Cylindrical phases of isotropic diblock copolymers as giant wormlike nematic liquid crystals: Frank elasticity and Fréedericksz transitions

Melts of unsymmetric diblock copolymers in the strong segregation limit can form a system of cylindrical micelle worms. We describe this composite material as a giant nematic phase, and calculate the Frank bend constant. As a nematic phase the giant worms are novel for three main reasons. (1) The diameter is of the order of 100 Å, i.e., about 100 times larger than ordinary nematic phases. (2) The system is self-organized and its properties can be tailored by choosing the lengths of the diblocks. (3) The system, despite its large size, exhibits a Fréedericksz transition at a critical voltage ${\mathit{V}}_{\mathit{c}}$ comparable to that of monomeric nematic phases. We calculate how ${\mathit{V}}_{\mathit{c}}$ depends on the microscopic diblock parameters. A macroscopic measurement of ${\mathit{V}}_{\mathit{c}}$ allows the measurement of one of these parameters.