Universality in the diffusion of knots

Abstract

We have evaluated a universal ratio between diffusion constants of the ring polymer with a given knot K and a linear polymer with the same molecular weight in solution through the Brownian dynamics under hydrodynamic interaction. The ratio is found to be constant with respect to the number of monomers, N , and hence the estimate at some N should be valid practically over a wide range of N for various polymer models. Interestingly, the ratio is determined by the average crossing number (N{AC}) of an ideal conformation of knotted curve K , i.e., that of the ideal knot. The N{AC} of ideal knots should therefore be fundamental in the dynamics of knots.