Liquid crystals are rod-like molecules that entropically prefer to align with one another. There are elastic energy costs to distorting the liquid crystal out of its preferred alignment. When the liquid crystal is greatly distorted, instead of having smooth distortions throughout the entire system, the liquid crystal can lower its energy by creating local regions of disorder, called defects.

Boundary conditions can be designed to necessarily require the presence of defects. The minimum number of required defects depends on the topology of the system, as dictated by the system boundary conditions. This can be intuitively understood by examining a globe --- ordering lines of longitude and latitude necessarily creates the North and South poles, points where lines are ill-defined. Just as the North and South poles are required by the spherical topology of the globe, ordering a liquid crystal on a sphere likewise requires the creation of defects.

Such defects can be used to assemble material inclusions --- the system has a tendency to combine distortions, not only those from defects but also those created by inclusions, to minimize its elastic energy.

Liquid crystal systems and their defects are also optically interesting because the dielectric constants along the long and short axes of a liquid crystal molecule differ. Liquid crystals can interact with light to alter its polarization and other properties, allowing it to be the basis of the display industry (recall LCDs - liquid crystal displays).

I currently investigate the patterns formed in liquid crystals and exploit their structures to assemble nanoparticles with tunable collective properties. Progress in the understanding and manipulation of liquid crystalline structures paves the way for new technologies. Specifically, nanoparticle assemblies are desirable for use in nanomedicine, energy harvesting, and optical devices. Utilizing liquid crystals to control particles harnesses the unique elasticity and molecular anchoring sensitivity of these fluids to produce particle arrangements with broad applications.

Nanoparticles on Cholesteric Droplets

Confocal reconstruction of 30 nm, fluorescent nanoparticles on cholesteric droplets.

Suspended Many-genus Body in Nematics

Cholesteric Shells

This work is done with Professors Randall D. Kamien and Kathleen J. Stebe, in collaboration with Dr. Teresa Lopez-Leon, Professor Martin F. Haase, Professor Shu Yang, Dr. Emmanuelle Lacaze, and Professor Daeyeon Lee.