Liquid crystalline systems exhibiting both macroscopic chirality and smectic order experience frustration resulting in mesophases possessing complex three-dimensional order. In the twist-grain-boundary phase, defect lattices mediate the propagation of twist throughout the system. We propose a new chiral smectic structure composed of a lattice of chiral bundles as a model of the helical nanofilament (B4) phase of bent core smectics.
Frustration is a powerful mechanism in condensed matter systems, driving both order and co plexity. In smectics, the frustration between macroscopic chirality and equally spaced layers generates textures characterised by a proliferation of defects. In this article, we study several different ground states of the chiral Landau-de Gennes free energy for a smectic liquid crystal. The standard theory finds the twist grain boundary (TGB) phase to be the ground state for chiral type II smectics. However, for very highly chiral systems, the hierarchical helical nanofilament (HN) phase can form and is…
General microscopic mechanism of ferroelectric ordering in chiral smectic C* liquid crystals is considered. It is shown that if the mesogenic molecules have a sufficiently low symmetry, the spontaneous polarization is proportional to one of the biaxial vector order parameters of the smectic C phase. This order parameter may be determined by intermolecular interactions which are not sensitive to molecular chirality. At the same time, the polarization is also proportional to a pseudoscalar parameter which vanishes if the molecules are nonchiral. The general statistical theory of ferroelectric or…
Smectic blue phases (BPSm) are new mesophases of thermotropic liquid crystals, which exhibit a double geometrical frustration: the extension of chirality in three spatial dimensions like the classical blue phases, and helical twist competing with smectic order, as in the TGB phases. The existence of a quasi-long range smectic order in BPSm phases breaks the cubic symmetry of classical blue phases. The symmetries of these new phases have been determined by X-ray scattering and optical polarizing microscopy experiments.
The order parameters for the phenomenological description of the smectic-{\it A} to smectic-{\it C} phase transition are formulated on the basis of molecular symmetry and structure. It is shown that, unless the long molecular axis is an axis of two-fold or higher rotational symmetry, the ordering of the molecules in the smectic-{\it C} phase gives rise to more than one tilt order parameter and to one or more polar order parameters. The latter describe the indigenous polarity of the smectic-{\it C} phase, which is not related to molecular chirality but underlies the appearance of spontaneous po…
We develop a theory of point defects in cholesterics and textures in spherical droplets with normal anchoring. The local structure of chiral defects is described by singularity theory and a smectic-like gradient field establishing a nexus between cholesterics and smectics mediated by their defects. We identify the defects of degree $-2$ and $-3$ observed experimentally with the singularities $D_4^{-}$ and $T_{4,4,4}$, respectively. Radial point defects typical of nematics cannot be perturbed into chiral structures with a single handedness by general topological considerations. For the same rea…
We formulate a simple Landau type model describing macroscopic behaviour recently discovered new smectic phases composed of achiral bent-shaped molecules. Films of such smectics exhibit three types of ordering related to dipole polarization, molecular tilt, and chirality. However due to specific third order coupling of the order parameters these three types of symmetry-breaking are not independent ones, and this fact leads to specific domain structures really observed in experiments.
We explore the possibility that the large electroclinic effect observed in ferroelectric liquid crystals arises from the presence of an ordered array of disclination lines and walls. If the spacing of these defects is in the subvisible range, this modulated phase would be similar macroscopically to a smectic A phase. The application of an electric field distorts the array, producing a large polarization, and hence a large electroclinic effect. We show that with suitable elastic parameters and sufficiently large chirality, the modulated phase is favored over the smectic A and helically twisted …
Smectic-A monolayers self-assembled in aqueous solutions of chiral fd viruses and a polymer depletant have been shown to exhibit a variety of structures including large, flat disks and twisted ribbons. The virus particles twist near the edge of the structure in a direction determined by the chirality of the viruses. When fd viruses and their mutants of opposite chirality are mixed together in nearly equal amounts unusual structures referred to as "crenellated disks" can appear. These disks are achiral overall but the twist at the edge alternates between left- and right-handedness. To minimize …
Curvature-induced smectic-C order of tangentially anchored hard spherocylinders on a sphere with a rigidly locked director field
Recognition Physics Institute（Recognition物理研究所）；Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫海因里希·海涅大学软物质理论物理第二研究所）；Department of Physics, Case Western Reserve University（凯斯西储大学物理系）；Theoretical Department, Joint Institute for High Temperatures, RAS（俄罗斯科学院高温联合研究所理论部）
We study the core structure of the twist-grain-boundary (TGB) phase of chiral liquid crystals by numerically minimizing the Landau-de Gennes free energy. We analyze the morphology of layers at the grain boundary, to better understand the mechanism of frustration between the smectic layer order and chirality. As the chirality increases, the effective bending rigidity of layers is reduced due to unlocking of the layer orientation and the director. This results in large deviation of the layer morphology from that of Scherk's first minimal surface and linear stack of screw dislocations (LSD).
Chiral domains of opposite chirality are observed surprisingly in a nematic phase of an achiral rod-like liquid crystalline mesogen that shows ferroelectric nematic and antiferroelectric smectic phases. The observations of chiral domains of opposite chirality are enabled by application of a weak electric field across a planar-aligned cell. However once domains of opposite chirality are created, these stay permanently even if the field is removed. The observed phenomenon is due to the symmetry breaking of achiral mesogens of rod-shaped molecules. These domains are similarly observed in the Nx p…
In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this paper, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active "odder" elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. Thi…
Confinement Reveals Hidden Splay-Bend Order in Twist-Bend Nematics
Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University（雅盖隆大学理论物理研究所与马克·卡克复杂系统研究中心）；International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM²), Hiroshima University（广岛大学缠绕手性超物质可持续发展国际研究所）
Chiral liquid crystals exhibit in-plane spontaneous polarizations, however in their smectic phase the primary order parameter is a tilt vector associated with molecular rotations around the long molecular axis parallel to the director. The molecular rotations lead to several distinct phases among which a domain-wall texture with a periodic-kink soliton profile. In this study the formation of domain walls in smectic chiral liquid crystals is analyzed, with emphasis on the competition between ising-type symmetric and antisymmetric nearest-neighbor interactions, and an in-plane electric field. It…
We report a detailed theoretical analysis of novel quadrupolar interactions observed between islands, which are disk-like inclusions of extra layers, floating in thin, freely suspended smectic C liquid crystal films. Strong tangential anchoring at the island boundaries result in a strength +1 chiral defect in each island and a companion -1 defect in the film, these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrup…
Stiff, elongated biomolecules such as filamentous viruses, DNA or cellulose nanocrystals are known to form liquid crystals often exhibiting a helical supramolecular organization. Little is known about the microscopic origin, size and handedness of the helical pitch in these, so-called cholesteric phases. Experimental observations in chiral lyotropics suggest that long-ranged chiral forces of electrostatic origin acting between the mesogens are responsible for such organization. Using large-scale computer simulation we study the sensitivity of the pitch imparted by soft microscopic helices and …
We review the impact of tetrahedral order on the macroscopic dynamics of bent-core liquid crystals. We discuss tetrahedral order comparing with other types of orientational order, like nematic, polar nematic, polar smectic, and active polar order. In particular, we present hydrodynamic equations for phases, where only tetrahedral order exists or tetrahedral order is combined with nematic order. Among the latter we discriminate between three cases, where the nematic director (a) orients along a 4-fold, or (b) along a 3-fold symmetry axis of the tetrahedral structure. For the optically isotropic…
