Orientational action of edge dislocations on the director field in antiferroelectric smectic-$C_A^{*}$ films

We report imaging of the director field near edge dislocations in thermotropic antiferroelecric smectic-$C_A^{*}$ $\left(\mathrm{Sm}{C}_A^{*}\right)$ liquid crystal. Measurements were made in freestanding films with thickness from two to ten smectic layers. We find two different orientations of the molecular tilt plane with respect to the edge dislocation line. The orientation is determined by the value of the Burgers vector of the dislocation. Elementary edge dislocation and dislocations with a Burgers vector equal to an odd number of layers orient the tilt plane perpendicular on the two sides of the dislocation. Dislocations with a Burgers vector equal to an even number of layers orient the molecular tilt plane parallel to the dislocation line. Difference in the orientation for an odd Burgers vector can be attributed to breaking of antiferroelectric symmetry by the edge dislocation.

Figure 1

Typical DRLM image of ferroelectric $\mathrm{Sm}{C}^{*}$ islands in a thin $\mathrm{Sm}{C}^{*}$ film (a) and sketches of director configuration in the islands (b,c). In small islands director configuration is circular (b), in large islands it is spiral (c). The orientation of the polarizer and the analyzer is shown in the lower right part of (a). The c director near the island boundary in the $\mathrm{Sm}{C}^{*}$ film is parallel to the boundary of the island. $T=25{}^{\circ }\mathrm{C}$. The horizontal size of the photograph is $125\mu \mathrm{m}$.

Figure 2

Ferroelectric $\mathrm{Sm}{C}^{*}$ film with a step-by-step increase of thickness by elementary edge dislocations with $\left|\mathit{b}\right|=d$ (a). A dislocation with vector $\left|\mathit{b}\right|=2d$ is present in (b). The layer steps are shown by arrows. Numbers denote the number of molecular layers in the different regions of the film. Orientations of the tilt planes are parallel to the edge dislocations regardless of the value of the Burgers vector and are shown by short lines. DRLM; bright regions of the films near the dislocations correspond to orientation of the tilt plane shown in Fig. 12 in Appendix pp2. The horizontal size of the image is $331\mu \mathrm{m}$. $T=21{}^{\circ }\mathrm{C}$.

Figure 3

DRLM image of antiferroelectric $\mathrm{Sm}{C}_A^{*}$ islands (a). Dark regions are located in different parts of two islands. (b,c) show the orientation of the tilt plane correspondingly in the upper and lower islands in (a). The c director near the island boundary in the $\mathrm{Sm}{C}_A^{*}$ films can be perpendicular and parallel (b,c) to the boundary of the island. Dark and bright regions in the islands correspond to orientation of the tilt plane depicted in Figs. 12 and 12 in Appendix pp2. The horizontal size of the photo is $182\mu \mathrm{m}$. $T=62{}^{\circ }\mathrm{C}$.

Figure 4

DRLM images of antiferroelectric $\mathrm{Sm}{C}_A^{*}$ films with edge dislocations. Numbers denote the number of molecular layers in different regions of the film. Their thickness differs by an even number of layers. Dislocations are shown by arrows. Orientation of the tilt plane near edge dislocation is parallel to the dislocation and is shown by short lines. In frame (a) the bright regions near the dislocations correspond to Fig. 12 in Appendix pp2; in panel (b) the dark region near the dislocation corresponds to Fig. 12 in Appendix pp2. The horizontal size of the images is $550\mu \mathrm{m}$ (a) and $331\mu \mathrm{m}$ (b). $T=60{}^{\circ }\mathrm{C}$.

Figure 5

DRLM images of antiferroelectric $\mathrm{Sm}{C}_A^{*}$ films with two regions which differ in thickness by one smectic layer. The number of molecular layers is denoted in each region of the films. The elementary edge dislocations separate bright and dark areas and are shown by arrows. Tilt planes on the two sides from the dislocation are perpendicular and are shown by short lines. Double dark and bright stripes are $2\pi$ walls. The bright region near the dislocation corresponds to Fig. 12 in Appendix pp2 for the five-layer film and for the four-layer film; the dark region near the dislocation corresponds to Fig. 12 in Appendix pp2 for the six-layer film and for the three-layer film. The horizontal size of the images is $497\mu \mathrm{m}$ (a) and $663\mu \mathrm{m}$ (b). $T=60{}^{\circ }\mathrm{C}$.

Figure 6

DRLM images of antiferroelectric films with regions which differ in thickness by three and five smectic layers. The number of molecular layers is indicated in each region of the films. Edge dislocations are denoted by arrows. Orientation of the tilt plane in the darkest and brightest region of the film is shown by short lines. The orientation of the tilt planes on two sides of the dislocations is mutually perpendicular. In (a) brightness near the dislocation corresponds to Fig. 12 in Appendix pp2 for the six-layer film and to Fig. 12 in Appendix pp2 for the three-layer film. In (b) brightness near the dislocation corresponds to Fig. 12 in Appendix pp2 for the five-layer film and to Fig. 12 in Appendix pp2 for the ten-layer film. The horizontal size of the images is $253\mu \mathrm{m}$ (a) and $166\mu \mathrm{m}$ (b). $T=59{}^{\circ }\mathrm{C}$.

Figure 7

Antiferroelectric $\mathrm{Sm}{C}_A^{*}$ film with an edge dislocation. The photograph was taken in linearly polarized light. Direction of light polarization is shown in the lower part of the image. Orientation of the tilt plane is perpendicular in the regions near the dislocation in films of different thickness. The horizontal size of the image is $249\mu \mathrm{m}$.

Figure 8

Antiferroelectric film with two regions of an even number of layers. The dislocation is shown by an arrow. The photograph was taken in linearly polarized light. Orientation of the tilt plane in the region near the dislocation is parallel to the dislocation. The horizontal size of the image is $249\mu \mathrm{m}$. $T=60{}^{\circ }\mathrm{C}$.

Figure 9

Schematic representation of a four-layer freestanding antiferroelectric $\mathrm{Sm}{C}_A^{*}$ film (a). Molecular orientation is shown in each layer. Panel (b) shows a film with a dislocation; one layer is added in the left part of the film. A ferroelectric pair is formed in the interior of the film (b) which breaks the antiferroelectric ordering. The ferroelectric pair is shown by gray. The orientational structure is transformed in the left part of the film and tilt planes on two sides from the dislocation become perpendicular (c). Orientation of the c director in the top layers of the films is shown by nails.

Figure 10

Schematic representation of a five-layer freestanding antiferroelectric film (a). Molecular orientation is shown in each layer. Panel (b) shows a film with a dislocation; one layer is removed in the left part of the film. A ferroelectric pair is formed in the interior of the film (b) which breaks the antiferroelectric ordering. The ferroelectric pair is shown by gray. The orientational structure is transformed in the left part of the film and tilt planes on two sides from the dislocation become perpendicular (c).

Figure 11

Schematic representation of a five-layer freestanding antiferroelectric film (a). Molecular orientation is shown in each layer. Frame (b) shows a film with a dislocation: two layers are removed in the left part of the film. A dislocation with the Burgers vector $\left|\mathit{b}\right|=2d$ (b) does not induce a ferroelectric pair. Tilt planes remain parallel on two sides from the dislocation.

Figure 12

(a–f) illustrate different orientations of the polarizer (P) and the analyzer (A) with respect to the tilt plane $kl$ in DRLM geometry. Words “bright” and “dark” describe the appearance of films in the regions where the tilt plane is parallel to the line $kl$. The curved arrow in each panel shows the direction of the effective rotation of the plane of polarization of light reflected from the film.