Mode-coupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations

We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c. m. velocity autocorrelation function (c. m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t(1) and the Rouse relaxation time t(N). We obtain an analytical expression for the c. m. VAF in terms of molecular parameters. In particular, the c. m. VAF scales as -N(-1)t(-5/4) (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted -t(-5/4) dependence of the c. m. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].