Electrostatics and Rheology in Semidilute Polyelectrolyte Solutions

Polyelectrolyte (PE) solutions, which are charged polymers in aqueous solvents, have been studied from many perspectives in the past century. However, the effect of added salt on semidilute PE solutions remains unclear. To understand the electrostatic interactions among the polyions and electrolyte ions, we use a mean-field approach to determine the electrostatic energy of a PE solution at various polymer concentration $n_p$ and salt concentration $n_s$. We derive asymptotic approximations for the potential and ion distributions in nano-confined charged systems by probing the Poisson-Boltzmann equation within and beyond the Debye-H\"uckel linearization, and obtain distinct scaling laws for the electrostatic energy and viscosity for PE solutions at different regimes of $n_p/n_s$. One of our predictions coincides with the empirical Fuoss law for viscosity $\eta \sim n_p^{0.5}$ under the same assumption $n_s \propto n_p$ as in de Gennes’ scaling theory. Our theory also captures an unexplained empirical observation $\eta \propto n_p^{0.68}$ for salt-free PE solutions [1], and provides more physical insights on the effects of salt and charge fraction on the properties of PE solutions. [1] C. G. Lopez, R. H. Colby, P. Graham and J. T. Cabral, Macromolecules, 50, 332 (2017)