Physicists at CU Boulder have gone to creative lengths to earn their scouting merit badges for knot-tying.
In a study , a team of researchers discovered a new way to tie microscopic knots within a solution of liquid crystals. This type of material is found in a wide range of electronics from high-definition TVs to cellphone screens.
And while the tiny knots won鈥檛 help you to secure a rowboat or pitch a tent, they are a feat of control, said Jung-Shen (Benny) Tai, lead author of the new research. Once tied, these molecular pretzels won鈥檛 untie, and they can come together to form large, three-dimensional crystals.
Top: A collection of knots in a solution of liquid crystals assembled into the shape of the CU Boulder logo using lasers; middle: A lattice of liquid crystal knots; bottom: A graphic showing trefoil knots of liquid crystals. (Credits: Smalyukh lab)
鈥淏y changing the voltage we apply to the liquid crystal with our knots, we can make them expand or shrink and even form the CU Boulder logo when manipulated using lasers,鈥� said Tai, a graduate student in the Department of Physics.
Co-author Ivan Smalyukh believes that the team鈥檚 liquid crystal knots will have other uses, too.听
Physicists, he explained, have long been interested in how knots might form in a wide range of physical fields, such as those emerging from magnets. The problem is that these phenomena aren鈥檛 easy to observe or manipulate using conventional tools.
鈥淪cientists have proposed knots like these in cosmology, nuclear physics, particle physics, everywhere,鈥� said Smalyukh, a professor of physics. 鈥淏ut what is beautiful about liquid crystals is that you can see and study them under a microscope.鈥�
Knotty fascination
He added that the study builds on humanity鈥檚 long-running obsession with knots. Such shapes have played a central role in the artwork of Celtic, Norse, Tibetan and Chinese cultures, to name a few.
鈥淗umankind has been fascinated by knots for millennia,鈥� Smalyukh said.
Scientists are no exception. In the 19th century, for example, famed physicists William Thomson and James Clerk Maxwell proposed that atoms themselves might be made up of tiny knots of energy. This model was eventually debunked, but it helped to inspire a current area of research called mathematical knot theory.
And it pushed a lot of scientists to look for knots in other physical phenomena. For their part, Smalyukh and Tai turned to liquid crystals.
These types of materials are useful because they behave a little like solids and a little like liquids.
In the new study, the researchers experimented with a type of liquid crystal molecule that is shaped like a helix, or a small screw. Because those screws don鈥檛 fit together well, they tend to twist, Smalyukh said. As a result, if you mix them under just the right conditions, small kinks will begin to appear. Through a microscope, those kinks look a bit like grains of sand floating in a glass of water.
But they鈥檙e not grains. They鈥檙e knots.
鈥淲e鈥檙e seeing a huge number of molecules that know how to tie knots,鈥� Smalyukh said.
Put another way, the molecules within the tiny kinks point in different directions than those around them. And if you measure their collective orientations in different locations, they trace the line of a knot.听
Knot theory
Tai added that the team has seen several different kinds of knots appear in their liquid crystal solutions. The most basic is the trefoil knot, which crosses over itself three times and was a popular motif in Celtic artwork.听
鈥淲e also had more complicated ones like cinquefoil knots, or knots with five crossings, and even ones with seven crossings,鈥� he said.听
Like the best knots, these creations won鈥檛 snap unless the researchers disturb the surrounding medium鈥攖he equivalent of using a scissors to snip them. As a result, the team was able to use lasers to move the knots around, nudging them together to form much bigger structures.
鈥淲ith liquid crystals, we can easily image and analyze these knots and compare them to actual mathematical knots,鈥� Tai said. 鈥淪o this provides a very nice platform to test knot theory.鈥�
Smalyukh agreed and said that it鈥檚 also just exciting to find a new way to play with knots.听
鈥淲e know that there is a beautiful history of people being fascinated by the possibility of knots in fields,鈥� he said. 鈥淏ut it was quite unexpected to see them in this embodiment right in front of our eyes.鈥�
