Knotting Particle Defect Lines

Loops and knots have been tied from microscopic topological defect lines that form when the ordering of a nematic liquid crystal is disrupted by the addition of colloidal particles.

Knots and links of arbitrary complexity are created and reconfigured from topological defect loops in the particle-stabilized chiral nematic liquid crystal using laser tweezers. The laser-induced micro-quenches locally rewire the disclination loops and essentially change the topology of entangled nematic braids. Designed by Simon Èopar. (Image: Science/AAAS)

When these lines are manipulated with laser tweezers, they can be woven into arbitrarily complex knots and links. The formation of these stable braided structures is enabled by using a sample cell similar to that commonly used in liquid crystal display technology. The findings could pave the way for the development of novel devices in the field of photonics.

In the experiment that was published by AAAS in the July 1 issue of Science, Igor Musevic and colleagues at the Jozef Stephan Institute in Slovenia saw that topological defect lines form when the normal order of molecules in a liquid crystal was disrupted. These lines normally become tangled and form knots sporadically, but the researchers discovered that knots from defect lines can be created by forcing liquid crystal molecules into a certain position. This action caused defect lines to form around each particle, like rope encircling a ball. Using laser tweezers the team tied the lines into complex knots.

Schematic presentation of made-to-order assembly of Borromean rings on a 4x4 particle array. The feasible tangle combinations were tested by the numerical algorithm based on the Jones polynomials. The selected configuration was identified by direct comparison with polynomials in the enumerated base of knot invariants and finally assembled using laser tweezers. Designed by Uroš Tkalec. (Image: Science/AAAS)

In a related perspectives piece, liquid crystals expert Randall D. Kamien of the University of Pennsylvania describes the findings and compares the knots formed in this study to knots found in biology, specifically in DNA.

For more information, visit: www.sciencemag.org