支化高分子的邻接矩阵及其结构参数计算

Adjacent matrix of randomly branched polymers for evaluation of its structural parameters

本文基于支化高分子的邻接矩阵获得了其子链分布,进而给出含溶剂效应在内的支化高分子尺度和结构参数的子链计算方案.作为应用,以AB2型单体聚合形成的无规支化高分子为例,本文计算了支化分子的均方回转半径、平均最大链长和平均链长,明确了它们与聚合度及支化点密度之间的标度关系.结果表明,在理想链和真实链的情形下,尽管支化高分子的均方回转半径与聚合度之间的标度关系存在差别,但二者与支化点密度之间标度关系保持一致.此外,平均链长和最大链长与聚合度和支化点密度之间均呈现出相同的标度关系.这些结果可为相关的材料设计提供指导.

We present a method of adjacent matrix for randomly branched polymers that can be used to evaluate typical dimensions of branched polymer under the cases of ideal and real chains.Given a branched polymer with known structure,the number of subchains of various length can be obtained through its adjacent matrix in a straightforward manner.Consequently,the mean length and maximal length of subchains,and the mean-square radius of gyration of the branched polymer can be carried out,which are especially useful for further evaluating the relevant physical properties.As an application,we calculated the corresponding polymeric quantities for hyperbranched polymers of AB2 type,and predicted the scaling relations between them and the number of branched units.It is expected that such a method is helpful for designing relevant polymeric materials.