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.

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.

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.

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.

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 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.

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.

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.

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.

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.

Free-energy model for nanoparticle self-assembly by liquid crystal sorting.

We modeled the experimentally observed self-assembly of nanoparticles (NPs) into shells with diameters up to 10 µm, via segregation from growing nematic domains. Using field-based Monte Carlo simulations, we found the equilibrium configurations of the system by minimizing a free-energy functional that includes effects of excluded-volume interactions among NPs, orientational elasticity, and the isotropic-nematic phase-transition energy. We developed a Gaussian-profile approximation for the liquid crystal (LC) order-parameter field that provides accurate analytical values for the free energy of LC droplets and the associated microshells. This analytical model reveals a first-order transition between equilibrium states with and without microshells, governed mainly by the competition of excluded-volume and phase-transition energies. By contrast, the LC elasticity effects are much smaller and mostly confined to setting the size of the activation barrier for the transition. In conclusion, field-based thermodynamic methods provide a theoretical framework for the self-assembly of NP shells in liquid crystal hosts and suggest that field-based kinetic methods could be useful to simulate and model the time evolution of NP self-assembly coupled to phase separation.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh.

A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.

Phase Transition-Driven Nanoparticle Assembly in Liquid Crystal Droplets.

When nanoparticle self-assembly takes place in an anisotropic liquid crystal environment, fascinating new effects can arise. The presence of elastic anisotropy and topological defects can direct spatial organization. An important goal in nanoscience is to direct the assembly of nanoparticles over large length scales to produce macroscopic composite materials; however, limitations on spatial ordering exist due to the inherent disorder of fluid-based methods. In this paper we demonstrate the formation of quantum dot clusters and spherical capsules suspended within spherical liquid crystal droplets as a method to position nanoparticle clusters at defined locations. Our experiments demonstrate that particle sorting at the isotropic-nematic phase front can dominate over topological defect-based assembly. Notably, we find that assembly at the nematic phase front can force nanoparticle clustering at energetically unfavorable locations in the droplets to form stable hollow capsules and fractal clusters at the droplet centers.

Plasmon-actuated nano-assembled microshells.

We present three-dimensional microshells formed by self-assembly of densely-packed 5 nm gold nanoparticles (AuNPs). Surface functionalization of the AuNPs with custom-designed mesogenic molecules drives the formation of a stable and rigid shell wall, and these unique structures allow encapsulation of cargo that can be contained, virtually leakage-free, over several months. Further, by leveraging the plasmonic response of AuNPs, we can rupture the microshells using optical excitation with ultralow power (<2 mW), controllably and rapidly releasing the encapsulated contents in less than 5 s. The optimal AuNP packing in the wall, moderated by the custom ligands and verified using small angle x-ray spectroscopy, allows us to calculate the heat released in this process, and to simulate the temperature increase originating from the photothermal heating, with great accuracy. Atypically, we find the local heating does not cause a rise of more than 50 °C, which addresses a major shortcoming in plasmon actuated cargo delivery systems. This combination of spectral selectivity, low power requirements, low heat production, and fast release times, along with the versatility in terms of identity of the enclosed cargo, makes these hierarchical microshells suitable for wide-ranging applications, including biological ones.

Effects of Low Concentrations of Docosahexaenoic Acid on the Structure and Phase Behavior of Model Lipid Membranes.

In this paper we report an X-ray diffraction study on the phase behavior of binary lipid mixtures of 1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphoethanolamine (DHA-PE) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) at low concentrations below 5.0 mol% DHA-PE. Our results show that DHA-PE induces phase separation into a DHA rich liquid crystalline (Lα) phase and a DHA poor gel (Lß') phase at overall DHA-PE concentrations as low as 0.1 mol%. In addition, we find that the structure of the Lß' phase, from which the DHA-PE molecules are largely excluded, is modified in the phase-separated state at low DHA-PE concentrations, with a decrease in bilayer thickness of 1.34 nm for 0.1 mol% at room temperature, compared to pure DPPC bilayers. This result is contrary to that seen in similar studies on mono-unsaturated lipids where an increase in bilayer thickness is observed. The surprising effect of such low DHA-PE concentrations on membrane structure may be important in understanding the role of highly polyunsaturated lipids in biological membrane-based structures and similar artificial surfactant systems.

Stability and instability for low refractive-index-contrast particle trapping in a dual-beam optical trap.

A dual-beam optical trap is used to trap and manipulate dielectric particles. When the refractive index of these particles is comparable to that of the surrounding medium, equilibrium trapping locations within the system shift from stable to unstable depending on fiber separation and particle size. This is due to to the relationship between gradient and scattering forces. We experimentally and computationally study the transitions between stable and unstable trapping of poly(methyl methacrylate) beads for a range of parameters relevant to experimental setups involving giant unilamellar vesicles. We present stability maps for various fiber separations and particle sizes, and find that careful attention to particle size and configuration is necessary to obtain reproducible quantitative results for soft matter stretching experiments.

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.