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The Rate of Spontaneous Formation of Microscopic Nuclei in Supersaturated Vapor

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Abstract

The equilibrium nucleus-size distribution determined by the method of statistical physics has been analyzed. The analysis has shown that nuclei composed of 1000 or fewer molecules are microscopic objects. They are described by partition functions and cannot be described by thermodynamic methods. An approach has been proposed that makes it possible to determine a partition function over internal degrees of freedom of a nucleus and express the aforementioned distribution via commonly accepted thermodynamic parameters. The solution of the problem is reduced to the determination of the evaporation rate of clusters by extrapolating the evaporation rate, which has been calculated for a macroscopic droplet of an incompressible liquid in terms of thermodynamic concepts with allowance for fluctuations, to the sizes of nuclei. As a result, a theory has been formulated for homogeneous stationary nucleation. The comparison of the proposed theory with experimental data has shown that the calculated sizes of critical nuclei coincide with the measured ones and that the theoretical nucleation rates either coincide with the measured rates or agree with them within one or two decimal orders of magnitude.

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References

  1. Volmer, M. and Weber, A., Z. Phys. Chem., 1926, vol. 119, p. 277.

    CAS  Google Scholar 

  2. Becker, R. and Döring, W., Ann. Phys., 1935, vol. 24, p. 719.

    Article  CAS  Google Scholar 

  3. Zel’dovich, Ya.B., Zh. Eksp. Teor. Fiz., 1942, vol. 12, p. 525.

    Google Scholar 

  4. Lothe, J. and Pound, G.M., J. Chem. Phys., 1962, vol. 36, p. 2080.

    Article  CAS  Google Scholar 

  5. Frenkel’, Ya.I., Sobranie izbrannykh trudov (Selected Works), Moscow–Leningrad: Akad. Nauk SSSR, 1959, vol. 3. Kinetic Theory of Liquids.

  6. Feder, J., Russell, K.C., Lothe, J., and Pound, G.M., Adv. Phys., 1966, vol. 15, p. 111.

    Article  CAS  Google Scholar 

  7. Reiss, H., Katz, J.L., and Cohen, E.R., J. Chem. Phys., 1968, vol. 48, p. 5553.

    Article  CAS  Google Scholar 

  8. Reiss, H., J. Stat. Phys., 1970, vol. 2, p. 83.

    Article  Google Scholar 

  9. Abraham, F.F., Homogeneous Nucleation Theory, New York: Academic, 1974.

    Google Scholar 

  10. Burton, J.J., in Modern Theoretical Chemistry, Berne, B.J., Ed., New York: Plenum, 1977, vol. 5, p. 195.

    CAS  Google Scholar 

  11. Kuni, F.M. and Rusanov, A.I., Phys. Lett. A, 1969, vol. 29, p. 337.

    Article  CAS  Google Scholar 

  12. Rusanov, A.I. and Kuni, F.M., in Poverkhnostnye yavleniya v zhidkostyakh (Surface Phenomena in Liquids), Rusanov, A.I., Ed., Leningrad, 1975, p. 112.

  13. Lushnikov, A.A. and Sutugin, A.G., Usp. Khim., 1976, vol. 45, p. 385.

    Article  Google Scholar 

  14. Dillmann, A. and Meier, G.E.A., J. Chem. Phys., 1991, vol. 94, p. 3872.

    Article  CAS  Google Scholar 

  15. Ford, I.J., J. Mech. Eng. Sci., 2004, vol. 218, p. 883.

    Article  CAS  Google Scholar 

  16. Kodenev, G.G., Colloid J., 2008, vol. 70, p. 589.

    Article  CAS  Google Scholar 

  17. Kodenev, G.G., Samodurov, A.V., Baldin, M.N., and Baklanov, A.M., Colloid J., 2014, vol. 76, p. 38.

    Article  CAS  Google Scholar 

  18. Landau, L.A. and Lifshits, E.M., Statistical Physics, New York: Pergamon, 1980.

    Google Scholar 

  19. Band, W., Quantum Statistics, New York: Van Nostrand, 1955.

    Google Scholar 

  20. Rusanov, A.I., Kuni, F.M., and Shchekin, A.K., Kolloidn. Zh., 1987, vol. 49, p. 309.

    CAS  Google Scholar 

  21. Girshick, S.L. and Chiu, C.-P., J. Chem. Phys., 1990, vol. 93, p. 1273.

    Article  CAS  Google Scholar 

  22. Katz, J.L., Fisk, J.A., and Chakarov, V., Abstracts of Papers, 13 Int. Conf. on Nucleation and Atmospheric Aerosols, Salt Lake City, 1992, Fukuta, N. and Wagner, P.E.P., Eds., p. 11.

    Google Scholar 

  23. Barnard, A.J., Proc. R. Soc. London A, 1953, vol. 220, p. 132.

    Article  CAS  Google Scholar 

  24. Bedanov, V.M., Vaganov, V.S., Gadiyak, G.V., and Kodenev, G.G., Khim. Fiz., 1988, vol. 7, p. 412.

    CAS  Google Scholar 

  25. Bronshtein, I.N. and Semendyaev, K.A., Spravochnik po matematike dlya inzhenerov i uchashchikhsya VTUZov (Handbook on Mathematics for Engineers and Students of Technical High Schools), Moscow: Nauka, 1967.

    Google Scholar 

  26. Kodenev, G.G., Preprint no. 3 (Institute of Geology and Geophysics, Siberian Branch, USSR Academy of Sciences, Novosibirsk, 1984).

    Google Scholar 

  27. Spravochnik khimika (Chemist’s Handbook), Nikol’skii, B.P., Ed., Moscow: Khimiya, 1965, vol. 1.

  28. Hare, D.E. and Sorensen, C.M., J. Chem. Phys., 1986, vol. 84, p. 5085.

    Article  CAS  Google Scholar 

  29. Archer, D.G. and Carter, R.W., J. Phys. Chem. B, 2000, vol. 104, p. 8563.

    Article  CAS  Google Scholar 

  30. Viisanen, Y., Strey, R., and Reiss, H., J. Chem. Phys., 1993, vol. 99, p. 4680.

    Article  CAS  Google Scholar 

  31. Holten, V., Bertrand, C.E., Anisimov, M.A., and Sengers, J.V., J. Chem. Phys., 2012, vol. 136, p. 094507.

    Article  CAS  Google Scholar 

  32. Bedanov, V.M., Vaganov, V.S., Gadiyak, G.V., Kodenev, G.G., and Rubakhin, E.A., Khim. Fiz., 1988, vol. 7, p. 555.

    CAS  Google Scholar 

  33. Vaganov, V.S., Kodenev, G.G., and Rubakhin, E.A., Preprint no. 14 (Institute of Geology and Geophysics, Siberian Branch, USSR Academy of Sciences, Novosibirsk: 1985).

    Google Scholar 

  34. Rohac, V., Fulem, M., Schmidt, H.-G., Rižicka, V., Rižicka, K., and Wolf, G., J. Therm. Anal. Calorim., 2002, vol. 70, p. 455.

    Article  CAS  Google Scholar 

  35. Hrubý, J., Vinš, V., Mareš, R., Hykl, J., and Kalová, J., J. Phys. Chem. Lett., 2014, vol. 25, p. 425.

    Article  Google Scholar 

  36. Hämeri, K. and Kulmala, M., J. Chem. Phys., 1996, vol. 105, p. 7696.

    Article  Google Scholar 

  37. Mikheev, V.B., Laulainen, N.S., Barlow, S.E., Knott, M., and Ford, I.J., J. Chem. Phys., 2000, vol. 113, p. 3704.

    Article  CAS  Google Scholar 

  38. Hämeri, K., Kulmala, M., Krissinel, E., and Kodenyov, G., J. Chem. Phys., 1996, vol. 105, p. 7683.

    Article  Google Scholar 

  39. Reid, R.C. and Sherwood, T.K., The Properties of Gases and Liquids, New York: McGraw-Hill, 1966.

    Google Scholar 

  40. Fuks, N.A. and Sutugin, A.G., Kolloidn. Zh., 1964, vol. 26, p. 110.

    Google Scholar 

  41. Görke, Neitola, K., Hyvärinen, A.-P., Lihavainen, H., Wölk, J., Strey, R., and Brus, D., J. Chem. Phys., 2014, vol. 140, p. 174301.

    Article  Google Scholar 

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Correspondence to G. G. Kodenev.

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Original Russian Text © G.G. Kodenev, 2018, published in Kolloidnyi Zhurnal, 2018, Vol. 80, No. 2, pp. 177–193.

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Kodenev, G.G. The Rate of Spontaneous Formation of Microscopic Nuclei in Supersaturated Vapor. Colloid J 80, 167–183 (2018). https://doi.org/10.1134/S1061933X18020047

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  • DOI: https://doi.org/10.1134/S1061933X18020047

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