Simulation of cholesteric blue phases using a Landau-de Gennes theory: Effect of an applied electric field

We investigate numerically static and dynamic properties of cholesteric blue phases. Our study is based on a Landau-de Gennes theory describing the orientational order of a liquid crystal in terms of a second-rank tensor. To find the shape and size of the unit cell conforming to the minimum of the free energy, we let the geometrical parameters characterizing the unit cell relax in the course of the time evolution via a simple relaxational equation. We investigate the effect of an electric field on the structure of cholesteric blue phases. We study how the deformation of the unit cell in response to the electric field E depends on the strength and direction of the electric field and the original structure of cholesteric blue phases. Our results qualitatively agree with the experimental findings. Although in a weak field, the strain tensor is proportional to E-2 as previously argued, for a moderate field the distortion is no longer proportional to E-2 and can be even non-monotonic with respect to E-2. Furthermore, we investigate the kinetic processes of the deformation, rearrangement, and extinction of disclination lines under a strong electric field. We show that the kinetics of disclination lines is highly complicated and sensitively depends on the initial structure of blue phases, the direction of the electric field, and the sign of dielectric anisotropy epsilon(a). In most cases, a strong field aligns the liquid crystals in a uniform (positive epsilon(a)) or helical (negative epsilon(a)) manner without disclination lines. However, for negative epsilon(a) and the direction of the electric field parallel to the body diagonal of the unit cell, disclination lines do not disappear and form a two-dimensional hexagonal lattice.