Optical Activity Produced by Layer Chirality in Bent-Core Liquid Crystals

Large optical activity has recently been observed in chiral smectic liquid crystalline phases formed from achiral bent-core molecules. The origin of the optical activity remains unclear and has been attributed to both a helical superstructure and the layer chirality produced by simultaneous tilt and polar ordering of bent-core mesogens in the $B2$ phase. Here, we directly demonstrate that layer chirality produces optical activity in the well ordered $\mathrm{Sm}{C}_A{P}_A$ subphase.

Figure 1

A sketch of the LOC model for the $\mathrm{Sm}{C}_S{P}_S$. Significant optical activity results from the achiral stacking (b) of chiral layers (a,c). This model incorporates tilt and polar ordering of the bent-core molecules, where the polar direction is represented by the black arrow (bull’s eye), and the tilt direction by the dark (magenta) $T$ on the surfaces of the cube (a), which in this case is curved to represent the chirality of the layer. The orientation of a typical bent-core molecule within a layer is shown in (c): the dark (magenta) envelope around the molecular structure represents the projection of the molecule out of the plane of the paper: it is thickest for portions of the molecule projecting toward the reader. Each layer is divided into four achiral sublayers, representing the four structural segments of a bent-core molecule: two uniaxial slabs with optic axes parallel to the arms of the bent-core molecule form the core (light cylinders) and two isotropic sublayers represent the aliphatic tails of the molecule (dark circles). (d) The molecular structure and phase sequence on cooling (deg C) of GDa104.

Figure 2

(a) A freely suspended film of GDa104 showing coexistence of $\mathrm{Sm}{C}_A{P}_A$ and $\mathrm{Sm}{C}_S{P}_A$. (b) Transverse polarization ($P_T$) is perpendicular to the tilt plane of the molecules, while longitudinal polarization ($P_L$) is within the tilt plane. (c,d) The polarization of each layer is diagrammed for the $\mathrm{Sm}{C}_A{P}_A$ (left column) and the $\mathrm{Sm}{C}_S{P}_A$ (right column). (c) Odd layered films of either the $\mathrm{Sm}{C}_A{P}_A$ or $\mathrm{Sm}{C}_S{P}_A$ have $P_T\ne 0$, in this case out of the plane of the page (bullseye) [7]). (d) Surface polarization along the long axis of the molecules (green/light gray arrows) results in $P_L\ne 0$ in even layered $\mathrm{Sm}{C}_A{P}_A$ films [18].

Figure 3

Optical activity is visible in chiral domains of GDa104 in the low birefringence ($\Delta n=0.003$) $\mathrm{Sm}{C}_A{P}_A$. (a) The tilt chirality of the domains was confirmed in the field-induced $\mathrm{Sm}{C}_S{P}_S$ (crossed polarizers), where domains of opposite chirality within a single fan-shaped region are separated by a dark line (red arrow). The birefringence of the $\mathrm{Sm}{C}_S{P}_S$ is $\Delta n=0.17$, and so it appears green in a $4.5\mu \mathrm{m}$ display cell. (b) In the $\mathrm{Sm}{C}_A{P}_A$, such domains appear identical under crossed polarizers. (c) Contrast between the domains becomes apparent when the analyzer is decrossed relative to the polarizer, and (d) this contrast inverts when the decrossing direction is reversed. In these images, the decrossing angle is 5 degrees, and the contrast has been enhanced for clarity.

Figure 4

Molecular orientation and typical texture within a fan-shaped domain of the (a) $\mathrm{Sm}{C}_S{P}_S$ and (b) $\mathrm{Sm}{C}_A{P}_A$ with tilt angle near 45 degrees. The layer chirality is indicated by the color of the schematic molecules (cyan or magenta), and portions of the bent-core molecules which project toward the reader are thicker. The polar direction is into (cross) or out of (bullseye) the plane of the paper. The optic axis in the $\mathrm{Sm}{C}_S{P}_S$ is nearly 45 degrees from the layer normal, in opposite directions for the two chiralities; as a result, the extinction brushes in the two domains are nearly parallel. The optic axes of the two domains are averaged at the resolution limited domain boundary, making it quite dark. In the $\mathrm{Sm}{C}_A{P}_A$, the optic axis is SmA-like (parallel to the layer normal) and thus continuous across the chiral domain boundary. The only difference between the two domains is the layer chirality, and the contrast between the domains visible (dark and light gray) when the analyzer is decrossed relative to the polarizer is due to optical activity.