Dynamics of polymer knots at equilibrium.

Abstract

The relaxation and diffusion dynamics of knotted polymers at equilibrium under good solvent conditions are investigated by dynamic Monte Carlo simulations. Prime knots of chain lengths up to N=240 monomers and knots up to 20 essential crossings are studied. The relaxation dynamics of the prime knots at equilibrium do not display the classification into group as in the case of the nonequilibrium relaxation of cut knots [Phys. Rev. E 58, R1222 (1998); Phys. Rev. Lett. 87, 175503 (2001)]. Furthermore, the time autocorrelation functions for the radius of gyration of the nontrivial knots can be fitted by a sum of two exponential decays of long and short characteristic relaxation times. These two relaxation times decrease with the number of essential crossings C. The faster relaxation follows the Rouse behavior and scales as N1+2nu and its dependence on C is consistent with the scaling analysis using the blob picture. The mean-square displacement of the center of mass of the knots obeys the free diffusion behavior compatible with the Rouse dynamics. The diffusion coefficients of the knots, D approximately 1/N for large N, but D decreases for knots with increasing C. These results are analyzed using scaling theories and discussed in terms of topological interactions in the knots.