Scaling Theory of Blanched Polymers in Solution

在目前的研究中，我构建了一个标度理论，其中一般聚合物网络的性质是从简单星型聚合物的性质中获得的。1993年夏天，我在美因茨大学呆了一个月，和Kurt Binder教授合作做星形聚合物的蒙特卡罗模拟。我们研究了股票的各种空间分布函数、非球面性和松弛时间。在考虑了排除体积效应的Rouse模型的基础上，探讨了用克莱默斯势的纯静态方法研究弛豫时间等动态量的可能性。在Kramers势存在的情况下，我们分别进行了基于富集算法的蒙特卡罗模拟和基于键波动模型的蒙特卡罗模拟，得到了松弛时间对臂数的依赖关系与Grest等人的预测在估计误差范围内一致的结果。根据Kramers势方法，有可能推导出构建任意拓扑聚合物网络剪切弛豫时间标度理论的基础，但这需要进一步的详细研究。我们还研究了星形聚合物溶液的统计量与A组分比B组分长得多、溶剂对A有利而对B不利的AB嵌段共聚物溶液中胶束形成统计量之间的关系。

In the present research, I have constructed a scaling theory in which the properties of general polymer networks are obtained from the knowledge of the properties of simple star polymers. In summer of 1993, I stayd Mainz University for one month and collaborated with Professor Kurt Binder to do Monte Carlo simulation of star polymers. We studied various spatial distribution functions, asphericity, and relaxiation times of shares. Considering the Rouse model including the excluded volume effect, we investigate the possibility of studying the dynamic quantities such as relaxiation times by purely static method but with Kramers potential. We performed a Monte Carlo simulation based on the enrichment algorithm as well as a Monte Carlo simulation based on the bond fluctuation model both in the presence of the Kramers potential, and obtained the results of relaxation time whose dependence on the number of arms is consistent with the prediction by Grest et al.within the error of estimates. According to the Kramers potential method, it might be possible to derive a basis of constructing the scaling theory of relaxation time of shear of polymer networks with arbitrary topology, but such an attempt requires futher detailed study. We also studied the relationship between the statistics of star polymer solutions and the statistics of the micelle formation in the AB blockcopolymer solution in which A Part is much longer than B part and the solvent is good for A and poor for B.