Fig. 1. Elasticity-directed placement and assembly of normally anchored polystyrene spheres in regions with splay deformations of the patterned director.

(A) A sphere with perpendicular surface anchoring placed in a uniform nematic causes an appearance of a hyperbolic hedgehog that can be located on either the left- or right-hand side; the resulting director deformations are of a dipolar type. (B) Periodic splay-bend stripe pattern; the normalized splay energy density is labeled by colors according to the scale on the right-hand side. A sphere is placed in the bend region by optical tweezers and released there, and migrates toward the splay region. The dark blue curve is the typical experimental trajectory of the sphere’s center. (C) Self-assembly of spheres into linear chains in the regions of maximum splay with p > 0 [bright-field microscope with unpolarized light, and nematic liquid crystal pentylcyanobiphenyl (5CB)]. (D) Polarizing microscopy images of a sphere moving from one splay region to the next splay region, with concomitant reorientation of the structural dipole from p < 0 to p > 0; the white arrows point toward the hyperbolic hedgehog. (E) Typical experimental trajectory of the sphere within the director configuration mapped in the PolScope mode of observation of the experimental cell. (F) Experimentally measured x(t) dependence for a sphere moving from y = l to y = 0 and its theoretical fit by Eq. 5. (G) Experimentally measured y(t) dependence for a sphere moving from y = l to y = 0 and its theoretical fit by Eq. 6. All spheres have a radius of R = 2.5 μm; the period of the patterned director is l = 80 μm. The nematic material corresponding to parts (D) to (G) is MLC6815.