Dynamics of polymer knots at equilibrium

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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 [formula presented] 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 [formula presented] R1222 (1998); Phys. Rev. Lett. [formula presented] 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 [formula presented] 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, [formula presented] 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.

Original languageEnglish
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
StatePublished - 26 Aug 2002


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