Classical nucleation theory from a dynamical approach to nucleation

An Overview of Modeling Approaches for Compositional Control in III-V Ternary Nanowires

Modeling of the growth process is required for the synthesis of III-V ternary nanowires with controllable composition. Consequently, new theoretical approaches for the description of epitaxial growth and the related chemical composition of III-V ternary nanowires based on group III or group V intermix were recently developed. In this review, we present and discuss existing modeling strategies for the stationary compositions of III-V ternary nanowires and try to systematize and link them in a general perspective. In particular, we divide the existing approaches into models that focus on the liquid-solid incorporation mechanisms in vapor-liquid-solid nanowires (equilibrium, nucleation-limited, and kinetic models treating the growth of solid from liquid) and models that provide the vapor-solid distributions (empirical, transport-limited, reaction-limited, and kinetic models treating the growth of solid from vapor). We describe the basic ideas underlying the existing models and analyze the similarities and differences between them, as well as the limitations and key factors influencing the stationary compositions of III-V nanowires versus the growth method. Overall, this review provides a basis for choosing a modeling approach that is most appropriate for a particular material system and epitaxy technique and that underlines the achieved level of the compositional modeling of III-V ternary nanowires and the remaining gaps that require further studies.

Leveraging dewetting models rather than nucleation models: current crystallographic challenges in interfacial and nanomaterials research

No scientific model has shaped crystallography as much as the classical nucleation theory (CNT). The majority of all growth processes and particle formation processes are attributed to the CNT. However, alternative descriptions exist that may be better suited to explain material formation under certain conditions. One of these alternatives is the dewetting theory (DWT). To describe the possibilities of DWT in more detail, we selected three material systems for three current application areas: Gold particles on silicon as catalysts for nanowire growth, indium particles on molybdenum as precursor material in novel solar cell concepts, and silicon layers on silicon germanium as potential wells in semiconductor quantum computers. Each of these material systems showed particular advantages of DWT over CNT. For example, the properties of surface particles with high atomic mobility could be described more realistically using DWT. Yet, there were clear indications that the DWT is not yet complete and that further research is needed to complete it. In particular, modern crystallographic challenges could serve this purpose, for example the development of semiconductor quantum computers, in order to re-evaluate known models such as the CNT and DWT and adapt them to the latest state of science and technology. For the time being, this article will give an outlook on the advantages of the DWT today and its potential for future research in crystallography.

Nucleation precursors compatible with a single energy barrier: catching the nonclassical culprit

In this work we link experimental results of SrSO4 precipitation with a mesoscopic nucleation model (MeNT) to stride towards a cohesive view of the nucleation process integrating both classical and...

The seven deadly sins: When computing crystal nucleation rates, the devil is in the details

The formation of crystals has proven to be one of the most challenging phase transformations to quantitatively model-let alone to actually understand-be it by means of the latest experimental technique or the full arsenal of enhanced sampling approaches at our disposal. One of the most crucial quantities involved with the crystallization process is the nucleation rate, a single elusive number that is supposed to quantify the average probability for a nucleus of critical size to occur within a certain volume and time span. A substantial amount of effort has been devoted to attempt a connection between the crystal nucleation rates computed by means of atomistic simulations and their experimentally measured counterparts. Sadly, this endeavor almost invariably fails to some extent, with the venerable classical nucleation theory typically blamed as the main culprit. Here, we review some of the recent advances in the field, focusing on a number of perhaps more subtle details that are sometimes overlooked when computing nucleation rates. We believe it is important for the community to be aware of the full impact of aspects, such as finite size effects and slow dynamics, that often introduce inconspicuous and yet non-negligible sources of uncertainty into our simulations. In fact, it is key to obtain robust and reproducible trends to be leveraged so as to shed new light on the kinetics of a process, that of crystal nucleation, which is involved into countless practical applications, from the formulation of pharmaceutical drugs to the manufacturing of nano-electronic devices.

Surface energy driven miscibility gap suppression during nucleation of III–V ternary alloys

We have explained how the surface energy influences the miscibility gap during nucleation from a liquid melt.

Advances in microcellular injection moulding

Injection moulding is a well-established replication process for the cost-effective manufacture of polymer-based components. The process has different applications in fields such as medical, automotive and aerospace. To expand the use of polymers to meet growing consumer demands for increased functionality, advanced injection moulding processes have been developed that modifies the polymer to create microcellular structures. Through the creation of microcellular materials, additional functionality can be gained through polymer component weight and processing energy reduction. Microcellular injection moulding shows high potential in creating innovation green manufacturing platforms. This review article aims to present the significant developments that have been achieved in different aspects of microcellular injection moulding. Aspects covered include core-back, gas counter pressure, variable thermal tool moulding and other advanced technologies. The resulting characteristics of creating microcellular injection moulding components through both plasticising agents and nucleating agents are presented. In addition, the article highlights potential areas for research exploitation. In particular, acoustic and thermal applications, nano-cellular injection moulding parts and developments of more accurate simulations.

Microcanonical Nucleation Theory for Anisotropic Materials Validated on Alumina Clusters

Nucleation kinetics in gas phase remains an open issue with no general model. The derivation of the reaction constants assuming a canonical ensemble fails to describe anisotropic materials such as oxides. We have developed a general and versatile model using activated complex kinetics with a microcanonical approach. This approach handles the kinetics issue in cluster growth when the transient nature of the processes hinders the use of the canonical ensemble. The model efficiently reproduces experimental size distributions of alumina clusters formed by laser ablation with different buffer gas densities, including magic numbers. We show that the thermodynamic equilibrium is not reached during the growth. The bounding energy measured is 10 times lower than the one deduced from DFT calculation, but also the one expected from the bulk cohesive energy.

Controlled protein crystal nucleation in microreactors: the effect of the droplet volume versus high supersaturation ratios

Control of the enhanced lysozyme nucleation under high supersaturation ratios for a broad range of droplet volumes.

Derivation of an exact, nonequilibrium framework for nucleation: Nucleation is a priori neither diffusive nor Markovian

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a nonequilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, i.e., the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics.

Microscopic aspects of wetting using classical density functional theory

Wetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid-fluid and fluid-substrate intermolecular interactions brings about an entire 'zoo' of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid-gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid-gas interface is already highly complex and non-trivial.

Classical density functional study of wetting transitions on nanopatterned surfaces

Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.

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.

Observing classical nucleation theory at work by monitoring phase transitions with molecular precision

It is widely accepted that many phase transitions do not follow nucleation pathways as envisaged by the classical nucleation theory. Many substances can traverse intermediate states before arriving at the stable phase. The apparent ubiquity of multi-step nucleation has made the inverse question relevant: does multistep nucleation always dominate single-step pathways? Here we provide an explicit example of the classical nucleation mechanism for a system known to exhibit the characteristics of multi-step nucleation. Molecular resolution atomic force microscopy imaging of the two-dimensional nucleation of the protein glucose isomerase demonstrates that the interior of subcritical clusters is in the same state as the crystalline bulk phase. Our data show that despite having all the characteristics typically associated with rich phase behaviour, glucose isomerase 2D crystals are formed classically. These observations illustrate the resurfacing importance of the classical nucleation theory by re-validating some of the key assumptions that have been recently questioned.

Many nanoscale systems can form ordered microphases through non-classical multistep nucleation. Here, the authors report that glucose isomerase, which is known to exhibit the characteristics of multi-step nucleation in 3D, nucleates along the pathway predicted by classical nucleation theory in 2D.