Controlling Chaos: Periodic Defect Braiding in Active Nematics Confined to a Cardioid.

This work examines self-mixing in active nematics, a class of fluids in which mobile topological defects drive chaotic flows in a system comprised of biological filaments and molecular motors. We present experiments that demonstrate how geometrical confinement can influence the braiding dynamics of the defects. Notably, we show that confinement in cardioid-shaped wells leads to realization of the golden braid, a maximally efficient mixing state of exactly three defects with no defect creation or annihilation. We characterize the golden braid state using different measures of topological entropy and the Lyapunov exponent. In particular, topological entropy measured from the stretching rate of material lines agrees well with an analytical computation from braid theory. Increasing the size of the confining cardioid produces a transition from the golden braid, to the fully chaotic active turbulent state.

Active nematic order and dynamic lane formation of microtubules driven by membrane-bound diffusing motors.

Dynamic lane formation and long-range active nematic alignment are reported using a geometry in which kinesin motors are directly coupled to a lipid bilayer, allowing for in-plane motor diffusion during microtubule gliding. We use fluorescence microscopy to image protein distributions in and below the dense two-dimensional microtubule layer, revealing evidence of diffusion-enabled kinesin restructuring within the fluid membrane substrate as microtubules collectively glide above. We find that the lipid membrane acts to promote filament-filament alignment within the gliding layer, enhancing the formation of a globally aligned active nematic state. We also report the emergence of an intermediate, locally ordered state in which apolar dynamic lanes of nematically aligned microtubules migrate across the substrate. To understand this emergent behavior, we implement a continuum model obtained from coarse graining a collection of self-propelled rods, with propulsion set by the local motor kinetics. Tuning the microtubule and kinesin concentrations as well as active propulsion in these simulations reveals that increasing motor activity promotes dynamic nematic lane formation. Simulations and experiments show that, following fluid bilayer substrate mediated spatial motor restructuring, the total motor concentration becomes enriched below the microtubule lanes that they drive, with the feedback leading to more dynamic lanes. Our results have implications for membrane-coupled active nematics in vivo as well as for engineering dynamic and reconfigurable materials where the structural elements and power sources can dynamically colocalize, enabling efficient mechanical work.

Submersed micropatterned structures control active nematic flow, topology, and concentration.

Coupling between flows and material properties imbues rheological matter with its wide-ranging applicability, hence the excitement for harnessing the rheology of active fluids for which internal structure and continuous energy injection lead to spontaneous flows and complex, out-of-equilibrium dynamics. We propose and demonstrate a convenient, highly tunable method for controlling flow, topology, and composition within active films. Our approach establishes rheological coupling via the indirect presence of fully submersed micropatterned structures within a thin, underlying oil layer. Simulations reveal that micropatterned structures produce effective virtual boundaries within the superjacent active nematic film due to differences in viscous dissipation as a function of depth. This accessible method of applying position-dependent, effective dissipation to the active films presents a nonintrusive pathway for engineering active microfluidic systems.

Colloidal aggregation in anisotropic liquid crystal solvent.

The mutual attraction between colloidal particles in an anisotropic fluid, such as the nematic liquid crystal phase, leads to the formation of hierarchical aggregate morphologies distinct from those that tend to form in isotropic fluids. Previously it was difficult to study this aggregation process for a large number of colloids due to the difficulty of achieving a well dispersed initial colloid distribution under good imaging conditions. In this paper, we report the use of a recently developed self-assembling colloidal system to investigate this process. Hollow, micron-scale colloids are formed in situ in the nematic phase and subsequently aggregate to produce fractal structures and colloidal gels, the structures of which are determined by colloid concentration and temperature quench depth through the isotropic to nematic phase transition point. This self-assembling colloidal system provides a unique method to study particle aggregation in liquid crystal over large length scales. We use fluorescence microscopy over a range of length scales to measure aggregate structure as a function of temperature quench depth, observe ageing mechanisms and explore the driving mechanisms in this unique system. Our analyses suggest that aggregate dynamics depend on a combination of Frank elasticity relaxation, spontaneous defect line annihilation and internal aggregate fracturing.

Fractal generation in a two-dimensional active-nematic fluid.

Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a quasi-two-dimensional (2D) nematic phase and driven by adenosine-triphosphate-fueled kinesin motor proteins. This system exhibits robust chaotic advection and gives rise to a pronounced fractal structure in the nematic contours. We characterize such experimentally derived fractals using the power spectrum and discover that the power spectrum decays as k-ß for large wavenumbers k. The parameter ß is measured for several experimental realizations. Though ß is effectively constant in time, it does vary with experimental parameters, indicating differences in the scale-free behavior of the microtubule-based active nematic. Though the fractal patterns generated in this active system are reminiscent of passively advected dye in 2D chaotic flows, the underlying mechanism for fractal generation is more subtle. We provide a simple, physically inspired mathematical model of fractal generation in this system that relies on the material being locally compressible, though the total area of the material is conserved globally. The model also requires that large-scale density variations are injected into the material periodically. The model reproduces the power-spectrum decay k-ß seen in experiments. Linearizing the model of fractal generation about the equilibrium density, we derive an analytic relationship between ß and a single dimensionless quantity r, which characterizes the compressibility.

Morphology transition in lipid vesicles due to in-plane order and topological defects.

Complex morphologies in lipid membranes typically arise due to chemical heterogeneity, but in the tilted gel phase, complex shapes can form spontaneously even in a membrane containing only a single lipid component. We explore this phenomenon via experiments and coarse-grained simulations on giant unilamellar vesicles of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine. When cooled from the untilted L(α) liquid-crystalline phase into the tilted gel phase, vesicles deform from smooth spheres to disordered, highly crumpled shapes. We propose that this shape evolution is driven by nucleation of complex membrane microstructure with topological defects in the tilt orientation that induce nonuniform membrane curvature. Coarse-grained simulations demonstrate this mechanism and show that kinetic competition between curvature change and defect motion can trap vesicles in deeply metastable, defect-rich structures.

All-optical switching of nematic liquid crystal films driven by localized surface plasmons.

We have demonstrated an all-optical technique for reversible in-plane and out-of-plane switching of nematic liquid crystal molecules in few micron thick films. Our method leverages the highly localized electric fields ("hot spots") and plasmonic heating that are generated in the near-field region of densely packed gold nanoparticle layers optically excited on-resonance with the localized surface plasmon absorption. Using polarized microscopy and transmission measurements, we observe this switching from homeotropic to planar over a temperature range starting at room temperature to just below the isotropic transition, and at on-resonance excitation intensity less than 0.03 W/cm(2). In addition, we controllably vary the in-plane directionality of the liquid crystal molecules in the planar state by altering the linear polarization of the incident excitation. Using discrete dipole simulations and control measurements, we establish spectral selectivity in this new and interesting perspective for photonic application using low light power.

Self-assembled nanoparticle micro-shells templated by liquid crystal sorting.

A current goal in nanotechnology focuses on the assembly of different nanoparticle types into 3D organized structures. In this paper we report the use of a liquid crystal host phase in a new process for the generation of micron-scale vesicle-like nanoparticle shells stabilized by ligand-ligand interactions. The constructs formed consist of a robust, thin spherical layer, composed of closely packed quantum dots (QDs) and stabilized by local crystallization of the mesogenic ligands. Ligand structure can be tuned to vary QD packing within the shell and made UV cross-linkable to allow for intact shell extraction into toluene. The assembly method we describe could be extended to other nanoparticle types (metallic, magnetic etc.), where hollow shell formation is controlled by thermally sorting mesogen-functionalized nanoparticles in a liquid crystalline host material at the isotropic to nematic transition. This process represents a versatile method for making non-planar 3D nano-assemblies.

Magnetic field induced quantum dot brightening in liquid crystal synergized magnetic and semiconducting nanoparticle composite assemblies.

The design and development of multifunctional composite materials from artificial nano-constituents is one of the most compelling current research areas. This drive to improve over nature and produce 'meta-materials' has met with some success, but results have proven limited with regards to both the demonstration of synergistic functionalities and in the ability to manipulate the material properties post-fabrication and in situ. Here, magnetic nanoparticles (MNPs) and semiconducting quantum dots (QDs) are co-assembled in a nematic liquid crystalline (LC) matrix, forming composite structures in which the emission intensity of the quantum dots is systematically and reversibly controlled with a small applied magnetic field (<100 mT). This magnetic field-driven brightening, ranging between a two- to three-fold peak intensity increase, is a truly cooperative effect: the LC phase transition creates the co-assemblies, the clustering of the MNPs produces LC re-orientation at atypical low external field, and this re-arrangement produces compaction of the clusters, resulting in the detection of increased QD emission. These results demonstrate a synergistic, reversible, and an all-optical process to detect magnetic fields and additionally, as the clusters are self-assembled in a fluid medium, they offer the possibility for these sensors to be used in broad ranging fluid-based applications.

Tuning quantum-dot organization in liquid crystals for robust photonic applications.

Mesogenic ligands have the potential to provide control over the dispersion and stabilization of nanoparticles in liquid crystal (LC) phases. The creation of such hybrid materials is an important goal for the creation of soft tunable photonic devices, such as the LC laser. Herein, we present a comparison of isotropic and mesogenic ligands attached to the surface of CdSe (core-only) and CdSe/ZnS (core/shell) quantum dots (QDs). The mesogenic ligand's flexible arm structure enhances ligand alignment, with the local LC director promoting QD dispersion in the isotropic and nematic phases. To characterize QD dispersion on different length scales, we apply fluorescence microscopy, X-ray scattering, and scanning confocal photoluminescent imaging. These combined techniques demonstrate that the LC-modified QDs do not aggregate into the dense clusters observed for dots with simple isotropic ligands when dispersed in liquid crystal, but loosely associate in a fluid-like droplet with an average interparticle spacing >10 nm. Embedding the QDs in a cholesteric cavity, we observe comparable coupling effects to those reported for more closely packed isotropic ligands.

Fiber-optic trap-on-a-chip platform for probing low refractive index contrast biomaterials.

Dual-beam fiber trapping is a versatile technique for manipulating microparticles. We fabricate and evaluate the performance of a compact trap-on-a-chip design and demonstrate, for what we believe is the first time, trapping of low-contrast (m<1.005) lipid vesicles in solution. Counterpropagating fibers are fixed along the chip channel, and we calibrate the trap by optically displacing polystyrene microspheres from the trap center. Measured scattering forces are ~30-49 pN from each beam. Stable trapping and reversible deformation of lipid vesicles is demonstrated under femtonewton trapping forces. This chip has applications in probing a variety of soft biomaterials, such as biological cells, lipid membranes, and protein assemblies.

Forming, Confining, and Observing Microtubule-Based Active Nematics.

The formation of biopolymer-based active phases has become an important technique for researchers interested in exploring the emerging field of active liquid crystals and their possible roles in cell biology. These novel systems consist of self-driven sub-units that consume energy locally, producing an out-of-equilibrium dynamic fluid. To form the active liquid crystal phase described in this report, purified protein components including biopolymers and molecular motors are combined, and the active nematic phase spontaneously forms in the presence of adenosine triphosphate (ATP). To observe the nematic state, the material must be confined in a suitable geometry for microscopy at a high enough density. This article describes two different methods for the formation of an active nematic phase using microtubules and kinesin motors: assembly of a two-dimensional active layer at an oil and water interface and assembly under an oil layer using an elastomeric well. Techniques to insert the active material into small wells of different shapes are also described.

Colloidal structure and proton conductivity of the gel within the electrosensory organs of cartilaginous fishes.

Cartilaginous fishes possess gel-filled tubular sensory organs called Ampullae of Lorenzini (AoL) that are used to detect electric fields. Although recent studies have identified various components of AoL gel, it has remained unclear how the molecules are structurally arranged and how their structure influences the function of the organs. Here we describe the structure of AoL gel by microscopy and small-angle X-ray scattering and infer that the material is colloidal in nature. To assess the relative function of the gel's protein constituents, we compared the microscopic structure, X-ray scattering, and proton conductivity properties of the gel before and after enzymatic digestion with a protease. We discovered that while proteins were largely responsible for conferring the viscous nature of the gel, their removal did not diminish proton conductivity. The findings lay the groundwork for more detailed studies into the specific interactions of molecules inside AoL gel at the nanoscale.

Directional, Low-Energy Driven Thermal Actuating Bilayer Enabled by Coordinated Submolecular Switching.

The authors reveal a thermal actuating bilayer that undergoes reversible deformation in response to low-energy thermal stimuli, for example, a few degrees of temperature increase. It is made of an aligned carbon nanotube (CNT) sheet covalently connected to a polymer layer in which dibenzocycloocta-1,5-diene (DBCOD) actuating units are oriented parallel to CNTs. Upon exposure to low-energy thermal stimulation, coordinated submolecular-level conformational changes of DBCODs result in macroscopic thermal contraction. This unique thermal contraction offers distinct advantages. It's inherently fast, repeatable, low-energy driven, and medium independent. The covalent interface and reversible nature of the conformational change bestow this bilayer with excellent repeatability, up to at least 70 000 cycles. Unlike conventional CNT bilayer systems, this system can achieve high precision actuation readily and can be scaled down to nanoscale. A new platform made of poly(vinylidene fluoride) (PVDF) in tandem with the bilayer can harvest low-grade thermal energy and convert it into electricity. The platform produces 86 times greater energy than PVDF alone upon exposure to 6 °C thermal fluctuations above room temperature. This platform provides a pathway to low-grade thermal energy harvesting. It also enables low-energy driven thermal artificial robotics, ultrasensitive thermal sensors, and remote controlled near infrared (NIR) driven actuators.

Evidence of chitin in the ampullae of Lorenzini of chondrichthyan fishes.

We previously reported that the polysaccharide chitin, a key component of arthropod exoskeletons and fungal cell walls, is endogenously produced by fishes and amphibians in spite of the widely held view that it was not synthesized by vertebrates [1]. Genes encoding chitin synthase enzymes were found in the genomes of a number of fishes and amphibians and shown to be correspondingly expressed at the sites where chitin was localized [1,2]. In this report, we present evidence suggesting that chitin is prevalent within the specialized electrosensory organs of cartilaginous fishes (Chondrichthyes). These organs, the Ampullae of Lorenzini (AoL), are widely distributed and comprise a series of gel-filled canals emanating from pores in the skin (Figure 1A). The canals extend into bulbous structures called alveoli that contain sensory cells capable of detecting subtle changes in electric fields (Figure 1B) [3,4]. The findings described here extend the number of vertebrate taxa where endogenous chitin production has been detected and raise questions regarding chitin's potential function in chondrichthyan fishes and other aquatic vertebrates.

Solution synchrotron x-ray diffraction reveals structural details of lipid domains in ternary mixtures.

The influence of cholesterol on lipid bilayer structure is significant and the effect of cholesterol on lipid sorting and phase separation in lipid-raft-forming model membrane systems has been well investigated by microscopy methods on giant vesicles. An important consideration however is the influence of fluorescence illumination on the phase state of these lipids and this effect must be carefully minimized. In this paper, we show that synchrotron x-ray scattering on solution lipid mixtures is an effective alternative technique for the identification and characterization of the l_{o} (liquid ordered) and l_{d} (liquid disordered) phases. The high intensity of synchrotron x rays allows the observation of up to 5 orders of diffraction from the l_{o} phase, whereas only two are clearly visible when the l_{d} phase alone is present. This data can be collected in approximately 1 min/sample , allowing rapid generation of phase data. In this paper, we measure the lamellar spacing in both the liquid-ordered and liquid-disordered phases simultaneously, as a function of cholesterol concentration in two different ternary mixtures. We also observe evidence of a third gel-phaselike population at 10-12 mol % cholesterol and determine the thickness of the bilayer for this phase. Importantly we are able to look at phase coexistence in the membrane independent of photoeffects.

Directed assembly of magnetic and semiconducting nanoparticles with tunable and synergistic functionality.

The ability to fabricate new materials using nanomaterials as building blocks, and with meta functionalities, is one of the most intriguing possibilities in the area of materials design and synthesis. Semiconducting quantum dots (QDs) and magnetic nanoparticles (MNPs) are co-dispersed in a liquid crystalline (LC) matrix and directed to form self-similar assemblies by leveraging the host's thermotropic phase transition. These co-assemblies, comprising 6 nm CdSe/ZnS QDs and 5-20 nm Fe3O4 MNPs, bridge nano- to micron length scales, and can be modulated in situ by applied magnetic fields <250 mT, resulting in an enhancement of QD photoluminescence (PL). This effect is reversible in co-assemblies with 5 and 10 nm MNPs but demonstrates hysteresis in those with 20 nm MNPs. Transmission electron microscopy (TEM) and energy dispersive spectroscopy reveal that at the nanoscale, while the QDs are densely packed into the center of the co-assemblies, the MNPs are relatively uniformly dispersed through the cluster volume. Using Lorentz TEM, it is observed that MNPs suspended in LC rotate to align with the applied field, which is attributed to be the cause of the observed PL increase at the micro-scale. This study highlights the critical role of correlating multiscale spectroscopy and microscopy characterization in order to clarify how interactions at the nanoscale manifest in microscale functionality.

Membrane mediated motor kinetics in microtubule gliding assays.

Motor-based transport mechanisms are critical for a wide range of eukaryotic cell functions, including the transport of vesicle cargos over long distances. Our understanding of the factors that control and regulate motors when bound to a lipid substrate is however incomplete. We used microtubule gliding assays on a lipid bilayer substrate to investigate the role of membrane diffusion in kinesin-1 on/off binding kinetics and thereby transport velocity. Fluorescence imaging experiments demonstrate motor clustering on single microtubules due to membrane diffusion in the absence of ATP, followed by rapid ATP-induced dissociation during gliding. Our experimental data combined with analytical modeling show that the on/off binding kinetics of the motors are impacted by diffusion and, as a consequence, both the effective binding and unbinding rates for motors are much lower than the expected bare rates. Our results suggest that motor diffusion in the membrane can play a significant role in transport by impacting motor kinetics and can therefore function as a regulator of intracellular transport dynamics.

Nanoparticle-based hollow microstructures formed by two-stage nematic nucleation and phase separation.

Rapid bulk assembly of nanoparticles into microstructures is challenging, but highly desirable for applications in controlled release, catalysis, and sensing. We report a method to form hollow microstructures via a two-stage nematic nucleation process, generating size-tunable closed-cell foams, spherical shells, and tubular networks composed of closely packed nanoparticles. Mesogen-modified nanoparticles are dispersed in liquid crystal above the nematic-isotropic transition temperature (TNI). On cooling through TNI, nanoparticles first segregate into shrinking isotropic domains where they locally depress the transition temperature. On further cooling, nematic domains nucleate inside the nanoparticle-rich isotropic domains, driving formation of hollow nanoparticle assemblies. Structural differentiation is controlled by nanoparticle density and cooling rate. Cahn-Hilliard simulations of phase separation in liquid crystal demonstrate qualitatively that partitioning of nanoparticles into isolated domains is strongly affected by cooling rate, supporting experimental observations that cooling rate controls aggregate size. Microscopy suggests the number and size of internal voids is controlled by second-stage nucleation.