Melting of colloidal crystal films

Controlled creation of point defects in three-dimensional colloidal crystals

Crystal defects crucially influence the properties of crystalline materials and have been extensively studied. Even for the simplest type of defect-the point defect-however, basic properties such as their diffusive behavior, and their interactions, remain elusive on the atomic scale. Here, we demonstrate in situ control over the creation of isolated point defects in a three-dimensional (3D) colloidal crystal allowing insight on a single-particle level. Our system consists of thermoresponsive microgel particles embedded in a crystal of nonresponsive colloids. Heating this mixed-particle system triggers the shrinking of the embedded microgels, which then vacate their lattice positions, creating vacancy-interstitial pairs. We use temperature-controlled confocal laser scanning microscopy to verify and visualize the formation of the point defects. In addition, by reswelling the microgels we quantify the local lattice distortion around an interstitial defect. Our experimental model system provides a unique opportunity to shed light on the interplay between point defects, on the mechanisms of their diffusion, on their interactions, and on collective dynamics.

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.

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.

Evidence for Enhanced Tracer Diffusion in Densely Packed Interfacial Assemblies of Hairy Nanoparticles

Nearly monodisperse nanoparticle (NP) spheres attached to a nonvolatile ionic liquid surface were tracked by in situ scanning electron microscopy to obtain the tracer diffusion coefficient Dtr as a function of the areal fraction ϕ. The in situ technique resolved both tracer (gold) and background (silica) particles for ∼1-2 min, highlighting their mechanisms of diffusion, which were strongly dependent on ϕ. Structure and dynamics at low and moderate ϕ paralleled those reported for larger colloidal spheres, showing an increase in order and a decrease in Dtr by over 4 orders of magnitude. However, ligand interactions were more important near jamming, leading to different caging and jamming dynamics for smaller NPs. The normalized Dtr at ultrahigh ϕ depended on particle diameter and ligand molecular weight. Increasing the PEG molecular weight by a factor of 4 increased Dtr by 2 orders of magnitude at ultrahigh ϕ, indicating stronger ligand lubrication for smaller particles.

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.

In situ single particle characterization of the themoresponsive and co-nonsolvent behavior of PNIPAM microgels and silica@PNIPAM core-shell colloids

Poly(N-isopropylacrylamide) (PNIPAM) microgels and PNIPAM colloidal shells attract continuous strong interest due to their thermoresponsive behavior, as their size and properties can be tuned by temperature. The direct single particle observation and characterization of pure, unlabeled PNIPAM microgels in their native aqueous environment relies on imaging techniques that operate either at interfaces or in cryogenic conditions, thus limiting the observation of their dynamic nature. Liquid Cell (Scanning) Transmission Electron Microscopy (LC-(S) TEM) imaging allows the characterization of materials and dynamic processes such as nanoparticle growth, etching, and diffusion, at nanometric resolution in liquids. Here we show that via a facile post-synthetic in situ polymer labelling step with high-contrast marker core-shell Au@SiO₂ nanoparticles (NPs) it is possible to determine the full volume of PNIPAM microgels in water. The labelling allowed for the successful characterization of the thermoresponsive behavior of PNIPAM microgels and core shell silica@PNIPAM hybrid microgels, as well as the co-nonsolvency of PNIPAM in aqueous alcoholic solutions. The interplay between electron beam irradiation and PNIPAM systems in water resulted in irreversible shrinkage due to beam induced water radiolysis products, which in turn also affected the thermoresponsive behavior of PNIPAM. The addition of 2-propanol as radical scavenger improved PNIPAM stability in water under electron beam irradiation.

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.

Local orderings in the melting process of a square crystal and in the resulting liquid

Using Brownian dynamics simulations we investigate the melting processes of a square crystalline lattice of colloidal particles interacting via an isotropic potential, which comprises both a hard-core repulsion and an additional softened square-well potential. For temperatures slightly lower than the transition one, we found a proliferation of small liquid clusters surrounded by the square lattice. These clusters are not static, quite the opposite, they have an intense dynamics and are continuously formed and destroyed over time. However, no unbound topological defects are observed. At the transition temperature, one of these liquid clusters starts to grow, until the entire system becomes in the liquid phase, then, characterizing a first-order phase transition. The tetratic intermediate phase, as given by the KTHNY theory, was not observed. Moreover, the liquid phase exhibits a considerable number of crystalline clusters having square and triangular orderings, which remain present even when increasing temperature by an order of magnitude. As the temperature increases, structural changes within the liquid phase are analyzed by evaluating the number and sizes of the square and triangular clusters. A transition of the dominant clusters is observed.

Observation of two-step melting on a sphere

Melting in two-dimensional flat space is typically two-step and via the hexatic phase. How melting proceeds on a curved surface, however, is not known. Topology mandates that crystalline particle assemblies on these surfaces harbor a finite density of defects, which itself can be ordered, like the icosahedral ordering of 5-coordinated disclination defects on a sphere. Thus, melting even on a sphere, the simplest closed surface, involves the loss of both crystalline and defect order. Probing the interplay of these two forms of order, however, requires a system in which melting can be performed in situ, and this has not been achieved hitherto. Here, by tuning interparticle interactions in situ, we report an observation of an intermediate hexatic phase during the melting of colloidal crystals on a sphere. Remarkably, we observed a precipitous drop in icosahedral defect order in the hexatic phase where the shear modulus is expected to vanish. Furthermore, unlike in flat space, where disorder can fundamentally alter the nature of the melting process, on the sphere, we observed the signature characteristics of ideal melting. Our findings have profound implications for understanding, for instance, the self-assembly and maturation dynamics of viral capsids and also phase transitions on curved surfaces.

Dynamic Reconfiguration of Compressed 2D Nanoparticle Monolayers

A Gibbs monolayer of jammed, or nearly jammed, spherical nanoparticles was imaged at a liquid surface in real time by in-situ scanning electron microscopy performed at the single-particle level. At nanoparticle areal fractions above that for the onset of two-dimensional crystallization, structural reorganizations of the mobile polymer-coated particles were visualized after a stepwise areal compression. When the compression was small, slow shearing near dislocations and reconfigured nanoparticle bonding were observed at crystal grain boundaries. At larger scales, domains grew as they rotated into registry by correlated but highly intermittent motions. Simultaneously, the areal density in the middle of the monolayer increased. When the compression was large, the jammed monolayers exhibited out-of-plane deformations such as wrinkles and bumps. Due to their large interfacial binding energy, few (if any) of the two-dimensionally mobile nanoparticles returned to the liquid subphase. Compressed long enough (several hours or more), monolayers transformed into solid nanoparticle films, as evidenced by their cracking and localized rupturing upon subsequent areal expansion. These observations provide mechanistic insights into the dynamics of a simple model system that undergoes jamming/unjamming in response to mechanical stress.

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.

Elastic Photonic Microcapsules Containing Colloidal Crystallites as Building Blocks for Macroscopic Photonic Surfaces

Colloidal crystals develop structural colors through wavelength-selective diffraction. Recently, a granular format of colloidal crystals has emerged as building blocks to construct macroscopic photonic surfaces or architectures with high reconfigurability through the secondary assembly. Here, we design elastic photonic microcapsules containing colloidal crystallites along the inner wall as a building block. Water-in-oil-in-water double-emulsion templates are microfluidically prepared to have an aqueous dispersion of polystyrene particles in the inner droplet and polydimethylsiloxane prepolymers in the shell. Colloidal particles are enriched in the presence of depletant and salt by osmotic compression, with the crystallization at the inner interface by depletion attraction. The number of nucleation sites depends on the rate of the enrichment, which enables control over the size and surface coverage of the crystallites with osmotic conditions. The enrichment is ceased by transferring the droplets into an isotonic solution, and the oil shell is cured to form an elastic membrane. As the elastic microcapsules have a large void in the core, they are deformable without structural damage in the crystallites. Therefore, the microcapsules can be closely packed to form macroscopic surfaces while achieving a high quality of structural colors with a collection of crystallites aligned along the flattened membrane.

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.

Buckling of two-dimensional plasma crystals with nonreciprocal interactions

Laboratory realizations of two-dimensional (2D) plasma crystals typically involve monodisperse microparticles confined into horizontal monolayers in radio-frequency (rf) plasma sheaths. This gives rise to the so-called plasma wakes beneath the microparticles. The presence of wakes renders the interactions in such systems nonreciprocal, a fact that can lead to a quite different behavior from the one expected for their reciprocal counterparts. Here we examine the buckling of a hexagonal 2D plasma crystal, occurring as the confinement strength is decreased, taking explicitly into account the nonreciprocity of the system via a well-established point-wake model. We observe that for a finite wake charge, the monolayer hexagonal crystal undergoes a transition first to a bilayer hexagonal structure, unrealizable in harmonically confined reciprocal Yukawa systems, and subsequently to a bilayer square structure. Our theoretical results are confirmed by molecular dynamics simulations for experimentally relevant parameters, indicating the potential of their observation in state-of-the-art experiments with 2D complex plasmas.

Front-Mediated Melting of Isotropic Ultrastable Glasses

Ultrastable vapor-deposited glasses display uncommon material properties. Most remarkably, upon heating they are believed to melt via a liquid front that originates at the free surface and propagates over a mesoscopic crossover length, before crossing over to bulk melting. We combine swap Monte Carlo with molecular dynamics simulations to prepare and melt isotropic amorphous films of unprecedendtly high kinetic stability. We are able to directly observe both bulk and front melting, and the crossover between them. We measure the front velocity over a broad range of conditions, and a crossover length scale that grows to nearly 400 particle diameters in the regime accessible to simulations. Our results disentangle the relative roles of kinetic stability and vapor deposition in the physical properties of stable glasses.

Direct imaging of structural disordering and heterogeneous dynamics of fullerene molecular liquid

Structural rearrangements govern the various properties of disordered systems and visualization of these dynamical processes can provide critical information on structural deformation and phase transformation of the systems. However, direct imaging of individual atoms or molecules in a disordered state is quite challenging. Here, we prepare a model molecular system of C₇₀ molecules on graphene and directly visualize the structural and dynamical evolution using aberration-corrected transmission electron microscopy. E-beam irradiation stimulates dynamics of fullerene molecules, which results in the first-order like structural transformation from the molecular crystal to molecular liquid. The real-time tracking of individual molecules using an automatic molecular identification process elucidates the relaxation behavior of a stretched exponential functional form. Moreover, the directly observed heterogeneous dynamics bear similarity to the dynamical heterogeneity in supercooled liquids near the glass transition. Fullerenes on graphene can serve as a new model system, which allows investigation of molecular dynamics in disordered phases.

Assessing Pair Interaction Potentials of Nanoparticles on Liquid Interfaces

The pair interaction potentials of polymer-grafted silica nanoparticles (NPs) at liquid surfaces were determined by scanning electron microscopy, exploiting the nonvolatility of ionic liquids to stabilize the specimens against microscope vacuum. Even at near contact, individual, two-dimensionally well-dispersed NPs were resolved. The potential of mean force, reduced to the pair interaction potential for dilute NPs, was extracted with good accuracy from the radial distribution function, as both NP diameter and grafted polymer chain length were varied. While NP polydispersity somewhat broadened the core repulsion, the pair potential well-approximated a hard sphere interaction, making these systems suitable for model studies of interfacially bound NPs. For short (5 kDa) poly(ethylene glycol) ligands, a weak (< k_B T) long-range attraction was discerned, and for ligands of identical length, pair potentials overlapped for NPs of different diameter; the attraction is suggested to arise from ligand-induced menisci. To understand better the interactions underlying the pair potential, NP surface-binding energies were measured by interfacial tensiometry, and NP contact angles were assessed by atomic force microscopy and transmission electron microscopy.

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.

Transition of Dielectrophoresis-Assembled 2D Crystals to Interlocking Structures under a Magnetic Field

Aspherical cubic hematite colloids with cylindrical arms protruding from each face, referred to as "hexapods", were assembled via negative dielectrophoresis and then manipulated using an applied magnetic field. Upon application of an ac electric field, the hexapods aligned in close-packed linear chains parallel to the field direction. The chains then aggregated to the center of the device, with adjacent chains separated by distances approximately equal to twice the arm length. The resulting open packing structure exhibited cmm plane group symmetry due to the obstruction of arms, with a high density of incorporated defects. Subsequent application of a magnetic field to the dielectrophoresis (DEP)-assembled structure was found to anneal the colloidal crystal by reorienting the hexapods to align their intrinsic magnetic dipoles with the magnetic field direction. During reorganization, the colloidal packing density was found to decrease by more than 10% at both the center and edges of the crystal, accompanied by a significant loss of ordering, prior to redensification of the 2D lattice with fewer defects. Reorganization at the edge was 1.5 times faster than at the center, consistent with the need for cooperative colloidal motion to remove defects at the centers of the crystals.

Photonic Capsule Sensors with Built-In Colloidal Crystallites

Technologies to monitor microenvironmental conditions and its spatial distribution are in high demand, yet remain unmet need. Herein, photonic microsensors are designed in a capsule format that can be injected, suspended, and implanted in any target volume. Colorimetric sensors are loaded in the core of microcapsules by assembling core-shell colloids into crystallites through the depletion attraction. The shells of the colloids are made of a temperature-responsive hydrogel, which enables the crystallites to rapidly and widely tune the structural color in response to a change in temperature while maintaining close-packed arrays. The spherical symmetry of the microcapsules renders them optically isotropic, i.e., displaying orientation-independent color. In addition, as a solid membrane is used to protect the delicate crystallites from external stresses, their high stability is assured. More importantly, each microcapsule reports the temperature of its microenvironment so that a suspension of capsules can provide information on the spatial distribution of the temperature.

Different routes into the glass state for soft thermo-sensitive colloids

We report an experimental and theoretical investigation of glass formation in soft thermo-sensitive colloids following two different routes: a gradual increase of the particle number density at constant temperature and an increase of the radius in a fixed volume at constant particle number density. Confocal microscopy experiments and the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory consistently show that the two routes lead to a dynamically comparable state at sufficiently long aging times. However, experiments reveal the presence of moderate but persistent structural differences. Successive cycles of radius decrease and increase lead instead to a reproducible glass state, indicating a suitable route to obtain rejuvenation without using shear fields.

Molecular dynamics simulation of charged colloids confined between hard walls: pre-melting and pre-freezing across the BCC-fluid coexistence

Molecular dynamics (MD) computer simulations are used to study the structure of hard-core Yukawa systems confined between two parallel hard walls. States around the coexistence between a fluid and a body-centered cubic (BCC) crystal are considered. In all cases a pronounced layering in the vicinity of the walls is observed. Using a thermodynamic integration scheme, we determine the wall-fluid interfacial free energy γ which is negative and monotonically decreasing with increasing bulk density of the fluid. In the case of the fluid, the layers next to the walls undergo a transition from a fluid to a hexagonal structure. This pre-freezing transition occurs well below the coexistence bulk density of the fluid. The confined BCC crystal in (111) orientation shows melted regions between crystalline face-centered cubic (FCC) layers close to the wall and the BCC bulk region.

Positional ordering of hard adsorbate particles in tubular nanopores

The phase behavior and structural properties of a monolayer of hard particles is examined in such a confinement where the adsorbed particles are constrained to the surface of a narrow hard cylindrical pore. The diameter of the pore is chosen such that only first- and second-neighbor interactions occur between the hard particles. The transfer operator method of [Percus and Zhang, Mol. Phys. 69, 347 (1990)MOPHAM0026-897610.1080/00268979000100241] is reformulated to obtain information about the structure of the monolayer. We have found that a true phase transition is not possible in the examined range of pore diameters. The monolayer of hard spheres undergoes a structural change from fluidlike order to a zigzaglike solid one with increasing surface density. The case of hard cylinders is different in the sense that a layering takes place continuously between a low-density one-row and a high-density two-row monolayer. Our results reveal a clear discrepancy with classical density functional theories, which do not distinguish smecticlike ordering in bulk from that in narrow periodic pores.

Bond-orientational order and Frank's constant in two-dimensional colloidal hard spheres

Recently, the full phase behaviour of 2D colloidal hard spheres was experimentally established, and found to involve a first order liquid to hexatic transition and a continuous hexatic to crystal transition (Thorneywork et al 2017 Phys. Rev. Lett. 118 158001). Here, we expand upon this work by considering the behaviour of the bond-orientational correlation time and Frank's constant in the region of these phase transitions. We also consider the excess entropy, as calculated from the radial distribution functions, for a wide range of area fractions covering the liquid, hexatic and crystal phases. In all cases, the behaviour of these quantities further corroborates the previously reported melting scenario of 2D colloidal hard spheres.

Isolating long-wavelength fluctuation from structural relaxation in two-dimensional glass: cage-relative displacement

It has recently been revealed that long-wavelength fluctuation exists in two-dimensional (2D) glassy systems, having the same origin as that given by the Mermin-Wagner theorem for 2D crystalline solids. In this paper, we discuss how to characterise quantitatively the long-wavelength fluctuation in a molecular dynamics simulation of a lightly supercooled liquid. We employ the cage-relative mean-square displacement (MSD), defined on relative displacement to its cage, to quantitatively separate the long-wavelength fluctuation from the original MSD. For increasing system size the amplitude of acoustic long wavelength fluctuations not only increases but shifts to later times causing a crossover with structural relaxation of caging particles. We further analyse the dynamic correlation length using the cage-relative quantities. It grows as the structural relaxation becomes slower with decreasing temperature, uncovering an overestimation by the four-point correlation function due to the long-wavelength fluctuation. These findings motivate the usage of cage-relative MSD as a starting point for analysis of 2D glassy dynamics.

Static and dynamic properties of two-dimensional Coulomb clusters

We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional confinements across the crossover from solid- to liquid-like behaviors. While static correlations that investigate the translational and bond orientational order in the confinements show the footprints of hexatic-like phase at low temperatures, dynamics of the particles slow down considerably in this phase, reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales show stretched-exponential decay of spatial correlations in irregular traps. Temperature dependence of characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries.

Triple Junction at the Triple Point Resolved on the Individual Particle Level

At the triple point of a repulsive screened Coulomb system, a fcc crystal, a bcc crystal, and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single-particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.

Diffusive and martensitic nucleation kinetics in solid-solid transitions of colloidal crystals

Solid–solid transitions between crystals follow diffusive nucleation, or various diffusionless transitions, but these kinetics are difficult to predict and observe. Here we observed the rich kinetics of transitions from square lattices to triangular lattices in tunable colloidal thin films with single-particle dynamics by video microscopy. Applying a small pressure gradient in defect-free regions or near dislocations markedly transform the diffusive nucleation with an intermediate-stage liquid into a martensitic generation and oscillation of dislocation pairs followed by a diffusive nucleus growth. This transformation is neither purely diffusive nor purely martensitic as conventionally assumed but a combination thereof, and thus presents new challenges to both theory and the empirical criterion of martensitic transformations. We studied how pressure, density, grain boundary, triple junction and interface coherency affect the nucleus growth, shape and kinetic pathways. These novel microscopic kinetics cast new light on control solid–solid transitions and microstructural evolutions in polycrystals.

Solid-solid transitions between different crystalline structures have broad implications in earth science, steel and ceramic materials. Peng et al. show a transformation pathway that starts off as being martensitic then switches to diffusive at the single particle level in a colloidal system under pressure.

Relating microstructure and particle-level stress in colloidal crystals under increased confinement

The mechanical properties of crystalline materials can be substantially modified under confinement. Such modified macroscopic properties are usually governed by the altered microstructures and internal stress fields. Here, we use a parallel plate geometry to apply a quasi-static squeeze flow crushing a colloidal polycrystal while simultaneously imaging it with confocal microscopy. The confocal images are used to quantify the local structure order and, in conjunction with Stress Assessment from Local Structural Anisotropy (SALSA), determine the stress at the single-particle scale. We find that during compression, the crystalline regions break into small domains with different geometric packing. These domains are characterized by a pressure and deviatoric stress that are highly localized with correlation lengths that are half those found in bulk. Furthermore, the mean deviatoric stress almost doubles, suggesting a higher brittleness in the highly-confined samples.

Measuring nonlinear stresses generated by defects in 3D colloidal crystals

The mechanical, structural and functional properties of crystals are determined by their defects, and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening, yield and fatigue.

Density Affects the Nature of the Hexatic-Liquid Transition in Two-Dimensional Melting of Soft-Core Systems

We find that both continuous and discontinuous hexatic-liquid transitions can happen in the melting of two-dimensional solids of soft-core disks. For three typical model systems, Hertzian, harmonic, and Gaussian-core models, we observe the same scenarios. These systems exhibit reentrant crystallization (melting) with a maximum melting temperature T_{m} happening at a crossover density ρ_{m}. The hexatic-liquid transition at a density smaller than ρ_{m} is discontinuous. Liquid and hexatic phases coexist in a density interval, which becomes narrower with increasing temperature and tends to vanish approximately at T_{m}. Above ρ_{m}, the transition is continuous, in agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For these soft-core systems, the nature of the hexatic-liquid transition depends on density (pressure), with the melting at ρ_{m} being a plausible transition point from discontinuous to continuous hexatic-liquid transition.

Direct observation of melting in a two-dimensional driven granular system

Melting is considered to be one of the most fundamental problems in physical science. Generally, dimensionality plays an important role in melting. In three-dimension, it’s well known that a crystal melts directly into a liquid via a first-order transition. In two-dimension (2D), however, the melting process has been widely debated whether it is a first-order transition or a two-step transition with an intermediate hexatic phase. Experimentally 2D melting has been intensively studied in equilibrium systems such as molecular and colloidal crystals, but rarely been explored in non-equilibrium system such as granular materials. In this paper, we experimentally studied the 2D melting in a driven granular model system at single particle level using video recording and particle tracking techniques. Measurements of orientational/translational correlation functions show evidences that the melting is a two-step transition. A novel concept of orientational/translational susceptibilities enable us to clearly resolve the intermediate hexatic phase. Our results are in excellent agreement with the two-step melting scenario predicted by KTHNY theory, and demonstrate that the KTHNY melting scenario can be extended to non-equilibrium systems.

Grain-boundary-induced melting in quenched polycrystalline monolayers

Melting in two dimensions can successfully be explained with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario which describes the formation of the high-symmetry phase with the thermal activation of topological defects within an (ideally) infinite monodomain. With all state variables being well defined, it should hold also as freezing scenario where oppositely charged topological defects annihilate. The Kibble-Zurek mechanism, on the other hand, shows that spontaneous symmetry breaking alongside a continuous phase transition cannot support an infinite monodomain but leads to polycrystallinity. For any nonzero cooling rate, critical fluctuations will be frozen out in the vicinity of the transition temperature. This leads to domains with different director of the broken symmetry, separated by a defect structure, e.g., grain boundaries in crystalline systems. After instantaneously quenching a colloidal monolayer from a polycrystalline to the isotropic fluid state, we show that such grain boundaries increase the probability for the formation of dislocations. In addition, we determine the temporal decay of defect core energies during the first few Brownian times after the quench. Despite the fact that the KTHNY scenario describes a continuous phase transition and phase equilibrium does not exist, melting in polycrystalline samples starts at grain boundaries similar to first-order phase transitions.

Viscoelasticity of colloidal polycrystals doped with impurities

We investigate how the microstructure of a colloidal polycrystal influences its linear visco-elasticity. We use thermosensitive copolymer micelles that arrange in water in a cubic crystalline lattice, yielding a colloidal polycrystal. The polycrystal is doped with a small amount of nanoparticles, of size comparable to that of the micelles, which behave as impurities and thus partially segregate in the grain boundaries. We show that the shear elastic modulus only depends on the packing of the micelles and varies neither with the presence of nanoparticles nor with the crystal microstructure. By contrast, we find that the loss modulus is strongly affected by the presence of nanoparticles. A comparison between rheology data and small-angle neutron-scattering data suggests that the loss modulus is dictated by the total amount of nanoparticles in the grain boundaries, which in turn depends on the sample microstructure.

Destabilisation of the hexatic phase in systems of hard disks by quenched disorder due to pinning on a lattice

We investigate the effect of quenched disorder on the melting mechanism of two-dimensional hard disks using large-scale event-driven molecular dynamics simulations. The two-stage melting scenario of a continuous solid-hexatic and a first-order hexatic-liquid transition for a 2D system of hard disks does not persist in the case of quenched disorder, which arises by pinning less than one percent of the particles on a triangular lattice. Based on the Halperin-Nelson-Young (HNY) renormalization group equation, we observe that a first-order solid-liquid transition preempts the Kosterlitz-Thouless-type solid-hexatic transition in a 2D system of hard disks with quenched disorder as the stiffness of the crystal is increased by the presence of pinned particles.

Two-step nucleation mechanism in solid-solid phase transitions

The microscopic kinetics of ubiquitous solid-solid phase transitions remain poorly understood. Here, by using single-particle-resolution video microscopy of colloidal films of diameter-tunable microspheres, we show that transitions between square and triangular lattices occur via a two-step diffusive nucleation pathway involving liquid nuclei. The nucleation pathway is favoured over the direct one-step nucleation because the energy of the solid/liquid interface is lower than that between solid phases. We also observed that nucleation precursors are particle-swapping loops rather than newly generated structural defects, and that coherent and incoherent facets of the evolving nuclei exhibit different energies and growth rates that can markedly alter the nucleation kinetics. Our findings suggest that an intermediate liquid should exist in the nucleation processes of solid-solid transitions of most metals and alloys, and provide guidance for better control of the kinetics of the transition and for future refinements of solid-solid transition theory.

Specific heat in two-dimensional melting

We report the specific heat cN around the melting transition(s) of micrometer-sized superparamagnetic particles confined in two dimensions, calculated from fluctuations of positions and internal energy, and corresponding Monte Carlo simulations. Since colloidal systems provide single particle resolution, they offer the unique possibility to compare the experimental temperatures of the peak position of cN(T) and symmetry breaking, respectively. While order parameter correlation functions confirm the Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario where translational and orientational order symmetries are broken at different temperatures with an intermediate so called hexatic phase, we observe a single peak of the specific heat within the hexatic phase, with excellent agreement between experiment and simulation. Thus, the peak is not associated with broken symmetries but can be explained with the total defect density, which correlates with the maximum increase of isolated dislocations. The absence of a latent heat strongly supports the continuous character of both transitions.

Two-stage melting induced by dislocations and grain boundaries in monolayers of hard spheres

Melting in two-dimensional systems has remained controversial as theory, simulations, and experiments show contrasting results. One issue that obscures this discussion is whether or not theoretical predictions on strictly 2D systems describe those on quasi-2D experimental systems, where out-of-plane fluctuations may alter the melting mechanism. Using event-driven molecular dynamics simulations, we find that the peculiar two-stage melting scenario of a continuous solid-hexatic and a first-order hexatic-liquid transition as observed for a truly 2D system of hard disks [Bernard and Krauth, Phys. Rev. Lett., 2011, 107, 155704] persists for a quasi-2D system of hard spheres with out-of-plane particle motions as high as half the particle diameter. By calculating the renormalized Young's modulus, we show that the solid-hexatic transition is of the Kosterlitz-Thouless type and occurs via dissociation of bound dislocation pairs. In addition, we find a first-order hexatic-liquid transition that seems to be driven by spontaneous proliferation of grain boundaries.

Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles

This review collects and describes experiments that employ colloidal suspensions to probe physics in ordered and disordered solids and related complex fluids. The unifying feature of this body of work is its clever usage of poly(N-isopropylacrylamide) (PNIPAM) microgel particles. These temperature-sensitive colloidal particles provide experimenters with a 'knob' for in situ control of particle size, particle interaction and particle packing fraction that, in turn, influence the structural and dynamical behavior of the complex fluids and solids. A brief summary of PNIPAM particle synthesis and properties is given, followed by a synopsis of current activity in the field. The latter discussion describes a variety of soft matter investigations including those that explore formation and melting of crystals and clusters, and those that probe structure, rearrangement and rheology of disordered (jammed/glassy) and partially ordered matter. The review, therefore, provides a snapshot of a broad range of physics phenomenology which benefits from the unique properties of responsive microgel particles.

Experimental modelling of single-particle dynamic processes in crystallization by controlled colloidal assembly

A comprehensive review of the experimental modeling of single particle dynamics in crystallization is presented.

Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

Using both video microscopy of superparamagnetic colloidal particles confined in two dimensions and corresponding computer simulations of repulsive parallel dipoles, we study the formation of fluctuating orientational clusters and topological defects in the context of the KTHNY-like melting scenario under quenched disorder. We analyze cluster densities, average cluster sizes, and the population of noncluster particles, as well as the development of defects, as a function of the system temperature and disorder strength. In addition, the probability distribution of clustering and orientational order is presented. We find that the well-known disorder-induced widening of the hexatic phase can be traced back to the distinct development characteristics of clusters and defects along the melting transitions from the solid phase to the hexatic phase to the isotropic fluid.

Far-from-equilibrium sheared colloidal liquids: disentangling relaxation, advection, and shear-induced diffusion

Using high-speed confocal microscopy, we measure the particle positions in a colloidal suspension under large-amplitude oscillatory shear. Using the particle positions, we quantify the in situ anisotropy of the pair-correlation function, a measure of the Brownian stress. From these data we find two distinct types of responses as the system crosses over from equilibrium to far-from-equilibrium states. The first is a nonlinear amplitude saturation that arises from shear-induced advection, while the second is a linear frequency saturation due to competition between suspension relaxation and shear rate. In spite of their different underlying mechanisms, we show that all the data can be scaled onto a master curve that spans the equilibrium and far-from-equilibrium regimes, linking small-amplitude oscillatory to continuous shear. This observation illustrates a colloidal analog of the Cox-Merz rule and its microscopic underpinning. Brownian dynamics simulations show that interparticle interactions are sufficient for generating both experimentally observed saturations.

Generalized Onsager theory of liquid crystals

The Onsager theory is known to be inaccurate in its prediction of the critical transition density for small aspect ratio hard rods. In this paper we generalize the Onsager theory in two dimensions by taking into account the short-range order as well as the higher-order virial coefficients, up to the fourth order. By carrying out molecular dynamics (MD) simulations on "molecules" comprising linked hard disks with an aspect ratio ℓ ranging from 5 to 13, we show that the generalized theory is much improved as compared to the traditional theory, with its predictions of the transition density agreeing well with the simulation results. This indicates the importance of short-range order considerations (in conjunction with steric repulsion) for molecules with ℓ≤10, a group which includes the most commonly encountered thermotropic liquid crystals. MD simulations further yield evidence for hexagonal order for molecules with ℓ≤8, indicating an intermediate hexagonal phase before solidifying at higher densities.