Long-range electrostatic attractions between identically charged particlesin confined geometries and the Poisson-Boltzmann theory

There has been much speculation about the origin of long-range electrostati c attractions between identical colloidal particles in confined geometries. Recently, we proved that such attractive interactions are not to be found in the well-established Poisson-Boltzmann theory, when the particles are im mersed in a 1:1 electrolyte whose average ion concentrations are equal. A s ubsequent approximate analytical investigation (Europhys. Lett. 1999, 46, 4 07-413) has suggested that such attractive interactions result from a combi nation of the effects of confinement, imbalance of the average ionic concen trations, and polarization effects in the confining surface. Consequently, we extend our previous proof to encompass the general case of an electrolyt e possessing any number of ionic species, where there is no restriction on their average concentrations. In so doing, we rigorously prove that within the framework of the Poisson-Boltzmann theory the interaction between ident ical colloidal particles is never attractive, irrespective of whether the p articles are isolated or confined. Furthermore, we establish a necessary co ndition for the existence of attractive interactions, which indicates the p ossibility that an osmotically driven process is behind the observed attrac tive interactions.