Tube Survival Fraction in Primitive Chain Network Simulations

Abstract

In the framework of the tube model, the survival fraction of dilated tube, φʹ(t), is essential since the relaxation of the entire system is described according to this quantity. However, a method to define it in multi-chain simulations has yet to be considered. In this study, primitive chain network simulations were performed, and a few structural quantities were discussed as possible candidates for use as φʹ(t). Before analysis, the simulation was evaluated against literature data for linear polyisoprene melts, and quantitative agreement was obtained for viscoelastic and dielectric relaxations. Afterward, the end-to-end relaxation function was compared to survival probability of the slip link φ_s(t) and the ratio of monomers between the most distant surviving slip link pair to the total number of monomers n_s(t)/n_t. The result implies that n_s(t)/n_t is comparable to φʹ(t). Comparison to atomistic molecular dynamics (MD) simulations for polyethylene showed similar results, implying that φʹ(t) can be obtained even in MD simulations if the surviving entanglement points can be specified.