Knotty LCD problems solved by silica Möbius strip

By reorienting substances like this, the researchers hope to understand how their intricate configurations and unique properties can be harnessed.

Liquid crystal possesses light-modulating properties and is used in products ranging from flat panel displays on computers, TVs and smartphones.

It is composed of long, thin, rod-like molecules that align themselves to point in the same direction, but controlling the alignment of these molecules can result in an entirely different orientation.

To do this, the Warwick team simulated adding a micron sized silica particle (or colloid, a substance dispersed through a material) to the liquid crystal, which disrupts the orientation of the liquid crystal molecules. A colloid in the shape of a sphere, for example, will cause the liquid crystal molecules to align perpendicular to the surface of the sphere.

Using a theoretical model, the Warwick University scientists have taken this principle and extended it to colloids which have a knotted shape in the form a Möbius strip.

A Möbius strip with one twist does not form a knot, however with three, four and five twists it becomes a trefoil knot, a Solomon’s knot or a cinquefoil knot respectively.

By adding these specially designed knotted particles they force the liquid crystal to take on the same structure, creating a knot in the liquid crystal.

In a statement, Gareth Alexander, assistant Prof in Physics and Complexity Science, at Warwick University said, ‘Knots are fascinating and versatile objects, familiar from tying your shoelaces.

‘Recently it has been demonstrated that knots can be created in a variety of natural settings including electromagnetic fields, laser light, fluid vortices and liquid crystals.

‘These knots are more intricate than those in your shoelaces, since it is the entire continuous material, and not just a piece of string, that is knotted.

‘Our research extends this previous work to apply to liquid crystal, the substance we use every day in our TVs, smartphones and computer screens.

‘We are interested in this as creating and controlling these intricate knotted fields is an emergent avenue for the design of new metamaterials and photonic devices.’

The study, published in the journal PNAS, is entitled Knots and nonorientable surfaces in chiral nematics and is authored by Thomas Machon and Gareth Alexander, both jointly based in the Department of Physics and the Centre for Complexity Science at Warwick University.