A simple classical model for predicting onset crystallization temperatures on curved substrates and its implications for phase transitions in confined volumes

For small confinement volumes, phase transition temperatures are determined by the scarcity of the crystallizing material, rather than the magnitude of the energy barrier, as the supply of molecules undergoing the phase transition can be depleted before a stable nucleus is attained. We show this for the case of crystallization from the melt and from the solution by using a simple model based on an extended classical nucleation theory. This has important implications because it enables a simple and direct measurement of the critical nucleus size in crystallization. It also highlights that predicting the observable melting points of nanoparticles by using the Gibbs-Thomson equation can lead to substantial errors.