Experimental evidence for two-step nucleation in colloidal crystallization

The pathway and kinetics of hierarchical assembly of ionic oligomers into a lyotropic columnar phase

Ionic benzene-1,3,5-tricarboxamide (BTA) molecules can self-assemble into hollow cylinders which further arrange into columnar phases in water. In situ investigations suggest a multi-step pathway of supramolecular assembly via formation of dispersed molecular aggregates followed by a less ordered intermediate phase before the equilibrium columnar phase is formed. The pathway and kinetics of the formation of lyotropic LC phases through hierarchical supramolecular assembly are similar to non-classical crystallization, in line with an emerging holistic view on crystallization and self-assembly.

Polymorphic transition and nucleation pathway of barium dititanate (BaTi2O5) during crystallization from undercooled liquid

The nucleation pathway plays an important role in vitrification, preparation of glass-ceramic composites and synthesis of metastable materials. In this paper, we studied the nucleation pathway of a novel ferroelectric BaTi₂O₅ (BT2) during crystallization from undercooled liquid by aerodynamic levitation (ADL) containerless processing and structural analysis. An interesting polymorphic transition of BT2 regulated by the undercooling was observed during the crystallization process: the ferroelectric monoclinic phase (γ-BT2) was fabricated at low undercoolings and the paraelectric orthorhombic metastable phase (β-BT2) was obtained from hypercooled liquid. This polymorphic transition phenomenon corresponds to a non-classical nucleation pathway: metastable β-BT2 preferentially nucleates from undercooled melt and γ-BT2 is generated from β phase by solid-state phase transition. The two-step nucleation pathway stems from the structural heredity between the undercooled liquid and crystals. A stronger structural homology exists between the undercooled melt and β-BT2 than γ-BT2 based on diffraction data and atomic configurations analysis. This structural homology coupled with nucleation barrier calculation was used to elucidate the non-classical nucleation pathway of BT2 crystallization: the similarity of the structural unit (Ti-O polyhedra) between the undercooled liquid and the metastable β-BT2 reduces the nucleation barrier and contributes to the preferential precipitation of β-like clusters. This work reveals the formation route of BT2 from cooling melt, which not only benefits the synthesis and application of this novel functional material but also provides a guideline of the crystallization process of titanates from melt at atomic level.

Gas Bubbles in Electrochemical Gas Evolution Reactions

Electrochemical gas evolution reactions are of vital importance in numerous electrochemical processes including water splitting, chloralkaline process, and fuel cells. During gas evolution reactions, gas bubbles are vigorously and constantly forming and influencing these processes. In the past few decades, extensive studies have been performed to understand the evolution of gas bubbles, elucidate the mechanisms of how gas bubbles impact gas evolution reactions, and exploit new bubble-based strategies to improve the efficiency of gas evolution reactions. In this feature article, we summarize the classical theories as well as recent advancements in this field and provide an outlook on future research topics.

Can the pathway of stepwise nucleation be predicted and controlled?

Predicting the critical nucleus size and the nucleation barrier is of central importance in controlling the dynamics of nucleation. However, as the nucleation of a crystal involves intermediate states, the prediction becomes inaccessible with currently available models. Here, we show that based on single-particle level observations, the properties of crystal nuclei in a microscopic stepwise nucleation (MSN) can be well-quantified by incorporating the size and structure order parameter into the formula of free energy without prior knowledge of interfacial tension. The quantified free energy reveals that the intermediate structures arise from thermodynamics rather than kinetics. Precritical and postcritical nuclei are distinct not only in structure but also in the mechanism of crystalline ordering. The relative stability of intermediate structures and the pathway of nucleation can be well-controlled by supercooling. Our studies offer a successful approach to quantify MSN and shed new light on resolving the long-standing discrepancies between simulations and experiments.

How crystals form: A theory of nucleation pathways

Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical nucleation pathways based on no input other than the interaction potential of the particles making up the system. The theory is formulated directly in terms of the density field, thus forgoing the need to define collective variables. It is illustrated by application to diffusion-limited nucleation of macromolecules in solution for both liquid-liquid separation and crystallization. Both involve nonclassical pathways with crystallization, in particular, proceeding by a two-step mechanism consisting of the formation of a dense-solution droplet followed by ordering originating at the core of the droplet. Furthermore, during the ordering, the free-energy surface shows shallow minima associated with the freezing of liquid into solid shells, which may shed light on the widely observed metastability of nanoscale clusters.

Observable Two-Step Nucleation Mechanism in Solid-State Formation of Tungsten Carbide

The nucleation of crystals from ubiquitous solid-state reactions impacts a wide range of natural and synthetic processes and is fundamental to physical and chemical synthesis. However, the microscopic organization mechanism of amorphous precursors to nanoscale clusters of ordered atoms (nucleus) in an all-solid environment is inaccessible by common experimental probes. Here, by using in situ transmission electron microscopy in combination with theoretical simulations, we show in the reactive formation of a metal carbide that nucleation actually occurs via a two-step mechanism, in which a spinodal-structured amorphous intermediate reorganizes from an amorphous precursor and precedes the emergence of a crystalline nucleus, rather than direct one-step nucleation from classical consideration. We further isolated a series of sophisticated dynamics during formation and development of the nucleus in real-space and interpreted them by thermodynamic favorability. We anticipate that such an indirect organization mechanism which contains a metastable intermedium among the free energy gap between precursors and nanocrystals has its chance in underlying most solid-state crystallizations, whereas the as-established experimental method represents a step forward in exploring fundamentals in chemical reaction, material engineering, etc.

Biomolecular Assemblies: Moving from Observation to Predictive Design

Biomolecular assembly is a key driving force in nearly all life processes, providing structure, information storage, and communication within cells and at the whole organism level. These assembly processes rely on precise interactions between functional groups on nucleic acids, proteins, carbohydrates, and small molecules, and can be fine-tuned to span a range of time, length, and complexity scales. Recognizing the power of these motifs, researchers have sought to emulate and engineer biomolecular assemblies in the laboratory, with goals ranging from modulating cellular function to the creation of new polymeric materials. In most cases, engineering efforts are inspired or informed by understanding the structure and properties of naturally occurring assemblies, which has in turn fueled the development of predictive models that enable computational design of novel assemblies. This Review will focus on selected examples of protein assemblies, highlighting the story arc from initial discovery of an assembly, through initial engineering attempts, toward the ultimate goal of predictive design. The aim of this Review is to highlight areas where significant progress has been made, as well as to outline remaining challenges, as solving these challenges will be the key that unlocks the full power of biomolecules for advances in technology and medicine.

Two-Step to One-Step Nucleation of a Zeolite through a Metastable Gyroid Mesophase

The importance of nonclassical nucleation pathways in the formation of complex crystals has become apparent in recent years. Nonclassical pathways were unraveled for, among others, the crystallization of proteins, colloids, and clathrates. In those cases, the formation of a metastable fluid with density close to the crystal decreases the crystallization barrier. Recent simulations indicate that mesophases can facilitate the nucleation of zeolites. Here, we use molecular simulations to investigate the role of a gyroid mesophase on the crystallization of a model zeolite from liquid. The nucleation pathway is always nonclassical. At warmer temperatures, the mechanism proceeds in two well-defined steps: nucleation of a metastable gyroid followed by its crystallization into a zeolite. At colder temperatures, the second barrier becomes negligible, and the crystallization occurs in one step. This second scenario is also nonclassical, as the critical nucleus for the crystallization has the structure of the gyroid and seamlessly transforms into a zeolite as it grows past its critical size. To our knowledge, this is the first report of a nonclassical mechanism of crystallization mediated by a mesophase.

Coupling between criticality and gelation in "sticky" spheres: a structural analysis

We combine experiments and simulations to study the link between criticality and gelation in sticky spheres. We employ confocal microscopy to image colloid-polymer mixtures and Monte Carlo simulations of the square-well (SW) potential as a reference model. To this end, we map our experimental samples onto the SW model. We find an excellent structural agreement between experiments and simulations, both for locally favored structures at the single particle level and large-scale fluctuations at criticality. We follow in detail the rapid structural change in the critical fluid when approaching the gas-liquid binodal and highlight the role of critical density fluctuations for this structural crossover. Our results link the arrested spinodal decomposition to long-lived energetically favored structures, which grow even away from the binodal due to the critical scaling of the bulk correlation length and static susceptibility.

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersaturations and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large effective interfacial tension.

Free energy landscape and molecular pathways of gas hydrate nucleation

Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p_B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p_B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

Enhanced thermoelectric performance of Cu3SbS4 flower-like hierarchical architectures composed of Cl doped nanoflakes via an in situ generated CuS template

In this work, Cu₃SbS₄ hierarchical flower-like microspheres composed of chlorine (Cl^-)-doped Cu₃SbS₄ nanoflakes are realized via a one pot solvothermal ion exchange reaction. The kinetic factors including the duration time, the ratio of source materials, and the KOH concentration, are systematically investigated. Using a suite of analytical techniques, including SEM, XRD and FTIR, the mechanism of the two stage in situ chemical transformation of CuS flower-like microspheres consisting of nanoflake intermediates to the target product Cu₃SbS₄ is elucidated. The difference in solubility between reactants and products (Ksp(CuS) > Ksp(CuSbS_x)) determines that the ion-exchange reaction from transition binary to ternary metal chalcogenides is favorable under the impetus of a thermodynamic driving force. In addition, the optical and enhanced thermoelectric transport properties are investigated. The results revealed that Cl-doped Cu₃SbS₄ exhibited an improved power factor, which was 8 times higher than that of undoped Cu₃SbS₄ at 500 K. The current study not only provides a facile and economical way to synthesize high-quality Cl-doped Cu-Sb-S three dimensional (3D) hierarchical nanostructures, but also opens up a new route for preparation of other I-V-VI multicomponent chalcogenide NCs, such as Cu-Bi-S and Cu-Pb-S systems, which would be difficult to obtain otherwise.

Nonclassical nucleation pathways in protein crystallization

Classical nucleation theory (CNT), which was established about 90 years ago, has been very successful in many research fields, and continues to be the most commonly used theory in describing the nucleation process. For a fluid-to-solid phase transition, CNT states that the solute molecules in a supersaturated solution reversibly form small clusters. Once the cluster size reaches a critical value, it becomes thermodynamically stable and favored for further growth. One of the most important assumptions of CNT is that the nucleation process is described by one reaction coordinate and all order parameters proceed simultaneously. Recent studies in experiments, computer simulations and theory have revealed nonclassical features in the early stage of nucleation. In particular, the decoupling of order parameters involved during a fluid-to-solid transition leads to the so-called two-step nucleation mechanism, in which a metastable intermediate phase (MIP) exists between the initial supersaturated solution and the final crystals. Depending on the exact free energy landscapes, the MIPs can be a high density liquid phase, mesoscopic clusters, or a pre-ordered state. In this review, we focus on the studies of nonclassical pathways in protein crystallization and discuss the applications of the various scenarios of two-step nucleation theory. In particular, we focus on protein solutions in the presence of multivalent salts, which serve as a model protein system to study the nucleation pathways. We wish to point out the unique features of proteins as model systems for further studies.

Interaction Heterogeneity can Favorably Impact Colloidal Crystal Nucleation

Colloidal particles with short-ranged attractions, e.g., micron-scale spheres functionalized with single-stranded DNA oligomers, are susceptible to becoming trapped in disordered configurations even when a crystalline arrangement is the ground state. Moreover, for reasons that are not well understood, seemingly minor variations in the particle formulation can lead to dramatic changes in the crystallization outcome. We demonstrate, using a combination of equilibrium and nonequilibrium computer simulations, that interaction heterogeneity-variations in the energetic interactions among different particle pairs in the population-may favorably impact crystal nucleation. Specifically, interaction heterogeneity is found to lower the free energy barrier to nucleation via the formation of clusters comprised preferentially of strong-binding particle pairs. Moreover, gelation is inhibited by "spreading out over time" the nucleation process, resulting in a reduced density of stable nuclei, allowing each to grow unhindered and larger. Our results suggest a simple and robust approach for enhancing colloidal crystallization near the "sticky sphere" limit, and support the notion that differing extents of interaction heterogeneity arising from various particle functionalization protocols may contribute to the otherwise unexplained variations in crystallization outcomes reported in the literature.

Heterogeneous Nucleation of Colloidal Crystals on a Glass Substrate with Depletion Attraction

The heterogeneous nucleation of colloidal crystals with attractive interactions has been investigated via in situ observations. We have found two types of nucleation processes: a cluster that overcomes the critical size for nucleation with a monolayer, and a method that occurs with two layers. The Gibbs free energy changes (ΔG) for these two types of nucleation processes are evaluated by taking into account the effect of various interfacial energies. In contrast to homogeneous nucleation, the change in interfacial free energy, Δσ, is generated for colloidal nucleation on a foreign substrate such as a cover glass in the present study. The Δσ and step free energy of the first layer, γ₁, are obtained experimentally based on the equation deduced from classical nucleation theory (CNT). It is concluded that the ΔG of q-2D nuclei is smaller than of monolayer nuclei, provided that the same number of particles are used, which explains the experimental result that the critical size in q-2D nuclei is smaller than that in monolayer nuclei.

Formation of porous crystals via viscoelastic phase separation

Viscoelastic phase separation of colloidal suspensions can be interrupted to form gels either by glass transition or by crystallization. With a new confocal microscopy protocol, we follow the entire kinetics of phase separation, from homogeneous phase to different arrested states. For the first time in experiments, our results unveil a novel crystallization pathway to sponge-like porous crystal structures. In the early stages, we show that nucleation requires a structural reorganization of the liquid phase, called stress-driven ageing. Once nucleation starts, we observe that crystallization follows three different routes: direct crystallization of the liquid phase, the Bergeron process, and Ostwald ripening. Nucleation starts inside the reorganized network, but crystals grow past it by direct condensation of the gas phase on their surface, driving liquid evaporation, and producing a network structure different from the original phase separation pattern. We argue that similar crystal-gel states can be formed in monatomic and molecular systems if the liquid phase is slow enough to induce viscoelastic phase separation, but fast enough to prevent immediate vitrification. This provides a novel pathway to form nanoporous crystals of metals and semiconductors without dealloying, which may be important for catalytic, optical, sensing, and filtration applications.

Electronic crystal growth

Interacting atoms or molecules condense into liquid, and, when cooled further, they form a crystal. The time evolution of the atomic or molecular ordering has been widely studied as a nonequilibrium emergence of order from a supercooled liquid or a glass. Interacting electrons in a variety of correlated electron systems also form crystals, but observing the time evolution of electronic crystallization has been experimentally challenging. Here, working with an organic conductor exhibiting a supercooled charge liquid or charge glass as a metastable state, we observed electronic crystal growth through resistivity and nuclear magnetic resonance measurements. The temperature profile of the crystal growth is similar to those observed in classical systems and reveals two distinct regimes for the mechanism of electronic crystallization.

Self-assembly of MoO3 needles in gas current for cubic formation pathway

Nucleation and subsequent rapid growth are enigmatic due to the unrevealed pathways. Despite the relatively simpler mechanism compared to nucleation and growth in solution, that in vapor has received little attention. The largest hindrance to unveiling this process may be observing the rapid and mesoscopic-scale phenomena. To overcome this hindrance, we combine an experimental approach with in situ spatial scanning Fourier-transform infrared spectroscopy, which reveals the nucleating and growing nanoparticles in vapor. The nanoparticles are then collected at different evolutionary stages and analyzed by ex situ transmission electron microscopy (TEM). Needle-shaped molybdenum oxide (MoO₃) nanoparticles were formed within ∼0.1 s after homogeneous nucleation from a highly supersaturated vapor. Over one second, the needle particles gradually evolved into a cubic shape by fusion in a crystallographically favored orientation in a free-flying state in vapor. The similar sizes of the elongated axes of the needle and cubic structures suggest an additional growth stage, in which the needle particles become the growth units of the cubic particles. The morphology of a final crystal should reflect the formation environment of the particle because growing crystals are sensitive to the formation conditions such as temperature, concentration, and impurities. Although nucleation under very high supersaturation induces the anisotropic growth of the needle particles, this information of the initial nucleation environment is lost in the final cubic crystal. These findings enrich our understanding of pathways in the nucleation and growth of nanoparticles and provide new insights into the growth stages driven by oriented attachment.

Tuning crystallization pathways through sequence engineering of biomimetic polymers

Two-step nucleation pathways in which disordered, amorphous, or dense liquid states precede the appearance of crystalline phases have been reported for a wide range of materials, but the dynamics of such pathways are poorly understood. Moreover, whether these pathways are general features of crystallizing systems or a consequence of system-specific structural details that select for direct versus two-step processes is unknown. Using atomic force microscopy to directly observe crystallization of sequence-defined polymers, we show that crystallization pathways are indeed sequence dependent. When a short hydrophobic region is added to a sequence that directly forms crystalline particles, crystallization instead follows a two-step pathway that begins with the creation of disordered clusters of 10-20 molecules and is characterized by highly non-linear crystallization kinetics in which clusters transform into ordered structures that then enter the growth phase. The results shed new light on non-classical crystallization mechanisms and have implications for the design of self-assembling polymer systems.

Phase behavior of colloid-polymer depletion mixtures with unary or binary depletants

Adding depletants to a colloidal suspension induces an attractive interparticle interaction that can be tuned to obtain desired structures or to probe phase behavior. When the depletant is not uniform in size, however, both the range and strength of the attraction become difficult to predict and hence control. We investigated the effects of depletant bidispersity on the non-equilibrium phase behavior of colloid-polymer mixtures. We added unary or binary mixtures of polystyrene as the depletant to suspensions of charged poly(methyl methacrylate) particles. The structure and dynamics of the particles were compared over three sets of samples with various mixtures of two different polystyrenes whose size varied by an order of magnitude. The structure and dynamics were nearly independent of depletant dispersity if the polymer concentration was represented as a sum of normalized concentrations of each species. Near the transition region between a fluid of clusters and an interconnected gel at intermediate volume fractions, partitioning of polymers in a binary mixture into colloid-rich and polymer-rich phase leads to a slightly different gelation pathway.

Two-Dimensional Nucleation on the Terrace of Colloidal Crystals with Added Polymers

Understanding nucleation dynamics is important both fundamentally and technologically in materials science and other scientific fields. Two-dimensional (2D) nucleation is the predominant growth mechanism in colloidal crystallization, in which the particle interaction is attractive, and has recently been regarded as a promising method to fabricate varieties of complex nanostructures possessing innovative functionality. Here, polymers are added to a colloidal suspension to generate a depletion attractive force, and the detailed 2D nucleation process on the terrace of the colloidal crystals is investigated. In the system, we first measured the nucleation rate at various area fractions of particles on the terrace, ϕ_area. In situ observations at single-particle resolution revealed that nucleation behavior follows the framework of classical nucleation theory (CNT), such as single-step nucleation pathway and existence of critical size. Characteristic nucleation behavior is observed in that the nucleation and growth stage are clearly differentiated. When many nuclei form in a small area of the terrace, a high density of kink sites of once formed islands makes growth more likely to occur than further nucleation because nucleation has a higher energy barrier than growth. The steady-state homogeneous 2D nucleation rate, J, and the critical size of nuclei, r*, are measured by in situ observations based on the CNT, which enable us to obtain the step free energy, γ, which is an important parameter for characterizing the nucleation process. The γ value is found to change according to the strength of attraction, which is tuned by the concentration of the polymer as a depletant.

Two types of amorphous protein particles facilitate crystal nucleation

Nucleation, the primary step in crystallization, dictates the number of crystals, the distribution of their sizes, the polymorph selection, and other crucial properties of the crystal population. We used time-resolved liquid-cell transmission electron microscopy (TEM) to perform an in situ examination of the nucleation of lysozyme crystals. Our TEM images revealed that mesoscopic clusters, which are similar to those previously assumed to consist of a dense liquid and serve as nucleation precursors, are actually amorphous solid particles (ASPs) and act only as heterogeneous nucleation sites. Crystalline phases never form inside them. We demonstrate that a crystal appears within a noncrystalline particle assembling lysozyme on an ASP or a container wall, highlighting the role of heterogeneous nucleation. These findings represent a significant departure from the existing formulation of the two-step nucleation mechanism while reaffirming the role of noncrystalline particles. The insights gained may have significant implications in areas that rely on the production of protein crystals, such as structural biology, pharmacy, and biophysics, and for the fundamental understanding of crystallization mechanisms.

Freezing of supercooledn-decane nanodroplets: from surface driven to frustrated crystallization

Decane condenses to form nanodroplets that freeze from the outside in, until it's so cold that fractal like frustrated crystals form instead.

Kinetic Pathways and Mechanisms of Two-Step Nucleation in Crystallization

Crystallizations often pass through multiple intermediate structures before reaching the final state, such as amorphous precursors, polymorphs, or denser liquid droplets. However, the atomistic pathways from these metastable phases to final crystals still remain unclear. Here, we investigated the structure evolution process from liquid to final crystals of homogeneous nucleation by atomic-scale simulations and analyzed the intrinsic mechanisms that influence the nucleation pathways. Three different pathways of two-step nucleation were found by visualizing the precursors' evolutions, and some new micromechanisms of two-step nucleation are revealed. We suggest that the solid bond fluctuations can trigger the formation of intermediate precursors, while the precursors' packing density dominates the structural transformation pathways from intermediate phases to crystals. These findings not only shed light on the mechanisms of nucleation but also provide guidance for future refinements of two-step nucleation theory.

Seed-Mediated Growth of Colloidal Metal Nanocrystals

Seed-mediated growth is a powerful and versatile approach for the synthesis of colloidal metal nanocrystals. The vast allure of this approach mainly stems from the staggering degree of control one can achieve over the size, shape, composition, and structure of nanocrystals. These parameters not only control the properties of nanocrystals but also determine their relevance to, and performance in, various applications. The ingenuity and artistry inherent to seed-mediated growth offer extensive promise, enhancing a number of existing applications and opening the door to new developments. This Review demonstrates how the diversity of metal nanocrystals can be expanded with endless opportunities by using seeds with well-defined and controllable internal structures in conjunction with a proper combination of capping agent and reduction kinetics. New capabilities and future directions are also highlighted.

Vibrational properties of quasi-two-dimensional colloidal glasses with varying interparticle attraction

We measure the vibrational modes and particle dynamics of quasi-two-dimensional colloidal glasses as a function of interparticle interaction strength. The interparticle attractions are controlled via a temperature-tunable depletion interaction. Specifically, the interparticle attraction energy is increased gradually from a very small value (nearly hard-sphere) to moderate strength (∼4k_{B}T), and the variation of colloidal particle dynamics and vibrations are concurrently probed. The particle dynamics slow monotonically with increasing attraction strength, and the particle motions saturate for strengths greater than ∼2k_{B}T, i.e., as the system evolves from a nearly repulsive glass to an attractive glass. The shape of the phonon density of states is revealed to change with increasing attraction strength, and the number of low-frequency modes exhibits a crossover for glasses with weak compared to strong interparticle attraction at a threshold of ∼2k_{B}T. This variation in the properties of the low-frequency vibrational modes suggests a new means for distinguishing between repulsive and attractive glass states.

Polymorph selection and nucleation pathway in the crystallization of Hertzian spheres

The crystallization process of Hertzian spheres is studied by means of molecular dynamics simulations in an NPT ensemble where the total number of particles N, the pressure P, and the temperature T are kept constant. It has been observed that the bond orientational ordering rather than the translational ordering (density) plays a primary role. The crystal polymorphs are determined by the state points. Under the conditions of small supercooling, the system is likely to be nucleated into crystals that have a preference for the metastable bcc structure, which can be regarded as a manifestation of the Alexander-McTague mechanism. In contrast, small nuclei are found to have a preference for fcc symmetry under conditions of a high degree of supercooling. Prestructured precursors that act as seeds and wet on the nuclei during nucleation always have a high degree of bcc-like ordering, despite different state points. The results above may provide a clue to the understanding of the crystallization process in core-softened particles.

Protein Conformational Flexibility Enables the Formation of Dense Liquid Clusters: Tests Using Solution Shear

According to recently proposed two-step nucleation mechanisms, crystal nuclei form within preexisting dense liquid clusters. Clusters with radii about 100 nm, which capture from 10(-7) to 10(-3) of the total protein, have been observed with numerous proteins and shown to host crystal nucleation. Theories aiming to understand the mesoscopic size and small protein fraction held in the clusters have proposed that in solutions of single-chain proteins, the clusters consist of partially misfolded protein molecules. To test this conjecture, we perturb the protein conformation by shearing solutions of the protein lysozyme. We demonstrate that shear rates greater than a threshold applied for longer than 1 h reduce the volume of the cluster population. The likely mechanism of the observed response involves enhanced partial unfolding of lysozyme molecules, which exposes hydrophobic surfaces between the constituent domains to the aqueous solution.

Tunable depletion potentials driven by shape variation of surfactant micelles

Depletion interaction potentials between micron-sized colloidal particles are induced by nanometer-scale surfactant micelles composed of hexaethylene glycol monododecyl ether (C_{12}E_{6}), and they are measured by video microscopy. The strength and range of the depletion interaction is revealed to arise from variations in shape anisotropy of the surfactant micelles. This shape anisotropy increases with increasing sample temperature. By fitting the colloidal interaction potentials to theoretical models, we extract micelle length and shape anisotropy as a function of temperature. This work introduces shape anisotropy tuning as a means to control interparticle interactions in colloidal suspensions, and it shows how the interparticle depletion potentials of micron-scale objects can be employed to probe the shape and size of surrounding macromolecules at the nanoscale.

Atomic Scale Imaging of Nucleation and Growth Trajectories of an Interfacial Bismuth Nanodroplet

Because of the lack of experimental evidence, much confusion still exists on the nucleation and growth dynamics of a nanostructure, particularly of metal. The situation is even worse for nanodroplets because it is more difficult to induce the formation of a nanodroplet while imaging the dynamic process with atomic resolution. Here, taking advantage of an electron beam to induce the growth of Bi nanodroplets on a SrBi2Ta2O9 platelet under a high resolution transmission electron microscope (HRTEM), we directly observed the detailed growth pathways of Bi nanodroplets from the earliest stage of nucleation that were previously inaccessible. Atomic scale imaging reveals that the dynamics of nucleation involves a much more complex trajectory than previously predicted based on classical nucleation theory (CNT). The monatomic Bi layer was first formed in the nucleation process, which induced the formation of the prenucleated clusters. Following that, critical nuclei for the nanodroplets formed both directly from the addition of atoms to the prenucleated clusters by the classical growth process and indirectly through transformation of an intermediate liquid film based on the Stranski-Krastanov growth mode, in which the liquid film was induced by the self-assembly of the prenucleated clusters. Finally, the growth of the Bi nanodroplets advanced through the classical pathway and sudden droplet coalescence. This study allows us to visualize the critical steps in the nucleation process of an interfacial nanodroplet, which suggests a revision of the perspective of CNT.

The relationship between local density and bond-orientational order during crystallization of the Gaussian core model

Whether nucleation is triggered by density or by bond-orientational order is one of the most hotly debated issues in recent investigations of the crystallization process. Here, we present a numerical study of the relationship between them for soft particles within the isothermal-isobaric ensemble. We compress the system and thus obtain the fluid-solid transition. By investigating locally dense-packed particles and particles with a relatively high bond-orientational order in the compressing process, we find a sharp increase of the spatial correlations for both densely packed particles and highly bond-orientational ordered particles at the phase transition point, which provide new characterization methods for the liquid-crystal transition. We also find that it is the bond-orientational order rather than density that triggers the nucleation process. The relationship between the local density and the bond-orientational order parameter is strongly affected by the characterization methods used. The local bond order parameter (q6) shows clear correlation with the local density (ρ) in the fluid stage, while the coarse-grained form (q[combining macron]6) does not correlate with ρ at all, owing to the comparable spatial scales of q6 and ρ. Nevertheless, q[combining macron]6 shows an obvious advantage in distinguishing between solid and liquid particles in our work. These results may elevate our understanding of the mechanism of the crystallization process.

Crystallization and arrest mechanisms of model colloids

We performed dynamic simulations of spheres with short-range attractive interactions for many values of interaction strength and range. Fast crystallization occurs in a localized region of this parameter space, but the character of crystallization pathways is not uniform within this region. Pathways range from one-step, in which a crystal nucleates directly from a gas, to two-step, in which substantial liquid-like clusters form and only subsequently become crystalline. Crystallization can fail because of slow nucleation from either gas or liquid, or because of dynamic arrest caused by strong interactions. Arrested states are characterized by the formation of networks of face-sharing tetrahedra that can be detected by a local common neighbor analysis.

Atomic-Level Mechanisms of Nucleation of Pure Liquid Metals during Rapid Cooling

To obtain a material with the desired performance, the atomic-level mechanisms of nucleation from the liquid to solid phase must be understood. Although this transition has been investigated experimentally and theoretically, its atomic-level mechanisms remain debatable. In this work, the nucleation mechanisms of pure Fe under rapid cooling conditions are investigated. The local atomic packing stability and liquid-to-solid transition-energy pathways of Fe are studied using molecular dynamics simulations and first-principle calculations. The results are expressed as functions of cluster size in units of amorphous clusters (ACs) and body-centered cubic crystalline clusters (BCC-CCs). We found the prototypes of ACs in supercooled liquids and successfully divided these ACs to three categories according to their transition-energy pathways. The information obtained in this study could contribute to our current understanding of the crystallization of metallic melts during rapid cooling.