Elastic moduli of a nematic liquid–crystalline solution of polyelectrolytes

The elastic moduli of polyelectrolyte liquid crystals are calculated within the second virial approximation. A quantitative numerical and analytical theory is set up for rod-like polyelectrolytes in excess salt, whereas qualitative relations are discussed for polyions under more general circumstances. Electrostatic interactions cause significant deviations from the usual hard rod interactions. The effective diameter increases, the persistence length increases as well, and a torsional or twisting effect manifests itself because two polyion rods want to adopt a perpendicular orientation with respect to each other. In consequence, for rod-like polyelectrolytes the twist modulus depends only weakly on the macromolecular concentration, whereas the bend modulus increases more strongly with concentration than it does for hard rods.