Observation of a chiral-symmetry-breaking twist-bend instability in achiral freely suspended liquid-crystal films

Twisted loxodromes in spindle-shaped polymer nematics

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

Microfluidic control over topological states in channel-confined nematic flows

Compared to isotropic liquids, orientational order of nematic liquid crystals makes their rheological properties more involved, and thus requires fine control of the flow parameters to govern the orientational patterns. In microfluidic channels with perpendicular surface alignment, nematics discontinuously transition from perpendicular structure at low flow rates to flow-aligned structure at high flow rates. Here we show how precise tuning of the driving pressure can be used to stabilize and manipulate a previously unresearched topologically protected chiral intermediate state which arises before the homeotropic to flow-aligned transition. We characterize the mechanisms underlying the transition and construct a phenomenological model to describe the critical behaviour and the phase diagram of the observed chiral flow state, and evaluate the effect of a forced symmetry breaking by introduction of a chiral dopant. Finally, we induce transitions on demand through channel geometry, application of laser tweezers, and careful control of the flow rate.

It is interesting phenomenon that chiral order can emerge in intrinsically achiral liquid crystals. Here Čopar et al. demonstrate achiral-to-chiral transition of the nematic liquid crystals flow in microfluidic channels and their behaviour, stability, and dependence on geometric and material parameters.

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.

Two-dimensional hexagonal smectic structure formed by topological defects

A two-dimensional hexagonal smectic structure formed by point topological defects and intersecting defect walls was discovered. This unique structure was predicted theoretically about 30 years ago but not observed. For a long time the hexagonal structure was a challenge for experimentalists. A different type of self-organization in smectic films was found and used to form the hexagonal structure. Methods applied for building the hexagonal phase can be used for the formation of complicated liquid-crystal structures.

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.

Self-organized chiral colloidal crystals of Brownian square crosses

We study aqueous Brownian dispersions of microscale, hard, monodisperse platelets, shaped as achiral square crosses, in two dimensions (2D). When slowly concentrated while experiencing thermal excitations, the crosses self-organize into fluctuating 2D colloidal crystals. As the particle area fraction φA is raised, an achiral rhombic crystal phase forms at φA ≈ 0.52. Above φA ≈ 0.56, the rhombic crystal gives way to a square crystal phase that exhibits long-range chiral symmetry breaking (CSB) via a crystal-crystal phase transition; the observed chirality in a particular square crystallite has either a positive or a negative enantiomeric sense. By contrast to triangles and rhombs, which exhibit weak CSB as a result of total entropy maximization, square crosses display robust long-range CSB that is primarily dictated by how they tile space at high densities. We measure the thermal distribution of orientation angles γ of the crosses' arms relative to the diagonal bisector of the local square crystal lattice as a function of φA, and the average measured γ (φA) agrees with a re-scaled model involving efficient packing of rotated cross shapes. Our findings imply that a variety of hard achiral shapes can be designed to form equilibrium chiral phases by considering their tiling at high densities.

Labyrinthine instability in freely suspended films of a polarization-modulated smectic phase

We report on fingering and labyrinthine instabilities of the layer dislocation lines in freely suspended polar liquid-crystalline films. These polar fingerlike and labyrinth structures reversibly form upon a transition into a modulated phase. External electric fields of several kV/m applied in the film plane can reversibly influence the formation of the finger textures. We show that the labyrinthine pattern is intrinsically related to regular splay deformations of the polarization.

Surface energetics of freely suspended fluid molecular monolayer and multilayer smectic liquid crystal films

A study of the surface energetics of the thinnest substrate-free liquid films, fluid molecular monolayer and multilayer smectic liquid crystal films suspended in air, is reported. In films having monolayer and multilayer domains, the monolayer areas contract, contrary to predictions from the van der Waals disjoining pressure of thin uniform slabs. This discrepancy is accounted for by modeling the environmental asymmetry of the surface layers in multilayer films, leading to the possibility that preferential end-for-end polar ordering of the rod shaped molecules can reduce the surface energy of multilayers relative to that of the monolayer, which is inherently symmetric.

Ambidextrous bend patterns in free-standing polar smectic- CP{F} films

We report an unusual behavior of a ferroelectric smectic-CP{F} film formed by bent-shaped molecules. The ground state of the c -director in such film is not uniform but forms a striped pattern with alternating bend deformation. We found that the sense of the alternating bend is not related to an alternating handedness defined by the mutual orientation of the tilt ( c director) and the bow ( p director) of the molecules. Despite its similarity to a previously described twist-bend instability [J. Pang and N. A. Clark, Phys. Rev. Lett. 73, 2332 (1994)], this pattern cannot be explained in terms of spontaneous chiral symmetry breaking with continuous variation of the chirality order parameter, since the synclinic order of the polar molecules predefines the chirality of the film. We discuss possible models describing the spontaneous formation of an ambidextrous bend pattern of the c director.

Field-induced phase transitions and reversible field-induced inversion of chirality in tilted smectic phases of bent-core mesogens

Three homologous achiral five-ring bent-core mesogens are presented where 4-chlororesorcinol is the central core and the aromatic rings are linked by ester groups. These compounds form smectic phases with a tilted arrangement of the molecules (tilt angle approximately 45 degrees). On cooling the isotropic liquid this phase adopts a fan-like texture which shows for two homologues at relatively high electric fields ( 25-35 V microm(-1)) an antiferroelectric electro-optical response based on the collective rotation of the molecules around their long axes. At lower temperature the application of a sufficiently high electric field leads to a continuous transition into a non-birefringent texture which exhibits randomly distributed domains of opposite handedness. These domains can be reversibly switched into a state of opposite chirality by reversal of the field polarity. This switching is bistable and shows a current response typical for a ferroelectric ground state. The possible mechanism of the field-induced phase transition, of the ferroelectric switching and of the field-induced inversion of the chirality is discussed on the base of XRD, 13C- and 1H-NMR investigations, dielectric and electro-optical measurements.

Substrate induced 1D tilt-modulated state in nematic monolayers

Symmetry considerations yield the general form, up to second order terms, for the deformation elastic energy of a nematic monolayer, composed by symmetric achiral molecules, on a rigid planar substrate. The deformation energy contains an elastic contribution linear in the deformation tensor, whose elements are the spatial derivatives of the average molecular orientation. This linear Lifshitz-invariant-like term can be responsible for a ground state of the nematic monolayer periodically deformed if the relevant elastic constant is stiffer than a critical value. The wave-length of the modulation diverges at the transition threshold. We show that only large variations of the tilt angle form stable states. The effect of a destabilizing electric or magnetic field on the layer is to induce (i) the transition towards the tilt-modulated phase, while (ii) for higher enough values of the field the modulation is destroyed.

Spontaneous breaking of minimal surface condition: labyrinths in free standing smectic films

We present a study of thin free standing films made of intercalated smectic-C liquid crystal in which, upon lowering the temperature, the minimal surface area condition is broken. A periodic modulation of the film thickness is obtained and a labyrinth structure of crests and valleys is formed. Thickness variation is coupled to the spatial variation of the molecular orientation. The transition to the labyrinth structure is explained to be driven by the mass density difference between the surface and the bulk layers.

Light-induced layer by layer thickening in photosensitive liquid crystal membranes

Photosensitive smectic membranes of pure liquid crystal (LC) were studied under white light illumination. A thickness increase is observed in the illuminated film area. Appropriate light and thermal conditions lead to a thickening layer by layer process. This unusual phenomenon is opposite to the well-known step-by-step thinning transitions under heating. We give a phenomenological interpretation for thickening based on layer transport of LC matter towards the illuminated area.

Modulated structures in nematic monolayers formed by symmetric molecules

An analysis based on symmetry yields a general form for the deformation elastic energy of a nematic monolayer, formed by achiral symmetric molecules, deposited on a solid substrate. Lifshitz-invariant-like terms in the energy, which originate from the substrate field, can induce a modulated-tilt state if the anchoring energy is sufficiently low. A way to enhance the symmetry breaking is to apply a destabilizing magnetic or electric field that serves to lower the anchoring energy. In the case of an initial state with homeotropic alignment, the phase diagram displays a cusp-shaped tilt-modulated state intervening between two uniform tilt states.

Reflection of light at structured chiral interfaces

Modified boundary conditions and general surface constitutive equations are derived for a very thin interface with some internal structure that separates two different media. The modified boundary conditions are reduced to the standard ones for an idealized steplike sharp interface without additional structure. These modified boundary conditions together with surface constitutive equations and Maxwell equations in the bulk form a complete set of macroscopic equations to describe optical properties of planar interfaces with thicknesses much less then the wavelength of light. In particular, two-dimensional chiral surfaces are considered that are characterized by surface gyrotropic coefficients even if the two different bulk media and the interface are made of nonchiral materials. It is shown that the rotation of the polarization state should occur for the light reflected from such a surface. This result is supported by recent experimental data.

Splayed polarization in the ferroelectric phase of a bent-core liquid crystal as studied by optical second-harmonic generation

Splayed polarization orientation has been confirmed in the anticlinic ferroelectric phase of a bent-core liquid crystal containing chiral end chains, P-8 -OPIMB6(*), by optical second-harmonic generation (SHG). The in-plane anisotropy of the SHG signal exhibits an unusual six-peak pattern under the rotation of parallel polarizers in the absence of an electric field, while a usual four-peak pattern simulatable using a uniform molecular orientation model is observed under a field. The unusual pattern was explained by considering a splayed polarization orientation including the effect of polarization charges.

Linear splay elasticity in surface-induced films of tilted smectic liquid crystals

The prefrozen films that may be observed at the surface of isotropic liquid crystal droplets, close to the isotropic-smectic phase transition, or surface-induced films, are essentially asymmetric. If moreover, the molecules are tilted inside the smectic layers, as in the smectic-C (SmC) or smectic-C(A) (SmC(A)) phases, the c director that we may define as the order parameter of the film, is a real vector. Thus, the surface-induced films of MHTAC exhibit vectorial or polar properties, though the molecules are not chiral. The film free energy therefore contains a surface-elasticity term, K(1)c(2) c, that is a linear function of the splay distortion, and that may be negative enough to promote a mechanical instability. A spontaneous c distortion, or c modulation, then invades the whole film and produces an array of parallel stripes, with a typical four-fringe periodicity when observed between crossed polarisers. Here, we present optical measurements of the distortion for different film thicknesses, and we propose a linear analysis of the data to test our model. Due to the limitations inherent to the Fourier expansion that we use, the calculations are valid only between two limits: a large q limit where splay domains collapse into disclination lines, and a small q borderline below which the distortion evolves towards a system of independent solitons. We find that the sign of the spontaneous splay elastic constant K1 alternates as a function of the number of layers, N, a property that is reminiscent of the alternate structure of the SmC(A) phase. We argue that the two-dimension elastic constant, K1, originates from the interactions between the molecules in contact to the isotropic phase, and we deduce K1 approximately -(-1)(N)x10(-11) N and the elastic anisotropy, with a ratio of the splay over bend elastic constants K(s)/K(b) approximately 4.5. Similar properties could be observed also in other types of ultrathin films, e.g., in free-standing, ferroelectric (SmC*) or antiferroelectric (SmC(*)(A)), films, in Langmuir films, and even in particular biological films. In some cases, a second, electric instability may occur and superimpose onto the elastic one.

Polarization-modulated smectic liquid crystal phases

Any polar-ordered material with a spatially uniform polarization field is internally frustrated: The symmetry-required local preference for polarization is to be nonuniform, i.e., to be locally bouquet-like or "splayed." However, it is impossible to achieve splay of a preferred sign everywhere in space unless appropriate defects are introduced into the field. Typically, in materials like ferroelectric crystals or liquid crystals, such defects are not thermally stable, so that the local preference is globally frustrated and the polarization field remains uniform. Here, we report a class of fluid polar smectic liquid crystals in which local splay prevails in the form of periodic supermolecular-scale polarization modulation stripes coupled to layer undulation waves. The polar domains are locally chiral, and organized into patterns of alternating handedness and polarity. The fluid-layer undulations enable an extraordinary menagerie of filament and planar structures that identify such phases.

Orientational ordering and chiral symmetry breaking in organic monolayers composed of disklike mesogenic molecules: molecular theory and computer simulations

Orientational ordering of disklike molecules on a flat surface is investigated using a molecular-statistical theory and Monte-Carlo simulations. The theory is based on the two-dimensional orientational order parameter for molecules with a threefold symmetry axis, and on a simple model interaction potential which has been derived taking into consideration only the symmetry of basic molecular structure. The theory reveals three different anisotropic phases. One of them exactly corresponds to the structure which has recently been observed experimentally in self-assembling monolayers of discotic mesogenic molecules on a pyrolitic graphite surface. This is a two-dimensional (2D) chiral anisotropic phase composed of nonchiral molecules. The phase consists of three sublattices with different orientational order. One sublattice is orientationally disordered, while the other two sublattices are ordered with the same scalar order parameter and different orientations of the ordering tensor. Both order parameters of the directions of ordering are determined self-consistently by minimizing the total free energy of the system. The detailed structure of this unusual phase is also confirmed by the results of Monte Carlo simulations based on the same model interaction potential. The results of the theory qualitatively explain existing experimental data and also shed some light on the origin of supramolecular structures observed in 3D columnar phases composed of similar molecules.

Chiral and antichiral order in bent-core liquid crystals

Recent experiments have found a bent-core liquid crystal in which the layer chirality alternates from layer to layer, giving a racemic or "antichiral" material, even though the molecules are uniformly chiral. To explain this effect, we map the liquid crystal onto an Ising model, analogous to a model for chiral order in polymers. We calculate the phase diagram for this model and show that it has a second-order phase transition between antichiral order and homogeneous chiral order. We discuss how this transition can be studied by further chemical synthesis or by doping experiments.

Macroscopic chirality of a liquid crystal from nonchiral molecules

The transfer of chirality from nonchiral polymer networks to the racemic B2 phase of nonchiral banana-shaped molecules is demonstrated. This corresponds to the transfer of chirality from an achiral material to another achiral material. There are two levels of chirality transfers. (a) On a microscopic level the presence of a polymer network (chiral or nonchiral) favors a chiral state over a thermodynamically stable racemic state due to the inversion symmetry breaking at the polymer-liquid crystal interfaces. (b) A macroscopically chiral (enantimerically enriched) sample can be produced if the polymer network has a helical structure, and/or contains chemically chiral groups. The chirality transfer can be locally suppressed by exposing the liquid crystal to a strong electric field treatment.

Formation of string defects at thinning transitions in smectic-C* free-standing films

The layer thinning transitions in freely suspended smectic-C* films have been investigated. The defect structure formed by stringlike lines was observed just before the thinning transitions. The string defects disappear after the thinning transition and appear again near the temperature of the next thinning transition. These results clearly indicate that thin free-standing films at the thinning transitions are slightly below the melting temperature of the interior layers.

Analysis of compression-induced chiral phase separation in Langmuir monolayers

We analyze the compression-induced chiral phase separation (CPS) in Langmuir films, taking into account the elastic theory of liquid crystals and the mixing energy of the two constituent enantiomers. The difference between the Selinger-Wang-Bruinsma-Knobler theory [J. V. Selinger et al., Phys. Rev. Lett. 70, 1139 (1993)] and our treatment is that we do not introduce the concentration-square-gradient term in the free energy, but alternatively take into account a line tension at CPS boundaries. Our model predicts that a two-domain pattern with opposite chiralities is energy minimized, but a multistripe pattern with two alternate constant chiralities is also possible, though metastable. This offers a tentative explanation for the CPS pattern consisting of homogeneously oriented stripes with diverse widths observed by Eckhardt et al. [Nature (London) 362, 614 (1993)].