Chiral symmetry breaking and surface faceting in chromonic liquid crystal droplets with giant elastic anisotropy

Spontaneous assembly of condensate networks during the demixing of structured fluids

Liquid-liquid phase separation, whereby two liquids spontaneously demix, is ubiquitous in industrial, environmental, and biological processes. While isotropic fluids are known to condense into spherical droplets in the binodal region, these dynamics are poorly understood for structured fluids. Here, we report the unique observation of condensate networks, which spontaneously assemble during the demixing of a mesogen from a solvent. Condensing mesogens form rapidly elongating filaments, rather than spheres, to relieve distortion of an internal smectic mesophase. As filaments densify, they collapse into bulged discs, lowering the elastic free energy. Additional distortion is relieved by retraction of filaments into the discs, which are straightened under tension to form a ramified network. Understanding and controlling these dynamics may provide different avenues to direct pattern formation or template materials.

Near-unity angular anisotropy of circularly polarized luminescence from microspheres of monodispersed chiral conjugated polymers

A microsphere, assembled from a chiral π-conjugated polymer with narrow polydispersity, features a well-organized twisted-bipolar structure and exhibits highly biased circularly polarized luminescence (CPL). The CPL emitted toward the equatorial direction is 61-fold greater than that emitted along the zenith direction, which is the highest anisotropy among existing microscopic CPL emitters.

Confinement twists achiral liquid crystals and causes chiral liquid crystals to twist in the opposite handedness: cases in and around sessile droplets

We study the chiral symmetry breaking and metastability of confined nematic lyotropic chromonic liquid crystals (LCLCs) with and without chiral dopants. The isotropic-nematic coexistence phase of the LCLC renders two confining geometries: sessile isotropic (I) droplets surrounded by the nematic (N) phase and sessile nematic droplets immersed in the isotropic background. In the achiral system with no dopants, LCLC's elastic anisotropy and topological defects induce a spontaneous twist deformation to lower the energetic penalty of splay deformation, resulting in spiral optical textures under crossed polarizers both in the I-in-N and N-in-I systems. While the achiral system exhibits both handednesses with an equal probability, a small amount of the chiral dopant breaks the balance. Notably, in contrast to the homochiral configuration of a chirally doped LCLC in the bulk, the spiral texture of the disfavored handedness appears with a finite probability both in the I-in-N and N-in-I systems. We propose director field models explaining how chiral symmetry breaking arises by the energetics and the opposite-twist configurations exist as meta-stable structures in the energy landscape. These findings help us create and control chiral structures using confined LCs with large elastic anisotropy.

Flow-induced periodic chiral structures in an achiral nematic liquid crystal

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.

Variations in activation energy and nuclei size during nucleation explain chiral symmetry breaking

We show that variations in enantiomer nuclei size and activation energy during the nucleation stage of crystallization are responsible for the chiral symmetry breaking resulting in excess of one of the possible enantiomers with respect to the other. By understanding the crystallisation process as a non-equilibrium self-assembly process, we quantify the enantiomeric excess through the probability distribution of the nuclei size and activation energy variations which are obtained from the free energy involved in the nucleation stage of crystallisation. We validate our theory by comparing it to Kondepudi et al. previous experimental work on sodium chlorate crystallisation. The results demonstrate that the self-assembly of enantiomeric crystals provides an explanation for chiral symmetry breaking. These findings could have practical applications for improving the production of enantiopure drugs in the pharmaceutical industry, as well as for enhancing our understanding of the origins of life since enantiomeric amino acids and monosaccharides are the building blocks of life.

Sunset Yellow Confined in Curved Geometry: A Microfluidic Approach

The behavior of lyotropic chromonic liquid crystals (LCLCs) in confined environments is an interesting research field that still awaits exploration, with multiple key variables to be uncovered and understood. Microfluidics is a highly versatile technique that allows us to confine LCLCs in micrometric spheres. As microscale networks offer distinct interplays between the surface effects, geometric confinement, and viscosity parameters, rich and unique interactions emerging at the LCLC-microfluidic channel interfaces are expected. Here, we report on the behavior of pure and chiral doped nematic Sunset Yellow (SSY) chromonic microdroplets produced through a microfluidic flow-focusing device. The continuous production of SSY microdroplets with controllable size gives the possibility to systematically study their topological textures as the function of their diameters. Indeed, doped SSY microdroplets produced via microfluidics, show topologies that are typical of common chiral thermotropic liquid crystals. Furthermore, few droplets exhibit a peculiar texture never observed for chiral chromonic liquid crystals. Finally, the achieved precise control of the produced LCLC microdroplets is a crucial step for technological applications in biosensing and anticounterfeiting.

Chiral symmetry breaking induced by energy dissipation

Spontaneous chiral symmetry breaking is observed in a wide variety of systems on very different scales, from the subatomic to the cosmological. Despite its generality and importance for a large number of applications, its origin is still a matter of debate. It has been shown that the existence of a difference between the energies of the intermediate states of optical enantiomers leads to disparate production rates and thus to symmetry breaking. However, it is still unclear why this occurs. We measured for the first time the optical rotation angle of NaClO₃ enantiomeric crystals in solution during their formation and found that the amount of energy needed to induce the enantiomeric excess is exactly the same as the energy dissipated per mole of solid salt calculated from the entropy production obtained from the proposed model. The irreversible nature of the process leading to entropy production thus explains the chiral symmetry breaking in the salt crystals studied. The proposed method could be used to explain the formation of self-organised structures generated by self-assembly of enantiomers arising from chiral symmetry breaking, such as those emerging in the production of advanced materials and synthetic biological tissues.

Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with an isotropic phase

Nuclei of ordered materials emerging from the isotropic state usually show a shape topologically equivalent to a sphere; the well-known examples are crystals and nematic liquid crystal droplets. In this work, we explore experimentally and theoretically the toroidal in shape nuclei of columnar lyotropic chromonic liquid crystals coexisting with the isotropic phase. The geometry of these toroids depends strongly on concentrations of the disodium cromoglycate (DSCG) and the crowding agent, polyethylene glycol (PEG). High concentrations of DSCG and PEG result in thick toroids with small central holes, while low concentrations yield thin toroids with wide holes. The multitude of the observed shapes is explained by the balance of bending elasticity and anisotropic interfacial tension.

Giant director fluctuations in liquid crystal drops

We report the discovery and elucidation of giant spatiotemporal orientational fluctuations in nematic liquid crystal drops with radial orientation of the nematic anisotropy axis producing a central "hedgehog" defect. We study the spatial and temporal properties of the fluctuations experimentally using polarized optical microscopy, and theoretically, by calculating the eigenspectrum of the Frank elastic free energy of a nematic drop of radius R_{2}, containing a spherical central core of radius R_{1} and constrained by perpendicular boundary conditions on all surfaces. We find that the hedgehog defect with radial orientation has a complex excitation spectrum with a single critical mode whose energy vanishes at a critical value μ_{c} of the ratio μ=R_{2}/R_{1}. When μ<μ_{c}, the mode has positive energy, indicating that the radial hedgehog state is stable; when μ>μ_{c}, it has negative energy indicating that the radial state is unstable to the formation of a lower-energy state. This mode gives rise to the large-amplitude director fluctuations we observe near the core, for μ near μ_{c}. A collapse of the experimental data corroborates model predictions for μ<μ_{c} and provides an estimate of the defect core size.

Tomographic measurement of dielectric tensors at optical frequency

The dielectric tensor is a physical descriptor of fundamental light-matter interactions, characterizing anisotropic materials with principal refractive indices and optic axes. Despite its importance in scientific and industrial applications ranging from material science to soft matter physics, the direct measurement of the three-dimensional dielectric tensor has been limited by the vectorial and inhomogeneous nature of light scattering from anisotropic materials. Here, we present a dielectric tensor tomographic approach to directly measure dielectric tensors of anisotropic structures including the spatial variations of principal refractive indices and directors. The anisotropic structure is illuminated with a polarized plane wave with various angles and polarization states. Then, the scattered fields are holographically measured and converted into vectorial diffracted field components. Finally, by inversely solving a vectorial wave equation, the three-dimensional dielectric tensor is reconstructed. Using this approach, we demonstrate quantitative tomographic measurements of various nematic liquid-crystal structures and their fast three-dimensional non-equilibrium dynamics.

Liquid Crystal Elastomer Twist Fibers toward Rotating Microengines

Untethered twist fibers do not require end-anchoring structures to hold their twist orientation and offer simple designs and convenient operation. The reversible responsiveness of these fibers allows them to generate torque and rotational deformation continuously upon the application of external stimuli. The fibers therefore have potential in rotating microengines. In practical applications, high torque and rotational deformation are desirable to meet work capacity requirements. However, the simultaneous endowment of reversible responsiveness and high rotational performance to untethered twist fibers remains a challenge. In this study, a liquid crystal elastomer twist fiber (LCETF) is designed and developed with a fixed twisting alignment of mesogens to provide untethered and reversible responsiveness. Outstanding rotational performance can be achieved when the mesogenic orientation is disrupted through heat triggering. Owing to the significant intrinsic contractile ratio of the LCE material, the rotational deformation of the LCETF can reach 243.6° mm^-1 . More importantly, the specific torque can reach 10.1 N m kg^-1 , which exceeds previously reported values. In addition, the LCETF can be exploited in a rotating microengine to convert heat into electricity with an induction voltage as high as 9.4 V. This work broadens the applications of LCEs for energy harvesters, micromachines, and soft robots.

Spherical Confinement of Chromonics: Effects of a Chiral Aminoacid

Induced or spontaneous chirality in natural systems is an intriguing issue. In recent years, a lot of attention has been focused on chirality of chromonic liquid crystals, a class of materials that is able to self-assemble in columnar structures. However, the mechanism involved in the arising of chirality in these materials, that starts at the molecular level and controls the supramolecular structure, is poorly understood; however, it is certainly affected by ionic strength. In this work we present the results obtained doping Cromolyn, a chromonic material, with a strong helical-twisting-power peptide, and confining it in a spherical geometry. We demonstrate, by means of optical polarized microscopy and structural analysis, that both the geometrical constraint and the presence of the chiral dopant enhance the chiral effect; we also demonstrate that they favor the rise of a highly ordered helical superstructure, that may be optimized upon adding an ionic dye to the system. Finally, we report a procedure for the preparation of free-standing polymeric films, embedding and preserving the microspheres, and paving the way for the creation of biocompatible and eco-friendly optical devices to be used in the sensor and anticounterfeiting fields.

Rods in a lyotropic chromonic liquid crystal: emergence of chirality, symmetry-breaking alignment, and caged angular diffusion

In lyotropic chromonic liquid crystals (LCLCs), twist distortion of the nematic director costs much less energy than splay or bend distortion. This feature leads to novel mirror-symmetry breaking director configurations when the LCLCs are confined by interfaces or contain suspended particles. Spherical colloids in an aligned LCLC nematic phase, for example, induce chiral director perturbations ("twisted tails"). The asymmetry of rod-like particles in an aligned LCLC offer a richer set of possibilities due to their aspect ratio (α) and mean orientation angle (〈θ〉) between their long axis and the uniform far-field director. Here we report on the director configuration, equilibrium orientation, and angular diffusion of rod-like particles with planar anchoring suspended in an aligned LCLC. Video microscopy reveals, counterintuitively, that two-thirds of the rods have an angled equilibrium orientation (〈θ〉 ≠ 0) that decreases with increasing α, while only one-third of the rods are aligned (〈θ〉 = 0). Polarized optical video-microscopy and Landau-de Gennes numerical modeling demonstrate that the angled and aligned rods are accompanied by distinct chiral director configurations. Angled rods have a longitudinal mirror plane (LMP) parallel to their long axis and approximately parallel to the substrate walls. Aligned rods have a transverse and longitudinal mirror plane (TLMP), where the transverse mirror plane is perpendicular to the rod's long axis. Effectively, the small twist elastic constant of LCLCs promotes chiral director configurations that modify the natural tendency of rods to orient along the far-field director. Additional diffusion experiments confirm that rods are angularly confined with strength that depends on α.

Microscopic modelling of nematic elastic constants beyond Straley theory

Recent findings on various classes of nematics, whose microscopic structure differs from the prototypical rod-like shape, evidence unusual elastic properties, which challenge existing theories. Here we develop a theoretical and numerical methodology for the calculation of Frank elastic constants, accounting for the coupling between the molecular shape and each specific deformation mode. This is done in the framework of Onsager-Straley's second-virial theory, using a non-local form of the orientational distribution function. The comparison between two benchmark systems, a straight and a bent rod, allows us to illustrate the distinct features of this approach, which include additional order parameters induced by the deformation and, related to this, an ideal contribution to the deformation free energy. Then, using a simple system that can be seen as a minimalist model of liquid crystal trimers, we discuss the impact of different molecular conformations on elastic constants.

Lattice Boltzmann and Jones matrix calculations for the determination of the director field structure in self-propelling nematic droplets

Nematic droplets immersed in aqueous surfactant solutions can show a self-propelled motion induced by a Marangoni flow in the droplet surface. In addition to the self-propulsion, the Marangoni flow induces within the droplet a convective flow which considerably influences the nematic director field of the droplet. We report numerical simulations aiming at the determination of the director field in the self-propelling droplet. The convective flow and the resulting structure of director field are described by a lattice Boltzmann model. The reliability of the obtained structures is proved by subsequent Jones matrix calculations which enable the direct comparison of experimental polarizing microscopy images of self-propelling droplets with calculated images based on the simulated structures.

Shape bistability in 2D chromonic droplets

An extensive experimental study of the shapes of two-dimensional bipolar droplets of the chromonic nematic phase of disodium cromoglycate (DSCG) sandwiched between glass plates, by Kimet alwas published in (2013J. Phys.: Condens. Matter25404202). The paper includes a mathematical model of this system. We have extended this study by further theoretical modelling. Our results are in good, quantitative agreement with the experimental data. The model has produced what promises to be a more accurate estimate for the isotropic surface tension at the nematic/isotropic solution interface-and predicts a regime of shape bistability (which has not yet been observed) for larger droplets, where tactoids (pointed, zeppelin-shaped droplets) and smooth-edged discoids can coexist in equilibrium. The general method presented in this paper is also applied to the tactoids formed by F-actin filaments in solution, for which an estimate is given for the value of the isotropic surface tension at the nematic/isotropic interface.

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Twisted loxodromes in spindle-shaped polymer nematics

We develop an energetic model that captures the twisting behavior of spindle-shaped polymer microparticles with nematic ordering, which display remarkably different twisting behavior to ordinary nematics confined to spindles. We have previously developed a geometric model of the twisting, based on experimental observations, in which we showed that the twist pattern follows loxodrome spirals [Ansell, et al., Phys. Rev. Lett., 2019, 123, 157801]. In this study, we first consider a spindle-shaped surface and show that the loxodrome twisting behavior of our system can be captured by the Frank free energy of the nematic with an additional term constraining the length of the integral curves of the system. We then extend the ideas of this model to the bulk and explore the parameter space for which the twisted loxodrome solution is energetically favorable.

Robust Angular Anisotropy of Circularly Polarized Luminescence from a Single Twisted-Bipolar Polymeric Microsphere

It has long been surmised that the circular polarization of luminescence (CPL) emitted by a chiral molecule or a molecular assembly should vary with the direction in which the photon is emitted. Despite its potential utility, this anisotropic CPL has not yet been demonstrated at the level of single molecules or supramolecular assemblies. Here we show that conjugated polymers bearing chiral side chains self-assemble into solid microspheres with a twisted bipolar interior, which are formed via liquid-liquid phase separation and subsequent condensation into a cholesteric lyotropic liquid crystalline mesophase. The resultant microspheres, when dispersed in methanol, exhibit CPL with a g_lum value as high as 0.23. The microspheres are mechanically robust enough to be handled with a microneedle under ambient conditions, allowing comprehensive examination of the angular anisotropy of CPL. The single microsphere is found to exhibit distinct angularly anisotropic birefringence and CPL with g_lum up to ∼0.5 in the equatorial plane, which is 2.5-fold greater than that along the polar axis. Such optically anisotropic solid materials are important for the application to next-generation microlight-emitting and visualizing devices as well as for fundamental optics studies of chiral light-matter interaction.

Emergence and stabilization of transient twisted defect structures in confined achiral liquid crystals at a phase transition

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

Nematic tactoid population

Tactoids are pointed, spindlelike droplets of nematic liquid crystal in an isotropic fluid. They have long been observed in inorganic and organic nematics, in thermotropic phases as well as lyotropic colloidal aggregates. The variational problem of determining the optimal shape of a nematic droplet is formidable and has only been attacked in selected classes of shapes and director fields. Here, by considering a special class of admissible solutions for a bipolar droplet, we study the prevalence in the population of all equilibrium shapes of each of the three that may be optimal (tactoids primarily among them). We show how the prevalence of a shape is affected by a dimensionless measure α of the drop's volume and the ratios k_{24} and k_{3} of the saddle-splay constant K_{24} and the bending constant K_{33} of the material to the splay constant K_{11}. Tactoids, in particular, prevail for α⪅16.2+0.3k_{3}-(14.9-0.1k_{3})k_{24}. Our class of shapes (and director fields) is sufficiently different from those employed so far to unveil a rather different role of K_{24}.

Production of giant unilamellar vesicles and encapsulation of lyotropic nematic liquid crystals

We describe a modified microfluidic method for making Giant Unilamellar Vesicles (GUVs) via water/octanol-lipid/water double emulsion droplets. At a high enough lipid concentration we show that the de-wetting of the octanol from these droplets occurs spontaneously (off-chip) without the need to use shear to aid the de-wetting process. The resultant mixture of octanol droplets and GUVs can be separated by making use of the buoyancy of the octanol. A simpler microfluidic device and pump system can be employed and, because of the higher flow-rates and much higher rate of formation of the double emulsion droplets (∼1500 s-1 compared to up to ∼75 s-1), it is easier to make larger numbers of GUVs and larger volumes of solution. Because of the potential for using GUVs that incorporate lyotropic nematic liquid crystals in biosensors we have used this method to make GUVs that incorporate the nematic phases of sunset yellow and disodium chromoglycate. However, the phase behaviour of these lyotropic liquid crystals is quite sensitive to concentration and we found that there is an unexpected spread in the concentration of the contents of the GUVs obtained.

Interplay between Confinement, Twist Elasticity, and Intrinsic Chirality in Micellar Lyotropic Nematic Liquid Crystals

Recent studies have shown that lyotropic nematic liquid crystals (LLCs) are exceptional in their viscoelastic behavior. In particular, LLCs display a remarkable softness to twist deformations, which may lead to chiral director configurations under achiral confinement despite the absence of intrinsic chirality. The twisted escaped radial (TER) and the twisted polar (TP) are the two representative reflection symmetry breaking director configurations in the case of cylindrical confinement with homeotropic anchoring. We demonstrate how such reflection symmetry breaking of micellar LLCs under cylindrical confinement is affected by intrinsic chirality, introduced by the addition of a chiral dopant. Similarities and differences between the effects of intrinsic chirality on the defect-free TER configuration, and on the TP configuration incorporating two half-unit twist disclination lines, are discussed. In the TP case, topological constraints facilitate stable heterochiral systems even in the presence of a small amount of chiral dopant, with unusual regions of rapidly reversing handedness between homochiral domains. At moderate dopant concentrations, the TP structure becomes homochiral. At high dopant concentrations, for which the induced cholesteric pitch is much smaller than the diameter of the capillary, the cholesteric fingerprint structure develops.

A chiral-racemic lyotropic chromonic liquid crystal system

The two main classes of liquid crystals are thermotropic (containing no solvent) and lyotropic (containing solvent). Both of these classes possess the nematic phase, the most simple of liquid crystal phases with only uniaxial orientational order. For both of these classes, if the constituent molecules are chiral or if a chiral dopant is added, the preferred direction of orientation rotates in helical fashion in what is called the chiral nematic phase. Recent research has shown that because the ordering entities of the two classes are quite different (molecules versus molecular assemblies), important differences in the properties of the nematic phase can result. While thermotropic chiral nematics have been extensively examined, less is known about lyotropic chiral nematics, especially for the most ideal case, a chiral-racemic system. Furthermore, none of the lyotropic chiral-racemic studies has included lyotropic chromonic liquid crystals, which are solutions of dyes, drugs, and nucleic acids. Inverse pitch measurements are reported for a chiral-racemic system of a chromonic liquid crystal across the entire chiral fraction range and over a 30 °C temperature interval. The inverse pitch depends linearly on chiral fraction and decreases with increasing temperature, indicating that achiral and chiral molecules participate in the assembly structure similarly. The helical twisting power is significantly larger than for other chiral lyotropic liquid crystals due to the very high scission energy of the investigated system.

Interplay of Particle Morphology and Director Distortions in Nematic Fluids

The existing microscopic theories for elasticity of nematics are challenged by recent findings on systems, whether bent molecules or semiflexible polymers, which do not comply with the model of rigid rodlike particles. Here, we propose an extension of Onsager-Straley second-virial theory, based on a model for the orientational distribution function that, through explicit account of the director profile along a particle, changes in the presence of deformations. The elastic constants reveal specific effects of particle morphology, which are not captured by the existing theories. This paves the way to microscopic modeling of the elastic properties of semiflexible liquid crystal polymers, which is a longstanding issue.

Time Dependent Lyotropic Chromonic Textures in Microfluidic Confinements

Nematic and columnar phases of lyotropic chromonic liquid crystals (LCLCs) have been long studied for their fundamental and applied prospects in material science and medical diagnostics. LCLC phases represent different self-assembled states of disc-shaped molecules, held together by noncovalent interactions that lead to highly sensitive concentration and temperature dependent properties. Yet, microscale insights into confined LCLCs, specifically in the context of confinement geometry and surface properties, are lacking. Here, we report the emergence of time dependent textures in static disodium cromoglycate (DSCG) solutions, confined in PDMS-based microfluidic devices. We use a combination of soft lithography, surface characterization, and polarized optical imaging to generate and analyze the confinement-induced LCLC textures and demonstrate that over time, herringbone and spherulite textures emerge due to spontaneous nematic (N) to columnar M-phase transition, propagating from the LCLC-PDMS interface into the LCLC bulk. By varying the confinement geometry, anchoring conditions, and the initial DSCG concentration, we can systematically tune the temporal dynamics of the N- to M-phase transition and textural behavior of the confined LCLC. Overall, the time taken to change from nematic to the characteristic M-phase textures decreased as the confinement aspect ratio (width/depth) increased. For a given aspect ratio, the transition to the M-phase was generally faster in degenerate planar confinements, relative to the transition in homeotropic confinements. Since the static molecular states register the initial conditions for LC flows, the time dependent textures reported here suggest that the surface and confinement effects—even under static conditions—could be central in understanding the flow behavior of LCLCs and the associated transport properties of this versatile material.

Periodic Arrays of Chiral Domains Generated from the Self-Assembly of Micropatterned Achiral Lyotropic Chromonic Liquid Crystal

Achiral building blocks forming achiral structures is a common occurrence in nature, while chirality emerging spontaneously from an achiral system is usually associated with important scientific phenomena. We report on the spontaneous chiral symmetry-breaking phenomena upon the topographic confinement of achiral lyotropic chromonic liquid crystals in periodically arranged micrometer scale air pillars. The anisotropic fluid arranges into chiral domains that depend on the arrangement and spacing of the pillars. We characterize the resulting domains by polarized optical microscopy, support their reconstruction by numerical calculations, and extend the findings with experiments, which include chiral dopants. Well-controlled and addressed chiral structures will be useful in potential applications like programmable scaffolds for living liquid crystals and as sensors for detecting chirality at the molecular level.

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.

Lyotropic Chromonic Liquid Crystals and Their Impurities Reveal the Importance of the Position of Functional Groups in Self-Assembly

We study the effect of purification and impurities on the self-assembly and phase behavior of lyotropic chromonic liquid crystals (LCLCs). LCLC molecules in water stack to form aggregates; then, the elongated nanoaggregates align to make liquid crystalline phases. Utilizing multiple experimental techniques, we unveil impurities in commercial Sunset Yellow FCF (SSY), a representative LCLC, and how the precipitation-based purification promotes the formation of the aggregates and mesophase. We further explore the roles of intrinsic impurities, i.e., byproducts of the SSY synthesis, whose molecular structures are almost identical to that of SSY but differ only in the number and position of sulfonate groups. Combining quantum chemical calculations of molecular structures and experimental investigation of aggregate structures and phase behavior, we propose that the impurities of the planar shapes behave as planar SSY, i.e., participating in aggregate formation, whereas the nonplanar one disrupts the nematic phase. These results highlight the critical roles of the impurities and deepen our understanding of self-assembled aggregates and their aligned mesophases.

Novel Trends in Lyotropic Liquid Crystals

We introduce and shortly summarize a variety of more recent aspects of lyotropic liquid crystals (LLCs), which have drawn the attention of the liquid crystal and soft matter community and have recently led to an increasing number of groups studying this fascinating class of materials, alongside their normal activities in thermotopic LCs. The diversity of topics ranges from amphiphilic to inorganic liquid crystals, clays and biological liquid crystals, such as viruses, cellulose or DNA, to strongly anisotropic materials such as nanotubes, nanowires or graphene oxide dispersed in isotropic solvents. We conclude our admittedly somewhat subjective overview with materials exhibiting some fascinating properties, such as chromonics, ferroelectric lyotropics and active liquid crystals and living lyotropics, before we point out some possible and emerging applications of a class of materials that has long been standing in the shadow of the well-known applications of thermotropic liquid crystals, namely displays and electro-optic devices.

Self-Assembly of Aqueous Soft Matter Patterned by Liquid-Crystal Polymer Networks for Controlling the Dynamics of Bacteria

The study of controlling the molecular self-assembly of aqueous soft matter is a fundamental scheme across multiple disciplines such as physics, chemistry, biology, and materials science. In this work, we use liquid-crystal polymer networks (LCNs) to control the superstructures of one aqueous soft material called lyotropic chromonic liquid crystals (LCLCs), which shows spontaneous orientational order by stacking the plank-like molecules into elongated aggregates. We synthesize a layer of patterned LCN films by a nematic liquid-crystal host in which the spatially varying molecular orientations are predesigned by plasmonic photopatterning. We demonstrate that the LCLC aggregates are oriented parallel to the polymer filaments of the LCN film. This patterned aqueous soft material shows immediate application for controlling the dynamics of swimming bacteria. The demonstrated control of the supramolecular assembly of aqueous soft matter by using a stimuli-responsive LCN film will find applications in designing dynamic advanced materials for bioengineering applications.

From Equilibrium Liquid Crystal Formation and Kinetic Arrest to Photonic Bandgap Films Using Suspensions of Cellulose Nanocrystals

The lyotropic cholesteric liquid crystal phase developed by suspensions of cellulose nanocrystals (CNCs) has come increasingly into focus from numerous directions over the last few years. In part, this is because CNC suspensions are sustainably produced aqueous suspensions of a fully bio-derived nanomaterial with attractive properties. Equally important is the interesting and useful behavior exhibited by solid CNC films, created by drying a cholesteric-forming suspension. However, the pathway along which these films are realized, starting from a CNC suspension that may have low enough concentration to be fully isotropic, is more complex than often appreciated, leading to reproducibility problems and confusion. Addressing a broad audience of physicists, chemists, materials scientists and engineers, this Review focuses primarily on the physics and physical chemistry of CNC suspensions and the process of drying them. The ambition is to explain rather than to repeat, hence we spend more time than usual on the meanings and relevance of the key colloid and liquid crystal science concepts that must be mastered in order to understand the behavior of CNC suspensions, and we present some interesting analyses, arguments and data for the first time. We go through the development of cholesteric nuclei (tactoids) from the isotropic phase and their potential impact on the final dry films; the spontaneous CNC fractionation that takes place in the phase coexistence window; the kinetic arrest that sets in when the CNC mass fraction reaches ∼10 wt.%, preserving the cholesteric helical order until the film has dried; the ’coffee-ring effect’ active prior to kinetic arrest, often ruining the uniformity in the produced films; and the compression of the helix during the final water evaporation, giving rise to visible structural color in the films.

Stable and Metastable Patterns in Chromonic Nematic Liquid Crystal Droplets Forced with Static and Dynamic Magnetic Fields

Spherical confinement of nematic liquid crystals leads to the formation of equilibrium director field configurations that include point and line defects. Driving these materials with flows or dynamic fields often results in the formation of alternative metastable states. In this article, we study the effect of magnetic field alignment, both under static and dynamic conditions, of nematic gems (nematic droplets in coexistence with the isotropic phase) and emulsified nematic droplets of a lyotropic chromonic liquid crystal. We use a custom polarizing optical microscopy assembly that incorporates a permanent magnet whose strength and orientation can be dynamically changed. By comparing simulated optical patterns with microscopy images, we measure an equilibrium twisted bipolar pattern within nematic gems that is only marginally different from the one reported for emulsified droplets. Both systems evolve to concentric configurations upon application of a static magnetic field, but behave very differently when the field is rotated. While the concentric texture within the emulsified droplets is preserved and only displays asynchronous oscillations for high rotating speeds, the nematic gems transform into a metastable untwisted bipolar configuration that is memorized by the system when the field is removed. Our results demonstrate the importance of boundary conditions in determining the dynamic behavior of confined liquid crystals even for configurations that share similar equilibrium bulk structures.

Molecular Dynamics Study of the Effect of l-Alanine Chiral Dopants on Diluted Chromonic Solutions

Atomistic molecular dynamics simulations have been performed for disodium cromoglycate (DSCG) chromonic solutions mixed with l-alanine chiral dopants. We study the fundamental molecular mechanisms induced by low concentrations of l-alanine on diluted DSCG solutions, including their effect on the chromonic aggregates, the solvent, and sodium counterions. Simulations reveal that l-alanine molecules primarily interact with DSCG stacks establishing salt bridges between their respective ammonium and carboxylate groups. Our results demonstrate that l-alanine and sodium counterions jointly establish an intricate network of noncovalent interactions around DSCG aggregates that decreases the global electrostatic repulsion of the chromonic system. Two possible structural effects in DSCG aggregates arise from this electronic stabilization: the increment of the total number of consecutively stacked aromatic planes per DSCG aggregate (intracolumnar effect) or the partial separation reduction between neighboring DSCG columnar sections due to the simultaneous bridging of intercolumnar DSCG carboxylate sites by sodium counterions, forming sodium bridges (intercolumnar effect). Sodium bridges may be responsible for the formation of stacking faults in DSCG aggregates in the form of lateral overlap junctions. This mechanism would explain the difference between lower X-ray correlation lengths with the expected persistence length in chromonics.

Effects of poly(ethylene glycol) on the wetting behavior and director configuration of lyotropic chromonic liquid crystals confined in cylinders

We investigate the effects of poly(ethylene glycol) (PEG) doping on nematic lyotropic chromonic liquid crystals (LCLCs) confined in a cylindrical cavity. First, PEG added to Sunset Yellow (SSY) renders confining glass surfaces nemato-phobic by adsorption. We also confirm that the grafting of PEG to bare glass surfaces changes them from nemato-philic to nemato-phobic. This change in the wetting behavior affects how nematic director configurations form and relax. Additionally, we observe that PEG-doped nematic SSY retains the double-twist director configuration as in the PEG-free case. However, the PEG-doped nematic SSY is accompanied by unprecedented domain-wall-like defects and heterogeneity in the director configuration. We propose multiple hypotheses on how PEG changes the director configuration, including the formation of meta-stable director configurations.

Effects of chiral dopants on double-twist configurations of lyotropic chromonic liquid crystals in a cylindrical cavity

We investigate how chiral dopants affect the chiral symmetry breaking of lyotropic chromonic liquid crystals (LCLCs) focusing on the double-twist (DT) director configurations in a cylindrical capillary. LCLCs of unusual elastic properties tend to exhibit chiral director configurations under confinement despite the absence of intrinsic chirality. The DT director configuration in a cylindrical cavity with a degenerate planar anchoring, resulting from the large saddle-splay-to-twist elastic modulus ratio, is a representative example. Here we start by reexamining the DT configuration of nematic disodium cromoglycate in a cylindrical capillary and estimate the ratio of saddle splay to bend modulus K_{24}/K_{3}=0.5±0.1. Additionally, we study the DT configurations of the chiral nematic LCLCs with chiral dopants. The DT configuration becomes homochiral when the dopant concentration surpasses the critical concentration. We characterize these chiral DT configurations and provide a theoretical model on their energetics. Finally, we observe how the enantiomeric excess of chiral dopants determines the director configuration when dopants of two different handednesses are mixed.

Ray-based optical visualisation of complex birefringent structures including energy transport

We propose an efficient method to simulate light propagation in lossless and non-scattering uniaxial birefringent media, based on a standard ray-tracing technique supplemented by a newly-derived transport equation for the electric field amplitude along a ray and a tailored interpolation algorithm for the reconstruction of the electromagnetic fields. We show that this algorithm is accurate in comparison to a full solution of Maxwell's equations when the permittivity tensor of the birefringent medium typically varies over a length much bigger than the wavelength. We demonstrate the usefulness of our code for soft matter by comparing experimental images of liquid crystal droplets with simulated bright-field optical micrographs, and conclude that our method is more general than the usual Jones method, which is only valid under polarised illumination conditions. We also point out other possible applications of our method, including liquid crystal based flat element design and diffraction pattern calculations for periodic liquid crystal samples.

Curved boundaries and chiral instabilities - two sources of twist in homeotropic nematic tori

Many liquid crystalline systems display spontaneous breaking of achiral symmetry, as achiral molecules aggregate into large chiral domains. In confined cylinders with homeotropic boundary conditions, chromonic liquid crystals - which have a twist elastic modulus which is at least an order of magnitude less than their splay and bend counter parts - adopt a twisted escaped radial texture (TER) to minimize their free energy, whilst 5CB - which has all three elastic constants roughly comparable - does not. In a recent series of experiments, we have shown that 5CB confined to tori and bent cylindrical capillaries with homeotropic boundary conditions also adopts a TER structure resulting from the curved nature of the confining boundaries [P. W. Ellis et al., Phys. Rev. Lett., 2018, 247803]. We shall call this microscopic twist, as the twisted director organization not only depends on the confinement geometry but also on the values of elastic moduli. Additionally, we demonstrate theoretically that the curved geometry of the boundary induces a twist in the escaped radial (ER) texture. Moving the escaped core of the structure towards the center of the torus not only lowers the splay and bend energies, but lowers the energetic cost of this distinct source for twist that we shall call geometric twist. As the torus becomes more curved, the ideal location for the escaped core approaches the inner radius of the torus.

Spherical-cap droplets of a photo-responsive bent liquid crystal dimer

Using a photo-responsive dimer exhibiting the transition between nematic (N) and twist-bend nematic (NTB) phases, we prepared spherical cap-shaped droplets on solid substrates exposed to air. The internal director structures of these droplets vary depending on the phase and on the imposed boundary conditions. The structural switching between the N and NTB phases was successfully performed either by temperature control or by UV light-irradiation. The N phase is characterized by an extremely small bend elastic constant K3, and surprisingly, we found that the droplet-air interface induces a planar alignment, in contrast to that seen for typical calamitic liquid crystals. As a consequence, the director configuration was stabilized in a structure substantially different from that normally found in conventional nematic liquid crystalline droplets. In the twist-bend nematic droplets characteristic structures with macroscopic length scales were formed, and they were well controlled by the droplet size. These results indicated that a continuum theory is effective in describing the stabilization mechanism of the macroscopic structure even in the twist-bend nematic liquid crystal droplets exhibiting director modulations on a scale of several molecular lengths.

Curvature-Induced Twist in Homeotropic Nematic Tori

We confine a nematic liquid crystal with homeotropic anchoring to stable toroidal droplets and study how geometry affects the equilibrium director configuration. In contrast to the case of cylindrical confinement, we find that the equilibrium state is chiral-a twisted and escaped radial director configuration. Furthermore, we find that the magnitude of the twist distortion increases as the ratio of the ring radius to the tube radius decreases; we confirm this with computer simulations of optically polarized microscopy textures. In addition, numerical calculations also indicate that the local geometry indeed affects the magnitude of the twist distortion. We further confirm this curvature-induced twisting using bent cylindrical capillaries.

Cylindrical nematic liquid crystal shell: effect of saddle-splay elasticity

This study introduces cylindrical nematic liquid crystal (LC) shells. Shells as confinement can provide soft matter with intriguing topology and geometry. Indeed, in spherical shells of LCs, rich defect structures have been reported. Avoiding the inherent Plateau-Rayleigh instability of cylindrical liquid-liquid interfaces, we realize the cylindrical nematic LC shell by two different methods: the phase separation in the nematic-isotropic coexistence phase and a cylindrical cavity with a glass rod suspended in the middle. Specifically, the director configurations of lyotropic chromonic LCs (LCLCs) in the cylindrical shell and their energetics are investigated theoretically and experimentally. Unusual elastic properties of LCLCs, i.e., a large saddle-splay modulus, and a shell geometry with both concave and convex curvatures, result in a double-twist director configuration.

Large Hexosomes from Emulsion Droplets: Particle Shape and Mesostructure Control

Soft, rotationally symmetric particles of dispersed hexagonal liquid crystalline phase are produced using a method previously developed for cubosome microparticle production. The technique forms hexosome particles via removal of ethanol from emulsion droplets containing monoolein, water, and one of the various hydrophobic molecules: vitamin E, hexadecane, oleic acid, cyclohexane, or divinylbenzene. The unique rotational symmetry of the particles is characterized by optical microscopy and small-angle X-ray scattering to link particle phase, shape, and structure to composition. Rheology of the soft particles can be varied independently of shape, enabling control of transport, deformation, and biological response by controlling composition and molecular structure of the additives. The direct observations of formation, and the resultant hexosome shapes, link the particle-scale and mesoscale properties of these novel self-assembled particles and broaden their applications. The micron-scale hexosomes provide a route to understanding the effects of particle size, crystallization rate, and rheology on the production of soft particles with liquid crystalline structure and unique shape and symmetry.

Controlled Assembly of Nanocellulose-Stabilized Emulsions with Periodic Liquid Crystal-in-Liquid Crystal Organization

Colloidal particles combined with a polymer can be used to stabilize an oil-water interface forming stable emulsions. Here, we described a novel liquid crystal (LC)-in-LC emulsion composed of a nematic oil phase and a cholesteric or nematic aqueous cellulose nanocrystal (CNC) continuous phase. The guest oil droplets were stabilized and suspended in liquid-crystalline CNCs, inducing distortions and topological defects inside the host LC phase. These emulsions exhibited anisotropic interactions between the two LCs that depended on the diameter-to-pitch ratio of suspended guest droplets and the host CNC cholesteric phase. When the ratio was high, oil droplets were embedded into a cholesteric shell with a concentric packing of CNC layers and took on a radial orientation of the helical axis. Otherwise, discrete surface-trapped LC droplet assemblies with long-range ordering were obtained, mimicking the fingerprint configuration of the cholesteric phase. Thus, the LC-in-LC emulsions presented here define a new class of ordered soft matter in which both nematic and cholesteric LC ordering can be well-manipulated.

Brownian Dynamics of Particles "Dressed" by Chiral Director Configurations in Lyotropic Chromonic Liquid Crystals

We study Brownian dynamics of colloidal spheres, with planar anchoring conditions, suspended in the nematic phase of the lyotropic chromonic liquid crystal disodium chromoglycate (DSCG). Unlike typical liquid crystals, the unusually small twist elastic modulus of DSCG permits two energetically distinct helical distortions (twisted tails) of the nematic director to "dress" the suspended spheres. Video microscopy is used to characterize the helical distortions versus particle size and to measure particle mean-square displacements. Diffusion coefficients parallel and perpendicular to the far-field director, and their anisotropy ratio, are different for the two twisted tail configurations. Moreover, the crossover from subdiffusive to diffusive behavior is anomalously slow for motion perpendicular to the director (>100  s). Simple arguments using Miesowicz viscosities and ideas about twist relaxation are suggested to understand the mean-square displacement observations.