Twist-Bend Nematic Phase: Role of Third-Order Legendre Polynomial Term in Chiral Interaction Potential

Abstract

Using a mean-field theory, a twist-bend nematic (N TB) phase has been described. In addition to second-order Legendre polynomial term, the chiral interaction potential includes third-order Legendre polynomial term also. It considers the coupling between a nematic director and a pitch axis of the N TB phase. The distortion free energy, order parameter for twist-bend nematic, and orientational distribution function in equilibrium state have been calculated. Based on the free energy minimization, we obtain that the inclusion of third-order Legendre polynomial term in interaction energy makes N TB phase more stable.

Twist-bend nematics and heliconical cholesterics: a physico-chemical analysis of phase transitions and related specific properties

“…Recently, however, it was shown that some banana-shaped molecules consisting of two identical or near-identical mesogenic units connected by an oddnumbered alkyl or alkoxy chain can form, at temperatures below their nematic range, another distinct liquid crystalline phasea phase with no smectic-like translational ordering, but with a rather peculiar kind of molecular arrangement with periodic twist and bend deformation of the director distribution. Such phase seems to be first reported in [5], and was later generally recognized as the "twist-bend nematic phase" ( [6][7][8][9][10] and references therein) and designated as Ntb. In the Ntb phase, the director forms a conical helix, and chirality appears spontaneously with equal fractions of helically-ordered "domains" of opposite handedness from an achiral liquid crystal at the molecular level.…”