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Spontaneous emergence of chirality is a pervasive theme in soft matter. We report a transient twist forming in achiral nematic liquid crystals confined to a capillary tube with square cross section. At the smectic-nematic phase transition, intertwined disclination line pairs are observed with both helical and kinked lozenge-like contours, configurations that we promote through capillary cross-section geometry and stabilize using fluorescent amphiphilic molecules. The observed texture is similar to that found in "exotic" materials such as chromonics, but it is here observed in common thermotropic nematics upon heating from the smectic into the nematic phase. Numerical modeling further reveals that the disclinations may possess winding characters that are intermediate between wedge and twist, and that vary along the defect contours. In our experiments, we utilize a phase transition to generate otherwise elusive defect structures in common liquid crystal materials.

Significance Active nematics are ordered liquid crystalline fluids that exhibit spontaneous persistent flows and collective dynamics. The development of motile biopolymer systems inspired by nature has recently attracted considerable attention to out-of-equilibrium soft materials. We report the formation of an active nematic in which microtubules are propelled by kinesin motors coupled to a lipid membrane substrate. The system exhibits apolar order in a globally aligned nematic phase and locally ordered dynamic lanes. Use of a fluid substrate represents a significant advance for active matter as it allows for spatial re-organization of motors, which generate force, in response to the dynamics of the aligning microtubules. This self-organized feedback mechanism may have implications in vivo and for engineering efficient dynamic and reconfigurable materials., 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.

We study avenues to shape multistability and shape morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium presenting a wide variety of tubular crystal deformation geometries, due to an interplay of effective defect interactions with out-of-tangent-plane deformations that reorient the tube axis. Importantly, this interplay often stabilizes defect configurations quite distinct from those predicted for a two-dimensional crystal confined to the surface of a rigid cylinder. We find that relative and absolute stability of competing states depend strongly on control parameters such as bending rigidity, applied stress, and spontaneous curvature. Using stable dislocation pair arrangements as building blocks, we demonstrate that targeted macroscopic three-dimensional conformations of thin crystalline tubes can be programmed by imposing certain sparse patterns of defects. Our findings reveal a broad design space for controllable and reconfigurable colloidal tube geometries, with potential relevance also to architected carbon nanotubes and microtubules.

Nematic liquid crystals (NLCs) offer remarkable opportunities to direct colloids to form complex structures. The elastic energy field that dictates colloid interactions is determined by the NLC director field, which is sensitive to and can be controlled by boundaries including vessel walls and colloid surfaces. By molding the director field via liquid-crystal alignment on these surfaces, elastic energy landscapes can be defined to drive structure formation. We focus on colloids in otherwise defect-free director fields formed near undulating walls. Colloids can be driven along prescribed paths and directed to well-defined docking sites on such wavy boundaries. Colloids that impose strong alignment generate topologically required companion defects. Configurations for homeotropic colloids include a dipolar structure formed by the colloid and its companion hedgehog defect or a quadrupolar structure formed by the colloid and its companion Saturn ring. Adjacent to wavy walls with wavelengths larger than the colloid diameter, spherical particles are attracted to locations along the wall with distortions in the nematic director field that complement those from the colloid. This is the basis of lock-and-key interactions. Here, we study ellipsoidal colloids with homeotropic anchoring near complex undulating walls. The walls impose distortions that decay with distance from the wall to a uniform director in the far field. Ellipsoids form dipolar defect configurations with the colloid's major axis aligned with the far field director. Two distinct quadrupolar defect structures also form, stabilized by confinement; these include the Saturn I configuration with the ellipsoid's major axis aligned with the far field director and the Saturn II configuration with the major axis perpendicular to the far field director. The ellipsoid orientation varies only weakly in bulk and near undulating walls. All configurations are attracted to walls with long, shallow waves. However, for walls with wavelengths that are small compared to the colloid length, Saturn II is repelled, allowing selective docking of aligned objects. Deep, narrow wells prompt the insertion of a vertical ellipsoid. By introducing an opening at the bottom of such a deep well, we study colloids within pores that connect two domains. Ellipsoids with different aspect ratios find different equilibrium positions. An ellipsoid of the right dimension and aspect ratio can plug the pore, creating a class of 2D selective membranes.

By confining soft materials within tailored boundaries it is possible to design energy landscapes to address and control colloidal dynamics. This provides unique opportunities to create reconfigurable, hierarchically organized structures, a leading challenge in materials science. Example soft matter systems include liquid crystals. For instance, when nematic liquid crystals (NLCs) are confined in a vessel with undulated boundaries, bend and splay distortions can be used to position particles. Here we confine this system in a twist cell. We also study cholesteric liquid crystals, which have an "intrinsic" twist distortion which adds to the ones imposed by the solid boundaries. The cholesteric pitch competes with the other length scales in the system (colloid radius, vessel thickness, wavelength of boundary undulations), enriching the possible configurations. Depending on the pitch-to-radius and pitch-to-thickness ratios the interaction can be attractive or repulsive. By tuning the pitch (i.e. changing the concentration of the chiral dopant), it is possible to selectively promote or inhibit particle trapping at the docking sites.

We study transformations of self-organized defect arrays at the nematic-smectic A liquid crystal phase transition, and show that these defect configurations are correlated, or "remembered", across the phase transition. A thin film of thermotropic liquid crystal is subjected to hybrid anchoring by an air interface and a water substrate, and viewed under polarized optical microscopy. Upon heating from smectic-A to nematic, a packing of focal conic domains melts into a dense array of boojums---nematic surface defects---which then coarsens by pair-annihilation. With the aid of Landau-de Gennes numerical modeling, we elucidate the topological and geometrical rules underlying this transformation. In the transition from nematic to smectic-A, we show that focal conic domain packings are organized over large scales in patterns that retain a geometric memory of the nematic boojum configuration, which can be recovered with remarkable fidelity., Comment: 25 pages, 6 figures

The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. In addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump's centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface. Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations., Comment: This preprint has also been posted to http://www.biorxiv.org with doi: 10.1101/406280. Seven pages with 5 figures, plus an appendix containing 3 pages with 1 figure

Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetting conditions of particles at the smectic film, are reported. This work paves the way to exploiting LC interfaces as a means to direct spontaneously formed, reconfigurable, and optically active materials., 8 pages, 6 figures. Supplementary Materials: 3 pages, 3 figures

© 2019 Elsevier Ltd When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic spatial wandering of both genetic lineages and the boundaries between genetically segregated sectors. Laboratory experiments on microbial range expansions have shown that this stochastic wandering, transverse to the front, is superdiffusive due to the front's growing roughness, implying much faster loss of genetic diversity than predicted by simple flat front diffusive models. We study the evolutionary consequences of this superdiffusive wandering using two complementary numerical models of range expansions: the stepping stone model, and a new interpretation of the model of directed paths in random media, in the context of a roughening population front. Through these approaches we compute statistics for the times since common ancestry for pairs of individuals with a given spatial separation at the front, and we explore how environmental heterogeneities can locally suppress these superdiffusive fluctuations.

Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical phyllotaxis, describing the spiral packings on cylinders commonly found in nature, have found application in all these systems. Several recent studies have examined defects in tubular crystals associated with crystalline packings that must accommodate a fixed tube radius. Here, we study the mechanics of tubular crystals with variable tube radius, with dislocations interposed between regions of different phyllotactic packings. Unbinding and separation of dislocation pairs with equal and opposite Burgers vectors allow the growth of one phyllotactic domain at the expense of another. In particular, glide separation of dislocations offers a low-energy mode for plastic deformations of solid tubes in response to external stresses, reconfiguring the lattice step by step. Through theory and simulation, we examine how the tube's radius and helicity affects, and is in turn altered by, the mechanics of dislocation glide. We also discuss how a sufficiently strong bending rigidity can alter or arrest the deformations of tubes with small radii., 17 pages, 11 figures

Controlling the molecular alignment of liquid crystal monomers (LCMs) within nano- and microstructures is essential in manipulating the actuation behavior of nematic liquid crystal elastomers (NLCEs). Here, we study how to induce uniformly vertical alignment of nematic LCMs within a micropillar array to maximize the macroscopic shape change using surface chemistry. Landau-de Gennes numerical modeling suggests that it is difficult to perfectly align LCMs vertically in every pore within a poly(dimethylsiloxane) (PDMS) mold with porous channels during soft lithography. In an untreated PDMS mold that provides homeotropic anchoring of LCMs, a radially escaped configuration of LCMs is observed. Vertically aligned LCMs, a preferred configuration for actuation, are only observed when using a PDMS mold with planar anchoring. Guided by the numerical modeling, we coat the PDMS mold with a thin layer of poly(2-hydroxyethyl methacrylate) (PHEMA), leading to planar anchoring of LCM. Confirmed by polarized optical microscopy, we observe monodomains of vertically aligned LCMs within the mold, in agreement with modeling. After curing and peeling off the mold, the resulting NLCE micropillars showed a relatively large and reversible radial strain (∼30%) when heated above the nematic to isotropic transition temperature.

The assembly of colloids in nematic liquid crystals via topological defects has been extensively studied for spherical particles, and investigations of other colloid shapes have revealed a wide array of new assembly behaviors. We show, using Landau-de Gennes numerical modeling, that nematic defect configurations and colloidal assembly can be strongly influenced by fine details of colloid shape, in particular the presence of sharp edges. For cylinder, microbullet, and cube colloid geometries, we obtain the particles' equilibrium alignment directions and effective pair interaction potentials as a function of simple shape parameters. We find that defects pin at sharp edges, and that the colloid consequently orients at an oblique angle relative to the far-field nematic director that depends on the colloid's shape. This shape-dependent alignment, which we confirm in experimental measurements, raises the possibility of selecting self-assembly outcomes for colloids in liquid crystals by tuning particle geometry., Comment: 10 pages, 3 figures

We explore micropatterned director structures of aqueous lyotropic chromonic liquid crystal (LCLC) films created on square-lattice cylindrical-micropost substrates. The structures are manipulated by modulating the LCLC mesophases and their elastic properties via concentration through drying. Nematic LCLC films exhibit preferred bistable alignment along the diagonals of the micropost lattice. Columnar LCLC films, dried from nematics, form two distinct director and defect configurations: a diagonally aligned director pattern with local squares of defects, and an off-diagonal configuration with zig-zag defects. The formation of these states appears to be tied to the relative splay and bend free energy costs of the initial nematic films. The observed nematic and columnar configurations are understood numerically using a Landau-de Gennes free energy model. Among other attributes, the work provide first examples of quasi-2D micropatterning of LC films in the columnar phase and lyotropic LC films in general, and it demonstrates alignment and configuration switching of typically difficult-to-align LCLC films via bulk elastic properties.

We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals (LCs) to assemble colloidal particles trapped at the LC interface into reconfigurable structures with complex symmetries and packings. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic LC 4-cyano-4′-pentylbiphenyl create quadrupolar distortions in the director field causing particles to repel and consequently form close-packed assemblies with a triangular habit. Here, we report on complex open structures organized via interactions with defects in the bulk. Specifically, by confining the nematic LC in an array of microposts with homeotropic anchoring conditions, we cause defect rings to form at well-defined locations in the bulk of the sample. These defects source elastic deformations that direct the assembly of the interfacially trapped colloids into ring-like assemblies, which recapitulate the defect geometry even when the microposts are completely immersed in the nematic. When the surface density of the colloids is high, they form a ring near the defect and a hexagonal lattice far from it. Because topographically complex substrates are easily fabricated and LC defects are readily reconfigured, this work lays the foundation for a versatile, robust mechanism to direct assembly dynamically over large areas by controlling surface anchoring and associated bulk defect structure.

In this work, we show that Janus washers, genus-one colloids with hybrid anchoring conditions, form topologically required defects in nematic liquid crystals. Experiments under crossed polarizers reveal the defect structure to be a rigid disclination loop confined within the colloid, with an accompanying defect in the liquid crystal. When confined to a homeotropic cell, the resulting colloid-defect ring pair tilts relative to the far field director, in contrast to the behavior of toroidal colloids with purely homeotropic anchoring. We show that this tilting behavior can be reversibly suppressed by the introduction of a spherical colloid into the center of the toroid, creating a new kind of multi-shape colloidal assemblage., Comment: 5 pages, 4 figures, accepted for publication in Soft Matter

Controlling topological defects in 3D liquid crystal phases is a crucial element in the development of novel devices, from blue-phase displays to passive biochemical sensors. However, it remains challenging to realize the 3D topological conditions necessary to robustly and arbitrarily direct the formation of defects. Here, using a series of short pillar arrays as topological templates, we demonstrate the hierarchical assembly of focal conic domains (FCDs) in smectic-A liquid crystals that break the underlying symmetry of the pillar lattice, exhibit tunable eccentricity, and together develop a nontrivial yet organized array of defects. The key to our approach lies in the selection of the appropriate ratio of the size of focal domain to the dimension of pillars such that the system favors the “pinning” of FCD centers near pillar edges while avoiding the opposing effect of confinement. Our study unequivocally shows that the arrangement of FCDs is strongly influenced by the height and shape of the pillars, a feature that promotes both a variety of nontrivial self-assembled lattice types and the attraction of FCD centers to pillar edges, especially at regions of high curvature. Finally, we propose a geometric model to reconstruct the smectic layer structure in the gaps between neighboring FCDs to estimate the energetic effects of nonzero eccentricity and assess their thermodynamic stability.

Microbullet particles, cylinders with one blunt and one spherical end, offer a novel platform to study the effects of anisotropy and curvature on colloidal assembly in complex fluids. Here, we disperse microbullets in 4-cyano-4'-pentylbiphenyl (5CB) nematic liquid crystal (NLC) cells and form oriented elastic dipoles with a nematic point defect located near the curved end. This feature allows us to study particle interactions as a function of dipole alignment. By careful control of the surface anchoring at the particle surface and the confining boundaries, we study the interactions and assembly of microbullets under various conditions. When microbullets with homeotropic surface anchoring are dispersed in a planar cell, parallel dipoles form linear chains parallel to the director, similar to the observations of spherical particles in a planar cell, while antiparallel dipoles orient side-to-side. In a homeotropic cell, however, particles rotate to orient their long axis parallel to the director. When so aligned, parallel dipoles repel and form 2D ordered assemblies with hexagonal symmetry that ripen over time owing to attraction between antiparallel neighbors. Further, we show that the anchoring conditions inside the cell can be altered by application of an electrical field, allowing us to flip microbullets to orient parallel to the director, an effect driven by an elastic torque. Finally, we detail the mechanisms that control the formation of 1D chains and hexagonal lattices with respect to the elasticity of the NLC., 12 pages, 8 figures, the full catastrophe, version to be published

Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are grown on real surfaces; eventually, surface imperfections are on the same scale as the lattice constant. Here, we gain insights into this general problem by studying two-dimensional smectic order on substrates with highly localized intrinsic curvature, constructed from cones and their intersections with planes. In doing so we take advantage of fully tractable "paper and tape" constructions, allowing us to understand, in detail, the induced cusps and singularities., Comment: 7 pages, figures included

We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool, we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot, in general, be translated from one phase to the other.