Direct measurement of critical nucleus size in confined volumes

Abstract

In crystallization, the critical nucleus size is of pivotal importance. Above this size, it is favorable for the new crystalline phase to form; below this size, the clusters will tend to dissolve rather than grow. To date, there has been no direct method for measuring the critical nucleus size. Instead, the size is typically calculated from the variation of crystallization rates with temperature. This involves using bulk values of the interfacial tension and enthalpy of fusion, which are inappropriate for small critical nucleus sizes. Here, we present a direct method for measuring the size of the critical nucleus, based on observing crystallization temperatures of materials within microemulsions. Using this approach, the number of molecules in the critical nucleus can be found simply by measuring the droplet size. Data on the freezing of water in water-in-oil microemulsions with and without the nucleating agent, heptacosanol, are presented to support our hypothesis. The results show that the critical nucleus contains 90-350 ice molecules for water pool radii of ~1.2-1.8 nm for the heptacosanol-doped microemulsions in which heterogeneous nucleation is initiated at the droplet interface. For the microemulsions without heptacosanol, the critical nucleus contains 70-210 ice molecules for water pool radii of ~1.2-1.8 nm. The smaller values arise because homogeneous nucleation occurs and therefore the crystallization temperatures are lower. We can also determine how bulk properties are perturbed at the nanoscale, and we find that the ratio of the ice-water interfacial tension to the enthalpy of fusion decreases significantly for water pool radii that are <2 nm.