Electrostatic interactions in concentrated colloidal dispersions

An explicit expression, free from adjustable parameters, is derived for the effective pair interaction between charged colloidal spheres at high concentration in a medium containing an electrolyte. This is accomplished by first considering the electrostatic interaction between two infinite charged plates placed in a stack of identical plates. These act as a reservoir defining the chemical potentials of solvent and electrolyte ions in a way that depends on the plate separation in the stack. The results for the planar case are then applied to a suspension of identical charged spheres. Also for this case the concentration defines the properties of a reservoir quantitatively affecting the particle–particle interaction. At short range this interaction can be determined using the Derjaguin approximation relating the interaction for the planar system to the inter-particle force. In the opposite limit the effective potential around the most probable separation is derived assuming pair-wise additive interactions from nearest neighbors. For very concentrated systems the Derjaguin approximation can be used. For a more dilute system an effective local potential is derived based on solutions of the Poisson–Boltzmann equation in the cell model.