Colloid Journal

, Volume 81, Issue 6, pp 634–641 | Cite as

Effective Surface Free Energy of Crystalline Phase Nuclei

  • V. G. BaidakovEmail author
  • K. R. Protsenko


Molecular-dynamics simulation by the mean lifetime, forward flux sampling, and seeding method has been employed to study the kinetics of the spontaneous crystallization of a supercooled Lennard-Jones liquid. The limiting values of supercooling (supercompression) of a liquid phase have been determined within wide ranges of temperature and pressure, with nucleation rate being varied by 195 orders of magnitude. The dependence of the effective surface free energy of crystalline phase nuclei on the dividing surface curvature has been calculated from the obtained data with the use of the classical nucleation theory. The calculations have been performed for three isotherms and four isobars. The first (Tolman length) and second corrections to the effective surface free energy for the interface curvature have been determined.



This work was supported by the Russian Science Foundation, project no. 18-19-00276.


The authors declare that they have no conflict of inter-est.


  1. 1.
    Volmer, M. and Weber, A., Z. Phys. Chem. (Munich), 1926, vol. A119, no. 1, p. 277.Google Scholar
  2. 2.
    Zeldovich, Ya.B., Zh. Eksp. Teor. Fiz., 1942, vol. 12, p. 525.Google Scholar
  3. 3.
    Turnbull, D. and Fisher, J.C., J. Chem. Phys., 1949, vol. 17, p. 71.CrossRefGoogle Scholar
  4. 4.
    Skripov, V.P. and Koverda, V.P., Spontannaya kristallizatsiya pereokhlazhdennykh zhidkostei (Spontaneous Crystallization of Supercooled Liquids), Moscow: Nauka, 1984.Google Scholar
  5. 5.
    Tolman, R., J. Chem. Phys., 1948, vol. 16, p. 758.CrossRefGoogle Scholar
  6. 6.
    Fisher, M.P.A. and Wortis, M., Phys. Rev. B: Condens. essential, 1984, vol. 29, p. 6252.CrossRefGoogle Scholar
  7. 7.
    Block, B.J., Das, S.K., Oettel, M., Virnau, P., and Binder, K., J. Chem. Phys., 2010, vol. 133, 154 702.CrossRefGoogle Scholar
  8. 8.
    Baidakov, V.G. and Skripov, V.P., Zh. Fiz. Khim., 1982, vol. 56, p. 818.Google Scholar
  9. 9.
    Baidakov, V.G. and Boltachev, G.Sh., J. Chem. Phys., 2004, vol. 121, p. 8594.CrossRefGoogle Scholar
  10. 10.
    Rusanov, A.I., Fazovye ravnovesiya i poverkhnostnye yavleniya (Phase Equilibria and Surface Phenomena), Leningrad: Khimiya, 1967.Google Scholar
  11. 11.
    Irving, J.H. and Kirkwood, J.G., J. Chem. Phys., 1950, vol. 18, p. 817.CrossRefGoogle Scholar
  12. 12.
    Blokhuis, E.M. and Bedeaux, D., J. Chem. Phys., 1992, vol. 97, p. 3576.CrossRefGoogle Scholar
  13. 13.
    Cheng, B. and Ceriotti, M., J. Chem. Phys., 2018, vol. 148, 231 102.CrossRefGoogle Scholar
  14. 14.
    Schmelzer, J.W.P., Abyzov, A.S., Ferreira, E.B., and Fokin, V.M., Int. J. Appl. Glass Sci., 2019, vol. 10, no. 1, p. 57.CrossRefGoogle Scholar
  15. 15.
    Landau, L.D., O ravnovesnoi forme kristallov. Sobranie trudov (On Equilibrium Form of Crystals. Collected Works), Moscow: Nauka, 1969, vol. 2.Google Scholar
  16. 16.
    Herring, C., Phys. Rev., 1951, vol. 82, p. 87.CrossRefGoogle Scholar
  17. 17.
    Statt, A., Virnau, P., and Binder, K., Phys. Rev. E: Stat. Phys., Plasmas, Liquids, Relat.Interdiscip. Top., 2014, vol. 96, 042 609.Google Scholar
  18. 18.
    Gibbs, J.W., The Collected Works, New York: Longmans & Green, 1928.Google Scholar
  19. 19.
    Baidakov, V.G. and Boltachev, G.Sh., Zh. Fiz. Khim., 1995, vol. 69, p. 515.Google Scholar
  20. 20.
    Baidakov, V.G. and Boltachev, G.Sh., Phys. Rev. E: Stat. Phys., Plasmas, Liquids, Relat.Interdiscip. Top., 1999, vol. 59, p. 469.Google Scholar
  21. 21.
    Baidakov, V.G., Boltachev, G.Sh., and Chernykh, G.G., Phys. Rev. E: Stat. Phys., Plasmas, Liquids, Relat.Interdiscip. Top., 2004, vol. 70, 011 603.Google Scholar
  22. 22.
    Skripov, V.P., Metastabil’naya zhidkost’ (Metastable Liquid), Moscow: Nauka, 1972.Google Scholar
  23. 23.
    Bolhuis, P.G., Chandler, D., Dellago, C., and Geissker, P.L., Annu. Rev. Phys. Chem., 2002, vol. 53, p. 291.CrossRefGoogle Scholar
  24. 24.
    Van Erp, T.S., Moroni, D., and Bolhuis, P.G., J. Chem. Phys., 2003, vol. 118, p. 7762.CrossRefGoogle Scholar
  25. 25.
    Allen, R.J., Valeriani, C., and Ten Wolde, P.R., J. Phys.: Condens. essential, 2009, vol. 21, 463 102.Google Scholar
  26. 26.
    Espinosa, J.R., Vega, C., Valeriani, C., and Sanz, E., J. Chem. Phys., 2015, vol. 142, 194 709.CrossRefGoogle Scholar
  27. 27.
    Espinosa, J.R., Vega, C., Valeriani, C., and Sanz, E., J. Chem. Phys., 2016, vol. 144, 034 501.CrossRefGoogle Scholar
  28. 28.
    Ten Wolde, P.R., Ruiz-Montero, M.J., and Frenkel, D., J. Chem. Phys., 1996, vol. 104, p. 9932.CrossRefGoogle Scholar
  29. 29.
    Lechner, W. and Dellago, C., J. Chem. Phys., 2008, vol. 129, 114 707.CrossRefGoogle Scholar
  30. 30.
    Plimpton, S., J. Comput. Phys., 1995, vol. 117, p. 1.CrossRefGoogle Scholar
  31. 31.
    Bussi, G., Donadio, D., and Parrinello, M., J. Chem. Phys., 2007, vol. 126, 014 101.CrossRefGoogle Scholar
  32. 32.
    Verlet, L., Phys. Rev., 1967, vol. 159, p. 98.CrossRefGoogle Scholar
  33. 33.
    Sidky, H., Colón, Y.J., Helfferich, J., et al., J. Chem. Phys., 2018, vol. 148, 044 104.CrossRefGoogle Scholar
  34. 34.
    Baidakov, V.G., Protsenko, S.P., and Tipeev, A.O., J. Chem. Phys., 2013, vol. 139, p. 224 703.CrossRefGoogle Scholar
  35. 35.
    Baidakov, V.G. and Protsenko, S.P., Dokl. Akad. Nauk, 2004, vol. 394, p. 752.Google Scholar
  36. 36.
    Baidakov, V.G. and Tipeev, A.O., J. Chem. Phys., 2012, vol. 136, 074 510.CrossRefGoogle Scholar
  37. 37.
    Baidakov, V.G. and Protsenko, S.P., JETP, 2006, vol. 103, p. 876.CrossRefGoogle Scholar
  38. 38.
    Boltachev, G.Sh. and Baidakov, V.G., High Temp., 2003, vol. 41, p. 270.CrossRefGoogle Scholar
  39. 39.
    Baidakov, V.G. and Protsenko, S.P., Phys. Rev. Lett., 2005, vol. 95, 015 701.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Thermal Physics, Ural Branch, Russian Academy of SciencesYekaterinburgRussia

Personalised recommendations