Los Alamos scientists solve a knotty problem

Scientists at the Department of Energy’s Los Alamos National Laboratory have been watching knots untie themselves in order to gain a better understanding of how granular materials flow and how filamentary objects like DNA molecules tangle.

The Los Alamos scientists studied chains made from tiny, nickel-plated steel balls interconnected by thin rods. These chains, consisting of up to 300 beads, were tied in tight trefoil knots with three crossover points and then laid on a vibrating steel plate. The constant and uniform shaking of the plate allowed the chain to stretch, wiggle and bend while scientists watched the many configurations the chain went through on its way toward untying itself.

‘Understanding the physical mechanisms governing the relaxation of knots is actually quite crucial to characterising the flow and deformation properties of materials like polymers, gels and rubber,’ said Los Alamos researcher Eli Ben-Naim. ‘Typically this kind of research is modelled mathematically or by using computer simulations, but this shaking experiment allowed us to actually compare a real-world physical system to theory.’

Ben-Naim and his team discovered that although the chain’s motion was complicated, the knot motion resembled a sequence of motions where the direction of each successive movement is random. They also found that the statistical properties of unknotting time depended almost completely on the locations of the three crossing points of the knots in the chain.

They also discovered that the unknotting time in seconds was proportional to the square of the chain’s length in beads. A chain of 150 beads in length took, on average, approximately 60 seconds to untie. In the end, each chain untied itself completely.

Despite the experiment’s simple construction, the model shows a simple correlation to real physical systems with the beads in the chains representing molecules or macromolecules, and the vibrating steel plate representing the application of energy to the system.

According to Ben-Naim this type of shaking experiment represents a new way to study the structures of polymers and certain granular materials as well as the dynamics of entanglements in DNA. These entanglements significantly slow down the flow of macromolecules such as polymers and DNA, making them more sluggish, and knots affect the strength of macromolecules.