Analysis of the validity of the Gouy-Chapman theory of the electric double layer

Approximate expressions for the influence of dielectric saturation, polarization of ions, and ionic interactions on the structure of the electric double layer were derived and were incorporated in a generalized Poisson-Boltzmann differential equation for the electric double layer. The solution of this extended equation in terms of a correction function, to be applied to the standard Gouy-Chapman treatment of the double layer, showed that in the case of colloid suspension with a low concentration of co-ions (relative to the concentration of counter-ions) these corrections are small, provided the surface density of charge of the colloid does not exceed 2 × 10−7 meq/cm.2 (= 20 μ Coulomb/cm.2). Especially the effects of dielectric saturation and polarization of the ions, being opposite in sign, balance each other rather closely. The effect of ionic interaction can be of some magnitude, the maximum effect probably occurring around the mentioned charge density of 2–3 × 10−7 meq/cm.2. Above this value the short-range repulsion will start to exceed the effect of the Coulombic interaction, and eventually lead to a uniform concentration of ions over some distance from the plate. It is expected, therefore, that if the charge density of a colloid does not exceed 2 × 10−7 meq/cm.2, the Gouy-Chapman theory will give fairly reliable results, especially if the charge density of the colloid under consideration is constant. The conclusions drawn are in agreement with certain experimental observations.