Lattice of disclinations: The structure of the blue phases of cholesteric liquid crystals

We argue that the basic mechanism stabilizing the blue phases is the appearance of double cholesteric twist. The free-energy cost of the disclination lattice that inevitably accompanies double twist becomes small near the clearing point. We use the director picture and the Oseen-Frank equations in a computer calculation of the free energy for three specific models, with O5, O2, and O8 symmetry. Disclinations are treated as having an isotropic core. Comparison of the results of the computation with a number of experimental quantities is given. In a final section, a mean-field theory of disclinations is presented. It is argued there that the biaxiality, which is a characteristic of Landau theories of the blue phase, can be considered as an "escape" of the core of the disclination, forced by the implicit requirement of analyticity.