Scientists create world’s toughest labyrinth with future potential to increase carbon capture

In new research, physicists have harnessed the power of chess to design a set of intricate mazes that could ultimately be used to tackle some of the world’s most pressing challenges.

Their unique labyrinthine creations, inspired by the moves of a knight on a chessboard, could help solve other extremely difficult problems, including streamlining industrial processes from carbon capture to fertilizer production. The study has been accepted for publication by Physical Review X and is posted on arXiv preprint server.

The main author Dr. Felix Flicker, senior lecturer in physics at the University of Bristol, said: “When we looked at the line shapes we built, we noticed that they formed incredibly complex mazes. The sizes of subsequent mazes grow exponentially – and there are a number of their infinity”.

In a knight tournament, the chess piece (which jumps two squares forward and one to the right) visits each square of the chessboard only once before returning to its starting square. This is an example of a “Hamiltonian cycle” – a loop through a map that visits all stopping points only once.

Theoretical physicists, led by the University of Bristol, built an infinity of increasingly large Hamiltonian cycles in the irregular structures that describe the exotic matter known as quasicrystals.

The atoms in quasicrystals are arranged differently than those in crystals such as salt or quartz. While atoms in crystals repeat at regular intervals, like the squares of a chessboard, quasicrystal atoms do not.

Instead, they do something much more mysterious: quasicrystals can be described mathematically as slices through crystals that live in six dimensions, as opposed to the three of our known universe.

Only three natural quasicrystals have ever been found, all in the same Siberian meteorite. The first artificial quasicrystal was accidentally created in the 1945 Trinity Test, the atomic bomb explosion dramatized in the film Oppenheimer.

Group Hamiltonian cycles visit each atom on the surface of some quasicrystal exactly once. The resulting paths form uniquely complex labyrinths, described by mathematical objects called “fractals”.

These paths have the unique property that an atomically sharp pencil can draw straight lines connecting all neighboring atoms without the pencil lifting or crossing the line itself. This has applications in a process known as scanning tunneling microscopy, where the stylus is an atomically sharp microscope tip capable of imaging individual atoms.

Hamiltonian cycles form the fastest possible paths to be followed by the microscope. This is useful, as a modern scanning tunneling microscopy image can take a month to produce.

The problem of finding Hamiltonian cycles in general environments is so difficult that its solution would automatically solve many important problems that have not yet been overcome in the mathematical sciences.

Dr. Flicker added, “We show that some quasicrystals provide a special case in which the problem is unexpectedly simple. In this setting, we make some seemingly impossible problems tractable. This may involve practical goals spanning various domains of science.”

For example, adsorption is a key industrial process in which molecules attach to crystal surfaces. So far, only crystals are used for industrial adsorption. If the atoms of a surface accept a Hamiltonian cycle, flexible molecules of the right size can be packed with perfect efficiency by stretching along these atomic labyrinths.

Research results show that quasicrystals can be very efficient adsorbents. One use of adsorption is carbon capture and storage, in which CO₂ molecules are prevented from entering the atmosphere.

Co-author Shobhna Singh, a Ph.D. researcher in Physics at Cardiff University, said: “Our work also shows that quasicrystals can be better than crystals for some absorption applications. For example, bent molecules will find more ways to sit in the irregularly arranged atoms of quasicrystals.Quasicrystals are also brittle, meaning they break easily into small grains, this maximizes their surface area for absorption.

Efficient adsorption can also make quasicrystals surprising candidates for catalysts, which increase industrial efficiency by lowering the energy of chemical reactions. For example, adsorption is a key step in the Haber catalysis process used to produce ammonia fertilizer for agriculture.