An $[\eta]$ Linear in $M$ Does Not Imply Rouse Dynamics

TL;DR

An observed linear relationship between polymer viscosity and molecular weight does not necessarily indicate Rouse-like dynamics, as other models like Kirkwood-Riseman also predict this linearity through different chain motion mechanisms.

Contribution

This paper clarifies that linear viscosity in polymers does not imply Rouse dynamics, highlighting the differences between Rouse and Kirkwood-Riseman models.

Findings

Kirkwood-Riseman model predicts linear viscosity without Rouse-like motions.

Rouse's calculation of intrinsic viscosity is invalid under certain assumptions.

Polymer chain motions differ fundamentally between models despite similar viscosity scaling.

Abstract

Contrary to some expectations, an experimental finding for a polymer that the solution intrinsic viscosity $[\eta]$ or the melt viscosity is linear in the polymer molecular weight $M$ does not indicate that polymer dynamics are Rouselike. Why? The other major polymer dynamic model, due to Kirkwood and Riseman [\emph{J. Chem.\ Phys.\ } \textbf{16}, 565-573 (1948)], leads in its free-draining form to a prediction $[\eta] \sim M$, even though the polymer motions in this model are totally unlike the polymer motions in the Rouse model. In the Rouse model, the chain motions are linear translation and internal ('Rouse') modes. In the Kirkwood-Riseman model (and its free-draining form, derived here), the chain motions are translation and whole-body rotation. The difference arises because Rouse's calculation implicitly refers only to chains subject to zero external shear force (And, as an aside, Rouse's construction of $[\eta]$ is invalid, because it concludes that there is viscous dissipation in a system that Rouse implicitly assumed to have no applied shear).