Chain conformations of liquid-crystalline polymers

Abstract

We extend our mean-field theory of backbone liquid-crystalline polymers (LCPs) to calculate chain anisotropy in nematic phase. The LCP theory applies to semiflexible, worm-like polymers and we use the Kratky—Porod formalism with a self-consistent mean-field approximation. We calculate the end-to-end distance of a polymer chain in the nematic phase as a function of concentration and temperature. For sufficiently long or sufficiently flexible polymers, we find for the ratio of z to x components of the end-to-end distance: (1 + 2S) (1 − S) , where S is the order parameter and z the director axis. At the transition this has a universal value of 2. The order parameter is described by the equation: (1 − S) 2(1 + 2S) 2 (2 + S) = 27 8εuc .