Application of a recently proposed test to the hypernettedchain approximation for the electric double layer

Abstract

Bhuiyan, Outhwaite, and Henderson, J. Electroanal. Chem., 2007, 607, 54, have studied the electric double layer formed by a symmetric electrolyte in the restricted primitive model and suggested that an examination of the product of the coion and counterion profiles, normalized to the one when the distance of an ion from the electrode is large, is an interesting and useful test of a theory. This product is identically one in the PoissonBoltzmann theory but simulation results show that, at contact, this product can be greater or smaller than one at small electrode charge but always seems to tend to zero at large electrode charge. In this study we report the results of the hypernetted chain approximation (HNC/MSA version) for this product and find that, at contact, for this theory this product is always greater than the one at small electrode charge but tends to zero at large electrode charge.

New results from the contact theorem for the charge profile for symmetric electrolytes

“…7 In agreement with the computer simulation results 6 the product can have a maximum at some value b = b max . This value can be found by the differentiation of Eq.…”

On the contact values of the density profiles in an electric double layer using density functional theory

“…As the concentration increases, the height of the maximum decreases and at sufficiently high concentrations the maximum disappears completely with f decreasing monotonously. Again, theoretical support for such a behavior of f came from the MPB [18] and although the hypernetted chain/mean spherical approximation theory does not show a maximum, the product f does become very small when the electrode charge is large [19].…”