# Viscoelastic properties of linear long polymers in melt

A model is presented for the lateral motion of linear polymer chains in a monodisperse melt. Because each pair of neighboring chains in a melt is highly entangled and randomly wound around each other, the lateral motion of each chain is taken to occur primarily along the contours of neighboring chains. This lateral motion is impeded by interactions with other chains, but not suppressed due to the multichain cooperative motion. A scaling analysis is applied to account for the correlations between the motions of neighboring chains, and the correlations between the motions of beads in the same chain. The model predicts that the mean-squared bead displacement scales with time as $t\sp{2/7}$ for time less than terminal time. The corresponding terminal time scales with chain length as $N\sp{7/2}$. A calculation of the center of mass diffusion constant, which is based on the correlated motion of all chains in a certain region, yields $D\sb{cm} \sim N\sp{-2.1}.$ The stress relaxation in polymer melts is investigated in detail in the post-plateau region. It is assumed that the stress is supported by interchain contacts and relaxed when the contacts break. The anisotropic environment effect is considered into the model. Computer simulations are performed for both monodisperse and bidisperse melts, and the results are compared with published experimental data. Very good agreement is found with experiments The characteristic feature of viscoelastic properties of linear polymers of high molecular weight is the presence of two sets of relaxation times relating to configurational rearrangements between short-range local structure and long-range chain conformation respectively. The plateau region is the intermediate times between these two relaxations. We establish a numerical model to study the plateau properties of linear long polymers. Monte Carlo method is employed to generate the possible multi-pathway for polymer chains to relax. The relaxing energy of this system is found to display a pronounced plateau, and the value of this plateau depends on initial deformation