Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers

Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.