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

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