Reptation and contour-length fluctuations in melts of linear polymers

We present an analytical theory of stress relaxation in monodisperse linear polymer melts that contains contributions from both reptation and contour-length fluctuations, modeled as in our previous work on arm retraction in star polymers. Our approach resolves two long-standing problems with reptation theory: it predicts a zero-shear viscosity η scaling as η∼N^3.4 over a broad range in chain length N before reaching an asymptotic N³ dependence, and a power law ω^-α in the dynamic loss modulus G”(ω) with 0 < α < 1/4 depending on chain length, in agreement with experiment.