A VARIATIONAL SOLUTION TO THE HYPERNETTED CHAIN EQUATIONS APPLIED TO THE ELECTRICAL DOUBLE-LAYER

A variational method is described for the solution of the HNC/MSA equations for electrolytes near a charged planar surface. The variational method involves a much simpler computational scheme than has been presented previously for this problem and avoids some convergence difficulties associated with iterative methods. The method is demonstrated with calculations in the restricted primitive model for electrolytes of several concentrations and ionic charges near a surface with a fixed charge density. We also consider a system containing a mixture of monovalent and divalent counterions. The results are compared with the modified Gouy-Chapman theory which is the theory, because of its relative simplicity, most widely used in applications. The variational method may be useful to workers in the many areas where the electrical double layer plays a role.