Director-Pitch Coupling-Induced Twist-Bend Nematic Phase

A mean field theory is introduced to describe a twist-bend nematic (NTB) phase, by taking into account the coupling between a nematic director and a pitch axis of the NTB phase. The free energy of the NTB phase is derived as a function of a usual orientational order parameter and an order parameter of the NTB phase. We calculate phase diagrams, including isotropic (I), nematic (N), chiral nematic N*, and NTB phases. Depending on the temperature and the strength of the director-pitch coupling, we predict the second-order phase transitions between NTB and N, and between NTB and N* phases. We also predict the first-order phase transitions between an isotropic phase and an NTB phase.