Transitional subphases near the electric-field-induced phase transition to the ferroelectric phase in Se-containing chiral smectic liquid crystals observed by resonant x-ray scattering

Resonant x-ray scattering experiments revealed transitional subphases near the electric-field-induced phase transition of a Se-containing chiral liquid crystal in a planar aligned cell geometry. In the lower-temperature range ($\mathrm{Sm}-C_A^{*}$ and three-layer periodicity $\mathrm{Sm}-C_{\gamma }^{*}$ phases), the six-layer periodicity subphase appeared with increasing electric field during the field-induced transition from $\mathrm{Sm}-C_{\gamma }^{*}$ to Sm-$C^{*}$. In the higher-temperature range [four-layer periodicity antiferroelectric (AF) phase], the peak positions of the three-layer satellites shifted to those of the four-layer satellites and then the satellites corresponding to the five- through seven-layer periodicity appeared in sequence. Near the AF to $\mathrm{Sm}-C_{\alpha }^{*}$ phase transition temperature, the layer periodicity increased with applied field. The molecular configurations of the subphases near the field-induced transition are discussed based on the Ising, distorted clock, and perfect clock models.

Figure 1

Sample photos observed at applied voltages of (a) $\pm 20.0$, (b) $\pm 30.0$, (c) $\pm 83.8$, and (d) $\pm 91.0\mathrm{V}$ at $81.6{}^{\circ }\mathrm{C}$. The layer normal was approximately horizontal. The black arrows show the phase boundary between the two-layer periodicity phase and the three-layer phase (b), and the boundary between the $C_{7\mathrm{p}}$-like phase and the streak state (c). In photo (d), most of the field of view transforms to the Sm-$C^{*}$ phase, while the streak state (elongated, islandlike region) remains. In (d), the white arrow indicates the typical measurement point and the scale bar represents 0.1 mm. The blotlike patterns of various sizes and shapes are due to the contamination on the outside of the glass plate. The $\omega$-angular profiles were obtained at $\pm 20.0$ (e) and $\pm 80.0\mathrm{V}$ (f). The molecular structure of the sample LC is shown at the top.

Figure 2

A series of resonant x-ray scattering (RXS) profiles obtained at applied voltages from $\pm 10.0$ to $\pm 91.0\mathrm{V}$ at $81.6{}^{\circ }\mathrm{C}$. In (c,g), thin chain dotted lines show the magnified profiles. Asterisks in (d,g) indicate the positions where the reflection peaks due to the $C_{6\mathrm{p}}$ and $C_{7\mathrm{p}}$ configurations, respectively, are expected to appear. The insets in (a,h) are the two-dimensional diffraction patterns from which the one-dimensional RXS profiles were extracted; in the inset, the white circles correspond to the shadow of the direct beam stopper, the strong arclike spot on the right is the first-order Bragg diffraction, and a weak RXS reflection in (a) and streak in (h) (A) are seen between the direct beam stopper and the first-order diffraction. The left (A) and right (B) insets in (h) correspond to $\pm 85.1$ and $\pm 91.0\mathrm{V}$, respectively. cps: counts/s.

Figure 3

A series of RXS profiles obtained at applied voltages from $\pm 70.8$ to $\pm 76.0\mathrm{V}$ at $82.2{}^{\circ }\mathrm{C}$. The asterisks in (b,d) are the expected peak positions for the $C_{6\mathrm{p}}$ and $C_{7\mathrm{p}}$ configurations, respectively.

Figure 4

A series of RXS profiles obtained at applied voltages from $\pm 18.0$ to $\pm 52.0\mathrm{V}$ at $83.9{}^{\circ }\mathrm{C}$. In (b), the broken and solid lines are obtained at the first and second measurements. The asterisks in (f–h) are the expected peak positions for the $C_{5\mathrm{p}}$ through $C_{7\mathrm{p}}$ configurations.

Figure 5

RXS satellite peak positions as a function of the applied voltage at $83.9{}^{\circ }\mathrm{C}$. Squares and circles correspond to the strong and weak peaks, respectively. Horizontal broken and dotted lines correspond to $q/q_0=1/3$ and 2/3, and $q/q_0=1/4$ and 3/4, respectively, for reference.

Figure 6

Sample photos observed at voltages of (a) $\pm 15.0$, (b) $\pm 26.7$, (c) $\pm 27.6$, and (d) $\pm 28.2\mathrm{V}$ at $84.5{}^{\circ }\mathrm{C}$. The black arrows show the phase boundary between the two four-layer periodicity phases (b), between the homogeneous texture and the four-layer state (c), and between the homogeneous texture and the seven-layer state (d). The white arrow in (c) indicates the typical measurement point.

Figure 7

A series of RXS profiles obtained at applied voltages from $\pm 25.5$ to $\pm 33.0\mathrm{V}$ at $84.5{}^{\circ }\mathrm{C}$. The broken curves in (a–c) are vertically magnified intensities to show the weak peaks. The asterisks in (c,e) are the expected peak positions for the $C_{6\mathrm{p}}$ and $C_{7\mathrm{p}}$ configurations, respectively.

Figure 8

A series of RXS resonant x-ray scattering profiles obtained at applied voltages of (a) $\pm 9.23\mathrm{V}$ (solid line) and $\pm 20.3\mathrm{V}$ (broken line), (b) $\pm 24.0\mathrm{V}$ (solid line) and $\pm 39.0\mathrm{V}$ (broken line) at $85.8{}^{\circ }\mathrm{C}$, and (c) at $86.0{}^{\circ }\mathrm{C}$ without an electric field.

Figure 9

Peak positions ($q/q_0$) as a function of the applied voltage at $85.8{}^{\circ }\mathrm{C}$ (squares) and $86.4{}^{\circ }\mathrm{C}$ (circles). The right axis is the inverse of the left axis.

Figure 10

Peak positions ($q/q_0$) as a function of temperature for the $\mathrm{Sm}-C_{\alpha }^{*}$ phase without an electric field.

Figure 11

Summary of the resonant x-ray scattering (RXS) experiments as a function of temperature and applied voltage. The circles and squares show the major field-induced phase transitions and the field-induced transitional subphases, respectively. “PS” indicates the voltage range in which the positions of the RXS peaks shift to the ones corresponding to a longer periodic structure with increasing electric field. “Streak” indicates diffuse scattering with no clear diffraction peaks along the layer normal and “Ferro” marks the region where no RXS satellite appears (Sm-$C^{*}$).

Figure 12

Calculated RXS reflection intensities as a function of the distortion angle for six independent six-layer periodicity configurations: squares, circles, and triangles show $q/q_0=1/6$ and 5/6, $q/q_0=2/6$ and 4/6, and $q/q_0=3/6$, respectively. Only $\sigma \pi$ scattering is shown. Solid lines correspond to the molecular configurations shown in the insets and the incident x rays were parallel to the electric field ($E$). Dotted lines and marks filled in white in (d,e) correspond to the configuration of the ${90}^{\circ }$ azimuthal rotation of the molecule.

Figure 13

Calculated RXS reflection intensities as a function of the distortion angle for five-layer periodicity configurations. Squares and circles correspond to reflections for $q/q_0=1/5$ and 4/5, and $q/q_0=2/5$ and 3/5, respectively. Incident x rays were parallel to the electric field.

Figure 14

Calculated RXS reflection intensities as a function of the distortion angle for four-layer periodicity configurations: filled squares and circles correspond to reflections for $q/q_0=1/4$ and 4/3, and $q/q_0=2/4$, respectively. Solid lines correspond to the molecular configurations shown in the insets and a dotted line and white circles in (a) correspond to the configuration of the ${90}^{\circ }$ azimuthal rotation of the molecule for $q/q_0=1/4$ and 4/3.