David W. Allender

Predicting a polar analog of chiral blue phases in liquid crystals.

In liquid crystals, if flexoelectric couplings between polar order and director gradients are strong enough, the uniform nematic phase can become unstable to formation of a modulated polar phase. Previous theories have predicted two types of modulation, twist-bend and splay-bend; the twistbend phase has been found in recent experiments. Here, we investigate other types of modulation, using lattice simulations and Landau theory. In addition to twist-bend and splay-bend, we also find polar blue phases, with 2D or 3D modulations of both director and polar order. We compare polar blue phases with chiral blue phases, and discuss opportunities for observing them experimentally.In liquid crystals, if flexoelectric couplings between polar order and director gradients are strong enough, the uniform nematic phase can become unstable to the formation of a modulated polar phase. Previous theories have predicted two types of modulation: twist bend and splay bend; the twist-bend phase has been found in recent experiments. Here, we investigate other types of modulation, using lattice simulations and Landau theory. In addition to twist bend and splay bend, we also find polar blue phases, with 2D or 3D modulations of both the director and the polar order. We compare polar blue phases with chiral blue phases, and discuss opportunities for observing them experimentally.

Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers

The nematic twist-bend (NTB) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase - the first distinct nematic variant discovered in many years. The NTB phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The NTB structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, NTB-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like pseudo-layers, defined by planes of equivalent phase in a coarse-grained description of the NTB state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two.

Fluctuation modes of a twist-bend nematic liquid crystal

We report a dynamic light-scattering study of the fluctuation modes in a thermotropic liquid crystalline mixture of monomer and dimer compounds that exhibits the twist-bend nematic (NTB) phase. The results reveal a spectrum of overdamped fluctuations that includes two nonhydrodynamic modes and one hydrodynamic mode in the N TB phase, and a single nonhydrodynamic mode plus two hydrodynamic modes (the usual nematic optic axis or director fluctuations) in the higher temperature, uniaxial nematic phase. The properties of these fluctuations and the conditions for their observation are comprehensively explained by a Landau-de Gennes expansion of the free-energy density in terms of heliconical director and helical polarization fields that characterize the N TB structure, with the latter serving as the primary order parameter. A coarse-graining approximation simplifies the theoretical analysis and enables us to demonstrate quantitative agreement between the calculated and experimentally determined temperature dependence of the mode relaxation rates.

The geometrical optics approach for multidimensional liquid crystal cells

We present an approach based on the geometrical optics approximation (GOA) for analysis of liquid crystal cells whose director varies in more than one spatial dimension (multidimensional liquid crystal cells). The GOA is applied to calculate light transmittance and far field diffraction patterns for two- and three-dimensional nematic liquid crystal films. Important features of the GOA, such as a method of eliminating non-convergence problems that can occur during the iterative numerical solution of the equations for the amplitudes of the electromagnetic field, are described. We compare the results obtained from the GOA with those produced by the quasi-one-dimensional Jones calculus and the beam propagation method, where the latter is applicable. It was found that the refraction (or ray bending) effects, produced by the GOA, are more important than effects of diffraction and light scattering, which means that the GOA (unlike the Jones calculus) is accurate for the considered type of liquid crystal cells, whose director varies on the micron scale. The GOA is about as fast as the Jones method and is applicable for calculating optical properties of liquid crystal cells with any number of dimensions of director variations.

P-77: A Simplified Model for the Director in Multidimensional LCDs

A model for describing the director and electric field for two dimensional (2D) and three dimensional (3D) liquid crystal displays (LCDs) with interdigitated electrodes located on one or both substrates is proposed. Calculations show good agreement between the model and direct computer solution of the Euler—Lagrange equations, but the model is about 30 times faster.

Phase Transitions In Liquid Crystal Droplets

Basic studies of a liquid crystal confined to a small droplet have been motivated by the use of polymer dispersed liquid crystals for a new generation of light shutters and displays.2 The structure of such a droplet is characterized by a specific director configuration and the spatial dependence of the orientational order parameter. Depending on temperature, droplet size, surface interaction, type of liquid crystal and external field, the phase of the material enclosed in the droplet can be either the isotropic (paranematic), nematic or boundary layer nematic phase.3 Director configurations in droplets have been studied extensi% ely,4-7 but the spatial dependence of the order parameter has been treated only for the case of a liquid crystal in contact with a solid planar surface.3.8-10 Lsing the Landaude Gennes approach, the order parameter profile was evaluated, showing how the orientational order varies with distance from the planar surface. In addition, for some values of the surface-liquid crystal coupling, the existence of the boundary layer nematic phase was predicted in a narrow tem-perature range between the isotropic (paranematic) and nematic phases.3

Light scattering study of the “pseudo-layer” compression elastic constant in a twist-bend nematic liquid crystal

The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or pseudo-layers, each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining layer compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant K. The magnitude of K is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼106 Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the pseudo-layer structure of the TB phase with Beff in the range 103-104 Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director.

Landau theory-based estimates for viscosity coefficients of uniaxial and biaxial nematic liquid crystals

Using Landau theory, it is shown that eight phenomenological parameters are needed to describe and distinguish the twelve viscosity coefficients of a biaxial nematic phase, or the five viscosity coefficients of a uniaxial nematic phase. The dependence of the coefficients on the macroscopic uniaxial and biaxial order parameters is established. Since these order parameters are determined by the anisotropies of the dielectric constant, we show that it should be possible to determine values for all eight of the phenomenological parameters of the theory from measurements of the temperature dependence of the five viscosities of a uniaxial phase.

The geometrical optics approach in liquid crystal cells with two- and three-dimensional director variations

A geometrical optics approach (GOA) to the optics of the nematic liquid crystals whose optic axis (director) varies in two or three space dimensions is presented. Two examples of the GOA applications are considered: calculation of light transmittance (1) through a liquid crystal (LC) film with two-dimensional (2D) director which combines the concepts of in-plane switching and vertical alignment, and (2) through a three-dimensional (3D) LC cell associated with a homeotropic to multidomainlike transition (HMD cell). Important details of the GOA applications for both cases are described. The GOA results are compared with those obtained from the quasi-one-dimensional Jones calculus and the beam propagation method (BPM) where the latter is applicable. Comparison between the results of different methods of calculating the near zone electromagnetic field (the radiation at points just on the exit of the analyzer) as well as the far zone diffraction pattern is provided. It is found that the GOA is about as fast as the Jones method for calculating optical properties of LC films with any number of dimensions of director variations, yet the GOA has the advantage of being more accurate than the Jones calculus.

P-78: Geometrical Optics Approach for LCDs with Three Dimensional Director Variations

The geometrical optics approach (GOA) is applied to the propagation of light through liquid crystal films whose director varies in three spatial dimensions. As an example of application, the GOA is applied to the calculation of light transmittance for the case of a LCD cell which exhibits the homeotropic to multidomainlike (HMD) transition. Comparison with Jones calculus is also provided. For smaller geometries, where the Jones calculus breaks down, the GOA provides a fast, accurate method for calculating the optical performance of LCDs.