The Free Energy of the Double Layer of a Colloidal Particle

Abstract

Some theorems concerning the free energy of the electric double layer of a collodial particle in a dilute sol are developed by making use of the Poisson-Boltzmann equation. It is shown that this free energy can be derived by employing the fictitious process of charging the excess ions in the double layer and that the surface density of ions may be an arbitrary function of the degree of charging. By integrating with respect to the charging parameter at constant surface density of ions we obtain an alternative form for the free energy which is expressed in terms of the electrostatic energy of the double layer and the excess osmotic pressure in the diffuse layer. The latter expression for the energy can also be derived by attributing to each volume element in the diffuse layer an energy term due to the thermal motion of the ions and an (electrostatic) field energy term.