Untying the Knot

Dealing with shoelaces is for most of us the first exposure to knots. Neckties, sailor hitches, twist-ties, and polymers are some of the other things that knot. To see how knots untie themselves, scientists at Los Alamos have studied model polymers made from 2-mm steel balls linked by thin rods. These chains, consisting of up to 300 beads, were laid in a pan, tied in knots that allows for three cross-over points, and then shaken (see figures at Physics News Graphics).

The rods allowed the shaking chain to stretch and bend, and hence to "explore" many conformations on its way toward untying itself. The unknotting time, not surprisingly, is proportional to the square of the chain length. What is surprising is that although the chain motion is complicated, the unknotting time depends only on the three crossing points, whose motions resemble a random-walk process, except that the points may not coincide.

According to Eli Ben-Naim (505-667-9471, ebn@lanl.gov) this type of shaking experiment represents a new way to study structures in granular materials and the dynamics of entanglements in DNA and other polymers. (Ben-Naim et al., Physical Review Letters, 19 February 2001; text at Physics News Select).