Simply knotted

Silica microspheres in liquid crystals offer the possibility of creating every knot conceivable.

August 18, 2011

Knots can now be tied systematically in the microscopic world. A team of scientists led by Uroš Tkalec from the Jožef Stefan Institute in Ljubljana (Slovenia), who has been working at the Max Planck Institute for Dynamics and Self-Organization in Göttingen (Germany) since September 2010, has now found a way to create every imaginable knot inside a liquid crystal. Starting points of the new method are tiny silica microspheres confined in thin liquid crystal layers. Surrounding these microspheres, a net of fine lines is formed where the molecular orientation of the liquid crystal is altered. The researchers discovered a method to twist and link these lines in such a manner as to create every knot imaginable.

"However, in such rows of spheres no knots can be assembled", says Tkalec. Creating knots requires the defect rings of neighbouring microspheres to be able to attach to each other in two directions. In order to achieve this, the scientists used a "trick": if the upper plate confining the liquid crystal layer is turned by 90 degrees, the alignment of the molecules is changed. While the lower molecules still point in the same direction as before, the upper ones are also rotated by 90 degrees. In between, the transition is gradual. Scientists refer to this as a twisted or chiral nematic liquid crystal. "In this experimental set-up, the defect rings surrounding the spheres are slightly buckled - like a buckled wheel of a bicycle", says Tkalec (see figure 2, right). The rings of neighbouring spheres can therefore cross and link: a crucial requirement for creating knots.

For every knot (left) an equivalent interpretation with the help silica microspheres can be found (centre). The right image shows the real experimental result.

In an essential step, the researchers discovered a way of manipulating the regions between the spheres by joining and separating neighbouring rings. First, they heated the region between the spheres with a laser. This destroys the characteristic alignment of the molecules. After switching off the laser, the alignment is re-established – but often in a different way than before. Thus, it is possible to join rings that bypassed each other before or reconnect rings in a different way.

But the researchers not only proved sleight of hand in the experimental handling of microspheres and lasers. In the theoretical part of their study they showed that for every conceivable knot a mathematically equivalent knot can be found which can be implemented in this way. "With the help of microspheres in a chiral nematic liquid crystal, we can create practically every knot that you can imagine", says Tkalec.

The researchers now hope that these findings will help to better understand the complex knotting of DNA. "The knotting of DNA molecules, for example, plays an important role in many vital processes such as replication or transcription of DNA", says Uroš Tkalec. In addition, the strategy may boost the assembly of reconfigurable optical circuits in soft materials which would guide a light in future photonic applications.


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