M. Paeßens, R. Willmann, and G.M. Schütz

We study how properties of the entanglement experienced by a single polymer chain in a polymer melt or a gel affect two key macroscopic properties of the polymer dynamics. Using a lattice gas model we prove rigorously that kinematic disorder leaves the scaling relation for the diffusion constant of the original reptation model unchanged and we also calculate the exact scaling amplitude as a function of the disorder distribution. From a numerical DMRG investigation we conclude that shape fluctuations of the tube caused by constraint release are not a likely candidate for improving Doi's crossover theory for the scaling of the polymer viscosity. The closely related tube renewal time depends on the entropic tensile force acting at the boundary segments of the polymer, but not on the details of the boundary dynamics by which this force is generated.