Invited Lecture. Hexagonal cholesteric blue phases

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Abstract
Using Landau theory, the possibility that two and three dimensional hexagonal structures can exist in cholesteric liquid crystals with positive dielectric anisotropy in an applied electric or magnetic field is considered. Both are found to be thermodynamically stable in different regions of the chirality-temperature-field phase diagram, in agreement with reported experimental data. Further, the theoretical results indicate that two different three dimensional hexagonal phases, having the same space group (P6222) but different structure factors, may exist. Ways of verifying this prediction by optical and N.M.R. studies are considered. Also noted is the need to develop further the theoretical model to allow for the existence of the experimentally observed body-centred tetragonal structure.