Transitions between paraelectric and ferroelectric phases of bent-core smectic liquid crystals in the bulk and in thin freely suspended films

We report on the contrasting phase behavior of a bent-core liquid crystal with a large opening angle between the mesogenic units in the bulk and in freely suspended films. Second-harmonic generation experiments and direct observation of director inversion walls in films in an applied electric field reveal that the nonpolar smectic $C$ phase observed in bulk samples becomes a ferroelectric “banana” phase in films, showing that a mesogen with a small steric moment can give a phase with polar order in freely suspended films even when the corresponding bulk phase is paraelectric.

Figure 1

Structural formula of compound 11.

Figure 2

Optical schlieren and fan-shaped textures of the (a) Sm-$A$ ($T=130{}^{\circ }$C), (b) Sm-$C$ ($T=110{}^{\circ }$C), and (c) Sm-$\mathit{CP}$${}_A$ ($T=98{}^{\circ }$C) phases of compound 11 between a pair of clean glass cover slips. The crossed polarizers are oriented parallel to the sides of the images.

Figure 3

Synchrotron x-ray diffraction measurements on bulk samples: (a) Temperature dependence of peak positions in the Sm-$A$, Sm-$C$, and Sm-$\mathit{CP}$${}_A$ phases. (b) Powder x-ray “structure factor” $I\left(q\right)$ of the Sm-$\mathit{CP}$${}_A$ phase at $T=102{}^{\circ }$C. The fit (red solid line) corresponds to a powder-averaged 2D rectangular lattice, for which the single crystal scattering pattern is sketched in the inset. This kind of powder x-ray pattern, with a single (100) peak accompanied by narrowly spaced side bands, is characteristic of the B${}_7$ liquid crystal phase.

Figure 4

Field-induced Sm-$A$–Sm-$C$ transition in 10-$\mu$m-thick ITO cells at $T=118{}^{\circ }$C: (a) $E=0$ V/$\mu$m, (b) $E=-40$ V/$\mu$m, and (c) $E=+40$ V/$\mu$m. The applied electric field causes the texture to break into stripes and the extinction brushes to rotate from the direction of the polarizer. The induced molecular tilt, estimated from the rotation angle of the extinction brushes, is similar to the Sm-$C$ tilt deduced from x-ray scattering.

Figure 5

Field-induced order in ITO cells: (a) Temperature dependence of the threshold for the electric field-induced Sm-$A$–Sm-$C$ transition and (b) temperature dependence of the SHG signal at constant field strength ($E=7.5$ V/$\mu$m). All applied fields here were dc and the cell thickness 10 $\mu$m. (c) Field dependence of second-harmonic generation in the Sm-$A$, Sm-$C$, and Sm-$\mathit{CP}$${}_A$ phases. In the banana phase, the sample transforms from the Sm-$\mathit{CP}$${}_A$ ground state to the Sm-$\mathit{CP}$${}_F$ above a threshold field.

Figure 6

Modulated director field in the ground state of the Sm-$\mathit{CP}$${}_F$ phase in films. (a) Branching pattern in a 5-$\mu$m-thick film at $T=116{}^{\circ }$C, just below the Sm-$A$–Sm-$\mathit{CP}$${}_F$ transition ($T=117{}^{\circ }$C). (b) Spontaneously formed target pattern decorated with modulation stripes in a 5-$\mu$m-thick film ($T=110{}^{\circ }$C). The films are viewed in transmission between crossed polarizers.

Figure 7

(a) Part of a $2\pi$-inversion wall in a film in a dc electric field ($E=2.4$ V/mm) viewed in transmission between crossed polarizers in the Sm-$C$ phase at $T=112{}^{\circ }$C. The $c$-director is shown by $⊢$. (b) Wall width dependence on electric field. The linearity of the data (the red line is a fit through the origin) indicates that the main contribution to the field coupling is from the spontaneous polarization. The film thickness is around 5 $\mu$m.

Figure 8

Response of thick freely suspended film in the Sm-$\mathit{CP}$${}_F$ phase to applied in-plane electric field (thickness 5 $\mu$m, $T=112{}^{\circ }$C): (a) ground state without electric field; (b) dielectric response in ac field ($f=200$ Hz, $E_{pp}=20$ V/mm), polar response in dc fields; (c) $E=+20$ V/mm; and (d) $E=-20$ V/mm. The crossed polarizers are aligned vertically and horizontally and the film is viewed in transmission. The orientation of the $c$-director is indicated by $⊢$.

Figure 9

Field response of chiral domains in a film of uniform thickness (approximately 5 $\mu$m) in the Sm-$\mathit{CP}$${}_F$ phase ($T=112{}^{\circ }$C) viewed in transmission between crossed polarizers with oblique incidence. The effective birefringence is sensitive to the tilt orientation, allowing us to distinguish left- and right-handed regions. (a) $E=+17$ V/mm and (b) $E=-17$ V/mm. The in-plane electric field is applied at ${45}^{\circ }$ to the polarizers to achieve optimal contrast.

Figure 10

Second-harmonic generation in a freely suspended film. (a) SHG intensity as a function of the polarization of the primary beam in the Sm-$\mathit{CP}$${}_{\mathrm{F}}$ phase ($T=110{}^{\circ }$C). Quadratic coupling to an ac electric field ($E=150$ V/mm, $f=200$ Hz) applied horizontally (along $0^{\circ }$) aligns the $c$-director and results in a finite polarization. (b) Temperature dependence of the SHG signal on cooling and heating. The film thickness is approximately 25 $\mu$m.

Figure 11

Film textures at the Sm-$\mathit{CP}$${}_F$–Sm-$\mathit{CP}$${}_A$ transition observed in transmission. (a) Schlieren texture in the Sm-$\mathit{CP}$${}_F$ phase in a thick film close to the Sm-$A$ phase transition ($T=115{}^{\circ }$C). (b) Irregular texture in the Sm-$\mathit{CP}$${}_A$ phase ($T=100{}^{\circ }$C). The original schlieren texture is strongly perturbed on going to the Sm-$\mathit{CP}$${}_A$ phase but the topological defects marked by a circle in (a) are still visible in (b). The film thickness is around 5 $\mu$m.

Figure 12

Director response to an applied electric field in a thin film with several layer steps. (a) Ferroelectric state at $E=0$ ($T=107{}^{\circ }$C); (b) ferroelectric state at $E=25$ V/mm; (c) antiferroelectric state at $E=0$ ($T=102{}^{\circ }$C); (d) antiferroelectric state at $E=25$ V/mm. In the antiferroelectric Sm-$\mathit{CP}$${}_A$ phase, the response of the inversion walls [the white lines and loops in (d)] shows a clear odd-even effect depending on layer number $N$. This film was circular, with a diameter of 3 mm observed in reflection mode between slightly uncrossed polarzers.

Figure 13

Director inversion walls in a partially decomposed film at the Sm-$\mathit{CP}$${}_F$ to Sm-$C$ phase transition observed between crossed polarizers in transmission. A $2\pi$ wall that is stabilized by a dc electric field ($E=15$ V/mm) in the ferroelectric Sm-$\mathit{CP}$${}_F$ phase (a) “unzips” in the paraelectric Sm-$C$ phase region, splitting into a pair of $\pi$ walls on further cooling to $T=107{}^{\circ }$C (b). (c) Proposed director structure of the inversion walls together with the corresponding intensity profiles obtained between crossed polarizers.