Energy dependence of resonant x-ray scattering for the twist bend nematic phase, a helix of liquid crystals*

We examined the manifestation of resonance effects in twist bend nematic (NTB), smectic A (SmA) and crystalline phases via tender resonant X-ray scattering (TReXS) at sulfur K-edge. While SmA layering peak is partially resonant, scattering peak of NTB is purely resonant visible only near S K-edge. The difference is attributed to the periodic molecular orientation variation with weak electron density modulation. We further demonstrate that the energy-dependence of such scattering peak arising from pure orientation variation scales with the sum of f1(E)^2 and f2(E)^2, corresponding to the real and imaginary parts of dispersion correction respectively, while the resonant contribution in sulfur-containing SmA scales with f1(E), and is a first order perturbation to the relatively strong non-resonant peak from electron density modulation.