Scaling properties of the critical nucleus in classical and density functional nucleation theories

Abstract

This chapter derives scaling properties for the critical nucleus, which are in harmony with novel findings from both experimental and theoretical studies and which are hoped to guide the phenomenological efforts in a more productive direction. Measurements of nucleation rate provide a direct probe of the nucleation barrier height, W*, critical nucleus, g*, and nucleus composition for multicomponent systems. In addition to providing an excellent description of the density functional (DF) results, the scaling theorems are supported by such measurements. The scaling theorems constrain the departure from CNT, and therefore can guide the construction of phenomenological nucleation theories. Scaling relations are developed for the number of molecules in g* and W*. DF calculations for vapor–liquid nucleation confirm these relations and show systematic departure of the ratio W*/(g*∆μ) from its classical value—1/2—with increasing difference in chemical potential between the supersaturated vapor and bulk condensed phase, ∆μ . Discrepancies between classical and DF nucleation theories and between the classical theory and experiment are interpreted using these results.