(30f) Nucleation From Solution: How Slow Diffusion Changes Everything

We show that a previously un-noted coupling exists between slow diffusion transport and barrier crossing in nucleation.  The effect is modeled 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 the classical nucleation theory as a special case because of the common theoretical foundations behind classical nucleation theory and the Ostwald-Freundlich equation.  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 suggests that local concentration fluctuations "stochastically gate" nucleation events, analogous to stochastic gating in the theory of chemical reactions.   Our analysis provides new insight on the mechanisms of two-step nucleation processes.  Finally, our analysis provides a starting point for further statistical field theory analyses of local concentration fluctuations and their effects on nucleation rates.  Time permitting, we will also show how slow diffusion on the free energy landscape can influence polymorph selection. 

B. Peters, J. Chem. Phys. 135, 044107 (2011)

B. Peters, J. Chem. Phys. 131, 224103, (2009)