橡胶交联网络非Gaussian链统计力学

宋义虎

doi:10.14028/j.cnki.1003-3726.2025.25.012

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橡胶交联网络非Gaussian链统计力学

教育与教学 | 更新时间：2025-06-25

- 橡胶交联网络非Gaussian链统计力学
- Statistical Mechanics of Non-Gaussian Chains for Crosslinking Network of Rubbers
- 高分子通报 2025年38卷第7期页码：1161-1172
- 作者机构：
  
  高分子合成与功能构造教育部重点实验室，浙江大学高分子科学与工程学系，杭州 310027
- 作者简介：
  
  s_yh0411@zju.edu.cn
- 基金信息：
- DOI：10.14028/j.cnki.1003-3726.2025.25.012
  中图分类号：
- 收稿日期：2025-01-09，
  
  录用日期：2025-03-07，
  
  纸质出版日期：2025-07-20
- 稿件说明：
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宋义虎. 橡胶交联网络非Gaussian链统计力学. 高分子通报, doi: 10.14028/j.cnki.1003-3726.2025.25.012

Song, Y. H. Statistical mechanics of non-gaussian chains for crosslinking network of rubbers. Polym. Bull. (in Chinese), doi: 10.14028/j.cnki.1003-3726.2025.25.012
宋义虎. 橡胶交联网络非Gaussian链统计力学. 高分子通报, doi: 10.14028/j.cnki.1003-3726.2025.25.012 DOI：

Song, Y. H. Statistical mechanics of non-gaussian chains for crosslinking network of rubbers. Polym. Bull. (in Chinese), doi: 10.14028/j.cnki.1003-3726.2025.25.012 DOI：

摘要

“橡胶弹性”是《高分子物理》中联系长链分子构象和熵弹性的重要章节之一。现行《高分子物理》教科书以讲授Gaussian链构象和收缩力以及Gaussian链网络熵变和应力为主，附带讲授Gaussian链统计力学的修正，而很少提及非Gaussian链统计力学及其近似表达形式。本文从无规行走问题出发回顾Gaussian链、非Gaussian链统计力学的主要来源与结果，介绍自由连接链、自避无规行走链末端位移分布和统计力学问题，以便让读者认识到Gaussian链网络模型仅是无穷长链Stirling近似结果的特例，而非Gaussian链统计力学在描述交联密度、链刚性、分子间/分子内作用力的贡献方面更有用。

Abstract

“Rubber elasticity” is one of the important chapters in

Polymer Physics

that connects the conformation and entropy elasticity of long-chain molecules. In the current textbooks of

Polymer Physics

the conformation and contraction force of Gaussian chains

as well as the entropy change and stress of Gaussian chain networks are introduced

with some corrections of Gaussian statistical mechanics

but the non-Gaussian chains statistical mechanics and their approximate expressions are rarely referred to. Reviewed in this article are the sources of statistical mechanics of long Gaussian chains and non-Gaussian chains from the perspective of random walking

the distributions of end-to-end vector of freely jointed chains and self-avoiding random walking chains so as to make readers realize that the Gaussian chain network models are only a special case of the Stirling approximation to infinitely long chains

and that the statistical mechanics of non-Gaussian chains are more useful in describing the contributions of crosslinking density

chain stiffness

and intermolecular and/or intramolecular forces to the rubber elasticity.

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Keywords

references

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高斯链网络模型与橡胶交联网络的差异