Isotropic, nematic, and columnar ordering in systems of persistent flexible hard rods

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Abstract
We extend previous work on the Khokhlov-Semenov approach to long-range order in solutions of persistent flexible main-chain polymers by including hexagonal columnar ordering. The description of long-range positional order uses a recent model developed for rigid rodlike particles, which is based on the tradeoff of translational entropy between liquidlike and crystal-like dimensions. For moderately flexible polymers, we find an isotropic-nematic-columnar phase sequence with increasing polymer concentration. As the polymers become more flexible, the isotropic-nematic transition recedes to higher concentrations, until finally, near the wormlike chain limit, a direct isotropic-to-columnar transition occurs. We show that the corresponding triple point occurs at longer persistence lengths for polymers of increasing contour length. In addition, we show that the longitudinal packing in the columnar phase becomes much tighter with increasing molecular flexibility to accommodate greater lateral freedom. Finally, we compare our theoretical equation of state with experimental measurements for poly-benzyl-L-glutamate (PBLG).