Tagged chain diffusion equation and effective friction tensor in dense polymer solutions

We start from the many-chain Smoluchowski equation that describes dynamics of dense polymer solutions and derive an effective diffusion equation for a tagged ~probe! chain distribution function. In the tagged chain diffusion equation the effects of the inter-chain interactions are incorporated through an effective friction tensor. We propose a simple phenomenological formula for the friction tensor in which the friction on a given bead depends only on the positions of its two neighbors along the chain. This formula is used in conjunction with an exact lower bound for the center of mass self-diffusion coefficient. We show that the necessary condition for reproducing N scaling of the self-diffusion coefficient is not weaker-than-linear dependence of the anisotropy on the chain length N . To check whether this also a sufficient condition, we perform a set of single chain Brownian dynamics simulations. We show that the linear chain length dependence of the anisotropy leads to Ds;N 21.6 whereas the N and N scaling of the anisotropy result in the chain length dependence of D that is consistent with the observed N behavior. © 1998 American Institute of Physics. @S0021-9606~98!51201-9#