ROLE OF THE MODEL DEPENDENT TRANSLATIONAL VOLUME SCALE IN THE CLASSICAL-THEORY OF NUCLEATION

The replacement free energy correction, for vapor phase nucleation, in the classical theory of nucleation (CNT), is investigated within the confines of the renormalized representation of the molecular system im plicit in the model, based on the capillarity approximation adopted by CNT. The replacement free energy is associated with the translational degrees of freedom of the clusters that serve as embryos for the form ation of drops, and it is shown that, unless extreme care is exercised , the evaluation of this contribution to the free energy can involve a redundant counting of molecular configurations that can lead to a pre dicted nucleation rate in error by many orders of magnitude. It is dem onstrated that the problem arises because of the use of a coarse grain ed renormalized version of the actual system and that the correction c an be extremely sensitive to the type of renormalization (model) emplo yed. In the case of CNT, in particular, error can arise from the fact that the drop used to model the cluster cannot be located more accurat ely than within the fluctuation of its volume. This fluctuation, in ef fect, generates a lattice whose sites the drop is restricted to occupy and whose lattice parameter is the cube root of the volume of fluctua tion. This denial of accessibility of the continuum volume to the drop eliminates redundant counting. The form for the replacement free ener gy factor is derived, discussions of various subtle issues are present ed, and similar problems are mentioned in connection with renormalized versions of molecular systems in other contexts (e.g., in the cases o f microemulsions and polymers, and even in cases such as that of the c onstant pressure ensemble) where renormalization does not play a role.