Uniaxial and biaxial nematic phases of banana-shaped molecules and the effects of an external field.

A mean field theory is introduced to describe uniaxial and biaxial nematic 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 and four orientational order parameters. Using the nematic free energy of the Maier-Saupe type, we calculate the phase diagram on the temperature − bend angle ( 0 < θ B < π) plane and find three uniaxial nematic ( N U i ) and three biaxial nematic ( N B i ) phases, where i (= a , b , c) is the primary axis of the orthogonal molecular axis. We also derive the approximate formulas of a nematic-isotropic phase transition ( N I T) and a biaxial-uniaxial phase transition ( B U T) temperature as a function of the bend angle. We also discuss the effects of the external field on the N I T temperature and find the negative dependence of the N I T temperature on the external field. [ABSTRACT FROM AUTHOR]