Microrheological Approach for Probing the Entanglement Properties of Polyelectrolyte Solutions

The entanglement dynamics and viscoelasticity of polyelectrolyte solutions remain active research topics. Previous studies have reported conflicting experimental results when compared to Dobrynin's scaling predictions derived from the Doi-Edwards (DE) tube model for entangled polymers. Herein, by combining classical bulk shear rheometry with diffusing wave spectroscopy (DWS) microrheometry, we investigate how the key viscoelastic parameters (the specific viscosity η_sp, the plateau modulus G_e, and the ratio of the reptation time to the Rouse time of an entanglement strand τ_rep/τ_e) depend on the polymer concentration for semidilute entangled (SE) solutions containing poly(sodium styrenesulfonate) with high molecular weight. Our experimental measurements yield G_e ∝ c^1.51±0.04, in good agreement with the scaling of G_e ∝ c^1.5 predicted by Dobrynin's model for salt-free polyelectrolyte SE solutions, suggesting that the electrostatic interaction influences the viscoelastic properties of polyelectrolyte SE solutions. On the other hand, the deviation in the scaling exponent for η_sp ∝ c^2.56±0.04 and τ_rep/τ_e ∝ c^1.82±0.28 is observed between our DWS experiments and Dobrynin's model prediction (∝ c^1.5), likely due to the fact that Dobrynin's scaling model does not account for mechanisms such as the contour length fluctuation, the constraint release, and the retardation of solvent dynamics, which are known to occur for SE solutions of neutral polymers. Our results demonstrate that DWS serves as a powerful rheological tool to study the entanglement dynamics of polyelectrolyte solutions. The scaling relationships obtained in this study provide new insights to the long-standing debate on the entanglement dynamics of polyelectrolyte solutions.