Shape and area fluctuation effects on nucleation theory

Abstract

In standard nucleation theory, the nucleation process is characterized by computing ΔΩ(V), the reversible work required to form a cluster of volume V of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly spherical cluster of volume V and a fluctuating surface area A, whereby the maximum of ΔΩ(V) is replaced by a saddle point in ΔΩ(V, A). Compared to the simpler theory based on volume only, the barrier height of ΔΩ(V, A) at the transition state is systematically larger by a few kBT. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non-spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence.