Modified Poisson-Boltzmann equation and free energy of electrical double layers in hydrophobic colloids

Abstract

Corrections are obtained to the Poisson-Boltzmann (P.B.) equation for the potential distribution in the diffuse part of the electric double layer for an aqueous medium. In addition to effects of ion-size, variation in dielectric constant and self-atmosphere-image terms, these corrections include the effect of medium compressibility and so-called cavity potentials. Numerical integration of the corrected P.B. equation for a single plate and for two parallel plates shows that the potential drops more rapidly with distance from a plate surface than is predicted by the P.B. equation. The free energy of the double layers with the modified P.B. equation is determined, in the absence of specific adsorption of counter-ions.