COUPLING BETWEEN THERMODYNAMICS AND CONFORMATIONS IN WORMLIKE POLYMERNEMATICS

We adapt the Gupta-Edwards theory of wormlike main-chain nematics to t he case of finite-length polymers. The thermodynamic parameters of lyo tropic and thermotropic phase transitions are obtained for arbitrary p olymer lengths and we find that the crossover between long- and short- chain regimes takes place for polymers of relatively low chain length (shorter than the persistence length). We show that this is related to the fact that in the nematic phase there are two qualitatively differ ent length scales, which are analogous to the persistence length in th e isotropic phase. One scale, xi(perpendicular to), defines the contou r length associated with independent fluctuations of chain segments ab out the nematic director and decreases with the nematic field. Another scale, xi(parallel to), determines the correlation length of the long itudinal component of the tangent vector. This size is larger than xi( perpendicular to) and increases exponentially with the strength of the nematic interaction. This allows one to identify an intermediate rang e of chain length xi(perpendicular to) much less than L much less than xi(parallel to), in which the isotropic-nematic phase transition is d etermined by the long-chain limit but the single-molecule conformation is practically a straight line. The implications of our results for t he crystallization of short polymers, such as normal alkanes, are disc ussed.