Imaging the homogeneous nucleation during the melting of superheated colloidal crystals

Melting entropy of crystals determined by electron-beam-induced configurational disordering

Upon melting, the molecules in a crystal explore numerous configurations, reflecting an increase in disorder. The molar entropy of disorder can be defined by Boltzmann's formula ΔSd = Rln(Wd), where Wd is the increase in the number of microscopic states, so far inaccessible experimentally. We found that the Arrhenius frequency factor A of the electron diffraction signal decay provides Wd through an experimental equation A = AINTWd, where AINT is an inelastic scattering cross section. The method connects Clausius and Boltzmann experimentally and supplements the Clausius approach, being applicable to a femtogram quantity of thermally unstable and biomolecular crystals. The data also showed that crystal disordering and crystallization of melt are reciprocal, both governed by the entropy change but manifesting in opposite directions.

Finding the differences: Classical nucleation perspective on homogeneous melting and freezing of hard spheres

By employing brute-force molecular dynamics, umbrella sampling, and seeding simulations, we investigate homogeneous nucleation during melting and freezing of hard spheres. We provide insights into these opposing phase transitions from the standpoint of classical nucleation theory. We observe that melting has both a lower driving force and a lower interfacial tension than freezing. The lower driving force arises from the vicinity of a spinodal instability in the solid and from a strain energy. The lower interfacial tension implies that the Tolman lengths associated with melting and freezing have opposite signs, a phenomenon that we interpret with Turnbull's rule. Despite these asymmetries, the nucleation rates for freezing and melting are found to be comparable.

Ultrathin, Cationic Covalent Organic Nanosheets for Enhanced CO2 Electroreduction to Methanol

Metalloporphyrins and metallophthalocyanines emerge as popular building blocks to develop covalent organic nanosheets (CONs) for CO2 reduction reaction (CO2RR). However, existing CONs predominantly yield CO, posing a challenge in achieving efficient methanol production through multielectron reduction. Here, ultrathin, cationic, and cobalt-phthalocyanine-based CONs (iminium-CONs) are reported for electrochemical CO2-to-CH3OH conversion. The integration of quaternary iminium groups enables the formation of ultrathin morphology with uniformly anchored cobalt active sites, which are pivotal for facilitating rapid multielectron transfer. Moreover, the cationic iminium-CONs exhibit a lower activity for hydrogen evolution side reaction. Consequently, iminium-CONs manifest significantly enhanced selectivity for methanol production, as evidenced by a remarkable 711% and 270% improvement in methanol partial current density (jCH3OH) compared to pristine CoTAPc and neutral imine-CONs, respectively. Under optimized conditions, iminium-CONs deliver a high jCH3OH of 91.7 mA cm-2 at -0.78 V in a flow cell. Further, iminium-CONs achieve a global methanol Faradaic efficiency (FECH3OH) of 54% in a tandem device. Thanks to the single-site feature, the methanol is produced without the concurrent generation of other liquid byproducts. This work underscores the potential of cationic covalent organic nanosheets as a compelling platform for electrochemical six-electron reduction of CO2 to methanol.

Anisotropic-Isotropic Transition of Cages at the Glass Transition

Characterizing the local structural evolution is an essential step in understanding the nature of glass transition. In this work, we probe the evolution of Voronoi cell geometry in simple glass models by simulations and colloid experiments, and find that the individual particle cages deform anisotropically in supercooled liquid and isotropically in glass. We introduce an anisotropy parameter k for each Voronoi cell, whose mean value exhibits a sharp change at the mode-coupling glass transition ϕ_{c}. Moreover, a power law of packing fraction ϕ∝q_{1}^{d} is discovered in the supercooled liquid regime with d>D, in contrast to d=D in the glass regime, where q_{1} is the first peak position of structure factor, and D is the space dimension. This power law is qualitatively explained by the change of k. The active motions in supercooled liquid are spatially correlated with long axes rather than short axes of Voronoi cells. In addition, the dynamic slowing down approaching the glass transition can be well characterized through a modified free-volume model based on k. These findings reveal that the structural parameter k is effective in identifying the structure-dynamics correlations and the glass transition in these systems.

Deterministic Formation and Growth of Dendritic Crystals of Attractive Colloids

Dendrites are ubiquitous crystals produced in supersaturated solutions and supercooled melts, but considerably less is known about their formation and growth kinetics. Here, the key factors are explored that dictate dendrite formation and growth, utilizing experimental colloidal models in which the particles act as molecules with Mie potential. Depletion attraction is employed to colloids and manipulate their strength to control supersaturation. Dendrites are predominantly produced under conditions of low supersaturation, where the separation between crystals is large due to slow nucleation. The dendrites do not emerge directly from nuclei. Instead, isotropic grains, initially produced from nuclei, morph into polygons. Arms then sprout from the vertices of these polygons, eventually giving rise to dendrites. Triggering this polygon-to-dendrite transformation requires a high diffusional flux. This necessitates a prolonged diffusion time to maintain a steep concentration gradient in the surrounding environment even after the transformation from circular grains to polygons.

Phase Reentrances and Solid Deformations in Confined Colloidal Crystals

A simple geometric constraint often leads to novel, complex crystalline phases distinct from the bulk. Using thin-film charge colloidal crystals, a model system with tunable interactions, we study the effects of geometric constraints. Through a combination of experiments and simulations, we systematically explore phase reentrances and solid deformation modes concerning geometrical confinement strength, identifying two distinct categories of phase reentrances below a characteristic layer number, N_{c}: one for bcc bulk-stable and another for fcc bulk-stable systems. We further verify that the dominant thermodynamic origin is the nonmonotonic dependence of solids' free energy on the degree of spatial confinement. Moreover, we discover transitions in solid deformation modes between interface-energy and bulk-energy dominance: below a specific layer number, N_{k}, geometric constraints generate unique soft deformation modes adaptive to confinement. These findings on the N-dependent thermodynamic and kinetic behaviors offer fresh insights into understanding and manipulating thin-film crystal structures.

Compression and fracture of ordered and disordered droplet rafts

We simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced to rearrange. The rearrangement occurs via a fracture, where depletion bonds are quickly broken between a subset of droplets. For monodisperse, hexagonally ordered droplet arrays, this fracture is preceded by a maximum force exerted on the walls, which drops rapidly after the fracture occurs. In small droplet arrays a fracture is a single well-defined event, but for larger droplet arrays, competing fractures can be observed. These are fractures nucleated nearly simultaneously in different locations. Finally, we also study the compression of bidisperse droplet arrays. The addition of a second droplet size further disrupts fracture events, showing differences between ideal crystalline arrays, crystalline arrays with a small number of defects, and fully amorphous arrays. These results are in good agreement with previously published experiments.

Melting Is Well-Known, but Is It Also Well-Understood?

Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is well-known and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.

Two-Step Melting in a Bulk Crystal via Intermediate Metastable Liquid

The mechanism of melting is significant, as it links the structure and dynamics between crystal and liquid. In two dimensions, the crystal could first melt into a hexatic liquid before finally reaching a disordered liquid. However, such a hexatic liquid phase is unstable in three dimensions, and melting is recognized as a one-step process. Here we report a two-step melting process in a three-dimensional system, (S)-(+)-ibuprofen. The crystal melts through an indirect pathway that first transforms into an intermediate liquid phase exhibiting an extremely long lifetime followed by the transition to the ordinary liquid phase at a spinodal point with the occurrence of long-range fluctuations. Such observations suggest that the complexity of liquid could affect the transition pathway of melting. These results could lead us to hypothesize the existence of continuous melting in three dimensions.

Changes in Tissue Fluidity Predict Tumor Aggressiveness In Vivo

Cancer progression is caused by genetic changes and associated with various alterations in cell properties, which also affect a tumor's mechanical state. While an increased stiffness has been well known for long for solid tumors, it has limited prognostic power. It is hypothesized that cancer progression is accompanied by tissue fluidization, where portions of the tissue can change position across different length scales. Supported by tabletop magnetic resonance elastography (MRE) on stroma mimicking collagen gels and microscopic analysis of live cells inside patient derived tumor explants, an overview is provided of how cancer associated mechanisms, including cellular unjamming, proliferation, microenvironment composition, and remodeling can alter a tissue's fluidity and stiffness. In vivo, state-of-the-art multifrequency MRE can distinguish tumors from their surrounding host tissue by their rheological fingerprints. Most importantly, a meta-analysis on the currently available clinical studies is conducted and universal trends are identified. The results and conclusions are condensed into a gedankenexperiment about how a tumor can grow and eventually metastasize into its environment from a physics perspective to deduce corresponding mechanical properties. Based on stiffness, fluidity, spatial heterogeneity, and texture of the tumor front a roadmap for a prognosis of a tumor's aggressiveness and metastatic potential is presented.

In situ observation of coalescence of nuclei in colloidal crystal-crystal transitions

Coalescence of nuclei in phase transitions significantly influences the transition rate and the properties of product materials, but these processes occur rapidly and are difficult to observe at the microscopic scale. Here, we directly image the coalescence of nuclei with single particle resolution during the crystal-crystal transition from a multilayer square to triangular lattices. The coalescence process exhibits three similar stages across a variety of scenarios: coupled growth of two nuclei, their attachment, and relaxation of the coalesced nucleus. The kinetics vary with nucleus size, interface, and lattice orientation; the kinetics include acceleration of nucleus growth, small nucleus liquefaction, and generation/annihilation of defects. Related mechanisms, such as strain induced by nucleus growth and the lower energy of liquid-crystal versus crystal-crystal interfaces, appear to be common to both atomic and colloidal crystals.

Porous crystals in charged sphere suspensions by aggregate-driven phase separation

The kinetics of phase transition processes often governs the resulting material microstructure. Using optical microscopy, we here investigate the formation and stabilization of a porous crystalline microstructure forming in low-salt suspensions of charged colloidal spheres containing aggregates comprising some 5-10 of these colloids. We observe the transformation of an initially crystalline colloidal solid with homogeneously incorporated aggregates to individual, compositionally refined crystallites of perforated morphology coexisting with an aggregate-enriched fluid phase filling the holes and separating individual crystallites. A preliminary kinetic characterization suggests that the involved processes follow power laws. We show that this route to porous materials is neither restricted to nominally single component systems nor to a particular microstructure to start from. However, it necessitates an early rapid solidification stage during which the aggregates become trapped in the bulk of the host-crystals. The thermodynamic stability of the reconstructed crystalline scaffold against melting under increased salinity was found comparable to that of pure phase crystallites grown very slowly from a melt. Future implications of this novel route to porous colloidal crystals are discussed.

A Nanoparticle-Based Model System for the Study of Heterogeneous Nucleation Phenomena

Heterogeneous nucleation processes are involved in many important phenomena in nature, including devastating human diseases caused by amyloid structures or the harmful frost formed on fruits. However, understanding them is challenging due to the difficulties of characterizing the initial stages of the process occurring at the interface between the nucleation medium and the substrate surfaces. This work implements a model system based on gold nanoparticles to investigate the effect of particle surface chemistry and substrate properties on heterogeneous nucleation processes. Using widely available techniques such as UV-vis-NIR spectroscopy and light microscopy, gold nanoparticle-based superstructure formation was studied in the presence of substrates with different hydrophilicity and electrostatic charges. The results were evaluated on grounds of classical nucleation theory (CNT) to reveal kinetic and thermodynamic contributions of the heterogeneous nucleation process. In contrast to nucleation from ions, the kinetic contributions toward nucleation turned out to be larger than the thermodynamic contributions for the nanoparticle building blocks. Electrostatic interactions between substrates and nanoparticles with opposite charges were crucial to enhancing the nucleation rates and decreasing the nucleation barrier of superstructure formation. Thereby, the described strategy is demonstrated advantageous for characterizing physicochemical aspects of heterogeneous nucleation processes in a simple and accessible manner, which could be potentially explored to study more complex nucleation phenomena.

Field-Pulse-Induced Annealing of 2D Colloidal Polycrystals

Two-dimensional colloidal crystals are of considerable fundamental and practical importance. However, their quality is often low due to the widespread presence of domain walls and defects. In this work, we explored the annealing process undergone by monolayers of superparamagnetic colloids adsorbed onto fluid interfaces in the presence of magnetic field pulses. These systems present the extraordinary peculiarity that both the extent and the character of interparticle interactions can be adjusted at will by simply varying the strength and orientation of the applied field so that the application of field pulses results in a sudden input of energy. Specifically, we have studied the effect of polycrystal size, pulse duration, slope and frequency on the efficiency of the annealing process and found that (i) this strategy is only effective when the polycrystal consists of less than approximately 10 domains; (ii) that the pulse duration should be of the order of magnitude of the time required for the outer particles to travel one diameter during the heating step; (iii) that the quality of larger polycrystals can be slightly improved by applying tilted pulses. The experimental results were corroborated by Brownian dynamics simulations.

Macroscopic Supramolecular Assembly of Rigid Building Blocks Facilitated by Layer-By-Layer Assembled Microgel Film

Macroscopic supramolecular assembly (MSA) of building blocks larger than 1 μm provides new methodology for fabrication of functional supramolecular materials and a platform for mechanism investigation of interfacial phenomena. Most reports on MSA are restricted to soft hydrogels, and supramolecular groups can be directly integrated into a hydrogel matrix to generate sufficient attraction for maintaining macroscopic assemblies. For non-hydrogel stiff building blocks, two layer-by-layer modification processes consisting of flexible spacing coating and additional interacting groups are necessary to enable MSA, which is laborious and time-consuming. Approaches for highly efficient MSA based on flexible spacing coating are desired. In this work, MSA of polydimethylsiloxane (PDMS) building blocks is demonstrated by inducing microgel films that serve as both flexible spacing coating and surface functional groups, thus avoiding a two-step LbL modification process. By the varying bilayer number of microgel films, the MSA probability of modified PDMS increases from 54% at 3 bilayers to 100% at 6 bilayers. Control experiments and in situ force measurement strongly support the obtained MSA results and verify the dominant role of the microgel film as a flexible spacing coating and a supramolecularly interactive layer in achieving MSA. Moreover, the underlying mechanism is interpreted as low Young's modulus microgel films rendering surface groups highly mobile to enhance the multivalent interfacial binding. Taken together, this work has demonstrated the feasibility of MSA of rigid building blocks assisted by microgel films as flexible spacing coating and supramolecularly interactive layer simultaneously, which may extend the application fields of microgel materials to interfacial adhesion and advanced manufacturing with MSA methodology.

Visualizing the Formation of High-Entropy Fluorite Oxides from an Amorphous Precursor at Atomic Resolution

High-entropy oxides (HEOs) have a large tuning space in composition and crystal structures, offering the possibility for improved material properties in applications including catalysis, energy storage, and thermal barrier coatings. Understanding the nucleation and growth mechanisms of HEOs at the atomic scale is critical to the design of their structure and functions but remains challenging. Herein, we visualize the entire formation process of a high-entropy fluorite oxide from a polymeric precursor using atomic resolution in situ gas-phase scanning transmission electron microscopy. The results show a four-stage formation mechanism, including nucleation during the oxidation of a polymeric precursor below 400 °C, diffusive grain growth below 900 °C, liquid-phase-assisted compositional homogenization under a "state of supercooling" at 900 °C, and entropy-driven recrystallization and stabilization at higher temperatures. The atomistic insights are critical for the rational synthesis of HEOs with controlled grain sizes and morphologies and thus the related properties.

In Situ Kinetic Observations on Crystal Nucleation and Growth

Nucleation and growth are critical steps in crystallization, which plays an important role in determining crystal structure, size, morphology, and purity. Therefore, understanding the mechanisms of nucleation and growth is crucial to realize the controllable fabrication of crystalline products with desired and reproducible properties. Based on classical models, the initial crystal nucleus is formed by the spontaneous aggregation of ions, atoms, or molecules, and crystal growth is dependent on the monomer's diffusion and the surface reaction. Recently, numerous in situ investigations on crystallization dynamics have uncovered the existence of nonclassical mechanisms. This review provides a summary and highlights the in situ studies of crystal nucleation and growth, with a particular emphasis on the state-of-the-art research progress since the year 2016, and includes technological advances, atomic-scale observations, substrate- and temperature-dependent nucleation and growth, and the progress achieved in the various materials: metals, alloys, metallic compounds, colloids, and proteins. Finally, the forthcoming opportunities and challenges in this fascinating field are discussed.

Direct Measurements of Surface Strain-Mediated Lateral Interactions between Adsorbates in Colloidal Heteroepitaxy

Surface strain can alter the dynamics of adsorbates, and often, the adsorbates themselves induce and interact via their surface strain fields. In epitaxy, such strain-mediated effects get further compounded when a misfit strain exists due to lattice mismatch between the growing film and substrate. Here, we carry out particle-resolved imaging of heteroepitaxial growth of multilayer colloidal films where the particles interact via a short-range attraction. Surprisingly, although the misfit strain relaxed systematically with film thickness, the adcolloid diffusivity was nonmonotonic. We show that this nonmonotonicity stems from the competition between the spatial extent of self-induced in-layer strain and the short interaction range. Importantly, we provide direct evidence for long-ranged strain-mediated interactions between adsorbates and show that it alters the growing film's morphology.

Dynamics of a colloid-in-tube host-guest system

Originated from supramolecular chemistry, the host-guest concept is generalized and appreciated across the fields of enzyme catalysis, biological channel conduction, and carbon nanotube transport, to name a few. Despite the extensive study of host-guest thermodynamics, it is still a fundamental challenge to directly measure its dynamics in real-space and real-time. Herein we approach such dynamics by direct imaging and tracking in a colloid-in-tube system, where self-assembled tubes are the hosts and sphere particles are the guests. The key difference from a previously reported static 1D confinement is that the present tubes are thermally actuated and capable of translations and rotations. It is the host tube thermal motions that impose a number of anomalies to guest particle dynamics including broadened distribution perpendicular to the tube, enhanced diffusion parallel to the tube phenomenologically resembling the rapid flow in ion channels or carbon nanotubes, and induced long-range particle-particle attraction analogous to capillary condensation. This work in the colloidal system is of wide implications for host-guest systems that are naturally embedded in thermal fluctuations such as transmembrane ion channels and carbon nanotube arrays in a soft matrix.

Correlation Tracking: Using simulations to interpolate highly correlated particle tracks

Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e., linking individual particle positions across time series data. The state-of-the-art tracking algorithm is highly effective for systems in which the particles behave mostly independently. However, these algorithms become inaccurate when particle motion is highly correlated, such as in dense or strongly interacting systems. Accurate particle tracking is essential in the study of the physics of dense colloids, such as the study of dislocation formation, nucleation, and shear transformations. Here, we present a method for particle tracking that incorporates information about the correlated motion of the particles. We demonstrate significant improvement over the state-of-the-art tracking algorithm in simulated data on highly correlated systems.

Superheating of grain boundaries within bulk colloidal crystals

Whether grain boundaries (GBs) premelt is a longstanding question, because of the difficulty of direct experimental tests. Here, we focused an optical beam to locally heat single GBs within bulk hard-sphere colloidal crystals, observing the melting dynamics at single-particle resolution by video microscopy. The melting point is determined by analysing both the Lindemann parameter and the critical nucleus size for homogeneous nucleation. We found that all the GBs, including the high-energy GBs, can be superheated and melt via a heterogeneous nucleation mechanism. Based on the classical nucleation theory of GBs, we measured the incubation time and contact angle of the critical nucleus to compute all relevant kinetic factors, as well as the energy barrier, nucleation rate and the diffusion coefficient at the solid–liquid interface under weak superheating. The superheat limits of GBs with various misorientations have also been measured to further explore the instability mechanism. Under traditional uniform heating, premelting occurs only at triple junctions, whereas GBs retain their original structures up to the melting point. The premelted regions at triple junctions further interrupt high-energy GBs from superheating, through intrusion by uniform liquid layers. Overall, our experiments confirm the existence of superheating of GBs.

Understanding the dynamics of grain boundaries and their melting behaviour is important for controlling the mechanical properties of materials. Now, experiments show that grain boundaries can be superheated, and that they melt via a nucleation mechanism.

The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems

Monolayer and two-dimensional (2D) systems exhibit rich phase behavior, compared with 3D systems, in particular, due to the hexatic phase playing a central role in melting scenarios. The attraction range is known to affect critical gas–liquid behavior (liquid–liquid in protein and colloidal systems), but the effect of attraction on melting in 2D systems remains unstudied systematically. Here, we have revealed how the attraction range affects the phase diagrams and melting scenarios in a 2D system. Using molecular dynamics simulations, we have considered the generalized Lennard-Jones system with a fixed repulsion branch and different power indices of attraction from long-range dipolar to short-range sticky-sphere-like. A drop in the attraction range has been found to reduce the temperature of the gas–liquid critical point, bringing it closer to the gas–liquid–solid triple point. At high temperatures, attraction does not affect the melting scenario that proceeds through the cascade of solid–hexatic (Berezinskii–Kosterlitz–Thouless) and hexatic–liquid (first-order) phase transitions. In the case of dipolar attraction, we have observed two triple points inherent in a 2D system: hexatic–liquid–gas and crystal–hexatic–gas, the temperature of the crystal–hexatic–gas triple point is below the hexatic–liquid–gas triple point. This observation may have far-reaching consequences for future studies, since phase diagrams determine possible routes of self-assembly in molecular, protein, and colloidal systems, whereas the attraction range can be adjusted with complex solvents and external electric or magnetic fields. The results obtained may be widely used in condensed matter, chemical physics, materials science, and soft matter.

In situ characterization of crystallization and melting of soft, thermoresponsive microgels by small-angle X-ray scattering

Depending on the volume fraction and interparticle interactions, colloidal suspensions can form different phases, ranging from fluids, crystals, and glasses to gels. For soft microgels that are made from thermoresponsive polymers, the volume fraction can be tuned by temperature, making them excellent systems to experimentally study phase transitions in dense colloidal suspensions. However, investigations of phase transitions at high particle concentration and across the volume phase transition temperature in particular, are challenging due to the deformability and possibility for interpenetration between microgels. Here, we investigate the dense phases of composite core-shell microgels that have a small gold core and a thermoresponsive microgel shell. Employing Ultra Small-Angle X-ray Scattering, we make use of the strong scattering signal from the gold cores with respect to the almost negligible signal from the shells. By changing the temperature we study the freezing and melting transitions of the system in situ. Using Bragg peak analysis and the Williamson-Hall method, we characterize the phase transitions in detail. We show that the system crystallizes into an rhcp structure with different degrees of in-plane and out-of-plane stacking disorder that increase upon particle swelling. We further find that the melting process is distinctly different, where the system separates into two different crystal phases with different melting temperatures and interparticle interactions.

Direct observation of crystal nucleation and growth in a quasi-two-dimensional nonvibrating granular system

We study a quasi-two-dimensional macroscopic system of magnetic spherical particles settled on a shallow concave dish under a temporally oscillating magnetic field. The system reaches a stationary state where the energy losses from collisions and friction with the concave dish surface are compensated by the continuous energy input coming from the oscillating magnetic field. Random particle motions show some similarities with the motions of atoms and molecules in a glass or a crystal-forming fluid. Because of the curvature of the surface, particles experience an additional force toward the center of the concave dish. When decreasing the magnetic field, the effective temperature is decreased and diffusive particle motion slows. For slow cooling rates we observe crystallization, where the particles organize into a hexagonal lattice. We study the birth of the crystalline nucleus and the subsequent growth of the crystal. Our observations support nonclassical theories of crystal formation. Initially a dense amorphous aggregate of particles forms, and then in a second stage this aggregate rearranges internally to form the crystalline nucleus. As the aggregate grows, the crystal grows in its interior. After a certain size, all the aggregated particles are part of the crystal and after that crystal growth follows the classical theory for crystal growth.

Colloidal Self-Assembly Approaches to Smart Nanostructured Materials

Colloidal self-assembly refers to a solution-processed assembly of nanometer-/micrometer-sized, well-dispersed particles into secondary structures, whose collective properties are controlled by not only nanoparticle property but also the superstructure symmetry, orientation, phase, and dimension. This combination of characteristics makes colloidal superstructures highly susceptible to remote stimuli or local environmental changes, representing a prominent platform for developing stimuli-responsive materials and smart devices. Chemists are achieving even more delicate control over their active responses to various practical stimuli, setting the stage ready for fully exploiting the potential of this unique set of materials. This review addresses the assembly of colloids into stimuli-responsive or smart nanostructured materials. We first delineate the colloidal self-assembly driven by forces of different length scales. A set of concepts and equations are outlined for controlling the colloidal crystal growth, appreciating the importance of particle connectivity in creating responsive superstructures. We then present working mechanisms and practical strategies for engineering smart colloidal assemblies. The concepts underpinning separation and connectivity control are systematically introduced, allowing active tuning and precise prediction of the colloidal crystal properties in response to external stimuli. Various exciting applications of these unique materials are summarized with a specific focus on the structure-property correlation in smart materials and functional devices. We conclude this review with a summary of existing challenges in colloidal self-assembly of smart materials and provide a perspective on their further advances to the next generation.

Fast crystal growth at ultra-low temperatures

It is believed that the slow liquid diffusion and geometric frustration brought by a rapid, deep quench inhibit fast crystallization and promote vitrification. Here we report fast crystal growth in charged colloidal systems under deep supercooling, where liquid diffusion is extremely low. By combining experiments and simulations, we show that this process occurs via wall-induced barrierless ordering consisting of two coupled steps: the step-like advancement of the rough interface that disintegrates frustration, followed by defect repairing inside the newly formed solid phase. The former is a diffusionless collective process, whereas the latter controls crystal quality. We further show that the intrinsic mechanical instability of a disordered glassy state subject to the crystal growth front allows for domino-like fast crystal growth even at ultra-low temperatures. These findings contribute to a deeper understanding of fast crystal growth and may be useful for applications related to vitrification prevention and crystal-quality control.

The microscopic mechanism of bulk melting of ice

We study the initial stages of homogeneous melting of a hexagonal ice crystal at coexistence and at moderate superheating. Our trajectory-based computer simulation approach provides a comprehensive picture of the events that lead to melting, from the initial accumulation of 5+7 defects, via the formation of L-D and interstitial-vacancy pairs, to the formation of a liquid nucleus. Of the different types of defects that we observe to be involved in melting, a particular kind of 5+7 type defect (type 5) plays a prominent role as it often forms prior to the formation of the initial liquid nucleus and close to the site where the nucleus forms. Hence, like other solids, ice homogeneously melts via the prior accumulation of defects.

2D colloids in rotating electric fields: A laboratory of strong tunable three-body interactions

Many-body forces play a prominent role in structure and dynamics of matter, but their role is not well understood in many cases due to experimental challenges. Here, we demonstrate that a novel experimental system based on rotating electric fields can be utilised to deliver unprecedented degree of control over many-body interactions between colloidal silica particles in water. We further show that we can decompose interparticle interactions explicitly into the leading terms and study their specific effects on phase behaviour. We found that three-body interactions exert critical influence over the phase diagram domain boundaries, including liquid-gas binodal, critical and triple points. Phase transitions are shown to be reversible and fully controlled by the magnitude of external rotating electric field governing the tunable interactions. Our results demonstrate that colloidal systems in rotating electric fields are a unique laboratory to study the role of many-body interactions in physics of phase transitions and in applications, such as self-assembly, offering exciting opportunities for studying generic phenomena inherent to liquids and solids, from atomic to protein and colloidal systems.

Fcc vs. hcp competition in colloidal hard-sphere nucleation: on their relative stability, interfacial free energy and nucleation rate

Hard-sphere crystallization has been widely investigated over the last six decades by means of colloidal suspensions and numerical methods. However, some aspects of its nucleation behaviour are still under debate. Here, we provide a detailed computational characterisation of the polymorphic nucleation competition between the face-centered cubic (fcc) and the hexagonal-close packed (hcp) hard-sphere crystal phases. By means of several state-of-the-art simulation techniques, we evaluate the melting pressure, chemical potential difference, interfacial free energy and nucleation rate of these two polymorphs, as well as of a random stacking mixture of both crystals. Our results highlight that, despite the fact that both polymorphs have very similar stability, the interfacial free energy of the hcp phase could be marginally higher than that of the fcc solid, which in consequence, mildly decreases its propensity to nucleate from the liquid compared to the fcc phase. Moreover, we analyse the abundance of each polymorph in grown crystals from different types of inserted nuclei: fcc, hcp and stacking disordered fcc/hcp seeds, as well as from those spontaneously emerged from brute force simulations. We find that post-critical crystals fundamentally grow maintaining the polymorphic structure of the critical nucleus, at least until moderately large sizes, since the only crystallographic orientation that allows stacking close-packed disorder is the fcc (111) plane, or equivalently the hcp (0001) one. Taken together, our results contribute with one more piece to the intricate puzzle of colloidal hard-sphere crystallization.

Mean-field model of melting in superheated crystals based on a single experimentally measurable order parameter

Melting is one of the most studied phase transitions important for atomic, molecular, colloidal, and protein systems. However, there is currently no microscopic experimentally accessible criteria that can be used to reliably track a system evolution across the transition, while providing insights into melting nucleation and melting front evolution. To address this, we developed a theoretical mean-field framework with the normalised mean-square displacement between particles in neighbouring Voronoi cells serving as the local order parameter, measurable experimentally. We tested the framework in a number of colloidal and in silico particle-resolved experiments against systems with significantly different (Brownian and Newtonian) dynamic regimes and found that it provides excellent description of system evolution across melting point. This new approach suggests a broad scope for application in diverse areas of science from materials through to biology and beyond. Consequently, the results of this work provide a new guidance for nucleation theory of melting and are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Revealing thermally-activated nucleation pathways of diffusionless solid-to-solid transition

Solid-to-solid transitions usually occur via athermal nucleation pathways on pre-existing defects due to immense strain energy. However, the extent to which athermal nucleation persists under low strain energy comparable to the interface energy, and whether thermally-activated nucleation is still possible are mostly unknown. To address these questions, the microscopic observation of the transformation dynamics is a prerequisite. Using a charged colloidal system that allows the triggering of an fcc-to-bcc transition while enabling in-situ single-particle-level observation, we experimentally find both athermal and thermally-activated pathways controlled by the softness of the parent crystal. In particular, we reveal three new transition pathways: ingrain homogeneous nucleation driven by spontaneous dislocation generation, heterogeneous nucleation assisted by premelting grain boundaries, and wall-assisted growth. Our findings reveal the physical principles behind the system-dependent pathway selection and shed light on the control of solid-to-solid transitions through the parent phase's softness and defect landscape.

Interface-induced hysteretic volume phase transition of microgels: simulation and experiment

Thermo-responsive microgel particles can exhibit a drastic volume shrinkage upon increasing the solvent temperature. Recently we found that the spreading of poly(N-isopropylacrylamide) (PNiPAm) microgels at a liquid interface under the influence of surface tension hinders the temperature-induced volume phase transition. In addition, we observed a hysteresis behavior upon temperature cycling, i.e. a different evolution in microgel size and shape depending on whether the microgel was initially adsorbed to the interface in expanded or collapsed state. Here, we model the volume phase transition of such microgels at an air/water interface by monomer-resolved Brownian dynamics simulations and compare the observed behavior with experiments. We reproduce the experimentally observed hysteresis in the microgel dimensions upon temperature variation. Our simulations did not observe any hysteresis for microgels dispersed in the bulk liquid, suggesting that it results from the distinct interfacial morphology of the microgel adsorbed at the liquid interface. An initially collapsed microgel brought to the interface and subjected to subsequent swelling and collapsing (resp. cooling and heating) will end up in a larger size than it had in the original collapsed state. Further temperature cycling, however, only shows a much reduced hysteresis, in agreement with our experimental observations. We attribute the hysteretic behavior to a kinetically trapped initial collapsed configuration, which relaxes upon expanding in the swollen state. We find a similar behavior for linear PNiPAm chains adsorbed to an interface. Our combined experimental - simulation investigation provides new insights into the volume phase transition of PNiPAm materials adsorbed to liquid interfaces.

Collapse-induced phase transitions in binary interfacial microgel monolayers

Microgels, consisting of a swollen polymer network, exhibit a more complex self-assembly behavior compared to incompressible colloidal particles, because of their ability to deform at a liquid interface or collapse upon compression. Here, we investigate the collective phase behavior of two-dimensional binary mixtures of microgels confined at the air/water interface. We use stimuli-responsive poly(N-isopropylacrylamide) microgels with different crosslinking densities, and therefore different morphologies at the interface. We find that the minority microgel population introduces lattice defects in the ordered phase of the majority population, which, in contrast to bulk studies, do not heal out by partial deswelling to accommodate in the lattice. We subsequently investigate the interfacial phase behavior of these binary interfacial assemblies under compression. The binary system exhibits three distinct isostructural solid-solid phase transitions, during which the coronae between two small particles collapse first, followed by the collapse between small-large and large-large microgel pairs. A similar hierarchy of phase transitions is found for mixtures of microgels and core-shell particles. Simulations based on augmented potentials qualitatively reproduce the experimentally observed phase transitions. We rationalize the presence of this hierarchy in phase transitions from differences in the interfacial morphology between the species: the larger coronae of softer (and therefore larger) microgels provide a higher resistance to phase transitions compared to the smaller coronae of the more crosslinked microgels and core-shell particles. The control of phase transitions via the molecular architecture further allows the formation of characteristic, flower-like defects by introducing particles with "weaker" coronae that are more prone to collapse with their neighboring particles. Our findings underline the dominating role of the corona for interfacial microgel assemblies, which acts as an energy barrier, shifting the collapse to higher surface pressures.

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.

Pervasive orientational and directional locking at geometrically heterogeneous sliding interfaces

Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and microscale objects on surfaces. In a previous work, we studied the orientational and directional locking of colloidal two-dimensional clusters with triangular structure driven across a triangular substrate lattice. Here we show with experiments and simulations that such locking features arise for clusters with arbitrary lattice structure sliding across arbitrary regular substrates. Similar to triangular-triangular contacts, orientational and directional locking are strongly correlated via the real- and reciprocal-space Moiré patterns of the contacting surfaces. Due to the different symmetries of the surfaces in contact, however, the relation between the locking orientation and the locking direction becomes more complicated compared to interfaces composed of identical lattice symmetries. We provide a generalized formalism which describes the relation between the locking orientation and locking direction with arbitrary lattice symmetries.

Mechanical properties of 2D aggregates of oil droplets as model mono-crystals

We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. The elastic properties of ideal mono-crystal samples are fully captured by a simple analytical model consisting of an assembly of individual capillary springs. The yielding properties of the crystal are captured with a minimal bond breaking model.

Electrocatalysis for CO2 conversion: from fundamentals to value-added products

This timely and comprehensive review mainly summarizes advances in heterogeneous electroreduction of CO₂: from fundamentals to value-added products.

Static and dynamic behavior of magnetic particles at fluid interfaces

This perspective work reviews the current status of research on magnetic particles at fluid interfaces. The article gives both a unified overview of recent experimental advances and theoretical studies centered on very different phenomena that share a common characteristic: they involve adsorbed magnetic particles that range in size from a few nanometers to several millimeters. Because of their capability of being remotely piloted through controllable external fields, magnetic particles have proven essential as building blocks in the design of new techniques, smart materials and micromachines, with new tunable properties and prospective applications in engineering and biotechnology. Once adsorbed at a fluid-fluid interfase, in a process that can be facilitated via the application of magnetic field gradients, these particles often result sorely confined to two dimensions (2D). In this configuration, inter-particle forces directed along the perpendicular to the interface are typically very small compared to the surface forces. Hence, the confinement and symmetry breaking introduced by the presence of the surface play an important role on the response of the system to the application of an external field. In monolayers of particles where the magnetic is predominant interaction, the states reached are strongly determined by the mode and orientation of the applied field, which promote different patterns and processes. Furthermore, they can reproduce some of the dynamic assemblies displayed in bulk or form new ones, that take advantage of the interfacial phenomena or of the symmetry breaking introduce by the confining boundary. Magnetic colloids are also widely used for unraveling the guiding principles of 2D dynamic self-assembly, in designs devised for producing interface transport, as tiny probes for assessing interfacial rheological properties, neglecting the bulk and inertia contributions, as well as actuated stabilizing agents in foams and emulsions.

Revealing roles of competing local structural orderings in crystallization of polymorphic systems

Most systems have more than two stable crystalline states in the phase diagram, which is known as polymorphism. Crystallization in such a system is often under strong influence of competing orderings linked to those crystals. However, how such competition affects crystal nucleation and ordering toward the final crystalline state is largely unknown. This is primarily because the competition takes place locally and thus is masked by large positional fluctuations. We develop a unique method to correctly identify local symmetries by removing their distortions due to positional fluctuations. This allows us to experimentally access the spatiotemporal fluctuations of local symmetries at a single-particle level in crystallization of a charged colloidal system near the body-centered cubic-face-centered cubic border. Thus, we successfully reveal the crucial roles of competing ordering in the initial selection of polymorphs and the final grain boundary motion toward the most stable state from a microscopic perspective.

Dynamics at the crystal-melt interface in a supercooled chalcogenide liquid near the glass transition

Direct quantitative measurements of nanoscale dynamical processes associated with structural relaxation and crystallization near the glass transition are a major experimental challenge. These type of processes have been primarily treated as macroscopic phenomena within the framework of phenomenological models and bulk experiments. Here, we report x-ray photon correlation spectroscopy measurements of dynamics at the crystal-melt interface during the radiation induced formation of Se nano-crystallites in pure Se and in binary AsSe₄ glass-forming liquids near their glass transition temperature. We observe a heterogeneous dynamical behaviour where the intensity correlation functions g₂(q, t) exhibits either a compressed or a stretched exponential decay, depending on the size of the Se nano-crystallites. The corresponding relaxation timescale for the AsSe₄ liquid increases as the temperature is raised, which can be attributed to changes in the chemical composition of the melt at the crystal-melt interface with the growth of the Se nano-crystallites.

Superheating and Homogeneous Melting Dynamics of Bulk Ice

Homogeneous melting of crystals is a complex multistep process involving the formation of transient states at temperatures considerably higher than the melting point. The nature and persistence of these metastable structures are intimately connected to the melting process, and a precise definition of the temporal boundaries of these phenomena is not yet available. We set up a specifically designed experiment to probe by transient infrared absorption spectroscopy the entire dynamics, ranging from tens of picoseconds to microseconds, of superheating and melting of an ice crystal. In spite of a large excess of energy provided, only about 30% of the micrometric crystal liquefies in the first 20-25 ns because of the long persistence of the superheated metastable phase that extends for more than 100 ns. This behavior is ascribed to the population of low-energy states that trap a large amount of energy, favoring the formation of a metastable, likely plastic, ice phase.

Stimuli-Responsive Behavior of PNiPAm Microgels under Interfacial Confinement

The volume phase transition of microgels is one of the most paradigmatic examples of stimuli-responsiveness, enabling a collapse from a highly swollen microgel state into a densely coiled state by an external stimulus. Although well characterized in bulk, it remains unclear how the phase transition is affected by the presence of a confining interface. Here, we demonstrate that the temperature-induced volume phase transition of poly(N-isopropylacrylamide) microgels, conventionally considered an intrinsic molecular property of the polymer, is in fact largely suppressed when the microgel is adsorbed to an air/liquid interface. We further observe a hysteresis in the core morphology and interfacial pressure between heating and cooling cycles. Our results, supported by molecular dynamics simulations, reveal that the dangling polymer chains of microgel particles, spread at the interface under the influence of surface tension, do not undergo any volume phase transition. The balance in free energy responsible for the volume phase transition is fundamentally altered by interfacial confinement. These results imply that important technological properties of such systems, including the temperature-induced destabilization of emulsions, do not occur via a decrease in the interfacial coverage of the microgels.

Stepwise Homogeneous Melting of Benzene Phase I at High Pressure

We investigate, using molecular dynamics simulations, the spontaneous homogeneous melting of benzene phase I under a high pressure of 1.0 GPa. We find an apparent stepwise transition via a metastable crystal phase, unlike the direct melting observed at ambient pressure. The transition to the metastable phase is achieved by rotational motions, without the diffusion of the center of mass of benzene. The metastable crystal completely occupies the whole space and maintains its structure for at least several picoseconds, so that the phase seems to have a local free energy minimum. The unit cell is found to be unique—no such crystalline structure has been reported so far. Furthermore, we discuss the influence of pressure control on the melting behavior.

Plastic Crystal-to-Crystal Transition of Janus Particles under Shear

Colloidal Janus spheres in the bulk typically spontaneously assemble into plastic crystalline phases, while particle orientations exhibit glasslike dynamics without long-range order. Through Brownian dynamics simulations, we demonstrate that shear can trigger a phase transition from an isotropic crystal with orientational disorder to an orientationally ordered crystal with lamellae along the shear direction. This nonequilibrium transition is accompanied with the orientational ordering following a nucleation and growth mechanism. By performing a phenomenological extension of free energy analysis, we reveal that the nucleation originates from the orientation fluctuations induced by shear. The growth of the orientationally crystalline cluster is examined to be disklike, captured by developing a lattice model with memoryless state functions. These findings bring new insights into the mechanisms for the ordering transition of anisotropic particles at nonequilibrium states.

Computational Study on Homogeneous Melting of Benzene Phase I

Molecular-dynamics simulations are used for examining the microscopic details of the homogeneous melting of benzene phase I. The equilibrium melting temperatures of our model were initially determined using the direct-coexistence method. Homogeneous melting at a higher temperature is achieved by heating a defect- and surfacefree crystal. The temperature-dependent potential energy and lattice parameters do not indicate a premelting phase even under superheated conditions. Further, statistical analyses using induction times computed from 200 melting trajectories were conducted, denoting that the homogeneous melting of benzene occurs stochastically, and that there is no intermediate transient state between the crystal and liquid phases. Additionally, the critical nucleus size is estimated using the seeding approach, along with the local bond order parameter. We found that the large diffusive motion arising from defect migration or neighbor-molecule swapping is of little importance during nucleation. Instead, the orientational disorder activated using the flipping motion of the benzene plane results in the melting nucleus.

Transformations of body-centered cubic crystals composed of hard or soft spheres to liquids or face-centered cubic crystals

The monodispersed hard-sphere system is one of the simplest models for the study of phase transitions. Despite intensive studies of crystallization and melting of hard-sphere face-centered cubic (FCC) crystals, the phase transformations of hard-sphere body-centered cubic (BCC) crystals have not been explored because hard spheres cannot form a stable BCC lattice. In fact, unstable BCC hard-sphere crystals and their related phase transformations can be experimentally achieved. Here, we measured the kinetics of the melting and solid-solid transformations of BCC hard-sphere crystals at various volume fractions via molecular dynamics simulations. When the volume fraction ϕ < 0.494, the system melts catastrophically. At ϕ > 0.545, the BCC crystal transforms to a metastable polycrystal consisting of FCC and hexagonal close-packed (HCP) domains, which is different from those crystallized from supercooled liquids, and then slowly equilibrates toward the FCC crystal. At 0.494 < ϕ < 0.545, the BCC crystal transforms to an intermediate-order metastable state consisting of BCC and non-crystal particles without FCC and HCP symmetries and then equilibrates toward the coexistence of the FCC crystal and liquid. We further studied the melting and BCC-FCC transitions of crystals composed of soft spheres with potential u(r) = ϵ(r/σ)^-n . The unstable BCC crystals at n = 12, 9, 8 exhibit similar melting and BCC-FCC transitions as hard-sphere BCC crystals, while the metastable BCC crystals at n = 5, 6, 7 melt quickly at low densities but take very long time for the BCC-FCC transition at high densities. We also estimate the BCC-FCC interfacial energy and critical nucleus size. These results cast light on the melting and solid-solid transformations of atomic BCC crystals, which exist widely in nature.

A new look at effective interactions between microgel particles

Thermoresponsive microgels find widespread use as colloidal model systems, because their temperature-dependent size allows facile tuning of their volume fraction in situ. However, an interaction potential unifying their behavior across the entire phase diagram is sorely lacking. Here we investigate microgel suspensions in the fluid regime at different volume fractions and temperatures, and in the presence of another population of small microgels, combining confocal microscopy experiments and numerical simulations. We find that effective interactions between microgels are clearly temperature dependent. In addition, microgel mixtures possess an enhanced stability compared to hard colloid mixtures - a property not predicted by a simple Hertzian model. Based on numerical calculations we propose a multi-Hertzian model, which reproduces the experimental behavior for all studied conditions. Our findings highlight that effective interactions between microgels are much more complex than usually assumed, displaying a crucial dependence on temperature and on the internal core-corona architecture of the particles.