Lattice symmetry of the cholesteric blue phases

Abstract

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 O2 (P4232),O5 (I432), and O8 (I4132) space-group symmetry. In the present paper calculations for a fourth model, also of O8 symmetry, are presented (we differentiate these models as O8(+) and O8(-), respectively). For a number of cholesterol derivatives we assign the O8(-) structure to the BP I, and the O2 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 O2 structure being lowest at the higher temperatures, and O8(-) 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. © 1983 The American Physical Society.