Suzuki Jiro, Takano Atsushi, Matsushita Yushu
Computing Research Center, High Energy Accelerator Research Organization, Oho, Tsukuba City, Ibaraki 305-0801, Japan.
J Chem Phys. 2008 Jul 21;129(3):034903. doi: 10.1063/1.2954018.
We studied equilibrium conformations of ring polymers in the melt over the wide range of segment number up to 1000 by the Monte Carlo simulations and the bond fluctuation model, and estimated Flory's scaling exponent nu. The radial distribution function of segments for the ring polymers in the melt is obtained. We have found that nu for ring polymers is decreased with increasing segment number N, and nu goes down to 0.365 when N reaches 1000, whose value is apparently smaller than the theoretically predicted one, i.e., 25. Those values are in contrast to the well established nu value of 0.5 for linear polymers in the melt. This is because ring polymer chains in the melt are squeezed both by their own topological effect and the compression effect by the neighboring ring polymer coils which are also squeezed at bulk state. The difference in our result and the theory may be due to the fact that the estimation of topological entropy loss was ignored in the theoretical prediction, while it has been taken into consideration in the present study. If polymer coils repel each other in melt at N --> infinity, we have the limiting nu value of 13, so we conclude that nu is in the range of 13 < or = nu << 0.365 when the molecular weight of a ring polymer is high enough.
我们通过蒙特卡罗模拟和键涨落模型，研究了熔体中环状聚合物在高达1000的宽链段数范围内的平衡构象，并估算了弗洛里标度指数ν。得到了熔体中环状聚合物链段的径向分布函数。我们发现，环状聚合物的ν随链段数N的增加而减小，当N达到1000时，ν降至0.365，该值明显小于理论预测值，即2/5。这些值与熔体中线性聚合物公认的ν值0.5形成对比。这是因为熔体中的环状聚合物链既受到自身拓扑效应的挤压，也受到相邻环状聚合物线团在本体状态下的压缩效应的挤压。我们的结果与理论的差异可能是由于理论预测中忽略了拓扑熵损失的估计，而本研究中已考虑了这一点。如果聚合物线团在熔体中当N→∞时相互排斥，我们得到的极限ν值为1/3，因此我们得出结论，当环状聚合物的分子量足够高时，ν在1/3≤ν<<0.365范围内。
