Classical nucleation theory from a dynamical approach to nucleation

Abstract

It is shown that diffusion-limited classical nucleation theory (CNT) can be recovered as a simple limit of the recently proposed dynamical theory of nucleation based on fluctuating hydrodynamics (Lutsko, JCP 136, 034509 (2012)). The same framework is also used to construct a more realistic theory in which clusters have finite interfacial width. When applied to the dilute solution/dense solution transition in globular proteins, it is found that the extension gives corrections to the the nucleation rate even for the case of small supersaturations due to changes in the monomer distribution function and to the excess free energy. It is also found that the monomer attachement/detachment picture breaks down at high supersaturations corresponding to clusters smaller than about 100 molecules. The results also confirm the usual assumption that most important corrections to CNT can be acheived by means of improved estimates of the free energy barrier. The theory also illustrates two topics that have received considerable attention in the recent literature on nucleation: the importance sub-dominant corrections to the capillary model for the free energy and of the correct choice of the reaction coordinate.

Classical density functional study of wetting transitions on nanopatterned surfaces

“…These lead to a very rich picture of possible surface phase behaviour occurring over different length-scales, that call for cross-disciplinary fundamental investigations. Surface effects are also highly relevant to nucleation [13][14][15][16], droplet formation and growth [17,18], vapour-liquid-solid growth of nanowires [19,20], and burgeoning laboratory-on-a-chip technologies.…”

Mesoscopic nucleation theory for confined systems: A one-parameter model

“…which is also called "the metric" [30,31,34]. The inverse of this matrix is seen below to be interpretable as the matrix of state-dependent kinetic coefficients.…”

“…In other words, nucleation is found to be inhibited as a consequence of the size of the container in which the experiment is being carried out. On the other hand, nucleation rate is affected for a certain range of volumes when we compare it with the CNT prediction calculated for infinite systems [34]. Indeed, such a ratio shows a maximum for system sizes close to that which inhibits nucleation.…”

“…The main goal of this work is therefore to extend dCNT to take into consideration the conservation of mass required for a finite volume with the aim of further developing the classical theory. Following a similar procedure as that presented in a previous work [34], a nucleation-rate equation is readily obtained. It turns out that the confinement has a strong effect on the energy barrier and, thus, on the nucleation rate.…”

“…MeNT provides a general stochastic differential equation (SDE) for the evolution of an arbitrary number of order parameters characterizing the number density field. When the simplest case is considered, which is a single-order parameter, a straightforward connection with CNT is found [34]. Such a reformulation of CNT, hereafter called dynamical CNT (dCNT), sheds light on the weaknesses of the classical derivation and can be used to construct a more realistic theory in which clusters have finite interfacial width.…”