Focal Conic Domains Research Articles

Dielectric characterization of the B7 and a BX phase

The first clear experimental evidence of a dielectric relaxation in the B7 phase is given. The associated molecular process is probably the reorientation of the bent-shaped molecules about the long molecular axis. It is also shown that the dielectric constant strongly increases at the phase transition I-B7 pointing to a co-operative motion of ferroelectric clusters. Furthermore, a phase transition B7-BX is observed. The values of about 10 for the high frequency limit of the dielectric constants of the B7 and BX phases and the static dielectric constants of the isotropic phase are in agreement. Thus, in all the phases the main dipoles can reorient faster than 10−8 s, i.e. the experimental limit. Only in the supercooled BX phase were the dynamics of the transversal dipoles measured. Using atomic force microscopy, focal-conic domains modulated by parallel lines have been observed at room temperature.

Characterization of the B4 phase by dielectric and AFM measurements

Dielectric measurements on a sample consisting of banana-shaped molecules were carried out in a frequency range between 0.1 Hz and 10 MHz. The sample exhibited B2 and B4 phases. As usual, two ranges of relaxation were detected in the B2 phase, the fast reorientation about the long axes of the molecules and a slow collective process. In the B4 phase, only one dielectric active process at low frequencies was found; this does not differ from the low frequency relaxation of the B2 modification. This relaxation is probably related to the dynamics of superstructures. Crystallization could be observed after keeping the sample for a longer time at higher temperature. Thus, it was possible to differentiate clearly between the crystalline and the B4 phases. AFM investigations prove the existence of focal-conic domains and periodic superstructures in the B4 phase; then do not appear in the crystalline state. For this reason the B4 phase is regarded as different from a classical crystalline phase.

Diffraction from Polymer-Stabilized Cholesteric Texture Films

We have performed diffraction experiments on polymer-stabilized cholesteric texture (PSCT) films made from E48-BAB6 mixtures cured at various UV intensities. The diffraction observed in these samples is the Qu'etelet-type ring pattern, which is generated from the scattering of light by the clusters of the polymer networks and the focal conic domains of cholesteric liquid crystals in a PSCT cell. We monitored the dynamic change of the intensity of the first ring of a sample during polymerization. After polymerization, both the electro-optical characteristics and the diffracted ring intensities of various orders were measured. The results showed that both the applied voltage and the UV curing intensity affected the diffraction intensity significantly. Furthermore, the results obtained from diffraction measurements correlate with the electro-optical ones. Thus, the diffraction measurements could provide us with another qualitative, nondestructive method to analyze PSCT devices.

Tiling the plane with noncongruent toric focal conic domains

This paper deals with regular arrays of macroscopic defects (focal conic domains) observed when a slab of lamellar phase is sandwiched between two substrates imposing different orientational anchorings. We report, in particular, detailed observations of the texture of a lyotropic lamellar phase in contact with a glass substrate and a lyotropic sponge phase. We consider several models for the defects depending on the material and the substrate parameters. Their energy has a common form, and the main features of the textures are explained in the framework of a simple model where disks of different sizes tile a plane in order to minimize a particular interface energy.

P‐70: Waveguide Based Cholesteric Liquid Crystal Displays

AbstractA waveguide based cholesteric liquid crystal display (WGCLCD) is demonstrated. Instead of using polarizers to control light intensity as in conventional LCDs or using reflection band to reflect light as in conventional reflective CLCD, a cholesteric cell is used in the WGCLCD to switch light out of a waveguide with high optical efficiency. Instead of an extra scattering screen as in conventional waveguide based LCDs, focal conic domains are used to scatter light out of the waveguide. Wide viewing angle, high peak brightness and high contrast ratio are obtained

AFM investigations of a sample showing the B2 phase

Atomic force microscopy (AFM) images reveal that the liquid crystalline B2 phase has no helical superstructure, in contrast to the B7 phase. This is demonstrated on comparing the AFM images of focal-conic domains in the smectic A, cholesteric, B2 and B7 phases. The B2 and B7 phases are phases formed by banana-shaped molecules. The results point to the existence of ferroelectric clusters with a random size distribution which also cause the low frequency dielectric relaxation.

Grain boundaries and the law of corresponding cones in smectics

Focal Conic Domains (FCDs) in smectic phases often assemble according to a particular rule, experimentally discovered by G. Friedel, the law of corresponding cones (l.c.c.). This paper reports various results relating to this type of association. First we show that a l.c.c. contact between 2 focal conic domains has a vanishing energy, yielding metastable local equilibrium. Then we use some projective properties of conic sections to extend the celebrated Apollonian tiling, which describes a tilt grain boundary (TiGB) of vanishing disorientation \(\) made of toric focal conic domains, to any \(\) TiGB. Finally we present a realistic model of the energy of the \(\) TiGB, which we compare to the energy of a TiGB split into dislocations, and to the energy of a curvature wall. This model explains why FCD tilings show macroscopic zones not filled with FCDs.

Curvature energy of a focal conic domain with arbitrary eccentricity

The most frequently observed focal conic domains (FCD's) in lamellar phases are those based on confocal paris of ellipse and hyperbola. Experimentally, the eccentricity of the ellipse takes a broad range of values 0</=e<1. We present an analytical expression for the curvature energy of a FCD that is valid in the entire range 0</=e<1. Generally, the curvature energy of an isolated FCD reaches a minimum only at e-->1 (under the constraint of a fixed major semiaxis of the ellipse); exceptions include situations with large saddle-splay elastic constant and small domains where the applicability of the elastic theory is limited. In realistic cases, a value of eccentricity smaller than 1 is stabilized by factors other than the curvature energy: by dislocations emerging from the FCD's with e not equal0, compression of layers and surface anchoring.

Curvature walls and focal conic domains in a lyotropic lamellar phase

In the quasi-ternary CPCl/brine/hexanol lyotropic system, the interface of the \({L_\alpha }\) lamellar and L3 sponge phases displays a phenomenon of epitaxy: the layers of the lamellar phase tend to make a constant non-trivial angle with the interface. Thin samples of lamellar phase embedded in the sponge phase are thus submitted to oblique anchoring conditions and defects are created in the lamellar phase in order to satisfy the bulk lamellar ordering and the boundary conditions. We have studied small droplets of lamellar phase in the sponge phase. They do not exhibit the classic \({L_\alpha }\) defects (focal conic domains) but wall defects, which appear in order to satisfy the smectic elasticity and the boundary conditions. Moreover we show through experiments in controlled geometry that, even in the presence of focal conic domains, wall defects control the size and periodicity of the textures which are observed at the interface.

Photocontrol of Smectic Spacing

We report on the results of optical, X-ray and NMR studies of light-induced phenomena in smectic phases triggered by molecular phototransformations. UV irradiation causes trans-to-cis isomerization of the dopant molecules while irradiation in the visible part of the spectrum facilitates cis-to-trans relaxation. Cis-to-trans isomerization decreases the smectic layers' spacing; as the result, a smectic slab undergoes an undulation instability and/or formation of focal conic domains. These textures are nonuniform and scatter light; this effect can be used for optical data storage. The opposite trans-to-cis isomerization disorders the orientation of molecules and increases the thickness of smectic layers. Two beams of different wavelengths with distinct yields of isomerisation can be used to write and erase optical information.

Bending moduli of a nonadsorbing-polymer-containing lyotropic lamellar phase: An experimental study

We investigate the effect of the incorporation of a neutral water-soluble nonadsorbing polymer polyvinylpyrrolidone (PVP) on the bilayer bending moduli \ensuremath{\kappa} and $\overline{\ensuremath{\kappa}}$ of the lamellar phase ${L}_{\ensuremath{\alpha}}$ composed of cetylpiridiniumchloride ${(\mathrm{CPCL})/\mathrm{h}\mathrm{e}\mathrm{x}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{l}/\mathrm{H}}_{2}\mathrm{O}.$ The mean bending modulus \ensuremath{\kappa} is obtained from the measurement of quadrupolar splittings of perdeuterated hexanol by deuterium solid state NMR. It is found that \ensuremath{\kappa} is insensitive to the amount of polymer in the lamellar phase, in agreement with the theoretical predictions. Observations with the polarizing microscope of topological defects in the lamellar phase allow a qualitative study of the Gaussian bending modulus $\overline{\ensuremath{\kappa}}.$ Addition of a small amount of polymer in the lamellar phase induces a large proliferation of focal conic domains of second species (positive Gaussian curvature). Cryo-TEM confirms that the polymer drastically modify the texture of the lamellar phase. These results indicate clearly that the presence of the nonadsorbing polymer strongly decreases $\overline{\ensuremath{\kappa}},$ in contradiction with theoretical predictions.

Second Harmonic Generation Studies of Polymer-Stabilized Cholesteric Texture Films

Using a mode-locking Nd:YAG laser, we measured the second harmonic generation (SHG) of polymer-stabilized cholesteric texture (PSCT) films. The SHG observed in these samples is due to the dielectric gradient which arises from the interfaces between the cholesteric liquid crystal/polymer and those between the adjacent cholesteric focal conic domains having a different helical axis. Both the SHG intensities and the electro-optical characteristics of PSCT films were measured as a function of the polymer concentration. In addition, polymer network structures formed in PSCT films were investigated. Good correlations among the SHG measurements, electro-optical characteristics, and the polymer network morphologies were found. This means that SHG measurements could provide us with another qualitative, nondestructive method to analyze the PSCT films.

Light-Induced Periodic Lattice of Defects in Smectic A and C Liquid Crystals: Structural and Dynamical Aspects

Structural and dynamical studies of Optically-induced effects in SmA and SmC* liquid crystals are presented. The smectic materials are doped with photosensitive molecules capable of trans-cis isomerization under light illumination. Laser irradiation leads to the formation of strongly scattering textures with periodical array of parabolic focal conic domains (PFCD's). What is most surprising is that the effect is caused by a low-power (≤ 10 mW) He-Ne laser beam; its efficiency is highest in the visible part of the spectrum. The written information can be erased by another beam with shorter wavelength, such as from an Ar laser or a UV source. The PFCD's lattice can be stabilized by a polymeric network. The most plausible mechanism of the light-induced effect is compression/dilation of smectic layers caused by phototransformation of the molecules.

Structure of the cholesteric focal conic domains at the free surface.

Atomic force microscope examinations of the free surface and of microtome cuts of a cholesteric oligomer are reported. The obtained images lead to a model of the structure of cholesteric focal conic domains that appear spontaneously at the free surface. These domains develop in order to fulfill the boundary condition at the free surface together with a planar bulk texture. Estimations of the free energy confirm this model. \textcopyright{} 1996 The American Physical Society.

Growth patterns of smectic A liquid crystals

We report observations on the growth patterns of smectic A liquid crystals from the nematic phase in binary mixtures which exhibit an induced smectic phase. In cells prepared with ‘homeotropic’ boundary conditions there is a clear indication of a microphase separation which leads to nucleation of the smectic layers in the centre of the cell, and formation of single focal conic domains. The domains attact each other to form chains which is ascribed to flexoelectric polarization. A high-frequency AC field produces a corrugation of the interface, the spatial period of which decreases rapidly as the field strength is increased. Dust particle motion around the domains indicates that there may be electrohydrodynamic motion in the nematic liquid crystal surrounding the smectic domains.

Preferred equilibrium structures of a smectic-A phase grown from an isotropic phase: Origin of focal conic domains.

Preferred equilibrium structures of a smectic-A phase grown from an isotropic phase: Origin of focal conic domains.

Unusual Patterns in the Growth of Smectic Liquid Crystals

Smectic liquid crystals have a layered arrangement of rod-like organic molecules. In the smectic A phase the average orientation direction of the molecules is parallel to the layer normal while in the smectic C, it is at an oblique angle. Usually when smectic A liquid crystals separate from the isotropic phase, they do so in the form of short rod-like structures called which are made of focal conic domains. It is now known that the batonnets arise because of the positive interfacial tension anisotropy γ∥ - γ⊥ of the smectic, in which the subscripts refer to directions ~arallel and perpendicular to the layer normal.In the present article we summarise our recent studies on some binary systems in which γ∥ - γ⊥ is negative, leading to some unusual structures like highly elongated cylinders which are stabilised by concentration gradients. We find other novel structures like discs, and 'ink-bottles' etc, when the interfacial tension anisotropy changes sign during the growth of smectics. In the smectic C phase, we find additional dynamics when the cylinders grow; soliton-like objects are generated at one end and propagate along the cylinder to the other end. Further, the cylinders as a whole have physical locomotion as they grow from the isotropic phase. We discuss the results in terms of simple physical models.

Freeze-fracture observations in the L? phase of a swollen surfactant in the vicinity of the L3 and the L1 phase transitions

Freeze-fractured specimens of the Lα phase of a swollen quasi-ternary surfactant (cetylpyridinium chloride/hexanol/brine), have been observed by electron microscopy. The textures show the same features as those oberved by optical microscopy, viz. defects with negative Gaussian curvature (focal conic domains of the usual type) close to the phase boundary with the L3 sponge phase, and defects with positive Gaussian curvature (focal conic domains of second species, mostly spherolites) close to the phase boundary with the L1 micellar phase. We have studied in more detail this latter region : the density of spherolites increases as one approaches the L1-Lα transition, up to the point where they seemingly fill the whole space ; their size distribution obeys an exponential law we explain by a simple thermodynamic model which predicts a transition when the elastic coefficient $\Lambda = 2 K + \bar{K}$ vanishes. Our experimental data yield indeed, with a reasonable precision, a very small value of Λd/kB T for a composition of the surfactant close to the phase boundary.

Nucleation of focal conic domains in smectic A liquid crystals

The first-order structural transitions caused by an external magnetic field or by a surface anchoring are considered for a smectic A liquid crystal in the restricted geometry of a flat cell. The transition occurs by nucleation of focal conic domains. The free energy of the system is calculated as a function of the order parameter ρ= domain radius/cell thickness for finite value of the splay (K) and a saddle-splay ($\bar{K}$) elastic constants and the anchoring coefficient. For small ρ the behavior of the system is defined by the balance of the stabilising elastic term and destabilising field (or anchoring) term. Homogeneous nucleation from ideal uniform state is hindered by high energetic barrier unless $\bar{K}$ is positive and comparable (or larger) than K. A few possible scenarios of heterogeneous nucleation have been considered, among them the nucleation at local layer undulations and the nucleation at field-induced dislocations. The most effective and general scenario is the nucleation at distortions (dislocations) caused by bulk or surface irregularities. The expansion of the domain (ρ≫1) is governed by the balance between the field and surface anchoring and does not depend directly on the elastic constants. The saturation field that provides the domain expansion can be smaller than the threshold field for other known mechanisms of the SmA instabilities.

Field-driven first-order structural transition in the restricted geometry of a smectic-A cell.

An external field gives rise to a first-order transition in a smectic-A cell; the transition occurs by nucleation of focal conic domains. The physical mechanisms that govern the behavior of the new domain phase are different for small (\ensuremath{\rho}\ensuremath{\ll}1) and large (\ensuremath{\rho}\ensuremath{\gg}1) values of the order parameters \ensuremath{\rho} [\ensuremath{\rho}=(domain radius)/(cell thickness)]. The nucleation (\ensuremath{\rho}\ensuremath{\ll}1) is governed by the elastic and field energies and is facilitated by bulk or surface irregularities, while the expansion (\ensuremath{\rho}\ensuremath{\gg}1) is determined by the balance of the field and anisotropic surface energy.