Falsity of the Rouse Mode Solution of the Rouse and Zimm Models

TL;DR

This paper identifies a fundamental mathematical error in the Rouse and Zimm models, showing that their mode solutions are qualitatively incorrect and do not account for whole-body rotation motions crucial for viscosity and dielectric relaxation.

Contribution

It reveals a key flaw in the classical Rouse and Zimm models and provides a corrected understanding of their mode solutions based on vibrational mode analysis.

Findings

Rouse and Zimm models contain a fundamental mathematical error.

The error causes these models to miss zero-relaxation-rate rotational motions.

Corrected solutions align with vibrational mode analysis of polyatomic molecules.

Abstract

The Rouse (J. Chem. Phys. 21, 1272 (1953)) and Zimm (J. Chem. Phys. 24}, 269 (1956)) treatments of the dynamics of a polymer chain are shown to contain a fundamental mathematical error, which causes them to lose the zero-relaxation-rate, whole-body rotation motions dominant in viscosity and dielectric relaxation. As a result, the oft-cited mode solutions for these models are qualitatively incorrect. Comparison with the Wilson-Decius-Cross treatment of vibrational modes of polyatomic molecules reveals qualitatively the correct form for the solutions to the Rouse model.