We theoretically study the stress relaxation process of small amounts of entangled ring polymer chains in a linear matrix by combining several important physical mechanisms: (1) Rouse relaxation, (2) longitudinal stress relaxation along the tube, and (3) constraint release. The contribution to stress relaxation of entangled rings by longitudinal modes is calculated analytically, and a compact expression of the relaxation modulus is given.

中文翻译：

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线性矩阵中缠结环聚合物链的应力松弛

我们通过结合几个重要的物理机制，从理论上研究了线性基体中少量缠结环聚合物链的应力松弛过程：（1）Rouse 松弛，（2）沿管的纵向应力松弛，以及（3）约束释放。分析计算了纵向模式对纠缠环应力松弛的贡献，并给出了松弛模量的紧凑表达式。