Mode-coupling approach to polymer diffusion in an unentangled melt. II. The effect of viscoelastic hydrodynamic interactions

Abstract

A mode-coupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the density-based MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the center-of-mass velocity autocorrelation function (c.m. VAF). We show that in most cases the VHI mechanism is dominant; for long chains and prediffusive times it yields a negative tail $\ensuremath{\propto}$$\ensuremath{-}{N}^{\ensuremath{-}1/2}{t}^{\ensuremath{-}3/2}$ for the c.m. VAF. The case of non-momentum-conserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first $\ensuremath{-}{N}^{\ensuremath{-}1}{t}^{\ensuremath{-}5/4}$ (as in the dMCT approach), then $\ensuremath{-}{N}^{\ensuremath{-}1/2}{t}^{\ensuremath{-}3/2}$. Both the amplitude and the duration of the first ${t}^{\ensuremath{-}5/4}$ stage crucially depend on the Langevin friction parameter $\ensuremath{\gamma}$. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the c.m. VAF, thus account for the anomalous subdiffusive regime of the c.m. mean square displacement widely observed in numerical and experimental works.