3D-printed machines that manipulate microscopic objects using capillary forces.

Objects that deform a liquid interface are subject to capillary forces, which can be harnessed to assemble the objects1-4. 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 forces5,6, 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.

Single-particle studies of the effects of RNA-protein interactions on the self-assembly of RNA virus particles.

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.

Braiding, twisting, and weaving microscale fibers with capillary forces.

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.

Designing angle-independent structural colors using Monte Carlo simulations of multiple scattering.

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.

Experimental observations of fractal landscape dynamics in a dense emulsion.

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.

Precise characterization of nanometer-scale systems using interferometric scattering microscopy and Bayesian analysis.

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.

Measurements of the self-assembly kinetics of individual viral capsids around their RNA genome.

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.

Improving holographic particle characterization by modeling spherical aberration.

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.

Investigating the trade-off between color saturation and angle-independence in photonic glasses.

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.

Large depth-of-field tracking of colloidal spheres in holographic microscopy by modeling the objective lens.

Holographic microscopy has developed into a powerful tool for 3D particle tracking, yielding nanometer-scale precision at high frame rates. However, current particle tracking algorithms ignore the effect of the microscope objective on the formation of the recorded hologram. As a result, particle tracking in holographic microscopy is currently limited to particles well above the microscope focus. Here, we show that modeling the effect of an aberration-free lens allows tracking of particles above, near, and below the focal plane in holographic microscopy, doubling the depth of field. Finally, we use our model to determine the conditions under which ignoring the effect of the lens is justified and in what conditions it leads to systematic errors.

Solution-Processable Photonic Inks of Mie-Resonant Hollow Carbon-Silica Nanospheres.

Hollow carbon-silica nanospheres that exhibit angle-independent structural color with high saturation and minimal absorption are made. Through scattering calculations, it is shown that the structural color arises from Mie resonances that are tuned precisely by varying the thickness of the shells. Since the color does not depend on the spatial arrangement of the particles, the coloration is angle independent and vibrant in powders and liquid suspensions. These properties make hollow carbon-silica nanospheres ideal for applications, and their potential in making flexible, angle-independent films and 3D printed films is explored.

Using DNA strand displacement to control interactions in DNA-grafted colloids.

Grafting DNA oligonucleotides to colloidal particles leads to specific, reversible interactions between those particles. However, the interaction strength varies steeply and monotonically with temperature, hindering the use of DNA-mediated interactions in self-assembly. We show how the dependence on temperature can be modified in a controlled way by incorporating DNA strand-displacement reactions. The method allows us to make multicomponent systems that can self-assemble over a wide range of temperatures, invert the dependence on temperature to design colloidal systems that melt upon cooling, controllably transition between structures with different compositions, or design systems with multiple melting transitions. This wide range of behaviors can be realized simply by adding a small number of DNA strands to the solution, making the approach modular and straightforward to implement. We conclude with practical considerations for designing systems of DNA-mediated colloidal interactions.

Colloids with valence and specific directional bonding.

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.

Effects of Contact-Line Pinning on the Adsorption of Nonspherical Colloids at Liquid Interfaces.

The effects of contact-line pinning are well known in macroscopic systems but are only just beginning to be explored at the microscale in colloidal suspensions. We use digital holography to capture the fast three-dimensional dynamics of micrometer-sized ellipsoids breaching an oil-water interface. We find that the particle angle varies approximately linearly with the height, in contrast to results from simulations based on the minimization of the interfacial energy. Using a simple model of the motion of the contact line, we show that the observed coupling between translational and rotational degrees of freedom is likely due to contact-line pinning. We conclude that the dynamics of colloidal particles adsorbing to a liquid interface are not determined by the minimization of interfacial energy and viscous dissipation alone; contact-line pinning dictates both the time scale and pathway to equilibrium.

Core-shell colloidal particles with dynamically tunable scattering properties.

We design polystyrene-poly(N'-isopropylacrylamide-co-acrylic acid) core-shell particles that exhibit dynamically tunable scattering. We show that under normal solvent conditions the shell is nearly index-matched to pure water, and the particle scattering is dominated by Rayleigh scattering from the core. As the temperature or salt concentration increases, both the scattering cross-section and the forward scattering increase, characteristic of Mie scatterers. The magnitude of the change in the scattering cross-section and scattering anisotropy can be controlled through the solvent conditions and the size of the core. Such particles may find use as optical switches or optical filters with tunable opacity.

Size limits of self-assembled colloidal structures made using specific interactions.

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.

Bayesian approach to analyzing holograms of colloidal particles.

We demonstrate a Bayesian approach to tracking and characterizing colloidal particles from in-line digital holograms. We model the formation of the hologram using Lorenz-Mie theory. We then use a tempered Markov-chain Monte Carlo method to sample the posterior probability distributions of the model parameters: particle position, size, and refractive index. Compared to least-squares fitting, our approach allows us to more easily incorporate prior information about the parameters and to obtain more accurate uncertainties, which are critical for both particle tracking and characterization experiments. Our approach also eliminates the need to supply accurate initial guesses for the parameters, so it requires little tuning.

Tracking E. coli runs and tumbles with scattering solutions and digital holographic microscopy.

We use in-line digital holographic microscopy to image freely swimming E. coli. We show that fitting a light scattering model to E. coli holograms can yield quantitative information about the bacterium's body rotation and tumbles, offering a precise way to track fine details of bacterial motility. We are able to extract the cell's three-dimensional (3D) position and orientation and recover behavior such as body angle rotation during runs, tumbles, and pole reversal. Our technique is label-free and capable of frame rates limited only by the camera.

Segregation of "isotope" particles within colloidal molecules.

Clusters of spherical particles are called "colloidal molecules" because they adopt structures that resemble those of true molecules. In this analogy, the particles are the atoms, the attractive interactions between them are bonds, and the different structures that appear in equilibrium are isomers. We take this analogy a step further by doping colloidal molecules with colloidal "isotopes," particles that have the same size but different bonding energies from the other particles in the system. Our molecules are two-dimensional clusters consisting of polystyrene and silica microspheres held together by depletion interactions. Using a combination of optical microscopy and particle tracking, we examine an ensemble of 4- and 5-particle molecules at different isotope ratios. We find that the isotopes tend to segregate to particular positions in the various isomers. We explain these findings using a statistical mechanical model that accounts for the rotational entropy of the isomers and the different interaction potentials between the different types of particles. The model shows how to optimize the yield of any particular isomer, so as to put the isotopes in desired locations. Our experiments and models show that even in systems of particles with isotropic interactions, the structures of self-assembled molecules can in principle be controlled to a surprisingly high extent.

Contact-line pinning controls how quickly colloidal particles equilibrate with liquid interfaces.

Previous experiments have shown that spherical colloidal particles relax to equilibrium slowly after they adsorb to a liquid-liquid interface, despite the large interfacial energy gradient driving the adsorption. The slow relaxation has been explained in terms of transient pinning and depinning of the contact line on the surface of the particles. However, the nature of the pinning sites has not been investigated in detail. We use digital holographic microscopy to track a variety of colloidal spheres-inorganic and organic, charge-stabilized and sterically stabilized, aqueous and non-aqueous-as they breach liquid interfaces. We find that nearly all of these particles relax logarithmically in time over timescales much larger than those expected from viscous dissipation alone. By comparing our results to theoretical models of the pinning dynamics, we infer the area per defect to be on the order of a few square nanometers for each of the colloids we examine, whereas the energy per defect can vary from a few kT for non-aqueous and inorganic spheres to tens of kT for aqueous polymer particles. The results suggest that the likely pinning sites are topographical features inherent to colloidal particles-surface roughness in the case of silica particles and grafted polymer "hairs" in the case of polymer particles. We conclude that the slow relaxation must be taken into account in experiments and applications, such as Pickering emulsions, that involve colloids attaching to interfaces. The effect is particularly important for aqueous polymer particles, which pin the contact line strongly.