Intrinsic Viscosity of Polymers: General Theory Based on a Partially Permeable Sphere Model

We present a general theory for the intrinsic viscosity of flexible polymers of arbitrary architecture. The theory is based on a partially permeable sphere model for which we introduce two phenomenological functions, the drag function ξ and the drainage function κ, that are determined by the density profile of the polymer. At the mean-field level, these functions capture the long-range, multibody, accumulative hydrodynamic interactions, that are responsible for the frictional dissipation in and around a polymer. The density profiles for a diversity of chain architectures are obtained by Monte Carlo simulation. Predictions from our theory are in good agreement with experimental data on all the polymer structures examined, ranging from linear, ring, and stars to hyperbranched and dendrimers. The concepts and methods we introduce in this work should be useful for studying other dilute solution frictional properties, such as the self-diffusivity, and provide a convenient framework for understanding the relationship between the molecular architecture and their dilute solution properties.