Spontaneous helielectric nematic liquid crystals: Electric analog to helimagnets

Recently, a type of ferroelectric nematic fluid has been discovered in liquid crystals in which the molecular polar nature at molecule level is amplified to macroscopic scales through a ferroelectric packing of rod-shaped molecules. Here, we report on the experimental proof of a polar chiral liquid matter state, dubbed helielectric nematic, stabilized by the local polar ordering coupled to the chiral helicity. This helielectric structure carries the polar vector rotating helically, analogous to the magnetic counterpart of helimagnet. The helielectric state can be retained down to room temperature and demonstrates gigantic dielectric and nonlinear optical responses. This matter state opens a new chapter for developing the diverse polar liquid crystal devices.

In nature , a new matter state usually arises as a result of unexpected combinations of hierarchical orderings. Helicity is one of the most essential nature of matter states for organizing superstructures in soft matters, spanning many length scales from the atomic to the macroscopic biological levels. When constructed from building blocks with inherent polarity, three hierarchical orderings could coexist in a helical structure: 1) the head-to-tail or polar symmetry of each building block (e.g., Fig. 1C), 2) the orientational order of a swarm of building blocks (Fig. 1A), and 3) the emergent helicity (Fig. 1B). While a simultaneous realization of these three orderings could lead to extraordinary material properties, such highly hierarchical structures are often challenging to achieve in man-made systems. Probably the most familiar example is the chiral magnet or helimagnet (Fig. 1B) in quantum systems, where the magnetic spins form two- or three-dimensional spiral structures (1, 2). The polar magnetic helical structures are considered mainly to originate from either the breaking of the space-inversion symmetry in crystal structures (3) or the magnetic frustration (1, 4, 5). Their strong magnetism-chirality coupling triggers enormous interests in condensed matter physics, leading to many unique quantum and information functionalities (6–9). From the mirror relationship between the magnetism and electricity, we anticipate the incidence of a possible electric version of the helimagnets, namely helielectrics. However, the diverse magnetic topological states rarely show up in electric systems, except a few recent breakthroughs (e.g., the observation of the electric skyrmions, polar vortices, and merons in metal-organic crystals) (10–12). The special electric states at nanoscale exhibit extraordinary properties such as local negative dielectric permittivity (13) and strain-polarization coupling (14, 15). Nevertheless, nearly all the aforementioned chiral magnet or electric-analog systems are based on elaborately fabricated inorganics. It is expected that the revolutionary realization of these topologies in a soft matter system would bring the advantages of flexibility, simple preparation, large-area film formation, and ease of integration into electric devices.Open in a separate windowFig. 1.Topological analogy: electric versus magnetic states. (A) Uniform magnetization or polarization. (B) Helimagnet or helielectric states. Possible helicoidal (top) and heliconical (bottom) textures are shown. (C) Molecular structure of the polar anisotropic entity, RM734. The molecular polar dipole is nearly parallel to the long molecular axis. (D) The ferroelectric nematic state with spontaneous polarization. (E) HN* state with heli realized by adding chiral generators into the polar chiral nematic state. One-dimensional polarization fields are also depicted in D and E for clarity. (F) The molecular structures of the chiral generators S1 and S2. (G) The state diagram of the two HN* materials by mixing RM734 with S1 or S2.Among the soft matter systems, liquid analogs of ferromagnet and helimagnet have been reported in liquid crystal (LC) colloids recently (16–20). For the electric versions, there already exist a category of materials possessing all the aforementioned three hierarchical orderings (i.e., the ferroelectric smectic LCs) (21–26). The smectic C* (SmC*) has layered heliconical structure with its local polarity aligning perpendicular to the long molecular axis. Confinement to thin LC cells leads to the unwound ferroelectric state of SmC* with microsecond switching time, thereby being a promising candidate for LC display applications. However, the unavoidable defect generation in the devices originated from the crystal-like structure has been one of the main technical difficulties. Moreover, the SmC* has intrinsically low fluidity and polarity (spontaneous polarization P_s < 1 μC). Here, we report a discovery of a helimagnetic analog state in polar LC materials, dubbed helielectric nematic (HN*). The spontaneous polar nematic ordering is coupled to the chiral orientational helicity (Fig. 1B), taking the form with a nearly helicoidal orientational field. Thanks to its much higher fluidity than the traditional SmC* ferroelectrics, uniform structures can be easily obtained by the typical thermal annealing process. The simultaneous observation of the traditional nonlinear second-harmonic generation (SHG) and SHG interferometry microscopies, as well as the optical observations of the selective reflection from HN* state, allow us to directly visualize the helical polar field. In contrast to the traditional nanoscopic helimagnetic or helielectric inorganics, a wide tunability of the periodic distance ranging from micrometers to near ultraviolet wavelength is achieved in the fluidic structure. Besides, the ability of switching between the polar and nonpolar helical LC states enables complementary physics study for the topology features in HN*. As gifts of the chirality–polarity interaction, the matter state uniquely expresses giant dielectric and SHG optical response, especially interesting SHG amplification when the SHG wavelength coincides with the reflection band of the HN* state.     

Living liquid crystals

Collective motion of self-propelled organisms or synthetic particles, often termed “active fluid,” has attracted enormous attention in the broad scientific community because of its fundamentally nonequilibrium nature. Energy input and interactions among the moving units and the medium lead to complex dynamics. Here, we introduce a class of active matter––living liquid crystals (LLCs)––that combines living swimming bacteria with a lyotropic liquid crystal. The physical properties of LLCs can be controlled by the amount of oxygen available to bacteria, by concentration of ingredients, or by temperature. Our studies reveal a wealth of intriguing dynamic phenomena, caused by the coupling between the activity-triggered flow and long-range orientational order of the medium. Among these are (i) nonlinear trajectories of bacterial motion guided by nonuniform director, (ii) local melting of the liquid crystal caused by the bacteria-produced shear flows, (iii) activity-triggered transition from a nonflowing uniform state into a flowing one-dimensional periodic pattern and its evolution into a turbulent array of topological defects, and (iv) birefringence-enabled visualization of microflow generated by the nanometers-thick bacterial flagella. Unlike their isotropic counterpart, the LLCs show collective dynamic effects at very low volume fraction of bacteria, on the order of 0.2%. Our work suggests an unorthodox design concept to control and manipulate the dynamic behavior of soft active matter and opens the door for potential biosensing and biomedical applications.Active matter has recently emerged as an important physical model of living systems that can be described by the methods of nonequilibrium statistical mechanics and hydrodynamics (1–3). Active matter is driven by the internal sources of energy, associated with the self-propelled particles such as bacteria or synthetic swimmers. The interaction of these active particles among themselves and with the medium produces a rich variety of dynamic effects and patterns. Most of the studies deal with active particles embedded into a Newtonian isotropic fluid. In this case the interactions among particles are caused by long-range hydrodynamic and short-range excluded volume effects (4–13). In this work, we conceive a general class of active fluids, termed living liquid crystals (LLCs). The suspending medium is a nontoxic liquid crystal (LC) that supports the activity of self-propelled particles, namely bacteria. At the very same time, the medium imposes long-range anisotropic interactions onto bacteria, thanks to the intrinsic orientational order that persists even when the bacteria are not active. The importance of this system is twofold. Firstly, the bacterial activity modifies the orientational order of the system, by producing well-defined and reproducible patterns with or without topological defects. Secondly, the orientational order of the suspending medium reveals facets of bacterial behavior, allowing one to control trajectories of individual bacteria and to visualize rotation of flagella through birefringence of the host. The LLCs represent an example of a biomechanical system, capable of controlled transduction of stored energy into a systematic movement, which is of critical importance in a variety of applications, from bioinspired micromachines to self-assembled microrobots (14,15). The study of bacterial motion in LCs and non-Newtonian fluids takes us a step closer to realizing in vitro environments that more closely resemble conditions in vivo (16,17).     

Direct mapping of local director field of nematic liquid crystals at the nanoscale

Liquid crystals (LCs), owing to their anisotropy in molecular ordering, are of wide interest in both the display industry and soft matter as a route to more sophisticated optical objects, to direct phase separation, and to facilitate colloidal assemblies. However, it remains challenging to directly probe the molecular-scale organization of nonglassy nematic LC molecules without altering the LC directors. We design and synthesize a new type of nematic liquid crystal monomer (LCM) system with strong dipole–dipole interactions, resulting in a stable nematic phase and strong homeotropic anchoring on silica surfaces. Upon photopolymerization, the director field can be faithfully “locked,” allowing for direct visualization of the LC director field and defect structures by scanning electron microscopy (SEM) in real space with 100-nm resolution. Using this technique, we study the nematic textures in more complex LC/colloidal systems and calculate the extrapolation length of the LCM.Ubiquitous as they are, it sometimes escapes our attention that liquid crystals (LCs) are the original nanomaterial. The manipulation of these nanometer-size molecules into coherent, centimeter-scale structures is now routine. Although we have become adept at deducing textures indirectly through optical microscopies (1–5), probing the molecular-scale organization requires either a glassy material or rapid cooling of samples, providing metastable states that can be directly visualized through scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM) (6–8). Although these techniques are effective to study a variety of more complex LC phases, including smectic LCs (6, 7, 9), cholesteric and blue phases (10), and biological LC polymers (11, 12), nonglassy, low molecular weight nematic LCs (NLCs) reorient during fast freezing. Polymer nematics can be quenched into metastable states but organization of static configurations through surface alignment is difficult. Flow alignment can be used but that often precludes complex, molecular scale patterning of the boundary conditions, essential for controlling and manipulating topological defects (13, 14). Although an undesired nuisance in NLC displays, topological defects mediate many of the rich interactions between colloids in NLCs (15). The defects, bearing quantized topological charge, resemble the defects in superconductors (16), soft ferromagnets (17), and even cosmic strings and monopoles (18). The fluidity of the phase and the weakly first-order nematic–isotropic phase transition allow for direct visualization of the creation/annihilation of defects via the Kibble–Zurek mechanism (19). Further, defects in a flat sheet of nematic gel or glass can be used to bend or twist local directors, inducing 3D shapes (20, 21). It is therefore critical to be able to characterize the defect structures at the nanoscale in a variety of settings. Here, we report the design and synthesis of a nematic liquid crystal monomer (LCM) system that has strong homeotropic anchoring on silica surfaces and does not reorient its director field during polymerization. Thus, the optical signatures remain unchanged in the liquid crystal polymers (LCPs), allowing for direct visualization of the defect structures by SEM in real space with 100-nm resolution. Using this technique, we study the nematic textures in more complex LC/colloidal systems and estimate the ratio between elastic and anchoring constants, i.e., the extrapolation length, of LCMs in the nematic phase.     

Mono- and bilayer smectic liquid crystal ordering in dense solutions of “gapped” DNA duplexes

Although its mesomorphic properties have been studied for many years, only recently has the molecule of life begun to reveal the true range of its rich liquid crystalline behavior. End-to-end interactions between concentrated, ultrashort DNA duplexes—driving the self-assembly of aggregates that organize into liquid crystal phases—and the incorporation of flexible single-stranded “gaps” in otherwise fully paired duplexes—producing clear evidence of an elementary lamellar (smectic-A) phase in DNA solutions—are two exciting developments that have opened avenues for discovery. Here, we report on a wider investigation of the nature and temperature dependence of smectic ordering in concentrated solutions of various “gapped” DNA (GDNA) constructs. We examine symmetric GDNA constructs consisting of two 48-base pair duplex segments bridged by a single-stranded sequence of 2 to 20 thymine bases. Two distinct smectic layer structures are observed for DNA concentration in the range ∼230to∼280 mg/mL. One exhibits an interlayer periodicity comparable with two-duplex lengths (“bilayer” structure), and the other has a period similar to a single-duplex length (“monolayer” structure). The bilayer structure is observed for gap length ≳10 bases and melts into the cholesteric phase at a temperature between 30 °C and 35 °C. The monolayer structure predominates for gap length ≲10 bases and persists to >40 °C. We discuss models for the two layer structures and mechanisms for their stability. We also report results for asymmetric gapped constructs and for constructs with terminal overhangs, which further support the model layer structures.

DNA is an iconic lyotropic liquid crystal (LC). When duplexes with lengths above the threshold for nematic ordering of hard rods, but below or comparable with the persistence length of the DNA polymer, are concentrated in an aqueous solvent, one observes a sequence of cholesteric, hexagonal columnar, and higher-ordered crystalline phases (1–5). Remarkably, LC structure also emerges spontaneously when ultrashort duplexes (well below the normal threshold for a nematic phase) are concentrated and through blunt end–end attraction, assemble into longer aggregates (6). LC ordering has also been observed in solutions of short single-stranded oligomers (7, 8), or even mononucleotides (9), that first pair (via base–base complementarity) and then stack to form rod-like aggregates.However, until its recent discovery (10), elementary layered (smectic) phases—so fundamental to small-molecule LCs with sufficiently long, flexible terminal groups—were conspicuously missing from an otherwise representative range of mesophases exhibited in concentrated DNA solutions. One key to stabilizing smectic layering is the introduction of a “gap,” or sequence of single bases of sufficient number, into the middle of a duplex, thereby producing a “gapped” DNA (GDNA) construct consisting of two rigid segments connected by a flexible spacer (Fig. 1). This architecture enables entropy-driven segregation of the spacer and the enthalpic attraction between blunt duplex ends to operate together to stabilize a smectic layer structure.Open in a separate windowFig. 1.Schematic motifs of GDNA constructs. (A) “Symmetric” GDNA composed of two 48-bp duplexes connected by a single-strand segment (gap) consisting of n = 2, 4, 7, 10, or 20 T (thymine) bases. (B and C) Asymmetric constructs containing 60/48- and 60/24-bp duplexes connected by a 20 T spacer. (D) Symmetric construct with terminal 2 T overhangs.Identifying and characterizing minimal, essential entropic and enthalpic factors for the self-assembly of smectic phases in dense solutions of semiflexible, anisotropic particles are important challenges in soft materials science. The present work further explores this problem in the GDNA system by examining the effects of altering basic architectural features of the GDNA construct and varying temperature on the nature and stability of the smectic phase.In particular, we demonstrate that basic characteristics of smectic ordering of GDNA depend sensitively on the gap length. We establish that two distinct smectic-A–type layer structures occur in concentrated GDNA solutions. One (the “bilayer” structure) is characterized by an interlayer periodicity comparable with the length of two-duplex segments. The other (“monolayer” structure) has a period comparable with the length of a single duplex. The bilayer structure prevails for longer gap lengths (≳10 bases). The monolayer morphology predominates when the gap length is shortened to ≲10 bases and is evident down to at least a 4-base gap. No evidence of smectic layer structure is observed for gaps ≤2 bases.We also establish that the GDNA system is amphotropic, with the smectic phases being sensitive to temperature in addition to DNA concentration. Specifically, we observe a smectic to cholesteric (chiral nematic) phase transition, occurring between 30 °C and 35 °C in solutions of GDNA constructs that exhibit the bilayer smectic phase. We argue that this transition reflects a temperature dependence of the enthalpic end-to-end interactions that stabilize the bilayer structure.Additionally, we report results on GDNA constructs containing either duplexes of unequal length (“asymmetric” GDNA) or duplexes with noncomplementary, single-strand “overhangs” positioned at the ends opposite the gap. These results further buttress the evidence for two distinct smectic layer structures and for the significance of blunt end-to-end attraction in stabilizing the bilayer smectic.The GDNA constructs investigated are summarized schematically in Fig. 1. Symmetric constructs consisted of two 48-base pair (bp) duplexes connected by a single-strand gap of n=2, 4, 7, 10, or 20 unpaired thymine (T) bases; we abbreviate these constructs as 48-nT-48 (Fig. 1A). We also assembled asymmetric constructs, designated 48-20T-60 and 24-20T-60, composed of 24- or 48- and 60-bp duplexes linked by a 20 T single strand (Fig. 1 B and C), and synthesized symmetric constructs, designated 2T-48-20T-48-2T, with two unpaired T bases “overhanging” the free ends of the duplexes (Fig. 1D).     

Extremely small twist elastic constants in lyotropic nematic liquid crystals

Recent measurements of the elastic constants in lyotropic chromonic liquid crystals (LCLCs) have revealed an anomalously small twist elastic constant compared to the splay and bend constants. Interestingly, measurements of the elastic constants in the micellar lyotropic liquid crystals (LLCs) that are formed by surfactants, by far the most ubiquitous and studied class of LLCs, are extremely rare and report only the ratios of elastic constants and do not include the twist elastic constant. By means of light scattering, this study presents absolute values of the elastic constants and their corresponding viscosities for the nematic phase of a standard LLC composed of disk-shaped micelles. Very different elastic moduli are found. While the splay elastic constant is in the typical range of 1.5 pN as is true in general for thermotropic nematics, the twist elastic constant is found to be one order of magnitude smaller (0.30 pN) and almost two orders of magnitude smaller than the bend elastic constant (21 pN). These results demonstrate that a small twist elastic constant is not restricted to the special case of LCLCs, but is true for LLCs in general. The reason for this extremely small twist elastic constant very likely originates with the flexibility of the assemblies that are the building blocks of both micellar and chromonic lyotropic liquid crystals.

A nematic liquid crystal is a three-dimensional (3D) fluid phase of matter in which the anisometric building blocks (e.g., molecules, molecular assemblies, micelles) making up the material maintain a certain amount of long-range orientational order as they diffuse in a fashion similar to that of liquids. At any point in a nematic liquid crystal phase, the anisometric building blocks tend to orient their principal axes along a specific direction called the director and given the symbol n^. If the building blocks are rodlike, the long axes are ordered along the director and if the blocks are disklike, the short axes are ordered.Liquid crystals (LCs) are prime examples of soft matter that are distinguished by having large response functions to even weak external perturbations. The elastic response of the nematic LC director field n^(r→) is governed by three elastic constants associated with the three principal deformations possible in nematics (K11 splay, K22 twist, and K33 bend; Fig. 1 A–C) with twist being the only chiral deformation of these three. The way a nematic liquid crystal elastically deforms under the action of external forces or under external confinement critically depends on the relative magnitudes of K11, K22, and K33. In common thermotropic nematic LCs consisting of rodlike molecules, all three constants are on the same order of magnitude (typically 10⁻¹² to 10⁻¹¹ N) which in most cases allows for the so-called “one-constant approximation” frequently used in liquid crystal theory (1). An exception from the one-constant approximation is probably the bent-core nematic phases (BCNs) formed by bent-core mesogens, the bowlike shape of which considerably deviates from the rodlike shape of common nematic mesogens. Here, values of K₂₂ and K₃₃ being one order of magnitude smaller than K₁₁ were reported (2).Open in a separate windowFig. 1.(A–C) The three bulk elastic deformations of a nematic liquid crystal phase: splay (A), twist (B), and bend (C). The blue disks represent the disk-shaped micelles of the investigated LLC, and the director n^ is indicated in red. (D) Polarized optical micrograph (crossed polarizers) of the twisted polar (TP) director configuration of the lyotropic micellar N_D phase under the confinement of a capillary (diameter: 700 µm). The TP director configuration breaks reflection symmetry and is characterized by two half-unit twist disclination lines forming a double helix. For more information see ref. 11. (E) In the scattering geometry measuring splay and twist fluctuations, the director n^ is perpendicular to the scattering plane. (F) In the scattering geometry measuring twist and bend fluctuations, the director n^ is parallel to the scattering plane. The incident light is perpendicular to the front and back planes representing the two glass substrates of the LC cell. The wave vectors k→i and ks→ indicate incident and scattered light; i (vertical) and f (horizontal) correspond to their polarizations, respectively. θ is the scattering angle.However, if the twist elastic constant is considerably smaller than the other two, K22≪K11,K33, twist deformations are least energetically costly. Thus reflection symmetry breaking might occur even in a nonchiral nematic under nonchiral confinement. A striking example was recently observed in a lyotropic chromonic nematic LC under cylindrical as well as under droplet confinement (3–5). Indeed, in this particular case K22 has been measured to be one order of magnitude smaller than K11 and K33 (6, 7).In a chromonic nematic LC, the orientationally ordered building blocks are rodlike stacks of dye molecules, suspended in a suitable solvent, usually water (8). They thus constitute a rather special class of lyotropic LCs. However, the most ubiquitous class of lyotropic LCs is formed by surfactants that in water assemble into rod- or disk-shaped micellar building blocks. In fact, these micellar or surfactant-based lyotropic LCs have been known for a long time and are abundant in biological structures (e.g., phospholipid membranes) and in our daily lives (e.g., detergents and soaps) (9, 10).Our recent observation of confinement-induced reflection symmetry breaking in a lyotropic micellar nematic phase (Fig. 1D) suggests that K22 might also be very small in this case (11). Searching the literature we recognized that very little is known about the elasticity of lyotropic nematic phases of disklike (N_D) as well as rodlike (N_C) micelles: A few K11/χa and K33/χa (with χa being the diamagnetic anisotropy) measured via magnetic Frederiks transition have been reported for two lyotropic surfactant systems with N_D phases (12, 13) and one with an N_C phase (13). Only one study investigating the N_D phase of the cesium perfluorooctanoate (CsPFO)/H₂O system by conductivity measurements reported absolute values for K11 and K33 (14). Importantly, to the best of our knowledge neither a single complete set of elastic constants nor a single value of K22 has been reported for surfactant-based lyotropic nematics.However, in other classes of lyotropic LCs, complete sets of elastic constants including K22 have been measured by means of depolarized dynamic light scattering. The first example in 1985 was the lyotropic polymeric nematic phase of racemic poly-γ-benzyl-glutamate (PBG) (15). Together with an independent measurement of K33 via the magnetic Freedericksz transition using the diamagnetic anisotropy of PBG (16), absolute values for the elastic constants K11,K22, and K33 as well as the corresponding viscosities η11,η22, and η33 were reported (15, 17). In 2014 Zhou et al. (7) enhanced the analysis of light-scattering data by introducing a calibration step using the common thermotropic nematic LC 4′-n-pentyl-4-cyanobiphenyl (5CB) for which all viscoelastic properties are well known. This calibration allowed absolute measurements of the elastic constants and their corresponding viscosities in the chromonic nematic LC disodium cromoglycate (DSCG)/H₂O (7). Since then, this technique has also been used for thermotropic nematics (18).Here we use the same light-scattering technique of Zhou et al. (7) to determine a complete set of elastic constants and viscosities for a surfactant-based lyotropic nematic LC, namely the ternary system N,N-dimethyl-N-ethylhexadecyl-ammonium bromide (CDEAB), decan-1-ol, and water. This system forms the N_D phase of disklike micelles for which we previously observed reflection symmetry breaking under capillary confinement (11). Very different elastic moduli are found: The twist elastic constant K22 =(0.300 ± 0.018) pN is one order of magnitude smaller than K11=(1.54±0.08) pN and almost two orders of magnitude smaller than the bend elastic constant K33=(20.8±1.3) pN. We further present a simple model based on the deformation modes of disk-shaped micelles, which makes a plausible argument for the relative magnitudes of the three elastic constants. In view of the finding of a low K22 value for a micellar lyotropic nematic, a low twist modulus is likely a generic property in all classes of lyotropic nematics, which implies that the one-constant approximation does not hold for lyotropic nematic systems. Likewise, the viscous behavior of lyotropic nematics does not seem to follow the predictions of the Ericksen–Leslie model in which ηtwist has the highest value. Furthermore, the very small K22 value makes these phases extremely responsive to chiral perturbations. The quest to understand reflection symmetry breaking in a fluid system (and in an aqueous solution in particular) is a long-standing scientific goal, with implications as far ranging as the origin of handedness in biology.     

Optic properties of bile liquid crystals in human body

AIM To further study the properties of bile liquid crystals, and probe into the relationship between bile liquid crystals and gallbladder stone formation, and provide evidence for the prevention and treatment of cholecystolithissis. METNODS The optic properties of bile liquid crystals in human body were determined by the method of crystal optics under polarizing microscope with plane polarized light and perpendicular polarized light. RESULTS Under a polarizing microscope with plane polarized light, bile liquid crystals scattered in bile appeared round, oval or irregularly round. The color of bile liquid crystals was a little lighter than that of the bile around. When the stage was turned round, the color of bile liquid crystals or the darkness and lightness of the color did not change obviously. On the border between bile liquid crystals and the bile around, brighter Becke-Line could be observed. When the microscope tube is lifted, Becke. Line moved inward, and when lowered,Becke-Line moved outward. Under a perpendicular polarized light, bile liquid crystals showd some special interference patterns, called Malta cross. When the stage was tuming round at an angle of 360°, the Malta cross showed four times of extinction. In the vibrating direction of 45° angle of relative to upper and lower polarizing plate, gypsum test-board with optical path difference of 530 nm was inserted, the first and the third quadrants of Malta cross appeared to be blue, and the second and the fourth quadrants appeared orange. When mica test-board with optical path difference of 147 nm was inserted, the first and the third quadrants of Malta cross appeared yellow, and the second and the fourth quadrants appeared dark grey. CONCLUSION The bile liquid crystals were distributed in bile in the form of global grains. Their polychroism and absorption were slight,but the edge and Becke-Line were very clear. Its refractive index was larger than that of the bile.These liquid crystals were uniaxial positive crystals. The interference colors were the first order grey-white. The double refractive index of the liquid crystals was Δn = 0.011-0.015.     

Straining soft colloids in aqueous nematic liquid crystals

Liquid crystals (LCs), because of their long-range molecular ordering, are anisotropic, elastic fluids. Herein, we report that elastic stresses imparted by nematic LCs can dynamically shape soft colloids and tune their physical properties. Specifically, we use giant unilamellar vesicles (GUVs) as soft colloids and explore the interplay of mechanical strain when the GUVs are confined within aqueous chromonic LC phases. Accompanying thermal quenching from isotropic to LC phases, we observe the elasticity of the LC phases to transform initially spherical GUVs (diameters of 2–50 µm) into two distinct populations of GUVs with spindle-like shapes and aspect ratios as large as 10. Large GUVs are strained to a small extent (R/r < 1.54, where R and r are the major and minor radii, respectively), consistent with an LC elasticity-induced expansion of lipid membrane surface area of up to 3% and conservation of the internal GUV volume. Small GUVs, in contrast, form highly elongated spindles (1.54 < R/r < 10) that arise from an efflux of LCs from the GUVs during the shape transformation, consistent with LC-induced straining of the membrane leading to transient membrane pore formation. A thermodynamic analysis of both populations of GUVs reveals that the final shapes adopted by these soft colloids are dominated by a competition between the LC elasticity and an energy (∼0.01 mN/m) associated with the GUV–LC interface. Overall, these results provide insight into the coupling of strain in soft materials and suggest previously unidentified designs of LC-based responsive and reconfigurable materials.The majority of living materials are soft. This characteristic emerges from noncovalent interactions that lead to the formation of supramolecular structures that reorganize in response to subtle chemical and mechanical cues (1). The regulation of mechanical strain in particular and the engineering of responses to it across a hierarchy of spatial scales (from the molecular to the supramolecular to the cellular level) are increasingly understood to be one of the central sciences of living systems (2, 3).Inspired in part by the functionality of biological materials, a wide range of soft synthetic materials has been assembled by noncovalent interactions of molecular and macromolecular components (1, 4). In particular, liquid crystals (LCs) (Fig. 1A), which are phases that combine the molecular mobility of liquids with the long-range orientational ordering of crystalline solids, have provided the basis for a spectrum of responsive materials, including systems where electrical fields and mechanical strain compete to control electrooptical properties (5, 6). More recently, micro- and nanometer-sized colloidal particles dispersed in LCs have been used to form tunable self-assembled structures for photonic crystals and metamaterials (7). In the systems studied to date, however, the colloids have been “hard” compared with the LC, leading to mechanical straining of the LC but not the colloids (8).Open in a separate windowFig. 1.(A) Schematic illustration of the long-range orientational order of a nematic LC, which can be characterized by a local director n^. (B) The chemical structure of a DSCG molecule. (C and E) Fluorescence and (D and F) crossed polar micrographs of GUVs in 15% (wt/wt) DSCG at (C and D) 48 °C (isotropic phase) and (E and F) at 25 °C (nematic phase). (Scale bars: 10 µm.)In this paper, we move beyond these past studies and consider the more complex situation in which soft colloids are dispersed in LCs, such that a coupling exists between colloid shape and LC strain. Specifically, we have used micrometer-sized synthetic giant unilamellar vesicles (GUVs) as model soft colloids and dispersed them in LCs. We hypothesized that elastic stresses arising from deformation of the LC would strain the GUVs, potentially giving rise, for example, to anisometric GUV shapes, expansion of the surface area of GUV membranes, and temporary poration and/or permanent rupture of the GUV bilayers. To test this hypothesis, we used the lyotropic chromonic LC phase formed from aqueous solutions of disodium cromoglygate (DSCG) (Fig. 1B). We used DSCG, because it is not amphiphilic, and thus, we predicted that it would not disrupt the lipid bilayers of GUVs (in contrast, many surfactants that form lyotropic phases solubilize lipid bilayers). DSCG molecules stack into anisometric assemblies when dissolved in water (9–11) and form mesophases in a manner that depends on temperature and the concentration. We note here that the ordering of nematic DSCG and other chromonic LCs has been explored in confined spherical (12) and cylindrical geometries (13) as well as surrounding rigid spherical inclusions (14).The results described in this paper yield fundamental insights into the ways in which elastic stresses are coupled to particle shape in soft matter systems, hinting at previously unidentified designs of LC-based responsive and/or active materials. In addition, we note that recent experiments suggest that curvature strain within bacterial and mitochondrial membranes may locally concentrate certain families of lipids to regions of highest membrane curvature. The elastically strained GUVs described in this paper may provide the basis of an experimental platform to further investigate biophysical questions relating to membrane curvature strain (2). Our results also have the potential to provide insights into the recent observation that elastic stresses imparted by LCs can alter bacterial cell shape (15).     

Control of active liquid crystals with a magnetic field

Living cells sense the mechanical features of their environment and adapt to it by actively remodeling their peripheral network of filamentary proteins, known as cortical cytoskeleton. By mimicking this principle, we demonstrate an effective control strategy for a microtubule-based active nematic in contact with a hydrophobic thermotropic liquid crystal. By using well-established protocols for the orientation of liquid crystals with a uniform magnetic field, and through the mediation of anisotropic shear stresses, the active nematic reversibly self-assembles with aligned flows and textures that feature orientational order at the millimeter scale. The turbulent flow, characteristic of active nematics, is in this way regularized into a laminar flow with periodic velocity oscillations. Once patterned, the microtubule assembly reveals its intrinsic length and time scales, which we correlate with the activity of motor proteins, as predicted by existing theories of active nematics. The demonstrated commanding strategy should be compatible with other viable active biomaterials at interfaces, and we envision its use to probe the mechanics of the intracellular matrix.Liquid crystals are viscous fluids that self-assemble into equilibrium molecular arrangements featuring anisotropic physical properties that can be easily tailored by suitable boundary conditions, and reversibly rearranged by using modest electric or magnetic fields (1). These soft matter mesophases are not exclusive of artificial materials, as they are ubiquitous in lipid solutions (2) and concentrated DNA fragments (3), and have been recently obtained by in vitro cytoskeletal reconstitutions based on aqueous suspensions of filamentous proteins cross-linked by compatible molecular motors (4–6). The latter type of materials is referred to as active liquid crystals because, unlike their passive counterparts, they exhibit out-of-equilibrium behavior with supramolecular orientational order that is dynamically self-assembled at the continuous expense of hydrolysable adenosine triphosphate (ATP). Experiments with active soft matter (7–17) reveal self-organizing features that are not present in passive materials. Despite the vast richness of behavior endowed by activity, traditional liquid crystals have a dramatic advantage: their orientation can be easily controlled to switch among different predesigned configurations, which is crucial for the operation of devices, and for fundamental research in partially ordered materials. Contrarily, experiments on active nematics have relied on establishing their composition, confinement geometry, or activity as design parameters, but they lack true control capabilities of the resulting dynamic self-assembly. This limits their potential to serve as in vitro model systems of the intracellular matrix or for the development of new functional biomaterials. Here, by interfacing an active nematic film with a hydrophobic oil that features smectic (lamellar) liquid-crystalline order (18), we reversibly align the originally turbulent flow of the active fluid into well-designed flow directions by means of a magnetic field.     

Thioether-Linked Liquid Crystal Trimers: Odd–Even Effects of Spacers and the Influence of Thioether Bonds on Phase Behavior

We report the synthesis, phase-transition behavior, and mesophase structures of the first homologous series of thioether-linked liquid crystal (LC) trimers, 4,4′-bis[ω-(4-cyanobiphenyl-4′-ylthio)alkoxy]biphenyls (CBSnOBOnSCB with a wide range of spacer carbon numbers, n = 3–11). All CBSnOBOnSCB homologs exhibited LC phases. Interestingly, even-n and odd-n homologs showed monotropic layered smectic A (SmA) and pseudo-layered twist-bend nematic (N_TB) phases, respectively, below a nematic (N) phase. This alternate formation, which depends on spacer chain parity, is attributed to different average molecular shapes, which are associated with the relative orientations of the biphenyl moieties: linear and bent shapes for even-n and odd-n homologs, respectively. In addition, X-ray diffraction analysis indicated a strong cybotactic N phase tendency, with a triply intercalated structure. The phase-transition behavior and LC phase structures of thioether-linked CBSnOBOnSCB were compared with those of the all-ether-linked classic LC trimers CBOnOBOnOCB. Overall, thioether linkages endowed CBSnOBOnSCB with a monotropic LC tendency and lowered phase-transition temperatures, compared to those of CBOnOBOnOCB, for the same n. This is attributed to enhanced flexibility and bending (less molecular anisotropy) of the molecules, caused by the greater bond flexibility and smaller inner bond angles of the C–S–C bonds, compared to those of the C–O–C bonds.     

Optical vector field rotation and switching with near-unity transmission by fully developed chiral photonic crystals

State-of-the-art nanostructured chiral photonic crystals (CPCs), metamaterials, and metasurfaces have shown giant optical rotatory power but are generally passive and beset with large optical losses and with inadequate performance due to limited size/interaction length and narrow operation bandwidth. In this work, we demonstrate by detailed theoretical modeling and experiments that a fully developed CPC, one for which the number of unit cells N is high enough that it acquires the full potentials of an ideal (N → ∞) crystal, will overcome the aforementioned limitations, leading to a new generation of versatile high-performance polarization manipulation optics. Such high-N CPCs are realized by field-assisted self-assembly of cholesteric liquid crystals to unprecedented thicknesses not possible with any other means. Characterization studies show that high-N CPCs exhibit broad transmission maxima accompanied by giant rotatory power, thereby enabling large (>π) polarization rotation with near-unity transmission over a large operation bandwidth. Polarization rotation is demonstrated to be independent of input polarization orientation and applies equally well on continuous-wave or ultrafast (picosecond to femtosecond) pulsed lasers of simple or complex (radial, azimuthal) vector fields. Liquid crystal–based CPCs also allow very wide tuning of the operation spectral range and dynamic polarization switching and control possibilities by virtue of several stimuli-induced index or birefringence changing mechanisms.

Optical vector field (more commonly called polarization) rotators and switches are essential components of all modern optical and photonic systems for communications, ellipsometry, metrology, biological/chemical detection, and quantum processing/computing (1–10). There are, however, some inherent limitations. Wave plates made with birefringent crystals, for example, require strict alignment of the optic axis with respect to the polarization orientation of incident light and generally do not work with laser vector beams of complex polarization fields; Faraday rotators that do not have this requirement are generally too cumbersome and bulky due to their weak optical rotatory powers. One promising approach to circumvent these limitations is to employ chiral optical materials such as chiral photonic crystals and metasurfaces. Nevertheless, structural chirality, such as chiral metamaterials, metasurfaces, and photonic crystals that are capable of very large optical rotatory power (up to ∼100,000°/mm), are inevitably accompanied by large absorption losses (11–15). In metamaterials/surfaces, the intrinsic noncircular absorption and nanofabrication difficulty also add to the limitation of their practical scalability in the interaction length, resulting in small (<π) net polarization rotation angle, very small aperture, and narrow operating spectral bandwidth (11–13). Similar issues confront most chiral photonic crystals (CPCs) due to the limitations of molecular self-assembly or nanofabrication/processing technique and high transmission loss associated with operation near the Bragg reflection band (14, 15).Here, we show by theory and experimental corroborations that a fully developed liquid crystal–based CPC, one for which the number of unit cells N approaches that (N → ∞) of an ideal crystal, can circumvent all the aforementioned limitations and possess several advantageous characteristics impossible with conventional low-N thin counterparts. Such high-period–number chiral photonic crystals (HN-CPCs) are achieved by fabricating cholesteric liquid crystals (CLCs) to thicknesses several hundred times that of conventional ones using a refined field-assisted self-assembly (FASA) technique (16, 17; see SI Appendix, Note 1, for more details). Optical properties of CLCs as CPCs arise from complex “collective” responses from many unit cells. While thicker crystals obviously give rise to larger effects, the resulting properties as the crystal thickness or period number N evolves from low values to a very high value do not lend themselves to such simple linear extrapolation; as a function of N, pleasant surprises and new insights and possibilities abound. Our studies show that for N > 500, these CLCs exhibit simultaneously broad transmission maxima and large polarization rotation power in the off-Bragg-resonance spectral regime. Polarization rotation is independent of input polarization orientation and acts equally well on simple or complex vector fields (18–22) of continuous-wave (CW) or ultrafast pulsed laser beams. Liquid crystal–based CPCs also allow dynamic polarization switching and control by virtue of field–induced index/birefringence changing mechanisms at modest or ultrafast (picosecond to femtosecond) speeds (23–34).     

Nanoparticle self-assembly at the interface of liquid crystal droplets

Nanoparticles adsorbed at the interface of nematic liquid crystals are known to form ordered structures whose morphology depends on the orientation of the underlying nematic field. The origin of such structures is believed to result from an interplay between the liquid crystal orientation at the particles’ surface, the orientation at the liquid crystal’s air interface, and the bulk elasticity of the underlying liquid crystal. In this work, we consider nanoparticle assembly at the interface of nematic droplets. We present a systematic study of the free energy of nanoparticle-laden droplets in terms of experiments and a Landau–de Gennes formalism. The results of that study indicate that, even for conditions under which particles interact only weakly at flat interfaces, particles aggregate at the poles of bipolar droplets and assemble into robust, quantized arrangements that can be mapped onto hexagonal lattices. The contributions of elasticity and interfacial energy corresponding to different arrangements are used to explain the resulting morphologies, and the predictions of the model are shown to be consistent with experimental observations. The findings presented here suggest that particle-laden liquid crystal droplets could provide a unique and versatile route toward building blocks for hierarchical materials assembly.A growing body of theoretical and experimental work has sought to direct the assembly of molecules and nanoparticles at interfaces by exploiting the elastic forces that arise in liquid crystals (LCs) (1–5). Nematic LCs possess orientational order along a unit vector, the so-called nematic director. They also exhibit defects—regions of low order whose morphology and position depends on a delicate balance between elastic, enthalpic, and interfacial contributions to the free energy. The orientation of nematic LCs and any corresponding defects can be perturbed by introducing particles. The symmetry and structure of the director field around a particle also depends on the interaction between the LC and the particle, often referred to as anchoring. Particles with perpendicular (homeotropic) anchoring induce either dipolar or quadrupolar symmetry in the LC, leading to formation of point defects or Saturn-ring defects, respectively (6). Particles with planar anchoring induce quadrupolar symmetry, which is accompanied by two surface defects, generally referred to as boojums (6). Distortions of the nematic field cost elastic energy and therefore give rise to anisotropic, long-range interactions between particles. Indeed, particles in nematic LCs aggregate and “bind,” thereby minimizing the volume of defects and the large free energy that is associated with their elastic strain. Equilibrium particle arrangements in nematic LCs depend strongly on the topology of the underlying defects. Homeotropic particles with point, dipolar defects form chains along the nematic director, whereas quadrupolar, Saturn-ring defects form kinked chains that are perpendicular to the nematic director (7). Particles with planar anchoring form chains whose main axis forms a 30° angle with the nematic director (8). Recent work has also shown that particles can be trapped in topological defects (9, 10) and in chiral defects (11, 12). Particles localized at a planar LC interface also exhibit LC-induced interactions. For the particular case of perpendicular anchoring, it has been shown that particles aggregate into ordered structures whose morphology can be controlled by addition of surfactants (13). Recently, a robust mechanism has been reported to direct assembly of homeotropic particles trapped at the LC interface into reconfigurable structures by controlling surface anchoring and bulk defect structure (14).This work considers the aggregation of nanoparticles at LC droplet interfaces. Past studies from our own groups have shown that LCs confined in small droplets can be used to induce formation of intriguing surfactant nanophases at their interfaces (15). Experiments and simulations have also shown that the defects that arise in LC droplets can be used to localize individual nanoparticles or pairs of nanoparticles with considerable precision (16, 17). More generally, droplets offer an effective, yet simple means for confining LCs, thereby controlling the balance of interfacial and elastic contributions to the free energy and the response of LCs to external cues (18, 19). Depending on surface anchoring, LC droplets can exhibit two primary morphologies (20). Homeotropic anchoring leads to radial LC droplets, with a single ring or point defect in the center, whereas planar anchoring leads to bipolar droplets having two surface point (or boojum) defects. The localization of particles at boojums reduces the splay elastic free energy significantly. Remarkably, the trapping of particles into the boojums is independent of the type of anchoring of LC at the particle surfaces (16). A recent study examined the self-assembly of homeotropic particles at the surface of a bipolar droplet and observed formation of star-like patterns (21). Dipole–dipole interactions between particles led to formation of linear chains along the longitudinal orientation of the director field that, upon finding the boojums, organized into stars.Our focus is to examine and understand the behavior of planar particles located at the surface of micrometer-sized bipolar droplets. We restrict our attention to degenerate planar anchoring and planar droplets because such conditions are much more permissive than homeotropic anchoring, and it is therefore difficult to anticipate the types of arrangements that may arise on the basis of symmetry arguments. By examining the structures and LC morphologies that arise as a function of particle number, we are able to provide a systematic view of nanoparticle assembly in such systems. Our past experiments have shown that a single polystyrene (PS) particle with planar anchoring and radius of 0.5 µm adsorbed at the surface of a bipolar 5CB droplet diffuses into a boojum defect (16). Here, we show that when more particles are adsorbed at the droplet surface, they migrate to the poles and assemble into arrangements that can be mapped into hexagonal arrays around the boojum. The predictions of our theoretical calculations are shown to be consistent with experimental observations (22).     

Formation of a crystal nucleus from liquid

Crystallization is one of the most fundamental nonequilibrium phenomena universal to a variety of materials. It has so far been assumed that a supercooled liquid is in a “homogeneous disordered state” before crystallization. Contrary to this common belief, we reveal that a supercooled colloidal liquid is actually not homogeneous, but has transient medium-range structural order. We find that nucleation preferentially takes place in regions of high structural order via wetting effects, which reduce the crystal–liquid interfacial energy significantly and thus promotes crystal nucleation. This novel scenario provides a clue to solving a long-standing mystery concerning a large discrepancy between the rigorous numerical estimation of the nucleation rate on the basis of the classical nucleation theory and the experimentally observed ones. Our finding may shed light not only on the mechanism of crystal nucleation, but also on the fundamental nature of a supercooled liquid state.     

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Lyotropic chromonic liquid crystals (LCLCs) are aqueous dispersions of organic disk-like molecules that self-assemble into cylindrical aggregates, which form nematic or columnar liquid crystal phases under appropriate conditions of concentration and temperature (1–6). These materials have gained increasing attention in both fundamental and applied research over the past decade, due to their distinct structural properties and biocompatibility (4, 7–14). Used as a replacement for isotropic fluids in microfluidic devices, nematic LCLCs have been employed to control the behavior of bacteria and colloids (13, 15–20).Nematic liquid crystals form topological defects under flow, which gives rise to complex dynamical structures that have been extensively studied in thermotropic liquid crystals (TLCs) and liquid crystal polymers (LCPs) (21–29). In contrast to lyotropic liquid crystals that are dispersed in a solvent and whose phase can be tuned by either concentration or temperature, TLCs do not need a solvent to possess a liquid-crystalline state and their phase depends only on temperature (30). Most TLCs are shear-aligned nematics, in which the director evolves toward an equilibrium out-of-plane polar angle. Defects nucleate beyond a critical Ericksen number due to the irreconcilable alignment of the directors from surface anchoring and shear alignment in the bulk flow (24, 31–33). With an increase in shear rate, the defect type can transition from π-walls (domain walls that separate regions whose director orientation differs by an angle of π) to ordered disclinations and to a disordered chaotic regime (34). Recent efforts have aimed to tune and control the defect structures by understanding the relation between the selection of topological defect types and the flow field in flowing TLCs. Strategies to do so include tuning the geometry of microfluidic channels, inducing defect nucleation through the introduction of isotropic phases or designing inhomogeneities in the surface anchoring (35–39). LCPs are typically tumbling nematics for which α2α3 < 0, where α2 and α3 are the Leslie viscosities. This leads to a nonzero viscous torque for any orientation of the director, which allows the director to rotate in the shear plane (22, 29, 30, 40). The tumbling character of LCPs facilitates the nucleation of singular topological defects (22, 40). Moreover, the molecular rotational relaxation times of LCPs are longer than those of TLCs, and they can exceed the timescales imposed by the shear rate. As a result, the rheological behavior of LCPs is governed not only by spatial gradients of the director field from the Frank elasticity, but also by changes in the molecular order parameter (25, 41–43). With increasing shear rate, topological defects in LCPs have been shown to transition from disclinations to rolling cells and to worm-like patterns (25, 26, 43).Topological defects occurring in the flow of nematic LCLCs have so far received much more limited attention (44, 45). At rest, LCLCs exhibit unique properties distinct from those of TLCs and LCPs (1, 2, 4–6, 44). In particular, LCLCs have significant elastic anisotropy compared to TLCs; the twist Frank elastic constant, K2, is much smaller than the splay and bend Frank elastic constants, K1 and K3. The resulting relative ease with which twist deformations can occur can lead to a spontaneous symmetry breaking and the emergence of chiral structures in static LCLCs under spatial confinement, despite the achiral nature of the molecules (4, 46–51). When driven out of equilibrium by an imposed flow, the average director field of LCLCs has been reported to align predominantly along the shear direction under strong shear but to reorient to an alignment perpendicular to the shear direction below a critical shear rate (52–54). A recent study has revealed a variety of complex textures that emerge in simple shear flow in the nematic LCLC disodium cromoglycate (DSCG) (44). The tumbling nature of this liquid crystal leads to enhanced sensitivity to shear rate. At shear rates γ˙<1 s−1, the director realigns perpendicular to the flow direction adapting a so-called log-rolling state characteristic of tumbling nematics. For 1 s−1<γ˙<10 s−1, polydomain textures form due to the nucleation of pure-twist disclination loops, for which the rotation vector is parallel to the loop normal, and mixed wedge-twist disclination loops, for which the rotation vector is perpendicular to the loop normal (44, 55). Above γ˙>10 s−1, the disclination loops gradually transform into periodic stripes in which the director aligns predominantly along the flow direction (44).Here, we report on the structure and dynamics of topological defects occurring in the pressure-driven flow of nematic DSCG. A quantitative evaluation of such dynamics has so far remained challenging, in particular for fast flow velocities, due to the slow image acquisition rate of current quantitative polarization-resolved imaging techniques. Quantitative polarization imaging traditionally relies on three commonly used techniques: fluorescence confocal polarization microscopy, polarizing optical microscopy, and LC-Polscope imaging. Fluorescence confocal polarization microscopy can provide accurate maps of birefringence and orientation angle, but the fluorescent labeling may perturb the flow properties (56). Polarizing optical microscopy requires a mechanical rotation of the polarizers and multiple measurements, which severely limits the imaging speed. LC-Polscope, an extension of conventional polarization optical microscopy, utilizes liquid crystal universal compensators to replace the compensator used in conventional polarization microscopes (57). This leads to an enhanced imaging speed and better compensation for polarization artifacts of the optical system. The need for multiple measurements to quantify retardance, however, still limits the acquisition rate of LC-Polscopes.We overcome these challenges by using a single-shot quantitative polarization microscopy technique, termed polarized shearing interference microscopy (PSIM). PSIM combines circular polarization light excitation with off-axis shearing interferometry detection. Using a custom polarization retrieval algorithm, we achieve single-shot mapping of the retardance, which allows us to reach imaging speeds that are limited only by the camera frame rate while preserving a large field-of-view and micrometer spatial resolution. We provide a brief discussion of the optical design of PSIM in Materials and Methods; further details of the measurement accuracy and imaging performance of PSIM are reported in ref. 58.Using a combination of experiments, numerical simulations and scaling analysis, we show that in the pressure-driven flow of nematic DSCG solutions in a microfluidic channel, pure-twist disclination loops emerge for a certain range of shear rates. These loops are elongated in the flow with a fixed aspect ratio. We demonstrate that the disclination loops nucleate at the boundary between regions where the director aligns predominantly along the flow direction close to the channel walls and regions where the director aligns predominantly perpendicular to the flow direction in the center of the channel. The large elastic stresses of the director gradient at the boundary are then released by the formation of disclination loops. We show that both the characteristic size and the fluctuations of the pure-twist disclination loops can be tuned by controlling the flow rate.     

Chiral structures from achiral liquid crystals in cylindrical capillaries

We study chiral symmetry-broken configurations of nematic liquid crystals (LCs) confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls (i.e., perpendicular surface alignment). Interestingly, achiral nematic LCs with comparatively small twist elastic moduli relieve bend and splay deformations by introducing twist deformations. In the resulting twisted and escaped radial (TER) configuration, LC directors are parallel to the cylindrical axis near the center, but to attain radial orientation near the capillary wall, they escape along the radius through bend and twist distortions. Chiral symmetry-breaking experiments in polymer-coated capillaries are carried out using Sunset Yellow FCF, a lyotropic chromonic LC with a small twist elastic constant. Its director configurations are investigated by polarized optical microscopy and explained theoretically with numerical calculations. A rich phenomenology of defects also arises from the degenerate bend/twist deformations of the TER configuration, including a nonsingular domain wall separating domains of opposite twist handedness but the same escape direction and singular point defects (hedgehogs) separating domains of opposite escape direction. We show the energetic preference for singular defects separating domains of opposite twist handedness compared with those of the same handedness, and we report remarkable chiral configurations with a double helix of disclination lines along the cylindrical axis. These findings show archetypally how simple boundary conditions and elastic anisotropy of confined materials lead to multiple symmetry breaking and how these broken symmetries combine to create a variety of defects.The emergence of chirality from achiral systems poses fundamental questions about which we have limited mechanistic understanding (1–11). When the chiral symmetry of an achiral system is broken, a handedness is established, and materials with different handedness commonly exhibit distinct and useful properties (10–14) relevant for applications ranging from chemical sensors (15, 16) to photonics (17–19). To date, considerable effort has been expended to control handedness in materials (for example, by chiral separation of racemic mixtures or chiral amplification of small enantiomeric imbalances) (1, 8, 20–22). Recently and in a different vein, identification and elucidation of pathways by which achiral building blocks spontaneously organize to create chiral structures have become an area of active study. Examples of these pathways include packing with multiple competing length scales (8–10, 23, 24), reconfiguration through mechanical instabilities of periodic structures (20, 25, 26), and helix formation of flexible cylinders through inter- and intracylinder interactions (27, 28). In addition, the system of a broken chiral symmetry often consists of domains of opposite handedness with defects separating the domains.Liquid crystals (LCs) are soft materials composed of anisotropic mesogens that provide remarkable examples of chiral symmetry breaking arising from elastic anisotropy (29–42). In essence, an LC can minimize elastic free energy by organizing its achiral units into chiral structures, such as helices and chiral layers, that incorporate twist deformation (7, 8). The elastic free energy describing nematic LC deformations depends on so-called splay, twist, bend, and saddle-splay elastic moduli, and when twist deformation is comparatively easy, twisting can relieve strong splay and/or bend deformation and lead to production of equilibrium chiral structures (29, 32, 35–38). Similarly, saddle-splay deformation can stabilize chiral structures (43–46).Elasticity-driven chiral symmetry breaking is perhaps most readily manifested in confined LCs (31–43), wherein surface anchoring imposes a preferred angle for LC mesogens at the interface of the confining boundary. Topological defects enforced by boundary conditions can play a key role in the symmetry breaking as well, because energetically costly deformations are often concentrated in the vicinity of the defects (35–37). A simple example of this phenomenon is found in spherical LC droplets with planar anchoring; here, two surface point defects, called Boojums, cause the director to adopt a twisted bipolar configuration, in which energetically cheap twist deformations relieve strong splay deformation near the Boojums.In this paper, we introduce chiral symmetry-broken configurations of nematic LCs in a cylindrical confinement geometry, and we explore the energetics of the configurations and their defects. This general class of configuration has been investigated in cylinders (47–52). However, this system differs significantly from earlier work. The configurations that we report on have homeotropic boundary conditions, and their chirality is not of molecular origin (i.e., handedness is not derived from chiral mesogens or dopants). Our chiral symmetry-breaking experiments use Sunset Yellow FCF (SSY), a lyotropic chromonic LC (LCLC) with small twist elastic constant, in polymer-coated capillaries. SSY is composed of columnar aggregates of organic, plank-like molecules in water. The conformal polymer coating is prepared through chemical vapor deposition. The coating induces homeotropic anchoring of the aggregates on the cylinder surfaces through noncovalent interactions (53) thereby enabling the experimental studies of LCLCs confined in curved geometries with homeotropic alignment. Other than for their biocompatibility (54, 55), LCLCs are known for their very small twist modulus compared with splay and bend moduli; this property renders LCLCs susceptible to spontaneous chiral symmetry breaking (56, 57).Nematic SSY was found to exhibit two different configurations in the cylinder: one twisted and escaped radial (TER) and one with a double helix of disclinations. The samples also contained a variety of chiral defects originating from symmetry breaking. We investigate their structure and energetics using polarized optical microscopy (POM), numerical calculations of director configurations based on elastic free energies, and Jones matrix-simulated optical textures. The chiral director configurations and defects provide a fascinating example of chiral symmetry breaking arising from elastic anisotropy and show the consequences of a delicate interplay between anisotropic elasticity, boundary conditions, chirality, and topological defects.     

Probing the Texture of the Calamitic Liquid Crystalline Dimer of 4-(4-Pentenyloxy)benzoic Acid

The liquid crystalline dimer of 4-(4-pentenyloxy)benzoic acid, a member of the n-alkoxybenzoic acid homologous series, was synthesized using potassium carbonate supported on alumina as catalyst. The acid dimer complex exhibited three mesophases; identified as nematic, smectic X1 and smectic X2. Phase transition temperatures and the corresponding enthalpies were recorded using differential scanning calorimetry upon both heating and cooling. The mesophases were identified by detailed texture observations by variable temperature polarized light microscopy. The nematic phase was distinguished by a fluid Schlieren texture and defect points (four and two brushes) while the smectic phases were distinguished by rigid marble and mosaic textures, respectively.     

Symmetry breaking in smectics and surface models of their singularities

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, whereas disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need to add compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.     

Scaling and spontaneous symmetry restoring of topological defect dynamics in liquid crystal

Topological defects—locations of local mismatch of order—are a universal concept playing important roles in diverse systems studied in physics and beyond, including the universe, various condensed matter systems, and recently, even life phenomena. Among these, liquid crystal has been a platform for studying topological defects via visualization, yet it has been a challenge to resolve three-dimensional structures of dynamically evolving singular topological defects. Here, we report a direct confocal observation of nematic liquid crystalline defect lines, called disclinations, relaxing from an electrically driven turbulent state. We focus in particular on reconnections, characteristic of such line defects. We find a scaling law for in-plane reconnection events, by which the distance between reconnecting disclinations decreases by the square root of time to the reconnection. Moreover, we show that apparently asymmetric dynamics of reconnecting disclinations is actually symmetric in a comoving frame, in marked contrast to the two-dimensional counterpart whose asymmetry is established. We argue, with experimental supports, that this is because of energetically favorable symmetric twist configurations that disclinations take spontaneously, thanks to the topology that allows for rotation of the winding axis. Our work illustrates a general mechanism of such spontaneous symmetry restoring that may apply beyond liquid crystal, which can take place if topologically distinct asymmetric defects in lower dimensions become homeomorphic in higher dimensions and if the symmetric intermediate is energetically favorable.

Topologically nontrivial configurations of order, called topological defects, may appear generically and spontaneously when order is formed. As such, topological defects have been studied in diverse disciplines (1, 2), including cosmology (3), crystals and liquid crystals (2), superconductivity and superfluid (4–9), and biology (10–19) to name but a few. While there exist various kinds of defects characterized by different symmetries and properties, defects may also enjoy common properties across different disciplines. In this context, liquid crystal has the advantage that it is amenable to direct optical observations; various compounds and techniques exist; and as a soft matter system, it shows large response to external fields, being suitable for studying nonequilibrium and nonlinear effects (2, 20). This advantage has been recognized and used for decades, with a notable example of observing liquid crystal defects to test predictions for cosmic strings (21). Moreover, the scope of studies of liquid crystalline defects has been recently extended remarkably, including the use of defects as templates for molecular self-assembly (22) and the recent surge of investigations of active nematic systems bearing relevance to life phenomena (10–19).Despite this history, resolving fully three-dimensional (3D) structures of liquid crystal defects has not been straightforward, even for the simplest kind of defects, namely nematic disclination lines. Well-known techniques for 3D observation of defects and other orientational structures are fluorescence confocal polarizing microscopy (23, 24) and two- or three-photon excitation fluorescence polarizing microscopy (25–27). Both techniques allow one to reconstruct the 3D structure of the director field, by which one can determine the position and structure of defects in principle. To do so, however, one needs to reduce the effect of defocusing and polarization changes due to the birefringence of liquid crystal. For singular defects, such as nematic disclinations, scattering at the core gives another difficulty. The effect of birefringence can be significantly reduced by partial polymerization of the medium (28), but this cannot be used to study dynamics of defects.Here, we propose a method to capture dynamically evolving 3D structures of nematic disclination lines by using confocal microscopy and a recently reported accumulation of fluorescent dyes around the singular core of defects (29). This method allows us to visualize the disclinations directly (Fig. 1), without reconstructing and analyzing the director field. Using this technique, we observe reconnections of disclinations—a hallmark of such topological defect lines—and characterize the reconnection dynamics in terms of scaling and symmetry.Open in a separate windowFig. 1.Reconnections and loop shrinkage. (A–C) Sketches of an in-plane reconnection (A), an intersecting reconnection (B), and a loop shrinkage (C). (D–F) Confocal observations of an in-plane reconnection (D), an intersecting reconnection (E), and a loop shrinkage (F) (Movies S1–S4). E, Insets display side views of the event shown in E. (Scale bars: D–F, 50 μm; E, Insets, 20 μm.).     

Polar in-plane surface orientation of a ferroelectric nematic liquid crystal: Polar monodomains and twisted state electro-optics

We show that surface interactions can vectorially structure the three-dimensional polarization field of a ferroelectric fluid. The contact between a ferroelectric nematic liquid crystal and a surface with in-plane polarity generates a preferred in-plane orientation of the polarization field at that interface. This is a route to the formation of fluid or glassy monodomains of high polarization without the need for electric field poling. For example, unidirectional buffing of polyimide films on planar surfaces to give quadrupolar in-plane anisotropy also induces macroscopic in-plane polar order at the surfaces, enabling the formation of a variety of azimuthal polar director structures in the cell interior, including uniform and twisted states. In a π-twist cell, obtained with antiparallel, unidirectional buffing on opposing surfaces, we demonstrate three distinct modes of ferroelectric nematic electro-optic response: intrinsic, viscosity-limited, field-induced molecular reorientation; field-induced motion of domain walls separating twisted states of opposite chirality; and propagation of polarization reorientation solitons from the cell plates to the cell center upon field reversal. Chirally doped ferroelectric nematics in antiparallel-rubbed cells produce Grandjean textures of helical twist that can be unwound via field-induced polar surface reorientation transitions. Fields required are in the 3-V/mm range, indicating an in-plane polar anchoring energy of w_P ∼3 × 10⁻³ J/m².

Nematic liquid crystals (LCs) are useful because of their facile collective response to applied fields and to surface forces (1). In a liquid crystal, the bulk response is the long-ranged deformation of a fluid, elastic field of molecular orientation, on which confining surfaces establish geometrical and topological structural constraints. In the realm of electro-optics, these two basic elements of LC phenomenology have been combined to create LC display technology (2), thereby enabling the portable computing revolution of the 20th century (3). In this development and until very recently, nematic electro-optics has been based on bulk dielectric alignment, in which a quadrupolar coupling to applied electric field induces polarization in a nonpolar LC to generate torque and molecular reorientation. Surface interactions employed to achieve desirable device structures are similarly quadrupolar, with common treatments such as buffing (4) or photo-alignment (5–8) described by the Rapini–Papoular (RP) model (9) and its variants.Nematic LCs are fluids having internal long-range orientational ordering. In statistical mechanical terms, because the isotropic-to-nematic phase transition breaks orientational symmetry, it yields Goldstone modes in the nematic, describing spatial variation of the director, n(r), the local average molecular orientation. Because of the full orientational symmetry of the isotropic phase, in the nematic phase the director has no globally preferred orientation and therefore the harmonic (elastic) energy cost of orientational variation of wavevector q decreases to zero as Kq² at long wavelengths, where K is the orientational (Frank) elastic constant. A bulk nematic sample can be oriented by providing an arbitrarily small force, for example an arbitrarily small applied electric or magnetic field, which couples to nematic orientation via quadrupolar dielectric or diamagnetic anisotropy. The nematic order is similarly infinitely responsive to boundary conditions imposed by surfaces on which there is orientational anisotropy. Because the nematic is a fluid, these conditions make it possible to put a nematic in a container, have it spontaneously anneal into a space-filling, three-dimensional (3D) director orientation structure dictated by the bounding surfaces, and have this structure respond in a predictable way to applied field. In practice, to be useful in applications, the surfaces and fields must be strong enough to eliminate defects and to produce sufficiently fast reorientations of the director.A novel nematic LC phase (10–13) has recently been shown to be a ferroelectric nematic (N_F) (14), offering a variety of opportunities to exploit LC field and surface phenomena in new ways. The ferroelectric nematic is a 3D liquid with a macroscopic electric polarization P(r) (14). On the nanoscale, each molecular dipole is constrained to be nearly parallel to its molecular steric long axis, which translates macroscopically into a strong orientational coupling making P(r) locally parallel to ±n(r), the local average molecular long axis orientation and uniaxial optic axis of the phase (14). The polarization thus endows the N_F with coupling between n(r) and applied electric field, E, that is linear and is dominant over the dielectric coupling at low E. The N_F phase exhibits self-stabilized, spontaneous polar ordering that is nearly complete (12, 14), with a polar order parameter, P = ⟨cos (β_i)⟩ ∼0.9, where β_i is the angle between a typical molecular dipole and the local average polarization density P. The resulting large spontaneous polarization (P ∼6 µC/cm²) enables field-induced nematic director reorientation and an associated electro-optic response with applied fields in typical cells as small as ∼1 V/cm, a thousand times smaller than those used to reorient dielectric nematics.The polar nature of the N_F also results in transformative changes in the interaction of the LC with bounding surfaces, a key aspect of nematic LC science and its potential for technology. Here, we demonstrate that structuring of the vectorial orientation distribution of a 3D volume of polar molecules can be achieved by controlling the polarity of its 2D bounding surfaces. In the simplest example, if the orientation of the preferred polarization is identical on the surfaces of the two parallel glass plates forming a cell, then the N_F volume polarization can be similarly oriented, that is, poled into a uniform orientation by the surfaces, without the need for an applied field.Materials with spontaneous vectorial order such as ferromagnets and ferroelectrics minimize their energy by breaking up into domains of different orientation of their magnetization, M(r), or polarization, P(r), respectively, with these fields aligned locally parallel to the domain boundaries in order to minimize the energy of the internal and external magnetic or electric fields they produce. Intentionally disrupting this domain structure by applying an external field (“field poling”) is a key process in the use of such materials, e.g., putting an iron rod in a magnetic field to create a bar magnet (15), or actively reversing the polarization of a ferroelectric nanocrystal that serves as a data element in nonvolatile solid-state memories (16). Field poling of soft materials, such as the corona poling of chromophore-containing polymers to generate poled monodomains for nonlinear optical and electronic electro-optical applications, has been less successful because of the high fields required (17, 18). In ferroelectric nematics, in contrast, we find that polar aligning surfaces can be used to achieve uniform alignment of their nearly saturated bulk polarization, in the absence of an applied electrical poling field.In a uniaxial (C_∞ symmetric) ferroelectric nematic, the reduction in symmetry associated with the appearance of the bulk polarization, P(r), yields a macroscopic coupling of P to applied field E, with a corresponding bulk energy density U_PE = −P⋅E. In materials where the net molecular dipole is nearly parallel to the steric long axis of the molecule, P(r) is macroscopically constrained to be parallel to ±n(r) by an orientational energy of the form U_Pn = −u_Pn(n⋅v)², where we define a unit vector polar director v(r) = P(r)/P. The energy density coefficient u_Pn can be estimated as u_Pn ∼k_BT/vol where vol is a molecular volume. If we apply a step change in the orientation of P(r) at x = 0, then n(r) will follow within a distance |x| = 𝜉 ∼√(K/u_Pn), which will be of molecular dimensions. v(r) and ±n(r) are therefore essentially locked together in orientation on the macroscopic scale, so that if a field is applied, the response is generally to reorient n(r) by reorienting P(r). An exception to this is the movement of pure polarization reversal (PPR) walls, which flip P by 180° with no reorientation of n (14).     

Polyoxomolybdate Layered Crystals Constructed from a Heterocyclic Surfactant: Syntheses,Pseudopolymorphism and Introduction of Metal Cations

Crystals with layered structures are crucial for the construction of functional materials exhibiting intercalation, ionic conductivity, or emission properties. Polyoxometalate crystals hybridized with surfactant cations have distinct layered packings due to the surfactants which can form lamellar structures. Introducing metal cations into such polyoxometalate-surfactant hybrid crystals is significant for the addition of specific functions. Here, polyoxomolybdate–surfactant hybrid crystals were synthesized as single crystals, and unambiguously characterized by X-ray structure analyses. Octamolybdate ([Mo₈O₂₆]^4–, Mo₈) and heterocyclic surfactant of 1-dodecylpyridinium (C₁₂py) were employed. The hybrid crystals were composed of α-type and β-type Mo₈ isomers. Two crystalline phases containing α-type Mo₈ were obtained as pseudopolymorphs depending on the crystallization conditions. Crystallization with the presence of rubidium and cesium cations caused the formation of metal cation-introduced hybrid crystals comprising β-Mo₈ (C₁₂py-Rb-Mo₈ and C₁₂py-Cs-Mo₈). The yield of the C₁₂py-Rb-Mo₈ hybrid crystal was almost constant within crystallization temperatures of 279–303 K, while that of C₁₂py-Cs-Mo₈ decreased over 288 K. This means that the C₁₂py-Mo₈ hybrid crystal can capture Rb⁺ and Cs⁺ from the solution phase into the solids as the C₁₂py-Rb-Mo₈ and C₁₂py-Cs-Mo₈ hybrid crystals. The C₁₂py-Mo₈ hybrid crystals could be applied to ion-capturing materials for heavy metal cation removal.