On the coupling between slow diffusion transport and barrier crossing in nucleation

Abstract

We model the coupling between slow diffusion transport and nucleation using the diffusion equation, an Ostwald-Freundlich boundary condition, and a mass balance linking nucleus size to flux across the nucleus-solution interface. The model retains some characteristics of the classical nucleation theory because of the common theoretical foundations behind classical nucleation theory and the Ostwald-Freundlich equation. For example, the classically critical-sized nucleus in the uniform supersaturated concentration field is an unstable equilibrium point. However, the model also shows that certain types of concentration profiles can drive a classically pre-critical nucleus over the nucleation barrier. We identify the separatrix as a function of both nucleus size and characteristics of the local concentration field. Our analysis may be useful for understanding the effects of local concentration fluctuations and especially for understanding the role of dense precursor particles in driving two-step nucleation processes. Our analysis may also provide a starting point for further statistical field theory analyses of local concentration fluctuations and their effects on nucleation rates.