  Rod-like objects at high packing fractions can form smectic phases, where the
rods break rotational and translational symmetry by forming lamellae. Smectic
defects thereby include both discontinuities in the rod orientational order
(disclinations), as well as in the positional order (dislocations). In this
work, we use both experiments and simulations to probe how local and global
geometrical frustrations affect defect formation in hard-rod smectics. We
confine a particle-resolved, colloidal smectic within elliptical wells of
varying size and shape for a smooth variation of the boundary curvature. We
find that the rod orientation near a boundary - the anchoring - depends upon
the boundary curvature, with an anchoring transition observed at a critical
radius of curvature approximately twice the rod length. The anchoring controls
the smectic defect structure. By analyzing local and global order parameters,
and the topological charges and loops of networks made of the density maxima
(rod centers) and density minima (rod ends), we quantify the amount of
disclinations and dislocations formed with varying confinement geometry. More
circular confinements, having only planar anchoring, promote disclinations,
while more elliptical confinements, with antipodal regions of homeotropic
anchoring, promote long-range smectic ordering and dislocation formation. Our
findings demonstrate how geometrical constraints can control the anchoring and
defect structures of liquid crystals - a principle that is applicable from
molecular to colloidal length scales.

Soft Condensed Matter