Formation of crystal nuclei near critical supersaturation in small volumes

Transient nucleation driven by solvent evaporation

We theoretically investigate homogeneous crystal nucleation in a solution containing a solute and a volatile solvent. The solvent evaporates from the solution, thereby continuously increasing the concentration of the solute. We view it as an idealized model for the far-out-of-equilibrium conditions present during the liquid-state manufacturing of organic electronic devices. Our model is based on classical nucleation theory, taking the solvent to be a source of the transient conditions in which the solute drops out of the solution. Other than that, the solvent is not directly involved in the nucleation process itself. We approximately solve the kinetic master equations using a combination of Laplace transforms and singular perturbation theory, providing an analytical expression for the nucleation flux. Our results predict that (i) the nucleation flux lags slightly behind a commonly used quasi-steady-state approximation. This effect is governed by two counteracting effects originating from solvent evaporation: while a faster evaporation rate results in an increasingly larger influence of the lag time on the nucleation flux, this lag time itself is found to decrease with increasing evaporation rate. Moreover, we find that (ii) the nucleation flux and the quasi-steady-state nucleation flux are never identical, except trivially in the stationary limit, and (iii) the initial induction period of the nucleation flux, which we characterize as a generalized induction time, decreases weakly with the evaporation rate. This indicates that the relevant time scale for nucleation also decreases with an increasing evaporation rate. Our analytical theory compares favorably with results from a numerical evaluation of the governing kinetic equations.

Nucleation of melt: From fundamentals to dispersed systems

The most evident aspects of a first order transition of a system from an old to a new phase, are the presence of a discontinuity at the interface between both phases and the thermal effects related to the latent heat exchanged with the surrounding environment. These effects are the result of a sequence of events promoted by thermodynamic conditions persisting over the equilibrium in a metastable state. The breakdown of metastability is promoted by infinitesimal energy fluctuations resulting in the germination of clusters of the new phase that can grow to a critical size (nucleus) and then develop or vanish. Examples of these sequences are common in various technological fields such as combustion, food processing, pharmaceutical manufacturing, condensation, and phase change heat transfer, etc. This work aims to highlight a logical path that leads the readers from the fundamental phenomenology to the most intricated aspects of the nucleation within dispersed systems such as oil-in-water emulsions. Differences between the homogeneous and heterogeneous mechanisms are, under the light of the Classical Nucleation Theory (CNT), presented in bulk and confined systems until defining a minimum confinement size. By collecting insights coming from a rich scientific literature mostly focused on the stability of emulsified systems, the discussion is then on the aspects related to the surface related mechanisms. Two main aspects are then considered: a) the wettability of the nucleating cluster by the surrounding melt; b) the affinity between the adsorbed layer, where a surfactant is located, and the oil melt phase (mainly n-alkanes and triacylglycerols with different moieties). In cases where nucleation is dominating over the dewetting of the nucleus, the contact angle can be considered as a constant value. The affinity in terms of molecular features between the surfactant and the oil phase can promote the template effect. Several factors seem to play a role in this interaction such as the thermal characteristics of the surfactant and comparable dimensions between the molecule (or fractions) of the dispersed compound and the tail of the surfactant.

Nucleation and superstabilization in small systems

Phase transitions are known to present peculiarities in small systems that are related to depletion effects of the ambient phase. Mass conservation affects the conditions of thermodynamic equilibrium between a nucleus of the new phase and the matrix as compared with nucleation in infinite systems. This finite-size effect is known to delay the phase transition but can also impede nucleation in very small systems as it stabilizes the initial state, originally metastable in infinite systems. In this work, we investigate this superstabilization effect in the context of classical nucleation theory in multicomponent solutions and we derive an analytical expression for the system size below which nucleation becomes thermodynamically impossible. Comparing with the exact solution, our simple result is shown to accurately predict the superstabilization effect, and can therefore be used, for instance, as a guideline for the design of novel nanomaterials.

Phase diagram of a binary mixture in a closed cavity

Normally, the phase diagram is reported as a property of the binary mixture. We show that the phase diagram (that is, the zones of thermodynamic stability of the states of the binary mixture) is also affected by the size of the container. We investigate the thermodynamic stability of the binary mixture in a closed cavity, and identify the zone in parameters where the binary mixture is heterogeneous in equilibrium (the zone of spinodal decomposition), the zone where the mixture is always homogeneous in equilibrium, and the zone where the transition between these two states is possible (the metastable nucleation zone). In addition, we investigate the properties of the smallest single droplet that may be in equilibrium in the closed cavity (for the given average concentration, all smaller droplets would always dissolve). We show that the size of such droplets depends on the cavity's size, as ∼L^{1/2}.

Supersaturation-induced hydrothermal formation of α-CaSO4·0.5H2O whiskers

Supersaturation-induced fast transformation from CaSO₄·2H₂O to α-CaSO₄·0.5H₂O was observed and the process followed the dissolution–precipitation and homogeneous nucleation mechanism according to classical nucleation theory.

Localizing and inducing primary nucleation

Do the differing properties of materials influence their nucleation mechanisms? We present different experimental approaches to study and control nucleation, and shed light on some of the factors affecting the nucleation process.

Crystals and crystallization in oil-in-water emulsions: implications for emulsion-based delivery systems

Many bioactive components intended for oral ingestion (pharmaceuticals and nutraceuticals) are hydrophobic molecules with low water-solubilities and high melting points, which poses considerable challenges to the formulation of oral delivery systems. Oil-in-water emulsions are often suitable vehicles for the encapsulation and delivery of this type of bioactive component. The bioactive component is usually dissolved in a carrier lipid phase by either dilution and/or heating prior to homogenization, and then the carrier lipid and water phases are homogenized to form an emulsion consisting of small oil droplets dispersed in water. The successful development of this kind of emulsion-based delivery system depends on a good understanding of the influence of crystals on the formation, stability, and properties of emulsions. This review article addresses the physicochemical phenomena associated with the encapsulation, retention, crystallization, release, and absorption of hydrophobic bioactive components within emulsions. This knowledge will be useful for the rational formulation of effective emulsion-based delivery systems for oral delivery of crystalline hydrophobic bioactive components in the food, health care, and pharmaceutical industries.

Nucleation on active centers in confined volumes

Kinetic equations describing nucleation on active centers are solved numerically to determine the number of supercritical nuclei, nucleation rate, and the number density of nuclei for formation both of droplets from vapor and also crystalline phase from vapor, solution, and melt. Our approach follows standard nucleation model, when the exhaustion of active centers is taken into account via the boundary condition, and thus no additional equation (expressing exhaustion of active centers) is needed. Moreover, we have included into our model lowering of supersaturation of a mother phase as a consequence of the phase transition process within a confined volume. It is shown that the standard model of nucleation on active centers (Avrami approach) gives faster exhaustion of active centers as compared with our model in all systems under consideration. Nucleation rate (in difference to standard approach based on Avrami model) is equal to the time derivative of the total number of nuclei and reaches some maximum with time. At lower nucleation barrier (corresponding to higher initial supersaturation or lower wetting angle of nucleus on the surface of active center) the exhaustion of active centers is faster. Decrease in supersaturation of the mother phase is faster at higher number of active centers.