Ion adsorption in the electrical double layer: Variational solution to the hypernetted chain equations

In order to investigate the effect of specific adsorption of counterions onto a charged planar surface, the HNC/MSA equations were solved using a variational method. Ion adsorption is introduced through a sticky potential. The variational method involves a simple computational algorithm, and although it does not yield exact solutions, the contact condition and electroneutrality are automatically satisfied. Results are presented for a surface charge density of -0.10 C m(-2) and for a range of bulk ion concentrations of 1:1 electrolyte and counterion adsorption tendencies. While the sticky potential provides a simple model of wall-ion interactions, the effect of increasing ion adsorption on the structure of the double layers can be seen. Comparisons are also made with the modified Gouy-Chapman theory, which neglects the finite size of the ions. At high bulk ion concentrations, ion size effects result in nonmonotonic ion distributions.