Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions II. Self-Diffusion of the Small Ions

The concepts developed in Part I of this series are applied to the self-diffusion of counterions and co-ions. The condensed counterions are assumed to have no mobility, while the uncondensed counterions and all co-ions execute Brownian motion subject to the locally inhomogeneous electric field created by the polyelectrolyte molecules. The polyelectrolyte field is assumed to have small amplitude, in analogy to the Debye–Hückel treatment of uncondensed mobile ions in Part I. The self-diffusion coefficients of the counterion and the co-ion are both less than the coresponding values in the absence of polyelectrolyte, but the coefficient for the counterion is much less than that for the co-ion. The results for the self-diffusion coefficient of the counterion in a salt-free polyelectrolyte solution are in good agreement with experimental data.