Free Energy of the Double Layers of Two Parallel Plates in a 1-2 Electrolyte

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Abstract
By making use of the Poisson-Boltzmann equation an expression is obtained for the free energy of the electric double layers of two parallel plates immersed in a large volume of an electrolyte of the 1-2 valency type. Two cases arise depending on whether or not the divalent ion and the surface charge have the same sign. The formula for the free energy is expressed in terms of elliptic integrals An approximate form for the free energy, which is more convenient for numerical computations, is also obtained. This is particularly suitable at large surface potentials and is derived for a symmetrical electrolyte as well as for the asymmetrical ones Numerical tables of the free energy as a function of plate separation are given and some applications are briefly indicated

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