Higher-order closures and potential problems in diffuse double layer and strong electrolyte solution theory

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Abstract
An nth-order closure is proposed between the higher-order fluctuation potentials of the mean electrostatic potentials and the potentials of the mean force. At the zeroth level the closure gives the Gouy-Chapman theory, at the first level the Loeb extension of the Gouy-Chapman theory and the Debye-Hückel theory, and at the second level the Outhwaite extension of the Debye-Hückel theory together with the equivalent problem in the diffuse double layer. Using the primitive model for the electrolyte with a plane uniformly charged electrode producing the double layer, a statistical mechanical analysis is carried out to determine the relations between the higher-order potentials of the mean force and the mean potentials. For the nth-order closure this gives a system of n + 1 differential equations in the diffuse double layer or n differential equations in the electrolyte bulk satisfied by the higher-order fluctuation potentials.