Coupling between Thermodynamics and Conformations in Wormlike Polymer Nematics

Abstract

We adapt the Gupta-Edwards theory of wormlike main-chain nematics to the case of finite-length polymers. The thermodynamic parameters of lyotropic and thermotropic phase transitions are obtained for arbitrary polymer 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 different length scales, which are analogous to the persistence length in the isotropic phase. One scale, ξ⊥, defines the contour length associated with independent fluctuations of chain segments about the nematic director and decreases with the nematic field. Another scale, ξ∥, determines the correlation length of the longitudinal component of the tangent vector. This size is larger than ξ⊥ and increases exponentially with the strength of the nematic interaction. This allows one to identify an intermediate range of chain length ξ⊥ << L << ξ∥, in which the isotropic-nematic phase transition is determined by the long-chain limit but the single-molecule conformation is practically a straight line. The implications of our results for the crystallization of short polymers, such as normal alkanes, are discussed.