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.

Focal conic flowers, dislocation rings, and undulation textures in smectic liquid crystal Janus droplets.

Liquid crystalline phases of matter often exhibit visually stunning patterns or textures. Mostly, these liquid crystal (LC) configurations are uniquely determined by bulk LC elasticity, surface anchoring conditions, and confinement geometry. Here, we experimentally explore defect textures of the smectic LC phase in unique confining geometries with variable curvature. We show that a complex range of director configurations can arise from a single system, depending on sample processing procedures. Specifically, we report on LC textures in Janus drops comprised of silicone oil and 8CB in its smectic-A LC phase. The Janus droplets were made in aqueous suspension using solvent-induced phase separation. After drop creation, smectic layers form in the LC compartment, but their self-assembly is frustrated by the need to accommodate both the bowl-shaped cavity geometry and homeotropic (perpendicular) anchoring conditions at boundaries. A variety of stable and metastable smectic textures arise, including focal conic domains, dislocation rings, and undulations. We experimentally characterize their stabilities and follow their spatiotemporal evolution. Overall, a range of fabrication kinetics produce very different intermediate and final states. The observations elucidate assembly mechanisms and suggest new routes for fabrication of complex soft material structures in Janus drops and other confinement geometries.

Orientational order of dyes in a lyotropic chromonic liquid crystal.

Absorption measurements allow the orientational order parameter of four dyes in the lyotropic chromonic liquid crystal di-sodium cromoglycate (DSCG) to be determined. The dye order parameters are small, except for dyes that intercalate between the DSCG molecules of the rod-like assemblies. The dye order parameters decrease with increasing temperature faster than the nematic order parameter of the DSCG assemblies. For intercalating dyes, the measured dye order parameter varies with the wavelength of the measurement because both intercalated and non-intercalated dye molecules contribute. On the contrary, measurements of the dye order parameter using fluorescence are sensitive only to intercalated dye molecules and produce values that reflect the order parameter of the DSCG assemblies. Therefore, the temperature and concentration dependence of the DSCG order parameter is also explored, since data of this kind on this often-studied system are lacking. Finally, the association constant of one of the intercalating dyes with the DSCG assemblies is determined, yielding a value considerably less than what is found for the same dye with DNA.

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.

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.

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.

Temperature dependence of the pitch in chiral lyotropic chromonic liquid crystals.

One of the most simple cases in which chirality at the microscopic level produces a chiral macroscopic structure is the chiral nematic liquid crystal phase. In such a phase, the preferred direction of molecular orientation rotates in helical fashion, with the pitch of the helix in different systems ranging from around 100 nm to as large as can be measured (∼10 mm). For almost all thermotropic and lyotropic liquid crystals, the ordered entities are formed from strong bonds, so the pitch varies in accordance with how the interactions between these largely immutable entities are affected by changing conditions. A unique exception are lyotropic chromonic liquid crystals (LCLCs) that spontaneously form weakly bound assemblies in solution, the size of which depends strongly on experimental parameters. While the temperature dependence of the pitch has been measured for chiral LCLCs formed by short strands of DNA (DNA-LCLCs), such is not the case for chiral LCLCs formed by small molecules. Polarized optical microscopy experiments on small molecule chiral LCLCs reveal the changing assembly size through a temperature dependence of the pitch not typical for many other systems, including the most recent measurements on DNA-LCLCs. In fact, the pitch measurements in small molecule chiral LCLCs strongly increase in value as the temperature is increased and the assemblies shrink in size. Theoretical considerations provide some help in understanding this phenomena, but leave much to be explained.

Chiral structures from achiral liquid crystals in cylindrical capillaries.

We study chiral symmetry-broken configurations of nematic liquid crystals (LCs) confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls (i.e., perpendicular surface alignment). Interestingly, achiral nematic LCs with comparatively small twist elastic moduli relieve bend and splay deformations by introducing twist deformations. In the resulting twisted and escaped radial (TER) configuration, LC directors are parallel to the cylindrical axis near the center, but to attain radial orientation near the capillary wall, they escape along the radius through bend and twist distortions. Chiral symmetry-breaking experiments in polymer-coated capillaries are carried out using Sunset Yellow FCF, a lyotropic chromonic LC with a small twist elastic constant. Its director configurations are investigated by polarized optical microscopy and explained theoretically with numerical calculations. A rich phenomenology of defects also arises from the degenerate bend/twist deformations of the TER configuration, including a nonsingular domain wall separating domains of opposite twist handedness but the same escape direction and singular point defects (hedgehogs) separating domains of opposite escape direction. We show the energetic preference for singular defects separating domains of opposite twist handedness compared with those of the same handedness, and we report remarkable chiral configurations with a double helix of disclination lines along the cylindrical axis. These findings show archetypally how simple boundary conditions and elastic anisotropy of confined materials lead to multiple symmetry breaking and how these broken symmetries combine to create a variety of defects.

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

Confined liquid crystals (LC) provide a unique platform for technological applications and for the study of LC properties, such as bulk elasticity, surface anchoring, and topological defects. In this work, lyotropic chromonic liquid crystals (LCLCs) are confined in spherical droplets, and their director configurations are investigated as a function of mesogen concentration using bright-field and polarized optical microscopy. Because of the unusually small twist elastic modulus of the nematic phase of LCLCs, droplets of this phase exhibit a twisted bipolar configuration with remarkably large chiral symmetry breaking. Further, the hexagonal ordering of columns and the resultant strong suppression of twist and splay but not bend deformation in the columnar phase, cause droplets of this phase to adopt a concentric director configuration around a central bend disclination line and, at sufficiently high mesogen concentration, to exhibit surface faceting. Observations of director configurations are consistent with Jones matrix calculations and are understood theoretically to be a result of the giant elastic anisotropy of LCLCs.

Self-organized assemblies of colloidal particles obtained from an aligned chromonic liquid crystal dispersion.

The behavior of mono-disperse colloidal particles in a chromonic liquid crystal was investigated. Poly(methyl methacrylate) spherical particles with three different functionalizations, with and without surface charges, were utilized in the nematic and columnar phases of disodium cromoglycate solutions. The nematic phase was completely aligned parallel to the glass substrates by a simple rubbing technique, and the columnar phase showed regions of similar alignment. The behavior of the colloidal particles in the chromonic liquid crystal depended critically on the functionality, with bromine functionalized particles not dispersing at all, and cationic trimethylammonium and epoxy functionalized particles dispersing well in the isotropic phase of the liquid crystal. At the transition to the nematic and especially the columnar phase, the colloidal particles were expelled into the remaining isotropic phase. Since the columnar phase grew in parallel ribbons, the colloidal particles ended up in chain-like assemblies. Such behavior opens the possibility of producing patterned assemblies of colloidal particles by taking advantage of the self-organized structure of chromonic liquid crystals.

Liquid crystal Janus emulsion droplets: preparation, tumbling, and swimming.

This study introduces liquid crystal (LC) Janus droplets. We describe a process for the preparation of these droplets, which consist of nematic LC and polymer compartments. The process employs solvent-induced phase separation in emulsion droplets generated by microfluidics. The droplet morphology was systematically investigated and demonstrated to be sensitive to the surfactant concentration in the background phase, the compartment volume ratio, and the possible coalescence of multiple Janus droplets. Interestingly, the combination of a polymer and an anisotropic LC introduces new functionalities into Janus droplets, and these properties lead to unusual dynamical behaviors. The different densities and solubilities of the two compartments produce gravity-induced alignment, tumbling, and directional self-propelled motion of Janus droplets. LC Janus droplets with remarkable optical properties and dynamical behaviors thus offer new avenues for applications of Janus colloids and active soft matter.

Homeotropic alignment of lyotropic chromonic liquid crystals using noncovalent interactions.

We report on the homeotropic alignment of lyotropic chromonic liquid crystals (LCLCs). Homeotropic anchoring of LCLCs is difficult to achieve, and this challenge has limited development of applications for LCLCs. In this work, homeotropic alignment is achieved using noncovalent interactions between the LCLC molecules and various alignment layers including graphene, parylene films, poly(methyl methacrylate) films, and fluoropolymer films. The LCLC molecules are unique in that they self-assemble via noncovalent interactions in water into elongated aggregates which, in turn, form nematic and columnar liquid crystal (LC) phases. Here we exploit these same noncovalent interactions to induce homeotropic anchoring of the nematic LCLC. Homeotropic alignment is confirmed by polarized optical microscopy and conoscopy. We also report on novel transient stripe textures that occur when an initial flow-induced planar alignment transforms into the equilibrium homeotropic alignment required by boundary conditions. An understanding of this behavior could be important for switching applications.

Elasticity-dependent self-assembly of micro-templated chromonic liquid crystal films.

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

Magnetic-field-driven director configuration transitions in radial nematic liquid crystal droplets.

We study the director configurations of nematic liquid crystal (NLC) droplets with homeotropic anchoring in a magnetic field and report observation of a magnetic-field-driven transition from a deformed radial to an axial-with-defect configuration. Magnetic-field-induced transitions in NLC droplets differ fundamentally from the traditional planar Freedericksz transition due to the spherical droplet geometry and resulting topological defect. This transition has been studied theoretically, but the director configurations and mechanism of defect evolution in an applied magnetic field have yet to be observed experimentally. To this end, we combine polarized optical microscopy with a variable electromagnet (≤1 T) for continuous observation of droplet director fields, and we employ Landau-de Gennes numerical simulations to elucidate the director configurations and first-order nature of the transition. We report a configuration transition from point defect to ring defect at a critical field, which varies inversely with droplet radius and is relatively independent of surfactant type and concentration. We also estimate anchoring strengths of commonly used surfactants at the NLC-aqueous interface.

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.

Theory of director fluctuations about a hedgehog defect in a nematic drop.

We present calculations of eigenmode energies and wave functions of both azimuthal and polar distortions of the nematic director relative to a radial hedgehog trapped in a spherical drop with a smaller concentric spherical droplet at its core. All surfaces interior to the drop have perpendicular (homeotropic) boundary conditions. We also calculate director correlation functions and their relaxation times. Of particular interest is a critical mode whose energy, with fixed Frank constants, vanishes as the ratio µ=R_{2}/R_{1} increases toward a critical value µ_{c}, where R_{2} is the radius of the drop and R_{1} that of the inner droplet, and then becomes negative for µ>µ_{c}. Our calculations form a basis for interpreting experimental measurements of director fluctuations relative to a radial hedgehog state in a spherical drop. We compare results with those obtained by previous investigations, which use a calculational approach different from ours, and with our experimental observations.

Aggregation behavior and chromonic liquid crystal phase of a dye derived from naphthalenecarboxylic acid.

Polarizing microscopy, X-ray scattering, and absorption spectroscopy are used to investigate the aggregation process and chromonic liquid crystal of the anionic compound Bordeaux dye, a product of the sulfonation of the dibenzimidazole derivative of naphthalenetetracarboxylic acid. Polarizing microscopy reveals that the liquid crystal phase forms at room temperature when the concentration is only about 6 wt%, a value lower than what is found in many aggregating systems. The X-ray results indicate that the aggregation is via columns, with a cross-sectional area about 2.5 times larger than the individual molecule. Absorption spectroscopy shows a significant change in the absorption spectrum due to aggregation, which is nicely explained by a simple theory of isodesmic aggregation and excitonic coupling between the molecules in an aggregate. The "stacking free energy change" for a molecule in an aggregate relative to a molecule in solution is estimated to be about 9 kBT, a larger value than that found in the one other system where it has been estimated.

Deposition and drying dynamics of liquid crystal droplets.

Drop drying and deposition phenomena reveal a rich interplay of fundamental science and engineering, give rise to fascinating everyday effects (coffee rings), and influence technologies ranging from printing to genotyping. Here we investigate evaporation dynamics, morphology, and deposition patterns of drying lyotropic chromonic liquid crystal droplets. These drops differ from typical evaporating colloidal drops primarily due to their concentration-dependent isotropic, nematic, and columnar phases. Phase separation occurs during evaporation, and in the process creates surface tension gradients and significant density and viscosity variation within the droplet. As a result, the drying multiphase drops exhibit different convective currents, drop morphologies, and deposition patterns (coffee-rings).

Tunable depletion potentials driven by shape variation of surfactant micelles.

Depletion interaction potentials between micron-sized colloidal particles are induced by nanometer-scale surfactant micelles composed of hexaethylene glycol monododecyl ether (C_{12}E_{6}), and they are measured by video microscopy. The strength and range of the depletion interaction is revealed to arise from variations in shape anisotropy of the surfactant micelles. This shape anisotropy increases with increasing sample temperature. By fitting the colloidal interaction potentials to theoretical models, we extract micelle length and shape anisotropy as a function of temperature. This work introduces shape anisotropy tuning as a means to control interparticle interactions in colloidal suspensions, and it shows how the interparticle depletion potentials of micron-scale objects can be employed to probe the shape and size of surrounding macromolecules at the nanoscale.