Self-diffusion of small ions in polyelectrolyte solutions

A method of calculating the self-diffusion coefficients of small ions in polyelectrolyte solutions is derived on the basis of the cell model with cylindrical symmetry. The method is applied to a salt-free polyelectrolyte solution and a limiting law for the self-diffusion coefficient of the counterion is formulated in a rigorous manner. The calculation leading to this result shows that at infinite dilution there is a condensation of counterions about the polyion chain. The limiting law is compared with Manning’s theory and with experimental data in the literature.