Direct measurement of repulsive and attractive pair potentials using pairs of optical traps.

We present a technique for measuring the interactions between pairs of colloidal particles in two optical traps. This method is particularly suitable for measuring strongly attractive potentials, an otherwise challenging task. The interaction energy is calculated from the distribution of inter-particle separations by accounting for the contribution from the optical traps with arbitrary trap profiles. The method is simple to implement and applicable to different types of pair potentials and optical trapping geometries. We apply the method to measure dipolar pair interactions in experiments with paramagnetic colloids in external magnetic fields. We obtain consistent and accurate results in all regimes, from strongly attractive to repulsive potentials. By means of computer simulations, we demonstrate that the proposed method can be successfully applied to systems with complex pair interactions characterized by multiple attractive and repulsive regimes, which are ubiquitous in soft and biological matter.

Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase.

Self-assembly of microscopic building blocks into highly ordered and functional structures is ubiquitous in nature and found at all length scales. Hierarchical structures formed by colloidal building blocks are typically assembled from monodisperse particles interacting via engineered directional interactions. Here, we show that polydisperse colloidal bananas self-assemble into a complex and hierarchical quasi-two-dimensional structure, called the vortex phase, only due to excluded volume interactions and polydispersity in the particle curvature. Using confocal microscopy, we uncover the remarkable formation mechanism of the vortex phase and characterize its exotic structure and dynamics at the single-particle level. These results demonstrate that hierarchical self-assembly of complex materials can be solely driven by entropy and shape polydispersity of the constituting particles.

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.

From ultra-fast growth to avalanche growth in devitrifying glasses.

During devitrification, pre-existing crystallites grow by adding particles to their surface via a process that is either thermally activated (diffusive mode) or happens without kinetic barriers (fast crystal growth mode). It is yet unclear what factors determine the crystal growth mode and how to predict it. With simulations of repulsive hard-sphere-like (Weeks-Chandler-Andersen) glasses, we show for the first time that the same system at the same volume fraction and temperature can devitrify via both modes depending on the preparation protocol of the glass. We prepare two types of glass: conventional glass (CG) via fast quenching and uniform glass (UG) via density homogenization. First, we bring either glass into contact with a crystal (X) and find the inherent structure (CGX/UGX). During energy minimization, the crystal front grows deep into the CG interface, while the growth is minimal for UG. When thermal noise is added, this behavior is reflected in different crystallization dynamics. CGX exhibits a density drop at the crystal growth front, which correlates with enhanced dynamics at the interface and a fast growth mode. This mechanism may explain the faster crystal growth observed below the glass transition experimentally. In contrast, UGX grows via intermittent avalanche-like dynamics localized at the interface, a combination of localized mechanical defects and the exceptional mechanical stability imposed by the UG glass phase.

Single-orientation colloidal crystals from capillary-action-induced shear.

We study the crystallization of colloidal dispersions under capillary-action-induced shear as the dispersion is drawn into flat walled capillaries. Using confocal microscopy and small angle x-ray scattering, we find that the shear near the capillary walls influences the crystallization to result in large random hexagonal close-packed (RHCP) crystals with long-range orientational order over tens of thousands of colloidal particles. We investigate the crystallization mechanism and find partial crystallization under shear, initiating with hexagonal planes at the capillary walls, where shear is highest, followed by epitaxial crystal growth from these hexagonal layers after the shear is stopped. We then characterize the three-dimensional crystal structure finding that the shear-induced crystallization leads to larger particle separations parallel to the shear and vorticity directions as compared to the equilibrium RHCP structure. Confocal microscopy reveals that competing shear directions, where the capillary walls meet at a corner, create differently oriented hexagonal planes of particles. The single-orientation RHCP colloidal crystals remain stable after formation and are produced without the need of complex shear cell arrangements.

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.

Synthesis of Rough Colloidal SU-8 Rods and Bananas via Nanoprecipitation.

Surface roughness plays an important role in determining the mechanical properties, wettability, and self-assembly in colloidal systems. In this work, we develop a simple and fast method to produce rough colloidal SU-8 rods, bananas, and spheres, via the nanoprecipitation of SU-8 in water. During this process, SU-8 nanospheres are absorbed onto the surface of the colloidal SU-8 particles and then cross-linked using UV-light. The size of the spherical asperities and the asperity density are controlled by the concentration of SU-8 used during the nanoprecipitation reaction. Fluorescent labeling of the rough SU-8 colloidal particles allows for their confocal imaging, which demonstrates their stability at high packing fractions. With these newly developed rough particles, we provide a colloidal model system that allows for studies addressing the impact of surface roughness on materials composed of anisotropic particles.

Stabilisation of hollow colloidal TiO2 particles by partial coating with evenly distributed lobes.

Photo-catalytically active crystalline TiO2 has attracted special attention due to its relevance for renewable energy and is typically obtained by the calcination of amorphous TiO2. However, stabilising hollow colloidal TiO2 particles against aggregation during calcination without compromising their photocatalytic activity poses two conflicting demands: to be stable their surface needs to be coated, while efficient photocatalysis requires an exposed TiO2 surface. Here, this incompatibility is resolved by partially coating TiO2 shells with evenly distributed 3-trimethoxysilyl propyl methacrylate (TPM) lobes. These lobes act both as steric barriers and surface charge enhancers that efficiently stabilise the TiO2 shells against aggregation during calcination. The morphology of the TPM lobes and their coverage, and the associated particle stability during the calcination-induced TiO2 crystallization, can be controlled by the pH and the contact angle between TPM and TiO2. The crystal structure and the grain size of the coated TiO2 shells are controlled by varying the calcination temperature, which allows tuning their photocatalytic activity. Finally, the durable photocatalytic activity over many usage cycles of the coated TiO2 compared to uncoated shells is demonstrated in a simple way by measuring the photo-degradation of a fluorescent dye. Our approach offers a general strategy for stabilising colloidal materials, without compromising access to their active surfaces.

Dislocation-controlled formation and kinetics of grain boundary loops in two-dimensional crystals.

The formation and kinetics of grain boundaries are closely related to the topological constraints imposed on their complex dislocation structure. Loop-shaped grain boundaries are unique structures to establish such a link because their overall topological "charge" is zero due to their null net Burgers vector. Here, we observe that a local rotational deformation of a 2D colloidal crystal with an optical vortex results in a grain boundary loop only if the product of its radius and misorientation exceeds a critical value. Above this value, the deformation is plastic and the grain boundary loop spontaneously shrinks at a rate that solely depends on this product, while otherwise, the deformation is elastically restored. We show that this elastic-to-plastic crossover is a direct consequence of the unique dislocation structure of grain boundary loops. At the critical value, the loop is structurally equivalent to the so-called "flower defect" and the shrinkage rate diverges. Our results thus reveal a general limit on the formation of grain boundary loops in 2D crystals and elucidate the central role of defects in both the onset of plasticity and the kinetics of grain boundaries.

Model-Free Measurement of the Pair Potential in Colloidal Fluids Using Optical Microscopy.

We report a straightforward, model-free approach for measuring pair potentials from particle-coordinate data, based on enforcing consistency between the pair distribution function measured separately by the distance-histogram and test-particle insertion routes. We demonstrate the method's accuracy and versatility in simulations of simple fluids, before applying it to an experimental system composed of superparamagnetic colloidal particles. The method will enable experimental investigations into many-body interactions and allow for effective coarse graining of interactions from simulations.

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.

Bulk synthesis of silver-head colloidal rodlike micromotors.

Colloidal particles with asymmetric catalytic activities are emerging micro/nanomotors that harvest chemical energy for propulsion in fluids. It is of general interest to produce such particles with high performance, in large quantity and at low cost. In this paper, we present a facile bulk method to synthesize silver-head colloidal silica rods. These particles self-propel towards their active sites by reacting with hydrogen peroxide, and the velocity is tuned via the fuel concentration. We show that these motors are highly efficient; compared to the currently available chemical-phoretic micro/nanomotors they show similar performance of self-propulsion at fuel concentrations that are two orders of magnitude smaller.

Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres.

Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self-van Hove correlation function and distinct van Hove correlation function by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self-part and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions of roughly 0.60. However, at even higher densities, deviations between the experiment and the theoretical approach become clearly visible. Upon increasing packing fraction, in experiments, the short-time self-diffusive behavior is strongly affected by hydrodynamic effects and leads to a significant decrease in the respective mean-squared displacement. By contrast, and in accordance with previous simulation studies, the present DDFT, which neglects hydrodynamic effects, shows no dependence on the particle density for this quantity.

Communication: Contact values of pair distribution functions in colloidal hard disks by test-particle insertion.

We apply Henderson's method for measuring the cavity distribution function y(r) [J. Henderson, Mol. Phys. 48, 389 (1983)] to obtain the pair distribution function at contact, g(σ+). In contrast to the conventional distance-histogram method, no approximate extrapolation to contact is required. The resulting equation of state from experiments and simulations of hard disks agrees well with the scaled particle theory prediction up to high fluid packing fractions. We also provide the first experimental measurement of y(r) inside the hard core, which will allow for a more complete comparison with theory. The method's flexibility is further illustrated by measuring the partial pair distribution functions of binary hard-disk mixtures in simulation. The equation for the contact values can be used to derive familiar results from statistical geometry.

Two-Dimensional Melting of Colloidal Hard Spheres.

We study the melting of quasi-two-dimensional colloidal hard spheres by considering a tilted monolayer of particles in sedimentation-diffusion equilibrium. In particular, we measure the equation of state from the density profiles and use time-dependent and height-resolved correlation functions to identify the liquid, hexatic, and crystal phases. We find that the liquid-hexatic transition is first order and that the hexatic-crystal transition is continuous. Furthermore, we directly measure the width of the liquid-hexatic coexistence gap from the fluctuations of the corresponding interface, and thereby experimentally establish the full phase behavior of hard disks.

Structural disorder, filament growth and self-poisoning in short rods confined onto a flat wall.

Confocal microscopy was used to directly observe the structural coarsening of the first layer of short colloidal rods sedimented onto a flat wall. Based on an image analysis algorithm we devised, quantitative information on the location, orientation and length of each particle can be extracted with high precision. At high density the system undergoes structural arrest, and becomes trapped in a disordered state of randomly arranged filaments that are composed of side-by-side aligned rods. The frustration of structural order is signalled by a new peak that emerges in the radial distribution function. Configuration analysis shows that the peak is primarily due to pairs of particles that are arranged in a "T" shape, a configuration that is compatible with neither crystallization nor filament growth. Our results point to a self-poisoning mechanism for the frustration of structural order, and highlight the importance of particle shape in controlling colloidal assembly thus materials properties.

Equilibrium Grain Boundary Segregation and Clustering of Impurities in Colloidal Polycrystalline Monolayers.

We investigate the segregation of impurities to grain boundaries in colloidal polycrystalline monolayers using video microscopy. A model colloidal alloy is prepared by embedding large spherical impurities in a polycrystalline monolayer of small host colloidal hard spheres, which stops grain growth at a finite grain size. The size ratio between the impurities and the host particles determines whether they behave as interstitial or substitutional impurities in the bulk crystal, akin to those in real alloys. We find that the partitioning of impurities between the grains and the grain boundaries is in very good agreement with the Langmuir-McLean adsorption model for equilibrium grain boundary segregation. This enables the direct measurement of the free energy of adsorption for the two types of impurities. Near saturation, we characterize the spatial distribution of the adsorbed impurities and find that it strongly depends on their interstitial or substitutional nature. This is because the relative importance of clustering and mixing due to nonadditivity is determined by geometrical constraints imposed by the crystalline host lattice.

On the Gaussian approximation in colloidal hard sphere fluids.

We study the behaviour of the self-intermediate scattering function and self-van Hove correlation function for quasi-two-dimensional colloidal hard sphere fluids at a range of area fractions. We compute these functions first directly from the particle coordinates and secondly from the mean squared displacement via the Gaussian approximation. This allows us to test the validity of this approximation over a range of length and time scales, where we find that the Gaussian approximation holds if the hydrodynamic limits are appropriately probed. Surprisingly, only small deviations from Gaussian behaviour are seen at intermediate times, even for dense fluids. We next consider these deviations from Gaussian behaviour firstly via the non-Gaussian parameter and secondly by considering the relaxation times of the intermediate scattering function. From these measurements we develop a scaling relation in order to directly determine the combinations of wavevectors and times at which the non-Gaussian behavior is seen. This allows for the clear identification of the hydrodynamic regimes and thus provides new insight into the crossover between long- and short-time self-diffusion.

Effect of Hydrodynamic Interactions on Self-Diffusion of Quasi-Two-Dimensional Colloidal Hard Spheres.

We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient D(S) scaled by the diffusion coefficient at infinite dilution, D(0), strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient D(L)/D(0) is in quantitative agreement with D(L)/D(0) obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of D(L)/D(0) on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions.

Thermal Analog of Gimbal Lock in a Colloidal Ferromagnetic Janus Rod.

We report an entropy-driven orientational hopping transition in a magnetically confined colloidal Janus rod. In a magnetic field, the sedimented rod randomly hops between horizontal and vertical states: the latter state comes at a substantial gravitational cost at no reduction of magnetic potential energy. The probability distribution over the angles of the rod shows that the presence of an external magnetic field leads to the emergence of a metastable vertical state separated from the ground state by an effective barrier. This barrier does not come from the potential energy but rather from the vast gain in phase space available to the rod as it approaches the vertical state. The loss of rotational degree of freedom that gives rise to this effect is a statistical mechanical analogue of the phenomenon of gimbal lock from classical mechanics.