Liquid crystal research, future applications advance

Dec 27, 2012
This image shows polarized light interacting with a particle injected into a liquid crystal medium. Credit: Bohdan Senyuk and Ivan Smalyukh, Colorado University

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.

UMass Amherst's Kusner explains, "There are two important aspects of this work. First, the experimental work by the Colorado team, who fabricated topologically complex micro-materials allowing controlled experiments of three-dimensional liquid crystals. Second, the theoretical work performed by us mathematicians and while visiting the University of California Santa Barbara's Kavli Institute for (KITP). We provided the geometric and topological analysis of these experiments, to explain the observed patterns and predict what patterns should be seen when experimental conditions are changed."

Kusner was the lone mathematician among four organizers of last summer's workshop on "Knotted Fields" at KITP, which led to this work. The workshop engaged about a dozen other mathematicians and about twice as many theoretical and in a month-long investigation of the interplay between low-dimensional topology and what physicists call "soft matter."

In their experiments, the physicists at UC Boulder showed that tiny topological particles injected into a medium behave in a manner consistent with established theorems in geometry and topology, Kusner says. The researchers say they have thus identified approaches for building new materials using topology.

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.

Explore further: New insights found in black hole collisions

add to favorites email to friend print save as pdf

Related Stories

Chern numbers of algebraic varieties

Jun 10, 2009

A problem at the interface of two mathematical areas, topology and algebraic geometry, that was formulated by Friedrich Hirzebruch, had resisted all attempts at a solution for more than 50 years. The problem concerns the ...

Topological matter in optical lattices

Nov 28, 2011

Atoms trapped by laser light have become excellent platforms for simulating solid state systems. These systems are also a playground for exploring quantum matter and even uncovering new phenomena not yet seen ...

Recommended for you

New insights found in black hole collisions

Mar 27, 2015

New research provides revelations about the most energetic event in the universe—the merging of two spinning, orbiting black holes into a much larger black hole.

X-rays probe LHC for cause of short circuit

Mar 27, 2015

The LHC has now transitioned from powering tests to the machine checkout phase. This phase involves the full-scale tests of all systems in preparation for beam. Early last Saturday morning, during the ramp-down, ...

Swimming algae offer insights into living fluid dynamics

Mar 27, 2015

None of us would be alive if sperm cells didn't know how to swim, or if the cilia in our lungs couldn't prevent fluid buildup. But we know very little about the dynamics of so-called "living fluids," those ...

Fluctuation X-ray scattering

Mar 26, 2015

In biology, materials science and the energy sciences, structural information provides important insights into the understanding of matter. The link between a structure and its properties can suggest new ...

Hydrodynamics approaches to granular matter

Mar 26, 2015

Sand, rocks, grains, salt or sugar are what physicists call granular media. A better understanding of granular media is important - particularly when mixed with water and air, as it forms the foundations of houses and off-shore ...

User comments : 1

Adjust slider to filter visible comments by rank

Display comments: newest first

dbmorpher
not rated yet Dec 28, 2012
One step closer to making Master Chief's armor!

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.