Algebraic repulsions between charged planes with strongly overlapping electrical double layers.

Langmuir's disjoining pressure between two flat, charged planes was calculated analytically for strongly overlapping double layers in the limit of zero electric field between the planes. The resulting repulsion has a long-range algebraic decay that stems from the thermodynamic equilibrium between homogeneously distributed interplate ions and ions in the surrounding electrolyte reservoir. Together with the van der Waals attraction, the repulsion forms the zero-field pendant of the exponentially screened DLVO potential, a pendant that is always repulsive at large plate-plate distances. The experimental occurrence of algebraic repulsions can be simply predicted from surface charge density and ionic strength.