Segment dynamics in entangled polymer melts

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Abstract
We calculate the dependence on time and on molecular weight of the mean‐squared displacement of a polymer segment in a dense fluid of linear chain molecules. Time scales are considered that range from times sufficiently short that a segment behaves as a free Brownian particle to times over which terminal diffusion occurs. We employ a stochastic model that has formed the basis of our earlier studies of the self‐diffusion coefficient in monodisperse and polydisperse melts. A macromolecule is represented by a freely jointed chain that moves through space by two mechanisms—a local conformational change and a cooperative slithering motion. The local motions are blocked by dynamical obstacles, whose relaxation rate is determined self‐consistently from the dynamics of the chain. Calculations of polymer properties are exactly mapped onto the solution of random walk problems with dynamical disorder, which are treated within the dynamical effective medium approximation. Our results are shown to share common features with recent molecular dynamics and dynamical Monte Carlo simulations of polymer melts. A procedure is suggested for assigning values to our model parameters in order to mimic specific experimental systems or other theoretical models.