Scaling Theory of Polyelectrolyte Solutions

We extend and generalize the scaling picture of de Gennes et al. and Pfeuty to both unentangled and entangled regimes of intrinsically flexible polyelectrolyte solutions. In semidilute solution the electrostatic persistence length of a polyelectrolyte is assumed to be proportional to the Debye screening length. If the salt concentration is low, the unentangled semidilute concentration regime spans three to four decades in polymer concentration. In this regime the dynamics of the chain is Rouse-like with viscosity weakly increasing with concentration η ~ cm^1/2 (Fuoss law), relaxation time decreasing with concentration ϊ_Rouse ~ c^-1/2, and diffusion coefficient independent of concentration. Polyelectrolytes should form entanglements at the same relative viscosity as neutral polymer solutions (η ≃ 50η_s). In the entangled regime of salt-free polyelectrolytes we predict the viscosity η ~ c^3/2, relaxation time to be independent of concentration, and diffusion coefficient D_seif ~ c^-1/2. Our predictions are found to compare favorably with experiments.