Pulling knotted polymers

We compare Monte Carlo simulations of knotted and unknotted polymers whose ends are connected to two parallel walls. The force f exerted on he polymer is measured as a function of the separation R between the walls. For unknotted polymers of several monomer numbers N, the product f N-v is a simple function of R/N-v, where v similar or equal to 0. 59. By contrast, knotted polymers exhibit strong finite-size effects which can be interpreted in terms of a new length scale related to the size of the knot. Based on this interpretation, we conclude that the number of monomers forming the knot scales as N-t, with t = 0.4 +/- 0.1.