Average Structures 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良溶媒中の平均構造を調べた研究(J. Phys. Soc. Jpn. 77(2008) No. 12)の結果について紹介する.平均構造は,シミュレーションで得た個々の構造を平均構造からの二乗変位が最小となるように回転・並進させた後,それらを平均した構造として反復法で得られる.三葉結び目をもつ環状高分子の平均構造を評価した結果,各平均構造の結び目部分は,鎖長が短いときには非局在状態にあるが,鎖長が長くなると局在化することがわかった.

The results of a Brownian dynamics study on average structures of a knotted ring polymer in good solvent (J. Phys. Soc. Jpn. 77 (2008) No. 12) are presented. The average structure is self-consistently calculated as the average of conformation vectors obtained from a simulation each of which is translated and rotated to minimize its distance from the average of the conformation vectors. In the estimated average structures of single ring polymers with the trefoil knot, the knotted part of each average structure is delocalized for small values of the number of segments N and becomes localized as N increases.