Solid nuclei and liquid droplets: A parallel treatment for 3 phase systems.

For solid phase self assembly into crystals or large diameter polymers, the presence of a liquid-liquid demixing transition has been known to have an accelerating effect on the nucleation process. We present a novel approach to the description of accelerated nucleation in which the formation of solid phase aggregates and liquid-like aggregates compete as parallel pathways to formation of dense phases. The central idea is that the small aggregates that would ultimately form the liquid phase are sufficiently labile to sample the configurations that would form the solid, so that the growing cluster begins as a liquid, and switches into growth as a solid when the aggregates have equal free energies. This can accelerate the reaction even when the liquid-demixed state is thermodynamically unfavorable. The rate-limiting barrier is therefore the energy at which there is a transition between liquid and solid, and the effective nucleus size is then concentration independent, even though for both nucleated demixing and nucleated crystallization, the nucleus size does depend on concentration. These ideas can be expressed in a chemical potential formalism that has been successfully used in nucleation of sickle hemoglobin, but not to our knowledge previously employed in describing LLD processes. The method is illustrated by considering existing data on Lysozyme.