Theory of uniaxial and biaxial nematic phases in bent-core systems

We present a phenomenological theory of the uniaxial and biaxial nematic phases recently observed in bent-core mesogenic systems. To take into account the molecular anisotropy we introduce two types of symmetry transformation: "external" rotations which turn the molecules with respect to the laboratory axes and "internal" rotations which turn them with respect to the molecular axes. We show then that the description of bent-core nematic phases involves two isomorphic copies of the conventional tensor order parameter instead of one for conventional rod like and disk like molecules. The second tensor stabilizes additional monoclinic and triclinic phases and merges the calamitic and diskotic uniaxial states into a single phase. The uniaxial and biaxial phases can appear, respectively, in six and 21 distinct configurations according to the molecular axis that dominates the ordering process. We predict a number of isostructural transitions between these configurations within a thermodynamic Landau-type approach. Because bent-core molecules have the same microscopic behavior as orthorhombic micelles, the biaxial phase can be stabilized in both systems.