Reconstruction of the Reptation Theory Based on the Dual Slip-Link Model

我们提出了一个新的模型，称为双滑移链模型，来描述缠结聚合物的粘弹性。它是经典爬行模型的一个新的扩展。在爬行模型中，缠结约束由聚合物可以通过的滑动链接表示。在经典的爬行模型中，滑动链接限制了单个聚合物，并且其位置固定在材料上。在双滑移链模型中，滑移链约束一对链，其位置由聚合物的动力学决定。双滑移链模型可以考虑缠结聚合物之间的相互作用，可以预测多分散体系的动力学行为，我们已经将双滑移链模型实现到模拟器中。模拟器有两个版本。在第一个版本中，滑动连杆被假定为固定到材料上：链之间的相互作用仅通过以下事实来考虑，即当由滑动连杆约束的两个链中的一个通过蠕动脱离滑动连杆时，滑动连杆被破坏。在第二个版本中，滑动连杆的位置通过求解滑动连杆位置的运动方程来确定。第一个版本比第二个版本更简单，更快，但不能考虑纠缠效应的波动。对于线性聚合物，两种模型给出了几乎相同的结果，而对于支化聚合物，模型之间的差异变得显著。这两个程序都放在公共领域http://octa.jp。

We have proposed a new model, called the dual slip-link model, to describe the viscoelasticity of entangled polymers. It is a new extension of the classical reptation model. In the reptation model, the entanglement constraint is represented by a slip-link through which the polymer can pass. In the classical reptation model, the slip link confines a single polymer, and its position is fixed to the material. In the dual slip-link model, the slip-link confine a pair of chains, and its position is determined by the dynamics of the polymers. The dual slip-link model can take into account of the interaction between the entangled polymers, and can predict the dynamics of the polydisperse systems.We have implemented the dual slip-link model into a simulator. There are two versions for the simulator. In the first version, the slip-links are assumed to be fixed to the material: the interaction between the chains is taken into account only through the fact that the slip-link is destructed when one of the two chains constrained by the slip-link disengage the slip-link by reptation. In the second version, the position of the slip-links are determined by solving the equation of motion for the position of the slip-links. The first version is simpler and faster than the second version, but cannot take into account the fluctuation of the entanglement effect. For linear polymers, both version give nearly the same results, while the difference between the model become 'significant for branched polymers. Both programs are placed on the public domain at http://octa.jp.