Microrheological study on the entanglement dynamics of salt-free polyelectrolyte solutions in the semidilute entangled regime

We investigate the entanglement dynamics of salt-free aqueous solutions of poly(sodium styrenesulfonate) (NaPSS) across a range of molecular weights, focusing on the semidilute entangled regime. By combining conventional bulk shear rheometry with diffusing wave spectroscopy (DWS) microrheometry, we characterize key parameters, including the entanglement concentration, plateau modulus, reptation time, and Rouse time of entanglement strands. A clear crossover from polyelectrolyte-like to neutral polymer-like behavior is identified as the degree of polymerization decreases, corresponding to a critical monomer concentration c_D ~ 0.3 M and a critical degree of polymerization N^* ~ 6000. The experimental scaling relationships closely agree with the predictions from the Dobrynin model. Our findings provide new insights into the long-standing debate on the entanglement dynamics of polyelectrolytes and establish a framework for analyzing and controlling the solution properties of salt-free polyelectrolytes in the semidilute entangled regime. Moreover, they demonstrate the power of DWS microrheology for probing complex rheological behavior in polyelectrolyte systems.