Comparison of theories of the aqueous electric double layer at a charged plane interface

Abstract

A modified Poisson–Boltzmann (P.B.) equation for the potential distribution in the diffuse part of the electric double layer at a plane charged interface is described. Based on the Güntelberg–Kirkwood–Loeb charging of an ion, this was derived by Outhwaite and Bell and Rangecroft in the form of a non-linear integro–difference–differential equation. It is shown that, for ions with a common distance of nearest approach a, this equation reduces to different simplified forms which appear in the literature and that above a critical κ₀a(≳1), where κ₀ is the Debye–Hückel parameter, charge oscillations as a function of distance are predicted. A comparison is made between the treatments by Buff and Stillinger and Levine and Bell of the so-called volume effect which is accounted for in this modified P.B. equation.

An alternative linearised modified P.B. equation for ions of equal size is obtained by applying the mean spherical approximation model. Use is made of the Ornstein–Zernike equation for the direct correlation function of the pair interfacial plane wall-molecular particle, as derived by Henderson, Abraham and Barker. The potential in the diffuse layer is shown to satisfy a linear integro–difference–differential equation which becomes nearly identical with that obtained by the charging method for small κ₀a. Comparison is made with a recent electric double layer theory by Blum.