Three-dimensional Orientational Order Research Articles

Chiral ground states of ferroelectric liquid crystals.

Ferroelectric nematic liquid crystals are formed by achiral molecules with large dipole moments. Their three-dimensional orientational order is described as unidirectionally polar. We demonstrate that the ground state of a flat slab of a ferroelectric nematic unconstrained by externally imposed alignment directions is chiral, with left- and right-handed twists of polarization. Although the helicoidal deformations and defect walls that separate domains of opposite handedness increase the elastic energy, the twists reduce the electrostatic energy and become weaker when the material is doped with ions. This work shows that the polar orientational order of molecules could trigger chirality in soft matter with no chemically induced chiral centers.

Umbilic Lines in Orientational Order

Three-dimensional orientational order in systems whose ground states possess non-zero, chiral gradients typically exhibits line-like structures or defects: $\lambda$ lines in cholesterics or Skyrmion tubes in ferromagnets for example. Here we show that such lines can be identified as a set of natural geometric singularities in a unit vector field, the generalisation of the umbilic points of a surface. We characterise these lines in terms of the natural vector bundles that the order defines and show that they give a way to localise and identify Skyrmion distortions in chiral materials -- in particular that they supply a natural representative of the Poincar\'{e} dual of the cocycle describing the topology. Their global structure leads to the definition of a self-linking number and helicity integral which relates the linking of umbilic lines to the Hopf invariant of the texture.

Three-dimensional imaging of liquid crystal structures and defects by means of holographic manipulation of colloidal nanowires with faceted sidewalls

We use nanowires with faceted sidewalls for mapping of the patterns of three-dimensional orientational order and defect structures. In chiral nematics, the nanowires follow the local average orientation of rod-shaped molecules. When spatially translated by use of holographic optical tweezers in three dimensions, they mediate direct nondestructive visualization of the helicoidal ground-state structures, edge and screw dislocations, and kinks, as well as enable non-contact manipulation of these defects. We probe interactions of faceted nanowires with different defects and demonstrate their spontaneous self-alignment along the cores of singular defect lines.

Guest Orientation in Uniplanar-Axial Polymer Host Films and in Co-Crystal Unit-Cell, Determined by Angular Distributions of Polarized Guest Fluorescence

Syndiotactic polystyrene (sPS) films with uniplanar-axial orientation of their co-crystalline phase with a fluorescent guest (naphthalene, NP) have been prepared and the orientation of their crystalline phase has been fully characterized by X-ray diffraction measurements. The prepared films have been examined in detail using Nishijima's method, where angular distribution of NP polarized fluorescence intensities was measured at each setting film angle by the rotation of films around the excitation light beam. This polarized fluorescence method turns out to be quite effective for monitoring the orientation of fluorescent guest molecules in the films. In particular, in semicrystalline films presenting uniplanar-axial orientation of their sPS/NP clathrate phase, NP molecules were found to exhibit a high three-dimensional orientational order all over the films. The experimental data have also allowed to determine the orientation of the NP guest molecule with respect the axes of the co-crystal unit-cell: in satisfactory agreement with molecular modeling results, angles formed by the short and the long axes of NP with the c axis are not far from 80° while the angle between the short axis of NP and the a axis is nearly 105°.

Biaxial Nematic and Smectic A Phases in a “Peelable Banana-Shaped” Molecule†

ABSTRACT The article discusses the observation of a fluid phase having three-dimensional orientational order and its transformation to a similar phase but with an additional one-dimensional positional order in a low molar system. X-ray and optical observations establish the phases to be biaxial nematic and biaxial smectic A respectively. The organic system used is a unique combination of a bent core molecule linked to a rod-like unit through a flexible aliphatic spacer. We argue that this special combination is responsible for the observation of especially the biaxial nematic phase and propose possible molecular arrangements in the two phases.

Three-dimensional orientational order in the bulk and on the surface of polymer films and its effect on liquid-crystal alignment.

The correlation between orientation ordering of polymer chains in the bulk of polymer film and at the polymer-liquid-crystal (LC) interface has been studied to determine it's role in LC alignment. The bulk and surface ordering of polymer were investigated by null ellipsometry and x-ray reflectivity, respectively. Two kinds of liquid-crystalline polymers were used; side-chain azopolymers with azochromophores containing hydrophobic OC4H9 alkyl chain (P1) and strongly polar NO2 group (P2) as the end substituents. The uniaxial tilt orientation of azochromophores in the films of both polymers was induced by the oblique irradiation with unpolarized UV light. The two polymers exhibit similar chain orientation but different ordering of azochromophores on the surface of the films of P1 and P2. Surface ordering of P1 films correlates very well with the order in the bulk of the film, which are essentially determined by the UV exposure. However, orientational order of polymer chains at the surface of P2 films is different from that in its bulk and is not determined by UV exposure. This is explained by strong aggregation of azochromophores during its self-assembling at the polymer-air interface. The LC alignment is determined by the surface ordering of azochromophores. The results imply that ordering tendency can be effectively transferred from polymer bulk to polymer surface and then to LC if it is not lost at the polymer-LC interface.

Liquid Crystals Exhibiting a Double Geometrical Frustration: The Smectic Blue Phases

Smectic blue phases (BPSm) are original mesophases of thermotropic liquid crystals, which exhibit both three-dimensional orientational order, such as classical blue phases, and smectic positional order. The BPSm phases appear to be the three-dimensional counterpart of the twist grain boundary (TGB) phases. The symmetries of these new phases have been determined by X-ray scattering and optical polarizing microscopy experiments.

Photoinduced three-dimensional orientational order in side chain liquid crystalline azopolymers.

We apply experimental technique based on the combination of methods dealing with principal refractive indices and absorption coefficients to study the photoinduced three-dimensional (3D) orientational order in the films of liquid crystalline (LC) azopolymers. The technique is used to identify 3D orientational configurations of trans azobenzene chromophores and to characterize the degree of ordering in terms of order parameters. We study two types of LC azopolymers which form structures with preferred in-plane and out-of-plane alignment of azochromophores, respectively. Using irradiation with the polarized light of two different wavelengths, we find that the kinetics of photoinduced anisotropy can be dominated by either photoreorientation (angular redistribution of trans chromophores) or photoselection (angular selective trans-cis isomerization) mechanisms depending on the wavelength. At the early stages of irradiation, the films of both azopolymers are biaxial. This biaxiality disappears on reaching a state of photosaturation. In the regime of photoselection, the photosaturated state of the film is optically isotropic. But, in the case of the photoreorientation mechanism, anisotropy of this state is uniaxial with the optical axis dependent on the preferential alignment of azochromophores. We formulate the phenomenological model describing the kinetics of photoinduced anisotropy in terms of the isomer concentrations and the order parameter tensor. We present the numerical results for absorption coefficients that are found to be in good agreement with the experimental data. The model is also used to interpret the effect of changing the mechanism with the wavelength of the pumping light.

Faceted monodomains of liquid crystal smectic blue phases.

Smectic blue phases (BP(Sm)) are mesophases of thermotropic liquid crystals, which exhibit both three-dimensional orientational order, such as classical blue phases, and smectic positional order. The BP(Sm) phases appear as the three-dimensional counterpart of the twist grain boundary phases. By growing large faceted monocrystals of BP(Sm) phase, we provide, for the first time at the length scale of the lattice parameter, information on the symmetry of the orientational unit cell. This study leads us to suggest an orthorhombic structure, contrary to the previous results obtained by x-ray scattering at the length scale of the smectic order.

Optical activity measurements in the smectic blue phases

Optical activity measurements have been performed on the smectic blue phases ( BPSm), which are a new kind of chiral liquid crystal. BPSm exhibit both three-dimensional orientational order, like the classical blue phases, and smectic positional order. Thus, they can be viewed as the three-dimensional counterpart of the twist grain boundary phases. A comparison with the optical activity of the classical blue phases is carried out, and an estimation of the BPSm lattice parameter is reported for the first time.

Structural investigations on smectic blue phases.

Smectic blue phases ( BP(Sm)) are thermotropic liquid crystalline phases which exhibit both three-dimensional orientational order, such as classical blue phases, and smectic positional order. BP(Sm) appear as the three-dimensional counterpart of twist grain boundary phases. X-ray scattering and optical polarizing microscopy provide information on the hexagonal and cubic symmetries of these new phases.