Field-induced hexagonal blue phases in positive and negative dielectric anisotropy systems: Phase diagrams and topological properties

Using Landau theory, the possibility that hexagonal structures can exist in cholesteric liquid crystals in an applied field is considered. Both positive and negative dielectric anisotropy systems are studied. It is found that two- and three-dimensional hexagonal phases are thermodynamically stable in different regions of the chirality-temperature field phase diagram when the anisotropy is positive, while for negative anisotropy only a three-dimensional phase occurs. This is in agreement with experimental data. In addition, the theoretical results indicate that two different three-dimensional hexagonal phases, having the same space group (P$6_2$22) but different structure factors, can exist when the anisotropy is positive. Ways of verifying this prediction by optical or NMR studies are considered. Finally, the topological aspects of disclinations in the hexagonal phases are considered. Each of the four stable hexagonal structures is found to have two uniaxial positive and one uniaxial negative defect line. The latter is the only topological disclination when the order parameter is taken to be a uniaxial director rather than a biaxial symmetric tensor.