Confinement Reveals Hidden Splay-Bend Order in Twist-Bend Nematics

Abstract

Using extensive Monte Carlo (MC) and molecular dynamics (MD) simulations, we investigate how spatial confinement affects molecular organization within thin films of the nematic twist-bend ($\mathrm{N_{TB}}$) phase. Our simulations show that confinement markedly amplifies the otherwise elusive splay-bend order, primarily by suppressing the intrinsic three-dimensional heliconical structure characteristic of bulk $\mathrm{N_{TB}}$. Remarkably, when the $\mathrm{N_{TB}}$ phase is confined between parallel walls imposing planar anchoring, and the bulk wave vector is oriented parallel to the walls, a smectic splay-bend ($\mathrm{S_{SB}}$) phase spontaneously emerges near the confining surfaces. This intermediate structure subsequently transforms into the bulk $\mathrm{N_{TB}}$ phase either directly via a smectic splay-bend-twist ($\mathrm{S_{SBT}}$) phase or through a sequence involving both the $\mathrm{S_{SBT}}$ and the nematic splay-bend-twist ($\mathrm{N_{SBT}}$) phases. Notably, the $\mathrm{N_{SBT}}$ phase becomes particularly pronounced as the molecular bend angle approaches its maximum attainable value in bulk $\mathrm{N_{TB}}$; this regime occurs in close proximity to the $\mathrm{N}\text{--}\mathrm{S_{A}}\text{--}\mathrm{S_{SB}}$ triple point on the bulk phase diagram. Our findings reveal a compelling and intricate interplay among chirality, confinement, and molecular ordering, further evidenced by the calculated elementary director distortions. Crucially, this study opens promising avenues for experimental exploration: confined thin-film geometries serve as powerful model systems for revealing and characterizing novel nematic and smectic liquid-crystal phases that remain elusive in, or currently inaccessible to, bulk experiments.

Figures (7)

• Figure 1: Illustration of how the experimentally observed reduction of the bend elastic constant ($K_{33}$)—typically the largest Frank elastic constant—drives bent-core mesogens to self-organize into periodically modulated nematic structures, most notably the ambidextrous chiral twist-bend ($\mathrm{N_{TB}}$) and the biaxial nonchiral splay-bend ($\mathrm{N_{SB}}$) phases. Left panel: Planar bend deformations are favored when $K_{33}\!\approx\!0$ but, if extended over macroscopic distances, incur costly defects (red dot). Center panel: "Escape into the third dimension" relieves defect-induced frustration, stabilizing the heliconical $\mathrm{N_{TB}}$ phase. Alternatively, a nonchiral $\mathrm{N_{SB}}$ phase with alternating planar splay--bend regions may form. Red arrows indicate local polarization; blue rods depict the director. More complex $\mathrm{N_{SB}}$-like textures can also arise from twist-free director fields constructed as normalized gradients of scalar fields. Right panel: Hybrid splay--bend--twist nematics ($\mathrm{N_{SBT}}$) can emerge by combining splay, bend, and twist deformations, thereby interpolating between $\mathrm{N_{SB}}$ and $\mathrm{N_{TB}}$.
• Figure 2: Model bent-shaped molecule (left) used in our simulations: a rigid assembly of eleven identical, mutually tangent spheres arranged along a circular arc, giving overall $C_{2v}$ molecular symmetry. The bend angle $\chi$ is defined as the angle between the tangents at the terminal spheres; larger $\chi$ corresponds to smaller molecular curvature. The unit vectors $\hat{\mathbf a}$ and $\hat{\mathbf b}$ denote the directions of the long molecular axis and the twofold-symmetry axis, respectively. The nearest mesogenic analogue is CB7CB (right), which exhibits a stable $\mathrm{N_{TB}}$ phase.
• Figure 3: Sketch of a partial phase diagram for the bent-core (banana-shaped) molecular model depicted in Fig. (\ref{['fig:phase_diagram']}), shown as a function of bend angle $\chi$ and packing fraction $\eta$. The two blue lines indicate the simulation paths explored in this work, and the red dots mark the specific state points for which detailed results are presented.
• Figure 4: Results of MC simulations of the $\mathrm{N_{TB}}$ phase confined between two parallel walls for $N = 12{,}000$ molecules with bend angle $\chi = 110^\circ$ and packing fraction $\eta = 0.327$. Here, $L_{{mol}}$ denotes the molecular length at $\chi = 180^\circ$ ($L_{{mol}} = 11$). Top panel: Simulation snapshot showing molecular organization between parallel walls. Molecular orientations are color-coded by the projection of the polarization axis $\mathbf{\hat{b}}$ onto the $xy$ plane, perpendicular to the wave vector $\mathbf k$. Bottom panel: Smectic order parameter $\tau$ and the director projections onto the $xy$ plane as functions of distance from the left wall. In the $\mathrm{N_{TB}}$ phase, the projection traces a circle; in the other phases, an ellipse. Sketches indicate the short and long semi-axes; complete ellipses are shown as insets. A sequence of three phases, $\mathrm{S_{SB}}$, $\mathrm{S_{SBT}}$, and $\mathrm{N_{TB}}$)—is observed upon moving from the wall toward the center of the sample. As the distance from the wall increases, the splay component weakens and eventually vanishes on entering the $\mathrm{N_{TB}}$ phase.
• Figure 5: Results of MD simulations of the $\mathrm{N_{TB}}$ phase confined between two parallel walls for $N=24{,}000$ molecules, bend angle $\chi=135^\circ$, and packing fraction $\eta=0.335$. (Here, $L_{\mathrm{mol}}$ is defined as in Fig. \ref{['fig:MC_full_column']}.) Top panel: Local number-density profiles across the slit and at the walls, normalized by the average density $\rho_0$. Pronounced smectic layering develops at the walls and decays approximately exponentially with distance toward the slit center, where the bulk-stable $\mathrm{N_{TB}}$ phase is recovered. Bottom panel: Smectic order parameter $\tau$ and the director projection $(n_x,n_y)$ onto the $xy$ plane as functions of distance from the left wall. In the $\mathrm{N_{TB}}$ phase, the locus of $(n_x,n_y)$ is a circle; in the other phases it is an ellipse. Sketches indicate the short $(n_x)$ and long $(n_y)$ semiaxes; complete ellipses are shown as insets. With increasing distance from the wall, a sequence of four phases— $\mathrm{S_{SB}}$, $\mathrm{S_{SBT}}$, $\mathrm{N_{SBT}}$, and $\mathrm{N_{TB}}$—is observed. The splay component weakens and ultimately vanishes on entering the $\mathrm{N_{TB}}$ phase.