title: Theory of bent-core liquid-crystal phases and phase transitions.
abstract: We study phases and phase transitions that can take place in the recently discovered bow-shaped or bent-core liquid-crystal molecules. We show that to completely characterize phases exhibited by such bent-core molecules a third-rank tensor T(ijk) order parameter is necessary in addition to the vector and the nematic (second-rank) tensor order parameters. We present an exhaustive list of possible liquid phases, characterizing them by their space-symmetry group and order parameters, and catalog the universality classes of the corresponding phase transitions that we expect to take place in such bent-core molecular liquid crystals. In addition to the conventional liquid-crystal phases such as the nematic phase, we predict the existence of other liquid phases, including the spontaneously chiral nematic (N(T)+2)(*) and chiral polar (V(T)+2)(*) phases, the orientationally ordered but optically isotropic tetrahedratic T phase, and a nematic N(T) phase with D(2d) symmetry that is neither uniaxial nor biaxial. Interestingly, the isotropic-tetrahedratic transition is continuous in mean-field theory, but is likely driven first order by thermal fluctuations. We conclude with a discussion of smectic analogs of these phases and their experimental signatures.