Relaxation of a Single Knotted Ring Polymer(General)

概要

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The relaxation of a single knotted ring polymer is studied by Brownian dynamics simulations. The relaxation rate λ_q for the wave number q is estimated by the least square fit of the equilibrium time-displaced correlation function C^^^_q(t)=N^<-1>Σ_iΣ_j(1/3)<R_i(t)・R_j(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 R_i 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 λ_q≃A(1/N)^x for q=1 and λ_q≃A'(q/N)^<x'> for q>1, where x≃2.10, x'≃2.17, 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 λ_q≃A(1/N)^x for q=1 and λ_q≃A'(q/N)^<x'> for q=2 and 3, where x≃2.61, x'≃2.02, and A>A'. The wave number q of the slowest relaxation rate λ_q 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.
社団法人日本物理学会の論文
2008-03-15