Refractive-index and density-matched emulsions with programmable DNA interactions.

Emulsion droplets on the colloidal length scale are a model system of frictionless compliant spheres. Direct imaging studies of the microscopic structure and dynamics of emulsions offer valuable insights into fundamental processes, such as gelation, jamming, and self-assembly. A microscope, however, can only resolve the individual droplets in a densely packed emulsion if the droplets are closely index-matched to their fluid medium. Mitigating perturbations due to gravity additionally requires the droplets to be density-matched to the medium. Creating droplets that are simultaneously index-matched and density-matched has been a long-standing challenge for the soft-matter community. The present study introduces a method for synthesizing monodisperse micrometer-sized siloxane droplets whose density and refractive index can be precisely and independently tuned by adjusting the volume fraction of three silane precursors. A systematic optimization protocol yields fluorescently labeled ternary droplets whose densities and refractive indexes match, to the fourth decimal place, those of aqueous solutions of glycerol or dimethylsiloxane. Because all of the materials in this system are biocompatible, we functionalize the droplets with DNA strands to endow them with programmed inter-droplet interactions. Confocal microscopy then reveals both the three-dimensional structure and the network of droplet-droplet contacts in a class of self-assembled droplet gels, free from gravitational effects. This experimental toolbox creates opportunities for studying the microscopic mechanisms that govern viscoelastic properties and self-assembly in soft materials.

A coarse-grained simulation model for colloidal self-assembly via explicit mobile binders.

Colloidal particles with mobile binding molecules constitute a powerful platform for probing the physics of self-assembly. Binding molecules are free to diffuse and rearrange on the surface, giving rise to spontaneous control over the number of droplet-droplet bonds, i.e., valence, as a function of the concentration of binders. This type of valence control has been realized experimentally by tuning the interaction strength between DNA-coated emulsion droplets. Optimizing for valence two yields droplet polymer chains, termed 'colloidomers', which have recently been used to probe the physics of folding. To understand the underlying self-assembly mechanisms, here we present a coarse-grained molecular dynamics (CGMD) model to study the self-assembly of this class of systems using explicit representations of mobile binding sites. We explore how valence of assembled structures can be tuned through kinetic control in the strong binding limit. More specifically, we optimize experimental control parameters to obtain the highest yield of long linear colloidomer chains. Subsequently tuning the dynamics of binding and unbinding via a temperature-dependent model allows us to observe a heptamer chain collapse into all possible rigid structures, in good agreement with recent folding experiments. Our CGMD platform and dynamic bonding model (implemented as an open-source custom plugin to HOOMD-Blue) reveal the molecular features governing the binding patch size and valence control, and opens the study of pathways in colloidomer folding. This model can therefore guide programmable design in experiments.

Self-assembly of emulsion droplets through programmable folding.

In the realm of particle self-assembly, it is possible to reliably construct nearly arbitrary structures if all the pieces are distinct1-3, but systems with fewer flavours of building blocks have so far been limited to the assembly of exotic crystals4-6. Here we introduce a minimal model system of colloidal droplet chains7, with programmable DNA interactions that guide their downhill folding into specific geometries. Droplets are observed in real space and time, unravelling the rules of folding. Combining experiments, simulations and theory, we show that controlling the order in which interactions are switched on directs folding into unique structures, which we call colloidal foldamers8. The simplest alternating sequences (ABAB...) of up to 13 droplets yield 11 foldamers in two dimensions and one in three dimensions. Optimizing the droplet sequence and adding an extra flavour uniquely encodes more than half of the 619 possible two-dimensional geometries. Foldamers consisting of at least 13 droplets exhibit open structures with holes, offering porous design. Numerical simulations show that foldamers can further interact to make complex supracolloidal architectures, such as dimers, ribbons and mosaics. Our results are independent of the dynamics and therefore apply to polymeric materials with hierarchical interactions on all length scales, from organic molecules all the way to Rubik's Snakes. This toolbox enables the encoding of large-scale design into sequences of short polymers, placing folding at the forefront of materials self-assembly.

DNA self-organization controls valence in programmable colloid design.

Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence-the number of interparticle bonds-is a prerequisite for the assembly of complex architectures. The assembly can be directed via solid "patchy" particles with prescribed geometries to make, for example, a colloidal diamond. We demonstrate here that the nanoscale ordering of individual molecular linkers can combine to program the structure of microscale assemblies. Specifically, we experimentally show that covering initially isotropic microdroplets with N mobile DNA linkers results in spontaneous and reversible self-organization of the DNA into Z(N) binding patches, selecting a predictable valence. We understand this valence thermodynamically, deriving a free energy functional for droplet-droplet adhesion that accurately predicts the equilibrium size of and molecular organization within patches, as well as the observed valence transitions with N Thus, microscopic self-organization can be programmed by choosing the molecular properties and concentration of binders. These results are widely applicable to the assembly of any particle with mobile linkers, such as functionalized liposomes or protein interactions in cell-cell adhesion.

Osmotically Driven and Detected DNA Translocations.

A salinity gradient propels a DNA molecule through a solid-state nanopore and generates an ionic current whose change allows for the detection of the translocation. Measurements and theoretical analyses reveal the role of diffusio-osmosis in driving these phenomena: After accounting for known salinity-dependent electrode effects, the measured current change caused by the presence of a DNA molecule inside the nanopore and the DNA translocation speed through it both increase with the magnitude of the applied salinity gradients. The effects are consistent with the theory of diffuisio-osmosis and strong enough to enable DNA translocations to overcome an applied retarding potential of tens of millivolts. This work illustrates how salinity gradients can be used to power and operate a nanopore sensor.

Assembly and Dynamic Analysis of Square Colloidal Crystals via Templated Capillary Assembly.

Capillary assembly has the ability to engineer centimeter-sized regions of discrete colloidal superstructures and microarrays. However, its use as a tool for directing crystallization of colloids into surface-bound nonclose-packed arrays is limited. Furthermore, the use of quantitative particle tracking tools to investigate evaporative assembly dynamics is rarely employed. In this contribution, we use templated capillary assembly to fabricate square-packed lattices of spherical, organosilica colloids using designed patterned boundaries. Particle tracking algorithms reveal that the assembly of square-packed regions is controlled by the interplay between confinement-driven nuclei formation and osmotic pressure-driven restructuring. We find that the incorporation of a square template increases the yield of particles bearing four nearest neighbors (Zn = 4) from 4 to 39%, obtained using a heavier and more viscous solvent. Maximal square-packed domains occur at specific initial particle concentrations (1.75-2.25 wt % or φ = 0.013-0.017), indicating that rearrangements are a function of osmotic force. We use particle tracking methods to dynamically monitor conversions between square and hexagonal packing, revealing a cyclical transition between 4 and 6 coordinated particles throughout meniscus recession. Our method is highly scalable and inexpensive and can be adapted for use with different particle sizes and compositions, as well as for targeted open-packed geometries. Our findings will inform the large area, defect-free assembly of nonclose-packed lattices of unexplored varieties that are necessary for the continued expansion of colloid-based materials with vast applications in optical electronics.

Freely Jointed Polymers Made of Droplets.

An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or "colloidomers." The distribution of cluster sizes is consistent with a polymerization process in which the droplets achieve their prescribed valence. Conformational statistics reveal that the chains are freely jointed, so that the Kuhn length is close to one bead diameter. The end-to-end length scales with the number of bonds N as N^{ν}, where ν≈3/4, in agreement with the Flory theory in two dimensions. The chain diffusion coefficient D approximately scales as D∝N^{-ν}, as predicted by the Zimm model. Unlike molecular polymers, colloidomers can be repeatedly assembled and disassembled under temperature cycling, allowing for reconfigurable, responsive matter.

Buckling Causes Nonlinear Dynamics of Filamentous Viruses Driven through Nanopores.

Measurements and Langevin dynamics simulations of filamentous viruses driven through solid-state nanopores reveal a superlinear rise in the translocation velocity with driving force. The mobility also scales with the length of the virus in a nontrivial way that depends on the force. These dynamics are consequences of the buckling of the leading portion of a virus as it emerges from the nanopore and is put under compressive stress by the viscous forces it encounters. The leading tip of a buckled virus stalls and this reduces the total viscous drag force. We present a scaling theory that connects the solid mechanics to the nonlinear dynamics of polyelectrolytes translocating nanopores.

Nanopore Measurements of Filamentous Viruses Reveal a Sub-nanometer-Scale Stagnant Fluid Layer.

We report measurements and analyses of nanopore translocations by fd and M13, two related strains of filamentous virus that are identical except for their charge densities. The standard continuum theory of electrokinetics greatly overestimates the translocation speed and the conductance associated with counterions for both viruses. Furthermore, fd and M13 behave differently from one another, even translocating in opposite directions under certain conditions. This cannot be explained by Manning-condensed counterions or a number of other proposed models. Instead, we argue that these anomalous findings are consequences of the breakdown of the validity of continuum hydrodynamics at the scale of a few molecular layers. Next to a polyelectrolyte, there exists an extra-viscous, sub-nanometer-thin boundary layer that has a giant influence on the transport characteristics. We show that a stagnant boundary layer captures the essential hydrodynamics and extends the validity of the electrokinetic theory beyond the continuum limit. A stagnant layer with a thickness of about half a nanometer consistently improves predictions of the ionic current change induced by virus translocations and of the translocation velocity for both fd and M13 over a wide range of nanopore dimensions and salt concentrations.

Sequential self-assembly of DNA functionalized droplets.

Complex structures and devices, both natural and manmade, are often constructed sequentially. From crystallization to embryogenesis, a nucleus or seed is formed and built upon. Sequential assembly allows for initiation, signaling, and logical programming, which are necessary for making enclosed, hierarchical structures. Although biology relies on such schemes, they have not been available in materials science. Here, we demonstrate programmed sequential self-assembly of DNA functionalized emulsions. The droplets are initially inert because the grafted DNA strands are pre-hybridized in pairs. Active strands on initiator droplets then displace one of the paired strands and thus release its complement, which in turn activates the next droplet in the sequence, akin to living polymerization. Our strategy provides time and logic control during the self-assembly process, and offers a new perspective on the synthesis of materials.Natural complex systems are often constructed by sequential assembly but this is not readily available for synthetic systems. Here, the authors program the sequential self-assembly of DNA functionalized emulsions by altering the DNA grafted strands.

Stiff filamentous virus translocations through solid-state nanopores.

The ionic conductance through a nanometer-sized pore in a membrane changes when a biopolymer slides through it, making nanopores sensitive to single molecules in solution. Their possible use for sequencing has motivated numerous studies on how DNA, a semi-flexible polymer, translocates nanopores. Here we study voltage-driven dynamics of the stiff filamentous virus fd with experiments and simulations to investigate the basic physics of polymer translocations. We find that the electric field distribution aligns an approaching fd with the nanopore, promoting its capture, but it also pulls fd sideways against the membrane after failed translocation attempts until thermal fluctuations reorient the virus for translocation. fd is too stiff to translocate in folded configurations. It therefore translocates linearly, exhibiting a voltage-independent mobility and obeying first-passage-time statistics. Surprisingly, lengthwise Brownian motion only partially accounts for the translocation velocity fluctuations. We also observe a voltage-dependent contribution whose origin is only partially determined.