Unique Pitch Evolution in the Smectic-$C_{\alpha }^{*}$ Phase

Employing resonant x-ray diffraction, we observed unique pitch evolutions in the smectic-$C_{\alpha }^{*}$ phase in mixtures of two antiferroelectric liquid crystals. Our results show that the pitch in this phase continuously evolves across 4 layers, contradicting a theoretical model that predicts that the smectic-$C_{\mathrm{FI}2}^{*}$ phase intervenes in the smectic-$C_{\alpha }^{*}$ phase. The phase sequences we found can be explained by another model that includes one type of long-range interaction among smectic layers.

Figure 1

INHP temperature evolution obtained from $R$-10OTBBB1M7 ($x$)—$R$-MHPOCBC ($1\mathrm{\text{−}}x$) mixtures. Data from five mixtures are included representing three different behaviors of INHP evolutions. The mixture of $x=0.25$ has the $\mathrm{Sm}{C}_{\alpha }^{*}$ phase with $\mathrm{INHP}<4\mathrm{L}$. The mixtures of $x=0.45$, 0.50, and 0.53 have INHP evolving across $\mathrm{INHP}=4\mathrm{L}$. The mixture of $x=0.75$ has the $\mathrm{Sm}{C}_{\alpha }^{*}$ phase with $\mathrm{INHP}>4\mathrm{L}$. Only data from 3.4 to 5 L are presented in order to emphasize the details around 4 L. The inset shows the INHP evolution around 4 layers for the $x=0.50$ and 0.53 mixtures. The lines are aids to the eye. ($A$) and ($B$) show the molecular structures of $R$-10OTBBB1M7 and $R$-MHPOCBC.

Figure 2

A comparison between the INHP vs temperature and the INHP vs layer spacing. $d_{\mathrm{AC}}$ is the layer spacing at $T_{\mathrm{AC}}$. The data came from the $x=0.50$ mixture.

Figure 3

Phase sequences of the mixtures were qualitatively mapped to Hamaneh and Taylor’s phase diagram. Four mixtures were presented, $x=0.25$, 0.45, 0.53, 0.75. I, II, III, IV, and VI indicate the regions of the $\mathrm{Sm}{C}^{*}$, $\mathrm{Sm}{C}_A^{*}$, the $\mathrm{Sm}{C}_{\mathrm{FI}1}^{*}$, the $\mathrm{Sm}{C}_{\mathrm{FI}2}^{*}$, and a phase having a 6-layer structure. The $\mathrm{Sm}{C}_{\alpha }^{*}$ phase is marked as incommensurate. $\eta$ is the strength of the long-range interaction. Temperature decreases from bottom left to top right of the phase diagram.

Figure 4

The empirical method to predict the INHP behavior of the mixtures from the INHP behavior of the pure compounds. The points in the $x=0$, 0.50, and 1 plots were obtained from interpolating the actual data points so the points are evenly spaced for calculations.