Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Optothermal crystallization of hard spheres in an effective bidimensional geometry

Using colloids effectively confined in two dimensions by a cell with a thickness comparable to the particle size, we investigate the nucleation and growth of crystallites induced by locally heating the solvent with a near-infrared laser beam. The particles, which are "thermophilic," move towards the laser spot solely because of thermophoresis with no convection effects, forming dense clusters whose structure is monitored using two order parameters that gauge the local density and the orientational ordering. We find that ordering takes place when the cluster reaches an average surface density that is still below the upper equilibrium limit for the fluid phase of hard disks, meaning that we do not detect any sign of a proper "two-stage" nucleation from a glass or a polymorphic crystal structure. The crystal obtained at late growth stage displays a remarkable uniformity with a negligible amount of defects, arguably because the incoming particles diffuse, bounce, and displace other particles before settling at the crystal interface. This "fluidization" of the outer crystal edge may resemble the surface enhanced mobility giving rise to ultra-stable glasses by physical vapor deposition.

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.

Crystal Polymorph Selection Mechanism of Hard Spheres Hidden in the Fluid

Nucleation plays a critical role in the birth of crystals and is associated with a vast array of phenomena, such as protein crystallization and ice formation in clouds. Despite numerous experimental and theoretical studies, many aspects of the nucleation process, such as the polymorph selection mechanism in the early stages, are far from being understood. Here, we show that the hitherto unexplained excess of particles in a face-centered-cubic (fcc)-like environment, as compared to those in a hexagonal-close-packed (hcp)-like environment, in a crystal nucleus of hard spheres can be explained by the higher order structure in the fluid phase. We show using both simulations and experiments that in the metastable fluid phase, pentagonal bipyramids, clusters with fivefold symmetry known to be inhibitors of crystal nucleation, transform into a different cluster, Siamese dodecahedra. These clusters are closely similar to an fcc subunit, which explains the higher propensity to grow fcc than hcp in hard spheres. We show that our crystallization and polymorph selection mechanism is generic for crystal nucleation from a dense, strongly correlated fluid phase.

Characterization and Optimization of Fluorescent Organosilica Colloids for 3D Confocal Microscopy Prepared Under "Zero-Flow" Conditions

We optimize and characterize the preparation of 3-trimethoxysilyl propyl methacrylate (TPM) colloidal suspensions for three-dimensional confocal microscopy. We revisit a simple synthesis of TPM microspheres by nucleation of droplets from prehydrolyzed TPM oil in a "zero-flow" regime and demonstrate how precise and reproducible control of particle size may be achieved via single-step nucleation with a focus on how the reagents are mixed. We also revamp the conventional dyeing method for TPM particles to achieve uniform transfer of a fluorophore to the organosilica droplets, improving particle identification. Finally, we illustrate how a ternary mixture of tetralin, trichloroethylene, and tetrachloroethylene may be used as a suspension medium which matches the refractive index of these particles while allowing independent control of the density mismatch between particle and solvent.

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Small Rigid Molecules

Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the direct-isomorph-check method. Recently a new method based on the scaling properties of forces was introduced and shown to work very well for atomic systems [T. B. Schrøder, Phys. Rev. Lett. 2022, 129, 245501]. A unique feature of this method is that it only requires a single equilibrium configuration for tracing out an isomorph. We here test generalizations of this method to molecular systems and compare to simulations of three simple molecular models: the asymmetric dumbbell model of two Lennard-Jones spheres, the symmetric inverse-power-law dumbbell model, and the Lewis-Wahnström o-terphenyl model. We introduce and test two force-based and one torque-based methods, all of which require just a single configuration for tracing out an isomorph. Overall, the method based on requiring invariant center-of-mass reduced forces works best.

Microstructural diversity, nucleation paths, and phase behavior in binary mixtures of charged colloidal spheres

We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Γ = 0.57, number densities below the eutectic number density n_E, and number fractions of p = 1.00-0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy with a body centered cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we also prepare the same samples by slow, mechanically undisturbed deionization in commercial slit cells. These cells feature a complex but well reproducible sequence of global and local gradients in salt concentration, number density, and composition as induced by successive deionization, phoretic transport, and differential settling of the components, respectively. Moreover, they provide an extended bottom surface suitable for heterogeneous nucleation of the β-phase. We give a detailed qualitative characterization of the crystallization processes using imaging and optical microscopy. By contrast to the bulk samples, the initial alloy formation is not volume-filling, and we now observe also α- and β-phases with low solubility of the odd component. In addition to the initial homogeneous nucleation route, the interplay of gradients opens various further crystallization and transformation pathways leading to a great diversity of microstructures. Upon a subsequent increase in salt concentration, the crystals melt again. Wall-based, pebble-shaped β-phase crystals and facetted α-crystals melt last. Our observations suggest that the substitutional alloys formed in bulk experiments by homogeneous nucleation and subsequent growth are mechanically stable in the absence of solid-fluid interfaces but thermodynamically metastable.

Even Strong Energy Polydispersity Does Not Affect the Average Structure and Dynamics of Simple Liquids

Size-polydisperse liquids have become standard models for avoiding crystallization, thereby enabling studies of supercooled liquids and glasses formed, e.g., by colloidal systems. Purely energy-polydisperse liquids have been studied much less, but provide an interesting alternative. We here study numerically the difference in structure and dynamics obtained by introducing these two kinds of polydispersity into systems of particles interacting via the Lennard-Jones and EXP pair potentials. To a very good approximation, the average pair structure and dynamics are unchanged even for strong energy polydispersity, which is not the case for size-polydisperse systems. When the system at extreme energy polydispersity undergoes a continuous phase separation into lower and higher particle-energy regions whose structure and dynamics are different from the average, the average structure and dynamics are still virtually the same as for the monodisperse system. Our findings are consistent with the fact that the distribution of forces on the individual particles do not change when energy polydispersity is introduced, while they do change in the case of size polydispersity. A theoretical explanation remains to be found, however.

Direct Imaging of the Kinetic Crystallization Pathway: Simulation and Liquid-Phase Transmission Electron Microscopy Observations

The crystallization of materials from a suspension determines the structure and function of the final product, and numerous pieces of evidence have pointed out that the classical crystallization pathway may not capture the whole picture of the crystallization pathways. However, visualizing the initial nucleation and further growth of a crystal at the nanoscale has been challenging due to the difficulties of imaging individual atoms or nanoparticles during the crystallization process in solution. Recent progress in nanoscale microscopy had tackled this problem by monitoring the dynamic structural evolution of crystallization in a liquid environment. In this review, we summarized several crystallization pathways captured by the liquid-phase transmission electron microscopy technique and compared the observations with computer simulation. Apart from the classical nucleation pathway, we highlight three nonclassical pathways that are both observed in experiments and computer simulations: formation of an amorphous cluster below the critical nucleus size, nucleation of the crystalline phase from an amorphous intermediate, and transition between multiple crystalline structures before achieving the final product. Among these pathways, we also highlight the similarities and differences between the experimental results of the crystallization of single nanocrystals from atoms and the assembly of a colloidal superlattice from a large number of colloidal nanoparticles. By comparing the experimental results with computer simulations, we point out the importance of theory and simulation in developing a mechanistic approach to facilitate the understanding of the crystallization pathway in experimental systems. We also discuss the challenges and future perspectives for investigating the crystallization pathways at the nanoscale with the development of in situ nanoscale imaging techniques and potential applications to the understanding of biomineralization and protein self-assembly.

Hedgehog, Chamomile, and Multipetal Polymeric Structures on the Nanoparticle Surface: Computer Modelling

A single spherical nanoparticle coated with a densely grafted layer of an amphiphilic homopolymer with identical A-graft-B monomer units was studied by means of coarse-grained molecular dynamics. In solvent, selectively poor for mainchain and good for pendant groups; the grafted macromolecules self-assemble into different structures to form a complex pattern on the nanoparticle surface. We distinguish hedgehog, multipetalar, chamomile, and densely structured shells and outline the area of their stability using visual analysis and calculate aggregation numbers and specially introduced order parameters, including the branching coefficient and relative orientation of monomer units. For the first time, the branching effect of splitting aggregates along with the distance to the grafting surface and preferred orientation of the monomer units with rearrangements of the dense compacted shell was described. The results explain the experimental data, are consistent with the analytical theory, and are the basis for the design of stimulus-sensitive matrix-free composite materials.

Polymorphism and Perfection in Crystallization of Hard Sphere Polymers

We present results on polymorphism and perfection, as observed in the spontaneous crystallization of freely jointed polymers of hard spheres, obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration, after an initial dominance of the hexagonal closed packed (HCP) polymorph and a transitory random hexagonal close packed (rHCP) morphology, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal, compared to the amorphous state. In spite of the significant local re-arrangements, as reflected in the bending and torsion angle distributions, the average chain size remains unaltered during crystallization. Polymers in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant.

Kinetic Phase Diagram for Nucleation and Growth of Competing Crystal Polymorphs in Charged Colloids

We determine the kinetic phase diagram for nucleation and growth of crystal phases in a suspension of charged colloids. Exploiting the seeding approach in extensive simulations, we calculate nucleation barrier heights for face-centered cubic (fcc) and body-centered cubic (bcc) phases for varying screening lengths and supersaturations. We determine for the entire metastable fluid region the crystal polymorph with the lowest nucleation barrier, and find a regime close to the triple point where metastable bcc can form due to a lower nucleation barrier, even though fcc is the stable phase. For higher supersaturation, we find that the difference in barrier heights decreases and we observe a mix of hexagonal close-packed, fcc, and bcc structures in the growth of crystalline seeds as well as in spontaneously formed crystals. Our kinetic phase diagram rationalizes the different crystallization mechanisms observed in previous work.

Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Role of diffusion in crystallization of hard-sphere colloids

Vital for a variety of industries, colloids also serve as an excellent model to probe phase transitions at the individual particle level. Despite extensive studies, origins of the glass transition in hard-sphere colloids discovered about 30 y ago remain elusive. Results of our numerical simulations and asymptotic analysis suggest that cessation of long-time particle diffusivity does not suppress crystallization of a metastable liquid-phase hard-sphere colloid. Once a crystallite forms, its growth is then controlled by the particle diffusion in the depletion zone surrounding the crystallite. Using simulations, we evaluate the solid-liquid interface mobility from data on colloidal crystallization in terrestrial and microgravity experiments and demonstrate that there is no drastic difference between the respective mobility values. The insight into the effect of vanishing particle mobility and particle sedimentation on crystallization of colloids will help engineer colloidal materials with controllable structure.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Towards Glasses with Permanent Stability

Unlike crystals, glasses age or devitrify over time, reflecting their nonequilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that the devitrification of quasi-hard-sphere glasses is prevented by suppressing volume-fraction inhomogeneities. A monodisperse glass known to devitrify with "avalanchelike" intermittent dynamics is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this entirely prevents structural relaxation and devitrification over aging time scales, even in the presence of crystallites. There is a dramatic homogenization in the number of load-bearing nearest neighbors each particle has, indicating that ultrastable glasses may be formed via "mechanical homogenization." Our finding provides a physical principle for glass stabilization and opens a novel route to the formation of mechanically stabilized glasses.

Crystallisation in a two-dimensional granular system at constant temperature

We study the crystallisation processes occurring in a nonvibrating two-dimensional magnetic granular system at various fixed values of the effective temperature. In this system, the energy loss due to dissipative effects is compensated by the continuous energy input coming into the system from a sinusoidal magnetic field. When this balance leads to high values of the effective temperature, no aggregates are formed, because particles’ kinetic energy prevents them from aggregating. For lower effective temperatures, formation of small aggregates is observed. The smaller the values of the applied field’s amplitude, the larger the number of these disordered aggregates. One also observes that when clusters form at a given effective temperature, the average effective diffusion coefficient decreases as time increases. For medium values of the effective temperature, formation of small crystals is observed. We find that the sixth bond-orientational order parameter and the number of bonds, when considering more than two, are very sensitive for exhibiting the order in the system, even when crystals are still very small.

Reflectance Confocal Microscopy: A Powerful Tool for Large Scale Characterization of Ordered/Disordered Morphology in Colloidal Photonic Structures

The development of appropriate methods to correlate the structure and optical properties of colloidal photonic structures is still a challenge. Structural information is mostly obtained by electron, X-ray, or optical microscopy methods and X-ray diffraction, while bulk spectroscopic methods and low resolution bright-field microscopy are used for optical characterization. Here, we describe the use of reflectance confocal microscopy as a simple and intuitive technique to provide a direct correlation between the ordered/disordered structural morphology of colloidal crystals and glasses, and their corresponding optical properties.

Crystallization of Active Emulsion

Active matter contains self-propelled units able to convert stored or ambient free energy into motion. Such systems demonstrate amazing features related to the phenomenon of self-organization and phase transitions and can be used for the development of artificial materials and machines that operate away from equilibrium. Significant advances in the fabrication of active matter were achieved when studying low-density gas and small crystallites. However, the technique of preparation of active matter, where one can observe the formation of stable crystals, is extremely challenging. Here, we describe the novel method to obtain a stable 2D crystal in the active octane-in-water emulsion during the process of heterogeneous crystallization. Active motion is driven by the Marangoni flow emerging at the interface of the droplet. It is established that the crystal volume increases linearly in time in the process of crystallization. Moreover, the dependence of the crystal growth rate on the average velocity of droplets motion in the emulsion has a maximum. The kinetics of crystal growth is defined by a competition between the processes of attachment and detachment of droplets from the crystal surface. Crystallization proceeds via condensation of droplets from the gas phase through the formation of liquid as an intermediate phase, which covers the crystal surface with a thin layer. Inside the liquid layer the bond-orientational order of droplets decreases from the crystal surface toward the gas phase. We anticipate our study to be a starting point for the development of new materials and technologies on the basis of nonequilibrium droplet systems.

Computation of the solid-liquid interfacial free energy in hard spheres by means of thermodynamic integration

We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the total free energy from the interface contribution, performed a finite-size scaling analysis, and obtained for the (100)-interface γ=0.591(11)k_{B}Tσ^{-2}.

Influence of ion size effects on the electrokinetics of aqueous salt-free colloids in alternating electric fields

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.

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.

Near field scattering for samples under forced flow

We describe a light scattering technique for characterizing colloidal samples under constant flow. It exploits the properties of speckles in the deep Fresnel region-the so-called near field speckles-providing absolute scattering measurements of the static form factor of the sample, as described extensively by Mazzoni et al. [Rev. Sci. Instrum. 84, 043704 (2013)] for static samples. We exploit a strongly astigmatic beam for illuminating the scattering volume with a light sheet a few microns thick. This largely improves the sensitivity of the method to small signals. Moreover, by flowing the sample in the direction perpendicular to the light sheet, the transit times are reduced to a minimum, allowing for fast measurements. We tested the instrument with suspensions of calibrated colloidal polystyrene spheres with a size comparable to the light wavelength. In particular, we recovered the static form factors of suspensions of spherical particles and the phase lag of the zero-angle scattering amplitude, which both compare well to Mie theory predictions. We then applied the method to colloidal fractal aggregates of sub-wavelength particles and measured their fractal dimension. The instrument is designed to be operational in continuous flow analysis systems.

Influence of Hydrodynamic Interactions on Colloidal Crystallization

One of the biggest unresolved problems in crystallization phenomena is the significant discrepancy in the nucleation rate between experiments and simulations even for the simplest liquid, i.e., the hard-sphere system. A popular explanation for this discrepancy is the neglect of hydrodynamic interactions (HI) in simulation studies. By comparing simulations with and without HI, we show that the long-time diffusive dynamics of the colloids is slowed down more rapidly by hydrodynamic lubrication effects with increasing volume fraction. We find that the kinetics of both nucleation and growth are controlled by this long-time diffusion and that it is possible to account for most of the effects of HI by rescaling with this timescale. Therefore, we conclude that HI is not the primary cause of the accelerated nucleation rates observed in experiments.

Experimental validation of interpolation method for pair correlations in model crystals

Accurate analysis of pair correlations in condensed matter allows us to establish relations between structures and thermodynamic properties and, thus, is of high importance for a wide range of systems, from solids to colloidal suspensions. Recently, the interpolation method (IM) that describes satisfactorily the shape of pair correlation peaks at short and at long distances has been elaborated theoretically and using molecular dynamics simulations, but it has not been verified experimentally as yet. Here, we test the IM by particle-resolved studies with colloidal suspensions and with complex (dusty) plasmas and demonstrate that, owing to its high accuracy, the IM can be used to experimentally measure parameters that describe interaction between particles in these systems. We used three- and two-dimensional colloidal crystals and monolayer complex (dusty) plasma crystals to explore suitability of the IM in systems with soft to hard-sphere-like repulsion between particles. In addition to the systems with pairwise interactions, if many-body interactions can be mapped to the pairwise ones with some effective (e.g., density-dependent) parameters, the IM could be used to obtain these parameters. The results reliably show that the IM can be effectively used for analysis of pair correlations and interactions in a wide variety of systems and therefore is of broad interest in condensed matter, complex plasma, chemical physics, physical chemistry, materials science, and soft matter.

Colloidal Organosilica Spheres for Three-Dimensional Confocal Microscopy

We describe the synthesis and application of 3-(trimethoxysilyl)propyl methacrylate (TPM) particles as a colloidal model system for three-dimensional (3D) confocal scanning laser microscopy. The effect of the initial TPM concentration on the growth and polydispersity of the particles and a recently developed solvent transfer method to disperse particles in a refractive index and density-matching solvent mixture are reviewed and discussed. To fully characterize the system as a colloidal model, we measure the pair potential between the TPM particles directly using optical tweezers. Finally, we use 3D confocal microscopy to image a sedimentation-diffusion equilibrium of TPM particles to characterize the phase behavior and particle dynamics through successful detection and tracking of all particles in the field of view.

Detection and tracking of anisotropic core-shell colloids

Optical microscopy techniques with three dimensional (3D) resolution are powerful tools for the real-space imaging of the structure and dynamics of colloidal systems. While real-space imaging of spherical particles is well established, the observation of shape anisotropic particles has only recently met a lot of interest. Apart from translation, shape anisotropic particles also possess additional rotational degrees of freedom. In this manuscript, we introduce a novel technique to find the position and the orientation of anisotropic particles in 3D. It is based on an algorithm which is applicable to core-shell particles consisting of a spherical core and a shell with arbitrary shape. We demonstrate the performance of this algorithm using PMMA/PMMA (polymethyl methacrylate) core-shell ellipsoids. The algorithm is tested on artificial images and on experimental data. The correct identification of particle positions with subpixel accuracy and of their orientations with high angular precision in dilute and dense systems is shown. In addition, we developed an advanced particle tracking algorithm that takes both translational and rotational movements of the anisotropic particles into account. We show that our 3D detection and tracking technique is suitable for the accurate and reliable detection of large and dense colloidal systems containing several thousands of particles.

Crystallization in melts of short, semiflexible hard polymer chains: An interplay of entropies and dimensions

What is the thermodynamic driving force for the crystallization of melts of semiflexible polymers? We try to answer this question by employing stochastic approximation Monte Carlo simulations to obtain the complete thermodynamic equilibrium information for a melt of short, semiflexible polymer chains with purely repulsive nonbonded interactions. The thermodynamics is obtained based on the density of states of our coarse-grained model, which varies by up to 5600 orders of magnitude. We show that our polymer melt undergoes a first-order crystallization transition upon increasing the chain stiffness at fixed density. This crystallization can be understood by the interplay of the maximization of different entropy contributions in different spatial dimensions. At sufficient stiffness and density, the three-dimensional orientational interactions drive the orientational ordering transition, which is accompanied by a two-dimensional translational ordering transition in the plane perpendicular to the chains resulting in a hexagonal crystal structure. While the three-dimensional ordering can be understood in terms of Onsager theory, the two-dimensional transition can be understood in terms of the liquid-hexatic transition of hard disks. Due to the domination of lateral two-dimensional translational entropy over the one-dimensional translational entropy connected with columnar displacements, the chains form a lamellar phase. Based on this physical understanding, orientational ordering and translational ordering should be separable for polymer melts. A phenomenological theory based on this understanding predicts a qualitative phase diagram as a function of volume fraction and stiffness in good agreement with results from the literature.

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

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

USAXS analysis of concentration-dependent self-assembling of polymer-brush-modified nanoparticles in ionic liquid: [I] concentrated-brush regime

Using ultra-small angle X-ray scattering (USAXS), we analyzed the higher-order structures of nanoparticles with a concentrated brush of an ionic liquid (IL)-type polymer (concentrated-polymer-brush-modified silica particle; PSiP) in an IL and the structure of the swollen shell layer of PSiP. Homogeneous mixtures of PSiP and IL were successfully prepared by the solvent-casting method involving the slow evaporation of a volatile solvent, which enabled a systematic study over an exceptionally wide range of compositions. Different diffraction patterns as a function of PSiP concentration were observed in the USAXS images of the mixtures. At suitably low PSiP concentrations, the USAXS intensity profile was analyzed using the Percus-Yevick model by matching the contrast between the shell layer and IL, and the swollen structure of the shell and "effective diameter" of the PSiP were evaluated. This result confirms that under sufficiently low pressures below and near the liquid/crystal-threshold concentration, the studied PSiP can be well described using the "hard sphere" model in colloidal science. Above the threshold concentration, the PSiP forms higher-order structures. The analysis of diffraction patterns revealed structural changes from disorder to random hexagonal-closed-packing and then face-centered-cubic as the PSiP concentration increased. These results are discussed in terms of thermodynamically stable "hard" and/or "semi-soft" colloidal crystals, wherein the swollen layer of the concentrated polymer brush and its structure play an important role.

Formation of a transient amorphous solid in low density aqueous charged sphere suspensions

Colloidal glasses formed from hard spheres, nearly hard spheres, ellipsoids and platelets or their attractive variants, have been studied in great detail. Complementing and constraining theoretical approaches and simulations, the many different types of model systems have significantly advanced our understanding of the glass transition in general. Despite their early prediction, however, no experimental charged sphere glasses have been found at low density, where the competing process of crystallization prevails. We here report the formation of a transient amorphous solid formed from charged polymer spheres suspended in thoroughly deionized water at volume fractions of 0.0002-0.01. From optical experiments, we observe the presence of short-range order and an enhanced shear rigidity as compared to the stable polycrystalline solid of body centred cubic structure. On a density dependent time scale of hours to days, the amorphous solid transforms into this stable structure. We further present preliminary dynamic light scattering data showing the evolution of a second slow relaxation process possibly pointing to a dynamic heterogeneity known from other colloidal glasses and gels. We compare our findings to the predicted phase behaviour of charged sphere suspensions and discuss possible mechanisms for the formation of this peculiar type of colloidal glass.

Multistep Heterogeneous Nucleation in Binary Mixtures of Charged Colloidal Spheres

Nucleation plays a decisive role in determining the crystal structure and size distribution; however, understanding of the fundamentals of nucleation is quite limited. In particular, it is unclear whether a nucleus forms spontaneously from solution via a single- or multiple-step process. Here we show how a binary mixture of charged colloidal spheres nucleates heterogeneously on a flat substrate by means of Bragg microscopy, laser diffraction, and laser microscopy. In contrast with the conventional one-step and two-step nucleation mechanisms, a novel pathway of multistep heterogeneous nucleation under certain experimental conditions is highlighted by four steps: initial homogeneous fluid → prenucleation clusters → preordered prenucleation clusters → intermediate ordered phase → final crystal. It is expected that the obtained results would be helpful in rationalizing the rich phase behavior exhibited by the binary mixture systems and in developing better and broadly applicable nucleation models as well as in designing defect-free single-crystal alloys.

Formation of porous crystals via viscoelastic phase separation

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

Free-energy barriers for crystal nucleation from fluid phases

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows us to extract the surface free energy of the nucleus. Neither the knowledge of the (in general nonspherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for colloid-polymer mixtures, which form face-centered cubic colloidal crystals. For a polymer to colloid size ratio of 0.15, the colloid packing fraction in the fluid phase can be varied from melt values to zero by the variation of an effective attractive potential between the colloids. It is found that the approximation of spherical crystal nuclei often underestimates actual nucleation barriers significantly. Nucleation barriers are found to scale as ΔF^{*}=(4π/3)^{1/3}γ[over ¯](V^{*})^{2/3}+const with the nucleus volume V^{*}, and the effective surface tension γ[over ¯] that accounts implicitly for the nonspherical shape can be precisely estimated.

Phase behavior of binary and polydisperse suspensions of compressible microgels controlled by selective particle deswelling

We investigate the phase behavior of suspensions of poly(N-isopropylacrylamide) (pNIPAM) microgels with either bimodal or polydisperse size distribution. We observe a shift of the fluid-crystal transition to higher concentrations depending on the polydispersity or the fraction of large particles in suspension. Crystallization is observed up to polydispersities as high as 18.5%, and up to a number fraction of large particles of 29% in bidisperse suspensions. The crystal structure is random hexagonal close-packed as in monodisperse pNIPAM microgel suspensions. We explain our experimental results by considering the effect of bound counterions. Above a critical particle concentration, these cause deswelling of the largest microgels, which are the softest, changing the size distribution of the suspension and enabling crystal formation in conditions where incompressible particles would not crystallize.

Self-Assembly of Colloidal Molecules due to Self-Generated Flow

The emergence of structure through aggregation is a fascinating topic and of both fundamental and practical interest. Here we demonstrate that self-generated solvent flow can be used to generate long-range attractions on the colloidal scale, with subpiconewton forces extending into the millimeter range. We observe a rich dynamic behavior with the formation and fusion of small clusters resembling molecules. The dynamics of this assembly is governed by an effective conservative energy that for large separations r decays as 1/r. Breaking the flow symmetry, these clusters can be made active.

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.