Lattice symmetry of the cholesteric blue phases

The cholesteric blue phases (BP I and BP II) can be modeled as cubic lattices of disclinations in a cholesteric matrix. In an earlier paper we presented results of free-energy calculations for three models with $O^2\left(P{4}_{2}32\right),O^5\mathrm{}\left(I432\mathrm{}\right)\mathrm{}$, and $O^8\left(I{4}_{1}32\right)$ space-group symmetry. In the present paper calculations for a fourth model, also of $O^8$ symmetry, are presented (we differentiate these models as $O^{8(+)\mathrm{}}$ and $O^{8(-)\mathrm{}}$, respectively). For a number of cholesterol derivatives we assign the $O^{8(-)\mathrm{}}$ structure to the BP I, and the $O^2$ structure to BP II, on the following evidence: For the case of equal elastic constants the calculations show a crossover of the free energy, the $O^2$ structure being lowest at the higher temperatures, and $O^{8(-)\mathrm{}}$ at lower temperatures. (However, the crossover may disappear for other values of the elastic constants.) The assignment is consistent with the observed BP I and BP II lattice constants in terms of cholesteric pitch. There is excellent agreement between calculated and observed intensities of the Bragg reflections. Some details of the observed Bragg-diffraction spectra are also discussed.