Pseudopolar smectic-$C$ phases of azo-substituted achiral bent-core hockey-stick-shaped molecules

We report experimental studies on an azo-substituted compound consisting of bent-core hockey-stick-shaped molecules. The experimental results establish two pseudopolar tilted smectic phases, which are characterized by an in-plane axial-vector order parameter in addition to tilt order in the smectic layers. Electro-optical measurements in the mesophases indicate that the birefringence of the sample strongly depends on the applied electric field. We develop a theoretical model to account for this observation. The change in the birefringence of the sample arises from the field-induced reorientation of the tilt plane of the molecules in the layer above a threshold field. The effect is analogous to the field-induced Freedericksz transition which is quadratic in the applied electric field.

Figure 1

(a) The zigzag configuration of the molecules in the layer. (b) The schematic representation of the order parameters in a given layer. (c) The possible layer stacking of the zigzag molecules in different tilted smectic phases (from Ref. [22]).

Figure 2

(a) The molecular structure of the compound A14 and the phase sequence observed on cooling the sample from the isotropic phase. (b) The DSC thermogram on heating and cooling the sample at a rate of 3 K/min showing the transition peaks. The inset shows the weak first-order transition peak between the observed $\mathrm{Sm}C$ phases.

Figure 3

The x-ray diffraction intensity profile in (a) $\mathrm{Sm}{C}_A$ phase with layer spacing 44.3 Å at $125{}^{\circ }\mathrm{C}$ and (b) $\mathrm{Sm}{C}_I$ phase with layer spacing 46.1 Å at $106{}^{\circ }\mathrm{C}$. The insets show the enlarged view of the wide-angle peak.

Figure 4

The variation of the layer spacing and the calculated tilt angle as a function of temperature. The dashed line indicates the transition temperature between the observed smectic phases and the solid lines through the data points are a guide to the eye.

Figure 5

Polarizing optical microscopy textures (left column) for a homeotropically aligned sample: (a) Schlieren texture with the unit- and half-strength defects just below the clearing temperature in the $\mathrm{Sm}{C}_A$ phase, (b) at a lower temperature in the $\mathrm{Sm}{C}_A$ phase, and (c) in the $\mathrm{Sm}{C}_I$ phase. Right: For a planar-aligned sample, (d) the smectic batonnet growth just below the clearing temperature in the $\mathrm{Sm}{C}_A$ phase, (e) completely grown focal conic fan texture in the $\mathrm{Sm}{C}_A$ phase, and (f) irregular band texture in the $\mathrm{Sm}{C}_I$ phase. The scale bar in the above images is 40 $\mu \text{m}$.

Figure 6

The variation of average transmitted intensity of POM images with temperature of a planar-aligned sample of thickness 5 $\mu \text{m}$ between crossed polarizers.

Figure 7

The current response of compound A14 under the application of triangular wave voltage in the (a) $\mathrm{Sm}{C}_A$ phase (40 V, 30 Hz) at $120{}^{\circ }\mathrm{C}$ and (b) $\mathrm{Sm}{C}_I$ phase (80 V, 1 kHz) at $102{}^{\circ }\mathrm{C}$.

Figure 8

Optical response of a planar-aligned sample of thickness 5 $\mu \text{m}$ under the application of a triangular wave voltage in the (a) $\mathrm{Sm}{C}_A$ and (b) $\mathrm{Sm}{C}_I$ phases.

Figure 9

The variation of the effective dielectric constant as a function of temperature for the planar-aligned sample of thickness 5 $\mu \text{m}$.

Figure 10

The changes in the birefringence color of the sample at $115{}^{\circ }\mathrm{C}$ in the $\mathrm{Sm}{C}_A$ phase under the application of an AC electric field of frequency 1 kHz with increasing amplitudes: (a) 0 V/$\mu \text{m}$, (b) 4.4 V/$\mu \text{m}$, (c) 8.6 V/$\mu \text{m}$, and (d) 16 V/$\mu \text{m}$. The scale bar used in all the images is 40 $\mu \text{m}$.

Figure 11

The changes in the POM texture of a planar-aligned sample in the $\mathrm{Sm}{C}_I$ phase under the application of an AC electric field of frequency 1 kHz with increasing amplitudes: (a) 0 V/$\mu \text{m}$, (b) 4.4 V/$\mu \text{m}$, (c) 8.6 V/$\mu \text{m}$, and (d) 16 V/$\mu \text{m}$ at $104{}^{\circ }\mathrm{C}$. The scale bar used in all the images is 40 $\mu \text{m}$.

Figure 12

(a) The variation of average transmitted intensity and (b) the effective birefringence of a planar-aligned sample in the $\mathrm{Sm}{C}_A$ phase with increasing amplitude of the applied electric field of frequency 1 kHz. The data points are experimental values whereas the solid line shows the theoretically calculated value of the effective birefringence using our model.

Figure 13

The zigzag configuration of BCHS molecules in a layer of the observed smectic phases. The order parameters $\vec{\xi }, \vec{\eta }$, and $\vec{c}$ denote the tilt order, axial-vector order, and $c$ director in the plane of the layer, respectively. Note that the order parameters $\vec{\xi }$ and $\vec{\eta }$ are parallel to each other.

Figure 14

The schematic representation of the molecular organization at the midplane of the cell in the smectic layers in a bookshelf geometry between two glass plates at different electric fields. The circles on the right side represent the orientation of the vectors $\vec{\xi }, \vec{\eta }$, and $\vec{c}$ (red arrow) in smectic layers viewed along the layer normal. The numbers 1,2,3, $...$ represent the corresponding sequence of the layers.

Figure 15

(a) The variation of tilt plane angle $\beta$ across the sample cell at different normalized electric fields. (b) The variation of the maximum value of $\beta$ at the midplane (${\beta }_m$) as a function of the normalized electric field $\frac{E}{E_{\text{th}}}$.