Monte Carlo simulation of long chain polymer melts: Crossover from Rouse to reptation dynamics

We present data from Monte Carlo simulations for monodisperse linear polyme r chains in dense melts with degrees of polymerization between N = 16 and N = 512. The aim of this study is to investigate the crossover from Rouse-li ke dynamics for short chains to reptation-like dynamics for long chains. To address this problem, we calculate a variety of different quantities: stan dard mean-square displacements of inner monomers and of the chain's center of mass, the recently proposed cubic invariant (Ebert, U.; et al. Phys. Rev . Lett. 1997, 78, 1592), persistence of bond-vector orientation with time, and the autocorrelation functions of the bond vector, the end-to-end vector , and the Rouse modes. This analysis reveals that the crossover from nonent angled to entangled dynamics is very protracted. Even the biggest chain len gth N = 512, which is about 14 times larger than the entanglement length, s hows no clear evidence for reptation. In the opposite limit of short chains , no pure Rouse behavior is found either. Local stiffness effects have to b e taken into account.