Long-Range Electrostatic Interaction between a Charged Wall and Two Similarly Charged Colloidal Spheres at Low Surface Potentials

Abstract

The long-range electrostatic interaction between a pair of similarly charged colloidal spheres and a charged planar wall atlowsurface potentials is theoretically investigated. The linear Poisson–Boltzmann equation (PBE) and the point charge approximation of the charged sphere are used. The electrical potential distribution in the electrolyte solution is found from the PBE at theconstant surface potentialsusing the image charge method. The electrostatic forces acting on the spheres are then calculated. The results show that the repulsive interaction between a pair of similarly charged colloidal spheres clearly decreases when a charged wall appears nearby, but it is impossible for an attractive force to emerge at the scaled surface potentials less than 1. There is, however, an attractive force between the chargedwalland the similarly charged colloidalspheres,when the surface potential ζpon the wall is sufficiently higher than the surface potential ζson the spheres to make ζp> ζsexp(κh) (his the distance from the wall to the sphere center). In this case, there are negative surface charges on the spheres at positive surface potential ζs. It is these negative charges that produce the above attraction.