Water nucleation: A comparison between some phenomenological theories and experiment

The predictions of several homogeneous nucleation theories are compared with experimental results for water for a range of temperatures and vapor supersaturations, S. The theoretical models considered are: classical theory (including the 1/S correction factor), the Gibbs p-form, mean-field kinetic nucleation theory (MKNT), the extended modified liquid drop model-dynamical nucleation theory, and two forms of density functional theory, one without and one with a contribution due to association. The theoretical expressions for the logarithm of the nucleation rate are expanded in a series in powers of the logarithm of S. The residual dependence (once the classical dependence has been factored out) of the experimental results shows a stronger decrease with increasing temperature than all the theories except MKNT. The residual S-dependence of the experimental results decreases with increasing supersaturation whereas all the theories except the Gibbs p-form predict an increase. The first correction term to classical theory involves both the liquid compressibility and curvature correction to the surface tension (Tolman length) so the experimental results suggest that the Tolman length is zero (as assumed in the Gibbs p-form) or positive whereas the other theories predict a negative Tolman length. The effect of including a term proportional to ln(lnS) in the series expansion is also discussed.