Theory of the dynamical viscosity of polymer solutions

Abstract

A dynamical theory of polymer viscosity in dilute polymer solutions is presented. This theory includes the internal chain dynamics and the full dynamics of the hydrodynamic interactions within a polymer chain. The formulation considers the full dynamical coupled equations describing the internal motions of the polymer, the hydrodynamic behavior of the fluid, the polymer-fluid coupling, and the random forces which are responsible for the Brownian motion of the chain. Thus, the theory would reduce to the generalized Kirkwood theory if the dynamics of the hydrodynamics were ignored and the explicit treatment of the polymer dynamics and the random forces were dropped in favor of the thermodynamic force of the Kirkwood theory. As illustrative examples, only the simplest hopping-type models for the polymer dynamics are considered; the nature of the random forces is elucidated by the use of the fluctuation dissipation theorem; and the preaveraged dynamical hydrodynamic interactions are incorporated (with a phenomenological description of excluded volume effects). When the internal dynamics of the chain is ignored along with the dynamics of the fluid, the standard Kirkwood-Riseman result for the intrinsic viscosity is recovered. But in the general case, the dynamics alters the relaxation spectrum. The internal chain dynamics (hopping of individual chain ``beads'') gives rise to the finite high frequency intrisic viscosity and its different molecular weight dependence than the low frequency case.