Relaxation of a Single Knotted Ring Polymer(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

Abstract

ブラウン動力学シミュレーション法を用いて,結び目をもつ孤立環状高分子の緩和率を調べた研究(J. Phys. Soc. Jpn. 77 (2008) 034001)の結果について紹介する.環状高分子は高分子鎖に沿った並進対称性を持っているため,その緩和率は波数で分類される.波数qの緩和率λ_qは,各セグメントの座標のフーリエ成分の時間相関関数から評価される.三葉結び目をもつ環状分子では,各鎖長ごとに最も遅い緩和率を与える波数が,鎖長が長くなるにつれ,q=2からq=1に変化した.この変化は,鎖長が長くなるにつれ結び目部分が局在することに対応すると考えられる.

The results of a Brownian dynamics study on the relaxation of a single knotted ring polymer (J. Phys. Soc. Jpn. 77 (2008) 034001) are presented. Relaxation rates of a ring polymer are classified by a wave number, because it has the translational symmetry along the polymer. The relaxation rate λ_q for the wave number q is estimated from the long-time behavior of the time correlation function of the Fourier component of the segment positions relative to the center of mass. In the case of a single ring polymer with the trefoil knot, the wave number q of the slowest relaxation rate λ_q for each N changes from q=2 to q=1 as N increases. This change is considered to correspond to the knot locaization where the knotted part of a ring polymer becomes localized to a part of the polymer as the polymer length increases.