Isothermal nucleation rates in supersonic nozzles and the properties of small water clusters

We make direct measurements of stationary, homogeneous nucleation rates, J = N/Deltat, in supersonic Laval nozzles. We determine the number densities, N, of droplets formed from small-angle neutron scattering (SANS) experiments and the time intervals during which nucleation occurs, Deltat approximate to 10 mus, from static pressure measurements along the axis of the nozzle. Applying these techniques to nozzles with different expansion rates, we obtain the first isothermal nucleation rate measurements as a function of supersaturation for these devices with a relatively small error margin in J of +/-50%. At temperatures T of 210, 220, and 230 K, the maximum nucleation rates for D2O lie in the range 4 x 10(16) < J/cm(-3)s(-1) < 3 x 10(17) for supersaturations S ranging from 46 to 143. At the highest temperature, the predictions of classical nucleation theory lie slightly below the experimental points but are still within experimental error. At the lower temperatures, the classical predictions lie well below the measured values, The discrepancy increases as the temperature is lowered and exceeds the measurement error bars. In contrast, the predictions of the empirical temperature correction function to the classical theory proposed by Wolk and Strey (Wolk, J.; Strey, R. J. Phys. Chem. B 2001, 105, 11683) agree quite well with the experimental data points over the entire supersaturation and temperature ranges. Finally, we apply the first and second nucleation theorems to the data and directly estimate the number of molecules in the critical cluster n* and the excess internal energy E-x(n*), respectively. The agreement between these values and the classical values predicted assuming that the critical cluster is a compact spherical object is really quite good even though under our conditions n* is less than 10. The good agreement for the classical values of the excess internal energy implies that the poor temperature dependence of the classical rate predictions arises from the classical theory's failure to treat correctly the excess internal entropy of the critical cluster.