Dynamics in nonentangled concentrated polymer solutions. I. The full dynamic multiple scattering approach to first order in concentration

Abstract

The concentration dependence of flexible polymer relaxation times in concentrated nonentangled solutions is studied by a full dynamic multiple scattering approach. In the absence of macroscopic entanglements effects the screening of the hydrodynamic interaction is the dominant phenomenon governing this concentration dependence. The leading concentration contribution to the relaxation times is used to introduce the screening constant through its effect on the hydrodynamic interaction matrix. The exact Langevin equation for the normal coordinates of the polymer is derived and analyzed through leading order in concentration. It is shown that there is a concentration-dependent memory kernel which emerges in the exact Langevin equation for the polymer chain dynamics in concentrated solutions, a departure from the infinite dilution situation where the (delta function) kernel is instantaneous. This implies that the relaxation matrix is frequency dependent. The general conditions for having an effective relaxation spectrum in concentrated solution are considered, and the structure of the relaxation of the normal coordinate time correlation functions is given. In general this relaxation is not described by a single exponential decaying term, but by a combination of many exponentially decaying and oscillatory exponentially decaying terms; however, the latter oscillation rates are generally very slow compared to the overall decay rates. The accompanying paper considers model calculations of the concentration dependent relaxation times.