$\pm$1/2 wedge disclinations stabilized by a sinusoidal boundary in a thin hybrid nematic liquid-crystal film

As an interesting example of how geometry affects the formation of defects, we study the defect structures of a hybrid nematic liquid-crystal film in a wedge-shaped cell made up of sinusoidal microwrinkles and an elastomer sheet. When the cell thickness is larger than a threshold value $h_c$, $+$1/2 and $-$1/2 disclinations are simultaneously stabilized along concave grooves and convex crests, respectively. A simple theoretical analysis gives a good estimate of $h_c$. The disclinations also show alternating optical rotations resulting from the curved boundary and liquid-crystal elastic anisotropy.

Figure 1

Schematic drawings of ±1/2 wedge disclinations in a HAN cell with unidirectional planar alignment in the $x$ direction. The open circles indicate disclination cores. The definition of the polar and the azimuthal angles θ and ϕ of the local nematic director n (bold line) is also given.

Figure 2

(a) Experimental setup of the wedge-shaped HAN cell. (b) Schematic drawing of a cross section of the cell.

Figure 3

Thickness profile and optical microscopy images of a wedge-shaped HAN cell. (a) Image of the optical interference pattern of the cell and (b) the corresponding optical microscopy image. (c) Profile of the interference pattern along a crest and (d) the corresponding thickness profile.

Figure 4

(a)–(d) Optical microscopy images of a wedge-shaped HAN cell (scale bars: 30 μm). The images are taken with the polarizer and analyzer depicted by $P$ and $A$ in (a) and (c), and those with a sensitive tint plate depicted by $S$ in (b) and (d). The definition of the zigzag segment length ${\Lambda }_{\pm }$ is shown. The nail symbols ($T$) indicate the projection of n onto the plane of the page. (e)–(g) Schematic drawings of HAN alignment with (e) large, (f) intermediate, and (g) minimum thicknesses. The signs of the slope of sinusoidal profile at $A$ and $B$ are positive and negative, respectively. Black dots indicate the disclination cores.

Figure 5

Zigzag segment length ${\Lambda }_{\pm }$. Open and closed circles indicate the data of ${\Lambda }_{-}$ and ${\Lambda }_{+}$, respectively. (a) Plots of ${\Lambda }_{\pm }$ vs $y$. Each plotted point corresponds to the length ${\Lambda }_{\pm }$ of a single segment at the position $y$ measured at each segment center. (b) Plots of ${\Lambda }_{\pm }$ vs $h_{\mathrm{crest}}$ and $h_{\mathrm{groove}}$. (Inset) Schematic drawings of the director profiles around the core of a ±1/2 disclination with twist distortions around the core.