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

ABSTRACT

We present a mean field theory to describe uniaxial ($N_{TB,U}$) and biaxial twist-bend nematic ($N_{TB,B}$) 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 ($0^{\circ }<{\theta }_{AB}<{180}^{\circ }$), a torsion angle $\xi$ 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 temperature$-$bend angle plane. We derive the analytical formulas for two Landau points (LPs): one is at the bend angle ${109.5}^{\circ }$ and the other is at ${\theta }_{AB}(\xi )(>{70.5}^{\circ })$, which depends on the torsion angle. We also find that the $N_{TB}$ 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 ($N_U)-N_{TB,B}$ and the second-order $N_{TB,U}-N_{TB,B}$ phase transitions, etc.

Graphical abstract

KEYWORDS:

• Twist-bend nematic
• biaxial nematic phase
• banana-shaped molecule
• axial chirality
• bend angle

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by JSPS KAKENHI Grant Number [18K03566].