To understand how simple knots untie themselves, 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 characterizing 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 modeled 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 collaborators discovered that although the chain's motion was complicated, the knot motion resembled what mathematicians call a "random walk," 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. For example, 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 rather 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.
Ben-Naim's collaborators on this project were Zahir Daya and Robert Ecke, also at Los Alamos. The Laboratory Directed Research and Development program funded the work.
Los Alamos National Laboratory, a multidisciplinary research institution engaged in strategic science on behalf of national security, is operated by Los Alamos National Security, LLC, a team composed of Bechtel National, the University of California, The Babcock & Wilcox Company, and the Washington Division of URS for the Department of Energy's National Nuclear Security Administration.
Los Alamos enhances national security by ensuring the safety and reliability of the U.S. nuclear stockpile, developing technologies to reduce threats from weapons of mass destruction, and solving problems related to energy, environment, infrastructure, health, and global security concerns.