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

Abstract

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.