Reptation and Contour-Length Fluctuations in Melts of Linear Polymers

Abstract

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 $\ensuremath{\eta}$ scaling as $\ensuremath{\eta}\ensuremath{\sim}{N}^{3.4}$ over a broad range in chain length $N$ before reaching an asymptotic ${N}^{3}$ dependence, and a power law ${\ensuremath{\omega}}^{\ensuremath{-}\ensuremath{\alpha}}$ in the dynamic loss modulus ${G}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})$ with $0<\ensuremath{\alpha}<1/4$ depending on chain length, in agreement with experiment.