Shimamura Miyuki K, Deguchi Tetsuo
Department of Applied Physics, Graduate School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 1):051802. doi: 10.1103/PhysRevE.65.051802. Epub 2002 May 20.
Several nontrivial properties are shown for the mean-square radius of gyration R2(K) of ring polymers with a fixed knot type K. Through computer simulation, we discuss both finite size and asymptotic behaviors of the gyration radius under the topological constraint for self-avoiding polygons consisting of N cylindrical segments with radius r. We find that the average size of ring polymers with the knot K can be much larger than that of no topological constraint. The effective expansion due to the topological constraint depends strongly on the parameter r that is related to the excluded volume. The topological expansion is particularly significant for the small r case, where the simulation result is associated with that of random polygons with the knot K.
对于具有固定纽结类型(K)的环状聚合物的均方回转半径(R^2(K))，展示了几个重要性质。通过计算机模拟，我们讨论了由(N)个半径为(r)的圆柱形链段组成的自回避多边形在拓扑约束下回转半径的有限尺寸行为和渐近行为。我们发现具有纽结(K)的环状聚合物的平均尺寸可能比无拓扑约束时大得多。由于拓扑约束导致的有效膨胀强烈依赖于与排除体积相关的参数(r)。对于小(r)情况，拓扑膨胀尤为显著，此时模拟结果与具有纽结(K)的随机多边形的结果相关。
