The ability to generate regular spatial arrangements of particles is an important technological and fundamental aspect of colloidal science. We showed that colloidal particles confined to a few-micrometer-thick layer of a nematic liquid crystal form two-dimensional crystal structures that are bound by topological defects. Two basic crystalline structures were observed, depending on the ordering of the liquid crystal around the particle. Colloids inducing quadrupolar order crystallize into weakly bound two-dimensional ordered structure, where the particle interaction is mediated by the sharing of localized topological defects. Colloids inducing dipolar order are strongly bound into antiferroelectric-like two-dimensional crystallites of dipolar colloidal chains. Self-assembly by topological defects could be applied to other systems with similar symmetry.

The light scattering and electro-optic response of new material with display potential are investigated. The materials consist of microdroplets of nematic liquid crystals which are spontaneously formed in a solid polymer at the time of its polymerization. Droplet size, spacing, and distribution are readily controlled in these materials to allow optimization of displays based upon electrically controlled light scattering from the liquid crystal droplets. Preliminary experimental and theoretical studies of the light scattering properties show these materials to offer new features suitable for many display applications.

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid-crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David, and the Borromean rings, are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are classified by the quantized self-linking number, a direct measure of the geometric, or Berry's, phase. Forming arbitrary microscopic knots and links in chiral nematic colloids is a demonstration of how relevant the topology can be for the material engineering of soft matter.