Geometrical Approach of Blue Phases

Abstract

Blue phases are liquid crystalline phases which appear in chiral compounds between the isotropic and the cholesteric phase in a narrow range of temperature^1,2. In the cholesteric phase, the periodicity which typically lies in the range of visible light wavelength is only due to orientational ordering. The mean orientation of the molecules or director n is constant inside planes perpendicular to one axis but twists when moving along this axis. This induces periodic properties of physical parameters such as the dielectric tensor in this direction with a period given by π/q where q is the cholesteric pitch. When this pitch is small enough, new phases may appear when temperature increases. These are the blue phases. There exist three blue phases : BPI, BPII and the blue fog. The two first ones are cubic phases with space group symmetry O ⁸ I4₁32 et O ² = P432 as determined by optical scattering experiments. The third one is still mysterious³.