Ray tracing matrix approach for refractive index mismatch aberrations in confocal microscopy.

The 2×2 ray tracing matrix (RTM) method is employed for the description of optical aberrations caused by the refractive index mismatch (RIM) in fluorescent confocal polarization microscopy. We predict and experimentally confirm that due to the RIM a liquid crystal layer with highly non-uniform director distribution appears to be imaged as a layer with non-uniform thickness, which shows up in the roughness of the rear surface. For the off-axial focusing of the probing beam in a droplet dispersed in an immiscible liquid, we have developed an extended method still keeping the 2×2 dimensionality of the RTM.

Elastic and viscous properties of the nematic dimer CB7CB.

We present a comprehensive set of measurements of optical, dielectric, diamagnetic, elastic, and viscous properties in the nematic (N) phase formed by a liquid crystalline dimer. The studied dimer, 1,7-bis-4-(4'-cyanobiphenyl) heptane (CB7CB), is composed of two rigid rodlike cyanobiphenyl segments connected by a flexible aliphatic link with seven methyl groups. CB7CB and other nematic dimers are of interest due to their tendency to adopt bent configurations and to form two states possessing a modulated nematic director structure, namely, the twist-bend nematic, N_{TB}, and the oblique helicoidal cholesteric, Ch_{OH}, which occurs when the achiral dimer is doped with a chiral additive and exposed to an external electric or magnetic field. We characterize the material parameters as functions of temperature in the entire temperature range of the N phase, including the pretransitional regions near the N-N_{TB} and N-to-isotropic (I) transitions. The splay constant K_{11} is determined by two direct and independent techniques, namely, detection of the Frederiks transition and measurement of director fluctuation amplitudes by dynamic light scattering (DLS). The bend K_{33} and twist K_{22} constants are measured by DLS. K_{33}, being the smallest of the three constants, shows a strong nonmonotonous temperature dependence with a negative slope in both N-I and N-N_{TB} pretransitional regions. The measured ratio K_{11}/K_{22} is larger than 2 in the entire nematic temperature range. The orientational viscosities associated with splay, twist, and bend fluctuations in the N phase are comparable to those of nematics formed by rodlike molecules. All three show strong temperature dependence, increasing sharply near the N-N_{TB} transition.

Lasing in imperfectly aligned cholesterics.

Optically pumped light emissions in imperfectly aligned dye-doped cholesteric cells with glance and frosted glass substrates of three different cell gap thicknesses are experimentally studied. Alignment imperfections show up in emission spectra by a broadening of the photonic bandgap (PhBG) lasing (allowed) lines at short- and long-wavelength PhBG edges and by an additional (forbidden) emission line inside the PhBG. Forbidden and allowed lines differ distinctively by their stability in the course of pumping. The origin of the forbidden line is discussed.

Elasticity of lyotropic chromonic liquid crystals probed by director reorientation in a magnetic field.

Using a magnetic Frederiks transition technique, we measure the temperature and concentration dependences of splay K1, twist K2, and bend K3 elastic constants for the lyotropic chromonic liquid crystal sunset yellow formed through noncovalent reversible aggregation of organic molecules in water. K1 and K3 are comparable to each other and are an order of magnitude higher than K2. At higher concentrations and lower temperatures, K1 and the ratios K1/K3 and K1/K2 increase, which is attributed to elongation of self-assembled lyotropic chromonic liquid crystal aggregates, a feature not found in conventional thermotropic and lyotropic liquid crystals formed by covalently bound units of a fixed length.

Surface alignment and anchoring transitions in nematic lyotropic chromonic liquid crystal.

The surface alignment of lyotropic chromonic liquid crystals can not only be planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and by three-dimensional imaging of the director field. With time, the homeotropic nematic undergoes a transition into a tangential state. The anchoring transition is discontinuous and can be described by a double-well anchoring potential with two minima corresponding to tangential and homeotropic orientation.

Optical characterization of the nematic lyotropic chromonic liquid crystals: light absorption, birefringence, and scalar order parameter.

We report on the optical properties of the nematic (N) phase formed by lyotropic chromonic liquid crystals (LCLCs) in well aligned planar samples. LCLCs belong to a broad class of materials formed by one-dimensional molecular self-assembly and are similar to other systems such as "living polymers" and "wormlike micelles." We study three water soluble LCLC forming materials: disodium chromoglycate, a derivative of indanthrone called Blue 27, and a derivative of perylene called Violet 20. The individual molecules have a planklike shape and assemble into rodlike aggregates that form the phase once the concentration exceeds about 0.1 M. The uniform surface alignment of the N phase is achieved by buffed polyimide layers. According to the light absorption anisotropy data, the molecular planes are on average perpendicular to the aggregate axes and thus to the nematic director. We determined the birefringence of these materials in the N and biphasic N-isotropic (I) regions and found it to be negative and significantly lower in the absolute value as compared to the birefringence of typical thermotropic low-molecular-weight nematic materials. In the absorbing materials Blue 27 and Violet 20, the wavelength dependence of birefringence is nonmonotonic because of the effect of anomalous dispersion near the absorption bands. We describe positive and negative tactoids formed as the nuclei of the new phase in the biphasic N-I region (which is wide in all three materials studied). Finally, we determined the scalar order parameter of the phase of Blue 27 and found it to be relatively high, in the range 0.72-0.79, which puts the finding into the domain of general validity of the Onsager model. However, the observed temperature dependence of the scalar order parameter points to the importance of factors not accounted for in the athermal Onsager model, such as interaggregate interactions and the temperature dependence of the aggregate length.

Liquid crystal helical ribbons as isometric textures.

Deformations that conserve the parallelism and the distances--between layers, in smectic phases; between columns, in columnar phases--are commonplace in liquid crystals. The resulting isometric deformed textures display specific geometric features. The corresponding order parameter singularities extend over rather large, macroscopic, distances, e.g., cofocal conics in smectics. This well-known picture is modified when, superimposed to the 1D or 2D periodicities, the structure is helical. However isometry can be preserved. This paper discusses the case of a medium whose structure is made of 1D modulated layers (a lamello-columnar phase), assuming that the modulations rotate helically from one layer to the next. The price to pay is that any isometric texture is necessarily frustrated; it consists of layers folded into a set of parallel helicoids, in the manner of a screw dislocation (of macroscopic Burgers vector), the modulations being along the helices, i.e. double-twisted. The singularity set is made of two helical disclination lines. We complete this geometric analysis by a crude calculation of the energy of a helical ribbon. It is suggested that the helical ribbons observed in the B7 phase of banana-like molecules are such isometric textures. As a side result, let us mention that the description of double-twist, traditionally made in terms of a partition of the director field into nested cylinders, could more than often be profitably tested against a partition into nested helicoids.

Pretransitional fluctuations in the isotropic phase of a lyotropic chromonic liquid crystal.

We have studied isotropic-to-nematic pretransitional fluctuations in an aqueous solution of disodium cromoglycate (cromolyn) by static and dynamic light scattering. Cromolyn is a representative of lyotropic chromonic liquid crystals with building units being elongated rods formed by aggregates of disk-like molecules. By combining light-scattering and viscosity measurements we have determined the correlation length and relaxation time of the orientational order-parameter fluctuations and estimated the size of the cromolyn aggregates. The pretransitional behavior of light scattering does not completely follow the classic Landau-de Gennes model. This feature is most probably associated with the variable length of cromolyn aggregates. We have observed a dramatic increase of the shear viscosity near the transition to the nematic phase, the fact which correlates with the idea of growing supramolecular aggregates. The steep temperature dependence of the viscosity is accompanied by a practically temperature-independent translational diffusion coefficient.

Textural analysis of a mesophase with banana shaped molecules.

Observed under the polarizing microscope, the B7bis phase in the banana compound D14F3 [J.P. Bedel et al., Liq. Cryst. 27, 1411 (2000)] displays two types of textures of defects, namely (a): helical ribbons, that nucleate in large quantities when the samples are quenched from a sufficiently high temperature in the isotropic phase (b)- shapes with no helicity having the structure of developable domains much akin to those observed in columnar phases, either resulting from the annealing of the helical ribbons or nucleating under slow cooling processes. The existence of these two kinds of defects points toward the complex nature of the structure of the B7 phase, which is at the same time a columnar and a smectic phase. Our observations fit the model [M. Kleman, J. Phys. France 46, 1193 (1985)] according to which the geometry of a helical ribbon is that one of the central region of a screw dislocation with a giant Burgers vector, split into two helical disclination lines of strength k = 1/2 which bound the ribbon. Textures and defects, already partly documented, and growth features and annealing processes, not yet reported in the literature, are analyzed. We conclude that the helical ribbons and the developable domains with no helicity are textures of two different B7 states, namely a metastable state and the ground state respectively. Comparative textural analysis is performed for two other banana compounds exhibiting B2 phases.

Defects in a TGBA phase: a theoretical approach.

Following our experimental observations of disclination lines in freely suspended droplets and free-standing films (Yu.A. Nastishin et al., Eur. Phys. J. E 5 353 (2001)), topological defects of the twist grain boundary (TGBA) phase are considered according to two aspects: topological and energetical. There are two classes of line defects, disclinations (as in the cholesteric (N*) phase and the liquid vortices phase (NL*), relating to the directors tripod symmetries) and dispirations (relating to the translation-rotation symmetries); there are no topological point defects. Differences between N*, NL* and TGBA disclinations are physical, not topological. The absence of focal conic domains in the TGBA phase is an immediate consequence of the materialization of the helical axis (along the chi-director); the same feature, coupled to the trend to parallelism of the smectic layers, accounts for the predominance of lambda-lines. Finally, the presence of defects akin to developable domains is explained in the frame of the least curvature model, that requires the introduction of a third type of defects: the densities of edge dislocations of the smectic layers.