Splay-bend textures involving tetrahedratic order.

We show that defect-free splay-bend textures are less energetic compared to uniform states in liquid-crystalline phases that possess both quadrupolar (nematic) and octupolar (tetrahedratic) order. This is because, in such systems, there is a symmetry-allowed linear gradient term in the energy. Another unusual feature of these splay-bend textures is the fact that they have a non-homogeneous, space-dependent free-energy density. These results may help clarify some mysterious features noted for the B7 liquid-crystal phase formed by achiral banana-shaped molecules.