Spatial distribution of ions around rod-like polyelectrolytes

Abstract

The nonlinear Poisson–Boltzmann equation for the spatial distribution of counterions and coions around thin cylindrical polyelectrolytes is studied. We give a perturbative treatment of the distribution functions when a small amount of salt is added. Activity coefficients for ions of different valencies are computed explicitly to dominant order in the salt concentration.In excess salt, and with equal valencies, the distribution functions are determined numerically for selected polyion charge densities. For line charge densities beyond a critical value these distributions are universal functions.