Kawai Shinnosuke, Nitta Yoko, Nishinari Katsuyoshi
Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada.
J Chem Phys. 2008 Apr 7;128(13):134903. doi: 10.1063/1.2894845.
A model for large deformation of polymer gels with physical cross-linking is developed and shown to be in good agreement with experimental stress-strain curves which show strain hardening in intermediate strains followed by strain softening in large deformations near the yield strain. The model takes into account the coil-helix transition equilibrium and allows for the distribution of the end-to-end distance. The gel is considered to be formed by long flexible chains and crystalline zones acting as junctions of the chains. The number of segments contained in a flexible chain is variable due to the equilibrium between the two regions. As the end-to-end distance increases due to the deformation, more and more segments are reeled out from the junction zone. Finally, one end of the chain is librated from the junction and the chain becomes dangling. The appearance of dangling chains causes the strain softening because they cease to contribute to the elasticity. From the parameter dependence of the stress-strain relations, it was found that the yield behavior depends strongly on the distribution of end-to-end distance. The yield strain is approximately given by the ratio of the upper limit of the number of segments and the average end-to-end distance. The standard deviation of the end-to-end distance affects significantly the width of the peak in the stress-strain curve, thus determining the degree of strain softening.
建立了一个具有物理交联的聚合物凝胶大变形模型，结果表明该模型与实验应力-应变曲线吻合良好。实验应力-应变曲线显示，在中等应变下出现应变硬化，随后在接近屈服应变的大变形下出现应变软化。该模型考虑了线圈-螺旋转变平衡，并考虑了端到端距离的分布。凝胶被认为是由长柔性链和作为链连接点的结晶区形成的。由于两个区域之间的平衡，柔性链中包含的链段数量是可变的。随着变形导致端到端距离增加，越来越多的链段从连接区被拉出。最后，链的一端从连接点释放，链变成悬垂状态。悬垂链的出现导致应变软化，因为它们不再对弹性有贡献。从应力-应变关系的参数依赖性发现，屈服行为强烈依赖于端到端距离的分布。屈服应变大约由链段数量上限与平均端到端距离的比值给出。端到端距离的标准偏差显著影响应力-应变曲线中峰值的宽度，从而决定应变软化程度。
