Computing Research Center, High Energy Accelerator Research Organization, KEK, Oho 1, Tsukuba, Ibaraki 305-0801, Japan.
J Chem Phys. 2011 Nov 28;135(20):204903. doi: 10.1063/1.3663383.
We studied equilibrium conformations of linear and ring polymers in dilute solutions over the wide range of segment number N of up to 2048 with Monte Carlo simulation, and evaluated N dependence of the radii of gyration, R(g), of chains. The polymer molecules treated in this study are assumed to be composed of beads and bonds, and they are put in a three-dimensional face-centered cubic (FCC) lattice. The values of Flory's critical exponent, ν, for linear and ring polymers were estimated from the N dependence of R(g), and the temperatures at which ν reach 1/2 were obtained. Here we define those as Θ-temperatures in this report. The simulation result shows that the Θ-temperature for ring polymers is evidently lower than that of the linear polymers, and the origin of the Θ-temperature depression is discussed. Since R(g) of a ring polymer is smaller than that for a linear polymer at the same N and temperature, the segment density for a ring polymer is increased by the topological effect and the repulsive force between segments of a ring polymer at the Θ-temperature for a linear polymer is stronger. Thus, the origin of the Θ-temperature depression for ring polymers is the repulsive force emphasized by the topological effect of rings.
我们使用蒙特卡罗模拟研究了线性和环状聚合物在稀溶液中的平衡构象，研究范围涵盖了多达 2048 个链段数 N，评估了旋转半径 R(g)随链段数 N 的变化。在这项研究中，假设聚合物分子由珠子和键组成，并将它们放置在三维面心立方 (FCC)晶格中。从 R(g)随 N 的变化中估计了线性和环状聚合物的 Flory 临界指数 ν，并得到了 ν 达到 1/2 的温度。在本报告中，我们将这些温度定义为 Θ-温度。模拟结果表明，环状聚合物的 Θ-温度明显低于线性聚合物，讨论了 Θ-温度降低的原因。由于在相同的 N 和温度下，环状聚合物的 R(g)小于线性聚合物，因此环状聚合物的链段密度由于拓扑效应而增加，并且在线性聚合物的 Θ-温度下，环状聚合物链段之间的排斥力更强。因此，环状聚合物的 Θ-温度降低的原因是拓扑效应强调的排斥力。
