Characterization of a chiral phase in an achiral bent-core liquid crystal by polarization studies of resonant x-ray forbidden reflections

The chiral antiferroelectric structure of an achiral bent-core liquid crystal is characterized by resonant x-ray scattering at chlorine K edge. The "forbidden" reflections resulting from the glide or screw symmetry elements are restored by the anisotropy of the tensor structure factor, which we calculate for two possible structural models. A careful analysis of the polarization states of the restored "forbidden" reflections enables an unambiguous identification of a chiral structure (i.e., the so-called anticlinic, antiferroelectric smectic-C or Sm-C_AP_A) coexisting with the achiral synclinic antiferroelectric smectic-C or Sm-C _SP_A. The method proves to be quite powerful as it identifies the chiral structure within coexisting phases despite an imperfect orientation of the sample. The volume fraction of the chiral phase and the distribution of alignment are extracted from the data.