Relating the shear-thinning curve to the molecular weight distribution in linear polymer melts

The double-reptation ansatz for stress relaxation in broadly polydisperse melts of linear chains relates the molecular weight distribution φ(n) and the dynamic viscosity η(ω), and has been used to infer φ(n) from rheological data. I show that the microscopic theory of constraint release implies the double-reptation model is valid for practical distributions φ(n). I also provide a heuristic theoretical argument for the Cox-Merz empirical rule that the shapes of the functions η*(ω) and η(γ̈) are similar, which allows the shear-thinning curve to be predicted.