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

ABSTRACT

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 ($0<{\theta }_B<\pi$) 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 ($NIT$) and a biaxial-uniaxial phase transition ($BUT$) temperature as a function of the bend angle. We also discuss the effects of the external field on the $NIT$ temperature and find the negative dependence of the $NIT$ temperature on the external field.

Graphical Abstract

KEYWORDS:

• Banana-shaped molecules
• bent-core molecules
• biaxial nematic
• Landau point
• applied fields

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by JSPS KAKENHI Grant Number 18K03566.Japan Society for the Promotion of Science [KAKENHI Grant Number 18K03566].