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

A minimal colloid model of solution crystallization nucleates crystals classically

A fundamental assumption of the classical theories of crystal nucleation is that the individual molecules from the "old" phase associate to an emerging nucleus individually and sequentially. Numerous recent studies of crystal nucleation in solution have revealed nonclassical pathways, whereby crystal nuclei are hosted and fed by amorphous clusters pre-formed in the solution. A sizable knowledge gap has persisted, however, in the definition of the molecular-level parameters that direct a solute towards classical or nonclassical nucleation. Here we construct a suspension of colloid particles of hydrodynamic diameter 1.1 μm and monitor their individual motions towards a quasi-two-dimensional crystal by scanning confocal microscopy. We combine electrostatic repulsion and polymer-induced attraction to obtain a simple isotropic pair interaction potential with a single attractive minimum of tunable depth between 1.2kBT and 2.7kBT. We find that even the smallest aggregates that form in this system structure as hexagonal two-dimensional crystals and grow and maturate by the association and exchange of single particles from the solution, signature behaviors during classical nucleation. The particles in the suspension equilibrate with those in the clusters and the volume fractions of suspensions at equilibrium correspond to straightforward thermodynamic predictions based on depth of the interparticle attraction. These results demonstrate that classical nucleation is selected by particles interacting with a minimal potential and present a benchmark for future modifications of the molecular interactions that may induce nonclassical nucleation.

Mechanisms of Biomolecular Self-Assembly Investigated Through In Situ Observations of Structures and Dynamics

Biomolecular self-assembly of hierarchical materials is a precise and adaptable bottom-up approach to synthesizing across scales with considerable energy, health, environment, sustainability, and information technology applications. To achieve desired functions in biomaterials, it is essential to directly observe assembly dynamics and structural evolutions that reflect the underlying energy landscape and the assembly mechanism. This review will summarize the current understanding of biomolecular assembly mechanisms based on in situ characterization and discuss the broader significance and achievements of newly gained insights. In addition, we will also introduce how emerging deep learning/machine learning-based approaches, multiparametric characterization, and high-throughput methods can boost the development of biomolecular self-assembly. The objective of this review is to accelerate the development of in situ characterization approaches for biomolecular self-assembly and to inspire the next generation of biomimetic materials.

Observing short-range orientational order in small-molecule liquids

Local molecular ordering in liquids has attracted a lot of interest from researchers investigating crystallization, but is still poorly understood on the molecular scale. Classical nucleation theory (CNT), a macroscopic thermodynamic description of condensation, has shortcomings when dealing with clusters consisting of tens of molecules. Cluster formation and local order fluctuations in liquid media are difficult to study due to the limited spatial resolution of electron- and photon-imaging methods. We used NMR relaxometry to demonstrate the existence of dynamic clusters with short-range orientational order in nominally isotropic liquids consisting of elongated molecules. We observed clusters in liquids where the local ordering is driven by polar, steric, and hydrogen-bond interactions between the molecules. In the case of a liquid crystal, measuring the local orientational order fluctuations allowed us to observe the size of these clusters diverging when approaching the phase transition from the isotropic to the nematic phase. These fluctuations are described in terms of rotational elasticity as a consequence of the correlated reorientations of the neighbouring molecules. Our quantitative observations of the dynamic clusters in liquids, numbering about ten or fewer molecules, indicate that this is a general phenomenon in various types of liquids.

Atomic-Scale Structure Dynamics of Nanocrystals Revealed By In Situ and Environmental Transmission Electron Microscopy

Nanocrystals are of great importance in material sciences and industry. Engineering nanocrystals with desired structures and properties is no doubt one of the most important challenges in the field, which requires deep insight into atomic-scale dynamics of nanocrystals during the process. The rapid developments of in situ transmission electron microscopy (TEM), especially environmental TEM, reveal insights into nanocrystals to digest. According to the considerable progress based on in situ electron microscopy, a comprehensive review on nanocrystal dynamics from three aspects: nucleation and growth, structure evolution, and dynamics in reaction conditions are given. In the nucleation and growth part, existing nucleation theories and growth pathways are organized based on liquid and gas-solid phases. In the structure evolution part, the focus is on in-depth mechanistic understanding of the evolution, including defects, phase, and disorder/order transitions. In the part of dynamics in reaction conditions, solid-solid and gas-solid interfaces of nanocrystals in atmosphere are discussed and the structure-property relationship is correlated. Even though impressive progress is made, additional efforts are required to develop the integrated and operando TEM methodologies for unveiling nanocrystal dynamics with high spatial, energy, and temporal resolutions.

Hydroxide films on mica form charge-stabilized microphases that circumvent nucleation barriers

Crystal nucleation is facilitated by transient, nanoscale fluctuations that are extraordinarily difficult to observe. Here, we use high-speed atomic force microscopy to directly observe the growth of an aluminum hydroxide film from an aqueous solution and characterize the dynamically fluctuating nanostructures that precede its formation. Nanoscale cluster distributions and fluctuation dynamics show many similarities to the predictions of classical nucleation theory, but the cluster energy landscape deviates from classical expectations. Kinetic Monte Carlo simulations show that these deviations can arise from electrostatic interactions between the clusters and the underlying substrate, which drive microphase separation to create a nanostructured surface phase. This phase can evolve seamlessly from a low-coverage state of fluctuating clusters into a high-coverage nanostructured network, allowing the film to grow without having to overcome classical nucleation barriers.

Multistep Crystallization of Pharmaceutical Amorphous Nanoparticles via a Cognate Pathway of Oriented Attachment: Direct Evidence of Nonclassical Crystallization for Organic Molecules

Crystallization of organic molecules is important in a wide range of scientific disciplines. However, in contrast to maturely studied crystallization of inorganic materials, the crystallization mechanisms of organic molecules involving nucleation and crystal growth are still poorly understood. Here, we used time-resolved cryogenic transmission electron microscopy to directly map the morphological evolution of amorphous cyclosporin A (CyA) nanoparticles during CyA crystallization. We successfully observed its initial nucleation and found that the amorphous CyA nanoparticles crystallized via a pathway cognate with oriented attachment, which is the nonclassical crystallization mechanism usually reported for inorganic compounds. Crystalline mesostructured intermediates (mesocrystals) were formed during crystallization. This study revealed clear and direct evidence of mesocrystal formation and oriented attachment in organic pharmaceuticals, providing new insights into the crystallization of organic molecules and theories of nonclassical crystallization.

Online Monitoring of the Concentrations of Amorphous and Crystalline Mesoscopic Species Present in Solution

Despite the growing evidence for the existence of amorphous mesoscopic species in a solution and their crucial roles in crystallization, there has been the lack of a suitable method to measure the time-resolved concentrations of amorphous and crystalline mesospecies in a lab-scale stirred reactor. This has limited experimental investigations to understand the kinetics of amorphous and crystalline mesospecies formation in stirred solutions and made it challenging to measure the crystal nucleation rate directly. Here, we used depolarized light sheet microscopy to achieve time-resolved measurements of amorphous and crystalline mesospecies concentrations in solutions at varying temperatures. After demonstrating that the concentration measurement method is reasonably accurate, precise, and sensitive, we utilized this method to examine mesospecies formation both in a mixture of two miscible liquids and in an undersaturated solution of dl-valine, thus revealing the importance of a temperature change in the formation of metastable and amorphous mesospecies as well as the reproducibility of the measurements. Moreover, we used the presented method to monitor both mesospecies formation and crystal nucleation in dl-valine solutions at four different levels of supersaturation, while achieving the direct measurement of the crystal nucleation rates in stirred solutions. Our results show that, as expected, the inherent variability in nucleation originating from its stochastic nature reduces with increasing supersaturation, and the dependence of the measured nucleation rate on supersaturation is in reasonable agreement with that predicted by the classical nucleation theory.

Molecular Mechanism of Organic Crystal Nucleation: A Perspective of Solution Chemistry and Polymorphism

Crystal nucleation determining the formation and assembly pathway of first organic materials is the central science of various scientific disciplines such as chemical, geochemical, biological, and synthetic materials. However, our current understanding of the molecular mechanisms of nucleation remains limited. Over the past decades, the advancements of new experimental and computational techniques have renewed numerous interests in detailed molecular mechanisms of crystal nucleation, especially structure evolution and solution chemistry. These efforts bifurcate into two categories: (modified) classical nucleation theory (CNT) and non-classical nucleation mechanisms. In this review, we briefly introduce the two nucleation mechanisms and summarize current molecular understandings of crystal nucleation that are specifically applied in polymorphic crystallization systems of small organic molecules. Many important aspects of crystal nucleation including molecular association, solvation, aromatic interactions, and hierarchy in intermolecular interactions were examined and discussed for a series of organic molecular systems. The new understandings relating to molecular self-assembly in nucleating systems have suggested more complex multiple nucleation pathways that are associated with the formation and evolution of molecular aggregates in solution.

Crystal Nucleation and Growth of Inorganic Ionic Materials from Aqueous Solution: Selected Recent Developments, and Implications

In this review article, selected, latest theoretical, and experimental developments in the field of nucleation and crystal growth of inorganic materials from aqueous solution are highlighted, with a focus on literature after 2015 and on non-classical pathways. A key point is to emphasize the so far underappreciated role of water and solvent entropy in crystallization at all stages from solution speciation through to the final crystal. While drawing on examples from current inorganic materials where non-classical behavior has been proposed, the potential of these approaches to be adapted to a wide-range of systems is also discussed, while considering the broader implications of the current re-assessment of pathways for crystallization. Various techniques that are suitable for the exploration of crystallization pathways in aqueous solution, from nucleation to crystal growth are summarized, and a flow chart for the assignment of specific theories based on experimental observations is proposed.

Multistep nucleation visualized during solid-state crystallization

Mechanisms of nucleation have been debated for more than a century, despite successes of classical nucleation theory. The nucleation process has been recently argued as involving a nonclassical mechanism (the "two-step" mechanism) in which an intermediate step occurs before the formation of a nascent ordered phase. However, a thorough understanding of this mechanism, in terms of both microscopic kinetics and thermodynamics, remains experimentally challenging. Here, in situ observations using transmission electron microscopy on a solid-state nucleation case indicate that early-stage crystallization can follow the non-classical pathway, yet proceed via a more complex manner in which multiple metastable states precede the emergence of a stable nucleus. The intermediate steps were sequentially isolated as spinodal decomposition of amorphous precursor, mass transport and structural oscillations between crystalline and amorphous states. Our experimental and theoretical analyses support the idea that the energetic favorability is the driving force for the observed sequence of events. Due to the broad applicability of solid-state crystallization, the findings of this study offer new insights into modern nucleation theory and a potential avenue for materials design.

Atom-Resolved Investigation on Dynamic Nucleation and Growth of Platinum Nanocrystals

Understanding the mechanism of nucleation and growth of nanocrystals is crucial for designing and regulating the structure and properties of nanocrystals. However, the process from molecules to nanocrystals remains unclear because of the rapid and complicated dynamics of evolution under reaction conditions. Here, the complete evolution process of solid-phase chloroplatinic acid during the electron beam irradiation triggered reduction and nucleation of platinum nanocrystals is recorded. Aberration-corrected environmental transmission electron microscopy is used for direct visualization of the dynamic evolution from H₂ PtCl₆ to Pt nanocrystals at the atomic scale, including the formation and growth of amorphous clusters, crystallization, and growth of clusters, and the ripening of Pt nanocrystals. At the first two stages, there exists a critical size of ≈2.0 nm, which represents the start of crystallization. Crystallization from the center and density fluctuation are observed in the second stage of the crystallization of a few clusters with a size obviously larger than the critical size. The work provides valuable information to understand the kinetics of the early stage of nanocrystal nucleation and crystallization at atomic scale.

Rotational dynamics and transition mechanisms of surface-adsorbed proteins

The exquisite organization exhibited by hybrid biomolecular–inorganic materials in nature has inspired the development of synthetic analogues for numerous applications. Nevertheless, a mechanistic picture of the energetic controls and response dynamics leading to organization is lacking. Here, we pair high-speed atomic force microscopy with machine learning and Monte Carlo simulations to analyze the rotational dynamics of rod-like proteins on a crystal lattice, simultaneously quantifying the orientational energy landscape and transition probabilities between energetically favorable orientations. Although rotations largely follow Brownian diffusion, proteins often make large jumps in orientation, thus rapidly overcoming barriers that usually inhibit rotation. Moreover, the rotational dynamics can be tuned via protein size and solution chemistry, providing tools for controlling biomolecular assembly at inorganic interfaces.

Assembly of biomolecules at solid–water interfaces requires molecules to traverse complex orientation-dependent energy landscapes through processes that are poorly understood, largely due to the dearth of in situ single-molecule measurements and statistical analyses of the rotational dynamics that define directional selection. Emerging capabilities in high-speed atomic force microscopy and machine learning have allowed us to directly determine the orientational energy landscape and observe and quantify the rotational dynamics for protein nanorods on the surface of muscovite mica under a variety of conditions. Comparisons with kinetic Monte Carlo simulations show that the transition rates between adjacent orientation-specific energetic minima can largely be understood through traditional models of in-plane Brownian rotation across a biased energy landscape, with resulting transition rates that are exponential in the energy barriers between states. However, transitions between more distant angular states are decoupled from barrier height, with jump-size distributions showing a power law decay that is characteristic of a nonclassical Levy-flight random walk, indicating that large jumps are enabled by alternative modes of motion via activated states. The findings provide insights into the dynamics of biomolecules at solid–liquid interfaces that lead to self-assembly, epitaxial matching, and other orientationally anisotropic outcomes and define a general procedure for exploring such dynamics with implications for hybrid biomolecular–inorganic materials design.

Precrystallization solute assemblies and crystal symmetry

Solution crystallization is a part of the synthesis of materials ranging from geological and biological minerals to pharmaceuticals, fine chemicals, and advanced electronic components. Attempts to predict the structure, growth rates and properties of emerging crystals have been frustrated, in part, by the poor understanding of the correlations between the oligomeric state of the solute, the growth unit, and the crystal symmetry. To explore how a solute monomer or oligomer is selected as the unit that incorporates into kinks and how crystal symmetry impacts this selection, we combine scanning probe microscopy, optical spectroscopy, and all-atom molecular simulations using as examples two organic materials, olanzapine (OZPN) and etioporphyrin I (EtpI). The dominance of dimeric structures in OZPN crystals has spurred speculation that the dimers preform in the solution, where they capture the majority of the solute, and then assemble into crystals. By contrast, EtpI in crystals aligns in parallel stacks of flat EtpI monomers unrelated by point symmetry. Raman and absorption spectroscopies show that solute monomers are the majority solute species in solutions of both compounds. Surprisingly, the kinetics of incorporation of OZPN into kinks is bimolecular, indicating that the growth unit is a solute dimer, a minority solution component. The disconnection between the dominant solute species, the growth unit, and the crystal symmetry is even stronger with EtpI, for which the (010) face grows by incorporating monomers, whereas the growth unit of the (001) face is a dimer. Collectively, the crystallization kinetics results with OZPN and EtpI establish that the structures of the dominant solute species and of the incorporating solute complex do not correlate with the symmetry of the crystal lattice. In a broader context, these findings illuminate the immense complexity of crystallization scenarios that need to be explored on the road to the understanding and control of crystallization.

An investigation of the kinetics and thermodynamics of NaCl nucleation through composite clusters

Having a good understanding of nucleation is critical for the control of many important processes, such as polymorph selection during crystallization. However, a complete picture of the molecular-level mechanisms of nucleation remains elusive. In this work, we take an in-depth look at the NaCl homogeneous nucleation mechanism through thermodynamics. Distinguished from the classical nucleation theory, we calculate the free energy of nucleation as a function of two nucleus size coordinates: crystalline and amorphous cluster sizes. The free energy surface reveals a thermodynamic preference for a nonclassical mechanism of nucleation through a composite cluster, where the crystalline nucleus is surrounded by an amorphous layer. The thickness of the amorphous layer increases with an increase in supersaturation. The computed free energy landscape agrees well with the composite cluster-free energy model, through which phase specific thermodynamic properties are evaluated. As the supersaturation increases, there is a change in stability of the amorphous phase relative to the solution phase, resulting in a change from one-step to two-step mechanism, seen clearly from the free energy profile along the minimum free energy path crossing the transition curve. By obtaining phase-specific diffusion coefficients, we construct the full mesoscopic model and present a clear roadmap for NaCl nucleation.

Protein Needles Designed to Self-Assemble through Needle Tip Engineering

The dynamic process of formation of protein assemblies is essential to form highly ordered structures in biological systems. Advances in structural and synthetic biology have led to the construction of artificial protein assemblies. However, development of design strategies exploiting the anisotropic shape of building blocks of protein assemblies has not yet been achieved. Here, the 2D assembly pattern of protein needles (PNs) is controlled by regulating their tip-to-tip interactions. The PN is an anisotropic needle-shaped protein composed of β-helix, foldon, and His-tag. Three different types of tip-modified PNs are designed by deleting the His-tag and foldon to change the protein-protein interactions. Observing their assembly by high-speed atomic force microscopy (HS-AFM) reveals that PN, His-tag deleted PN, and His-tag and foldon deleted PN form triangular lattices, the monomeric state with nematic order, and fiber assemblies, respectively, on a mica surface. Their assembly dynamics are observed by HS-AFM and analyzed by the theoretical models. Monte Carlo (MC) simulations indicate that the mica-PN interactions and the flexible and multipoint His-tag interactions cooperatively guide the formation of the triangular lattice. This work is expected to provide a new strategy for constructing supramolecular protein architectures by controlling directional interactions of anisotropic shaped proteins.

Accounting for the Presence of Molecular Clusters in Modeling and Interpreting Nucleation and Growth

The effect of molecular cluster formation on the estimation of kinetic parameters for primary nucleation and growth in different systems has been studied using computationally generated data and three sets of experimental data in the literature. It is shown that the formation of molecular clusters decreases the concentration of monomers and hence the thermodynamic driving force for crystallization, which consequently affects the crystallization kinetics. For a system exhibiting a strong tendency to form molecular clusters, accounting for cluster formation in a kinetic model is critical to interpret kinetic data accurately, for instance, to estimate the specific surface energy γ from a set of primary nucleation rates. On the contrary, for a system with negligible cluster formation, a consideration of cluster formation does not affect parameter estimation outcomes. Moreover, it is demonstrated that using a growth kinetic model that accounts for cluster formation allows the estimation of γ from typical growth kinetic data (i.e., de-supersaturation profiles of seeded batch crystallization), which is a novel method of estimating γ developed in this work. The applicability of the novel method to different systems is proven by showing that the estimated values of γ are closely comparable to the actual values used for generating the kinetic data or the corresponding estimates reported in the literature.

Mesoscale clusters of organic solutes in solution and their role in crystal nucleation

It is becoming evident that primary nucleation of crystals of organic molecules from solution is often anything but ‘classical’ in its complexity. It is also becoming increasingly clear that mesoscopic...

Temperature-dependent kinetic pathways of heterogeneous ice nucleation competing between classical and non-classical nucleation

Ice nucleation on the surface plays a vital role in diverse areas, ranging from physics and cryobiology to atmospheric science. Compared to ice nucleation in the bulk, the water-surface interactions present in heterogeneous ice nucleation complicate the nucleation process, making heterogeneous ice nucleation less comprehended, especially the relationship between the kinetics and the structures of the critical ice nucleus. Here we combine Markov State Models and transition path theory to elucidate the ensemble pathways of heterogeneous ice nucleation. Our Markov State Models reveal that the classical one-step and non-classical two-step nucleation pathways can surprisingly co-exist with comparable fluxes at T = 230 K. Interestingly, we find that the disordered mixing of rhombic and hexagonal ice leads to a favorable configurational entropy that stabilizes the critical nucleus, facilitating the non-classical pathway. In contrast, the favorable energetics promotes the formation of hexagonal ice, resulting in the classical pathway. Furthermore, we discover that, at elevated temperatures, the nucleation process prefers to proceed via the classical pathway, as opposed to the non-classical pathway, since the potential energy contributions override the configurational entropy compensation. This study provides insights into the mechanisms of heterogeneous ice nucleation and sheds light on the rational designs to control crystallization processes.

General Design Concept for Single-Atom Catalysts toward Heterogeneous Catalysis

As a new and popular material, single-atom catalysts (SACs) exhibit excellent activity, selectivity, and stability for numerous important reactions, and show great potential in heterogeneous catalysis due to their high atom utilization efficiency and the controllable characteristics of the active sites. The composition and coordination would determine the geometric and electronic structures of SACs, and thus greatly influence the catalytic performance. Based on atom economy, rational design and controllable synthesis of SACs have become central tasks in the fields of low-cost and green catalysis. Herein, an introduction to the recent progress in the precise synthesis of SACs including the regulation of the coordination structure and the choice of different systems is presented. Thereafter, the potentials of SACs in different applications are comprehensively summarized and discussed. Furthermore, a detailed discussion of the recent developments regarding the large-scale preparation of SACs is provided, including the major issues and prospects for industrialization. Finally, the main challenges and opportunities of rapid large-scale industrialization of SACs are briefly discussed.

Nucleation of protein mesocrystals via oriented attachment

Self-assembly of proteins holds great promise for the bottom-up design and production of synthetic biomaterials. In conventional approaches, designer proteins are pre-programmed with specific recognition sites that drive the association process towards a desired organized state. Although proven effective, this approach poses restrictions on the complexity and material properties of the end-state. An alternative, hierarchical approach that has found wide adoption for inorganic systems, relies on the production of crystalline nanoparticles that become the building blocks of a next-level assembly process driven by oriented attachment (OA). As it stands, OA has not yet been observed for protein systems. Here we employ cryo-transmission electron microscopy (cryoEM) in the high nucleation rate limit of protein crystals and map the self-assembly route at molecular resolution. We observe the initial formation of facetted nanocrystals that merge lattices by means of OA alignment well before contact is made, satisfying non-trivial symmetry rules in the process. As these nanocrystalline assemblies grow larger we witness imperfect docking events leading to oriented aggregation into mesocrystalline assemblies. These observations highlight the underappreciated role of the interaction between crystalline nuclei, and the impact of OA on the crystallization process of proteins.

Engineering Biomolecular Self-Assembly at Solid-Liquid Interfaces

Biomolecular self-assembly is a key process used by life to build functional materials from the "bottom up." In the last few decades, bioengineering and bionanotechnology have borrowed this strategy to design and synthesize numerous biomolecular and hybrid materials with diverse architectures and properties. However, engineering biomolecular self-assembly at solid-liquid interfaces into predesigned architectures lags the progress made in bulk solution both in practice and theory. Here, recent achievements in programming self-assembly of peptides, proteins, and peptoids at solid-liquid interfaces are summarized and corresponding applications are described. Recent advances in the physical understandings of self-assembly pathways obtained using in situ atomic force microscopy are also discussed. These advances will lead to novel strategies for designing biomaterials organized at and interfaced with inorganic surfaces.

Real-time monitoring of crystallization from solution by using an interdigitated array electrode sensor

Monitoring crystallization events in real-time is challenging but crucial for understanding the molecular dynamics associated with nucleation and crystal growth, some of nature's most ubiquitous phenomena. Recent observations have suggested that the traditional nucleation model, which describes the nucleus having already the final crystal structure, may not be valid. It appears that the molecular assembly can range during nucleation from crystalline to partially ordered to totally amorphous phases, and can change its structure during the crystallization process. Therefore, it is of critical importance to develop methods that are able to provide real-time monitoring of the molecular interactions with high temporal resolution. Here, we demonstrate that a simple and scalable approach based on interdigitated electrode array sensors (IESs) is able to provide insights on the dynamics of the crystallization process with a temporal resolution of 15 ms.

2D Self-assembled molecular networks and on-surface reactivity under nanoscale lateral confinement

Supramolecular self-assembly at surfaces provides a pathway for building chemically customized interfaces. Over the last three decades, research on the role of key parameters such as temperature, solute concentration, and molecular design has enabled a steady increase in the complexity of self-assembled molecular networks (SAMNs) that can thus be created. However, the structure and quality of SAMNs is often determined during the early stages of nucleation and growth. To study and influence self-assembly processes at this deterministic length scale, spatial confinement of molecular adsorbates to well-defined surface patterns with nanoscale lateral dimensions offers exciting possibilities. The aim of this tutorial review is to give an overview of the various ways in which confinement impacts SAMN formation, and how we can use that knowledge to direct assemblies towards desired structures. The possibility to exploit confinement for improved control over on-surface reactions is also contemplated.

Identification of critical nuclei in the rapid solidification via configuration heredity

The identification and characterization of critical nuclei is a long-standing issue in the rapid solidification of metals and alloys. An ambiguous description for their sizes and shapes used to lead to an overestimation or underestimation of homogeneous nucleation ratesITin the framework of classical nucleation theory (CNT). In this paper, a unique method able to distinguish the critical nucleus from numerous embryos is put forward on the basis of configuration heredities of clusters during rapid solidifications. As this technique is applied to analyze the formation and evolution of various fcc-Al single crystal clusters in a large-scale molecular dynamics simulation system, it is found that the sizen_cand geometrical configuration of critical nuclei as well as their liquid-solid interfacial structure can be determined directly. For the present deep super-cooled system with an undercooling ofTm=0.42Tmcal, the average size of critical nuclei is demonstrated to benc̄≈26, but most of which are non-spherical lamellae. Also, their liquid-solid interfaces are revealed to be not an fcc-liquid duplex-phase interface but an fcc/hcp-liquid multi-phase structure. These findings shed some lights on the CNT, and a good agreement with previous simulations and experiments inITindicates this technique can be used to explore the early-stage of nucleation from atomistic levels.

Nucleation of melt: From fundamentals to dispersed systems

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

Reversible disorder-order transitions in atomic crystal nucleation

Nucleation in atomic crystallization remains poorly understood, despite advances in classical nucleation theory. The nucleation process has been described to involve a nonclassical mechanism that includes a spontaneous transition from disordered to crystalline states, but a detailed understanding of dynamics requires further investigation. In situ electron microscopy of heterogeneous nucleation of individual gold nanocrystals with millisecond temporal resolution shows that the early stage of atomic crystallization proceeds through dynamic structural fluctuations between disordered and crystalline states, rather than through a single irreversible transition. Our experimental and theoretical analyses support the idea that structural fluctuations originate from size-dependent thermodynamic stability of the two states in atomic clusters. These findings, based on dynamics in a real atomic system, reshape and improve our understanding of nucleation mechanisms in atomic crystallization.

Kinetics of domain growth and aging in a two-dimensional off-lattice system

We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-"liquid" as well as vapor-"solid" coexistence. For the vapor-liquid phase separation we observe that ℓ, the average domain length, grows with time (t) as t^{1/2}, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying "solid"-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to ℓ/ℓ_{w}, ℓ, and ℓ_{w} being the average domain lengths at times t and t_{w} (≤t), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: ∼(ℓ/ℓ_{w})^{-λ} for t≫t_{w}. The decay exponent λ, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.

Designing the disorder: the kinetics of nonisothermal crystallization of the orientationally disordered crystalline phase in a nematic mesogen

This article presents the molecular dynamics and solidification behavior of a 2,3-difluoro-4-propylphenyl 2,3-difluoro-4-(4-pentylcyclohexyl)benzoate nematic liquid crystal (5C4FPB3) observed by broadband dielectric spectroscopy (BDS) and differential scanning calorimetry (DSC). Polarized optical microscopy (POM) is also performed to confirm the phase transition temperatures. Our investigation reveals rare crystallization of the orientationally disordered crystal (ODIC) phase from the nematic phase and a glass transition of the crystal at cooling rates higher than 1 K min-1. The deconvolution of the dielectric spectra with derivative techniques is necessary because of the complex molecular dynamics in the crystalline phase. The BDS method enables us to capture the relaxation processes reflecting pre-crystallization molecular movements. The kinetics of nonisothermal crystallization is studied using the Ozawa, Mo, and isoconversional methods. The present studies suggest that the dominant factor of the crystal growth mechanism depends on the cooling rate. Two types of crystallization mechanisms are identified at cooling rates lower and higher than 5 K min-1. We design a diagram with crystallization and glass transition borders against the cooling rates. Estimations show that crystallization of the present compound can be bypassed at cooling rates higher than 78 kK min-1, at which a glass transition of the nematic phase occurs. We show various scenarios of the molecular order and the crystallization mechanism designed based on the process rate.

Predicting heterogeneous ice nucleation with a data-driven approach

Water in nature predominantly freezes with the help of foreign materials through a process known as heterogeneous ice nucleation. Although this effect was exploited more than seven decades ago in Vonnegut's pioneering cloud seeding experiments, it remains unclear what makes a material a good ice former. Here, we show through a machine learning analysis of nucleation simulations on a database of diverse model substrates that a set of physical descriptors for heterogeneous ice nucleation can be identified. Our results reveal that, beyond Vonnegut's connection with the lattice match to ice, three new microscopic factors help to predict the ice nucleating ability. These are: local ordering induced in liquid water, density reduction of liquid water near the surface and corrugation of the adsorption energy landscape felt by water. With this we take a step towards quantitative understanding of heterogeneous ice nucleation and the in silico design of materials to control ice formation.

Thermodynamic and kinetics investigation of homogeneous and heterogeneous nucleation

Nucleation is a fundamental process widely studied in different areas of industry and biology. This review paper comprehensively discussed the principles of classical nucleation theory (primary homogeneous), and heterogeneous nucleation. In the homogeneous part, the nucleation rate in the transient and intransient state is monitored and also heterogeneous nucleation is covered. Finally, conclusions have been deduced from the collected works studied here, and offers for future studies are proposed.

Stochastic Differential Scanning Calorimetry by Nonlinear Optical Microscopy

Stochastic phase transformations within individual crystalline particles were recorded by integration of second harmonic generation (SHG) imaging with differential scanning calorimetry (DSC). The SHG activity of a crystal is highly sensitive to the specific molecular packing arrangement within a noncentrosymmetric lattice, providing access to information otherwise unavailable by conventional imaging approaches. Consequently, lattice transformations associated with dehydration/desolvation events were readily observed by SHG imaging and directly correlated to the phase transformations detected by the DSC measurements. Following studies of a model system (urea), stochastic differential scanning calorimetry (SDSC) was performed on trehalose dihydrate, which has a more complex phase behavior. From these measurements, SDSC revealed a broad diversity of single-particle thermal trajectories and direct evidence of a "cold phase transformation" process not observable by the DSC measurements alone.

Delayed nucleation in lipid particles

Metastable states in first-order phase-transitions have been traditionally described by classical nucleation theory (CNT). However, recently an increasing number of systems displaying such a transition have not been successfully modelled by CNT. The delayed crystallization of phospholipids upon super-cooling is an interesting case, since the extended timescales allow access into the dynamics. Herein, we demonstrate the controllable behavior of the long-lived metastable liquid-crystalline phase of dilauroyl-phosphatidylethanolamine (DLPE), arranged in multi-lamellar vesicles, and the ensuing cooperative transition to the crystalline state. Experimentally, we find that the delay in crystallization is a bulk phenomenon, which is tunable and can be manipulated to span two orders of magnitude in time by changing the quenching temperature, solution salinity, or adding a secondary phospholipid. Our results reveal the robust persistence of the metastability, and showcase the apparent deviation from CNT. This distinctive suppression of the transition may be explained by the resistance of the multi-lamellar vesicle to deformations caused by nucleated crystalline domains. Since phospholipids are used as a platform for drug-delivery, a programmable design of cargo hold and release can be of great benefit.

Recent experimental explorations of non-classical nucleation

This work provides a clearer picture for non-classical nucleation by revealing the presence of various intermediates using advanced characterization techniques.

A bacterial surface layer protein exploits multistep crystallization for rapid self-assembly

Many microbes assemble a crystalline protein layer on their outer surface as an additional barrier and communication platform between the cell and its environment. Surface layer proteins efficiently crystallize to continuously coat the cell, and this trait has been utilized to design functional macromolecular nanomaterials. Here, we report that rapid crystallization of a bacterial surface layer protein occurs through a multistep pathway involving a crystalline intermediate. Upon calcium binding, sequential changes occur in the structure and arrangement of the protein, which are captured by time-resolved small angle X-ray scattering and transmission electron cryo-microscopy. We demonstrate that a specific domain is responsible for enhancing the rate of self-assembly, unveiling possible evolutionary mechanisms to enhance the kinetics of 2D protein crystallization.

Surface layers (S-layers) are crystalline protein coats surrounding microbial cells. S-layer proteins (SLPs) regulate their extracellular self-assembly by crystallizing when exposed to an environmental trigger. However, molecular mechanisms governing rapid protein crystallization in vivo or in vitro are largely unknown. Here, we demonstrate that the Caulobacter crescentus SLP readily crystallizes into sheets in vitro via a calcium-triggered multistep assembly pathway. This pathway involves 2 domains serving distinct functions in assembly. The C-terminal crystallization domain forms the physiological 2-dimensional (2D) crystal lattice, but full-length protein crystallizes multiple orders of magnitude faster due to the N-terminal nucleation domain. Observing crystallization using a time course of electron cryo-microscopy (Cryo-EM) imaging reveals a crystalline intermediate wherein N-terminal nucleation domains exhibit motional dynamics with respect to rigid lattice-forming crystallization domains. Dynamic flexibility between the 2 domains rationalizes efficient S-layer crystal nucleation on the curved cellular surface. Rate enhancement of protein crystallization by a discrete nucleation domain may enable engineering of kinetically controllable self-assembling 2D macromolecular nanomaterials.

Multistep nucleation and growth mechanisms of organic crystals from amorphous solid states

Molecular self-assembly into crystallised films or wires on surfaces produces a big family of motifs exhibiting unique optoelectronic properties. However, little attention has been paid to the fundamental mechanism of molecular crystallisation. Here we report a biomimetic design of phosphonate engineered, amphiphilic organic semiconductors capable of self-assembly, which enables us to use real-time in-situ scanning probe microscopy to monitor the growth trajectories of such organic semiconducting films as they nucleate and crystallise from amorphous solid states. The single-crystal film grows through an evolutionary selection approach in a two-dimensional geometry, with five distinct steps: droplet flattening, film coalescence, spinodal decomposition, Ostwald ripening, and self-reorganised layer growth. These sophisticated processes afford ultralong high-density microwire arrays with high mobilities, thus promoting deep understanding of the mechanism as well as offering important insights into the design and development of functional high-performance organic optoelectronic materials and devices through molecular and crystal engineering.

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.

Revealing the Cluster-Cloud and Its Role in Nanocrystallization

Elucidating the early stages of crystallization from supersaturated solutions is of critical importance, but remains a great challenge. An in situ liquid cell transmission electron microscopy study reveals an intermediate state of condensed atomic clusters during Pd and Au crystallizations, which is named a "cluster-cloud." It is found that nucleation is initiated by the collapse of a cluster-cloud, first forming a nanoparticle. The subsequent particle maturation proceeds via multiple out-and-in relaxations of the cluster-cloud to improve crystallinity: from a poorly crystallized phase, the particle evolves into a well-defined single-crystal phase. Both experimental investigations and atomistic simulations suggest that the cluster-cloud-mediated nanocrystallization involves an order-disorder phase separation and reconstruction, which is energetically favored compared to local rearrangements within the particle. This finding grants new insights into nanocrystallization mechanisms, and provides useful information for the improvement of synthesis pathways of nanocrystals.

Epitaxial Crystallization of Insulin on an Ordered 2D Polymer Template

Two-dimensional polymers (2DP) are a new class of materials that consist of a monolayer of ordered molecular building blocks, which have been covalently linked. One of these monomers was self-assembled on a flat muscovite mica scaffold and subsequently the organic layer was polymerized. The resulting flat and stable 2DP layer was used as a template for protein crystallization. Crystals of insulin were epitaxially grown on the template, whereas insulin crystals grown on clean muscovite mica had a random orientation. The template was selective, considering that no epitaxially ordered crystals formed of hen egg white lysozyme, bovine serum albumin, or talin.

-60 °C solution synthesis of atomically dispersed cobalt electrocatalyst with superior performance

Temperature can govern morphologies, structures and properties of products from synthesis in solution. A reaction in solution at low temperature may result in different materials than at higher temperature due to thermodynamics and kinetics of nuclei formation. Here, we report a low-temperature solution synthesis of atomically dispersed cobalt in a catalyst with superior performance. By using a water/alcohol mixed solvent with low freezing point, liquid-phase reduction of a cobalt precursor with hydrazine hydrate is realized at -60 °C. A higher energy barrier and a sluggish nucleation rate are achieved to suppress nuclei formation; thus atomically dispersed cobalt is successfully obtained in a catalyst for oxygen reduction with electrochemical performance superior to that of a Pt/C catalyst. Furthermore, the atomically dispersed cobalt catalyst is applied in a microbial fuel cell to obtain a high maximum power density (2550 ± 60 mW m^-2) and no current drop upon operation for 820 h.

Peculiarities of Protein Crystal Nucleation and Growth

This paper reviews investigations on protein crystallization. It aims to present a comprehensive rather than complete account of recent studies and efforts to elucidate the most intimate mechanisms of protein crystal nucleation. It is emphasized that both physical and biochemical factors are at play during this process. Recently-discovered molecular scale pathways for protein crystal nucleation are considered first. The bond selection during protein crystal lattice formation, which is a typical biochemically-conditioned peculiarity of the crystallization process, is revisited. Novel approaches allow us to quantitatively describe some protein crystallization cases. Additional light is shed on the protein crystal nucleation in pores and crevices by employing the so-called EBDE method (equilibration between crystal bond and destructive energies). Also, protein crystal nucleation in solution flow is considered.