Elucidation of the de Vries behavior in terms of the orientational order parameter, apparent tilt angle, and field-induced tilt angle for smectic liquid crystals by polarized infrared spectroscopy

We report experimental results of the orientational order parameter, the apparent tilt angle, and the field-induced tilt angle for three chiral smectic liquid crystalline materials investigated using infrared (IR) polarized spectroscopy. The common feature in these materials is use of the core 5-methyl-2- pyrimidine benzoate as the central part of the mesogen. This core is terminated by siloxane or carbosilane chains on one of the ends and by the chiral alkoxy chains on the opposite. These compounds exhibit low concomitant layer shrinkage at the smectic $A^{*}$ ($\mathrm{Sm}{A}^{*}$) to smectic $C^{*}$ ($\mathrm{Sm}{C}^{*}$) transition temperature and within the $\mathrm{Sm}{C}^{*}$ phase itself. The maximum layer shrinkage in $\mathrm{Sm}{C}^{*}$ is observed as ∼1.5%. We calculate the apparent orientational order parameter, $S_{\mathrm{app}}$ in the laboratory reference frame from the observed IR absorbance for homeotropic aligned samples, and the true order parameter, S, is calculated using the measured tilt angle and is also interpolated from Iso-$\mathrm{Sm}{A}^{*}$ transition temperature closer to $\mathrm{Sm}{C}^{*}$ phase. The apparent tilt angle in the $\mathrm{Sm}{A}^{*}$ phase calculated from a comparison of order parameters S and $S_{\mathrm{app}}$ is found to be significantly large. A low magnitude of $S_{\mathrm{app}}$ found for homeotropic aligned samples in the $\mathrm{Sm}{A}^{*}$ phase indicates that the order parameter plays a vital role in determining the de Vries characteristics, especially of exhibiting larger apparent tilt angles. Furthermore there is a significant increase in the true order parameter at temperatures close to $\mathrm{Sm}{A}^{*}$ to $\mathrm{Sm}{C}^{*}$ transition temperature in all three compounds. The planar-aligned samples are used to study the dependence of induced tilt angle on the applied electric field. The generalized Langevin–Debye model given by Shen et al. reasonably fits the experimental data on the field-induced tilt angle. The results show that the dipole moment of the tilt correlated domain in $\mathrm{Sm}{A}^{*}$ diverges as temperature is lowered to the $\mathrm{Sm}{A}^{*}-\mathrm{Sm}{C}^{*}$ transition temperature. The generalized Langevin-Debye model is also found to be extremely effective in confirming some of the conclusions of the de Vries behavior.

Figure 1

Molecular structures of the compounds DR276, DR133, and DR118 and the transition temperatures determined by differential scanning calorimetry (DSC) are given. The phase transition temperatures are also obtained by polarized optical microscopy. The cooling rate used for both techniques is 1 °C/min.

Figure 2

Absorbance of the phenyl band as a function of temperature/phase for (a) DR276, (b) DR133, and (c) DR118.

Figure 3

Variation of the apparent order parameter ($S_{\mathrm{app}}$) with temperature for homeotropically aligned cells of (a) DR276 (b) DR133, and (c) DR118.

Figure 4

Representation of experiments performed on homeotropically aligned samples. X, Y, and Z denote the axes of the laboratory frame of reference; $x$, $y$, and $z$ are the axes of the molecular reference frame. Θ is one of the Euler angles which describe the orientation of the molecular reference frame versus the laboratory reference frame. The direction of the IR transition dipole moment µ relative to the long axis of mesogens in the molecular frame of reference is denoted by the polar angle ${\beta }_l$ and azimuthal angle ${\gamma }_l$. The inset shows the definition of the local system described in the text: X′, Y′, and Z' are axes of the local frame of reference; $\theta$ is the in-layer tilt angle made by the director, $\theta =\langle \mathrm{\Theta }\rangle$ (averaging is done for a single smectic layer).

Figure 5

Results of the order parameters for (a) DR 276 (b) DR133, and (C) DR118: The apparent order parameter ($S_{\mathrm{app}}$) [black squares] calculated with respect to the fixed laboratory frame of reference, the green triangles denote the true order parameter, S, calculated by using Eq. (5) and the experimentally obtained tilt angles measured close to the $\mathrm{Sm}{A}^{*}$ to $\mathrm{Sm}{C}^{*}$ transition temperature, and red filled circles denote the interpolated values of S. These order parameters are used to calculate the apparent molecular tilt angle (blue squares) plotted for the entire range of temperatures in a homeotropically aligned cell.

Figure 6

Optical textures of planar-aligned sample of DR276 for two temperatures (a) 84 °C, 0 V and (b) 85 °C at 40 V in the $\mathrm{Sm}{A}^{*}$ phase.

Figure 7

Polar plots of the absorbance profile in terms of the polarizer angle for the compound DR118, as an example.

Figure 8

The voltage dependence of the molecular IR tilt angle (${\mathrm{\Omega }}_{\mathrm{ind}}$), determined from the absorbance profiles of the C-C phenyl ring stretching vibration at different temperatures in the $\mathrm{Sm}{A}^{*}$ phase close to the $\mathrm{Sm}{A}^{*}-\mathrm{Sm}{C}^{*}$ transition for (a) DR276 (b) DR118, and (c) DR133 at $1605\mathrm{c}{\mathrm{m}}^{-1}$, respectively. The symbols correspond to the experimental data, and the solid lines are fits to the generalized Langevin-Debye model given in Sec. 3b. The thickness of the sample is 5 μm.

Figure 9

The local dipole moment $p_o$ obtained from the fitting of the experimental data to the Shen et al. model plotted as a function of the temperature in the $\mathrm{Sm}{A}^{*}$ phase for (a) DR276, (b) DR118, and (c) DR133.

Figure 10

Plots of the temperature dependence of the phenomenological scaling factor α for (a) DR276, (b) DR118, and (c) DR133.