On the statistical theory of strong electrolytes and high-temperature plasmas: new applications of the work of Yukhnovskii and Kelbg
DOI:
https://doi.org/10.5488/cmp.29.23501Keywords:
statistical physics, strong electrolytes, high-temperature plasmas, convergence of expansionsAbstract
Remembering here the work of two pioneers of the statistical physics of Coulomb systems, Günter Kelbg, and Ihor Yukhnovskii, we analyze their methods and give some new applications to ionic solutions and quantum plasmas. In particular, we develop applications of the theory to strong electrolytes and to thermal high-temperature plasmas at T > 105 K using the exponential interaction model. We show the strong structural similarity of these two classes of Coulomb systems, which physics is determined mostly by contributions proportional to e4 and e6. We predict at higher densities a structural transition to oscillating correlations. The thermodynamic functions show a smooth transition from a quadratic root increase to a slower increase like ni1/4 which observes the Onsager bound. Effects of asymmetries in charges and masses are studied with applications to ionic systems with multiple charges and to high-temperature plasmas, in particular, to plasmas with He2+-ions.
References
Yukhnovskii I., Selected Works. Physics, Publishing House of Lviv Polytechnic National University, Lviv, 2002 (in Ukrainian).
Yukhnovskii I., Binary Distribution Function for a System of Charged Interacting Particles (Based on PhD Thesis by I. R. Yukhnovskii), Eurosvit, Lviv, 2010 (in Ukrainian).
Glauberman A. E., Yukhnovskii I. R., Zh. Eksp. Teor. Fiz., 1952, 22, 562 (in Russian).
Yukhnovskii I. R., Zh. Eksp. Teor. Fiz., 1954, 27, 690 (in Russian).
Iukhnovskii I. R., Sov. Phys. JETP, 1958, 7, No. 2, 263–270. DOI: https://doi.org/10.1007/978-3-662-42634-0_13
Bogoliubov N. N., Nonequilibrium Statistical Mechanics, 1939–1980, Statistical Mechanics, Vol. 5, Nauka, Moscow, 2006 (in Russian).
Bogoliubov N. N., Equilibrium Statistical Mechanics, 1945–1986, Statistical Mechanics, Vol. 6, Nauka, Moscow, 2006 (in Russian).
Iukhnovskii I. R., Golovko M. F., Statistical Theory of the Classical Equilibrium Systems, Naukova Dumka, Kyiv, 1980 (in Russian).
Yukhnovskii I. R., Holovko M. F., Statistical Theory of Classical Equilibrium Systems, 2nd ed., Akademperiodyka, Kyiv, 2025. DOI: https://doi.org/10.15407/akademperiodyka.558.444
Falkenhagen H., Theorie der Elektrolyte, Hirzel, Leipzig, 1971 (in German).
Falkenhagen H., Ebeling W., In: Satyendranath Bose 70th Birthday Commemoration Volume, Vol. 2, Prof. S. N. Bose 70th Birthday Celebration Committee [1965–66], Calcutta, 1966.
Glauberman A. Y., Visn. Lviv. Derzh. Univ., Ser. Fiz., 1962, 1, 10–31 (in Ukrainian).
Barthel J., Krienke H., Kunz W., Physical Chemistry of Electrolyte Solutions: Modern Aspects, Topics in Physical Chemistry, Vol. 5, Springer, New York, 1998.
Harned H. S., Owen B. B., The Physical Chemistry of Electrolytic Solutions, Reinhold Publishing Corporation, 1958.
Kelbg G., Wiss. Z. U. Rostock MNR, 1959/60, 9, 41. DOI: https://doi.org/10.1080/03736245.1959.10559346
Kelbg G., In: Electrolytes, Pesce B. (Ed.), Pergamon Press, New York, London, 1962.
Kelbg G., Ann. Phys., 1962, 464, 159–167 (in German). DOI: https://doi.org/10.1002/andp.19624640307
Kelbg G., Ann. Phys., 1963, 467, 219–224 (in German). DOI: https://doi.org/10.1002/andp.19634670308
Kelbg G., Ann. Phys., 1963, 467, 354–360 (in German). DOI: https://doi.org/10.1002/andp.19634670703
Bonitz M., Ebeling W., Filinov A., Kraeft W. D., Redmer R., Röpke G., Contrib. Plasma Phys., 2023, 63, e202300029. DOI: https://doi.org/10.1002/ctpp.202300029
Holovko M., In: Proceeding of Shevchenko Scientific Society, Vol. XXIX, Collected Physical Papers, 2011, 8, 452–467 (in Ukrainian).
Ebeling W., Condens. Matter Phys., 2025, 28, 23101. DOI: https://doi.org/10.5488/cmp.28.23101
Kelbg G., Hoffmann H. J., Ann. Phys., 1963, 469, 310–318 (in German). DOI: https://doi.org/10.1002/andp.19644690508
Krienke H., Condens. Matter Phys., 2013, 16, 43006. DOI: https://doi.org/10.5488/CMP.16.43006
Ebeling W., Feistel R., Krienke H., J. Mol. Liq., 2022, 346, 117814. DOI: https://doi.org/10.1016/j.molliq.2021.117814
Ebeling W., Feistel R., Krienke H., On Statistical Calculations of Individual Ionic Activity Coefficients of Electrolytes and Seawater. I. Basics — Draft 14 Apr 2019, 2019.
Ebeling W., Krienke H., Condens. Matter Phys., 2023, 26, 23602. DOI: https://doi.org/10.5488/CMP.26.23602
Golovko M. F., Krienke H., Mol. Phys., 1989, 68, 967. DOI: https://doi.org/10.1080/00268978900102671
Onsager L., J. Phys. Chem., 1939, 43, 189. DOI: https://doi.org/10.1021/j150389a001
Hemmer P. C., Holden H., Kjelstrup Ratkje S. (Eds.), The collected works of Lars Onsager, World Scientific, Singapore, 1996. DOI: https://doi.org/10.1142/3027
Salpeter E. E., Aust. J. Phys., 1954, 7, 373. DOI: https://doi.org/10.1071/PH540373
Nordholm S., Chem. Phys. Lett., 1984, 105, 302. DOI: https://doi.org/10.1016/0009-2614(84)85035-6
Friedman H. L., Ionic Solution Theory: Based on Cluster Expansion Methods, Interscience Publishers, New York, 1962.
Martynov G. A., Fundamental Theory of Liquids: Method of Distribution Functions, Adam Hilger, Bristol, 1992.
Evans R., Leote de Carvalho R. J. F., Henderson J. R., Hoyle D. C., J. Chem. Phys., 1994, 100, 591. DOI: https://doi.org/10.1063/1.466920
Leote de Carvalho R. J. F., Evans R., Mol. Phys., 1994, 83, 619. DOI: https://doi.org/10.1080/00268979400101491
Ebeling W., Fortov V. E., Filinov V., Quantum Statistics of Dense Gases and Nonideal Plasmas, Springer Series in Plasma Science and Technology, Springer International Publishing, Cham, 2017. DOI: https://doi.org/10.1007/978-3-319-66637-2
Fortov V. E., Filinov V. S., Larkin A. S., Ebeling W., Statistical Physics of Dense Gases and Nonideal Plasmas, FizMatLit, Moscow, 2020 (in Russian).
Alastuey A., Martin P. A., Statistical Mechanics of Coulomb Systems, EPFL Press, Lausanne, 2025.
Hau-Riege S. P., Weisheit J., Castor J. I., London R. A., Scott H., Richards D. F., New J. Phys., 2013, 15, 015011. DOI: https://doi.org/10.1088/1367-2630/15/1/015011
Stolzmann W., Ebeling W., Phys. Lett. A, 1998, 249, 242. DOI: https://doi.org/10.1016/S0375-9601(98)00659-8
DeWitt H. E., Phys. Rev. A, 1976, 14, 1290. DOI: https://doi.org/10.1103/PhysRevA.14.1290
Kremp D., Kraeft W. D., Ebeling W., Röpke G., Quantum Statistics of Charged Particle Systems, Plenum Press, New York, 1986. DOI: https://doi.org/10.1007/978-1-4613-2159-0
Outhwaite C. W., Hutson V. L. C., Mol. Phys., 1975, 29, 1521. DOI: https://doi.org/10.1080/00268977500101331
Cats R., Evans A., Härtel R., van Roij R., J. Chem. Phys., 2021, 154, 124504. DOI: https://doi.org/10.1063/5.0039619
Ebeling W., Röpke G., Plasma, 2023, 6, 1. DOI: https://doi.org/10.3390/plasma6010001
Ebeling W., Kraeft W. D., Kremp D., Theory of Bound States and Ionization Equilibrium in Plasmas and Solids, Akademie-Verlag, Berlin, 1976.
Ebeling W., Röpke G., Contrib. Plasma Phys., 2025, 65, e70009. DOI: https://doi.org/10.1002/ctpp.70009
Ebeling W., Ann. Phys., 1967, 19, 104 (in German). DOI: https://doi.org/10.2307/25294106
Ebeling W., Ann. Phys., 1968, 21, 315 (in German). DOI: https://doi.org/10.1016/0024-3841(68)90043-0
Ebeling W., Ann. Phys., 1969, 22, 383 (in German). DOI: https://doi.org/10.1103/PhysRevLett.22.383
Ebeling W., Physica, 1968, 40, 290. DOI: https://doi.org/10.1016/0031-8914(68)90025-6
Ebeling W., Physica, 1969, 43, 293. DOI: https://doi.org/10.1016/0031-8914(69)90009-3
Alastuey A., Cornu F., Perez A., Phys. Rev. E, 1995, 51, 1725. DOI: https://doi.org/10.1103/PhysRevE.51.1725
Kahlbaum T., J. Phys. IV, 2000, 10, No. Pr5, 455–459. DOI: https://doi.org/10.1051/jp4:2000588
Röpke G., Lin C., Ebeling W., Reinholz H., Contrib. Plasma Phys., 2026, e70078.
Ebeling W., Röpke G., Plasma Phys., 2026, 33, 032705. DOI: https://doi.org/10.1063/5.0313273
Ebeling W., Contrib. Plasma Phys., 2016, 56, 163. DOI: https://doi.org/10.1002/ctpp.201500118
Ebeling W., Hoffmann H., Kelbg G., Contrib. Plasma Phys., 1967, 8, 233 (in German). DOI: https://doi.org/10.1002/ctpp.19670070307
Hoffmann H., Ebeling W., Contrib. Plasma Phys., 1968, 8, 43 (in German). DOI: https://doi.org/10.1002/ctpp.19680080105
Sadykova S. P., Ebeling W., Tkachenko I. M., Eur. Phys. J. D, 2011, 61, 117. DOI: https://doi.org/10.1140/epjd/e2010-10118-y
Whitley H. D., Alastuey A., Gaffney J. A., Cauble R., Kraeft W. D., Bonitz M., Contrib. Plasma Phys., 2015, 55, 102. DOI: https://doi.org/10.1002/ctpp.201400083
Filinov A., Bonitz M., Phys. Rev. E, 2023, 108, 055212.
Bonitz M., Vorberger J., Bethkenhagen M., Böhme M. P., Ceperley D. M., Filinov A., Gawne T., Graziani F., Gregori G., Hamann P. et al., Phys. Plasmas, 2024, 31, 110501. DOI: https://doi.org/10.1063/5.0219405
Filinov A. V., Bonitz M., Phys. Rev. E, 2023, 108, 055212. DOI: https://doi.org/10.1103/PhysRevE.108.055212
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