Distribution Theory, Charles Griffin & Company, London, 3rd edn., 1963.
  15. R. Kubo, Generalized cumulant expansion method, J. Phys. Soc. Jpn. 17, no. 7, (1962) 1100-1120, https://doi.org/10.1143/JPSJ.17.1100
  16. I. R. Yukhnovskii, Partition function of the three-dimensional Ising model, Theor. Math. Phys. 36, (1978) 798-815, https://doi.org/10.1007/BF01035756
  17. I. R. Yukhnovskii, Method of Displacements and Collective Variables, Kyiv, 1971, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-71-26R), (in Russian).
  18. I. R. Yukhnovskyi and M. K. Ostrovskyi, Properties of the transition function to collective variables, Visn. L’viv. Derzh. Univ., Ser. Fiz. 5, (1969) 3-11, (in Ukrainian).
  19. I. R. Yukhnovskyi, On the statistical theory of ionic systems, Ukr. Fiz. Zh. 4, no. 2, (1959) 167-176, (in Ukrainian).
  20. J. E. Mayer, The theory of ionic solutions, J. Chem. Phys. 18, no. 11, (1950) 1426-1436, https://doi.org/10.1063/1.1747934
  21. H. L. Friedman, Ionic solution theory, based on cluster expansion methods, vol. 3 of Monographs in statistical physics and thermodynamics, Interscience Publishers, New York, 1962.
  22. I. R. Yukhnovskii, Binary distribution function for systems of interacting charged particles, Zh. Eksp. Teor. Fiz. 27, no. 6, (1954) 690-698, (in Russian).
  23. A. Y. Glauberman, Methods of modern statistical theory of solutions, Visn. L’viv. Derzh. Univ., Ser. Fiz. 1, (1962) 10-31, (in Ukrainian).
  24. H. Falkenhagen, W. Ebeling, and H.-G. Hertz, Theorie der Electrolytes, S. Hirzel Verlag, Leipzig, 1971.
  25. I. R. Yukhnovskii and A. A. Nekrot, Virial expansions for plasma in the method of collective variables, Ukr. Fiz. Zh. 11, no. 4, (1966) 363-371, (in Ukrainian).
  26. V. I. Danilov, Structure and Crystallization of Liquids: Selected Papers, Publishing House of the Academy of Sciences of the Ukrainian SSR, Kyiv, 1956, (in Russian).
  27. M. F. Holovko and O. A. Pizio, Basic consideration of short-range interactions in the theory of ionic systems, Ukr. Fiz. Zh. 21, no. 4, (1976) 653-662, (in Russian).
  28. I. R. Yukhnovskii and R.N. Petrashko, Virial expansions for the free energy of electrons in metals, Ukr. Fiz. Zh. 22, no. 11, (1977) 1780-1790, (in Russian).
  29. F. Y. Wu and M. K. Chien, Convolution approximation for the n-particle distribution function, J. Math. Phys. 11, no. 6, (1970) 1912-1916, https://doi.org/10.1063/1.1665343
  30. F. M. Kuni, On the condition for the weakening of Bogolyubov correlations in statistical mechanics, Vestn. Leningr. Univ., Fiz., Khim. 4, (1968) 30-41, (in Russian).
  31. F. M. Kuni, Structure of polar liquids. I. Asymptotics of the direct correlation function at large molecular separations, Zh. Strukt. Khim. 9, no. 6, (1968) 938- 943, (in Russian). https://doi.org/10.1007/BF00744375
  32. J. S. Høye, J. L. Lebowitz, and G. Stell, Generalized mean spherical approximations for polar and ionic fluids, J. Chem. Phys. 61, no. 8, (1974) 3253-3260, https://doi.org/10.1063/1.1682485
  33. J. S. Høye and G. Stell, New self-consistent approximations for ionic and polar fluids, J. Chem. Phys. 67, no. 2, (1977) 524-529, https://doi.org/10.1063/1.434908
  34. I. R. Yukhnovskii, Reference Frame Separation in the Method of Collective Variables, Kyiv, 1974, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-74-149R), (in Russian).
  35. R. W. Zwanzig, High-temperature equation of state by a perturbation method. I. Nonpolar gases, J. Chem. Phys. 22, no. 8, (1954) 1420-1426, https://doi.org/10.1063/1.1740409
  36. R. W. Zwanzig, High-temperature equation of state by a perturbation method. II. Polar gases, J. Chem. Phys. 23, no. 10, (1955) 1915-1922, https://doi.org/10.1063/1.1740604
  37. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, vol. 5 of Course of Theoretical Physics, Pergamon Press, Oxford, 3rd edn., 1980. https://doi.org/10.1016/B978-0-08-023039-9.50007-X
  38. M. Katz, G. E. Uhlenbeck, and P. C. Hemmer, On the van der Waals Theory of the Vapor-Liquid Equilibrium. I. Discussion of a One?Dimensional Model, J. Math. Phys. 4, (1963) 216-228, https://doi.org/10.1063/1.1703946
  1. M. Katz, G. E. Uhlenbeck, and P. C. Hemmer, Van der Waals theory of the equilibrium between gas and liquid, in: Probability and Related Questions in Physics, (ed.) M. Katz, pp. 271-395, Mir, Moscow, 1965, (in Russian).
  2. P. C. Hemmer, On the van der Waals theory of the vapor-liquid equilibrium. IV. The pair correlation function and equation of state for long-range forces, J. Math. Phys. 5, no. 1, (1964) 75-84, https://doi.org/10.1063/1.1704066
  3. J. L. Lebowitz, G. Stell, and S. Baer, Separation of the interaction potential into two parts in treating many-body systems. I. General theory and applications to simple fluids with short-range and long-range forces, J. Math. Phys. 6, no. 8, (1965) 1282-1298, https://doi.org/10.1063/1.1704772
  4. G. Stell, Relation between γ ordering and the mode expansion, J. Chem. Phys. 55, no. 3, (1971) 1485-1486, https://doi.org/10.1063/1.1676258
  5. J. L. Lebowitz and O. Penrose, Rigorous treatment of the van der Waals- Maxwell theory of the liquid-vapor transition, J. Math. Phys. 7, no. 1, (1966) 98-113, https://doi.org/10.1063/1.1704821
  6. J. Rasaiah and G. Stell, Upper bounds on free energies in terms of hard-sphere results, Mol. Phys. 18, no. 2, (1970) 249-260, https://doi.org/10.1080/00268977000100261
  7. A. Isihara, Statistical Physics, Academic Press, 1971.
  8. J. S. Høye and G. Stell, Thermodynamics of the MSA for simple fluids, J. Chem. Phys. 67, no. 2, (1977) 439-445, https://doi.org/10.1063/1.434887
  9. I. R. Yukhnovskii, Phase Transition of the Second Order: Collective Variables Method, World Scientific, Singapore, 1987. https://doi.org/10.1142/0289
  10. I. R. Yukhnovskii, M. P. Kozlovskii, and I. V. Pylyuk, Microscopic Theory of Phase Transitions in Three-Dimensional Systems, Evrosvit, Lviv, 2001, (in Ukrainian).
  11. M. S. Wertheim, Exact solution of the Percus-Yevick integral equation for hard spheres, Phys. Rev. Lett. 10, no. 8, (1963) 321-323, https://doi.org/10.1103/PhysRevLett.10.321
  12. M. S. Wertheim, Analytic solution of the Percus-Yevick equation, J. Math. Phys. 5, no. 5, (1964) 643-651, https://doi.org/10.1063/1.1704158
  13. E. Thiele, Equation of state for hard spheres, J. Chem. Phys. 39, no. 2, (1963) 474-479, https://doi.org/10.1063/1.1734272
  14. L. F. T’oth, Regular Figures, Macmillan, New York, 1964.
  15. T. L. Hill, Statistical mechanics: Principles and selected applications, Dover Publications, New York, 1987.
  16. B. R. A. Nijboer and L. Van Hove, Radial distribution function of a gas of hard spheres and the superposition approximation, Phys. Rev. 85, no. 5, (1952) 777-783, https://doi.org/10.1103/PhysRev.85.777
  17. F. H. Ree, R. N. Keeler, and S. L. McCarthy, Radial distribution function of hard spheres, J. Chem. Phys. 44, no. 9, (1966) 3407-3425, https://doi.org/10.1063/1.1727245
  18. F. H. Ree and W. G. Hoover, Fifth and sixth virial coefficients for hard spheres and hard disks, J. Chem. Phys. 40, no. 4, (1964) 939-950, https://doi.org/10.1063/1.1725286
  19. W. G. Hoover and J. C. Poirier, Determination of virial coefficients from the potential of mean force, J. Chem. Phys. 37, no. 5, (1962) 1041-1042, https://doi.org/10.1063/1.1733209
  20. E. Meeron and A. J. F. Siegert, Statistical mechanics of hardparticle systems, J. Chem. Phys. 48, no. 7, (1968) 3139-3155, https://doi.org/10.1063/1.1669587
  21. M. V. Fedoryuk, The Method of Steepest Descent, Nauka, Moscow, 1977, (in Russian).
  1. Z. W. Salsburg, R. W. Zwanzig, and J. G. Kirkwood, Molecular distribution functions in a one-dimensional fluid, J. Chem. Phys. 21, no. 6, (1953) 1098- 1107, https://doi.org/10.1063/1.1699116
  2. Y. Singh and F. F. Abraham, Statistical mechanical theory for nonuniform fluids: Properties of the hard-sphere system and a perturbation theory for nonuniform simple fluids, J. Chem. Phys. 67, no. 2, (1977) 537-546, https://doi.org/10.1063/1.434910
  3. H. Reiss, H. L. Frisch, and J. L. Lebowitz, Statistical mechanics of rigid spheres, J. Chem. Phys. 31, no. 2, (1959) 369-380, https://doi.org/10.1063/1.1730361
  4. E. Helfand, H. L. Frisch, and J. L. Lebowitz, Theory of the two- and onedimensional rigid sphere fluids, J. Chem. Phys. 34, no. 3, (1961) 1037-1042, https://doi.org/10.1063/1.1731629
  5. F. H. Stillinger and M. A. Cotter, Free energy in the presence of constraint surfaces, J. Chem. Phys. 55, no. 7, (1971) 3449-3458, https://doi.org/10.1063/1.1676598
  6. D. M. Tully-Smith and H. Reiss, Further development of scaled particle theory of rigid sphere fluids, J. Chem. Phys. 53, no. 10, (1970) 4015-4025, https://doi.org/10.1063/1.1673873
  7. H. Reiss and D. M. Tully-Smith, Further development of scaled particle theory for rigid spheres: Application of the statistical thermodynamics of curved surfaces, J. Chem. Phys. 55, no. 4, (1971) 1674-1689, https://doi.org/10.1063/1.1676297
  8. M. A. Cotter and F. H. Stillinger, Extension of scaled particle theory for rigid disks, J. Chem. Phys. 57, no. 8, (1972) 3356-3378, https://doi.org/10.1063/1.1678767
  9. J. J. Vieceli and H. Reiss, Thermodynamics of curved boundary layers, J. Chem. Phys. 57, no. 9, (1972) 3745-3748, https://doi.org/10.1063/1.1678840
  10. F. C. Andrews, Simple approach to the equilibrium statistical mechanics of the hard sphere fluid, J. Chem. Phys. 62, no. 1, (1975) 272-275, https://doi.org/10.1063/1.430271
  11. H. Reiss and R. V. Casberg, Radial distribution function for hard spheres from scaled particle theory, and an improved equation of state, J. Chem. Phys. 61, no. 3, (1974) 1107-1114, https://doi.org/10.1063/1.1681981
  12. J. Mathews and R. L. Walker, Mathematical Methods of Physics, W. A. Benjamin, New York, 2nd edn., 1970.
  13. A. G. Sveshnikov and A. N. Tikhonov, Theory of Functions of a Complex Variable, Nauka, Moscow, 1974, (in Russian).
  14. R. J. Baxter, Ornstein-Zernike relation for a disordered fluid, Aust. J. Phys. 21, no. 5, (1968) 563-570, https://doi.org/10.1071/ph680563
  15. N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, no. 2, (1969) 635-636, https://doi.org/10.1063/1.1672048
  16. N.W. Ashcroft and J. Lekner, Structure and resistivity of liquid metals, Phys. Rev. 145, no. 1, (1966) 83-90, https://doi.org/10.1103/PhysRev.145.83
  17. J. W. Perram, Hard sphere correlation functions in the Percus-Yevick approximation, Mol. Phys. 30, no. 5, (1975) 1505-1509, https://doi.org/10.1080/00268977500103021
  18. P. Perry and G. J. Throop, Decay of pair correlations in hard sphere fluids, J. Chem. Phys. 57, no. 5, (1972) 1827-1829, https://doi.org/10.1063/1.1678497
  19. W. R. Smith and D. Henderson, Analytical representation of the Percus-Yevick hard-sphere radial distribution function, Mol. Phys. 19, no. 3, (1970) 411-415, https://doi.org/10.1080/00268977000101421
  20. G. J. Throop and R. J. Bearman, Numerical solutions of the Percus-Yevick equation for the hard-sphere potential, J. Chem. Phys. 42, no. 7, (1965) 2408- 2411, https://doi.org/10.1063/1.1696308
  21. F. Mandel, R. J. Bearman, and M. Y. Bearman, Numerical solutions of the Percus-Yevick equation for the Lennard-Jones (6-12) and hard-sphere potentials, J. Chem. Phys. 52, no. 7, (1970) 3315-3323, https://doi.org/10.1063/1.1673491
  22. L. Verlet and J.-J. Weis, Equilibrium theory of simple liquids, Phys. Rev. A 5, no. 2, (1972) 939-952, https://doi.org/10.1103/PhysRevA.5.939
  23. D. Henderson and E. W. Grundke, Direct correlation function: Hard sphere fluid, J. Chem. Phys. 63, no. 2, (1975) 601-607, https://doi.org/10.1063/1.431378
  24. E. Waisman, The radial distribution function for a fluid of hard spheres at high densities: Mean spherical integral equation approach, Mol. Phys. 25, no. 1, (1973) 45-48, https://doi.org/10.1080/00268977300100061
  25. S. V. Tyablikov, On the question of crystallization, Zh. Eksp. Teor. Fiz. 17, no. 5, (1947) 386-389, (in Russian) 127. H. J. Ravech’e and C. A. Stuart, Towards a molecular theory of freezing, J. Chem. Phys. 63, no. 3, (1975) 1099-1111, https://doi.org/10.1063/1.431453
  26. H. J. Ravech’e and C. A. Stuart, Towards a molecular theory of freezing. II. Study of bifurcation as a function of density, J. Chem. Phys. 65, no. 6, (1976) 2305-2312, https://doi.org/10.1063/1.433341
  27. H. J. Ravech’e and C. A. Stuart, Bifurcation of solutions with crystalline symmetry, J. Math. Phys. 17, no. 11, (1976) 1949-1953, https://doi.org/10.1063/1.522832
  28. M. A. Krasnosel’skii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, London, New York, Paris, 1964.
  29. C. Kittel and P. McEuen, Introduction to solid state physics, Wiley, Hoboken, NJ, 9th edn., 2018.
  30. D. A. McQuarrie and J. L. Katz, High-temperature equation of state, J. Chem. Phys. 44, no. 6, (1966) 2393-2397, https://doi.org/10.1063/1.1727054
  31. J. A. Barker and D. Henderson, Perturbation theory and equation of state for fluids. II. A successful theory of liquids, J. Chem. Phys. 47, no. 11, (1967) 4714-4721, https://doi.org/10.1063/1.1701689
  32. J. D. Weeks, D. Chandler, and H. C. Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54, no. 12, (1971) 5237-5247, https://doi.org/10.1063/1.1674820
  33. L. Verlet and J.-J. Weis, Perturbation theory for the thermodynamic properties of simple liquids, Mol. Phys. 24, no. 5, (1972) 1013-1024, https://doi.org/10.1080/00268977200102111
  34. J. A. Barker and D. Henderson, What is “liquid”? Understanding the states of matter, Rev. Mod. Phys. 48, no. 4, (1976) 587-671, https://doi.org/10.1103/RevModPhys.48.587
  35. S. H. Sung and D. Chandler, Optimized cluster theory, the Lennard-Jones fluid, and the liquid-gas phase transition, Phys. Rev. A 9, no. 4, (1974) 1688-1697, https://doi.org/10.1103/PhysRevA.9.1688
  36. S. K. Sinha, J. Ram, and Y. Singh, Equilibrium properties of dense simple fluids in the presence of three-body forces, J. Chem. Phys. 66, no. 11, (1977) 5013- 5020, https://doi.org/10.1063/1.433805
  37. M. F. Holovko, On the Static Treatment of Intermolecular Interactions in Condensed Systems, Kyiv, 1974, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITP-74-173R), (in Russian).
  38. E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics, Part 2: Theory of the Condensed State, vol. 9 of Course of Theoretical Physics, Butterworth-Heinemann, 1980.
  39. H. D. Jones, Method for finding the equation of state of liquid metals, J. Chem. Phys. 55, no. 6, (1971) 2640-2642, https://doi.org/10.1063/1.1676472
  40. I. R. Yukhnovskii and M. F. Holovko, Osmotic Theory of Surface and Bulk Properties of Solutions, Kyiv, 1976, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-76-107R), (in Russian).
  41. W. G. McMillan and J. E. Mayer, The statistical thermodynamics of multicomponent systems, J. Chem. Phys. 13, no. 7, (1945) 276-305, https://doi.org/10.1063/1.1724036
  42. E.W. Grundke and D. Henderson, Distribution functions of multi-component fluid mixtures of hard spheres, Mol. Phys. 24, no. 2, (1972) 269-281, https://doi.org/10.1080/00268977200101431
  43. J. L. Lebowitz, E. Helfand, and E. Praestgaard, Scaled particle theory of fluid mixtures, J. Chem. Phys. 43, no. 3, (1965) 774-779, https://doi.org/10.1063/1.1696842
  44. R. J. Baxter, Ornstein-Zernike relation and Percus-Yevick approximation for fluid mixtures, J. Chem. Phys. 52, no. 9, (1970) 4559-4562, https://doi.org/10.1063/1.1673684
  45. J. L. Lebowitz and J. S. Rowlinson, Thermodynamic properties of mixtures of hard spheres, J. Chem. Phys. 41, no. 1, (1964) 133-138, https://doi.org/10.1063/1.1725611
  46. J. L. Lebowitz, Exact solution of generalized Percus-Yevick equation for a mixture of hard spheres, Phys. Rev. 133, no. 4A, (1964) A895-A899, https://doi.org/10.1103/PhysRev.133.A895
  47. L. Blum and J. S. Hoeye, Mean spherical model for asymmetric electrolytes. 2. Thermodynamic properties and the pair correlation function, J. Phys. Chem. 81, no. 13, (1977) 1311.1316, https://doi.org/10.1021/j100528a019
  48. P. J. Leonard, D. Henderson, and J. A. Barker, Calculation of the radial distribution function of hard-sphere mixtures in the Percus-Yevick approximation, Mol. Phys. 21, no. 1, (1971) 107-111, https://doi.org/10.1080/00268977100101221
  49. J. L. Lebowitz and D. Zomick, Mixtures of hard spheres with nonadditive diameters: Some exact results and solution of PY equation, J. Chem. Phys. 54, no. 8, (1971) 3335-3346, https://doi.org/10.1063/1.1675348
  50. S. Ahn and J. L. Lebowitz, Results of Percus-Yevick approximation for a binary mixture of hard spheres with nonadditive diameters; R11 = R22 = 0, R12 > 0, J. Chem. Phys. 60, no. 2, (1974) 523-533, https://doi.org/10.1063/1.1681070
  51. B. Widom and J. S. Rowlinson, New model for the study of liquid. vapor phase transitions, J. Chem. Phys. 52, no. 4, (1970) 1670-1684, https://doi.org/10.1063/1.1673203
  52. E. Bergmann, Scaled particle theory for non-additive hard spheres: General theory and solution of the Widom-Rowlinson model, Mol. Phys. 32, no. 1, (1976) 237-256, https://doi.org/10.1080/00268977600101751
  53. S. H. Sung, D. Chandler, and B. J. Alder, Optimized cluster theory correction to the van der Waals model of mixtures, J. Chem. Phys. 61, no. 3, (1974) 932-935, https://doi.org/10.1063/1.1682038
  54. L. L. Lee and D. Levesque, Perturbation theory for mixtures of simple liquids, Mol. Phys. 26, no. 6, (1973) 1351-1370, https://doi.org/10.1080/00268977300102531
  55. S. Sung and D. Chandler, Perturbation theory for repulsive forces in classical fluids: Selected applications, J. Chem. Phys. 56, no. 10, (1972) 4989-4994, https://doi.org/10.1063/1.1676979
  56. V. B. Fedorov and E. I. Kharkov, Ewald electrostatic energy of liquid metallic binary alloys, Ukr. Fiz. Zh. 21, no. 8, (1976) 1233-1236, (in Ukrainian).
  57. L. Onsager, Electrostatic interaction of molecules, J. Phys. Chem. 43, no. 2, (1939) 189-196, https://doi.org/10.1021/j150389a001
  58. F. J. Dyson and A. Lenard, Stability of matter. I, J. Math. Phys. 8, no. 3, (1967) 423-434, https://doi.org/10.1063/1.1705209
  59. A. Lenard and F. J. Dyson, Stability of matter. II, J. Math. Phys. 9, no. 5, (1968) 698-711, https://doi.org/10.1063/1.1664631
  60. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Elsevier, 2013.
  61. F. H. Stillinger and R. Lovett, Ion-pair theory of concentrated electrolytes. I. Basic concepts, J. Chem. Phys. 48, no. 9, (1968) 3858-3868, https://doi.org/10.1063/1.1669709
  62. P. Debye and E. H¨uckel, Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen, Phys. Z. 24, no. 9, (1923) 185-206.
  63. G. A. Martynov, Statistical theory of electrolyte solutions of moderate concentration, Physics-Uspekhi 91, no. 3, (1967) 445-483, (in Russian).
  64. G. A. Martynov, Transformation of the Bogoliubov chain to an exact closed system of equations for the unary and binary distribution functions, Theor. Math. Phys. 22, no. 2, (1975) 184-190. https://doi.org/10.1007/BF01036325
  65. D. J. Mitchell, D. A. McQuarrie, A. Szabo, and J. Groeneveld, On the second moment condition of Stillinger and Lovett, J. Stat. Phys. 17, no. 1, (1977) 15-20, https://doi.org/10.1007/BF01089374
  66. I. R. Yukhnovskii and A. A. Nekrot, On the classical statistical theory of equilibrium systems of charged particles, Ukr. Fiz. Zh. 12, no. 2, (1967) 177-185, (in Russian).
  67. W. Ebeling and G. Kelbg, Zur statistischen Thermodynamik elektrolytischer L¨osungen mit großem Bjerrum-Parameter, Z. Phys. Chem. 233, no. 1, (1966) 209-230, https://doi.org/10.1515/zpch-1966-23326
  68. G. Kelbg, W. Ebeling, and H. Krienke, Zur statistischen thermodynamik elektrolytischer l¨osungen mit großem Bjerrum-parameter. II., Z. Phys. Chem. 238O, no. 1, (1968) 76-88, https://doi.org/10.1515/zpch-1968-23811
  69. H. Falkenhagen, W. Ebeling, and H. G. Hertz, Theorie der Elektrolyte: 90 Tabellen, Hirzel, Stuttgart, 1971.
  70. G. Kelbg, Untersuchungen zur statistisch-mechanischen theorie starker elektrolyte III. Coulomb-potential mit ¨uberlagertem Herzfeld-potential, Z. Phys. Chem. 214O, no. 1, (1960) 141-152, https://doi.org/10.1515/zpch-1960-21412
  71. G. Kelbg, Untersuchungen zur statistisch-mechanischen theorie starker elektrolyte IV. Vergleich der theorie mit dem experiment, Z. Phys. Chem. 214O, no. 1, (1960) 153-164, https://doi.org/10.1515/zpch-1960-21413
  72. I. R. Yukhnovskyi, L. A. Nevidomska, and S. S. Tokar, Chemical potential of a system of charged particles and its parametric curves to second virial coefficient accuracy, Visn. L’viv. Derzh. Univ., Ser. Fiz. 2, (1965) 19-26, (in Ukrainian).
  1. J. C. Rasaiah, Computations for higher valence electrolytes in the restricted primitive model, J. Chem. Phys. 56, no. 6, (1972) 3071-3085, https://doi.org/10.1063/1.1677643
  2. J. C. Rasaiah and H. L. Friedman, Integral equation methods in the computation of equilibrium properties of ionic solutions, J. Chem. Phys. 48, no. 6, (1968) 2742-2752, https://doi.org/10.1063/1.1669510
  3. J. C. Rasaiah and H. L. Friedman, Integral equation computations for aqueous 1-1 electrolytes. Accuracy of the method, J. Chem. Phys. 50, no. 9, (1969) 3965-3976, https://doi.org/10.1063/1.1671657
  4. J. C. Rasaiah, D. N. Card, and J. P. Valleau, Calculations on the “restricted primitive model” for 1.1 electrolyte solutions, J. Chem. Phys. 56, no. 1, (1972) 248-255, https://doi.org/10.1063/1.1676854
  5. P. N. Vorontsov-Veliaminov, A. M. Eliashevich, J. C. Rasaiah, and H. L. Friedman, Comparison of hypernetted chain equation and Monte Carlo results for a system of charged hard spheres, J. Chem. Phys. 52, no. 2, (1970) 1013-1014, https://doi.org/10.1063/1.1673001
  6. J. C. Rasaiah, Equilibrium properties of ionic solutions; the primitive model and its modification for aqueous solutions of the alkali halides at 25 ◦C, J. Chem. Phys. 52, no. 2, (1970) 704-715, https://doi.org/10.1063/1.1673043
  7. G. Stell and J. L. Lebowitz, Equilibrium properties of a system of charged particles, J. Chem. Phys. 49, no. 8, (1968) 3706-3717, https://doi.org/10.1063/1.1670656
  8. G. Stell and K. C. Wu, Pad’e approximant for the internal energy of a system of charged particles, J. Chem. Phys. 63, no. 1, (1975) 491-498, https://doi.org/10.1063/1.431076
  9. B. Larsen, Studies in statistical mechanics of Coulombic systems. I. Equation of state for the restricted primitive model, J. Chem. Phys. 65, no. 9, (1976) 3431-3438, https://doi.org/10.1063/1.433596
  10. B. Larsen, G. Stell, and K. C. Wu, Evaluation of a new self-consistent approximation for an ionic fluid, J. Chem. Phys. 67, no. 2, (1977) 530-536, https://doi.org/10.1063/1.434909
  11. J. G. Kirkwood and J. C. Poirier, The statistical mechanical basis of the Debye- H¨uekel theory of strong electrolytes, J. Phys. Chem. 58, no. 8, (1954) 591-596, https://doi.org/10.1021/j150518a004
  12. R. Lovett and F. H. Stillinger, Ion-pair theory of concentrated electrolytes. II. Approximate dielectric response calculation, J. Chem. Phys. 48, no. 9, (1968) 3869-3884, https://doi.org/10.1063/1.1669710
  13. C. W. Outhwaite and V. C. L. Hutson, The mean spherical model for charged hard spheres, Mol. Phys. 29, no. 5, (1975) 1521-1531, https://doi.org/10.1080/00268977500101331
  14. B. Larsen, J. C. Rasaiah, and G. Stell, Thermodynamic perturbation theory for multipolar and ionic liquids, Mol. Phys. 33, no. 4, (1977) 987-1027, https://doi.org/10.1080/00268977700100901
  15. G. Stell, K. C. Wu, and B. Larsen, Critical point in a fluid of charged hard spheres, Phys. Rev. Lett. 37, no. 21, (1976) 1369-1372, https://doi.org/10.1103/PhysRevLett.37.1369
  16. P. N. Vorontsov-Velyaminov and V. P. Chasovskikh, Critical point in an ionic system from the results of a mathematical experiment: Comparison with salt melts, High Temperature 13, no. 6, (1976) 1015-1021.
  17. V. P. Chasovskikh, P. N. Vorontsov-Velyaminov, and A. M. Elyashevich, Study of the temperature dependence of radial distribution functions of a Coulomb system of hard spheres calculated via Monte Carlo method in the NPT ensemble, Dokl. Akad. Nauk Tadzh. SSR 16, no. 5, (1973) 30-34, (in Russian).
  1. C. Y. Mou and R. M. Mazo, Pair correlation function of dense electrolyte system: Restricted primitive model, J. Chem. Phys. 65, no. 11, (1976) 4530-4536, https://doi.org/10.1063/1.432906
  2. E. Waisman and J. L. Lebowitz, Mean spherical model integral equation for charged hard spheres I. Method of solution, J. Chem. Phys. 56, no. 6, (1972) 3086-3093, https://doi.org/10.1063/1.1677644
  3. E. Waisman and J. L. Lebowitz, Mean spherical model integral equation for charged hard spheres. II. Results, J. Chem. Phys. 56, no. 6, (1972) 3093-3099, https://doi.org/10.1063/1.1677645
  4. L. Blum, Mean spherical model for asymmetric electrolytes: I. Method of solution, Mol. Phys. 30, no. 5, (1975) 1529-1535, https://doi.org/10.1080/00268977500103051
  5. K. Hiroike, Supplement to Blum’s theory for asymmetric electrolytes, Mol. Phys. 33, no. 4, (1977) 1195-1198, https://doi.org/10.1080/00268977700101011
  6. M. Gillan, B. Larsen, M. P. Tosi, and N. H. March, Structure of classical liquid of charged hard spheres and point ions, J. Phys. C: Solid State Phys. 9, no. 6, (1976) 889-907, https://doi.org/10.1088/0022-3719/9/6/010
  7. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, Singapore, 1988. https://doi.org/10.1142/0270
  8. A. S. Davydov, Quantum Mechanics, vol. 1 of International Series in Natural Philosophy, Pergamon Press, Kent, 2nd edn., 1976.
  9. W. A. Steele, Statistical mechanics of nonspherical molecules, J. Chem. Phys. 39, no. 12, (1963) 3197-3208, https://doi.org/10.1063/1.1734181
  10. D. W. Jepsen and H. L. Friedman, Cluster expansion methods for systems of polar molecules: Some solvents and dielectric properties, J. Chem. Phys. 38, no. 4, (1963) 846-864, https://doi.org/10.1063/1.1733773
  11. L. Blum and A. J. Torruella, Invariant expansion for two-body correlations: Thermodynamic functions, scattering, and the Ornstein-Zernike equation, J. Chem. Phys. 56, no. 1, (1972) 303-310, https://doi.org/10.1063/1.1676864
  12. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Elsevier, 2013.
  13. L. Blum, Invariant expansion. II. The Ornstein-Zernike equation for nonspherical molecules and an extended solution to the mean spherical model, J. Chem. Phys. 57, no. 5, (1972) 1862-1869, https://doi.org/10.1063/1.1678503
  14. L. Blum, Invariant expansion III: The general solution of the mean spherical model for neutral spheres with electostatic interactions, J. Chem. Phys. 58, no. 8, (1973) 3295-3303, https://doi.org/10.1063/1.1679655
  15. S. A. Adelman and J. M. Deutch, Exact solution of the mean spherical model for simple polar mixtures, J. Chem. Phys. 59, no. 8, (1973) 3971-3980, https://doi.org/10.1063/1.1680587
  16. M. S. Wertheim, Fluids of hard convex molecules III. The third virial coefficient, Molecular Physics 89, no. 4, (1996) 1005-1017, https://doi.org/10.1080/002689796173453
  17. M. S. Wertheim, Third virial coefficient of hard spheroids, Molecular Physics 99, no. 3, (2001) 187-196, https://doi.org/10.1080/00268970010008397
  18. R. M. Gibbons, The scaled particle theory for particles of arbitrary shape, Mol. Phys. 17, no. 1, (1969) 81-86, https://doi.org/10.1080/00268976900100811
  19. T. Boublik, Statistical thermodynamics of convex molecule fluids, Mol. Phys. 27, no. 5, (1974) 1415-1427, https://doi.org/10.1080/00268977400101191
  20. T. Boublik, Two-dimensional convex particle liquid, Mol. Phys. 29, no. 2, (1975) 421-428, https://doi.org/10.1080/00268977500100361
  21. T. Boublik, Hard convex body equation of state, J. Chem. Phys. 63, no. 9, (1975) 4084-4084, https://doi.org/10.1063/1.431882
  22. M. A. Cotter and D. E. Martire, Statistical mechanics of rodlike particles. II. A scaled particle investigation of the aligned→isotropic transition in a fluid of rigid spherocylinders, J. Chem. Phys. 52, no. 4, (1970) 1909-1919, https://doi.org/10.1063/1.1673232
  23. I. Nezbeda, Approximate hard convex body equations of state and boundaries of their validity, Czech. J. Phys. B 26, no. 3, (1976) 355-358, https://doi.org/10.1007/BF01594272
  24. M. A. Cotter, Hard-rod fluid: Scaled particle theory revisited, Phys. Rev. A 10, no. 2, (1974) 625-636, https://doi.org/10.1103/PhysRevA.10.625
  25. G. Lasher, Nematic ordering of hard rods derived from a scaled particle treatment, J. Chem. Phys. 53, no. 11, (1970) 4141-4146, https://doi.org/10.1063/1.1673914
  26. A. I. Kitaygorodskii, Molecular Crystals, Nauka, Moscow, 1971, (in Russian).
  27. D. Chandler, Derivation of an integral equation for pair correlation functions in molecular fluids, J. Chem. Phys. 59, no. 5, (1973) 2742-2746, https://doi.org/10.1063/1.1680393
  28. D. Chandler, Cluster diagrammatic analysis of the RISM equation, Mol. Phys. 31, no. 4, (1976) 1213-1223, https://doi.org/10.1080/00268977600100941
  29. D. Chandler, The dielectric constant and related equilibrium properties of molecular fluids: Interaction site cluster theory analysis, J. Chem. Phys. 67, no. 3, (1977) 1113-1124, https://doi.org/10.1063/1.434962
  30. D. Chandler and H. C. Andersen, Mode expansion in equilibrium statistical mechanics. II. A rapidly convergent theory of ionic solutions, J. Chem. Phys. 54, no. 1, (1971) 26-33, https://doi.org/10.1063/1.1674601
  31. D. Chandler and H. C. Andersen, Optimized cluster expansions for classical fluids. II. Theory of molecular liquids, J. Chem. Phys. 57, no. 5, (1972) 1930- 1937, https://doi.org/10.1063/1.1678513
  32. D. Chandler, C. S. Hsu, and W. B. Streett, Comparisons of Monte Carlo and RISM calculations of pair correlation functions, J. Chem. Phys. 66, no. 11, (1977) 5231-5234, https://doi.org/10.1063/1.433787
  33. D. Chandler and L. R. Pratt, Statistical mechanics of chemical equilibria and intramolecular structures of nonrigid molecules in condensed phases, J. Chem. Phys. 65, no. 8, (1976) 2925-2940, https://doi.org/10.1063/1.433529
  34. B. M. Ladanyi and D. Chandler, New type of cluster theory for molecular fluids: Interaction site cluster expansion, J. Chem. Phys. 62, no. 11, (1975) 4308-4324, https://doi.org/10.1063/1.431001
  35. D. A. MacInnes and I. E. Farquhar, Transformation of the Chandler-Andersen RISM equation for fluids of diatomic molecules, J. Chem. Phys. 64, no. 4, (1976) 1481-1484, https://doi.org/10.1063/1.432363
  36. L. J. Lowden and D. Chandler, Erratum and addenda: Solution of a new integral equation for pair correlation function in molecular liquids, J. Chem. Phys. 62, no. 10, (1975) 4246-4246, https://doi.org/10.1063/1.430278
  37. L. J. Lowden and D. Chandler, Theory of intermolecular pair correlations for molecular liquids. Applications to the liquids carbon tetrachloride, carbon disulfide, carbon diselenide, and benzene, J. Chem. Phys. 61, no. 12, (1974) 5228- 5241, https://doi.org/10.1063/1.1681868
  1. A. O. Nekrot, Method of angular collective variables for calculating the partition function of a mixed ion-dipole system, Ukr. Fiz. Zh. 8, no. 5, (1963) 560-568, (in Ukrainian).
  2. I. R. Yukhnovskyi and A. O. Nekrot, Free energy and binary distribution functions of a mixed ion-dipole system, Ukr. Fiz. Zh. 8, no. 6, (1963) 633-644, (in Ukrainian).
  3. M. F. Holovko, On the Calculation of the Configuration Integral of Systems of Particles with Electrostatic Interaction, Kyiv, 1973, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-73-118R), (in Russian).
  4. W. F. Brown, Dielectrics, in: Dielectrics / Dielektrika, vol. 4 / 17, pp. 1-154, Springer Berlin Heidelberg, Berlin, Heidelberg, 1956, https://doi.org/10.1007/978-3-642-45841-5_1
  5. M. S. Wertheim, Exact solution of the mean spherical model for fluids of hard spheres with permanent electric dipole moments, J. Chem. Phys. 55, no. 9, (1971) 4291-4298, https://doi.org/10.1063/1.1676751
  6. D. Isbister and R. J. Bearman, Solution of the mean spherical model for dipolar mixtures, Mol. Phys. 28, no. 5, (1974) 1297-1304, https://doi.org/10.1080/00268977400102611
  7. G. S. Rushbrooke, G. Stell, and J. S. Høye, Theory of polar liquids: I. Dipolar hard spheres, Mol. Phys. 26, no. 5, (1973) 1199-1215, https://doi.org/10.1080/00268977300102411
  8. J.W. H. Sutherland, G. Nienhuis, and J. M. Deutch, Thermodynamics of pure and multicomponent dipolar hard-sphere fluids, Mol. Phys. 27, no. 3, (1974) 721-739, https://doi.org/10.1080/00268977400100631
  9. G. N. Patey and J. P. Valleau, Dipolar hard spheres: A Monte Carlo study, J. Chem. Phys. 61, no. 2, (1974) 534-540, https://doi.org/10.1063/1.1681928
  10. L. Verlet and J.-J. Weis, Perturbation theories for polar fluids, Mol. Phys. 28, no. 3, (1974) 665-682, https://doi.org/10.1080/00268977400102051
  11. G. Stell and J. J. Weis, Pair correlation in simple polar liquids, Phys. Rev. A 16, no. 2, (1977) 757-765, https://doi.org/10.1103/PhysRevA.16.757
  12. J. S. Høye and G. Stell, Approximate equilibrium pair correlation function for simple polar fluids, J. Chem. Phys. 63, no. 12, (1975) 5342-5347, https://doi.org/10.1063/1.431339
  13. G. Stell, J. C. Rasaiah, and H. Narang, Thermodynamic perturbation theory for simple polar fluids. I, Mol. Phys. 23, no. 2, (1972) 393-406, https://doi.org/10.1080/00268977200100381
  14. W. G. Madden and D. D. Fitts, Integral-equation perturbation theory for polar fluids, Mol. Phys. 31, no. 6, (1976) 1923-1928, https://doi.org/10.1080/00268977600101511
  15. G. N. Patey and J. P. Valleau, Fluids of spheres containing quadrupoles and dipoles: A study using perturbation theory and Monte Carlo computations, J. Chem. Phys. 64, no. 1, (1976) 170-184, https://doi.org/10.1063/1.431968
  16. K. C. Mo and K. E. Gubbins, A new perturbation expansion for fluids of nonspherical molecules, J. Chem. Phys. 63, no. 4, (1975) 1490-1498, https://doi.org/10.1063/1.431513
  17. J. C. Rasaiah, B. Larsen, and G. Stell, Thermodynamic perturbation theory for potentials of multipolar symmetry. I, J. Chem. Phys. 63, no. 2, (1975) 722-733, https://doi.org/10.1063/1.431350
  18. M. Flytzani-Stephanopoulos, K. B. Gubbins, and C. G. Gray, Thermodynamics of mixtures of non-spherical molecules. II. Strong polar, quadrupolar and overlap forces, Mol. Phys. 30, no. 6, (1975) 1649-1676, https://doi.org/10.1080/00268977500103191
  19. C. H. Twu, K. E. Gubbins, and C. G. Gray, Excess thermodynamic properties for liquid mixtures of non-spherical molecules, Mol. Phys. 29, no. 3, (1975) 713-729, https://doi.org/10.1080/00268977500100651
  20. C. H. Twu, K. E. Gubbins, and C. G. Gray, Thermodynamics of mixtures of nonspherical molecules. III. Fluid phase equilibria and critical loci, J. Chem. Phys. 64, no. 12, (1976) 5186-5197, https://doi.org/10.1063/1.432193
  21. A. Rahman and F. H. Stillinger, Molecular dynamics study of liquid water, J. Chem. Phys. 55, no. 7, (1971) 3336-3359, https://doi.org/10.1063/1.1676585
  22. F. H. Stillinger and A. Rahman, Molecular dynamics study of temperature effects on water structure and kinetics, J. Chem. Phys. 57, no. 3, (1972) 1281-1292, https://doi.org/10.1063/1.1678388
  23. F. H. Stillinger and A. Rahman, Improved simulation of liquid water by molecular dynamics, J. Chem. Phys. 60, no. 4, (1974) 1545-1557, https://doi.org/10.1063/1.1681229
  24. F. H. Stillinger and A. Rahman, Revised central force potentials for water, J. Chem. Phys. 68, no. 2, (1978) 666-670, https://doi.org/10.1063/1.435738
  25. H. L. Lemberg and F. H. Stillinger, Central-force model for liquid water, J. Chem. Phys. 62, no. 5, (1975) 1677-1690, https://doi.org/10.1063/1.430718
  26. A. Rahman, F. H. Stillinger, and H. L. Lemberg, Study of a central force model for liquid water by molecular dynamics, J. Chem. Phys. 63, no. 12, (1975) 5223- 5230, https://doi.org/10.1063/1.431307
  27. H. Kistenmacher, G. C. Lie, H. Popkie, and E. Clementi, Study of the structure of molecular complexes. VI. Dimers and small clusters of water molecules in the Hartree-Fock approximation, J. Chem. Phys. 61, no. 2, (1974) 546-561, https://doi.org/10.1063/1.1681930
  28. H. Popkie, H. Kistenmacher, and E. Clementi, Study of the structure of molecular complexes. IV. The Hartree-Fock potential for the water dimer and its application to the liquid state, J. Chem. Phys. 59, no. 3, (1973) 1325-1336, https://doi.org/10.1063/1.1680187
  29. G. C. Lie and E. Clementi, Study of the structure of molecular complexes. XII. Structure of liquid water obtained by Monte Carlo simulation with the Hartree- Fock potential corrected by inclusion of dispersion forces, J. Chem. Phys. 62, no. 6, (1975) 2195-2199, https://doi.org/10.1063/1.430787
  30. E. Clementi, Determination of Liquid Water Structure, vol. 2 of Lecture Notes in Chemistry, Springer Berlin Heidelberg, Berlin, Heidelberg, 1976, https://doi.org/10.1007/978-3-642-93052-2
  31. G. C. Lie, E. Clementi, and M. Yoshimine, Study of the structure of molecular complexes. XIII. Monte Carlo simulation of liquid water with a configuration interaction pair potential, J. Chem. Phys. 64, no. 6, (1976) 2314-2323, https://doi.org/10.1063/1.432539
  32. B. R. Lentz and H. A. Scheraga, Water molecule interactions. Stability of cyclic polymers, J. Chem. Phys. 58, no. 12, (1973) 5296-5308, https://doi.org/10.1063/1.1679143
  33. A. Ben-Naim, Statistical mechanical study of hydrophobic interaction. I. Interaction between two identical nonpolar solute particles, J. Chem. Phys. 54, no. 3, (1971) 1387-1404, https://doi.org/10.1063/1.1674979
  34. L. R. Pratt and D. Chandler, Theory of the hydrophobic effect, J. Chem. Phys. 67, no. 8, (1977) 3683-3704, https://doi.org/10.1063/1.435308
  35. M. V. Volkenstein, Molecular Biophysics, Academic Press, New York, 1977.
  36. J. D. Ramshaw, On the molecular theory of dielectric polarization in rigid-dipole fluids, J. Chem. Phys. 55, no. 4, (1971) 1763-1774, https://doi.org/10.1063/1.1676308
  37. F. M. Kuni, Structure of polar liquids. 2. Asymptotics of correlation functions and distribution functions at large molecular separations, Zh. Strukt. Khim. 10, no. 1, (1969) 12-17, (in Russian). https://doi.org/10.1007/BF00751945
  1. G. Nienhuis and J. M. Deutch, Structure of dielectric fluids. I. The twoparticle distribution function of polar fluids, J. Chem. Phys. 55, no. 9, (1971) 4213-4229, https://doi.org/10.1063/1.1676739
  2. H. Fr¨ohlich, Theory of Dielectrics: Dielectric Constant and Dielectric Loss, Oxford University Press, Oxford, 2nd edn., 1958.
  3. D. W. Jepsen, Calculation of the dielectric constant of a fluid by cluster expansion methods, J. Chem. Phys. 44, no. 2, (1966) 774-781, https://doi.org/10.1063/1.1726758
  4. D. W. Jepsen, Calculation of the dielectric constant of a fluid by a cluster expansion method, J. Chem. Phys. 45, no. 2, (1966) 709-721, https://doi.org/10.1063/1.1727632
  5. J. D. Ramshaw, Existence of the dielectric constant in rigid-dipole fluids: The direct correlation function, J. Chem. Phys. 57, no. 7, (1972) 2684-2690, https://doi.org/10.1063/1.1678651
  6. J. D. Ramshaw, Existence of the dielectric constant in rigid-dipole fluids: The functional-derivative approach, J. Chem. Phys. 66, no. 7, (1977) 3134-3138, https://doi.org/10.1063/1.434334
  7. J. S. Høye and G. Stell, Statistical mechanics of polar systems. II, J. Chem. Phys. 64, no. 5, (1976) 1952-1966, https://doi.org/10.1063/1.432458
  8. J. S. Høye and G. Stell, Statistical mechanics of polar systems: Dielectric constant for dipolar fluids, J. Chem. Phys. 61, no. 2, (1974) 562-572, https://doi.org/10.1063/1.1681931
  9. J. D. Ramshaw, Debye-H¨uckel theory for rigid-dipole fluids, J. Chem. Phys. 64, no. 9, (1976) 3666-3669, https://doi.org/10.1063/1.432730
  10. J. S. Høye and G. Stell, Dielectric constant in terms of atom- atom correlation functions, J. Chem. Phys. 65, no. 1, (1976) 18-22, https://doi.org/10.1063/1.432793
  11. M. S. Wertheim, Dielectric constant of non-polar fluids, Mol. Phys. 25, no. 1, (1973) 211-223, https://doi.org/10.1080/00268977300100201
  12. M. S. Wertheim, Theory of polar fluids. I, Mol. Phys. 26, no. 6, (1973) 1425- 1444, https://doi.org/10.1080/00268977300102591
  13. M. S. Wertheim, Theory of polar fluids. II, Mol. Phys. 33, no. 1, (1977) 95-109, https://doi.org/10.1080/00268977700103081
  14. G. Nienhuis and J. M. Deutch, Structure of dielectric fluids. II. The free energy and the Kerr effect in polar fluids, J. Chem. Phys. 56, no. 1, (1972) 235-247, https://doi.org/10.1063/1.1676853
  15. J. D. Ramshaw, D. W. Schaefer, J. S. Waugh, and J. M. Deutch, Dielectric polarization and alignment and the structure of polar fluids, J. Chem. Phys. 54, no. 3, (1971) 1239-1251, https://doi.org/10.1063/1.1674962
  16. J. S. Høye and G. Stell, Kerr constant and related quantities in terms of atom. Atom correlation functions, J. Chem. Phys. 66, no. 2, (1977) 795-801, https://doi.org/10.1063/1.433958
  17. I. R. Yukhnovskii, On the statistical theory of mixed ion-dipole systems of interacting particles, Dokl. Akad. Nauk SSSR 136, no. 6, (1961) 1317-1320, (in Russian).
  18. I. R. Yukhnovskyi, On the statistical theory of systems of interacting ions and dipolar particles, Ukr. Fiz. Zh. 6, no. 3, (1961) 333-339, (in Ukrainian).
  19. I. R. Yukhnovskyi, Spatially distributed particles in the method of collective variables, Ukr. Fiz. Zh. 7, no. 3, (1962) 267-277, (in Ukrainian).
  1. M. F. Holovko and M. Gabashi, Free Energy and Screened Potentials in Mixed Ion-Water Systems, Kyiv, 1973, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-73-170R), (in Russian).
  2. I. R. Yukhnovskii and A. A. Nekrot, On some properties of binary distribution functions of a mixture of ions and dipolar molecules, Ukr. Fiz. Zh. 9, no. 4, (1964) 365-374, (in Russian).
  3. V. S. Vysochanskyi, Dipole-dipole distribution function (Fdd) in mixed iondipole systems, Ukr. Fiz. Zh. 22, no. 2, (1977) 209-212, (in Russian).
  4. I. R. Yukhnovskii, V. S. Vysochanskyi, and M. F. Holovko, Binary distribution functions of ion-dipole systems, Ukr. Fiz. Zh. 18, no. 1, (1973) 66-74, (in Russian).
  5. I. R. Yukhnovskii, M. F. Holovko, and V. S. Vysochanskyi, Toward the study of binary distribution functions of ion-dipole systems, Ukr. Fiz. Zh. 18, no. 11, (1973) 1842-1847, (in Russian).
  6. I. R. Yukhnovskii, M. F. Holovko, and V. S. Vysochanskii, Study of binary distribution functions of mixed ion-dipole systems represented as an exponential of the mean force potential, Ukr. Fiz. Zh. 22, no. 8, (1977) 1330-1335, (in Russian).
  7. I. R. Yukhnovskii, M. F. Holovko, and V. S. Vysochanskii, Binary distribution functions of mixed ion-dipole systems, Fiz. Zhidk. Sostoyaniya 6, (1978) 101- 114, (in Russian).
  8. I. R. Yukhnovskii and A. O. Nekrot, Binary distribution functions of a mixed ion-dipole system, Ukr. Fiz. Zh. 13, no. 10, (1968) 1637-1644, (in Russian).
  9. I. R. Yukhnovskii, V. S. Vysochanskyi, and M. F. Holovko, Binary distribution functions of ion-dipole systems in the fourth virial coefficient approximation, Ukr. Fiz. Zh. 20, no. 5, (1975) 817-828, (in Russian).
  10. K. P. Mishchenko and H. M. Poltoratskyi, Thermodynamics and Structure of Aqueous and Non-Aqueous Electrolyte Solutions, Khimia, Leningrad, 1976, (in Russian).
  11. S. Levine and D. K. Rosenthal, The interaction energy of an ion pair in an aqueous medium, in: Chemical Physics of Ionic Solutions, (eds.) B. E. Conway and R. G. Barradas, pp. 119-162, Wiley, New York, 1966.
  12. P. S. Ramanathan and H. L. Friedman, Study of a refined model for aqueous 1-1 electrolytes, J. Chem. Phys. 54, no. 3, (1971) 1086-1099, https://doi.org/10.1063/1.1674941
  13. R. W. Gurney, Ions in Solution, Cambridge University Press, Cambridge, 1936.
  14. H. S. Frank, Solvent models and the interpretation phenomena of ionization and solvatation phenomena, in: Chemical Physics of Ionic Solutions, (eds.) B. E. Conway and R. G. Barradas, pp. 53-66, Wiley, New York, 1966.
  15. G. Stell, Ionic solution theory for nonideal solvents, J. Chem. Phys. 59, no. 8, (1973) 3926-3933, https://doi.org/10.1063/1.1680579
  16. V. D. Gruba and M. F. Holovko, Study of the Dependence of Ion Mean Force Potentials on the Density and Polarity of Solvent Molecules: (Fourth Virial Coefficient Approximation), Kyiv, 1978, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-78-94R), (in Russian).
  17. V. D. Gruba and M. F. Holovko, Mean Force Potentials Between Like-Charged Ions, Kyiv, 1978, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-78-114R), (in Russian).
  18. I. R. Yukhnovskii, V. D. Gruba, M. F. Holovko, and Y. M. Kessler, Ion Mean Force Potentials with Account for Ion-Molecular Interactions: (Third Virial Coefficient Approximation), Kyiv, 1978, (Preprint of theAcademy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-77-142R), (in Russian).
  1. I. R. Yukhnovskii, V. D. Gruba, M. F. Holovko, and Y. M. Kessler, Ion Mean Force Potentials with Account for Ion-Molecular and Intermolecular Interactions: (Fourth Virial Coefficient Approximation), Kyiv, 1978, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-77-143R), (in Russian).
  2. I. R. Yukhnovskii, V. D. Gruba, M. F. Holovko, and Y. M. Kessler, Interionic Mean Force Potentials with Account for the Elementary Diagram of the Fourth Virial Coefficient, Kyiv, 1978, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-78-113R), (in Russian).
  3. K. Heinzinger and P. C. Vogel, A molecular dynamics study of aqueous solutions I. First results for LiCl in H2O, Z. Naturforsch. A 29, no. 8, (1974) 1164-1171, https://doi.org/10.1515/zna-1974-0809
  4. I. R. McDonald and J. C. Rasaiah, Monte Carlo simulation of the average force between two ions in a Stockmayer solvent, Chem. Phys. Lett. 34, no. 2, (1975) 382-386, https://doi.org/10.1016/0009-2614(75)85299-7
  5. G. N. Patey and J. P. Valleau, A Monte Carlo method for obtaining the interionic potential of mean force in ionic solution, J. Chem. Phys. 63, no. 6, (1975) 2334- 2339, https://doi.org/10.1063/1.431685
  6. H. P. Roshchyna and P. L. Sverdan, Study of the concentration dependence of some properties of electrolyte solutions, Fiz. Zhidk. Sostoyaniya 1, (1971) 112-121, (in Russian).
  7. H. P. Roshchyna and P. L. Sverdan, Regularities in the isotropic component of rayleigh light scattering, Ukr. Fiz. Zh. 18, no. 2, (1973) 201-207, (in Russian).
  8. P. L. Sverdan and H. P. Roshchyna, Fluctuations and light scattering in electrolyte solutions, Ukr. Fiz. Zh. 21, no. 10, (1976) 1724-1728, (in Russian).
  9. A. V. Popov and A. M. Shkodin, Calculation of the degree of dissociation of strong electrolytes based on the free energy of ion-dipole systems, Ukr. Fiz. Zh. 19, no. 12, (1974) 1974-1979, (in Russian).
  10. L. Blum, Solution of a model for the solvent-electrolyte interactions in the mean spherical approximation, J. Chem. Phys. 61, no. 5, (1974) 2129-2133, https://doi.org/10.1063/1.1682224
  11. S. A. Adelman and J. M. Deutch, Exact solution of the mean spherical model for strong electrolytes in polar solvents, J. Chem. Phys. 60, no. 10, (1974) 3935- 3949, https://doi.org/10.1063/1.1680841
  12. R. R. Dogonadze, A. A. Kornyshev, and A. M. Kuznetsov, Phenomenological theory of polar systems, Phys. Status Solidi B 53, no. 2, (1972) 573-582. https://doi.org/10.1002/pssb.2220530205
  13. Y. A. Kruglyak, Quantum Theory of Ion Solvation, Kyiv, 1973, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITP-73-42R, ITP-73-60R), Part 1-2, (in Russian).
  14. B. K. Bunyatyan and D. A. Zhogolev, Quantum mechanical study of the interaction of metal and halogen ions with water molecules, Zh. Strukt. Khim. 17, no. 4, (1976) 708-727, (in Russian). https://doi.org/10.1007/BF00753448
  15. M. D. Dolgushin, V. M. Pinchuk, and Y. A. Kruglyak, Ab Initio Calculation of Molecular Complexes Li+…OH2 and H2O…H2O in Limited Gaussian Bases, Kyiv, 1973, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-73-116R), (in Russian).
  1. E. Clementi and H. Popkie, Study of the structure of molecular complexes. I. Energy surface of a water molecule in the field of a lithium positive ion, J. Chem. Phys. 57, no. 3, (1972) 1077-1094, https://doi.org/10.1063/1.1678361
  2. J. Fromm, E. Clementi, and R. O. Watts, Coordination number for the Li+-F- ion pair in water, J. Chem. Phys. 62, no. 4, (1975) 1388-1398, https://doi.org/10.1063/1.430596
  3. M. R. Mruzik, F. F. Abraham, D. E. Schreiber, and G. M. Pound, A Monte Carlo study of ion-water clusters, J. Chem. Phys. 64, no. 2, (1976) 481-491, https://doi.org/10.1063/1.432264
  4. T. Morita and K. Hiroike, A new approach to the theory of classical fluids. III: General treatment of classical systems, Prog. Theor. Phys. 25, no. 4, (1961) 537-578, https://doi.org/10.1143/PTP.25.537
  5. G. Stell, Cluster expansions for classical systems in equilibrium, in: The equilibrium theory of classical fluids; a lecture note and reprint volume, (eds.) H. L. Frisch and J. L. Lebowitz, pp. 171-267, W. A. Benjamin, New York, 1964.
  6. I. R. Yukhnovskyi, I. S. Rakhimova, and V. V. Vladimirov, On the theory of systems of charged particles in an external field, Ukr. Fiz. Zh. 4, no. 3, (1959) 334-344, (in Ukrainian).
  7. I. R. Yukhnovskii and O. L. Gonopol’skii, Collective Variables in the Grand Canonical Ensemble, Kyiv, 1974, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-74-93R), (in Russian).
  8. D. di Caprio, J. Stafiej, and J. P. Badiali, A field-theoretical study of the effect of specific interactions in ionic systems, J. Chem. Phys. 108, no. 20, (1998) 8572-8583, https://doi.org/10.1063/1.476286
  9. D. di Caprio and J. P. Badiali, A formally exact field theory for classical systems at equilibrium, J. Phys. A: Math. Theor. 41, no. 12, (2008) 125401, https://doi.org/10.1088/1751-8113/41/12/125401
  10. D. di Caprio, J. P. Badiali, and M. F. Holovko, Simple field-theoretical approach of coulomb systems: entropic effects, J. Phys. A: Math. Theor. 42, no. 21, (2009) 214038, https://doi.org/10.1088/1751-8113/42/21/214038
  11. H. Frusawa and R. Hayakawa, Field theoretical representation of the hohenbergkohn free energy for fluids, Phys. Rev. E 60, no. 5, (1999) R5048(R), https://doi.org/10.1103/PhysRevE.60.R5048
  12. H.-J. Woo and X. Song, Functional integral formulations for classical fluids, J. Chem. Phys. 114, no. 13, (2001) 5637-5641, https://doi.org/10.1063/1.1353553
  13. O. Patsahan and I. Mryglod, The method of collective variables: A link with the density functional theory, Condens. Matter Phys. 15, no. 2, (2012) 24001, https://doi.org/10.5488/CMP.15.24001
  14. D. di Caprio, J. Stafiej, M. F. Holovko, and I. Kravtsiv, Yukawa fluid at a hard wall: field-theory description, Mol. Phys. 109, no. 5, (2011) 695-708, https://doi.org/10.1080/00268976.2010.547524
  15. I. Kravtsiv, T. Patsahan, M. Holovko, and D. di Caprio, Two-Yukawa fluid at a hard wall: Field theory treatment, J. Chem. Phys. 142, no. 19, (2015) 194708, https://doi.org/10.1063/1.4921242
  16. I. Kravtsiv, T. Patsahan, M. Holovko, and D. di Caprio, Soft core fluid with competing interactions at a hard wall, J. Mol. Liq. 362, (2022) 119652, https://doi.org/10.1016/j.molliq.2022.119652
  17. M. F. Holovko, On the Distribution of Microfields in a System of Charged Particles, Kyiv, 1975, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-75-135R), (in Russian).
  1. M. F. Holovko, Distribution of Microfields in Systems with Electrostatic Interaction, Kyiv, 1976, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-76-26R), (in Russian).
  2. G. Ecker, Theory of Fully Ionized Plasmas, Academic Press, New York, 1972. 337. J. Holtsmark, Uber die verbreiterung von spektrallinien. II, ¨ Phys. Z. 25, no. 4, (1924) 73-84.
  3. H. R. Griem, Spectral Line Broadening by Plasmas, Academic Press, New York, 1974.
  4. S. Ono and S. Kondo, Molecular Theory of Surface Tension in Liquids, McGrawHill Book Company, New York, 1960.
  5. H. T. Davis, Statistical mechanics of interfacial properties of polyatomic fluids. I. Surface tension, J. Chem. Phys. 62, no. 9, (1975) 3412-3415, https://doi.org/10.1063/1.430996
  6. G. M. Nazarian, Statistical mechanical calculation of the density variation through a liquid-vapor interface, J. Chem. Phys. 56, no. 3, (1972) 1408-1409, https://doi.org/10.1063/1.1677376
  7. F. F. Abraham, D. E. Schreiber, and J. A. Barker, On the structure of a free surface of a Lennard-Jones liquid: A Monte Carlo calculation, J. Chem. Phys. 62, no. 5, (1975) 1958-1960, https://doi.org/10.1063/1.430685
  8. B. Borˇstnik and A. Aˇzman, The numerical solution of the BGYB equation for the liquid-vapour interface, Mol. Phys. 29, no. 4, (1975) 1165-1169, https://doi.org/10.1080/00268977500100981
  9. S. Toxvaerd, Statistical mechanical and quasithermodynamic calculations of surface densities and surface tension, Mol. Phys. 26, no. 1, (1973) 91-99, https://doi.org/10.1080/00268977300101401
  10. V. Bongiorno and H. T. Davis, Modified van der Waals theory of fluid interfaces, Phys. Rev. A 12, no. 5, (1975) 2213-2224, https://doi.org/10.1103/PhysRevA.12.2213
  11. A. J. M. Yang, P. D. Fleming, and J. H. Gibbs, Molecular theory of surface tension, J. Chem. Phys. 64, no. 9, (1976) 3732-3747, https://doi.org/10.1063/1.432687
  12. R. Lovett, P. W. DeHaven, J. J. Vieceli, and F. P. Buff, Generalized van der Waals theories for surface tension and interfacial width, J. Chem. Phys. 58, no. 5, (1973) 1880-1885, https://doi.org/10.1063/1.1679447
  13. M. S. Wertheim, Correlations in the liquid-vapor interface, J. Chem. Phys. 65, no. 6, (1976) 2377-2381, https://doi.org/10.1063/1.433352
  14. J. D. Weeks, Structure and thermodynamics of the liquid-vapor interface, J. Chem. Phys. 67, no. 7, (1977) 3106-3121, https://doi.org/10.1063/1.435276
  15. D. E. Sullivan, Comment on “Statistical mechanics of interfacial properties of polyatomic fluids. I. Surface tension” [H. Ted Davis, J. Chem. Phys. 62, 3412 (1975)], J. Chem. Phys. 63, no. 8, (1975) 3684-3685, https://doi.org/10.1063/1.431773
  16. C. G. Gray and K. E. Gubbins, Theory of surface tension for molecular fluids, Mol. Phys. 30, no. 1, (1975) 179-192, https://doi.org/10.1080/00268977500101861
  17. J. M. Haile, C. G. Gray, and K. E. Gubbins, Theory of surface tension for molecular liquids. II. Perturbation theory calculations, J. Chem. Phys. 64, no. 6, (1976) 2569-2578, https://doi.org/10.1063/1.432509
  18. R. C. Brown and N. H. March, Structure and excitations in liquid and solid surfaces, Phys. Rep. 24, no. 2, (1976) 77-169, https://doi.org/10.1016/0370-1573(76)90023-5
  19. D. E. Sullivan and G. Stell, Correlations at a fluid surface, J. Chem. Phys. 67, no. 6, (1977) 2567-2576, https://doi.org/10.1063/1.435224
  20. D. Henderson, F. F. Abraham, and J. A. Barker, The Ornstein-Zernike equation for a fluid in contact with a surface, Mol. Phys. 31, no. 4, (1976) 1291-1295, https://doi.org/10.1080/00268977600101021
  21. J. K. Percus, Model for density variation at a fluid surface, J. Stat. Phys. 15, no. 5, (1976) 423-435, https://doi.org/10.1007/BF01020344
  22. E. Waisman, D. Henderson, and J. L. Lebowitz, Solution of the mean spherical approximation for the density profile of a hardsphere fluid near a wall, Mol. Phys. 32, no. 5, (1976) 1373-1381, https://doi.org/10.1080/00268977600102751
  23. I. R. Yukhnovskii and I. I. Kurilyak, Generalization of the method of collective variables for the case of confined systems of charged particles, Ukr. Fiz. Zh. 21, no. 11, (1976) 1772-1781, (in Russian).
  24. I. R. Yukhnovskii and I. I. Kurilyak, Consideration of Short-Range Potentials in the Case of Confined Systems of Charged Particles, Kyiv, 1976, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITP-76-99R), (in Russian).
  25. I. R. Yukhnovskii and I. I. Kurilyak, Application of the Collective Variables Method to the Study of Electrolyte Films, Kyiv, 1975, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-75-25R), (in Russian).
  26. L. Blum, Theory of electrified interfaces, J. Phys. Chem. 81, no. 2, (1977) 136- 147, https://doi.org/10.1021/j100517a009
  27. L. Blum and G. Stell, Solution of Ornstein-Zernike equation for wallparticle distribution function, J. Stat. Phys. 15, no. 6, (1976) 439-449, https://doi.org/10.1007/BF01020798
  28. L. I. Antropov, Theoretical Electrochemistry, MIR Publishers, Moscow, 1977. 364. I. R. Yukhnovskii, M. F. Holovko, and I. I. Kurilyak, Screened potential in confined ion-dipole systems, Ukr. Fiz. Zh. 23, no. 6, (1978) 927-937, (in Russian).
  29. M. F. Holovko, I. I. Kuriliak, O. A. Pizio, and E. M. Soviak, On the reference system treatment of interactions in statistical theory of ionic and molecular systems, in: Problems of Modern Statistical Physics, (ed.) M. M. Bogolyubov, pp. 62-96, Naukova Dumka, Kyiv, 1985, (in Russian).
  30. A. Rebenko, Distribution functions in confined ion-dipolar systems, Kyiv, 1981, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-81-118R), (in Russian).
  31. I. Yukhnovskii, M. Holovko, and E. Soviak, Screened potentials in spatially inhomogeneous ion-molecular systems. A general solution method, Kyiv, 1982, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-82-152R), (in Russian).
  32. A. Zagorodny, A. Usenko, and A. Yakimenko, Balescu-Lennard equation for semi-confined plasma, Kyiv, 1982, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-82-75R), (in Russian).
  33. B. Jancovici, Classical coulomb systems near a plane wall. I, J. Stat. Phys. 28, no. 1, (1982) 43-65, https://doi.org/10.1007/BF01011622
  34. M. F. Holovko, Cluster expansions and integral equations in an optimized cluster theory, Kyiv, 1985, (Preprint of the Academy of Sciences of the Ukrainian SSR. Institute for Theoretical Physics; ITF-84-187R), (in Russian).
  35. M. F. Golovko and H. Krienke, Generalized virial expansions, Mol. Phys. 68, no. 4, (1989) 967-977, https://doi.org/10.1080/00268978900102671
  36. M. F. Holovko and E. M. Sovyak, On taking account of interactions in the statistical theory of electrolyte solution, Condens. Matter Phys. 4, no. 6, (1995) 49-78, https://doi.org/10.5488/CMP.6.49
  37. M. F. Holovko, The multi-density integral equation approach in the theory of complex liquids, Condens. Matter Phys. 2, no. 18, (1999) 205-220, https://doi.org/10.5488/CMP.2.2.205
  38. Y. V. Kalyuzhnyi, M. F. Holovko, and A. D. J. Haymet, Integral equation theory for associating liquids: Weakly associating 2-2 electrolytes, J. Chem. Phys. 95, no. 12, (1991) 9151-9164, https://doi.org/10.1063/1.461195
  39. M. F. Holovko, Association and clusterization in liquids and solutions, J. Mol. Liq. 96-97, (2002) 65-85, https://doi.org/10.1016/S0167-7322(01)00327-0
  40. M. F. Holovko, Statistical theory of mixed ion-molecular systems, Habilitation thesis, Institute for Theoretical Physics, Academy of Sciences of the Ukrainian SSR, Kyiv, 1979, (in Ukrainian).
  41. F. Vericat and L. Blum, Mean spherical model for hard ions and dipoles: Thermodynamics and correlation functions, J. Stat. Phys. 22, no. 5, (1980) 593-604, https://doi.org/10.1007/BF01011340
  42. A. R. Allnatt, Integral equations in ionic solution theory, Mol. Phys. 8, no. 6, (1964) 533-539, https://doi.org/10.1080/00268976400100591
  43. F. Lado, Perturbation correction for the free energy and structure of simple fluids, Phys. Rev. A 8, no. 5, (1973) 2548-2556, https://doi.org/10.1103/PhysRevA.8.2548
  44. W. Ebeling, W. D. Kraeft, and D. Kremp, Theory of Bound States and Ionization Equilibrium in Plasmas and Solids, Akademie-Verlag, Berlin, 1976.
  45. J. N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London; San Diego, 3rd edn., 2011.
  46. L. Boltzmann, Lectures on Gas Theory. Part II, University of California Press, Berkeley, 1964, translated by S. G. Brush. Original work published 1898, Chapter 6.
  47. G. Stell, Model fluids of associating particles, Condens. Matter Phys. no. 2, (1993) 4-20, https://doi.org/10.5488/CMP.2.4
  48. Y. V. Kalyuzhnyi and G. Stell, On the effects of association in fluids with spherically symmetric interactions. I. Cluster expansions and integral equations, Mol. Phys. 78, no. 5, (1993) 1247-1258, https://doi.org/10.1080/00268979300100821
  49. M. F. Holovko and Y. V. Kalyuzhnyi, On the effects of association in the statistical theory of ionic systems. Analytical solution of the PY-MSA version of the Wertheim theory, Mol. Phys. 73, no. 5, (1991 1145-1157, https://doi.org/10.1080/00268979100101831
  50. Y. V. Kalyuzhnyi and M. F. Holovko, An analytical study of the effects of association in a 2-2 electrolyte solution. I. Associative mean spherical approximation, Mol. Phys. 80, no. 5, (1993) 1165-1176, https://doi.org/10.1080/00268979300102951
  51. L. Blum and O. Bernard, The general solution of the binding mean spherical approximation for pairing ions, J. Stat. Phys. 79, no. 3-4, (1995) 569-583, https://doi.org/10.1007/BF02184871
  52. Y. V. Kalyuzhnyi and V. Vlachy, Integral equation theory for highly asymmetric electrolyte solutions, Chem. Phys. Lett. 215, no. 5, (1993) 518-522, https://doi.org/10.1016/0009-2614(93)85712-W
  53. Y. V. Kalyuzhnyi, V. Vlachy, M. F. Holovko, and G. Stell, Multidensity integralequation theory for highly asymmetric electrolyte solutions, J. Chem. Phys. 102, no. 14, (1995) 5770-5780, https://doi.org/10.1063/1.469308
  54. Y. V. Kalyuzhnyi, L. Blum, M. F. Holovko, and I. A. Protsykevych, Primitive model for highly asymmetric electrolytes. Associative mean spherical approximation, Physica A 236, (1997) 85-96, https://doi.org/10.1016/S0378-4371(97)00359-7
  55. J. Chang and S. J. Sandler, The correlation functions of hard-sphere chain fluids: Comparison of the Wertheim integral equation theory with the Monte Carlo simulation, J. Chem. Phys. 102, no. 1, (1995) 437-449, https://doi.org/10.1063/1.469421
  56. Y. V. Kalyuzhnyi, C. T. Lin, and G. Stell, Primitive models of chemical association. II. Polymerization into flexible chain molecules of prescribed length, J. Chem. Phys. 106, no. 5, (1997) 1940-1950, https://doi.org/10.1063/1.473331
  57. Y. Duda, E. Vakarin, Y. Kalyuzhnyi, and M. Holovko, Analytical treatment of the fused hard-sphere chain model: 0.5 < L < 1, Physica A 245, no. 3-4, (1997) 393-410, https://doi.org/10.1016/S0378-4371(97)00308-7
  58. E. V. Vakarin, Y. Duda, and M. F. Holovko, Integral equation theory for the four bonding sites model of associating fluids. I. Structure factor and compressibility, Mol. Phys. 90, no. 4, (1997) 611-623, https://doi.org/10.1080/002689797172336
  59. Y. V. Kalyuzhnyi and P. T. Cummings, Solution of the Chandler-Silbey- Ladanyi equation for the multicomponent hard-sphere site-site molecular fluid: Percus-Yevick approximation, J. Chem. Phys. 105, no. 5, (1996) 2011-2019, https://doi.org/10.1063/1.472069
  60. Y. V. Kalyuzhnyi, Solution of the polymer Percus-Yevick approximation for the multiarm star polymerization, Condens. Matter Phys. 11, (1997) 71-86, https://doi.org/10.5488/CMP.11.71
  61. J. M. G. Barthel, H. Krienke, and W. Kunz, Physical Chemistry of Electrolyte Solutions: Modern Aspects, vol. 5 of Topics in Physical Chemistry, Steinkopff; Springer, Darmstadt; New York, 1st edn., 1998.
  62. M. S. Wertheim, Fluids of dimerizing hard spheres, and fluid mixtures of hard spheres, J. Chem. Phys. 85, no. 5, (1986) 2929-2936, https://doi.org/10.1063/1.451002
  63. Y. V. Kalyuzhnyi, I. A. Protsykevytch, and M. F. Holovko, Solution of the associative Percus-Yevick approximation for the n-component mixture of dimerizing hard spheres, Chem. Phys. Lett. 215, no. 1-3, (1993) 1-4, https://doi.org/10.1016/0009-2614(93)89253-E
  64. Y. Y. Duda, Y. V. Kalyuzhnyi, and M. F. Holovko, Solution of the associative mean spherical approximation for the shielded sticky point electrolyte model, J. Chem. Phys. 104, no. 3, (1996) 1081-1089, https://doi.org/10.1063/1.470763
  65. O. Bernard and L. Blum, Binding mean spherical approximation for pairing ions: An exponential approximation and thermodynamics, J. Chem. Phys. 104, no. 12, (1996) 4746-4754, https://doi.org/10.1063/1.471168
  66. N. Bjerrum, Untersuchungen uber ionenassoziation. I. Der einfluss der ionenassoziation auf die aktivitat der ionen bei mittleren assoziationsgraden, K. Dan. Vidensk. Selsk., Mat.-Fys. Medd. 7, no. 9, (1926) 3-48.
  67. Y. V. Kalyuzhnyi and M. F. Holovko, Thermodynamics of the associative mean spherical approximation for the fluid of dimerizing particles, J. Chem. Phys. 108, no. 9, (1998) 3709-3715, https://doi.org/10.1063/1.475764
  68. H. Krienke, J. Barthel, M. F. Holovko, I. A. Protsykevich, and Y. V. Kalyuzhnyi, Osmotic and activity coefficients of strongly associated electrolytes over large concentration ranges from chemical model calculations, J. Mol. Liq. 87-88, (2000) 191-216, https://doi.org/10.1016/S0167-7322(00)00121-5
  69. H. Falkenhagen, W. Ebeling, and W. D. Kraeft, Transport properties of dilute solutions, in: Ionic Interactions, (ed.) S. Petrucci, vol. 1, pp. 62-116, Academic Press, New York and London, 1971.
  1. J. Chang and S. J. Sandler, The Wertheim integral equation theory with the ideal chain approximation and a dimer equation of state: Generalization to mixtures of hard-sphere chain fluids, J. Chem. Phys. 103, no. 8, (1995) 3196- 3211, https://doi.org/10.1063/1.470252
  2. Y. V. Kalyuzhnyi, C. T. Lin, and G. Stell, Primitive models of chemical association. IV. Polymer Percus-Yevick ideal-chain approximation for heteronuclear hard-sphere chain fluids, J. Chem. Phys. 108, no. 16, (1998) 6525-6534, https://doi.org/10.1063/1.476059
  3. C. T. Lin, Y. V. Kalyuzhnyi, and G. Stell, Primitive models of chemical association. III. Totally flexible sticky two-point model for multicomponent heteronuclear fixed-chain-length polymerization, J. Chem. Phys. 108, no. 15, (1998) 6513-6524, https://doi.org/10.1063/1.476058
  4. Y. V. Kalyuzhnyi and G. Stell, Solution of the polymer mean spherical approximation for the polymerizing primitive model of electrolytes, Chem. Phys. Lett. 240, no. 2-4, (1995) 157-164, https://doi.org/10.1016/0009-2614(95)00490-U
  5. I. A. Protsykevytch, Y. V. Kalyuzhnyi, M. F. Holovko, and L. Blum, Solution of the polymer mean spherical approximation for the totally flexible sticky twopoint electrolyte model, J. Mol. Liq. 73-74, (1997) 1-20, https://doi.org/10.1016/S0167-7322(97)00053-6
  6. Y. Y. Duda and M. F. Holovko, Structure of liquid sulfur through polymer Percus-Yevick theory, Phys. Chem. Liq. 35, no. 3, (1997) 175-189, https://doi.org/10.1080/00319109708030585
  7. A. D. Trokhymchuk, M. F. Holovko, and K. Heinzinger, On the structure factor for water at small wavenumbers, Z. Naturforsch. A 50, no. 1, (1995) 18-20, https://doi.org/10.1515/zna-1995-0104
  8. Yu. Duda, C. J. Segura, E. Vakarin, M. F. Holovko, W. G. Chapman, Network forming fluids: Monte Carlo simulations and integral equations, J. Chem. Phys. 108, no. 21, (1998) 9168-9176, https://doi.org/10.1063/1.476363
  9. M. P. Tosi, Structure of covalent liquids, J. Phys.: Condens. Matter 6, no. 23A, (1994) A13-A28, https://doi.org/10.1088/0953-8984/6/23A/003

 

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