Unwinding of the twist-bend nematic structure under an external field

TL;DR

This paper studies how external magnetic or electric fields influence the twist-bend nematic phase, revealing how the pitch of the helical structure can be controlled or become uniform under certain field orientations and strengths.

Contribution

It provides a theoretical analysis of the effect of external fields on the twist-bend nematic phase, extending elastic energy models to include field interactions and predicting pitch behavior changes.

Findings

Magnetic field parallel to the helical axis shifts the phase stability range.

Perpendicular magnetic field increases the pitch, leading to uniform alignment at a critical field.

Results encompass behavior of cholesteric liquid crystals as a special case.

Abstract

The recently discovered twist-bend nematic phase, $\rm N_{tb}$, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, $\textbf{n}$, on a conical helix with a tilt angle $\theta$ and helical pitch $P$. The stability of the $\rm N_{tb}$ phase has been recently demonstrated from the elastic point of view by extending the Frank elastic energy density of the nematic phase to include the symmetry element of helical axis, $\bf t$. In the present communication, we investigate the influence of an external bulk field (magnetic or electric) on the pitch of the $\rm N_{tb}$ phase. For a material with positive magnetic susceptibility anisotropy, when the magnetic field $\bf{H}$ is parallel to the helical axis, $\bf{t}$, the field modifies the coupling parameter between the director and the helical axis, thus shifting the interval of values for which this coupling results in the $\rm N_{tb}$ phase. If $\bf{H}$ is perpendicular to $\bf{t}$, it is shown that the pitch of the nematic director $\bf n$ precession increases with $\bf{H}$, and at a critical value of $H_c$ it becomes infinite as in a cholesteric liquid crystal, that is, one gets a uniform orientation of n. Our results include the behaviour of a cholesteric under field as a limiting case.