Review: Kirkwood-Riseman Model in Non-Dilute Polymeric Fluids

In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of polymeric fluid dynamics, such as reptation/scaling models. One therefore rationally asks whether there is a replacement. There is, namely by extending the Kirkwood-Riseman model. Here, I present a comprehensive review of one such set of extensions, namely the hydrodynamic scaling model. This model assumes that polymer dynamics in dilute and concentrated solution is dominated by solvent-mediated hydrodynamic interactions; chain crossing constraints are taken to create only secondary corrections. Many other models assume, contrariwise, that in concentrated solutions, the chain crossing constraints dominate the dynamics. An extended Kirkwood-Riseman model incorporating interchain hydrodynamic interactions is developed. It yields pseudovirial series for the concentration and molecular weight dependencies of the self-diffusion coefficient Ds and the low-shear viscosity η. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler positive-function renormalization group are presented. The rationales correctly predict how Ds and η depend on polymer concentration and molecular weight. The renormalization group approach leads to a two-parameter ansatz that correctly predicts the functional forms of the frequency dependencies of the storage and loss moduli. A short description is given of each of the papers that led to the hydrodynamic scaling model. Experiments supporting the aspects of the model are noted.