Self-Consistent Determination of the Ice–Air Interfacial Tension and Ice–Water–Air Line Tension from Experiments on the Freezing of Water Droplets

We propose an indirect experimental method to self-consistently determine the line tension of a solid–liquid–vapor contact region and the interfacial tension of the solid–vapor interface via experiments on the homogeneous crystallization of droplets. The crucial idea of our method is that, even in the surface-stimulated mode, when a crystal nucleus forms with one of its facets at the droplet surface it initially emerges (as a subcritical cluster) homogeneously in the subsurface layer, not “pseudo-heterogeneously” at the surface. This mode is negligible for large droplets but becomes increasingly important with decreasing droplet size and is dominant in small droplets. The proposed method requires experimental data on the rate of homogeneous crystal nucleation as a function of droplet size. Using this method to examine experimental data on homogeneous crystal nucleation in droplets of 1.0, 1.7, and 2.9 μm radii in the temperature range from 234.8 to 236.2 K, we evaluated the line tension τ of ice–water–air contact to be a monotonically increasing function of temperature, almost linearly increasing from 1.2 × 10–7 to 2.5 × 10–7 dyn in this temperature range. Extrapolating this dependence to lower temperatures, one can predict τ to become negative at temperatures below about 232 K. The ice–air interfacial tension is about 90 dyn/cm, virtually independent of temperature.