Hexagonal and nematic phases of chains. I. Correlation functions

We consider the statistical mechanics of a system of semiflexible chains, which can represent polymer liquid crystals, long-chain biomolecules, stiff wormlike micelles, or columns of discotic liquid crystals. Semiflexible chains can order in a hexagonal lattice (also called a columnar or canonic phase), and they can form nematic and isotropic fluids. We calculate the structure factor and the director fluctuation spectrum in the hexagonal and nematic phases using continuum elastic theory. The structure factor and the director fluctuation spectrum of the hexagonal phase are found to be intimately related to those of smectic-A liquid crystals through a ‘‘line-plane’’ duality. The elastic constants of the hexagonal phase are computed for the case of pure steric repulsion between chains. These elastic constants show ‘‘universal’’ behavior in the close-packing limit where steric repulsion dominates.