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Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

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

George David Joseph Phillies¹

¹Department of Physics, Worcester Polytechnic Institute, Worcester, MA 01609, USA.

|August 12, 2023

Summary

The Rouse model for polymer dynamics is flawed. The hydrodynamic scaling model, an extension of the Kirkwood-Riseman model, offers a valid alternative by emphasizing hydrodynamic interactions over chain crossing constraints.

Keywords:

diffusion hydrodynamic scaling model hydrodynamics models molecular models theoretical polymer polymer solution dynamics polymers solution viscosity

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Area of Science:

Polymer Physics
Fluid Dynamics
Statistical Mechanics

Background:

The Rouse model, foundational to polymer dynamics theories, has been shown to be invalid in polymer melts and dilute solutions.
Existing theories like reptation/scaling models are based on the flawed Rouse model.
A need exists for a more accurate model of polymer dynamics.

Purpose of the Study:

To review and present the hydrodynamic scaling model as a valid replacement for the Rouse model.
To detail an extended Kirkwood-Riseman model incorporating interchain hydrodynamic interactions.
To explain the theoretical underpinnings and experimental support for the hydrodynamic scaling model.

Main Methods:

Reviewing prior simulational studies invalidating the Rouse model.
Developing an extended Kirkwood-Riseman model focusing on hydrodynamic interactions.
Applying self-similarity and renormalization group theories for extrapolation to high concentrations.
Developing a two-parameter ansatz from renormalization group theory.

Main Results:

The hydrodynamic scaling model correctly predicts concentration and molecular weight dependencies for self-diffusion (Ds) and viscosity (η) via pseudovirial series.
Self-similarity and renormalization group approaches accurately predict Ds and η dependencies.
The renormalization group approach yields a two-parameter ansatz that accurately predicts frequency dependencies of storage and loss moduli.
Experimental evidence supports key aspects of the hydrodynamic scaling model.

Conclusions:

The hydrodynamic scaling model provides a valid framework for understanding polymer dynamics, particularly in dilute and concentrated solutions.
Hydrodynamic interactions, not chain crossing constraints, are the dominant factor in polymer dynamics.
The model successfully predicts key rheological properties and their dependencies on concentration, molecular weight, and frequency.