Structure of nanoscale-pitch helical phases: blue phase and twist-bend nematic phase resolved by resonant soft X-ray scattering

Periodic structures of phases with orientational order of molecules, but homogenous electron density distribution: a short pitch cholesteric, blue phase and twist-bend nematic phase, were probed by a resonant soft x-ray scattering (RSoXS) at the carbon K-edge. The theoretical model shows that in case of a simple heliconical nematic structure two resonant signals corresponding to the full and half pitch band should be present, while only the full pitch band is observed in experiment. This suggests that the twist-bend nematic phase has complex structure with a double-helix, built of two interlocked, shifted helices. We confirm that the helical pitch in the twist-bend nematic phase is in a 10 nm range, for both, the chiral and achiral materials. We also show that the symmetry of a blue phase can unambiguously be determined through a resonant enhancement of x-ray diffraction signals, by including polarization effects, which are found to be an important indicator in phase structure determination.