Statics and dynamics of hairpins in worm-like main chain nematic polymer liquid crystals

We derive some exact results for the statics of solitary defects (« hairpins ») in the conformations of nematic main chain worm-like polymer liquid crystals in which there is both a bending and a nematic contribution to the potential energy. It is shown that for a polymer of finite length in mechanical equilibrium there can exist only a finite number of hairpins and that these are all unstable configurations. These results (which are also applicable to combs) are then used to prove that the destruction of a long single hairpin proceeds via the hairpin reptating along its own length even in the absence of entanglements. The two separate cases of a continuous worm, and a worm consisting of N links are studied. The implications for the frequency dependent dielectric response are discussed.