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生物高分子、液晶高分子和共轭高分子都是具有半刚性性质的一维线型链状分子.半刚性高分子的链长与高分子的持久长度在同一数量级,蠕虫链是最好的用来研究这类半刚性高分子统计性质的理论模型之一.其特性表现为高分子键的取向极大地影响统计行为,同时链的不可伸长性约束了高分子链的构象.这些性质可以通过结构因子的分析来开展研究.结构因子是描述体系在各个尺度上密度关联的物理量,是联系散射实验和高分子理论研究的桥梁,既可以通过散射实验测量,也可以通过理论上对链模型对应的传播子积分得到.由于蠕虫链模型的构象同时依赖位置和取向自由度,因而严格求解其传播子非常困难.这严重限制了蠕虫链模型场论理论的发展,特别是限制了应用高斯涨落理论进行有序结构的稳定性分析.本文综述了广泛采用的蠕虫链模型结构因子的渐近解和经验公式,并着重介绍近年来严格求解结构因子的最新进展.通过分析结构因子在不同波数区域上的标度规律,展示了蠕虫链模型的多尺度特点,以及其他经典的高分子链模型的关系.
Biopolymers, liquid crystal polymers and conjugated polymers are all one-dimensional linear chain molecules with semi-rigid properties. The chain lengths of semi-rigid polymers and the long-lasting polymers are in the same order of magnitude, and the worm chains are the best One of the theoretical models used to study the statistical properties of these semi-rigid macromolecules is characterized by the fact that the orientation of the polymer bonds greatly affects the statistical behavior, while the non-extensibility of the chains constrain the conformation of the polymer chains, Through the analysis of structural factors to carry out research.Structure factor is to describe the system at all scales density-related physical quantities, is a bridge linking the scattering experiments and polymer theory, either by scattering experiments, or by theoretical analysis of the chain model The corresponding propagator sub-integrals are obtained.Because the conformation of the worm-worm model relies on the degree of freedom of position and orientation, it is very difficult to solve its propagator strictly.This severely limits the development of the theory of the worm-chain model field theory, Off theory to analyze the stability of ordered structure.This paper reviews the widely used asymptotic solution of the structural factor of the worm chain model and Formulary and emphatically introduces the recent progress of solving structural factors strictly in recent years.After analyzing the scaling rules of structural factors in different wavenumber regions, the multi-scale features of the worm-chain model and the relations of other classical polymer chain models .