Creating arbitrary arrays of two-dimensional topological defects

An atomic force microscope was used to scribe a polyimide-coated substrate with complex patterns that serve as an alignment template for a nematic liquid crystal. By employing a sufficiently large density of scribe lines, two-dimensional topological defect arrays of arbitrary defect strength were patterned on the substrate. When used as the master surface of a liquid crystal cell, in which the opposing slave surface is treated for planar degenerate alignment, the liquid crystal adopts the pattern's alignment with a disclination line emanating at the defect core on one surface and terminating at the other surface.

Figure 1

AFM image of a section of the polyimide surface scribed at low line density.

Figure 2

(a) Computer-generated scribing pattern for a checkerboard of $s=+1$ (red solid circles) and −1 (blue open circles) defects, where the constant $c_i$ is set equal to zero; (b) theoretical polarized micrograph for the liquid crystal between crossed polarizers; (c) actual experimental polarized micrograph of the liquid crystal cell scribed with a high density of lines (120–300 nm line spacing). The initial soft cloth rubbing was horizontal with respect to the image in (c). The lines then were scribed at a stylus speed of 18 μm/s and with a force of 3 μN. The bar represents 10 μm.

Figure 3

Same as Fig. 2 except that the $s=+1$ and −1 defects have been offset from each other.

Figure 4

Photomicrograph of a cell with low density of scribe lines, corresponding to the pattern in Fig. 3. The bar represents 10 μm.

Figure 5

Theoretical polarized micrograph for a pair of $s=\pm 1/2$ defects offset diagonally from each other. A similar intensity profile can be seen in some individual defect cores in Fig. 2.