Pair correlation functions and density profiles in the primitive model of the electric double layer

Abstract

In the primitive model of the electric double layer an electrolyte near a charged surface is modeled by an assembly of charged hard spheres in a medium of dielectric constant ε. We solve numerically the inhomogeneous Ornstein–Zernike equation for the pair correlation functions in the hypernetted chain and mean spherical approximations together with the Lovett–Mou–Buff–Wertheim equation for the density of the ions near a charged surface. For highly charged surfaces the profiles display layering and charge reversal. The density profiles and diffuse layer potential are generally in excellent agreement with Monte Carlo data. The pair correlation functions at small separation are significantly different from correlation functions in the bulk and at larger separation have the well-known power law decay (r−3) as function of separation when both hard spheres are kept at constant distance from the surface.