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

Abstract

Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J. F. Lutsko and M. A. Durán-Olivencia, Classical nucleation theory from a dynamical approach to nucleation, J. Chem. Phys. 138, 244908 (2013).]. The present work extends this effort to the case of nucleation in confined systems such as small pores and vesicles. The finite available mass imposes a maximal supercritical cluster size and prohibits nucleation altogether if the system is too small. We quantity the effect of system size on the nucleation rate. We also discuss the effect of relaxing the capillary-model assumption of zero interfacial width resulting in significant changes in the nucleation barrier and nucleation rate.

Dynamical Density Functional Theory for Orientable Colloids Including Inertia and Hydrodynamic Interactions

“…On the other hand, it has been extensively used in statistical mechanics 17,44,67,80 . For instance, the same hypothesis underlies a recent derivation of a unified DDFT to include inertia and HIs 35 , and is also involved in modern theories describing nucleation of colloidal systems and macromolecules 26,[54][55][56] . Moreoever, the results obtained are in perfect agreement with experiments and simulations, corroborating the smallness of the error related to Equation (A.28) when it comes to describing systems of interacting colloidal particles.…”

General framework for nonclassical nucleation

“…This expression is not covariant, meaning that estimations made with it will depend on the choice of the order parameter [62]. However, the results produced by equation (D.5) and the covariant counterpart from one-parameter MeNT only differ slightly, as discussed in detail in previous works [46][47][48]. This way, we can use as a benchmark either where R max and λ are constants that must be provided to the model.…”

“…Therefore, describing the evolution of a single density fluctuation using FH would provide an alternative theory of nucleation. A decisive first step in this direction was the recent mesoscopic nucleation theory (MeNT) put forward in [45][46][47][48]. In MeNT the number of parameters (so-called order parameters) we may choose to effectively describe a nucleation cluster is free.…”

“…However, the rising complexity of such multi-parameter models means that exact expressions for observables, such as nucleation rate and cluster distribution, do not necessarily exist, even for the vanilla two-parameter model accounting for changes in the size and inner density of the cluster (the first necessary step towards a nonCNT). Under the MeNT picture, such observable quantities are approximated by utilizing the concepts of mean first-passage time (MFPT) and the equilibrium distribution derived from the corresponding Fokker-Planck equation, respectively [45][46][47][48]. Nevertheless, beyond the simplest one-parameter model, these approximations also rise in complexity, which might be an important factor that has hindered the applicability of MeNT so far.…”

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.…”