Electrostatics, conformation, and rheology of unentangled semidilute polyelectrolyte solutions

Polyelectrolyte (PE) solutions, which are charged polymers in polar solvents, are ubiquitous and essential to life. Due to the electrostatic interactions among the charged monomers and mobile ions, the dependence of the rheological properties on the polymer concentration of PE solutions differs significantly from that of solutions of uncharged macromolecules. In addition, salt in PE solutions, whether added intentionally or intrinsically present, can affect the properties of the solutions. Here, we analyze the ion distribution near a monomer using the nonlinear Poisson–Boltzmann equation for scenarios with nonoverlapping and overlapping electric double layers. Consequently, by incorporating the electrostatic interactions into the blob model and Zimm–Rouse dynamic model, we obtain different scaling laws for the electrostatic energy per monomer, correlation length, end-to-end distance, relaxation time and viscosity $η$ of semidilute, unentangled PE solutions in consecutive regimes of polymer concentration $np$⁠, and salt concentration $ns$⁠, which are summarized in tables. With our theory, we anticipate that the empirical Fuoss law $η∝np1/2$ is expected for solutions prepared with salt-contaminated PE samples, while $η∝np0.68$ might be found for those with purer PE samples. A new critical charge fraction $φc$ is defined, where we predict that the peak, which is present in the measurements of the reduced viscosity $η/np$ as a function of $np$⁠, is only expected for weakly charged PEs $φ<φc$ prepared with pure PE samples. Comparisons with the experimental data as well as the classical scaling theories are provided, and the range of applicability of the theory is discussed.