Journal of Statistical Physics

, Volume 28, Issue 3, pp 487–495 | Cite as

A monte carlo method for approximating critical cluster size in the nucleation of model systems

  • Barbara N. Hale
  • Richard C. Ward


A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n2/3] is used to predict critical cluster size and critical supersaturation ratio, S*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.

Key words

Homogeneous nucleation critical cluster size free energy of formation Monte Carlo simulation Lennard-Jones vapor clusters critical supersaturation ratio partition function 


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  1. 1.
    N. G. Garcia and J. M. Torroja,Phys. Rev. Lett. 47:186 (1981).Google Scholar
  2. 2.
    J. K. Lee, J. A. Barker, and F. F. Abraham,J. Chem. Phys. 58:3166 (1973).Google Scholar
  3. 3.
    N. H. Fletcher,The Physics of Rainclouds (Cambridge University Press, Cambridge, 1969), Chap. 3.Google Scholar
  4. 4.
    J. J. Burton and C. L. Briant, inNucleation Phenomena, A. C. Zettlemoyer, ed. (Elsevier, New York, 1977); J. J. Burton,Surf. Sci. 26:1 (1971).Google Scholar
  5. 5.
    M. R. Hoare, P. Pal, and P. P. Wegener,J. Colloid Interface Sci. 75:126 (1980).Google Scholar
  6. 6.
    C. H. Bennett,J. Computational Phys. 22:245 (1976).Google Scholar
  7. 7.
    F. F. Abraham,Homogeneous Nucleation Theory (Academic Press, New York, 1974), Chap. 5.Google Scholar
  8. 8.
    J. Miyazaki, G. M. Pound, F. F. Abraham, and J. A. Barker,J. Chem. Phys. 67:3851 (1977).Google Scholar
  9. 9.
    C. S. Kiang, D. Stauffer, G. H. Walker, O. P. Puri, J. D. Wise, Jr., and E. M. Patterson,J. Atmos. Sci. 28:1222 (1970); K. Binder and D. Stauffer,J. Stat. Phys. 6:49 (1972).Google Scholar
  10. 10.
    R. D. McCarty, National Bureau of Standards Technical Note No. 1025, U. S. Department of Commerce, National Bureau of Standards U. S. Government Printing Office, Washington, D. C. (1980).Google Scholar
  11. 11.
    G. M. Torrie and J. P. Valleau,J. Computational Phys. 23:187 (1977).Google Scholar
  12. 12.
    B. J. Wu, P. P. Wegener, and G. D. Stein,J. Chem. Phys. 69:1776 (1978).Google Scholar
  13. 13.
    G. D. Stein,Argon nucleation in a supersonic nozzle, Report to the Office of Naval Research (1974); National Technical Information Service No. AD-A007357/7GI.Google Scholar
  14. 14.
    F. H. Stillinger and A. Rahman,J. Chem. Phys. 68:666 (1978).Google Scholar
  15. 15.
    B. N. Hale, J. Kiefer, S. Terrazas, and R. C. Ward,J. Phys. Chem. 84:1473 (1980); R. C. Ward, J. Holdman, and B. N. Hale, unpublished.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Barbara N. Hale
    • 1
  • Richard C. Ward
    • 1
  1. 1.Department of Physics, and Graduate Center for Cloud Physics ResearchUniversity of Missouri-RollaRolla

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