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北京交通大学理学院,北京,100044
纸质出版日期:2016-8-1,
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杨扬, 步项禹, 张兴华. 基于蠕虫链模型的半刚性单链高分子的结构因子[J]. 高分子学报, 2016,(8):1002-1010.
Yang Yang, Xiang-yu Bu, Xing-hua Zhang. Structure Factor Based on the Wormlike-chain Model of Single Semiflexible Polymer[J]. Acta Polymerica Sinica, 2016,(8):1002-1010.
杨扬, 步项禹, 张兴华. 基于蠕虫链模型的半刚性单链高分子的结构因子[J]. 高分子学报, 2016,(8):1002-1010. DOI: 10.11777/j.issn1000-3304.2016.16066.
Yang Yang, Xiang-yu Bu, Xing-hua Zhang. Structure Factor Based on the Wormlike-chain Model of Single Semiflexible Polymer[J]. Acta Polymerica Sinica, 2016,(8):1002-1010. DOI: 10.11777/j.issn1000-3304.2016.16066.
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.
Wormlike chain model is one of so far the best theoretical models for the semiflexible biological polymer
liquid crystal polymer and conjugate polymer.The chain length is in the same length scale with the persistent length of semiflexible chains.In this condition
the orientation of bonds becomes important for the conformational statics and the in-extendable constraint decrease number of possible conformation of the chain.Structure factor characterizes the density correlation in different length scales
which can be obtained by both scattering experiment and theoretical computation.Generally
it is hard to compute the structure factor of wormlike chain model exactly
because it has the degrees of freedom in both positional and orientational space.This strangles the development of theory based on wormlike chain model
especially
applying Gaussian fluctuation theory on the stability analysis of ordered systems.In this review
the commonly used approximated formulations of structure factor of wormlike chain model are introduced and the development on predicting the structure factor exactly.Through analyzing the scaling relation in different wavenumber regions
the multi scale properties of wormlike chain model are well demonstrated.
半刚性高分子蠕虫链模型结构因子
Semiflexible chain modelWormlike chain modelStructure factor
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