Nucleation of colloids and macromolecules: does the nucleation pathway matter?

A microscopic approach to crystallization: Challenging the classical/non-classical dichotomy

We present a fundamental framework for the study of crystallization based on a combination of classical density functional theory and fluctuating hydrodynamics that is free of any assumptions regarding order parameters and that requires no input other than molecular interaction potentials. We use it to study the nucleation of both droplets and crystalline solids from a low-concentration solution of colloidal particles using two different interaction potentials. We find that the nucleation pathways of both droplets and crystals are remarkably similar at the early stages of nucleation until they diverge due to a rapid ordering along the solid pathways in line with the paradigm of "non-classical" crystallization. We compute the unstable modes at the critical clusters and find that despite the non-classical nature of solid nucleation, the size of the nucleating clusters remains the principle order parameter in all cases, supporting a "classical" description of the dynamics of crystallization. We show that nucleation rates can be extracted from our formalism in a systematic way. Our results suggest that in some cases, despite the non-classical nature of the nucleation pathways, classical nucleation theory can give reasonable results for solids but that there are circumstances where it may fail. This contributes a nuanced perspective to recent experimental and simulation work, suggesting that important aspects of crystal nucleation can be described within a classical framework.

Nudged elastic band calculation of the binding potential for liquids at interfaces

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential g(h) which is an excess free energy per unit area that depends on the liquid film height h. Given a microscopic theory for the liquid, to determine g(h), one must calculate the free energy for liquid films of any given value of h, i.e., one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of h, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate g(h) and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We also show that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.

Classical nucleation theory for solute precipitation amended with diffusion and reaction processes near the interface

During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its average bulk value. This feature affects the rates of attachment and detachment of solute atoms at the interface, and, therefore, the entire nucleation-growth kinetics is altered. Unless quite obvious, this effect has been ignored in classical nucleation theory. To illustrate the results of this approach, for the case of homogeneous nucleation, we calculate the total solubility and the nucleation rate as functions of two parameters of the model (the reduced interface energy and the inverse second Damköhler number), and we compare these results to the classical ones. One can conclude that discrepancies with classical nucleation theory are great in the diffusion-limited regime, when the rate of bulk diffusion is small compared to the rate of interface reactions, while in the opposite interface-limited case they vanish.

Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation

Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer.

A two-parameter extension of classical nucleation theory

A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard classical nucleation theory (CNT). The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that CNT underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier.

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

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.

Water in the formation of biogenic minerals: peeling away the hydration layers

Minerals of biogenic origin form and crystallize from aqueous environments at ambient temperatures and pressures. The in vivo environment either intracellular or intercellular, contains many components that modulate both the activity of the ions which associate to form the mineral, as well as the activity and structure of the crowded water. Most of the studies about the mechanism of mineralization, that is, the detailed pathways by which the mineral ions proceed from solution to crystal state, have been carried out in relatively dilute solutions and clean solutions. These studies have considered both thermodynamic and kinetic controls. Most have not considered the water itself. Is the water a passive bystander, or is it intimately a participant in the mineral ion densification reaction? A wide range of experiments show that the mineralization pathways proceed through a series of densification stages with intermediates, such as a "dense liquid" phase and the prenucleation clusters that form within it. This is in contrast to the idea of a single step phase transition, but consistent with the Gibbs concept of discontinuous phase transitions from supersaturated mother liquor to crystal. Further changes in the water structure at every surface and interface during densification guides the free energy trajectory leading to the crystalline state. In vertebrates, mineralization takes place in a hydrated collagen matrix, thus water must be considered as a direct participant. Although different in detail, the crystallization of calcium phosphates, as apatite, and calcium carbonates, as calcite, are mechanistically identical from the viewpoint of water.