Forces between plates with surface dipole layers

Abstract

Two parallel plates in an aqueous electrolyte medium each carry surface dipoles which are immersed in the adjacent electrolyte. The object of this paper is to calculate the potential field between the plates and hence obtain the interplate force due to the dipole layers. The discreteness of the dipoles at each interface is represented by regarding them as situated at the sites of a plane triangular lattice. The potential then has the same periodicity in planes parallel to the plates and is expressed as a Fourier series. Series expressions for the free energy and force are deduced in the linear approximation and the effect of lateral plate shift is examined. However, except at very small plate separations, only the zero wave number or “smeared dipole” term proves to be appreciable and this is calculated using the nonlinear Poisson-Boltzmann equation. A comparison is made between expressions for the force derived, respectively, from point-dipole and finite-dipole models. Finally the effect on the force of specific adsorption of ions into the dipole layers is considered.