A new method of deriving electrical double layer equations from electrolyte theories

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Abstract
By assuming that one of the species of a liquid mixture is made of charged, planar walls of infinite extension such that its concentration tends to zero (here called the direct method), an electrical double layer theory is obtained from the Kirkwood and Poirier theory for ionic solutions. It is shown that this double layer theory is equivalent to the theory of Stillinger and Kirkwood. Another electrical double layer theory is obtained from the Kirkwood and Poirier theory by taking the limits of infinite radius and zero concentration in one of the species of a liquid mixture (here called the asymptotic method). It is shown that this theory is also equivalent to the Stillinger and Kirkwood theory and therefore the direct and the asymptotic methods are equivalent. This happens also when the hypernetted chain and mean spherical approximations are considered. Finally, the electrostatic interaction potential between a charged plate and an ion is discussed in view of its importance in the application of the direct and asymptotic methods.

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