Phase transitions in lattice solutions of semiflexible chains

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Abstract
A mean field theory for two- and three-dimensional cubic lattice solutions of long semiflexible chains is developed using Di Marzio’s treatment of excluded volume. The configurational term of the partition function at a fixed level of macroscopic orientation is evaluated in close analogy with recent treatments of wormlike chain systems. In the presence of macroscopic orientation, the effective one-chain partition function shows typical Ising features. Mesomorphic phases of intermediate orientation are predicted to become more stable than the isotropic solution below a characteristic temperature which depends on concentration. In two dimensions, a continuous set of coexisting phases of different concentration and corresponding orientation joins the isotropic solution at the transition temperature. In three dimensions our analysis, restricted to states of uniaxial symmetry, predicts a first order transition whose order parameter decreases with concentration and approaches the limiting value 1/2 for very dilute systems. The change of the fraction of ‘‘gauche’’ bonds at the transition is modest, except in the immediate vicinity of the bulk limit, where the classical isotropic-crystalline mean field alternative is found again.

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