The Hydrodynamic Scaling Model for the Dynamics of Non-Dilute Polymer Solutions: A Comprehensive Review

Abstract

This article presents a comprehensive review of the Hydrodynamic Scaling Model for the dynamics of polymers in dilute and nondilute solutions. The Hydrodynamic Scaling Model differs from some other treatments of non-dilute polymer solutions in that it takes polymer dynamics up to high concentrations to be dominated by solvent-mediated hydrodynamic interactions, with chain crossing constraints presumed to create at most secondary corrections. Many other models take the contrary stand, namely that chain crossing constraints dominate the dynamics of nondilute polymer solutions, while hydrodynamic interactions only create secondary corrections. This article begins with a historical review. We then consider single-chain behavior, in particular the Kirkwood-Riseman model; contradictions between the Kirkwood-Riseman and more familiar Rouse-Zimm models are emphasized. An extended Kirkwood-Riseman model that gives interchain hydrodynamic interactions is developed and applied to generate pseudovirial series for the self-diffusion coefficient and the low-shear viscosity. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler Positive-Function Renormalization Group are developed and applied to the pseudovirial series for Ds and η. Based on the renormalization group method, a two-parameter temporal scaling ansatz is invoked as a path to determining the frequency dependences of the storage and loss moduli. A short description is given for each of the individual papers that developed the Hydrodynamic Scaling Model. Phenomenological evidence supporting aspects of the model is noted. Finally, directions for future development of the Hydrodynamic Scaling Model are presented.

Viscosity of Aqueous Polysaccharide Solutions and Selected Homogeneous Binary Mixtures

“…• α a C exp(( ) ) r (2) Phillies 19,20 reviewed the concentration dependence of η r for a large number of systems and showed that in many cases, it can be well described by eq 2 even at low concentrations with α between 0.5 and 1.…”

“…It is therefore often not possible to distinguish experimentally the two approaches within the scatter of the data. However, Phillies noted in his review 20 that in a number of cases, a clear deviation from a stretched exponential increase has been observed at higher concentration with a transition to a power law increase. This transition could be an indication that topological constraints become the dominant effect on the viscosity at high concentrations.…”

“…However, Phillies argued that the transition can also be understood in the framework of dominant hydrodynamic interactions, pointing out that a similar transition was observed in suspensions of microgels that cannot entangle. 20 Finally, Sato et al 27−29 extended the theory for the viscosity of rigid rod suspensions to cover the case of neutral semiflexible polymers for which the persistence length is not very small compared to the contour length so that they can be described as fuzzy cylinders with an effective length and thickness. They derived the following equation…”

Simulational Tests of the Rouse Model

“…The Kirkwood–Riseman model refers to an isolated chain in a shear field. Analytical–theoretical extensions of the model to treat non-dilute polymers have been made [ 7 , 8 ] and could be extended further.…”

“…The author of Refs. [ 7 , 8 ] extended the Kirkwood–Riseman model to concentrated polymer solutions.…”