Twist-bend nematic phases of banana-shaped molecules with an axial chirality

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ABSTRACTWe present a mean field theory to describe uniaxial () and biaxial twist-bend nematic () phases of banana-shaped liquid crystalline molecules with an axial chirality. We first derive a tensor order parameter for the banana-shaped molecules as a function of a bend angle (), a torsion angle for the axial chirality, and four orientational order parameters, which describe uniaxial and biaxial nematic phases. Depending on the bend angle and the strength of an oblique twisting power of the banana-shaped molecules, we calculate phase diagrams on the temperaturebend angle plane. We derive the analytical formulas for two Landau points (LPs): one is at the bend angle and the other is at , which depends on the torsion angle. We also find that the phase appears outside the two LP angles and the phase diagrams show a rich variety of phase transitions, such as the second-order uniaxial nematic ( and the second-order phase transitions, etc.