Chiral smectic-$A$ and smectic-$C$ phases with de Vries characteristics

Infrared and dielectric spectroscopic techniques are used to investigate the characteristics of two chiral smectics, namely, 1,1,3,3,5,5,5-heptamethyltrisiloxane 1-[$4^{\prime }$-(undecyl-1-oxy)-4-biphenyl(S,S)-2-chloro-3-methylpentanoate] ($\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$) and tricarbosilane-hexyloxy-benzoic acid (S)-4′-(1-methyl-hexyloxy)-3′-nitro-biphenyl-4-yl ester (W599). The orientational features and the field dependencies of the apparent tilt angle and the dichroic ratio for homogeneous planar-aligned samples were calculated from the absorbance profiles obtained at different temperatures especially in the smectic-A* phase of these liquid crystals. The dichroic ratios of the C-C phenyl ring stretching vibrations were considered for the determination of the tilt angle at different temperatures and different voltages. The low values of the order parameter obtained with and without an electric field applied across the cell in the $\mathrm{Sm}-A^{*}$ phase for both smectics are consistent with the de Vries concept. The generalized Langevin-Debye model introduced in the literature for explaining the electro-optical response has been applied to the results from infrared spectroscopy. The results show that the dipole moment of the tilt-correlated domain diverges as the transition temperature from $\mathrm{Sm}-A^{*}$ to $\mathrm{Sm}-C^{*}$ is approached. The Debye-Langevin model is found to be extremely effective in confirming some of the conclusions of the de Vries chiral smectics and gives additional results on the order parameter and the dichroic ratio as a function of the field across the cell. Dielectric spectroscopy finds large dipolar fluctuations in the $\mathrm{Sm}-A^{*}$ phase for both compounds and again these confirm their de Vries behavior.

Figure 1

Schematic illustration of the de Vries diffuse-cone model in the $\mathrm{Sm}-A^{*}$ phase. Here $\vec{k}$ is the layer normal, $\vec{n}$ is the direction of long molecular axis, $d_A$ is the layer spacing, while ${\mathrm{\Omega }}_{\max }$ is the maximum tilt angle at a large field, and ${\mathrm{\Omega }}_{\min }$ is evaluated from the experimental data on birefringence at zero field. The azimuthal angle is distributed on the cone at zero field. The apparent tilt angle is thus zero. For higher fields, the azimuthal angle condenses to an almost single value leading to the maximum apparent angle, ${\mathrm{\Omega }}_{\max }$. The apparent tilt angle ${\mathrm{\Omega }}_0$ varies with the field.

Figure 2

The molecular structures of $\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$ (top) and W599 (bottom) with their corresponding phase transition temperatures ($\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$: $\mathrm{Cr}16{}^{\circ }\mathrm{C}, \mathrm{Sm}-C^{*} 47{}^{\circ }\mathrm{C}, \mathrm{Sm}-A^{*} 59{}^{\circ }\mathrm{C}$, Iso; W599: $\mathrm{Sm}-C^{*} 29{}^{\circ }\mathrm{C}, \mathrm{Sm}-A^{*} 43{}^{\circ }\mathrm{C}$, Iso) obtained by polarized optical microscopy at a cooling rate of 1 °C/min are specified.

Figure 3

A schematic representation of the measurement system for the de Vries $\mathrm{Sm}-A^{*}$ phase. ZnSe windows coated with ITO containing the sample are mounted on the hot stage. The polarizer can be automatically rotated by an angle ${\mathrm{\Omega }}_p$. The constituent molecules are tilted by Ω from the layer normal $\vec{k}$. The polarization $P$ that is normal to the $c$ director (projection of the molecular director on the smectic plane) makes an angle φ with the normal drawn to the cell, while ${\mathrm{\Omega }}_o$ is the angle between the layer normal and the projection of the effective optic axis onto the plane of the cell's windows.

Figure 4

Polar plots of the absorbance profiles for the C-C phenyl ring stretching vibrational band for both negative and positive fields at temperatures of (a) $49.5{}^{\circ }\mathrm{C}$ for $\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$ and (b) $31{}^{\circ }\mathrm{C}$ for W599. These temperatures correspond to the $\mathrm{Sm}-A^{*}$ phase of these materials at zero field.

Figure 5

Voltage dependence of the molecular tilt angle (${\mathrm{\Omega }}_0$), determined from the absorbance profiles of the C-C phenyl ring stretching vibration at various temperatures in the $\mathrm{Sm}-A^{*}$ phase but close to the $\mathrm{Sm}-A^{*}$ to $\mathrm{Sm}-C^{*}$ transition for (a) $\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$ at $1608\mathrm{c}{\mathrm{m}}^{-1}$ and (b) W599 at $1605\mathrm{c}{\mathrm{m}}^{-1}$. The symbols correspond to the experimental data, while the solid lines are fits to the generalized Langevin-Debye model given in Sec. 3b. The thickness of the sample is 5 μm. (+) Temperatures in the inset denote above the transition temperature $T_{AC}$ in the $\mathrm{Sm}{A}^{*}$ phase.

Figure 6

Dichroic ratio ($R=A_{\parallel }/A_{\perp }$) versus the applied dc voltage for the phenyl band $1608\mathrm{c}{\mathrm{m}}^{-1}$ at different temperatures for a homogeneous planar-aligned cell of 5 μm thickness for (a) $\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$ and (b) W599. (+) Temperatures in the inset denote above $T_{AC}$ transition temperature in the $\mathrm{Sm}{A}^{*}$ phase and (−) denote below it in the $\mathrm{Sm}{C}^{*}$ phase.

Figure 7

Variation of $A_{\perp }$ with voltage for a homogeneous planar-aligned cell of 5 μm thickness. (a) $\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$ and (b) W599.

Figure 8

Voltage dependence of $A_{\parallel }$ at different temperatures for (a) $\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$ and (b) W599 for a homogeneous planar-aligned cell of 5 μm thickness. (+) and (−) temperatures in the insets as in Figures 5 and 6.

Figure 9

Dependence of $S$ on applied voltage for a homogeneous planar-aligned cell of 5 μm thickness. (a) $\mathrm{MS}{\mathrm{i}}_3\mathrm{M}{\mathrm{R}}_{11}$ and (b) W599. (+) and (−) in the inset imply the same as in Figs. 6 to 8.

Figure 10

The local dipole moment $p_0$ obtained from the fitting of the experimental data to the model as a function of the reduced temperature in the $\mathrm{Sm}-A^{*}$ phase.

Figure 11

Electro-optical response of W599 as a function of temperature in the $\mathrm{Sm}-A^{*}$ phase.

Figure 12

Two-dimensional dielectric loss spectra as a function of frequency and temperature for a homogenously aligned 7 μm cell of W599. The dominant ITO peak is encompassing the ${\varepsilon }^{\prime \prime }$ spectra for frequencies higher than 30 kHz.

Figure 13

Plots of the relaxation frequency ($f_R$) and the dielectric relaxation strength ($\mathrm{\Delta }\varepsilon$) with temperature for W599 in a homogeneous planar-aligned 7 μm thick cell. GM and SM denote Goldstone and soft modes, respectively.