Universality classes for the isotropic-to-nematic transition in systems of interacting, semiflexible polymers

This paper discusses the behavior of simple models of interacting, semiflexible, nonchiral polymers. The Ursell-Mayer expansion is used to systemize calculation of the properties of such systems and avoid problems encountered with the strong, bonding interactions in a direct analysis of this problem. The formation of a nematic phase is discussed within a field theory which is equivalent, order by order in perturbation theory, to the Ursell-Mayer expansion. Symmetry analysis allows two universality classes; one has the usual, tensor order parameter, the other has a vectorlike order parameter. The vectorlike order parameter has no direct physical interpretation (distinguishing the transition from a ferroelectric transition) but must be introduced because of the strong, bonding interactions between monomers on a polymer. The behavior of some physical observables near the critical point in systems with phase transitions controlled by the vectorlike order parameter is discussed, including a brief discussion of nonclassical critical behavior. Evidence is given that transitions with either type of order parameter are realizable in model systems.