Entanglement effects in mode coupling theories of polymers

摘要

Entanglement effects in polymer melts are investigated using mode coupling theory. For a system of long thin rods that perform only translation motion, we find an exact solution to the mode oupling theory, and demonstrate that it predicts that the self-diffusion coefficient becomes isotropic as the aspect ratio becomes infinite, i.e., it does not describe entanglement effects. One has to go beyond the usual Gaussian approximation in mode coupling theory to obtain nontrivial results for the self-diffusion coefficient, and a simple approximation is investigated which gives results consistent with the reptation theory and a dynamical mean field theory.