Counter-ion penetration in ionized monolayers at a dielectric interface

The equilibrium depth of immersion d in the aqueous phase of the head groups of long-chain molecules forming an ionized monolayer at an oil/water interface is considered. The free energy of formation of the monolayer is regarded as the sum of an electric double layer or "collective" term due to an average electric potential at the plane of head groups, a term due to the electrical images of the individual ions in the interface and a chemical term which includes the free energy of immersion of the CH₂ chain groups in the aqueous phase. The balance of forces determining d is obtained by minimizing this free energy with respect to d. It is assumed that the diffuse layer ions penetrate behind the plane of head groups and the Poisson-Boltzmann equation is applied on both sides of this plane. The effects of this ion penetration have been emphasized by Haydon and Taylor but it is shown that both the electrostatic equations and the equilibrium conditions of these authors are incorrect. If, like Haydon and Taylor, one omits the image term then the correct equilibbrium relations with the remaining terms do not yield any solution for d with their values of the chain immersion free energy.