Scaling Properties of the Critical Nucleus in Classical and Molecular-Based Theories of Vapor-Liquid Nucleation

Scaling relations are developed for the number $g^{*}$ of molecules in the critical nucleus and the nucleation barrier height $W^{*}$. Density functional (DF) calculations for vapor-liquid nucleation confirm these relations and show systematic departure of the ratio $W^{*}{/g}^{*}\Delta \mu$ from its classical value of $1/2$ with increasing difference $\Delta \mu$ in the chemical potential between the supersaturated vapor and bulk condensed phase. Discrepancies between classical and DF nucleation theories and between the classical theory and experiment are interpreted using these results.