# The application of the hypernetted chain approximation to the electrical double layer: Comparison with Monte Carlo results for symmetric salts

## Abstract

The hypernetted chain integral equations (HNC/MSA version) for the reduced density profiles of a model electrolyte near a charged electrode (the so-called electrical double layer problem) are solved and the resulting density and potential profiles are compared with recent Monte Carlo calculations. Good agreement is found when the bulk electrolyte direct correlation functions are calculated from the mean spherical approximation. In particular, the HNC/MSA correctly predicts that for divalent salts, the potential profile is nonmonotonic and changes sign. As a result, there is charge oscillation or a layering of charge. That is, near the electrode the ions predominately have the opposite charge as the electrode but in some situations the ions at a greater distance generally have the same charge as the electrode. In contrast, the Gouy-Chapman theory gives poor results. The Gouy-Chapman density and potential profiles are always monotonic. Thus, the widely used practice of estimating the effects of solvent or non-Coulombic interactions by subtracting the Gouy-Chapman theory results from experimental results may in certain situations lead to erroneous estimates of these effects. © 1982 American Institute of Physics.