Mode coupling description of dynamics in dilute polymer solutions

A calculation of the dynamic structure factor for a dilute polymer solution which explicitly takes into account the coupling to the viscous modes of the fluid is presented. The techniques of mode–mode coupling are used to extract this contribution from the Liouville equation for the relevant polymer variable. In the small wave vector regime it is shown that this contribution yields exactly the hydrodynamic contribution to the diffusion coefficient which appears in other theories when the interactions between the monomers via the solvent are calculated by using the Oseen tensor. For large wave vectors the long range correlations in the polymer chain give rise to a nonlocal memory kernel similar to that of the anomalous part of the mutual diffusion coefficient near the binary mixture critical point. The form of this wave vector dependence is examined for several models of the polymer chain.