Nonequilibrium relaxation times in polymer knot groups - art. no. 175503

Flexible polymer knots with strict topological constraint of no segment cro ssing are studied by Monte Carlo simulations. The nonequilibrium relaxation time of an equilibrated polymer knot cut at one point to relax to a linear chain is measured. Prime knots up to 20 essential crossings from the group s (3(1),5(1),7(1)....), (4(1), 6(1), 8(1),...) and (5(2), 7(2), 9(2)....), (6(2), 8(2), 10(2)....) are studied. The nonequilibrium relaxation time for knots within a group are found to increase stepwise linearly with the numb er of essential crossings of the original knot. Our results suggest an equa lly spaced topological interaction energy spectrum for knots in the same gr oup and thus provide a quantitative description of topological interactions .