Coarse-grained model of the nematic twist-bend phase from a stable state elastic energy

The twist-bend nematic ($N_{\mathrm{TB}}$) phase is a doubly degenerated heliconical structure with nanometric pitch and spontaneous bend and twist deformations. It is favored by symmetry-breaking molecular structures, such as bent dimers and bent-core molecules, and it is currently one of the burgeoning fields of liquid-crystal research. Although tremendous advances have been reported in the past five years, especially in molecular synthesis, most of its potential applications are held back by the lack of a proper and definitive elastic model to describe its behavior under various situations such as confinement and applied field. In this work we use a recently proposed stable state elastic model and the fact that the mesophase behaves as a lamellar structure to propose a mesoscopic or coarse-grained model for the $N_{\mathrm{TB}}$ phase. By means of standard procedures used for smectic and cholesteric liquid crystals, we arrive at a closed-form energy for the phase and apply it to a few situations of interest. The predicted compressibility for several values of the cone angle and the critical field for field-induced deformation agree well with recent experimental data.

Figure 1

Twist-bend nematic phase represented by the molecular arrangement and the augmented scale, in terms of the pseudolayer structure.

Figure 2

(a) Splay, (b) twist, and (c) bend of the director field $\mathbf{t}$, related to $K_{\mathrm{eff}}, {\alpha }_2$, and ${\alpha }_3$, respectively. The pseudolayers' distortions and separations are exaggerated for didactic purposes.

Figure 3

Cone angle in the $N_{\text{TB}}$ as a function of the compressibility. The black solid line exhibits the variation of CB7CB, while the red dashed line is the measure of KA(0.2).

Figure 4

Elastic constants from Eq. (13) vs $\theta$ when the physical parameters of CB7CB are used.

Figure 5

Illustration of the twist-bend nematic phase with a magnetic field perpendicular to the helical axis.