Simplified Forms for Free Energy of the Double Layers of Two Plates in a Symmetrical Electrolyte

Abstract

Approximate formulae are obtained for the interaction (free) energy of the electric double layers of two parallel plates immersed in an electrolyte of the binary, symmetrical valency type. The three separate simplified expressions which are derived are good approximations at (i) large separations between the plates, (ii) small separations between the plates, and (iii) moderate potentials. The first form is an extension of a result proposed by Verwey and Overbeek in their recent book on the theory of the stability of lyophobic colloids. The third form is a power series in the surface potential, the first term of which is identical with the expression obtained when the linear Debye-Huckel equation in the theory of electrolytes is used. These results are more suitable for numerical computations than the exact formula for the free energy, which is expressed in terms of elliptic integrals.