A Monte Carlo Method for Approximating Critical Cluster Size in the Nucleation of Model Systems
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 containing n and n-1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of the n cluster [including a term A (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 by lnS*=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.
B. N. Hale and R. C. Ward, "A Monte Carlo Method for Approximating Critical Cluster Size in the Nucleation of Model Systems," Journal of Statistical Physics, vol. 28, no. 3, pp. 487-495, Kluwer Academic Publishers-Plenum Publishers, Jul 1982.
The definitive version is available at http://dx.doi.org/10.1007/BF01008320
Keywords and Phrases
Critical Cluster Size; Critical Supersaturation Ratio; Free Energy Of Formation; Homogeneous Nucleation; Lennard-Jones Vapor Clusters; Monte Carlo Simulation; Partition Function
International Standard Serial Number (ISSN)
Article - Journal
© 1982 Kluwer Academic Publishers-Plenum Publishers, All rights reserved.