Chirality transfer in lyotropic twist-bend nematics

TL;DR

The paper addresses how particle chirality controls the handedness of chiral liquid-crystalline phases in lyotropic bent-rod mesogens, focusing on the twist-bend nematic. It combines coarse-grained simulations of center-twist bent particles with a classical density functional theory framework to predict how chirality transfers to the cholesteric and twist-bend phases. The main findings are that cholesterics have handedness opposite to the particle chirality, while twist-bend nematics tend to adopt the same handedness as the particles, with chirality enhancing the TB stability and modifying director-field torsion and pitch; chiral dopants further bias TB handedness toward their own chirality. These results highlight phase-order dependencies in chirality transfer, challenge simplistic one-term free-energy descriptions, and suggest experimental realizations via DNA origami bent rods or other lyotropic chiral assemblies.

Abstract

Using molecular simulations and classical density functional theory, we study the liquid-crystalline phase behaviour of a series of bent rod-like mesogens with a controlled degree of chirality introduced through a twist at the centre of the particle. In the achiral limit, isotropic, uniaxial nematic, twist-bend nematic and smectic phases form as the packing fraction increases. On introducing chirality, the symmetry between the right- and left-handed twist-bend phases is broken. The phase with the same-handedness as the particles quickly becomes overwhelmingly favoured as the magnitude of the particle twist is increased, because the particles are then able to better follow the helical director field lines in the twist-bend phase and pack more efficiently. By contrast, the cholesteric phase is predicted to have the opposite handedness to that of the particle due to the relatively weakly-twisted nature of the particles. That the cholesteric and twist-bend phases have opposite handedness illustrates the differences in the mechanisms of chirality transfer in the two phases. We also found that doping a system of achiral mesogens with a small fraction of chiral particles led to selection of the twist-bend phase with the same chirality as the particle.

Figures (10)

• Figure 1: (a) The variation of the nematic director (arrows) associated with the heliconical order in the twist-bend phase. The angle between the local nematic director and the direction of modulation is constant and is termed the cone angle $\theta$. (b) and (c) A helical path of a nematic directory field line decorated with achiral bent particles showing how the particles are able to approximately follow the director field. In all cases the sense of the rotation of the nematic director is left-handed and one pitch length has been visualized. The pitch $\mathcal{P}$ and cone angle $\theta$ are in (a) and (b) $89.5\,\sigma$ and $40.43^\circ$ and in (c) $39.6\,\sigma$ and $10.98^\circ$. These have been chosen to match the values for the $\alpha$=0 and $\alpha$=$-90^\circ$ particles, respectively, at $p$=0.05 $\epsilon\sigma^{-3}$. In (c) the deviations of the achiral particles from the field lines are more significant due to the latter's greater torsion.
• Figure 2: (a) Model achiral mesogen consisting of 21 tangent spheres placed on an arc with a central angle of 45$^\circ$. The molecular axis $\mathbf{\hat{a}}$ is defined as the tangent to the arc at the centre of the particle. All the spheres lie on a plane that corresponds to a mirror plane of the system. The secondary $\mathbf{\hat{b}}$ axis is perpendicular to $\mathbf{\hat{a}}$ and in the plane of the particle. (b) A model chiral mesogen derived from the achiral mesogen by rotating the two halves of the particle by an angle $\alpha/2$ about the molecular axis but in opposite directions. The angle between the planes on which the two halves lie is $\alpha$. The illustrated example has $\alpha$=90$^\circ$, is right-handed (as is clear from the second view) and the curvature of the two halves of the particle has been adjusted so that the angle between the two midpoint-to-end vectors is the same as that for the achiral particle, namely 157.5$^\circ$.
• Figure 3: Example liquid-crystalline phases for the achiral ($\alpha$=0) bent mesogen: (a) uniaxial nematic ($N$) ($\eta$=0.242), (b) twist-bend nematic ($N_\mathrm{TB}$) ($\eta$=0.294); the box length in $z$ corresponds to one pitch length, (c) Smectic ($Sm$) ($\eta$=0.411). The middle sphere in a particle is white to aid the identification of smectic order or its absence.
• Figure 4: An example of the equilibration of the properties of the nematic twist-bend phase: (a) nematic order parameter $S$ and (b) pitch length of the twist-bend nematic phase versus time. $\alpha$=0 and pressure $P=0.05\,\epsilon\sigma^{-3}$.
• Figure 5: Phase diagram as a function of chiral angle $\alpha$ and packing fraction $\eta$. The points are coloured by the phase observed in the majority of the simulations at that state point. For some state points on the $N$/$N_\mathrm{TB}$ boundary, although there seemed to be a tendency to director modulations, clear heliconical was not yet present. The lines are guides to the eye.