Shaikh Shamid

Statistical Mechanics of Bend Flexoelectricity and the Twist-Bend Phase in Bent-Core Liquid Crystals

We develop a Landau theory for bend flexoelectricity in liquid crystals of bent-core molecules. In the nematic phase of the model, the bend flexoelectric coefficient increases as we reduce the temperature toward the nematic to polar phase transition. At this critical point, there is a second-order transition from high-temperature uniform nematic phase to low-temperature nonuniform polar phase composed of twist-bend or splay-bend deformations. To test the predictions of Landau theory, we perform Monte Carlo simulations to find the director and polarization configurations as functions of temperature, applied electric field, and interaction parameters.

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.

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.