Detailed analysis of Rouse mode and dynamic scattering function of highly entangled polymer melts in equilibrium

We present large-scale molecular dynamics simulations for a coarse-grained model of polymer melts in equilibrium. From detailed Rouse mode analysis we show that the time-dependent relaxation of the autocorrelation function (ACF) of modes $p$ can be well described by the effective stretched exponential function due to the crossover from Rouse to reptation regime. The ACF is independent of chain sizes $N$ for $N/p<N_e$ ($N_e$ is the entanglement length), and there exists a minimum of the stretching exponent as $N/p \rightarrow N_e$. As $N/p$ increases, we verify the crossover scaling behavior of the effective relaxation time $\tau_{{\rm eff},p}$ from the Rouse regime to the reptation regime. We have also provided evidence that the incoherent dynamic scattering function follows the same crossover scaling behavior of the mean square displacement of monomers at the corresponding characteristic time scales. The decay of the coherent dynamic scattering function is slowed down and a plateau develops as chain sizes increase at the intermediate time and wave length scales. The tube diameter extracted from the coherent dynamic scattering function is equivalent to the previous estimate from the mean square displacement of monomers.