Biaxial and antiferroelectric structure of the orthogonal smectic phase of a bent-shaped molecule and helical structure in a chiral mixture system

We examined the biaxial and antiferroelectric properties in the Smectic-$A{P}_A$ (Sm-$A{P}_A$) phase of bent-shaped DC-S-8. The biaxiality, which results from the existence of a secondary director, was well established from birefringence observations in the homeotropically aligned Sm-$A{P}_A$. By entering into Sm-$A{P}_A$ phase, the birefringence ($\Delta n$, difference between two refractive indices of short axes) continuously increased from 0 to 0.02 with decreasing temperature. The antiferroelectric switching and second harmonic generation (SHG) activity on the field-on state were also observed in the Sm-$A{P}_A$ phase, and the evaluated spontaneous polarization ($P_S$) value strongly depended on temperature. The temperature dependence of $\Delta n$ and $P_S$ resembles each other and follows Haller's approximation, showing that the biaxiality is due to polar packing in which the molecules are preferentially packed with their bent direction arranged in the same direction, and that the phase transition of Sm-$A{P}_A$ to Sm-$A$ is second order. The biaxiality was further examined in chiral Sm-$A{P}_A$${}^{*}$. Doping with chiral components induced the helical twisting of the secondary director in the Sm-$A{P}_A$${}^{*}$ phase, which was confirmed by observing the reflection of the circular dichroism (CD) bands in the homeotropically aligned cell. The helical pitch of Sm-$A{P}_A$${}^{*}$ is tunable in the range of 300–700 nm wavelength with a variation in the chiral content of 5 to 10 weight (wt)$\%$.

Figure 1

Structure and phase sequence of (a) DC-S-8 and (b) DC-S-8${}^{*}$. The following abbreviations are used: crystal (Cry), isotropic fluid ($I$), nonpolar uniaxial smectic (Sm-$A$) phase, and antiferroelectric and biaxial smectic (Sm-$A{P}_A$) phase. Transition enthalpies (kJ mol${}^{-1}$) are given in parenthesis for cooling process.

Figure 2

Optical photomicrographs of DC-S-8 observed in various surface-treated ITO sandwich cells at different temperatures: (a) and (b) show the typical fan-shaped textures of Sm-$A$ and Sm-$A{P}_A$ at 90 °C and 80 °C in 5-μm thickness planar cells, respectively. (c) and (d) show the dark and birefringent Schlieren textures of Sm-$A$ and Sm-$A{P}_A$, respectively, in the homeotropically aligned sample. The scale bar indicates 25 μm.

Figure 3

Optical photomicrographs of the DC-S-8 in the vertically aligned cell with a thickness of 4.8 μm upon applying an in-plane DC voltage of 10 V across a gap of 25 μm: (a) polydomain Schlieren texture at the DC-off state and (b) uniform birefringent texture at the DC-on state. The scale bar indicates 25 μm.

Figure 4

(a) Light transmittance intensity of DC-S-8 as a function of light wavelength at various temperatures measured in the in-plane switching ITO cells with vertical alignment (cell thickness: ∼14 μm) by POM equipped with spectrometer. Since the net retardation is too small to precisely determine the birefringence, a wavelength plate (3λ) was used to enlarge the total transmitted retardation [18]. Then, the birefringence was calculated by using equation (1) and (2). (b) Birefringence of DC-S-8 on $E_{\mathrm{ON}}$ state (Sm-$A{P}_F$) as a function of light wavelength at various temperatures. Due to the absorption band in 400–450 nm, the calculated birefringence value in this region also bears less reliability. The arrow in each figure indicates a direction of temperature decreasing.

Figure 5

Temperature dependence of the birefringence $({\mathbf{n}}_{\mathbf{p}}-{\mathbf{n}}_{\mathbf{o}})$ observed by homeotropic alignment and order parameter (S${}_2$) in the Sm-$A{P}_A$ phase. The order parameter (for 550 nm) was calculated by using Haller's approximation in Eq. (3).

Figure 6

(a) Refractive index ellipsoid of a bent-core molecule along the primary $\left({\mathbf{n}}_{\mathbf{z}}\right)$ and two secondary $({\mathbf{n}}_{\mathbf{p}},{\mathbf{n}}_{\mathbf{o}})$ directors in each layer of the Sm-$AP$ phase and (b) schematic structure of the helical superstructure in the Sm-$A{P}^{*}$ phase, possibly formed from the helical rotation of the two secondary $({\mathbf{n}}_{\mathbf{p}},{\mathbf{n}}_{\mathbf{o}})$ directors perpendicular to the smectic layer as in Sm-$C^{*}$ and Sm-$C_A$${}^{*}$. In this study, the birefringence refers a difference between two secondary refractive indices $({\mathbf{n}}_{\mathbf{p}},{\mathbf{n}}_{\mathbf{o}})$.

Figure 7

(a) Switching current in the Sm-$A{P}_A$${}^{*}$ phase recorded at 75 °C in the 6.8-μm thick planar orientation ITO cell. The applied electric field was 100 Vpp (V peak to peak) triangular wave. (b) and (c) Optical photomicrographs before and during the application of the DC electric field. (d) The calculated spontaneous electric polarization of all mixtures from the integration of switching peaks upon applying a triangular electric field (24 Vpp μm${}^{-1}$) as a function of normalized temperature. The arrows indicate the directions of the cross polarizers. The scale bar indicates 50 μm.

Figure 8

Temperature dependence of the SHG intensity on cooling from the Sm-$A$ to Sm-$A{P}_A$ phase. Red circles and blue triangles were observed at the electric field-on state and field-off states, respectively. The arrow indicates the transition temperature of Sm-$A$ to Sm-$A{P}_A$ upon cooling.

Figure 9

(a) DSC thermograms of the binary mixtures with DC-S-8${}^{*}$ content of 0 to 9.7 wt$\%$ and (b) phase transition behavior as a function of chiral content.

Figure 10

Schematic illustration of the change in molecular alignment that results in birefringence $({\mathbf{n}}_{\mathbf{p}}-{\mathbf{n}}_{\mathbf{o}})$ change for observation in homeotropically aligned cell during cooling process in Sm-$A$ to Sm-$A{P}_A$ regime.

Figure 11

(a)–(d) Optical photomicrographs of the 5.0 wt$\%$ mixture (DC-S-8:DC-S-8${}^{*}$ $=$ 95:5) observed in the homogeneous and homeotropic aligned surface treated with the ITO sandwich cells at different temperatures: (a) and (b) typical fan-shaped textures of Sm-$A^{*}$ and Sm-$A{P}_A$${}^{*}$ at 86 °C and 77 °C in 5.1 μm thickness planar cells, respectively. (c) and (d) Nonbirefringent textures of the Sm-$A^{*}$ and Sm-$A{P}_A$${}^{*}$ phase in the homeotropically aligned cell with a thickness of 5 μm. The arrows indicate the direction of the cross-polarizers. The scale bar indicates 50 μm.

Figure 12

CD reflection bands observed in the homeotropically aligned Sm-$A{P}_A$${}^{*}$ phases of chiral mixtures on cooling from the isotropic state at a scanning rate of 2 °C min${}^{-1}$. Reflection bands were observed upon the transformation of Sm-$A^{*}$ to Sm-$A{P}_A$${}^{*}$ with increasing its intensity by decreasing temperature (the arrow in each chiral content indicates the change of direction by temperature decreasing). It is obvious the selective reflection bands decreased with increasing chiral content. The inset indicates the chiral content dependence of the helical twisting power, 1/P.