A Reexamination of Homogeneous Nucleation Theory

The homogeneous nucleation theory of liquid droplets in supersaturated vapors is reviewed. Taking into consideration the microscopic surface tension and extrapolating from the triple point to the critical point (T = Te) of the liquid-gas phase transition, we reexamine homogeneous nucleation theory. A calculation of the growth rate for microscopic clusters due to the incorporation of much smaller clusters (instead of single molecules) is given and an appropriate variable, scaled supersaturation, is presented to study the mechanism of homogeneous nucleation. For a given nucleation rate, the scaled supersaturation is expected to be nearly independent of temperature below Te.; this is confirmed by experimental data. A generalized form for the droplet model is proposed. Previous theories (“classical,” Lothe-Pound, Reiss, Katz, Cohen) are shown to be special cases of this generalized form and all are shown to be invalid near the critical point. A quantitative theory is made by extrapolating Fisher's droplet model from the critical region to the triple point. For the free energy of embryo formation we include the contributions due to internal vibrations and self-avoiding walks. The microscopic surface tension for the droplet is estimated from the measured coexistence curve; it is found to agree with the bulk macroscopic surface tension near the triple and critical points and to be smaller in the intermediate region. With these considerations we have calculated the scaled supersaturation for water vapor as a function of temperature for given measured nucleation rates. The proposed theory is in good agreement with experiment.