# Publications

Fitting scattering solutions to time series of digital holograms is a precise way to measure three-dimensional dynamics of microscale objects such as colloidal particles. However, this inverse-problem approach is computationally expensive. We show that the computational time can be reduced by an order of magnitude or more by fitting to a random subset of the pixels in a hologram. We demonstrate our algorithm on experimentally measured holograms of micrometer-scale colloidal particles, and we show that 20-fold increases in speed, relative to fitting full frames, can be attained while introducing errors in the particle positions of 10 nm or less. The method is straightforward to implement and works for any scattering model. It also enables a parallelization strategy wherein random-subset fitting is used to quickly determine initial guesses that are subsequently used to fit full frames in parallel. This approach may prove particularly useful for studying rare events, such as nucleation, that can only be captured with high frame rates over long times.

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.

We present a new, high-speed technique to track the three-dimensional translation and rotation of non-spherical colloidal particles. We capture digital holograms of micrometer-scale silica rods and sub-micrometer-scale Janus particles freely diffusing in water, and then fit numerical scattering models based on the discrete dipole approximation to the measured holograms. This inverse-scattering approach allows us to extract the position and orientation of the particles as a function of time, along with static parameters including the size, shape, and refractive index. The best-fit sizes and refractive indices of both particles agree well with expected values. The technique is able to track the center of mass of the rod to a precision of 35 nm and its orientation to a precision of 1.5°, comparable to or better than the precision of other 3D diffusion measurements on non-spherical particles. Furthermore, the measured translational and rotational diffusion coefficients for the silica rods agree with hydrodynamic predictions for a spherocylinder to within 0.3%. We also show that although the Janus particles have only weak optical asymmetry, the technique can track their 2D translation and azimuthal rotation over a depth of field of several micrometers, yielding independent measurements of the effective hydrodynamic radius that agree to within 0.2%. The internal and external consistency of these measurements validate the technique. Because the discrete dipole approximation can model scattering from arbitrarily shaped particles, our technique could be used in a range of applications, including particle tracking, microrheology, and fundamental studies of colloidal self-assembly or microbial motion.

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.

Colloidal crystals are promising structures for photonic applications requiring dynamic control over optical properties. However, for ease of processing and reconfigurability, the crystals should be encapsulated to form ‘ink’ capsules rather than confined in a thin film. Here we demonstrate a class of encapsulated colloidal photonic structures whose optical properties can be controlled through osmotic pressure. The ordering and separation of the particles within the microfluidically created capsules can be tuned by changing the colloidal concentration through osmotic pressure-induced control of the size of the individual capsules, modulating photonic stop band. The rubber capsules exhibit a reversible change in the diffracted colour, depending on osmotic pressure, a property we call osmochromaticity. The high encapsulation efficiency and capsule uniformity of this microfluidic approach, combined with the highly reconfigurable shapes and the broad control over photonic properties, make this class of structures particularly suitable for photonic applications such as electronic inks and reflective displays.

Particle-doped thin films that are translucent and diffusive have applications in cosmetics, coatings, and display technologies, but finding material combinations that produce these effects simultaneously is challenging: formulations tend to be either transparent or opaque. Using a combination of Mie scattering calculations and spectral transmission measurements on monodisperse colloidal suspensions, we demonstrate that the two characteristic optical properties of the films, total transmittance and haze, scale with the effective backscattering and forward scattering cross sections, both of which are properties of single particles. These scalings enable an efficient computational search for combinations of particle sizes, concentrations, and refractive indices that break the trade-off between translucency and diffusion. The optimum particle sizes and concentrations obey power-law dependences on the refractive index difference, a result of the interference condition for resonances in the scattering cross sections. The power laws serve as design equations for formulating particle-doped thin films.

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.

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.

The optical theorem provides a powerful tool for calculating the extinction cross section of a particle from a solution to Maxwell’s equations, relating the cross section to the scattering amplitude in the forward direction. The theorem has been generalized by a number of other workers to consider a particle near an interface between media with different refractive indices. Here we present a derivation of the generalized optical theorem that is valid for a particle embedded in the interface, as well as an incident beam undergoing total internal reflection. We also obtain an additional useful physical result: we show that the far-field scattered field must be zero in the direction parallel to the interface. Our results enable the verification of computations of scattering by particles embedded in interfaces and may be relevant to experiments on colloidal particles at fluid interfaces.

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.

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.

We discuss digital holographic microscopy (DHM), a 3D imaging technique capable of measuring the positions of micron-sized colloidal particles with nanometer precision and sub-millisecond temporal resolution. We use exact electromagnetic scattering solutions to model holograms of multiple colloidal spheres. While the Lorenz-Mie solution for scattering by isolated spheres has previously been used to model digital holograms, we apply for the first time an exact multisphere superposition scattering model that is capable of modeling holograms from spheres that are sufficiently close together to exhibit optical coupling.

We study the dynamics of colloidal particles as they approach and breach a water-oil interface. We use a fast 3D imaging technique, digital holographic microscopy, to track particles with 2 nm precision and sub-millisecond time resolution. We find that polystyrene particles dispersed in water or water-glycerol mixtures relax logarithmically with time after breaching the interface and do not reach equilibrium on experimental timescales. By contrast, decane-dispersed PMMA particles show fast dynamics and reach a steady-state height within milliseconds. We attribute the difference to the surface properties of the particles. We also probe the dependence of the relaxation rate on surface charge by studying carboxyl-functionalized particles under varying acid concentrations. We conclude that the slow relaxation may be due to contact-line pinning on topographical defects rather than surface charges.

Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to—or “park” on—smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences, and we vary the ratio α of large to small sphere radii. Once bound, the large spheres cannot rearrange, and thus the clusters do not form dense or symmetric packings. Nevertheless, this stochastic aggregation process yields a remarkably narrow distribution of clusters with nearly 90% tetrahedra at α=2.45. The high yield of tetrahedra, which reaches 100% in simulations at α=2.41, arises not simply because of packing constraints, but also because of the existence of a long-time lower bound that we call the “minimum parking” number. We derive this lower bound from solutions to the classic mathematical problem of spherical covering, and we show that there is a critical size ratio αc=(1+√2)≈2.41, close to the observed point of maximum yield, where the lower bound equals the upper bound set by packing constraints. The emergence of a critical value in a random aggregation process offers a robust method to assemble uniform clusters for a variety of applications, including metamaterials.

Ultrasmooth, highly spherical monocrystalline gold particles were prepared by a cyclic process of slow growth followed by slow chemical etching, which selectively removes edges and vertices. The etching process effectively makes the surface tension isotropic, so that spheres are favored under quasi-static conditions. It is scalable up to particle sizes of 200 nm or more. The resulting spherical crystals display uniform scattering spectra and consistent optical coupling at small separations, even showing Fano-like resonances in small clusters. The high monodispersity of the particles we demonstrate should facilitate the self-assembly of nanoparticle clusters with uniform optical resonances, which could in turn be used to fabricate optical metafluids. Narrow size distributions are required to control not only the spectral features but also the morphology and yield of clusters in certain assembly schemes.

We present a new, high-speed technique to track the three-dimensional translation and rotation of non-spherical colloidal particles. We capture digital holograms of micrometer-scale silica rods and sub-micrometer-scale Janus particles freely diffusing in water, and then fit numerical scattering models based on the discrete dipole approximation to the measured holograms. This inverse-scattering approach allows us to extract the position and orientation of the particles as a function of time, along with static parameters including the size, shape, and refractive index. The best-fit sizes and refractive indices of both particles agree well with expected values. The technique is able to track the center of mass of the rod to a precision of 35 nm and its orientation to a precision of 1.5°, comparable to or better than the precision of other 3D diffusion measurements on non-spherical particles. Furthermore, the measured translational and rotational diffusion coefficients for the silica rods agree with hydrodynamic predictions for a spherocylinder to within 0.3%. We also show that although the Janus particles have only weak optical asymmetry, the technique can track their 2D translation and azimuthal rotation over a depth of field of several micrometers, yielding independent measurements of the effective hydrodynamic radius that agree to within 0.2%. The internal and external consistency of these measurements validate the technique. Because the discrete dipole approximation can model scattering from arbitrarily shaped particles, our technique could be used in a range of applications, including particle tracking, microrheology, and fundamental studies of colloidal self-assembly or microbial motion.

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, sp2, sp3, sp3d, sp3d2 and sp3d3. 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 |[lsquo]|colloidal molecules|[rsquo]| with triangular, tetrahedral and other bonding symmetries, and should also give access to a rich variety of new microstructured colloidal materials.

Making materials that display angle-independent structural color requires control over both scattering and short-range correlations in the refractive index. We demonstrate a simple way to make such materials by packing core-shell colloidal particles consisting of high-refractive-index cores and soft, transparent shells. The core-shell structure allows us to control the scattering cross-section of the particles independently of the interparticle distance, which sets the resonance condition. At the same time, the softness of the shells makes it easy to assemble disordered structures through centrifugation. We show that packings of these particles display angle-independent structural colors that can be tuned by changing the shell diameter, either by using different particles or simply by varying the concentration of the suspension. The transparency of the suspensions can be tuned independently of the color by changing the core diameter. These materials might be useful for electronic displays, cosmetics, or long-lasting dyes.

Digital holographic microscopy is a fast three-dimensional (3D) imaging tool with many applications in soft matter physics. Recent studies have shown that electromagnetic scattering solutions can be fit to digital holograms to obtain the 3D positions of isolated colloidal spheres with nanometer precision and millisecond temporal resolution. Here we describe the results of new techniques that extend the range of systems that can be studied with fitting. We show that an exact multisphere superposition scattering solution can fit holograms of colloidal clusters containing up to six spheres. We also introduce an approximate and computationally simpler solution, Mie superposition, that is valid for multiple spheres spaced several wavelengths or more from one another. We show that this method can be used to analyze holograms of several spheres on an emulsion droplet, and we give a quantitative criterion for assessing its validity.

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.