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

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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.