Effect of Nonzero Solid Permittivity on the Electrical Repulsion between Charged Surfaces

The electrical repulsion between two charged solid surfaces separated by an electrolyte is studied as a function of the permittivity epsilon(s) of the solid in the limit in which potentials are small, and the gap between the plane solid surfaces is small compared to the Debye length kappa(-1) within the electrolyte. The solid surfaces are uniformly charged in a central region vertical bar x vertical bar < L outside which they are uncharged. When epsilon(s) = 0, ions from the charge cloud between the charged surfaces spill out into regions of length O(kappa(-1)) beyond x = +/- L, thereby reducing the pressure between the surfaces from that predicted by Derjaguin-Landau-Verwey-Overbeek theory for infinite, uniformly charged surfaces. When epsilon(s)>0, ions spill out over much larger O(L) regions, thereby reducing still further both the electrical potential between the solid surfaces and the repulsive force between them. However, this reduction becomes smaller as kappa L becomes large.