Russian Journal of Physical Chemistry A

, Volume 92, Issue 12, pp 2424–2434 | Cite as

Gibbs Calculations of the Equilibrium Surface Tension in a Vapor–Liquid System

  • Yu. K. TovbinEmail author


A correct way of calculating the equilibrium surface tension of planar and curved vapor–liquid interfaces is formulated for the first time according to Gibbs (i.e., as the excess free energy in the region of immiscible phase transitions). Calculations are performed using a modified lattice gas model that reflects a discrete–continuous distribution in the space of mixture components. The discrete size scale is associated with regions of around the size of a molecule that form the cells of the lattice structure. The continuous scale corresponds to the intermolecular motion of components inside the cells. The intermolecular interactions of comparable components are considered in a quasi-chemical approximation that describes direct correlations. It is shown that considering only the discreteness of the molecular distribution on a rigid lattice does not provide simultaneous satisfaction of two special conditions of chemical and mechanical equilibria for any degrees of interface curvature, and that the conditions of phase partitioning are insufficient for unambiguous calculations of the surface tension. The condition for the complete equilibrium of two phases must be supplemented with the conditions of the local mechanical and chemical equilibria at each point of the boundary transition region, and the local pressure value must be adjusted to the local value of the chemical potential.


molecular theory surface tension equilibrium droplets intermolecular motion of components 



This work was supported by the Russian Foundation for Basic Research, project code 18-03-00030a.


  1. 1.
    Physical Encyclopedy (Bol’sh. Ross. Entsiklopediya, Moscow, 1992), Vol. 3, p. 648 [in Russian].Google Scholar
  2. 2.
    J. W. Gibbs, Elementary Principles in Statistical Mechanics (Yale Univ., New Haven, Conn., 1902; Nauka, Moscow, 1982).Google Scholar
  3. 3.
    S. Ono and S. Kondo, Molecular Theory of Surface Tension in Liquids (Springer, Berlin, 1960; Inostr. Liter., Moscow, 1963).Google Scholar
  4. 4.
    J. Rowlinson and B. Widom, Molecular Theory of Capillarity (Oxford Univ., Oxford, UK, 1978).Google Scholar
  5. 5.
    V. K. Semenchenko, Surface Phenomena in Metals and Alloys (Moscow, 1957) [in Russian].Google Scholar
  6. 6.
    A. I. Rusanov, Phase Equilibria and Surface Phenomena (Khimiya, Leningrad, 1967) [in Russian].Google Scholar
  7. 7.
    A. Adamson, The Physical Chemistry of Surfaces (Wiley, New York, 1976).Google Scholar
  8. 8.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 84, 1717 (2010).CrossRefGoogle Scholar
  9. 9.
    Yu. K. Tovbin and A. B. Rabinovich, Russ. Chem. Bull. 58, 2193 (2009).CrossRefGoogle Scholar
  10. 10.
    Yu. K. Tovbin and A. B. Rabinovich, Russ. Chem. Bull. 59, 677 (2010).CrossRefGoogle Scholar
  11. 11.
    Yu. K. Tovbin and A. B. Rabinovich, Russ. Chem. Bull. 59, 857 (2010).CrossRefGoogle Scholar
  12. 12.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 92, 1045 (2018).CrossRefGoogle Scholar
  13. 13.
    T. Hill, Statistical Mechanics; Principles and Selected Applications (Dover, New York, 1987; Inostr. Liter., Moscow, 1960).Google Scholar
  14. 14.
    Yu. K. Tovbin, Theory of Physicochemical Processes at the Gas–Solid Interface (Nauka, Moscow, 1990; CRC, Boca Raton, FL, 1991).Google Scholar
  15. 15.
    Yu. K. Tovbin, The Molecular Theory of Adsorption in Porous Solids (Nauka, Moscow, 2012; CRC, Boca Raton, FL, 2017).Google Scholar
  16. 16.
    G. Bakker, Kapillaritat und Oberflachenspannung, Vol. 6 of Handbuch der Experimental Physik (Harms, Leipzig, Wien, 1928).Google Scholar
  17. 17.
    F. P. Buff, J. Chem. Phys. 23, 419 (1955).CrossRefGoogle Scholar
  18. 18.
    L. I. Sedov, Mechanics of Continuous Media (Nauka, Moscow, 1970), Vol. 1 [in Russian].Google Scholar
  19. 19.
    S. Kondo, J. Chem. Phys. 25, 662 (1956).CrossRefGoogle Scholar
  20. 20.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 92, 1 (2018).CrossRefGoogle Scholar
  21. 21.
    C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952).CrossRefGoogle Scholar
  22. 22.
    T. D. Lee and C. N. Yang, Phys. Rev. 87, 410 (1952).CrossRefGoogle Scholar
  23. 23.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 90, 1439 (2016).CrossRefGoogle Scholar
  24. 24.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 80, 1554 (2006).CrossRefGoogle Scholar
  25. 25.
    I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans Green, London, 1954).Google Scholar
  26. 26.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 91, 1621 (2017).CrossRefGoogle Scholar
  27. 27.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 89, 1971 (2015).CrossRefGoogle Scholar
  28. 28.
    Yu. K. Tovbin, Russ. J. Phys. Chem. A 91, 403 (2017).CrossRefGoogle Scholar
  29. 29.
    E. A. Moelwin-Hughes, Physical Chemistry (Pergamon, London, New York, Paris, 1961; Inostr. Liter., Moscow, 1962), Vols. 1, 2.Google Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of SciencesMoscowRussia
  2. 2.Karpov Institute of Physical ChemistryMoscowRussia

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