Discovery of a Novel Smectic-$C^{*}$ Liquid-Crystal Phase with Six-Layer Periodicity

We report the discovery of a new smectic-$C^{*}$ liquid-crystal phase with six-layer periodicity by resonant x-ray diffraction. Upon cooling, the new phase appears between the $\mathrm{Sm}{C}_{\alpha }^{*}$ phase having a helical structure and the $\mathrm{Sm}{C}_{d4}^{*}$ phase with four-layer periodicity. This $\mathrm{Sm}{C}_{d6}^{*}$ phase was identified in two mixtures which have an unusual reversed $\mathrm{Sm}{C}_{d4}^{*}\mathrm{\text{−}}\mathrm{Sm}{C}^{*}$ phase sequence. The $\mathrm{Sm}{C}_{d6}^{*}$ phase shows a distorted clock structure. Three theoretical models have predicted the existence of a six-layer phase. However, our experimental findings are not consistent with the theories.

Figure 1

(a) Schematic representation of the average molecular tilt in a $\mathrm{Sm}{C}^{*}$ layer. $\theta$ and $\varphi$ are the tilt and azimuthal angles. (b) Intermolecular layer arrangements in the $\mathrm{Sm}{C}_{\alpha }^{*}$, $\mathrm{Sm}{C}^{*}$, $\mathrm{Sm}{C}_{d4}^{*}$, $\mathrm{Sm}{C}_{d3}^{*}$, and $\mathrm{Sm}{C}_A^{*}$ phases. Ellipses, numbered by layer indices, represent the projections of the molecules onto the layer plane. In the $\mathrm{Sm}{C}_{\alpha }^{*}$ phase, the tilt angle is usually small compared to the other phases. (c) The chemical structures and phase sequences (upon cooling) of the homologous series nOHF and Cn. The sulfur atoms in the Cn compounds are essential for the RXRD experiments.

Figure 2

Temperature dependences of pitch (triangles) and layer spacing (squares) for (a) mixture $A$ and (b) mixture $B$. Different phases are divided by dashed lines. Noisy resonant signals are obtained in the regions between the $\mathrm{Sm}{C}_{d6}^{*}$ and $\mathrm{Sm}{C}_{d4}^{*}$ phases. They are called noisy region (NR). No pitch data are given in these regions.

Figure 3

The resonant satellite peak (circles) from mixture $A$ at $80.89°\mathrm{C}$ and the simulation (line). Crosses are off-resonance data obtained at $E=2.460\mathrm{keV}$. The center of the split peaks is located at $Q_z/Q_0=1.167$, corresponding to a pitch of six layers. The split peaks indicate a distorted structure. The positions and intensities of the two peaks give an optical pitch of $350$ layers ($1.36\mu \mathrm{m}$) and a distortion angle $\delta$ of $27\pm 2°$. The simulation has been normalized to match the measured intensities. The illustration is the structure used in our fitting.

Figure 4

X-ray intensity scans from mixture $B$ at four different temperatures during the $\mathrm{Sm}{C}_{\alpha }^{*}\mathrm{\text{−}}\mathrm{Sm}{C}_{d6}^{*}$ transition. Short red arrows and long blue arrows point to the peaks of the $\mathrm{Sm}{C}_{d6}^{*}$ phase and the $\mathrm{Sm}{C}_{\alpha }^{*}$ phase, respectively. The temperature range of the coexistence of the $\mathrm{Sm}{C}_{\alpha }^{*}$ and the $\mathrm{Sm}{C}_{d6}^{*}$ phases is about $0.4°\mathrm{C}$ for mixture $B$. In mixture $A$, we did not identify the coexistence region experimentally.