Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity

Chiral ground states in a nematic liquid crystal confined to a cylinder with homeotropic anchoring

The singular potential method in the Q tensor order parameter representation is used to determine the ground state configuration of an elastically anisotropic nematic liquid crystal when confined to a cylindrical geometry with homeotropic anchoring. Ground states of broken chiral symmetry are found for sufficiently small values of the twist elastic constant relative to bend and splay constants. For small cylinder radius, twisted configurations, which feature two disclinations lines that wind around the long axis of the cylinder, are generally found to minimize the free energy of the nematic. For larger radii, ground state configurations are (non singular) escaped configuration. Twisted and untwisted escaped configurations are almost degenerate in energy in this region. This near degeneracy is broken when splay-bend contrast is allowed.

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.

Geometric method to determine planar anchoring strength for chromonics

Chromonic nematics are lyotropic liquid crystals that have already been known for half a century, but have only recently raised interest for their potential applications in life sciences. Determining elastic constants and anchoring strengths for rigid substrates has thus become a priority in the characterization of these materials. Here we present a method to determine chromonics' planar anchoring strength. We call it geometric as it is based on recognition and fitting of the stable equilibrium shapes of droplets surrounded by the isotropic phase in a thin cell with plates enforcing parallel alignments of the nematic director. We apply our method to shapes observed in experiments; they resemble elongated rods with round ends, which are called bâtonnets. Our theory also predicts other droplets' equilibrium shapes, which are either slender and round, called discoids, or slender and pointed, called tactoids. In particular, sufficiently small droplets are expected to display shape bistability, with two equilibrium shapes, one tactoid and one discoid, exchanging roles as stable and metastable shapes upon varying their common area.

On the elusive saddle-splay and splay-bend elastic constants of nematic liquid crystals

The elastic behavior of nematics is commonly described in terms of the three so-called bulk deformation modes, i.e., splay, twist, and bend. However, the elastic free energy contains also other terms, often denoted as saddle-splay and splay-bend, which contribute, for instance, in confined systems. The role of such terms is controversial, partly because of the difficulty of their experimental determination. The saddle-splay (K24) and splay-bend (K13) elastic constants remain elusive also for theories; indeed, even the possibility of obtaining unambiguous microscopic expressions for these quantities has been questioned. Here, within the framework of Onsager theory with Parsons-Lee correction, we obtain microscopic estimates of the deformation free energy density of hard rod nematics in the presence of different director deformations. In the limit of a slowly changing director, these are directly compared with the macroscopic elastic free energy density. Within the same framework, we derive also closed microscopic expressions for all elastic coefficients of rodlike nematics. We find that the saddle-splay constant K24 is larger than both K11 and K22 over a wide range of particle lengths and densities. Moreover, the K13 contribution comes out to be crucial for the consistency of the results obtained from the analysis of the microscopic deformation free energy density calculated for variants of the splay deformation.

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.

Local chiral inversion of chiral nematic liquid crystals in cylinders

On the basis of Landau-de Gennes theory and the finite-difference iterative method, the autonomic modulation of chiral inversion in a cylindrical cavity with degenerate planar anchoring is investigated. Under the applied helical twisting power (inversely related to the pitch P), a chiral inversion can be achieved due to the nonplanar geometry effect, and the inversion capacity rises with the increase of the helical twisting power. The combined effect of the saddle-splay K_{24} contribution (corresponding to the L_{24} term in Landau-de Gennes theory) and the helical twisting power are analyzed. It is found that the chiral inversion is more strongly modulated on the condition that the chirality of spontaneous twist is opposite to that of applied helical twisting power. Further, larger values of K_{24} will induce larger modulation of the twist degree and smaller modulation of the inverted region. The autonomic modulation of chiral inversion shows great potential for chiral nematic liquid crystal materials to be used in smart devices, such as light-controlled switches and nanoparticle transporters.

Explicit demonstration of geometric frustration in chiral liquid crystals

Many solid materials and liquid crystals exhibit geometric frustration, meaning that they have an ideal local structure that cannot fill up space. For that reason, the global phase must be a compromise between the ideal local structure and geometric constraints. As an explicit example of geometric frustration, we consider a chiral liquid crystal confined in a long cylinder with free boundaries. When the radius of the tube is sufficiently small, the director field forms a double-twist configuration, which is the ideal local structure. However, when the radius becomes larger (compared with the natural twist of the liquid crystal), the double-twist structure cannot fill space, and hence the director field must transform into some other chiral structure that can fill space. This space-filling structure may be either (1) a cholesteric phase with single twist, or (2) a set of double-twist regions separated by a disclination, which can be regarded as the beginning of a blue phase. We investigate these structures using theory and simulations, and show how the relative free energies depend on the system size, the natural twist, and the disclination energy. As another example, we also study a cholesteric liquid crystal confined between two infinite parallel plates with free boundaries.

Spontaneous Twisting of Achiral Hard Rod Nematics

Since Onsager's seminal work, hard rods have been taken as a prototype of nematic liquid crystals, characterized by uniaxial order and a uniform director field as a ground state. Here, using Onsager theory to calculate the free energy in the presence of arbitrary deformations, we find that hard rod nematics have an intrinsic tendency to twist around their ordering axis (double twist), driven by a mechanism in which the orientational fluctuations of particles play a key role. The anisotropic hard core potential used here is arguably the simplest form of interaction able to originate spontaneous breaking of mirror symmetry in a 3D fluid. Our results are discussed in relation to the recent discovery of a double twisted ground state in cylindrically confined lyotropic chromonic liquid crystals.

Paradoxes for chromonic liquid crystal droplets

Chromonic liquid crystals constitute a novel lyotropic phase, whose elastic properties have so far been modeled within the classical Oseen-Frank theory, provided that the twist constant is assumed to be considerably smaller than the saddle-splay constant, in violation of one Ericksen inequality. This paper shows that paradoxical consequences follow from such a violation for droplets of these materials surrounded by an isotropic fluid. For example, tactoids with a degenerate planar anchoring simply disintegrate indefinitely in myriads of smaller ones.

Thin liquid films down a vertical microfiber: Effect of curvature elasticity

In this paper, we use a long-wave model to examine how the curvature elasticity modifies the famous Plateau-Rayleigh mechanism and the formation of viscous beads on a vertically placed fiber. By blending the analyses of linear stability, weakly nonlinear stability, exact nonlinear solutions, and numerical simulations, the effects of spontaneous curvature, surface bending rigidity, Gaussian curvature, and Van der Waals forces on the Plateau-Rayleigh mechanism and breakup of the liquid film are examined. The spontaneous curvature and surface bending rigidity are stabilizing the interface, which can reduce the amplitude and wave speed of nonlinear traveling waves and retard the breakup of film caused by Van der Waals attractions. However, the Gaussian curvature effect reinforces the Plateau-Rayleigh mechanism, which accelerates the rupture of film.

Modulated phases of nematic liquid crystals induced by tetrahedral order

Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes: twist, bend, splay, and a fourth mode Δ related to saddle-splay. The first three of these modes are known to induce modulated phases. Here, we consider modulated phases induced by the fourth mode. We develop a theory for tetrahedral order in liquid crystals, and show that it couples to the Δ mode of director deformation. Because of geometric frustration, the Δ mode cannot fill space by itself, but rather must be accompanied by twist or splay. Hence, it may induce a spontaneous cholesteric phase, with either handedness, or a splay nematic phase.

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.

Double-twisted nematic director configurations in cylindrical capillaries with a photocontrollable angle of twist

The orientational configurations of thermotropic nematic liquid crystal in cylindrical capillaries with nondegenerated planar surface anchoring are investigated. The boundary conditions were determined by a photoaligning coating on the inner wall of the capillary treated with a linearly polarized UV light while rotating the capillary around its long axis, thus providing the easy alignment axis perpendicular to the polarization direction of illuminating light. By changing the angle between the incident light polarization and the capillary axis, this procedure allows us to realize axially symmetric twisted structure with any angle of twist, ranging from a trivial axial alignment with zero twist (when the UV polarization is perpendicular to the capillary axis) to the 180^{∘}-twisted configuration (when the UV polarization is along the capillary). These two extreme configurations together with an intermediate configuration induced by UV light polarized at an angle of 45^{∘} to the capillary axis were produced and their director profiles were studied using polarizing microscopy techniques. UV light intensity and polarization distribution over inner capillary surface covered with photoaligning layer were analyzed using optical ray tracing calculations. An analytical model of the observed configurations of the liquid crystal director field is proposed, which takes into account the finite anchoring on the capillary surface. By comparing the theoretically calculated and experimentally estimated director profiles, the liquid crystal anchoring energy on the photoaligned capillary surface was estimated.

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.

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.

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.

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.

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.

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.

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.

Dynamic and reversible shape response of red blood cells in synthetic liquid crystals

Mammalian cells are soft, and correct functioning requires that cells undergo dynamic shape changes in vivo. Although a range of diseases are associated with stiffening of red blood cells (RBCs; e.g., sickle cell anemia or malaria), the mechanical properties and thus shape responses of cells to complex viscoelastic environments are poorly understood. We use vapor pressure measurements to identify aqueous liquid crystals (LCs) that are in osmotic equilibrium with RBCs and explore mechanical coupling between RBCs and LCs. When transferred from an isotropic aqueous phase into a LC, RBCs exhibit complex yet reversible shape transformations, from initially biconcave disks to elongated and folded geometries with noncircular cross-sections. Importantly, whereas the shapes of RBCs are similar in isotropic fluids, when strained by LC, a large variance in shape response is measured, thus unmasking cell-to-cell variation in mechanical properties. Numerical modeling of LC and cell mechanics reveals that RBC shape responses occur at constant cell membrane area but with membrane shear moduli that vary between cells from 2 to 16 × 10^-6 N/m. Temperature-dependent LC elasticity permits continuous tuning of RBC strains, and chemical cross-linking of RBCs, a model for diseased cells, leads to striking changes in shape responses of the RBCs. Overall, these results provide insight into the coupling of strain between soft mammalian cells and synthetic LCs, and hint at new methods for rapidly characterizing mechanical properties of single mammalian cells in a population and thus cell-to-cell variance.

Saddle-splay-induced periodic edge undulations in smectic-A disks immersed in a nematic medium

We report experimental studies on the phase behavior of binary mixtures of 1″,7″-bis(4-cyanobiphenyl-4'-yl)heptane (CB7CB) and 4,4-diheptyloxyazoxybenzene, which exhibit, apart from the nematic (N) and twist-bend nematic (N_{TB}) phases, the induced smectic-A (Sm-A) phase for weight fraction of CB7CB between 0.05 and 0.70. In planar nematic layers, the N_{TB} phase separates as droplets of tactoidlike planform; the chirality of droplets manifests in the optical dissimilarity between their opposite angular ends. Our main result is that, in the appropriate two phase region, Sm-A nuclei with positive dielectric anisotropy change over to disks immersed in the nematic above some electric field, their edges decorated by periodic bright spots, a result which was earlier reported in another binary system exhibiting the induced Sm-A phase [R. Pratibha and N. V. Madhusudana, Physica A 224, 9 (1996)10.1016/0378-4371(95)00311-8]. We develop a simple theory for the threshold of this distortion, which is a periodic undulation of the edge of the disk, demonstrating that it arises from saddle-splay elasticity of Sm-A, the low Sm-A-N interfacial tension unable to suppress the distortion. The observed increases in the number of bright spots with field, and with the radius of the disk at a given field, in both the experimental systems are also accounted for by the model. The distortion, which results in the most direct visualization of saddle splay in Sm-A, is also exhibited by disks nucleating on surfaces treated for homeotropic anchoring.

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.

Programming emergent symmetries with saddle-splay elasticity

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid's internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant [Formula: see text]. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering [Formula: see text] immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring [Formula: see text]. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

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.

Self-Organized, One-Dimensional Periodic Structures in a Gold Nanoparticle-Doped Nematic Liquid Crystal Composite

Composite structures exhibiting a periodic arrangement of building blocks can be found in natural systems at different length scales. Recreating such systems in artificial composites using the principles of self-assembly has been a great challenge, especially for 1D microscale systems. Here, we present a purposely designed composite material consisting of gold nanoparticles and a nematic liquid crystal matrix that has the ability to self-create a periodic structure in the form of a one-dimensional photonic lattice through a phase separation process occurring in a confined space. Our strategy is based on the use of a thermoswitchable medium that reversibly and quickly responds to both heating and cooling. We find that the period of the structure is strongly related to the size of the confining space. We believe that our findings will allow us to not only better understand the phase separation process in multicomponent soft/colloid mixtures with useful optical properties but also improve our understanding of the precise assembly of advanced materials into one-dimensional periodic systems, with prospective applications in future photonic technologies.

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.

Molecularly-ordered hydrogels with controllable, anisotropic stimulus response

Hydrogels which morph between programmed shapes in response to aqueous stimuli are of significant interest for biosensors and artificial muscles, among other applications. However, programming hydrogel shape change at small size scales is a significant challenge. Here we use the inherent ordering capabilities of liquid crystals to create a mechanically anisotropic hydrogel; when coupled with responsive comonomers, the mechanical anisotropy in the network guides shape change in response to the desired aqueous condition. Our synthetic strategy hinges on the use of a methacrylic chromonic liquid crystal monomer which can be combined with a non-polymerizable chromonic of similar structure to vary the magnitude of shape change while retaining liquid crystalline order. This shape change is directional due to the mechanical anisotropy of the gel, which is up to 50% stiffer along the chromonic stack direction than perpendicular. Additionally, we show that the type of stimulus to which these anisotropic gels respond can be switched by incorporating responsive, hydrophilic comonomers without destroying the nematic phase or alignment. The utility of these properties is demonstrated in polymerized microstructures which exhibit Gaussian curvature in response to high pH due to emergent ordering in a micron-sized capillary.

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.

Non-monotonic, lily-like twist distribution in toroidal nematics

Toroidal nematics are droplets of nematic liquid crystals in the form of a circular torus. When the nematic director is subject to planar degenerate boundary conditions, the bend-only director field with vector lines along the parallels of all nested torodial shells is an equilibrium solution for all values of the elastic constants. Local stability analyses have shown that an instability is expected to occur for sufficiently small values of the twist elastic constant. It is natural to wonder whether in this regime the global equilibrium would be characterized by a monotonic twist, or not. In the former case, the twist distribution over the torus' circular cross-section would be represented pictorially by a fennel-like surface emanating from the centre. We prove that instead the stable twist distribution is represented by a lily-like surface. Thus, generically the twist distribution is not monotonic and its maximum may fall well within the torus, far away from the boundary. To cope with the peculiar complexity of the elastic free-energy functional in the fully non-linear setting, we developed an ad hoc deep-learning optimization method, which here is also further validated and documented for it promises to be applicable to other similar problems, equally intractable analytically.

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.

In Silico Measurement of Elastic Moduli of Nematic Liquid Crystals

Experiments on confined droplets of the nematic liquid crystal 5CB have questioned long-established bounds imposed on the elastic free energy of nematic systems. This elasticity, which derives from molecular alignment within nematic systems, is quantified through a set of moduli which can be difficult to measure experimentally and, in some cases, can only be probed indirectly. This is particularly true of the surfacelike saddle-splay elastic term, for which the available experimental data indicate values on the cusp of stability, often with large uncertainties. Here, we demonstrate that all nematic elastic moduli, including the saddle-splay elastic constant k_{24}, may be calculated directly from atomistic molecular simulations. Importantly, results obtained through in silico measurements of the 5CB elastic properties demonstrate unambiguously that saddle-splay elasticity alone is unable to describe the observed confined morphologies.

Chiral Structures from Achiral Micellar Lyotropic Liquid Crystals under Capillary Confinement

Recently, the emergence of spontaneous reflection-symmetry-broken configurations in achiral chromonic liquid crystals confined in cylindrical capillaries with homeotropic anchoring at the cylinder walls was reported, namely, the so-called twisted-escaped radial (TER) and twisted planar polar (TPP) configurations. This new example of spontaneous reflection symmetry breaking in liquid crystals was attributed to the twist elastic modulus, which is known to be unusually small in comparison to the splay and bend moduli in the case of chromonic liquid crystals. We now report the experimental observation of reflection symmetry breaking in cylindrical capillaries in the case of a classical, achiral, and nonchromonic lyotropic liquid crystal forming a nematic phase of disklike micelles orienting homeotropically at the capillary walls. We observed the same chiral TER configuration, as well as a nonplanar twisted polar (TP) configuration. The TP configuration is characterized by two half-unit so-called twist disclinations, where the director twist around the line defects drives the formation of a double helix of the disclinations along the axis of the capillary. Additionally, there is a transverse twist between the two disclination lines with the same handedness as the axial twist. Similarities with and differences from the case of chromonic liquid crystals are discussed; in particular, we examine the conditions under which spontaneous reflection symmetry breaking occurs in the nonchromonic system. It seems that the chiral TER configuration can be stabilized by the presence of point defects.

Liquid crystals in micron-scale droplets, shells and fibers

The extraordinary responsiveness and large diversity of self-assembled structures of liquid crystals are well documented and they have been extensively used in devices like displays. For long, this application route strongly influenced academic research, which frequently focused on the performance of liquid crystals in display-like geometries, typically between flat, rigid substrates of glass or similar solids. Today a new trend is clearly visible, where liquid crystals confined within curved, often soft and flexible, interfaces are in focus. Innovation in microfluidic technology has opened for high-throughput production of liquid crystal droplets or shells with exquisite monodispersity, and modern characterization methods allow detailed analysis of complex director arrangements. The introduction of electrospinning in liquid crystal research has enabled encapsulation in optically transparent polymeric cylinders with very small radius, allowing studies of confinement effects that were not easily accessible before. It also opened the prospect of functionalizing textile fibers with liquid crystals in the core, triggering activities that target wearable devices with true textile form factor for seamless integration in clothing. Together, these developments have brought issues center stage that might previously have been considered esoteric, like the interaction of topological defects on spherical surfaces, saddle-splay curvature-induced spontaneous chiral symmetry breaking, or the non-trivial shape changes of curved liquid crystal elastomers with non-uniform director fields that undergo a phase transition to an isotropic state. The new research thrusts are motivated equally by the intriguing soft matter physics showcased by liquid crystals in these unconventional geometries, and by the many novel application opportunities that arise when we can reproducibly manufacture these systems on a commercial scale. This review attempts to summarize the current understanding of liquid crystals in spherical and cylindrical geometry, the state of the art of producing such samples, as well as the perspectives for innovative applications that have been put forward.

Using chiral tactoids as optical probes to study the aggregation behavior of chromonics

Tactoids are nuclei of an orientationally ordered nematic phase that emerge upon cooling the isotropic phase. In addition to providing a natural setting for exploring chromonics under confinement, we show that tactoids can also serve as optical probes to delineate the role of temperature and concentration in the aggregation behavior of chromonics. For high concentrations, we observe the commonly reported elongated bipolar tactoids. As the concentration is lowered, breaking of achiral symmetry in the director configuration is observed with a predominance of twisted bipolar tactoids. On further reduction of concentration, a remarkable transformation of the director configuration occurs, wherein it conforms to a unique splay-minimizing configuration. Based on a simple model, we arrive at an interesting result that lower concentrations have longer aggregates at the same reduced temperature. Hence, the splay deformation that scales linearly with the aggregate length becomes prohibitive for lower concentrations and is relieved via twist and bend deformations in this unique configuration. Raman scattering measurements of the order parameters independently verify the trend in aggregate lengths and provide a physical picture of the nematic-biphasic transition.

Pattern-induced anchoring transitions in nematic liquid crystals

In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross-section sculpted on a chemically homogeneous substrate which favours local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinct far-field orientations, as well as the anchoring transitions between them, are associated with the presence of topological defects either on or close to the substrate. For the sawtooth and sinusoidal cases, we observe a homeotropic to planar anchoring transition as the substrate roughness increases. On the other hand, a homeotropic to oblique anchoring transition is observed for crenellated substrates. In this case, the anchoring phase diagram shows a complex dependence on the substrate roughness and substrate anchoring strength.

Nematic liquid crystals on sinusoidal channels: the zigzag instability

Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy of the elastic constants and the interplay of the relevant lengths scales, such as the correlation length and the surface geometrical parameters. Transitions between different textures, usually with different symmetries, may occur under a wide range of conditions. We use the Landau-de Gennes free energy to investigate the texture of nematics in sinusoidal channels with parallel anchoring bounded by nematic-air interfaces that favour perpendicular (hometropic) anchoring. In micron size channels 5CB was observed to exhibit a non-trivial texture characterized by a disclination line, within the channel, which is broken into a zigzag pattern. Our calculations reveal that when the elastic anisotropy of the nematic does not favour twist distortions the defect is a straight disclination line that runs along the channel, which breaks into a zigzag pattern with a characteristic period, when the twist elastic constant becomes sufficiently small when compared to the splay and bend constants. The transition occurs through a twist instability that drives the defect line to rotate from its original position. The interplay between the energetically favourable twist distortions that induce the defect rotation and the liquid crystal anchoring at the surfaces leads to the zigzag pattern. We investigate in detail the dependence of the periodicity of the zigzag pattern on the geometrical parameters of the sinusoidal channels, which in line with the experimental results is found to be non-linear.

Lassoing saddle splay and the geometrical control of topological defects

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.

Relevance of saddle-splay elasticity in complex nematic geometries

We demonstrate the relevance of saddle-splay elasticity in nematic liquid crystalline fluids in the context of complex surface anchoring conditions and the complex geometrical confinement. Specifically, nematic cells with patterns of surface anchoring and colloidal knots are shown as examples where saddle-splay free energy contribution can have a notable role which originates from nonhomogeneous surface anchoring and the varying surface curvature. Patterned nematic cells are shown to exhibit various (meta)stable configurations of nematic field, with relative (meta)stability depending on the saddle-splay. We show that for high enough values of saddle-splay elastic constant K24 a previously unstable conformation can be stabilised, more generally indicating that the saddle-splay can reverse or change the (meta)stability of various nematic structures affecting their phase diagrams. Furthermore, we investigate saddle-splay elasticity in the geometry of highly curved boundaries - the colloidal particle knots in nematic - where the local curvature of the particles induces complex spatial variations of the saddle-splay contributions. Finally, a nematic order parameter tensor based saddle-splay invariant is shown, which allows for the direct calculation of saddle-splay free energy from the Q-tensor, a possibility very relevant for multiple mesoscopic modelling approaches, such as Landau-de Gennes free energy modelling.