Viscosity of a solution of polyelectrolytes near the rod limit

Herein, I consider a solution of rodlike polyelectrolytes far from the isotropic-nematic critical concentration and focus on the solution viscosity. Varying the polymer concentration, a series of screening regimes is unveiled with the corresponding effects on the solution rheological behavior. I propose a conformational approach to explain the experimental results: the presence of screened electrostatic interactions modifies the persistence length which induces variable rod bending. A hydrodynamic approach leads to closed expressions for the reduced viscosity in the dilute and semidilute regimes by extending the derivation for the neutral rod case. In my derivation, intermediate results for the rotational diffusion constant and viscous stress are exact while the one for the elastic stress is approximate. The predictions for the reduced viscosity as a function of concentration throughout the dilute and semidilute regimes show a non-monotonic behavior similar to that of flexible polyelectrolytes. Although the final expressions cannot be expressed in terms of scaling laws, a comparison with the experimental results shows very good agreement.