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 eta similar to c(1/2) (Fuoss law) relaxation time decreasing with concentration tau(Rouse) similar to c(-1/2), and diffusion coefficient independent of concentration. Polyelectrolytes should form entanglements at the same relative viscosity as neutral polymer solutions (eta congruent to 50 eta(s)). In the entangled regime of salt-free polyelectrolytes we predict the viscosity eta similar to c(3/2), relaxation time to be independent of concentration, and diffusion coefficient D-self similar to c(-1/2). Our predictions are found to compare favorably with experiments.