Multiple scattering theory calculation of the concentration dependence of the tracer and cooperative friction coefficients for Gaussian polymer chains

The cooperative and tracer translational friction coefficients of Gaussian polymer chains are evaluated through order c in concentration using the full dynamic bead-to-bead space time correlation functions within the framework of a recent reformulation involving a discrete bead-type model of the multiple scattering theory for the concentration dependence of the viscoelastic properties of polymer solutions. It is shown that, using preaveraging approximation of the Oseen tensor, the order c cooperative translational friction coefficient differs from the tracer friction coefficient due to a higher order contribution in the multiple scattering expansion, one varying as the inverse seventh power of the separations between chains. The leading term for the cooperative translational friction coefficient of order c, equal to the tracer one, is calculated to be 0.62, about 10%–25% smaller than recent experimental results obtained in sedimentation experiments. The difference may be due, in part, to the higher terms in the multiple scattering expansion which turn out to be very difficult to compute even in a very rough approximation.