模糊随机聚合物网络的统计力学

Science in China Series A-Mathematics, Physics, Astronomy & Technological Science Pub Date : 1995-09-20 DOI:10.1360/YA1995-38-9-1095

C. Xiaohong

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引用次数: 4

摘要

基于模糊系统理论，建立了模糊随机聚合物网络的统计力学框架。引入纠缠张量和隶属函数定量表征纠缠效应，将非晶结构视为由随机纠缠的大分子线圈组成的模糊随机网络。选择一个随机四面体纠缠交联细胞作为模糊随机聚合物网络结构的平均代表单元。利用模糊概率论和统计力学的理论，给出了变形自由能的表达式，该表达式与橡胶在各种变形模式下的弹性实验数据吻合较好。经典统计理论和Mooney-Rivlin方程都可以作为它的特例。

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Statistical mechanics of fuzzy random polymer networks

A statistical mechanics framework of fuzzy random polymer networks is established based on the theories of fuzzy systems. The entanglement effect is manifested quantitatively by introducing an entanglement tensor and membership function and the amorphous structure is treated as the fuzzy random network made up of macromolecular coils entangled randomly. A random tetrahedral entangled-crosslinked cell is chosen as an average representative unit of the fuzzy random polymer network structure. By making use of the theory of fuzzy probability and statistical mechanics, the expression for the free energy of deformation is given, which fits well with the experimental data on rubber elasticity under various deformation modes. Both classical statistical theory and Mooney-Rivlin equation can be taken as its special cases.

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Science in China Series A-Mathematics, Physics, Astronomy & Technological Science

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