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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.

Understanding how soft matter deforms in response to mechanical interactions is central to the design of functional synthetic materials as well as elucidation of the behaviors of biological assemblies. Here we explore how cycles of thermally induced transitions between nematic (N) and isotropic (I) phases can be used to exert cyclical elastic stresses on dispersions of giant unilamellar vesicles (GUVs) and thereby evolve GUV shape and properties. The measurements were enabled by the finding that I–N–I phase transitions of the lyotropic chromonic liquid crystal disodium cromoglycate, when conducted via an intermediate columnar (M) phase, minimized transport of GUVs on phase fronts to confining surfaces. Whereas I to N phase transitions strained spherical GUVs into spindle-like shapes, with an efflux of GUV internal volume, subsequent N to I transitions generated a range of complex GUV shapes, including stomatocyte, pear- and dumbbell-like shapes that depended on the extent of strain in the N phase. The highest strained GUVs were observed to form buds (daughter vesicles) that we show, via a cycle of I–N–I–N phase transitions, are connected via a neck to the parent vesicle. Additional experiments established that changes in elasticity of the phase surrounding the GUVs and not thermal expansion of membranes were responsible for the shape transitions, and that I–N–I transformations that generate stomatocytes can be understood from the Bilayer-Coupling model of GUV shapes. Overall, these observations advance our understanding of how LC elastic stresses can be regulated to evolve the shapes of soft biological assemblies as well as provide new approaches for engineering synthetic soft matter.

The use of the biphasic isotropic/nematic region in a bisperylene imide-based lyotropic liquid crystal system allows the extraction of proton-carbon 1 DCH residual dipolar couplings in aqueous solution from a single F1-coupled HSQC experiment. The method was successfully applied to the RDC-based conformational analysis of sucrose.

This article demonstrates a new approach enabling the active control of swimming trajectories of flagellated bacteria in space and time. Bacteria were mixed with water solutions of disodium cromogl...

Spatial confinement of water-based lyotropic chromonic liquid crystals made of achiral molecules produces chiral structures with alternating left and right twists.

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.

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., Well-addressed chiral domains are generated with achiral lyotropic chromonic liquid crystal materials using periodic air pillars, which can be potentially used for scaffolds for living matters.

Lyotropic chromonic liquid crystals (LCLCs) confined in cylindrical cavity can form an escaped-twisted (ET) configuration, resulting from the saddle-splay elastic constant is great much than twist ...

In a cylindrical cavity with a degenerate planar anchoring, the lyotropic chromonic nematic liquid crystals without intrinsic chirality tend to exhibit an escaped twisted configuration for the larg...

Coating-type polarizing films with a high dichroic ratio (DR) and polarization efficiency in the visible region were fabricated using a solution of ternary lyotropic chromonic liquid crystals (LCLCs). Optical characteristics of these anisotropic LCLC polarizing films were then determined. DR increased with increasing LCLC concentrations. Molecular ordering of these LCLCs on a rubbed polyimide (PI) layer increased because LCLC molecules' orientation was enhanced by the dielectric anisotropy effect from rubbing the surface of the PI. In addition, this study demonstrated how the interaction between liquid crystal aggregates and the PI surface with different LCLC solutions correlated with LCLC molecular orientations on the PI which is significantly dependent on whether the coating direction of the LCLC solution was parallel or perpendicular to the PI rubbing direction. It was found that the ordering direction at high LCLC concentrations was determined by shearing direction of the LCLC solution coating, whereas the ordering direction at low LCLC concentrations was governed by the dielectric anisotropy effect from the PI rubbing direction.

Positional order in the lyotropic chromonic liquid crystals (LCLCs) is investigated in the supramolecular assembly of benzene 1,3,5-tricarboxamide (BTA) derivatives with the glucono-delta-lactone (GdL) acid additive by high-resolution synchrotron radiation small-angle X-ray scattering. The formation of positionally ordered hexagonal phase is found to profoundly depend on the concentrations of BTA derivatives, cBTA, and GdL additives, caddtive, giving rise to unusual behavior distinctive from conventional lyotropic liquid crystals (LCs) with covalent bonds and fixed length. The hexagonal phase is observed to coexist with another phase in certain range of caddtive/cBTA. Intriguingly, the lattice spacing R of the hexagonal phase remains almost constant by varying caddtive but changes with cBTA. The above observations are attributed to unique sensitivities of the LCLC properties, such as the contour length and flexibility of individual cylinder assemblies and phase coexistence, to additives in the solutions. Our study reveals the complexity in positional ordering in the LCLCs which not only relates to the underlying principles of hierarchical reversible self-assembly but also attracts fundamental interests in LCs.

Ionic self-assembly is a simple yet powerful method to obtain robust nanostructures. Herewith, we use mixtures of oppositely-charged porphyrins that can act as mesogens to form chromonic liquid crystals in water, i.e., molecular stacks with orientational (nematic) or positional (hexagonal) order. Electrostatic locking coupled with π–π interactions between aromatic groups within the stacks, together with inter-stack hydrogen bonding induce formation of all-organic crystalline nanofibers with high aspect ratio (a few tenths of nanometers in width but several tenths of micrometers in length) and that display branching. The nanofibers prepared from metal-free porphyrin units feature interesting optical properties, including an absorption spectrum that is different from the simple sum of the individual spectra of the components, which is attributed to a striking aggregation-induced chromism. When in contact with some polar organic solvents the materials become fluorescent, as a result of disaggregation. In a proof-of-concept, the obtained self-assembled one-dimensional (1D) materials were carbonized (yield ca. 60%) to produce nitrogen-doped carbon nanofibers that can be used as active electrode materials for energy storage applications., C. R. acknowledges the financial support from Generalitat de Catalunya (2017SGR1778 grant), and from the Spanish Ministry of Science, Innovation and Universities (CTQ2017-84998-P project). C. R. is also grateful to the Agencia Estatal de Investigación and to the European Regional Development Fund (Fondo Europeo de Desarrollo Regional, FEDER). We thank ALBA staff for their help and support in the Synchrotron SAXS experiments performed at BL11-NCD beamline at ALBA (Spain). This work is partially supported by supported by JSPS KAKENHI Grant Number JP 16H06518 (Coordination Asymmetry), CREST JST Grant Number JPMJCR1665, and Grants-in-Aid for Scientific Research (C) Grant Number 20K05590.

Questa tesi si occupa di una classe particolare di liotropici: i cristalli liquidi cromatici (CLCs). Essi in fase nematica godono della simmetria testa-coda, cioè sono materiali non chirali con una tendenza dei loro elementi costitutivi a raggrupparsi in modo da poter definire un direttore su scala mesoscopica che non ha polarità. Lo stato fondamentale dei cristalli liquidi nematici ordinari è raggiunto quando il direttore è uniforme nello spazio. Quando i CLCs sono confinati in capillari cilindrici con condizioni al contorno degeneri, si osserva che acquisiscono una configurazione non uniforme. In particolare, il loro stato fondamentale nel capillare cilindrico, spesso indicato come 'escaped twist' (ET), consiste in due configurazioni simmetriche di opposta chiralità, ognuna che si verifica con la stessa probabilità come ci si aspetta dalla mancanza di chiralità negli aggregati molecolari che costituiscono questi materiali. Nonostante la chiara indicazione che i CLCs nello spazio tridimensionale mostrano un comportamento diverso dai comuni cristalli liquidi nematici, la teoria di Oseen-Frank per i nematici è stata applicata per razionalizzare gli esperimenti con i capillari e quindi per determinare la configurazione dello stato fondamentale ET. Si tratta di una teoria variazionale che postula una densità di energia libera quadratica nel gradiente del direttore che penalizza tutte le distorsioni dall'allineamento uniforme. Classicamente vengono identificate quattro distorsioni, che corrispondono a quattro costanti elastiche indipendenti; si tratta delle costanti splay K_{11}, twist K_{22}, bend K_{33}, e saddle-splay K_{24}. Le disuguaglianze di Ericksen assicurano che la densità di energia di Frank sia positiva definita, e l'emergere spontaneo della chiralità non è concepibile quando sono valide. Così, la teoria elastica di Frank giustifica le configurazioni osservate dei CLCs sotto confinamento cilindrico solo se la disuguaglianza di Ericksen pertinente, K_{22}>=K_{24}, è violata, e quindi solo se l'energia libera funzionale di Frank è illimitata dal basso nello spazio euclideo 3D. Infatti, la configurazione che assumono è di equilibrio solo se questa disuguaglianza è violata. La forma alternativa della densità di energia libera di Oseen-Frank proposta da Selinger distribuisce il contributo del saddle-splay negli altri modi elastici. Così facendo, la torsione pura corrisponde qui alla costante elastica K_{22}-K_{24} (invece che solo K_{22} nella formulazione precedente) e viene chiamata double-twist, poiché non ha una direzione caratteristica nel piano perpendicolare al direttore. La negatività di (K_{22}-K_{24}) suggerisce che la configurazione di double-twist pura, la configurazione che eccita solo il modo double-twist, è lo stato fondamentale dei CLCs nello spazio 3D. Questo partciolare campo di direttori non appartiene a nessuna delle famiglie di direttori uniformi; è possibile solo lungo una curva 1D e produce frustrazione elastica se si richiede di occupare una particolare geometria con particolari condizioni al contorno. Estendere quindi il double twist a una regione tubolare introduce per necessità una trama non uniforme che risulta dalla combinazione di altri modi di deformazione fondamentali con il double-twist puro solo lungo l'asse del cilindro. Questa è esattamente la configurazione osservata sperimentalmente per i CLCs in capillari cilindrici soggetti a condizioni al contorno degeneri. Assumento che lo stato fondamentale dei CLCs è una caratteristica doppia torsione, diciamo che il cosiddetto stato fondamentale ET è in realtà uno `pseudo stato fondamentale', poiché è il risultato dell'estensione indotta dal confinamento della configurazione di double-twist, che inietta una frustrazione elastica nel sistema. Quali sono le problematiche dovute all'applicazione della teoria elastica di Frank ai CLCs? Perché abbiamo bisogno di una nuova teoria elastica? This dissertation is concerned with a peculiar class of lyotropics: chromatic liquid crystals (CLCs). Chromonics in the nematic phase enjoy the head-tail symmetry, that is, they are non-chiral materials with a tendency for their constitutive to bundle together so that a director can be defined at a mesoscopic scale which lacks polarity. The ground state of ordinary nematic liquid crystals is attained when the director is uniform in space. When CLCs are confined in capillary cylinders with degenerate boundary conditions that would be compatible with the uniform alignment of the director along the cylinder's axis, they are observed to acquire a nonuniform arrangement instead. Expecially, their ground state in cylindrical capillary, often referred to as escaped twist (ET) ground state, is two-fold; it consists of two symmetric twisted configurations (left- and right-handed), each variant occurring with the same likelihood, as was to be expected from the lack of chirality in the molecular aggregates that constitute these materials. Despite the clear indication that CLCs in three-dimensional space exhibit a different behavior from common nematic liquid crystals, the Oseen-Frank theory for nematics has been applied to rationalize the experiments with capillary tubes and so to determine the configuration of the ET ground state. This is a variational theory which posits a free energy density quadratic in the director gradient that penalizes all distortions of the director away from the unifom alignment. Four basic distortions are classically identified, which correspond to four independent elastic constants; these are the splay K_{11}, twist K_{22}, bend K_{33}, and saddle-splay K_{24} constants, which have recently been re-interpreted in a new light by Selinger. Ericksen's inequalities ensure that Frank's energy density is positive definite, and the spontaneous emergence of chirality in the nematic texture is not conceivable when they hold. Thus, Frank's elastic theory justifies the observed configurations of CLCs under cylindrical confinement only if the relevant Ericksen's inequality, K_{22}>=K_{24}$, is violated, and so only if Frank's free energy functional is unbounded below in 3D Euclidean space. Ideed, the configuration they fall in is an equilibrium one only if this inequality is violated. The alternative form of the Oseen-Frank free energy density proposed by Selinger distributes the saddle-splay contribution in the other elastic modes. In so doing, the pure twist here corresponds to the elastic constant K_{22}-K_{24} (instead of only K_{22} in the previous formulation) and it is termed double twist, as it has no characteristic direction in the plane perpenditular to the director. The negativity of (K_{22}-K_{24}) suggests that the pure double-twisted configuration, the director configuration exiciting only the double twist mode, is the gound state of CLCs in 3D space. This peculiar director field belongs to neither of the families of uniform director; it is only possible along a 1D curve and produces elastic frustration if requested to occupy a particular geometry with particular boundary conditions. As a result, exending the ideal double twisted texture to a tubolar region introduces by necessity a non uniform texture which results from the combination of other fundamental deformation modes with pure double twist only along the axis of the cylinder. This is exatly the configuration experimentally observed for CLCs in cylidrical capillaries subject to degenerate boundary conditions. Taken for granted that the ground state of CLCs is a characteristic double-twist, we say that the so called escaped-twist ground state actually is a `pseudo-ground state' since it is the result of the confinement-induced extension of the pure double twist, which injects a elastic frustration in the system. What is wrong with the application of Frank's elastic theory to CLCs? Why do we need a new elastic theory for them?

Perylene tetracarboxylic acid bisimides are compounds that show intense visible light absorption and exhibit excellent chemical, photochemical and thermal stability. As such, they have been widely used as dyes and have a range of industrial applications. These dyes have also been investigated for various applications in aqueous media as chromonic liquid crystals: lyotropic systems characterised by the association of aromatic mesogenic cores into stacked structures. In this study, we focus on one perylene dye bis-(N,N-diethylaminoethyl)perylene-3,4,9,10-tetracarboxylic diimide dihydrochloride, PER, and study its self-assembly in aqueous solution through both atomistic and coarse-grained molecular models. All-atom molecular dynamics simulations demonstrate spontaneous self-assembly into chromonic H-aggregate stacks with an interparticle twist between molecules. The coarse-graining of complex chromonic mesogens introduces a wealth of subtle complexities that presents a significant challenge to overcome. Consequently, we developed coarse-grained (CG) models using both bottom-up and top-down approaches: the multiscale coarse-graining method (MS-CG) in the form of hybrid force matching (FM) and the MARTINI 3 force field, respectively. We discuss the successes/deficiencies of these approaches and introduce changes to improve upon their performance and representability. For the MARTINI 3 model, careful optimisation of parameters allows it to exactly reproduce the atomistic self-assembly behaviour including the relevant thermodynamic properties in solution. The bottom-up CG model, produced using a conventional MS-CG treatment, fails to reproduce most of the target properties, but the implementation of the potentials into a combined FM-MARTINI 3 framework allows the recovery of the correct self-assembly behaviour in solution.

Lyotropic chromonic liquid crystals (LCLCs) are a special type of hierarchical material in which self-assembled molecular aggregates are responsible for the formation of liquid crystal phases. Thanks to its unusual material properties and bio compatibility, it has found wide applications including the formation of active nematic liquid crystals. Recent experiments have uncovered tumbling character of certain LCLCs. However, how tumbling behavior modifies structure and flow in driven and active nematics is poorly understood. Here, we rely on continuum simulation to study the interplay of extensile active stress and externally driven flow in a flow-tumbling nematic with a low twist modulus to mimic nematic LCLCs. We find that a spontaneous transverse flow can be developed in a flow-tumbling active nematic confined to a hybrid alignment cell when it is in log-rolling mode at sufficiently high activities. The orientation of the total spontaneous flow is tunable by tuning the active stress. We further show that activity can suppress pressure-driven flow of a flow-tumbling nematic in a planar-anchoring cell but can also promote a transition of the director field under a pressure gradient in a homeotropic-anchoring cell. Remarkably, we demonstrate that the frequency of unsteady director dynamics in a tumbling nematic under Couette flow is invariant against active stress when below a threshold activity but exhibits a discontinuous increase when above the threshold at which a complex, periodic spatiotemporal director pattern emerges. Taken together, our simulations reveal qualitative differences between flow-tumbling and flow-aligning active nematics and suggest potential applications of tumbling nematics in microfluidics.

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.

Significance A material’s topology is more than its shape. It governs the material’s physical properties, such as how it interacts with acoustic waves and transports charge carriers. Utilizing liquid crystals (LCs) and their defects, researchers have pursued understanding topological aspects of condensed matter. Our work discusses the topological properties of cholesteric LCs that twist spontaneously. The traditional topological descriptions of LC do not extend to a complete characterization of cholesterics, and yet they often exhibit behavior with a strong topological and geometric character. We show that a more subtle chiral topology, protected by nonvanishing twist, can be used to define new topological numbers and understand these systems’ behavior, including the metastability, layering transitions, and soliton structures that traditional invariants cannot describe.

A striking feature of lyotropic chromonic liquid crystals confined in cylinder model exhibit double-twist director configurations. Evidence suggests that saddle-splay deformation is among t...

As a preparation method for organic–inorganic or mesoporous inorganic materials via sol–gel condensation of a metal alkoxide, the combination of lyotropic liquid crystals (LLCs) and sol–gel chemistry is a versatile tool to fabricate various nanostructures. Despite previous investigations into such systems, no attempt has been made to utilize the dynamic switching functions of such nanostructures via the phase transition of LLCs in films. A polysiloxane containing an amine-hydrochloride group and a vinyl group was recently synthesized. By controlling the relative humidity, we achieved the phase transition of LLCs and on-demand UV-curing of LLC phases in the polysiloxane film. We further developed vertically oriented organic–inorganic nanochannels by using π−π interactions between discotic molecules and the substrate surface or the spontaneous vertical alignment of LLC containing azobenzene units. A method to control on-demand phase transition and alignment of organic–inorganic hybrid containing lyotropic liquid crystals (LLCs) have been developed. By using polysiloxane containing hygroscopicity and photocrosslinking groups, the phase transition of the LLCs can be induced by changes in humidity. The phase-transition behavior of the LLCs in polysiloxane can be suppressed by light irradiation. Further, the author proposed new methods for vertically aligning nanochannels by using surface interaction or the spontaneous vertical-aligned nature, and photopatterning of chromonic dye aggregates.

The nematic (chromonic N) and isotropic phases formed by aqueous solutions of a perylene dye are investigated by x-ray diffraction and visible light absorption spectroscopy. X-ray diffracti...

Lyotropic chromonic liquid crystals (LCLCs) constitute a unique variety of water-soluble mesogens that spontaneously assemble into elongated aggregates, thereby resulting in the formation of liquid crystal phases depending on the temperature and concentration. The influence of ionic additives on the aggregation of LCLC has been extensively studied, but the molecular mechanisms governing these effects remain unclear. In this investigation, we perform atomistic molecular dynamics simulations of dilute sunset yellow (SSY) LCLC solutions doped with NaCl and MgCl2 salts. Structural and dynamical properties of SSY hydration shells are considerably modified by the partial substitution of their H bonds with sodium/magnesium-sulfonate ion pairs. Although the intermolecular distance of ∼3.4 A between SSY mesogens is preserved regardless of the ionic content, the growing number of ion pairs favors the reduction of the electrostatic repulsion between mesogens, increasing the length of SSY stacks. Moreover, magnesium ...

Amplification of chirality across length scales is a key concept pertinent to many models aiming to unravel the origin of homochirality. Tactoids of lyotropic chromonic liquid crystals formed by DNA, dyes, and other flat ionic molecules in water in the biphasic nematic + isotropic regime turn out to be a particularly relevant system to investigate chirality transfer and amplification. Herein, we present experiments to determine the amplification of chirality by luminescent gold nanoclusters decorated with adenosine monophosphate inducing chiral nematic tactoids formed by disodium cromoglycate in water. Polarized optical microscopy investigations of the induced homochiral tactoids reveal that adenosine monophosphate shows a higher optical activity when bound to the surface of such gold nanoclusters in comparison to free adenosine monophosphate, despite a three-time lower overall concentration. Free adenosine monophosphate also induces the opposite chiral twist both in the bulk nematic phase as shown by induced thin film circular dichroism spectropolarimetry and in the tactoids in comparison to adenosine monophosphate bound to the gold nanocluster. Overall, these experiments demonstrate that lyotropic chromonic liquid crystal tactoids are powerful systems to image and quantify chirality amplification by key biological chiral molecules that would have played a role in the origin of homochirality.

We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen–Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives.This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

An extensive experimental study of the shapes of two-dimensional bipolar droplets of the chromonic N nematic phase of disodium cromoglycate (DSCG) sandwiched between glass plates, by Y.-K. Kim et al. was published in [Y.-K. Kim et al., J. Phys.: Condens. Matter 25, 404202 (2013)]. 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 ten- sion 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.

Cyanine dyes are known to form large-scale aggregates of various morphologies via spontaneous self-assembly in aqueous solution, akin to chromonic liquid crystals. Atomistic molecular dynamics simulations have been performed on four cyanine dyes: pseudoisocyanine chloride (PIC), pinacyanol chloride (PCYN), 5,5’,6,6’-tetrachloro-1,1’,3,3’- tetraethylbenzimidazolylcarbocyanine chloride (TTBC) and 1,1’-disulfopropyl-3,3’-diethyl-5,5’,6,6’- tetrachloro-benzimidazolylcarbocyanine sodium salt (BIC). Simulations employed an optimised general AMBER force field and demonstrate the organisation of the dyes into stacked structures at dilute concentrations. The thermodynamics of self-assembly was studied by calculating potentials of mean force for n-mers (n = 2, 3 or 4), from which the free energies of association are determined. We report binding free energies in the range of 8 to 15 kBT for dimerisation, concordant with typical values for ionic chromonics (7 to 14 kBT), and examine the enthalpic and entropic contributions to the aggregation process. The self-assembly of these dyes yields two distinct classes of structures. We observe the formation of H-aggregate stacks for PCYN, with further complexity in these assemblies for PIC; where the aggregates contain shift and Y junction defects. TTBC and BIC associate into a J-aggregate sheet structure of unimolecular thickness, and is composed of a brickwork arrangement between molecules. These sheet structures are characteristic of the smectic chromonic mesophase, and such assemblies provide a route to the emergence of nanoscale tubular architectures.

The elastic and viscous properties of lyotropic chromonic liquid crystals have a very sharp, often exponential temperature dependence. Self-propelled bacteria swimming in this viscoelastic medium induce director deformations which can strongly influence their velocity, and we study the temperature behavior of their motility in the whole range of the nematic phase. We observe experimentally that, with increasing temperature, while the viscosity drops exponentially and the frequency of the flagellum rotation grows linearly, the swimmers' speed first conventionally increases but then, above some crossover temperature, slows down and at the same time bacteria-induced director distortions become visible. It is shown that the physics behind this temperature-driven effect is in a sharp rise in the ability of the bacterium's flagellum to induce director deformations. As temperature increases, the splay and bend elastic constants sharply decrease and the anchoring extrapolation length of the flagellum surface gets shorter and shorter. At the crossover temperature the resulting effective anchoring effect dominates the fast dropping viscosity and the distortion strengthens. As a result, a fraction of the torque the flagellum applies for the propulsion is spent for the elastic degrees of freedom, which results in a bacterium slowdown. To find the director distortions, the flagellum is presented as a collection of anchoring-induced elastic monopoles, and the bacterium velocity is found from the balance of the energy spent for the propulsion and the viscous drag and nematodynamic dissipation.

We describe the influence of competing self-organizing phenomena on the formation of cholesteric mesophase in liquid crystalline brush block terpolymers (LCBBTs) and liquid crystalline random brush terpolymers (LCRBTs) containing chromonic molecules. A library of LCBBTs and LCRBTs are synthesized using ring-opening metathesis polymerization (ROMP) of norbornene side-chain functionalized monomers comprising cholesteryl mesogen (NBCh9), chromonic xanthenone (NBXan), and poly(ethylene glycol) (NBMPEG). Compression molded films of LCRBTs containing chromonic molecules display multilevel hierarchical structure in which cholesteric mesophase co-exists with π–π stacking of the chromonic mesophase along with PEG microphase segregated domains. This is unexpected as conventional LCBCPs and LCBBCs that lack chromonic molecules do not form cholesteric mesophases. The presence of π–π interactions modifies the interface at the IMDS so that both chromonic and cholesteric mesophases coexist leading to the manifestation of cholesteric phase for the first time within block architecture and is very reminiscent of previously published LCRBCs without chromonic molecules. The key to the observed hierarchical assembly in these LCBBTs containing chromonic molecules lies in the interplay of LC order, chromonic π–π stacking, PEG side chain microphase segregation, and their supramolecular cooperative motion. This unique “single component” polymer scaffold transforms our capacity to attain nanoscale hierarchies and optical properties from block architecture similar to nanoscale mesophases resulting in random architecture.

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.

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.