Liquid crystal research, future applications advance - Mathematics explains the observed 'beautiful and complex patterns revealed' in three-dimensional liquid crystal experiments, expected to lead to creation of new materials that can be actively controlled.
AMHERST, Mass. – Contributing geometric and topological analyses of micro-materials, University of Massachusetts Amherst mathematician Robert Kusner aided experimental physicists at the University of Colorado (UC) by successfully explaining the observed "beautiful and complex patterns revealed" in three-dimensional liquid crystal experiments. The work is expected to lead to creation of new materials that can be actively controlled.
Kusner is a geometer, an expert in the analysis of variational problems in low-dimensional geometry and topology, which concerns properties preserved under continuous deformation such as stretching and bending. His work over 3 decades has focused on the geometry and topology of curves, surfaces and other spaces that arise in nature, such as soap films, knots and the shapes of fluid droplets. Kusner agrees with physicist and lead author Ivan Smalyukh of UC Boulder that their collaboration is the first to show in experiments that some of the most fundamental topological theorems hold up in real materials. Their findings appear in the current early online issue of Nature.
UC Boulder's Smalyukh and colleagues set up the experiment by first creating colloids, solutions in which tiny particles are dispersed but not dissolved in a host medium, such as milk, paint and shaving cream. Specifically, they injected tiny, different-shaped particles into a liquid crystal, which behaves something like a liquid and a solid. Once injected into a liquid crystal, the particles behaved as predicted by topology.
Smalyukh says, "Our study shows that interaction between particles and molecular alignment in liquid crystals follows the predictions of topological theorems, making it possible to use these theorems in designing new composite materials with unique properties that cannot be encountered in nature or synthesized by chemists. These findings lay the groundwork for new applications in experimental studies of low-dimensional topology, with important potential ramifications for many branches of science and technology."
For example, he adds, these topological liquid crystal colloids could be used to upgrade current liquid crystal displays like those used in laptops and television screens, to allow them to interact with light in new, more energy efficient ways.
Besides Kusner at UMass Amherst and Smalyukh's group at UC Boulder, other investigators for this study are Sailing He of Zhejiang University, China and Randall Kamien and Tom Lubensky at the University of Pennsylvania.
Contact: Robert Kusner firstname.lastname@example.org 413-545-6022 University of Massachusetts at Amherst