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.

Effect of coat-protein concentration on the self-assembly of bacteriophage MS2 capsids around RNA.

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 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.

Effect of coat-protein concentration on the self-assembly of bacteriophage MS2 capsids around RNA.

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.

Geometric frustration of hard-disk packings on cones.

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.

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.

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.

Measuring intramolecular connectivity in long RNA molecules using two-dimensional DNA patch-probe arrays.

We describe a simple method to infer intramolecular connections in a population of long RNA molecules in vitro. First we add DNA oligonucleotide "patches" that perturb the RNA connections, then we use a microarray containing a complete set of DNA oligonucleotide "probes" to record where perturbations occur. The pattern of perturbations reveals couplings between different regions of the RNA sequence, from which we infer connections as well as their prevalences in the population. We validate this patch-probe method using the 1,058-nucleotide RNA genome of satellite tobacco mosaic virus (STMV), which has previously been shown to have multiple long-range connections. Our results not only indicate long duplexes that agree with previous structures but also reveal the prevalence of competing connections. Together, these results suggest that globally-folded and locally-folded structures coexist in solution. We show that the prevalence of connections changes when pseudouridine, an important component of natural and synthetic RNA molecules, is substituted for uridine in STMV RNA.

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.

Programming Directed Motion with DNA-Grafted Particles.

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.

Voltage-tunable elastomer composites that use shape instabilities for rapid structural color changes.

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.

Polyhedral plasmonic nanoclusters through multi-step colloidal chemistry.

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.

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.

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.

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.

Self-Assembly of Patchy Colloidal Rods into Photonic Crystals Robust to Stacking Faults.

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.

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.

Tracking and Analyzing the Brownian Motion of Nano-objects Inside Hollow Core Fibers.

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.

Effects of multiple scattering on angle-independent structural color in disordered colloidal materials.

Disordered packings of colloidal spheres show angle-independent structural color when the particles are on the scale of the wavelength of visible light. Previous work has shown that the positions of the peaks in the reflectance spectra can be predicted accurately from a single-scattering model that accounts for the effective refractive index of the material. This agreement shows that the main color peak arises from short-range correlations between particles. However, the single-scattering model does not quantitatively reproduce the observed color: the main peak in the reflectance spectrum is much broader and the reflectance at low wavelengths is much larger than predicted by the model. We use a combination of experiment and theory to understand these features. We find that one significant contribution to the breadth of the main peak is light that is scattered, totally internally reflected from the boundary of the sample, and then scattered again. The high reflectance at low wavelengths also results from multiple scattering but can be traced to the increase in the scattering cross section of individual particles with decreasing wavelength. Both of these effects tend to reduce the saturation of the structural color, which limits the use of these materials in applications. We show that while the single-scattering model cannot reproduce the observed saturations, it can be used as a design tool to reduce the amount of multiple scattering and increase the color saturation of materials, even in the absence of absorbing components.

Before the breach: Interactions between colloidal particles and liquid interfaces at nanoscale separations.

Particles bound to fluid-fluid interfaces are widely used to study self-assembly and to make materials such as Pickering emulsions. In both contexts, the lateral interactions between such particles have been studied extensively. However, much less is known about the normal interactions between a particle and the interface prior to contact. We use digital holographic microscopy to measure the dynamics of individual micrometer-size colloidal particles as they approach an interface between an aqueous phase and oil. Our measurements show that the interaction between the particle and interface changes nonmonotonically as a function of salt concentration, from repulsive at 1 mM to attractive at tens of mM to negligible at 100 mM and attractive again above 200 mM. In the attractive regimes, the particles can bind to the interface at nanometer-scale separation without breaching it. Classical Derjaguin-Landau-Verwey-Overbeek theory does not explain these observations. However, a theory that accounts for nonlinear screening and correlations between the ions does predict the nonmonotonic dependence on salt concentration and produces trajectories that agree with experimental data. We further show that the normal interactions determine the lateral interactions between particles that are bound to the interface. Because the interactions we observe occur at salt concentrations used to make Pickering emulsions and other particle-laden interfaces, our results suggest that particle arrangements at the interface are likely out of equilibrium on experimental timescales.