Simulational Analysis of Relaxation in Polymer Systems

1. 研究了受排斥力壁限制在狭缝中的单链聚合物的弛豫速率和模式。它们在平行于壁面的方向上的行为可以理解为一个二维排除体积链的行为，其大小与狭缝的宽度相当。垂直方向的行为可以通过假设相邻斑点位移的垂直分量之间存在排斥相互作用来理解。研究了星形聚合物的弛豫速率和模式。从松弛模式和速率与臂数和臂段数的关系出发，得到了与整体形状变形和相邻臂位置交换相对应的两个松弛过程。虽然前者已被理论预测到，但后者还没有。本文从二维和三维的角度研究了聚合物链在管网中的弛豫速率和模式。在两维中，由于排除了体积相互作用，松弛率随线段数的幂律依赖指数大于没有排除体积相互作用情况下的理论值。最小弛豫速率的行为与其他弛豫速率的行为不同。在三维空间中，排除的体积相互作用影响不大。研究了聚合物链在熔体中的弛豫速率和模式。随着N的增加，最小松弛率的逆的幂律依赖的表观指数随着N的增加而增加，超过了理论预测值3。从最大N值的数据中，估计表观指数为3.5，与实验结果一致。第p个最小弛豫速率对p的幂律依赖指数小于理论值2。第一和第二慢弛豫模式的行为与理论预测一致。研究了单链聚合物的弛豫速率和模式，其中考虑了排除的体积相互作用和水动力相互作用。提出了松弛速率谱随水动力相互作用强度变化的理论公式，并通过仿真得到了验证。少

1. Relaxation rates and modes of a single polymer chain confined in a slit by repulsive walls are studied. Their behaviors for the directions parallel to the walls can be understood as those of a two-dimensional excluded volume chain of blobs, of which size is comparable to the width of the slit. The behaviors for the perpendicular direction can be understood by assuming a repulsive interaction between the perpendicular components of the displacements of neighboring blobs.2. Relaxation rates and modes of a star polymer are studied. From the dependence of the relaxation modes and rates on the number of arms and the number of segments per arm, two relaxation processes corresponding to the deformation of the overall shape and the exchange of the positions of two neighboring arms are found. Although the former has been predicted by a theory, the latter has not.3. Relaxation rates and modes of a polymer chain trapped in a tube network are studied in two and three dimensions. In two dimensio … More ns, because of the excluded volume interaction, the exponent of the power law dependence of the relaxation rates on the number of segments is larger than the theoretical value for the case of no excluded volume interaction. The behavior of the smallest relaxation rate is different form that of the other relaxation rates. In three dimensions, the excluded volume interaction has little effect.4. Relaxation rates and modes of a polymer chain in a melt are studied. The apparent exponent of the power law dependence of the inverse of the smallest relaxation rate on the number N of segments increases beyond the theoretically predicted value, three, as N increases. From the data for the largest values of N, the apparent exponent is estimated as 3.5, which is consistent with the experimental results. The exponent of the power law dependence of the p-th smallest relaxation rate on p is smaller than the theoretical value, two. The behaviors of the first and second slowest relaxation modes are consistent with the theoretical prediction.5. Relaxation rates and modes of a single polymer chain are studied, where the excluded volume interaction and the hydrodynamic interaction are taken into account. A theoretical formula which describes how the relaxation rate spectrum changes as the strength of the hydrodynamic interaction changes is proposed and is confirmed by simulations. Less