Charged dielectric spheres in electrolyte solutions: Induced dipole and counterion exclusion effects

Abstract

The electrostatic interaction between two charged spheres in the presence of a screening electrolyte is calculated at the level of the linearized Debye–Hückel theory. The calculation was performed analytically as a multipole expansion by applying two-center spherical harmonic expansions and computer symbolic manipulation methods. We focus on charge–charge and charge–induced dipole interactions, calculated here for two spheres of possibly unequal size. The former interaction is given to good approximation by the familiar Debye–Hückel form ∼q1q2 exp[−κ(R−2a)]/[εr(1+κa)2]. The new results are the charge-induced dipole interactions. Physically, these terms arise from two sources, namely (i) surface polarization charge at the surface of each sphere, and (ii) exclusion of the counterion cloud of each sphere from the volume occupied by the other sphere. With parameters appropriate for micelles, at small separations the charge-induced dipole interactions dominate the charge–charge interaction.