KINETICS OF HOMOGENEOUS NUCLEATION IN THE FREEZING OF LARGE WATER CLUSTERS

Water clusters of 4000-6000 molecules were produced by condensation of vapor in supersonic flow and cooled by evaporation until they froze a t about 200 K. Rates of nucleation up to 10(30) m(-3) s(-1) were deter mined by electron diffraction measurements at microsecond intervals. A lthough nucleation rates were 20 orders of magnitude higher than in pr evious investigations of the freezing of water, this enormous disparit y was accounted for naturally by the classical theory of nucleation. T he free energy sigma(sl) of the solid-liquid interface implied by the results increases with temperature as T-n, with n approximately 0.3-0. 4, the same range of values as found for mercury in the only well-esta blished trend known to the present investigators. The interfacial free energy of 21.6 mJ/m(2) derived for clusters of water is virtually the same as that obtained for small water droplets by several workers but is substantially lower than the value inferred from the interfacial t ension in the bulk system at 0 degrees C. This difference is a consequ ence of the different forms of ice encountered in the different experi ments. Bulk water freezes to the thermodynamically stable hexagonal ic e (Ih), whereas highly supercooled-water freezes to the kinetically fa vored cubic ice (Ic), a reaction product offering a lower free energy barrier. Anomalously, the ratio of sigma(sl) to the heat of fusion per unit area derived for supercooled water is only about two-thirds that suggested originally for water by Turnbull but since found to apply q uite well to other nonmetallic substances. Two variants of the classic al theory of homogeneous nucleation are compared, and some deficiencie s of the theory are discussed.