Molecular Crystals and Liquid Crystals, Vol.683, No.1, 3-13, 2019
Cholesteric-isotropic phase transitions of banana-shaped liquid crystalline molecules
A mean field theory is introduced to describe cholesteric (Ch) phases of banana-shaped liquid crystalline molecules. From a geometric point of view, we derive the tensor order parameter of the banana-shaped molecules as a function of a bend angle (theta(B)) and four orientational order parameters. Using the tensor order parameter, we derive the free energy of the cholesteric phase for the banana-shaped molecules and obtain the approximate formula of a cholesteric-isotropic phase transition (CIT) temperature as a function of the bend angle. We find a cholesteric C phase for < 70.5 or > 109.5 where the the two arm vectors of the banana-shaped molecule tend to parallel to the director and a cholesteric C phase for 70.5 < < 109.5 where the two arm vectors tend to perpendicular to the director. These Ch phases are also distinguished by using the primary axis of the orthogonal molecular axis.