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We measure all nonzero elements of the three-dimensional diffusion tensor D for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres, for which no analytical calculations of the diffusion tensor exist. We observe anisotropic rotational and translational diffusion arising from the asymmetries of the clusters. In the case of the three-particle triangular cluster, we also detect a small but statistically significant difference in the rotational diffusion about the two in-plane axes. We attribute this difference to weak breaking of threefold rotational symmetry due to a small amount of particle polydispersity. Our experimental measurements agree well with numerical calculations and show how diffusion constants can be measured under conditions relevant to colloidal self-assembly, where theoretical and even numerical prediction is difficult. [ABSTRACT FROM AUTHOR]

Hydrated networks of glycans (polysaccharides)-in the form of cell walls, periplasms or gel-like matrices-are ubiquitously present adjacent to cellular plasma membranes. Yet, despite their abundance, the function of glycans in the extracellular milieu is largely unknown. Here we show that the spatial configuration of glycans controls the phase behaviour of multiphase model lipid membranes: inhomogeneous glycan networks stabilize large lipid domains at the characteristic length scale of the network, whereas homogeneous networks suppress macroscopic lipid phase separation. We also find that glycan-patterned phase separation is thermally reversible-thus indicating that the effect is thermodynamic rather than kinetic-and that phase patterning probably results from a preferential interaction of glycans with ordered lipid phases. These findings have implications for membrane-mediated transport processes, potentially rationalize long-standing observations that differentiate the behaviour of native and model membranes and may indicate an intimate coupling between cellular lipidomes and glycomes. [ABSTRACT FROM AUTHOR]

Young's law predicts that a colloidal sphere in equilibrium with a liquid interface will straddle the two fluids, its height above the interface defined by an equilibrium contact angle. This has been used to explain why colloids often bind to liquid interfaces, and has been exploited in emulsification, water purification, mineral recovery, encapsulation and the making of nanostructured materials. However, little is known about the dynamics of binding. Here we show that the adsorption of polystyrene microspheres to a water/oil interface is characterized by a sudden breach and an unexpectedly slow relaxation. The relaxation appears logarithmic in time, indicating that complete equilibration may take months. Surprisingly, viscous dissipation appears to play little role. Instead, the observed dynamics, which bear strong resemblance to ageing in glassy systems, agree well with a model describing activated hopping of the contact line over nanoscale surface heterogeneities. These results may provide clues to longstanding questions on colloidal interactions at an interface. [ABSTRACT FROM AUTHOR]

A colloidal particle straddling an air/water interface experiences an unexpectedly large viscous drag., Engineering and Applied Sciences, Physics

Structurally colored materials could potentially replace dyes and pigments in many applications, but it is challenging to fabricate structural colors that mimic the appearance of absorbing pigments. We demonstrate the microfluidic fabrication of “photonic pigments” consisting of microcapsules containing dense amorphous packings of core–shell colloidal particles. These microcapsules show non-iridescent structural colors that are independent of viewing angle, a critical requirement for applications such as displays or coatings. We show that the design of the microcapsules facilitates the suppression of incoherent and multiple scattering, enabling the fabrication of photonic pigments with colors spanning the visible spectrum. Our findings should provide new insights into the design and synthesis of materials with structural colors., Engineering and Applied Sciences

Coalescence of two kinds of pre-processed droplets is necessary to perform chemical and biological assays in droplet-based microfluidics. However, a robust technique to accomplish this does not exist. Here we present a microfluidic device to synchronize the reinjection of two different kinds of droplets and coalesce them, using hydrostatic pressure in conjunction with a conventional syringe pump. We use a device consisting of two opposing T-junctions for reinjecting two kinds of droplets and control the flows of the droplets by applying gravity-driven hydrostatic pressure. The hydrostatic-pressure operation facilitates balancing the droplet reinjection rates and allows us to synchronize the reinjection. Furthermore, we present a simple but robust module to coalesce two droplets that sequentially come into the module, regardless of their arrival times. These re-injection and coalescence techniques might be used in lab-on-chip applications requiring droplets with controlled numbers of solid materials, which can be made by coalescing two pre-processed droplets that are formed and sorted in devices., Engineering and Applied Sciences

We have developed a new method to produce hybrid particles with polyhedral shapes in very high yield (liter quantities at up to 70% purity) using a combination of emulsion polymerization and inorganic surface chemistry. The procedure has been generalized to create complex geometries, including hybrid line segments, triangles, tetrahedra, octahedra, and more. The optical properties of these particles are tailored for studying their dynamics and self-assembly. For example, we produce systems that consist of index-matched spheres allowing us to define the position of each elementary particle in three-dimensional space. We present some preliminary studies on the self-assembly of these complex shaped systems based on electron and optical microscopy., Engineering and Applied Sciences, Physics

Although the effects of kinetics on crystal growth are well understood, the role of substrate curvature is not yet established. We studied rigid, two-dimensional colloidal crystals growing on spherical droplets to understand how the elastic stress induced by Gaussian curvature affects the growth pathway. In contrast to crystals grown on flat surfaces or compliant crystals on droplets, these crystals formed branched, ribbon-like domains with large voids and no topological defects. We show that this morphology minimizes the curvature-induced elastic energy. Our results illustrate the effects of curvature on the ubiquitous process of crystallization, with practical implications for nanoscale disorder-order transitions on curved manifolds, including the assembly of viral capsids, phase separation on vesicles, and crystallization of tetrahedra in three dimensions. [ABSTRACT FROM AUTHOR]

Digital holographic microscopy (DHM) can measure the 3D positions as well as the scattering properties of colloidal particles in a single 2D image. We describe DHM and our analysis of recorded holograms with exact scattering solutions, which permit the measurement of 3D particle positions with ~10 nm precision and millisecond time resolution, and discuss studies of the Brownian dynamics of clusters of spheres with DHM. [ABSTRACT FROM AUTHOR]

Most of the colloidal clusters have been produced from oil-in-water emulsions with identical microspheres dispersed in oil droplets. Here, we present new types of binary colloidal clusters from phase-inverted water-in-oil emulsions using various combinations of two different colloids with several size ratios: monodisperse silica or polystyrene microspheres for larger particles and silica or titania nanoparticles for smaller particles. Obviously, a better understanding of how finite groups of different colloids self -organize in a confined geometry may help us control the structure of matter at multiple length scales. In addition, since aqueous dispersions have much better phase stability, we could produce much more diverse colloidal materials from water-in-oil emulsions rather than from oil-in-water emulsions. Interestingly, the configurations of the large microspheres were not changed by the presence of the small particles. However, the arrangement of the smaller particles was strongly dependent on the nature of the interparticle interactions. The experimentally observed structural evolutions were consistent with the numerical simulations calculated using Surface Evolver. These clusters with nonisotropic structures can be used as building blocks for novel colloidal structures with unusual properties or by themselves as light scatterers, diffusers, and complex adaptive matter exhibiting emergent behavior. [ABSTRACT FROM AUTHOR]

Soft materials made from braided or woven microscale fibers can display unique properties that can be exploited in electromagnetic, mechanical, and biomedical applications. These properties depend on the topology of the braids or weaves-that is, the order in which fibers cross one another. Current industrial braiding and weaving machines cannot easily braid or weave micrometer-scale fibers into controllable topologies; they typically apply forces that are large enough to break the fibers, and each machine can typically make only one topology. Here we use a 3D-printed device called a "capillary machine" to manipulate micrometer-scale fibers without breaking them. The operating principle is the physics of capillary forces: as the machines move vertically, they exert lateral capillary forces on floating objects, which in turn move small fibers connected to them. We present a new type of capillary machine that is based on principles of braid theory. It implements all the possible fiber-swapping operations for a set of four fibers and can therefore make any four-strand topology, including braids, twists, hierarchical twists, and weaves. We make these different topologies by changing the pattern of vertical motion of the machine. This approach is a mechanically simple, yet versatile way to make micro- and nano-textiles. We describe the prospects and limitations of this new type of machine for applications.

Self-assembly is a vital part of the life cycle of certain icosahedral RNA viruses. Furthermore, the assembly process can be harnessed to make icosahedral virus-like particles (VLPs) from coat protein and RNA in vitro . Although much previous work has explored the effects of RNA-protein interactions on the assembly products, relatively little research has explored the effects of coat-protein concentration. We mix coat protein and RNA from bacteriophage MS2, and we use a combination of gel electrophoresis, dynamic light scattering, and transmission electron microscopy to investigate the assembly products. We show that with increasing coat-protein concentration, the products transition from well-formed MS2 VLPs to "monster" particles consisting of multiple partial capsids to RNA-protein condensates consisting of large networks of RNA and partially assembled capsids. We argue that the transition from well-formed to monster particles arises because the assembly follows a nucleation-and-growth pathway in which the nucleation rate depends sensitively on the coat-protein concentration, such that at high protein concentrations, multiple nuclei can form on each RNA strand. To understand the formation of the condensates, which occurs at even higher coat-protein concentrations, we use Monte Carlo simulations with coarse-grained models of capsomers and RNA. These simulations suggest that the formation of condensates occurs by the adsorption of protein to the RNA followed by the assembly of capsids. Multiple RNA molecules can become trapped when a capsid grows from capsomers attached to two different RNA molecules or when excess protein bridges together growing capsids on different RNA molecules. Our results provide insight into an important biophysical process and could inform design rules for making VLPs for various applications.

Conical surfaces pose an interesting challenge to crystal growth: A crystal growing on a cone can wrap around and meet itself at different radii. We use a disk-packing algorithm to investigate how this closure constraint can geometrically frustrate the growth of single crystals on cones with small opening angles. By varying the crystal seed orientation and cone angle, we find that-except at special commensurate cone angles-crystals typically form a seam that runs along the axial direction of the cone, while near the tip, a disordered particle packing forms. We show that the onset of disorder results from a finite-size effect that depends strongly on the circumference and not on the seed orientation or cone angle. This finite-size effect occurs also on cylinders, and we present evidence that on both cylinders and cones, the defect density increases exponentially as circumference decreases. We introduce a simple model for particle attachment at the seam that explains the dependence on the circumference. Our findings suggest that the growth of single crystals can become frustrated even very far from the tip when the cone has a small opening angle. These results may provide insights into the observed geometry of conical crystals in biological and materials applications.

Interferometric scattering microscopy can image the dynamics of nanometer-scale systems. The typical approach to analyzing interferometric images involves intensive processing, which discards data and limits the precision of measurements. We demonstrate an alternative approach: modeling the interferometric point spread function and fitting this model to data within a Bayesian framework. This approach yields best-fit parameters, including the particle's three-dimensional position and polarizability, as well as uncertainties and correlations between these parameters. Building on recent work, we develop a model that is parameterized for rapid fitting. The model is designed to work with Hamiltonian Monte Carlo techniques that leverage automatic differentiation. We validate this approach by fitting the model to interferometric images of colloidal nanoparticles. We apply the method to track a diffusing particle in three dimensions, to directly infer the diffusion coefficient of a nanoparticle without calculating a mean-square displacement, and to quantify the ejection of DNA from an individual lambda phage virus, demonstrating that the approach can be used to infer both static and dynamic properties of nanoscale systems.

Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening foam, suggested that the random motions of its bubbles are due to the system configuration moving over a fractal energy landscape in high-dimensional space. Here we show that the salient geometrical features of such high-dimensional fractal landscapes can be explored and reliably quantified, using empirical trajectory data from many degrees of freedom, in a model-free manner. For a mayonnaise-like dense emulsion, analysis of the observed trajectories of oil droplets quantitatively reproduces the high-dimensional fractal geometry of the configuration path and its associated local energy minima generated using a computational model. That geometry in turn drives the droplets' complex random motion observed in real space. Our results indicate that experimental studies can elucidate whether the similar dynamics in different soft and biological materials may also be due to fractal landscape dynamics.

Objects that deform a liquid interface are subject to capillary forces, which can be harnessed to assemble the objects 1-4 . Once assembled, such structures are generally static. Here we dynamically modulate these forces to move objects in programmable two-dimensional patterns. We 3D-print devices containing channels that trap floating objects using repulsive capillary forces 5,6 , then move these devices vertically in a water bath. Because the channel cross-sections vary with height, the trapped objects can be steered in two dimensions. The device and interface therefore constitute a simple machine that converts vertical to lateral motion. We design machines that translate, rotate and separate multiple floating objects and that do work on submerged objects through cyclic vertical motion. We combine these elementary machines to make centimetre-scale compound machines that braid micrometre-scale filaments into prescribed topologies, including non-repeating braids. Capillary machines are distinct from mechanical, optical or fluidic micromanipulators in that a meniscus links the object to the machine. Therefore, the channel shapes need only be controlled on the scale of the capillary length (a few millimetres), even when the objects are microscopic. Consequently, such machines can be built quickly and inexpensively. This approach could be used to manipulate micrometre-scale particles or to braid microwires for high-frequency electronics., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Understanding the pathways by which simple RNA viruses self-assemble from their coat proteins and RNA is of practical and fundamental interest. Although RNA-protein interactions are thought to play a critical role in the assembly, our understanding of their effects is limited because the assembly process is difficult to observe directly. We address this problem by using interferometric scattering microscopy, a sensitive optical technique with high dynamic range, to follow the in vitro assembly kinetics of more than 500 individual particles of brome mosaic virus (BMV)-for which RNA-protein interactions can be controlled by varying the ionic strength of the buffer. We find that when RNA-protein interactions are weak, BMV assembles by a nucleation-and-growth pathway in which a small cluster of RNA-bound proteins must exceed a critical size before additional proteins can bind. As the strength of RNA-protein interactions increases, the nucleation time becomes shorter and more narrowly distributed, but the time to grow a capsid after nucleation is largely unaffected. These results suggest that the nucleation rate is controlled by RNA-protein interactions, while the growth process is driven less by RNA-protein interactions and more by protein-protein interactions and intraprotein forces. The nucleated pathway observed with the plant virus BMV is strikingly similar to that previously observed with bacteriophage MS2, a phylogenetically distinct virus with a different host kingdom. These results raise the possibility that nucleated assembly pathways might be common to other RNA viruses.

Structurally colored materials can switch colors in response to external stimuli, which makes them potentially useful as colorimetric sensors, dynamic displays, and camouflage. However, their applications are limited by the angular dependence, slow response, and absence of synchronous control in time and space. In addition, out-of-plane deformation from shape instability easily occurs in photonic films, leading to inhomogeneous colors in photonic-crystal materials. To address these challenges, we combine structurally colored photonic glasses and dielectric elastomer actuators. We use an external voltage signal to tune color changes quickly (much less than 0.1 s). The photonic glassses produce colors with low angular dependence, so that their colors are homogeneous even when they become curved due to voltage-triggered instabilities (buckling or wrinkling). As proof of concept, we present a pixelated display in which segments can be independently and rapidly turned on and off. This wide-angle, instability-tolerant, color-changing platform could be used in next-generation soft and curved color displays, camouflage with both shape and color changes, and multifunctional sensors.

Colloidal particles can be programmed to interact in complex ways by functionalizing them with DNA oligonucleotides. Adding DNA strand-displacement reactions to the system allows these interparticle interactions to respond to specific changes in temperature. We present the requirements for thermally driven directed motion of colloidal particles, and we explore how these conditions can be realized experimentally using strand-displacement reactions. To evaluate the concept, we build and test a colloidal "dancer": a single particle that can be driven to move through a programmed sequence of steps along a one-dimensional track composed of other particles. The results of these tests reveal the capabilities and limitations of using DNA-mediated interactions for applications in dynamic systems. Specifically, we discuss how to design the substrate to limit complexity while permitting full control of the motile component, how to ratchet the interactions to move over many substrate positions with a limited regime of control parameters, and how to use technological developments to reduce the probability of detachment without sacrificing speed.

Photonic glasses-isotropic structures with short-range correlations-can produce structural colors with little angle-dependence, making them an alternative to dyes in applications such as cosmetics, coatings, and displays. However, the low angle-dependence is often accompanied by low color saturation. To investigate how the short-range correlations affect the trade-off between saturation and angle-independence, we vary the structure factor and use a Monte Carlo model of multiple scattering to investigate the resulting optical properties. We use structure factors derived from analytical models and calculated from simulations of disordered sphere packings. We show that the trade-off is controlled by the first peak of the structure factor. It is possible to break the trade-off by tuning the width of this peak and controlling the sample thickness. Practically, this result shows that the protocol used to pack particles into a photonic glass is important to the optical properties.

Holographic microscopy combined with forward modeling and inference allows colloidal particles to be characterized and tracked in three dimensions with high precision. However, current models ignore the effects of optical aberrations on hologram formation. We investigate the effects of spherical aberration on the structure of single-particle holograms and on the accuracy of particle characterization. We find that in a typical experimental setup, spherical aberration can result in systematic shifts of about 2% in the inferred refractive index and radius. We show that fitting with a model that accounts for spherical aberration decreases this aberration-dependent error by a factor of two or more, even when the level of spherical aberration in the optical train is unknown. With the new generative model, the inferred parameters are consistent across different levels of aberration, making particle characterization more robust.

Diamond-structured colloidal photonic crystals are much sought-after for their applications in visible light management because of their ability to support a complete photonic band gap (PBG). However, their realization via self-assembly pathways is a long-standing challenge. This challenge is rooted in three fundamental problems: the design of building blocks that assemble into diamond-like structures, the sensitivity of the PBG to stacking faults, and ensuring that the PBG opens at an experimentally attainable refractive index. Here we address these problems simultaneously using a multipronged computational approach. We use reverse engineering to establish the design principles for the rod-connected diamond structure (RCD), the so-called "champion" photonic crystal. We devise two distinct self-assembly routes for designer triblock patchy colloidal rods, both proceeding via tetrahedral clusters to yield a mixed phase of cubic and hexagonal polymorphs closely related to RCD. We use Monte Carlo simulations to show how these routes avoid a metastable amorphous phase. Finally, we show that both the polymorphs support spectrally overlapping PBGs. Importantly, randomly stacked hybrids of these polymorphs also display PBGs, thus circumventing the requirement of polymorph selection in a scalable fabrication method.

We describe a new approach to making plasmonic metamolecules with well-controlled resonances at optical wavelengths. Metamolecules are highly symmetric, subwavelength-scale clusters of metal and dielectric. They are of interest for metafluids, isotropic optical materials with applications in imaging and optical communications. For such applications, the morphology must be precisely controlled: the optical response is sensitive to nanometer-scale variations in the thickness of metal coatings and the distances between metal surfaces. To achieve this precision, we use a multi-step colloidal synthesis approach. Starting from highly monodisperse silica seeds, we grow octahedral clusters of polystyrene spheres using seeded-growth emulsion polymerization. We then overgrow the silica and remove the polystyrene to create a dimpled template. Finally, we attach six silica satellites to the template and coat them with gold. Using single-cluster spectroscopy, we show that the plasmonic resonances are reproducible from cluster to cluster. By comparing the spectra to theory, we show that the multi-step synthesis approach can control the distances between metallic surfaces to nanometer-scale precision. More broadly, our approach shows how metamolecules can be produced in bulk by combining different, high-yield colloidal synthesis steps, analogous to how small molecules are produced by multi-step chemical reactions.

Disordered nanostructures with correlations on the scale of visible wavelengths can show angle-independent structural colors. These materials could replace dyes in some applications because the color is tunable and resists photobleaching. However, designing nanostructures with a prescribed color is difficult, especially when the application-cosmetics or displays, for example-requires specific component materials. A general approach to solving this constrained design problem is modeling and optimization: Using a model that predicts the color of a given system, one optimizes the model parameters under constraints to achieve a target color. For this approach to work, the model must make accurate predictions, which is challenging because disordered nanostructures have multiple scattering. To address this challenge, we develop a Monte Carlo model that simulates multiple scattering of light in disordered arrangements of spherical particles or voids. The model produces quantitative agreement with measurements when we account for roughness on the surface of the film, particle polydispersity, and wavelength-dependent absorption in the components. Unlike discrete numerical simulations, our model is parameterized in terms of experimental variables, simplifying the connection between simulation and fabrication. To demonstrate this approach, we reproduce the color of the male mountain bluebird ( Sialia currucoides ) in an experimental system, using prescribed components and a microstructure that is easy to fabricate. Finally, we use the model to find the limits of angle-independent structural colors for a given system. These results enable an engineering design approach to structural color for many different applications., Competing Interests: Competing interest statement: A provisional patent application has been filed on the subject of this work, with V.H., A.B.S., M.X., and V.N.M. as inventors.

Tracking and analyzing the individual diffusion of nanoscale objects such as proteins and viruses is an important methodology in life science. Here, we show a sensor that combines the efficiency of light line illumination with the advantages of fluidic confinement. Tracking of freely diffusing nano-objects inside water-filled hollow core fibers with core diameters of tens of micrometers using elastically scattered light from the core mode allows retrieving information about the Brownian motion and the size of each particle of the investigated ensemble individually using standard tracking algorithms and the mean squared displacement analysis. Specifically, we successfully measure the diameter of every gold nanosphere in an ensemble that consists of several hundreds of 40 nm particles, with an individual precision below 17% (±8 nm). In addition, we confirm the relevance of our approach with respect to bioanalytics by analyzing 70 nm λ-phages. Overall these features, together with the strongly reduced demand for memory space, principally allows us to record thousands of frames and to achieve high frame rates for high precision tracking of nanoscale objects.

Self-assembly is widely used by biological systems to build functional nanostructures, such as the protein capsids of RNA viruses. But because assembly is a collective phenomenon involving many weakly interacting subunits and a broad range of timescales, measurements of the assembly pathways have been elusive. We use interferometric scattering microscopy to measure the assembly kinetics of individual MS2 bacteriophage capsids around MS2 RNA. By recording how many coat proteins bind to each of many individual RNA strands, we find that assembly proceeds by nucleation followed by monotonic growth. Our measurements reveal the assembly pathways in quantitative detail and also show their failure modes. We use these results to critically examine models of the assembly process., Competing Interests: The authors declare no competing interest., (Copyright © 2019 the Author(s). Published by PNAS.)

Colloidal particles with well-controlled shapes and interactions are an ideal experimental system for exploring how matter organizes itself. Like atoms and molecules, these particles form bulk phases such as liquids and crystals. But they are more than just crude analogs of atoms; they are a form of matter in their own right, with complex and interesting collective behavior not seen at the atomic scale. Their behavior is affected by geometrical or topological constraints, such as curved surfaces or the shapes of the particles. Because the interactions between the particles are often short-ranged, we can understand the effects of these constraints using geometrical concepts such as packing. The geometrical viewpoint gives us a window into how entropy affects not only the structure of matter, but also the dynamics of how it forms., (Copyright © 2015, American Association for the Advancement of Science.)

DNA-grafted nanoparticles have been called "programmable atom-equivalents": Like atoms, they form three-dimensional crystals, but unlike atoms, the particles themselves carry information (the sequences of the grafted strands) that can be used to "program" the equilibrium crystal structures. We show that the programmability of these colloids can be generalized to the full temperature-dependent phase diagram, not just the crystal structures themselves. We add information to the buffer in the form of soluble DNA strands designed to compete with the grafted strands through strand displacement. Using only two displacement reactions, we program phase behavior not found in atomic systems or other DNA-grafted colloids, including arbitrarily wide gas-solid coexistence, reentrant melting, and even reversible transitions between distinct crystal phases., (Copyright © 2015, American Association for the Advancement of Science.)

We establish size limitations for assembling structures of controlled size and shape out of colloidal particles with short-ranged interactions. Through simulations we show that structures with highly variable shapes made out of dozens of particles can form with high yield, as long as each particle in the structure binds only to the particles in their local environment. To understand this, we identify the excited states that compete with the ground-state structure and demonstrate that these excited states have a completely topological characterization, valid when the interparticle interactions are short-ranged. This allows complete enumeration of the energy landscape and gives bounds on how large a colloidal structure can assemble with high yield. For large structures the yield can be significant, even with hundreds of particles.

Although the effects of kinetics on crystal growth are well understood, the role of substrate curvature is not yet established. We studied rigid, two-dimensional colloidal crystals growing on spherical droplets to understand how the elastic stress induced by Gaussian curvature affects the growth pathway. In contrast to crystals grown on flat surfaces or compliant crystals on droplets, these crystals formed branched, ribbon-like domains with large voids and no topological defects. We show that this morphology minimizes the curvature-induced elastic energy. Our results illustrate the effects of curvature on the ubiquitous process of crystallization, with practical implications for nanoscale disorder-order transitions on curved manifolds, including the assembly of viral capsids, phase separation on vesicles, and crystallization of tetrahedra in three dimensions.

The ability to design and assemble three-dimensional structures from colloidal particles is limited by the absence of specific directional bonds. As a result, complex or low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. Here we demonstrate a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically distinct surface patches that imitate hybridized atomic orbitals, including sp, sp(2), sp(3), sp(3)d, sp(3)d(2) and sp(3)d(3). Functionalized with DNA with single-stranded sticky ends, patches on different particles can form highly directional bonds through programmable, specific and reversible DNA hybridization. These features allow the particles to self-assemble into 'colloidal molecules' with triangular, tetrahedral and other bonding symmetries, and should also give access to a rich variety of new microstructured colloidal materials.

We describe a procedure to synthesize colloidal clusters with polyhedral morphologies in high yield (liter quantities at up to 70% purity) using a combination of emulsion polymerization and inorganic surface chemistry. We show that the synthesis initially used for silica-polystyrene hybrid clusters can be generalized to create clusters from other inorganic and polymer particles. We also show that high yields of particular morphologies can be obtained by precise control of the inorganic seed particle size, a finding that can be explained using a hard-sphere packing model. These clusters can be further chemically modified for a variety of applications. Introducing a cross-linker leads to colloidal clusters that can be index matched in an appropriate solvent, allowing them to be used for particle tracking or optical studies of colloidal self-assembly. Also, depositing a thin silica layer on these colloids allows the surface properties to be controlled using silane chemistry.

The self-assembly of colloids is an alternative to top-down processing that enables the fabrication of nanostructures. We show that self-assembled clusters of metal-dielectric spheres are the basis for nanophotonic structures. By tailoring the number and position of spheres in close-packed clusters, plasmon modes exhibiting strong magnetic and Fano-like resonances emerge. The use of identical spheres simplifies cluster assembly and facilitates the fabrication of highly symmetric structures. Dielectric spacers are used to tailor the interparticle spacing in these clusters to be approximately 2 nanometers. These types of chemically synthesized nanoparticle clusters can be generalized to other two- and three-dimensional structures and can serve as building blocks for new metamaterials.

The study of clusters has provided a tangible link between local geometry and bulk condensed matter, but experiments have not yet systematically explored the thermodynamics of the smallest clusters. Here we present experimental measurements of the structures and free energies of colloidal clusters in which the particles act as hard spheres with short-range attractions. We found that highly symmetric clusters are strongly suppressed by rotational entropy, whereas the most stable clusters have anharmonic vibrational modes or extra bonds. Many of these clusters are subsets of close-packed lattices. As the number of particles increases from 6 to 10, we observe the emergence of a complex free-energy landscape with a small number of ground states and many local minima.

When small numbers of colloidal microspheres are attached to the surfaces of liquid emulsion droplets, removing fluid from the droplets leads to packings of spheres that minimize the second moment of the mass distribution. The structures of the packings range from sphere doublets, triangles, and tetrahedra to exotic polyhedra not found in infinite lattice packings, molecules, or minimum-potential energy clusters. The emulsion system presents a route to produce new colloidal structures and a means to study how different physical constraints affect symmetry in small parcels of matter.