The Theory of Competing Nematic Phases of Comb Polymers

Comb polymers have been proposed to exhibit a variety of nematic states according to the relative nematic tendencies of the backbone and teeth, and the molecular attachment of the two. The equilibria of such nematic phases with each other and with the isotropic state can be described by a mean field model, which combines a Maier-Saupe theory of conventional liquid crystals and the worm concept of semiflexible polymers. Here the model is solved analytically in terms of universal functions. Graphical constructions on the free energy reminiscent of the Maxwell area rules are derived. The method allows both qualitative and quantitative conclusions to be made of the shape and gradients of phase diagrams. Triple points and a critical point inside one of the nematic phases are predicted. The stability of equilibria is examined. The occurrence of re-entrant nematic phases is identified as a consequence of the main-chain flexibility.