# Hypernetted chain approximation for the distribution of ions around a cylindrical electrode. II. Numerical solution for a model cylindrical polyelectrolyte

## Abstract

The structure of the electrical double layer associated with a cylindrical polyelectrolyte is studied through a simple charged hard sphere/charged hard cylinder model in which the diameter of the ions in the solution is considered. The hypernetted chain (HNC) equation (HNC/MSA version) is established and solved numerically giving the ionic distribution around the polyelectrolyte. Calculations are made for 1-1 and 2-2 electrolytes for various values of the concentration, ionic diameter, and polyelectrolyte radius and electrical charge. Using these ionic distributions, excess charge adsorption isotherms, zeta potentials, and mobilities are calculated. These quantities are compared with results of the nonlinear Poisson-Boltzmann (PB) equation and, in the case of the mobility, with electrophoresis measurements for double-stranded DNA. Important quantitative and qualitative differences between the PB and HNC results are found. The HNC zeta potential is found to be nonmontonic function of various parameters, for example, the charge density. The HNC mobilities are in better agreement with experiment than are the PB results. For the concentrations considered here, no significance is found for any value of the reduced linear charge density parameter. © 1985 American Institute of Physics.