Experimental evidence for two-step nucleation in colloidal crystallization

Micro-structural Change During Nucleation: From Nucleus To Bicontinuous Morphology

Although the microstructure of coexistence phase provides direct insights of the nucleation mechanism and their change is substantial in the phase transition, their study is limited due to the lack of suitable tools capturing the thermodynamically unstable transient states. We resolve this problem in computational study by introducing a generalized canonical ensemble simulation and investigate the morphological change of the nucleus during the water evaporation and condensation. We find that at very low pressure, where the transition is first order, classical nucleation theory holds approximately. A main nucleus is formed in the supersaturation near spinodal, and the overall shape of the nucleus is finite and compact. On increasing the pressure of the system, more nuclei are formed even before spinodal. They merge into a larger nuclei with a smaller free energy penalty to form ramified shapes. We suggest order parameters to describe the extent of fluctuation, and their relation to the free energy profile.

Self-organized target and spiral patterns through the "coffee ring" effect

We studied the precipitation pattern of fullerene C60 nanocrystals generated through the evaporation of a confined liquid bridge. In contrast to the usual "coffee ring" pattern, both target and spiral patterns were observed. The characteristics of the pattern critically depended on the concentration of the solution, the temperature, and the level of vacuum. In addition, the morphology of the microscopic precipitates varied greatly as a function of these experimental parameters. This pattern formation can be interpreted as a two-step rhythmic nucleation/precipitation of fullerene crystals during receding motion of the contact line. Symmetric motion of the contact line produces a target pattern, and the propagation of distortion of the liquid interface caused by a disturbance generates a spiral pattern.

Do protein crystals nucleate within dense liquid clusters?

Protein-dense liquid clusters are regions of high protein concentration that have been observed in solutions of several proteins. The typical cluster size varies from several tens to several hundreds of nanometres and their volume fraction remains below 10(-3) of the solution. According to the two-step mechanism of nucleation, the protein-rich clusters serve as locations for and precursors to the nucleation of protein crystals. While the two-step mechanism explained several unusual features of protein crystal nucleation kinetics, a direct observation of its validity for protein crystals has been lacking. Here, two independent observations of crystal nucleation with the proteins lysozyme and glucose isomerase are discussed. Firstly, the evolutions of the protein-rich clusters and nucleating crystals were characterized simultaneously by dynamic light scattering (DLS) and confocal depolarized dynamic light scattering (cDDLS), respectively. It is demonstrated that protein crystals appear following a significant delay after cluster formation. The cDDLS correlation functions follow a Gaussian decay, indicative of nondiffusive motion. A possible explanation is that the crystals are contained inside large clusters and are driven by the elasticity of the cluster surface. Secondly, depolarized oblique illumination dark-field microscopy reveals the evolution from liquid clusters without crystals to newly nucleated crystals contained in the clusters to grown crystals freely diffusing in the solution. Collectively, the observations indicate that the protein-rich clusters in lysozyme and glucose isomerase solutions are locations for crystal nucleation.

On the question of two-step nucleation in protein crystallization

We report a real-time study on protein crystallization in the presence of multivalent salts using small angle X-ray scattering (SAXS) and optical microscopy, focusing particularly on the nucleation mechanism as well as on the role of the metastable intermediate phase (MIP). Using bovine beta-lactoglobulin as a model system in the presence of the divalent salt CdCl2, we have monitored the early stage of crystallization kinetics which demonstrates a two-step nucleation mechanism: protein aggregates form a MIP, which is followed by the nucleation of crystals within the MIP. Here we focus on characterizing and tuning the structure of the MIP using salt and the related effects on the two-step nucleation kinetics. The results suggest that increasing the salt concentration near the transition zone pseudo-c** enhances the energy barrier for both MIPs and crystal nucleation, leading to slow growth. The structural evolution of the MIP and its effect on subsequent nucleation is discussed based on the growth kinetics. The observed kinetics can be well described, using a rate-equation model based on a clear physical two-step picture. This real-time study not only provides evidence for a two-step nucleation process for protein crystallization, but also elucidates the role and the structural signature of the MIPs in the nonclassical process of protein crystallization.

Controlling enantiomeric populations in fluctuating Brownian monolayers of chiral colloids

An ideal parallelogram platelet, although achiral in 3D, has an identifiable chirality when confined in a 2D monolayer. We lithographically fabricate microscale parallelogram platelets, disperse them in an aqueous surfactant solution, and allow them to settle towards a lower glass wall. To reduce the thermal-gravitational height, we add polystyrene nanospheres as a depletion agent to create a depletion attraction between the parallelograms and the wall. Surprisingly, by increasing the volume fraction of the depletion agent, we show that a nearly enantiopure monolayer can be created. We explain this by developing a model of 2D monolayer formation based on anisotropic facial attractions; one face of a platelet is more strongly attracted to the wall than the other as a consequence of an anisotropy introduced by the lithographic process. We study enantiopure Brownian systems of parallelograms as a function of particle area fraction and show that oblique chiral crystals form at high densities. By mixing parallelogram platelets printed in opposite senses, we also dictate the chiral ratio in the monolayer over the entire possible range. This approach is not limited to parallelograms and provides a means for tuning the chiral ratio in fluctuating 2D monolayers composed of a wide variety of chiral shapes.

Real-time observation of nonclassical protein crystallization kinetics

We present a real-time study of protein crystallization of bovine β-lactoglobulin in the presence of CdCl(2) using small-angle X-ray scattering and optical microscopy. From observing the crystallization kinetics, we propose the following multistep crystallization mechanism that is consistent with our data. In the first step, an intermediate phase is formed, followed by the nucleation of crystals within the intermediate phase. During this period, the number of crystals increases with time, but the crystal growth is slowed down by the surrounding dense intermediate phase due to the low mobility. In the next step, the intermediate phase is consumed by nucleation and slow growth, and the crystals are exposed to the dilute phase. In this stage, the number of crystals becomes nearly constant, whereas the crystals grow rapidly due to access to the free protein molecules in the dilute phase. This real-time study not only provides evidence for a two-step nucleation process for protein crystallization but also elucidates the role and the structural signature of the metastable intermediate phase in this process.

Recent advances in the understanding of two-step nucleation of protein crystals

The two-step mechanism of nucleation of crystals in solutions posits that the formation of crystal nuclei occurs within structures of extended lifetimes, in which the nucleating solute is at high concentration. The validity of this mechanism has been demonstrated for proteins, small-molecule organic and inorganic materials, colloids, and polymers. Due to large molecule sizes, proteins are an ideal system to study the details of this nucleation pathway, in particular the formation mechanisms of the nucleation precursors and the associated physico-chemical rules. The precursors of protein crystal nuclei are protein-rich clusters of sizes ∼100 nm that contain 10 000–100 000 molecules and occupy less than 10⁻³of the total solution volume. Here we demonstrate, using oblique illumination microscopy, the liquid nature of the clusters of the protein lysozyme and reveal their inhomogeneous structure. We test a hypothesis put forth by theory that clusters primarily consist of transient protein oligomers. For this, we explore how varying the strength of the Coulomb interaction affects the cluster characteristics. We find that the cluster’s size is insensitive to variations of pH and ionic strength. In contrast, the addition of urea, a chaotropic agent that leads to protein unfolding, strongly decreases the cluster size. Shear stress, a known protein denaturant, induced by bubbling of the solutions with an inert gas, elicits a similar response. These observations support partial protein unfolding, followed by dimerization, as the mechanism of cluster formation. The amide hydrogen–deuterium exchange, monitored by nuclear magnetic resonance, highlights that lysozyme conformational flexibility is a condition for the formation of the protein-rich clusters and facilitates the nucleation of protein crystals.

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.

Melting of a finite-sized two-dimensional colloidal crystal

We have studied the melting process of a finite-sized two-dimensional colloidal crystal by video microscopy. The local area fraction ϕ and the local hexatic orientational order parameter ψ(6) have been evaluated for respective Voronoi cells in the crystal. The histogram of ϕ exhibits a peak and the peak ϕ continuously decreases with the time elapsed. The histogram of |ψ(6)| shows an abrupt broadening for ϕ < 0.65. This critical value of ϕ is the transition point between the hexatic and dense liquid phases in finite crystal. We have also evaluated ϕ and |ψ(6)| as a function of the distance from the center of the crystal r. ϕ(r) is almost constant within the crystal and monotonously decreases with the time elapsed. |ψ(6)(r)| gradually decreases with r but there is the core with |ψ(6) = 1 at earlier time stage. The temporal change of the average ϕ within the crystal is qualitatively explained by the slow diffusion of the particles situated at the crystal edge. The steric repulsion between the particles within the crystal enhances the expansion rate of the crystal edge. Overall melting behavior is same in the crystals with different sizes. We have also studied the melting of a finite-sized crystal composed of soft-core particles by Brownian dynamics simulation and verified the finite-size effect on the melting process. The simulated behavior is qualitatively in good agreement with the experimental results.

Nucleation precursors in protein crystallization

Protein crystal nucleation is a central problem in biological crystallography and other areas of science, technology and medicine. Recent studies have demonstrated that protein crystal nuclei form within crucial precursors. Here, methods of detection and characterization of the precursors are reviewed: dynamic light scattering, atomic force microscopy and Brownian microscopy. Data for several proteins provided by these methods have demonstrated that the nucleation precursors are clusters consisting of protein-dense liquid, which are metastable with respect to the host protein solution. The clusters are several hundred nanometres in size, the cluster population occupies from 10(-7) to 10(-3) of the solution volume, and their properties in solutions supersaturated with respect to crystals are similar to those in homogeneous, i.e. undersaturated, solutions. The clusters exist owing to the conformation flexibility of the protein molecules, leading to exposure of hydrophobic surfaces and enhanced intermolecular binding. These results indicate that protein conformational flexibility might be the mechanism behind the metastable mesoscopic clusters and crystal nucleation. Investigations of the cluster properties are still in their infancy. Results on direct imaging of cluster behaviors and characterization of cluster mechanisms with a variety of proteins will soon lead to major breakthroughs in protein biophysics.

Role of clusters in nonclassical nucleation and growth of protein crystals

The development of multistep nucleation theory has spurred on experimentalists to find intermediate metastable states that are relevant to the solidification pathway of the molecule under interest. A great deal of studies focused on characterizing the so-called "precritical clusters" that may arise in the precipitation process. However, in macromolecular systems, the role that these clusters might play in the nucleation process and in the second stage of the precipitation process, i.e., growth, remains to a great extent unknown. Therefore, using biological macromolecules as a model system, we have studied the mesoscopic intermediate, the solid end state, and the relationship that exists between them. We present experimental evidence that these clusters are liquid-like and stable with respect to the parent liquid and metastable compared with the emerging crystalline phase. The presence of these clusters in the bulk liquid is associated with a nonclassical mechanism of crystal growth and can trigger a self-purifying cascade of impurity-poisoned crystal surfaces. These observations demonstrate that there exists a nontrivial connection between the growth of the macroscopic crystalline phase and the mesoscopic intermediate which should not be ignored. On the other hand, our experimental data also show that clusters existing in protein solutions can significantly increase the nucleation rate and therefore play a relevant role in the nucleation process.

Self-assembly of colloidal polymers via depletion-mediated lock and key binding

We study the depletion-induced self-assembly of indented colloids. Using state-of-the-art Monte Carlo simulation techniques that treat the depletant particles explicitly, we demonstrate that colloids assemble by a lock-and-key mechanism, leading to colloidal polymerization. The morphology of the chains that are formed depends sensitively on the size of the colloidal indentation, with smaller values additionally permitting chain branching. In contrast to the case of spheres with attractive patches, Wertheim's thermodynamic perturbation theory fails to provide a fully quantitative description of the polymerization transition. We trace this failure to a neglect of packing effects and we introduce a modified theory that accounts better for the shape of the colloids, yielding improved agreement with simulation.

Entropy-driven crystal formation on highly strained substrates

In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropy-driven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substrate-mediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate.

Impurity partitioning during colloidal crystallization

We have found that an impurity partitioning takes place during growth of colloidal crystals, which was recognized by the fact that the impurity concentration in the solid (CS) was different from that in the initial solution (C0). The effective partition coefficient k(eff) (=CS/C0) was investigated for pure polystyrene and polystyrene dyed with fluorescent particles by changing the ratio of particle diameters d(imp)/d(cryst) and growth rate V. At each size ratio for the polystyrene impurity, k(eff) was less than unity and increased to unity with increasing V, whereas at a given growth rate, k(eff) increased to unity as d(imp)/d(cryst) approached unity. These results were consistent with the solute behavior analyzed using the Burton, Prim, and Slichter (BPS) model. The obtained k0, equilibrium partition coefficient, from a BPS plot increased as d(imp)/d(cryst) approached unity. In contrast, while the fluorescent particles also followed the BPS model, they showed higher k0 values than those of the same size of polystyrene particles. A k0 value greater than unity was obtained for impurities that were similar in size to the host particle. This behavior is attributed to the positive free energy of fusion associated with the incorporation of the fluorescent particles into the host matrix. Such positive free energy of fusion implies the presence of the enthalpy associated with interaction between particles.

Effect of confinement on melting behavior of cadmium arachidate Langmuir-Blodgett multilayer

The effect of confinement between two metallic layers on the melting behavior of a 13 monolayer cadmium arachidate (CdA) Langmuir-Blodgett (LB) multilayer has been studied. Temperature dependent diffraction measurements provide information about structural changes occurring in the film plane as well as in the out-of-plane direction. X-ray standing waves have been used to achieve depth selectivity in diffraction measurements. It is found that the difference in melting behavior of the surface and the bulk, which is observed in the film with free surface, disappears in the case of confined films; while the free surface transforms to hexaticlike phase via an intermediate smectic phase, confinement results in disappearance of this phase, and the sequence of transformations in the bulk and the interfacial regions becomes identical. Some anisotropy between (01 + 11¯) and (10) directions remains, with coherence along (10) direction decreasing at a faster rate. The confinement between metallic layers also significantly reduces the tilting of the chains observed at higher temperature. Further, both in the case of film with free surface and confined films, melting at the surface/interface occurs at a lower temperature as compared to the bulk.

Nucleation and growth of thermoreversible polymer gels

We study the spatiotemporal low-frequency microrheology of a gelatin gel during the sol-gel transition after a fast temperature quench by tracking the motion of embedded colloidal particles. From the particle dynamics two different mechanisms responsible for the gelation of the sol phase can be identified: a fast process associated to the local nucleation of triple helices and a slow fiber growth triggered by presence of an intact network. We associate the latter to a gelation front propagating into the sol phase whose speed depends linearly on the quench depth and which accelerates the local rate of the sol-gel transition.

Temperature as an external field for colloid-polymer mixtures: 'quenching' by heating and 'melting' by cooling

We investigate the response to temperature of a well-known colloid-polymer mixture. At room temperature the gas-liquid critical value of the second virial coefficient of the effective pairwise colloid-colloid interaction for the Asakura-Oosawa model predicts the onset of gelation observed experimentally with remarkable accuracy. Upon cooling the system the effective attraction between colloids induced by polymer depletion is reduced, because the polymer radius of gyration decreases as the θ-temperature is approached. Paradoxically this raises the effective temperature, leading to 'melting' of colloidal gels. We find that the Asakura-Oosawa model of effective colloid interactions, together with a simple description of the polymer temperature response, provides a quantitative description of the observed location of the fluid-gel transition in the colloid volume fraction polymer reservoir number density plane. Further, we present evidence for enhancement of crystallization rates in the vicinity of the metastable critical point.

Colloidal cluster crystallization dynamics

The crystallization dynamics of a colloidal cluster is modeled using a low-dimensional Smoluchowski equation. Diffusion mapping shows that two order parameters are required to describe the dynamics. Using order parameters as metrics for condensation and crystallinity, free energy, and diffusivity landscapes are extracted from brownian dynamics simulations using bayesian inference. Free energy landscapes are validated against Monte Carlo simulations, and mean first-passage times are validated against dynamic simulations. The resulting model enables a low-dimensional description of colloidal crystallization dynamics.

Nucleation pathway of core-shell composite nucleus in size and composition space and in component space

The kinetics of nucleation of a core-shell composite nucleus that consists of a core of stable final phase surrounded by a wetting layer of intermediate metastable phase is studied using the kinetic theory of binary nucleation not only in the size and composition space but also in the component space. The steady-state solution of the Fokker-Planck equation is considered. Various formulas for the critical nucleus at the saddle point as well as for the postcritical nucleus are derived. The kinetics of nucleation at the saddle point is more appropriately characterized in the size and composition space, while the kinetics of the postcritical nucleus is more appropriately described in the component space. Although both the free-energy landscape and the reaction rates play decisive role to determine the kinetics of nucleation at the saddle point, the details of the free-energy landscape are irrelevant to the kinetics of the postcritical nucleus.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

The microscopic pathway to crystallization in supercooled liquids

Despite its fundamental and technological importance, a microscopic understanding of the crystallization process is still elusive. By computer simulations of the hard-sphere model we reveal the mechanism by which thermal fluctuations drive the transition from the supercooled liquid state to the crystal state. In particular we show that fluctuations in bond orientational order trigger the nucleation process, contrary to the common belief that the transition is initiated by density fluctuations. Moreover, the analysis of bond orientational fluctuations shows that these not only act as seeds of the nucleation process, but also i) determine the particular polymorph which is to be nucleated from them and ii) at high density favour the formation of fivefold structures which can frustrate the formation of crystals. These results can shed new light on our understanding of the relationship between crystallization and vitrification.

Crystal Nucleation without Supersaturation

Classical nucleation theory (CNT) has been extensively employed to interpret crystal nucleation phenomena and postulates the formation of an ordered crystalline nucleus directly from vapor or solution. Here, we provide the first experimental demonstration of a two-step mechanism that facilitates deposition of crystals on solid surfaces from vapor. Crucially, this occurs from saturated vapor without the need for supersaturation, conditions that, according to CNT, cannot lead to direct deposition of crystals from vapor. Instead, the process relies on condensation of supercooled liquid in surface cavities below the melting point. Crystals then nucleate in this liquid, leading to rapid deposition of more solid. Such a mechanism has been postulated for atmospheric nucleation of ice on aerosol particles and may have analogies in the crystallization of biominerals via amorphous precursor phases.

Direct observation of nanoparticle superlattice formation by using liquid cell transmission electron microscopy

Direct imaging of nanoparticle solutions by liquid phase transmission electron microscopy has enabled unique in situ studies of nanoparticle motion and growth. In the present work, we report on real-time formation of two-dimensional nanoparticle arrays in the very low diffusive limit, where nanoparticles are mainly driven by capillary forces and solvent fluctuations. We find that superlattice formation appears to be segregated into multiple regimes. Initially, the solvent front drags the nanoparticles, condensing them into an amorphous agglomerate. Subsequently, the nanoparticle crystallization into an array is driven by local fluctuations. Following the crystallization event, superlattice growth can also occur via the addition of individual nanoparticles drawn from outlying regions by different solvent fronts. The dragging mechanism is consistent with simulations based on a coarse-grained lattice gas model at the same limit.

Nucleation pathways of clathrate hydrates: effect of guest size and solubility

Understanding the microscopic mechanism of nucleation of clathrate hydrates is important for their use in hydrogen storage, CO(2) sequestration, storage and transport of natural gas, and the prevention of the formation of hydrate plugs in oil and gas pipelines. These applications involve hydrate guests of varied sizes and solubility in water that form different hydrate crystal structures. Nevertheless, molecular studies of the mechanism of nucleation of hydrates have focused on the single class of small hydrophobic guests that stabilize the sI crystal. In this work, we use molecular dynamics simulations with a very efficient coarse-grained model to elucidate the mechanisms of nucleation of clathrate hydrates of four model guests that span a 2 orders of magnitude range in solubility in water and that encompass sizes which stabilize each one a different hydrate structure (sI and sII, with and without occupancy of the dodecahedral cages). We find that the overall mechanism of clathrate nucleation is similar for all guests and involves a first step of formation of blobs, dense clusters of solvent-separated guest molecules that are the birthplace of the clathrate cages. Blobs of hydrophobic guests are rarer and longer-lived than those for soluble guests. For each guest, we find multiple competing channels to form the critical nuclei, filled dodecahedral (5(12)) cages, empty 5(12) cages, and a variety of filled large (5(12)6(n) with n = 2, 3, and 4) clathrate cages. Formation of empty dodecahedra is an important nucleation channel for all but the smallest guest. The empty 5(12) cages are stabilized by the presence of guests from the blob in their first solvation shell. Under conditions of high supercooling, the structure of the critical and subcritical nuclei is mainly determined by the size of the guest and does not reflect the cage composition or ordering of the stable or metastable clathrate crystals.

Histone-based self-assembly into DNA-wrapped meso-clusters

The recent discovery of meso-cluster phase includes not only colloidal molecules of synthetic polymer particles but also equilibrium protein clusters. Here we report self-assembly of histone protein into stable submicron clusters that can be generated even in centrifuged supernatants containing no initial aggregates. Furthermore, dark-field microscopy of the electrophoresis has verified charge reversal of individual histone clusters by adding DNA. We have determined the critical nucleotide concentration at which the electrophoretic mobility vanishes in three types of DNA, revealing the coexistence of nucleosomes with DNA-wrapped meso-clusters.

Melting of multilayer colloidal crystals confined between two walls

Video microscopy is employed to study the melting behaviors of multilayer colloidal crystals composed of diameter-tunable microgel spheres confined between two walls. We systematically explore film thickness effects on the melting process and on the phase behaviors of single crystal and polycrystalline films. Thick films (>4 layers) are observed to melt heterogeneously, while thin films (≤4 layers) melt homogeneously, even for polycrystalline films. Grain-boundary melting dominates other types of melting processes in polycrystalline films thicker than 12 layers. The heterogeneous melting from dislocations is found to coexist with grain-boundary melting in films between 5- and 12-layers. In dislocation melting, liquid nucleates at dislocations and forms lakelike domains embedded in the larger crystalline matrix; the "lakes" are observed to diffuse, interact, merge with each other, and eventually merge with large strips of liquid melted from grain boundaries. Thin film melting is qualitatively different: thin films homogeneously melt by generating many small defects which need not nucleate at grain boundaries or dislocations. For three- and four-layer thin films, different layers are observed to have the same melting point, but surface layers melt faster than bulk layers. Within our resolution, two- to four-layer films appear to melt in one step, while monolayers melt in two steps with an intermediate hexatic phase.

Nucleation

Crystallization starts with nucleation and control of nucleation is crucial for the control of the number, size, perfection, polymorphism and other characteristics of crystalline materials. This is particularly true for crystallization in solution, which is an essential part of processes in the chemical and pharmaceutical industries and a major step in physiological and pathological phenomena. There have been significant recent advances in the understanding of the mechanism of nucleation of crystals in solution. The foremost of these are the two-step mechanism of nucleation and the notion of the solution-crystal spinodal. According to the two-step mechanism, the crystalline nucleus appears inside pre-existing metastable clusters of size several hundred nanometers, which consist of dense liquid and are suspended in the solution. While initially proposed for protein crystals, the applicability of this mechanism has been demonstrated for small molecule organic materials, colloids, polymers, and biominerals. This mechanism helps to explain several long-standing puzzles of crystal nucleation in solution: nucleation rates which are many orders of magnitude lower than theoretical predictions, the significance of the dense protein liquid, and others. At high supersaturations typical of most crystallizing systems, the generation of crystal embryos occurs in the spinodal regime, where the nucleation barrier is negligible. The solution-crystal spinodal helps to understand the role of heterogeneous substrates in nucleation and the selection of crystalline polymorphs. Importantly, these ideas provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.

The two-step mechanism of nucleation of crystals in solution

The formation of crystalline nanoparticles starts with nucleation and control of nucleation is crucial for the control of the number, size, perfection, polymorph modification and other characteristics of particles. Recently, there have been significant advances in the understanding of the mechanism of nucleation of crystals in solution. The most significant of these is the two-step mechanism of nucleation, according to which the crystalline nucleus appears inside pre-existing metastable clusters of size several hundred nanometers, which consist of dense liquid and are suspended in the solution. While initially proposed for protein crystals, the applicability of this mechanism has been demonstrated for small-molecule organic and inorganic materials, colloids, and biominerals. This mechanism helps to explain several long-standing puzzles of crystal nucleation in solution: nucleation rates which are many orders of magnitude lower than theoretical predictions, nucleation kinetic dependencies with steady or receding parts at increasing supersaturation, the role of heterogeneous substrates for polymorph selection, the significance of the dense protein liquid, and others. More importantly, this mechanism provides powerful tools for control of the nucleation process by varying the solution thermodynamic parameters so that the volume occupied by the dense liquid shrinks or expands.

Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3D, and determine the line free energy in 2D and the height of the nucleation barrier in 2D and 3D for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that, in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close-packed structures (hcp) compete, while the simple cubic structure is unstable, and that phase preference can be tuned by changing the model parameters: close to the critical point the bcc structure is stable, while far from the critical point the fcc prevails, with an hcp stability domain in between. We note that with increasing distance from the critical point the equilibrium shapes vary from the sphere to specific faceted shapes: rhombic dodecahedron (bcc), truncated octahedron (fcc), and hexagonal prism (hcp). Solving the equation of motion of the PFC model supplied with conserved noise, solidification starts with the nucleation of an amorphous precursor phase, into which the stable crystalline phase nucleates. The growth rate is found to be time dependent and anisotropic; this anisotropy depends on the driving force. We show that due to the diffusion-controlled growth mechanism, which is especially relevant for crystal aggregation in colloidal systems, dendritic growth structures evolve in large-scale isothermal single-component PFC simulations. An oscillatory effective pair potential resembling those for model glass formers has been evaluated from structural data of the amorphous phase obtained by instantaneous quenching. Finally, we present results for eutectic solidification in a binary PFC model.