Isotropic-to-nematic transition in liquid-crystalline heteropolymers: I. Formalism andmain-chain liquid-crystalline polymers

Abstract

We formulate a density functional approach for arbitrarily branched liquid-crystalline (LC)heteropolymers consisting of elongated rigid rods coupled through elastic joints. The theoryexactly accounts for the energetic and entropic single-chain effects, whereas the interchainexcluded volume effects are treated within the Onsager approximation. We apply thetheory to finite-length main-chain LC polymers composed of rigid mesogens coupled byflexible spacers of finite length, modelled initially as chains of thin rods. The theory thenallows an easy passage to the wormlike chain limit for the spacers. Employing a bifurcationanalysis we analytically obtain the stability boundaries of the isotropic phasetowards the nematic liquid crystalline phase, as a function of the relative size of themesogens with respect to the spacers and the spacer flexibility. From the sameanalysis we also obtain the distribution of the incipient nematic ordering at thespinodal density as a function of position along the chain, including the end-effects.