Electrical forces between particles with discrete periodic surface charge distributions in ionic solution

Abstract

The interaction, across aqueous electrolyte, of two charged plates is studied. The charges on each plate take up a discrete periodic lattice structure. Our treatment is based on a Debye–Hückel procedure and use of Fourier–Bloch functions similar to those used in solid state physics. The interaction energy depends on the relative configuration of the charge lattices on the particles. For like charges, the energy is always positive giving a repulsive force. The minimum energy is obtained when the charge lattices interlace each other and leads to a primary maximum in the total interaction energy which is depressed considerably below the smeared out result. The maximum energy is sufficiently large that one would expect particles never to approach with superposed charge lattices.

For oppositely charged plates, the minimum energy is for superposed charged lattices and is considerably more negative than the smeared out result. The former tends to –∞ as l→ 0; the latter tends to a finite value. For interlaced equal and opposite charged lattices, we obtain a new result namely that the interaction energy may becomes positive at small separations giving a repulsive force.