Optical and Resonant X-Ray Diffraction Studies Confirm a $\mathrm{Sm}{C}_{FI2}^{*}\mathrm{\text{−}}\mathrm{Sm}{C}^{*}$ Liquid Crystal Phase Sequence Reversal

Employing both null transmission ellipsometry and resonant x-ray diffraction, we confirmed the $\mathrm{Sm}{C}_{FI2}^{*}\mathrm{\text{−}}\mathrm{Sm}{C}^{*}$ phase sequence reversal in one liquid crystal compound and specially prepared binary mixtures. This phase sequence reversal was predicted by two recent theoretical advances. Moreover, the temperature range for the $\mathrm{Sm}{C}_{FI2}^{*}$ phase increases significantly in the mixture suggesting that such a phase sequence may exist in other compounds.

Figure 1

$\Delta$ as a function of temperature for a 60-layer film of 10OHF under $|E|=14.3\mathrm{V}/\mathrm{cm}$ at $\alpha =90°$ (circles) and $\alpha =270°$ (crosses) upon cooling. The ramping rate was $70\mathrm{mK}/\min$. $T_1$, $T_2$, and $T_3$ are the transition temperatures through the $\mathrm{Sm}A\mathrm{\text{−}}\mathrm{Sm}{C}_{\alpha }^{*}\mathrm{\text{−}}\mathrm{Sm}{C}_{FI2}^{*}\mathrm{\text{−}}\mathrm{Sm}{C}^{*}$ phase sequence. The chemical structure of 10OHF is shown at the top.

Figure 2

$\Delta$ as a function of $\alpha$ for a 60-layer film of 10OHF in the (a) $\mathrm{Sm}{C}^{*}$ phase at 63.7 °C and (b) $\mathrm{Sm}{C}_{FI2}^{*}$ phase at 72.2 °C, and for a 56-layer film of the mixture $(10\mathrm{OHF}{)}_{0.75}(\mathrm{C}9{)}_{0.25}$ in the (c) $\mathrm{Sm}{C}^{*}$ phase at 50.0 °C and (d) $\mathrm{Sm}{C}_{FI2}^{*}$ phase at 65.8 °C. The dots are the data and the lines are the simulation results. The fitting parameters are $n_e=1.635$, $n_o=1.483$, and $d=39.0\AA$ for (a),(b), and $n_e=1.645$, $n_o=1.485$, and $d=38.9\AA$ for (c),(d). Other parameters are as follows: (a) $\theta =15.6°$, $p=0.57\mu \mathrm{m}$; (b) $\theta =14.2°$, $p=1.25\mu \mathrm{m}$, $\delta =18°$; (c) $\theta =17.5°$, $p=0.60\mu \mathrm{m}$; (d) $\theta =17°$, $p=3.1\mu \mathrm{m}$, $\delta =24°$. To save space, only $\Delta$ vs $\alpha$ data are shown.

Figure 3

(a) Phase diagram obtained from simulations of a free energy having five expansion terms: three effective interlayer interactions and chiral and steric interaction terms [10]. $a_1$ and $a_2$ are coefficients of the nearest- and next-nearest-neighbor interaction terms. The parameters of the three other terms are set to constants in this diagram. $\mathrm{Sm}{C}_{d4}^{*}$ and $\mathrm{Sm}{C}_{d3}^{*}$ are phases having 4- and 3-layer unit cells with distorted clock structures, which are similar to $\mathrm{Sm}{C}_{FI2}^{*}$ and $\mathrm{Sm}{C}_{FI1}^{*}$ phases, respectively. The color scale represents the overall helical pitch of the structure. Line 1 (magenta) represents the phase sequence $\mathrm{Sm}{C}_{\alpha }^{*}\mathrm{\text{−}}\mathrm{Sm}{C}^{*}\mathrm{\text{−}}\mathrm{Sm}{C}_{FI2}^{*}\mathrm{\text{−}}\mathrm{Sm}{C}_{FI1}^{*}\mathrm{\text{−}}Sam{C}_A^{*}$ upon cooling found in the majority of antiferroelectric liquid crystal compounds. Line 2 (red) shows the phase sequence reversal $\mathrm{Sm}{C}_{\alpha }^{*}\mathrm{\text{−}}\mathrm{Sm}{C}_{FI2}^{*}\mathrm{\text{−}}\mathrm{Sm}{C}^{*}$ found in 10OHF and its binary mixtures. (b) The phase diagram of the $(10\mathrm{OHF}{)}_{1-y}(\mathrm{C}9{)}_y$ mixtures with C9. The dots are experimental data from our NTE measurements acquired in cooling runs except for $y=0.10$ [25]. The chemical structure of C9 is shown at the top.

Figure 4

X-ray intensity scans in the (a) $\mathrm{Sm}{C}_{\alpha }^{*}$ phase at 81.4 °C, the $\mathrm{Sm}{C}_{FI2}^{*}$ phase at (b) 61.0 °C and (c) 76.5 °C, and (d) the $\mathrm{Sm}{C}^{*}$ phase at 45.3 °C of the mixture $(10\mathrm{OHF}{)}_{0.75}(\mathrm{C}9{)}_{0.25}$. The dots and open circles are the data at resonant energy $E_0$ and nonresonant energy $E_0+10\mathrm{eV}$, respectively. The solid lines in (b) are the simulated resonant peaks.