Multivariate Analysis of Homogeneous Nucleation Rate Measurements: Ii. Temperature and Vapor Concentration Dependence

The multivariate analysis of nucleation rate dependency on vapor concentration, initiated in Part I [McGraw and Zhang, 2007], is extended to include temperature. Nucleation rate sensitivity to changes in vapor concentration and temperature are described using kinetic extensions of the nucleation theorem (KNTs). The nucleation rate is found to be highly multi-linear in selected KNT-suggested temperature and concentration coordinates with little curvature over the tested range of measurements. Bivariate analyses of measurements for the homogeneous nucleation rates of water, methanol, hexanol, and nonane vapors are presented. Estimates for critical cluster energy, and number of molecules present in the critical nucleus are compared with predictions from the liquid drop model of classical nucleation theory. Surprisingly a simple Arrhenius temperature dependence provides an excellent description of the rate measurements for each of the studied cases. The quality of the planar fits to the full data sets are also excellent with R values ranging from 0.89 (methanol) to 0.97 (hexanol). These results yield a physically based parameterization of the measurements, valid over about five orders of magnitude in nucleation rate, as well as a measurement-based determination of critical cluster properties suitable for comparing with molecular simulations and phenomenological nucleation theories. Comparison with the capillary drop model of classical nucleation theory reveals generally good agreement for critical cluster size. Nevertheless, with the exception of water vapor, the drop model tends to grossly overestimate critical cluster energy.