We compare the phase behavior of a mutant filamentous virus, fd Y21M, to that of a conventional fd wild-type (wt). We find significantly different macroscopic phase behavior despite the only microscopic difference between the two viruses being in a single amino acid of the major coat protein pVIII. Compared to fd wt, the location of the isotropic-cholesteric phase transition for fd Y21M shifts to lower densities. This is attributable to a significant difference in the flexibility of the two viruses. The persistence length of fd wt is 2.8 AE 0.7 mm, whereas the persistence length of fd Y21M is 9.9 AE 1.6 mm. The large persistence length of fd Y21M makes it an essentially rigid rod, thus allowing for the first time a quantitative test of the Onsager theory for the isotropic-nematic phase transition. Even more striking, is the difference in the chiral phase behavior of the two viruses. Both viruses form cholesteric phases, with the fd wt forming a left-handed cholesteric helix, and the fd Y21M forming a right-handed one. At a given density, the magnitude of the cholesteric pitch between the two systems is different by fivefold. Using mixtures of the two viruses, we create a liquid crystalline system with a tunable control over its macroscopic chirality.

Point-like motile topological defects control the universal dynamics of diverse twodimensional active nematics ranging from shaken granular rods to cellular monolayers. A comparable understanding in higher dimensions has yet to emerge. We report the creation of three-dimensional active nematics by dispersing extensile microtubule bundles in a passive colloidal liquid crystal. Light-sheet microscopy reveals the millimeter-scale structure of active nematics with a single bundle resolution and the temporal evolution of the associated nematic director field. The dominant excitations of three-dimensional active nematics are extended charge-neutral disclination loops that undergo complex dynamics and recombination events. These studies introduce a distinct class of non-equilibrium systems whose turbulent-like dynamics arises from the interplay between internally generated active stresses, the chaotic flows and the topological structure of the constituent defects.

SU-8 pillar-assisted epitaxial assembly of toric focal conic domains (TFCDs) arrays of smectic-A liquid crystals is studied. The 3D nature of the pillar array is crucial to confine and direct the formation of TFCDs on the top of each pillar and between neighboring pillars, leading to highly ordered square and hexagonal array TFCDs. Excellent agreement between the experimentally obtained critical pillar diameter and elasticity calculation is found.

The liquid crystalline phases of matter each possess distinct types of defects that have drawn great interest in areas such as topology, self-assembly and material micropatterning. However, relatively little is known about how defects in one liquid crystalline phase arise from defects or deformations in another phase upon crossing a phase transition. Here, we directly examine defects in the in situ thermal phase transition from nematic to smectic A in hybrid-aligned liquid crystal droplets on water substrates, using experimental, theoretical and numerical analyses. The hybrid-aligned nematic droplet spontaneously generates boojum defects. During cooling, toric focal conic domains arise through a sequence of morphological transformations involving nematic stripes and locally aligned focal conic domains. This simple experiment reveals a surprisingly complex pathway by which very different types of defects may be related across the nematic–smectic A phase transition, and presents new possibilities for controlled deformation and patterning of liquid crystals.

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.lassically, the bulk of a material system is where the action is, and the interface is often relegated to a set of "boundary conditions." However, crystal faceting (1), the quantum hall effect (2), and even the anti-de Sitter space-conformal field theory (AdS-CFT) correspondence (3) fundamentally reverse this relationship: The bulk properties can be read off from their effects on the boundaries. In this contribution, we demonstrate migration and organization of colloids constrained to a liquid crystal (LC)-air interface, driven remotely by the elastic distortion created by the presence of topological defects in the liquid crystalline bulk. Just as phantoms are used in MRI (4), it is necessary for us to prepare bulk defects in known configurations to verify our bulk/ boundary connection. To do this, we prepare a substrate patterned with microposts that, with appropriate surface treatment, seed a reproducible defect complexion. Colloidal spheres on the interface experience an attraction to the regions above the submerged defects, as well as an elastic repulsion from each other, leading to complex new assemblies. The long range of these elastic interactions allows defects in the bulk nematic phase far below the interface to direct assembly at the interface. Other recent work on producing ordered arrangements of particles at LC interfaces beyond simple triangular lattices, such as chains (5), stripes (6), and dense quasihexagonal lattices (7), has focused on confining the nematic in thin film or droplet geometries and on varying the surface coverage fraction. Our sensitive control over substrate topography provid...

Focal conic domains (FCDs) in smectic-A liquid crystals have drawn much attention both for their exquisitely structured internal form and for their ability to direct the assembly of micro- and nanomaterials in a variety of patterns. A key to directing FCD assembly is control over the eccentricity of the domain. Here, we demonstrate a new paradigm for creating spatially varying FCD eccentricity by confining a hybrid-aligned smectic with curved interfaces. In particular, we manipulate interface behavior with colloidal particles in order to experimentally produce two examples of what has recently been dubbed the flower texture, where the focal hyperbolae diverge radially outward from the center of the texture, rather than inward as in the canonical eventail or fan texture. We explain how this unconventional assembly can arise from appropriately curved interfaces. Finally, we present a model for this system that applies the law of corresponding cones, showing how FCDs may be embedded smoothly within a "background texture" of large FCDs and concentric spherical layers, in a manner consistent with the qualitative features of the smectic flower. Such understanding could potentially lead to disruptive liquid crystal technologies beyond displays, including patterning, smart surfaces, microlens arrays, sensors and nanomanufacturing

Controlling topological defects in 3D liquid crystal phases is a crucial element in the development of novel devices, from bluephase 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.iquid crystals (LCs) are anisotropic materials with physical properties that depend sensitively on both global and local molecular alignment. In LCs, average local molecular orientations assume geometries that can be controlled by boundary conditions (1, 2) and external fields (3, 4), and the resulting mechanical and electric anisotropies of LCs provide powerful tools in controlling the propagation of light and the assembly of soft materials (5-10). A quintessential example is the blue-phase LC organized around a 3D disclination network (11, 12); as a display component, it offers rapid response time without surface alignment (13). The ability to tailor LCs with complex, topologically structured geometries will be necessary for the next generation of display technologies and beyond.Under appropriate boundary conditions, the smectic-A (SmA) LC phase develops a regular array of micrometer-scale defect structures known as focal conic domains (FCDs), which have gone from mere geometric curiosities to the focus of much attention in recent years as an enabling technological tool (14-17). The smectic layers in each FCD form concentric sections of Dupin cyclides, generalizations of tori, with two linear focal sets (centers of curvature), an ellipse and a confocal hyperbola (18). Whereas FCDs arise as the prototypical, kinetically trapped texture in bulk, a 2D lattice of axially symmetric toric FCDs (TFCDs) can be robustly produced in thin smectic films with antagonistic boundary conditions at the substrate and air interfaces. These TFCD arrays have been used to fabricate functional surfaces (19,20), to direct the self-assembly of soft micro...

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.