Shimamura M K, Deguchi T
Department of Physics, Faculty of Science and Graduate School of Humanities and Sciences, Ochanomizu University 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Aug;64(2 Pt 1):020801. doi: 10.1103/PhysRevE.64.020801. Epub 2001 Jul 11.
It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we numerically evaluate the mean-square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil, and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.
在拓扑约束下，环形聚合物的平均尺寸是变小还是变大并非易事。利用一些纽结不变量，我们对具有固定纽结类型的环形聚合物的均方回转半径进行了数值评估，其中环形聚合物由由自由连接的硬圆柱体组成的自回避多边形给出。我们得到了平凡纽结、三叶纽结和八字纽结的回转半径与多边形节点数的关系图。我们讨论了拓扑约束下回转半径可能的渐近行为。在渐近极限中，当聚合物很细时，具有给定纽结的环形聚合物的尺寸大于无拓扑约束时的尺寸，而当聚合物足够厚时，有效膨胀会变弱。
