抄録
The relaxation of a single knotted ring polymer is studied by Brownian dynamics simulations. The relaxation rate λq for the wave number q is estimated by the least square fit of the equilibrium time-displaced correlation function \\hatCq(t)=N−1∑i∑j(1⁄3)‹Ri(t)·Rj(0)›exp[i2πq(j−i)⁄N] to a double exponential decay at long times. Here, N is the number of segments of a ring polymer and Ri denotes the position of the ith segment relative to the center of mass of the polymer. The relaxation rate distribution of a single ring polymer with the trivial knot appears to behave as λq\\simeqA(1⁄N)x for q=1 and λq\\simeqA′(q⁄N)x′ for q>1, where x\\simeq2.10, x′\\simeq2.17, and A<A′. These exponents are similar to that found for a linear polymer chain. The topological effect appears as the separation of the power law dependences for q=1 and q>1, which does not appear for a linear polymer chain. In the case of the trefoil knot, the relaxation rate distribution appears to behave as λq\\simeqA(1⁄N)x for q=1 and λq\\simeqA′(q⁄N)x′ for q=2 and 3, where x\\simeq2.61, x′\\simeq2.02, and A>A′. The wave number q of the slowest relaxation rate λq for each N is given by q=2 for small values of N, while it is given by q=1 for large values of N. This crossover corresponds to the change of the structure of the ring polymer caused by the localization of the knotted part to a part of the ring polymer.
