Self-consistent mode-coupling theory for the viscosity of rod-like polyelectrolyte solutions

TL;DR

This paper develops a self-consistent mode-coupling theory to predict the viscosity behavior of charged rod-like polymer solutions, emphasizing the importance of accurate static structure factors beyond Debye-Hückel approximation.

Contribution

It introduces a novel theoretical framework combining polymer integral equations with mode-coupling theory for polyelectrolyte viscosity prediction.

Findings

Predicts non-monotonic viscosity dependence on concentration.

Identifies the peak in reduced excess viscosity occurs below the overlap threshold.

Shows peak height increases with molecular weight and decreases with salt concentration.

Abstract

A self-consistent mode-coupling theory is presented for the viscosity of solutions of charged rod-like polymers. The static structure factor used in the theory is obtained from polymer integral equation theory; the Debye-H\"{u}ckel approximation is inadequate even at low concentrations. The theory predicts a non-monotonic dependence of the reduced excess viscosity, $\eta_R$, on concentration from the behaviour of the static structure factor in polyelectrolyte solutions. The theory predicts that the peak in $\eta_R$ occurs at concentrations slightly lower than the overlap threshold concentration, $c^\ast$. The peak height increases dramatically with increasing molecular weight and decreases with increased concentrations of added salt. The position of the peak, as a function of concentration divided by $c^\ast$ is independent of salt concentration or molecular weight. The predictions can be tested experimentally.