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

We present data from Monte Carlo simulations for monodisperse linear polymer 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-like dynamics for short chains to reptation-like dynamics for long chains. To address this problem, we calculate a variety of different quantities: standard 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 nonentangled to entangled dynamics is very protracted. Even the biggest chain length N = 512, which is about 14 times larger than the entanglement length, shows no clear evidence for reptation. In the opposite limit of short chains, no pure Rouse behavior is found either. Local stiffness effects have to be taken into account.