Arrays of focal conic domains in smectic liquid crystals

In smectic liquid crystals, molecules self-organize into layers with a strong preference for constant layer spacing. Curvature of these equally spaced layers would generically necessitate the existence of focal surfaces where the layer normal changes suddenly, but in nature the focal set instead consists of conic sections in the case of the focal conic domain (in smectics-A). Antagonistic boundary conditions requiring layer curvature have been known to induce close-packed arrays of focal conic domains. Here, by confining the smectic-A liquid crystal in topographically patterned substrates, we demonstrate a versatile approach to produce arrays of focal conic domains with controllable spacing and symmetry over large areas. Image at right: schematic illustration of smectic layers deformed into two simultaneous square lattices of focal conic domains, which form on top of and between a regular square array of cyindrical microposts.

Numerical modeling of nematic liquid crystals and their defects in nontrivial geometries

Nematic liquid crystals are anisotropic fluids, with long-ranged orientational order of molecules along a director field. Topological defects in this director field may be points or lines, called disclinations. Boundary conditions may induce defects in the nematic, with significant consequences for optical and mechanical properties of the liquid crystal, including assembly of colloidal inclusions. We use numerical tools along with analytic approximations to study nematics and their defects in the presence of colloids and confining boundaries with nontrivial shapes, such as the micropost shown below, to determine how boundary geometry can be used to manipulate the director field and self-assembly outcomes.