Hexagonal and nematic phases of chains. II. Phase transitions

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Abstract
We develop a model for the phase transitions of a system of infinitely long, semiflexible chains that interact through a steric, excluded-volume repulsion. This model combines density-functional theory for freezing with the Onsager theory of orientational ordering. We derive phase diagrams in terms of pressure or density versus persistence length or temperature. If the temperature is low or the persistence length is long, the phase diagram shows an isotropic fluid, a nematic liquid-crystal phase, and a hexagonal lattice (also known as a columnar or canonic phase) as the pressure or density is increased. If the temperature is high or the persistence length is short, the phase diagram shows a direct isotropic-hexagonal transition, with no intermediate nematic phase. The theoretical phase diagram agrees qualitatively with several experiments on lyotropic discotic liquid crystals, and it should also apply to polymer liquid crystals, long-chain biomolecules, and wormlike micelles.