Polarization splay as the origin of modulation in the B1 and B7 smectic phases of bent-core molecules

We report a generalized scenario for the formation of modulated smectic phases of bent-core molecules based on locally ferroelectric layering and spontaneous splay of the polarization. Twelve phases are proposed, distinguished by neighboring splay stripes with either syn- or antiorder of the polarization and undulation slope, in addition to layer continuity versus layer discontinuity at the intervening defects. We outline the experimental techniques necessary to differentiate among the phases and interpret previous results in the present context, using high resolution x-ray scattering diffraction and block and undulation models of the layer organization to distinguish among the three 2D lattice types which emerge.