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

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