Some simulation and modified Poisson–Boltzmann theory results for the contact values of an electrolyte near a charged electrode

Since the development of a contact value theorem by Henderson et al. it has been known that the prediction of the venerable Gouy–Chapman (GC) theory for the contact value of the density profile of an electrolyte near an electrode is incorrect. The more recent semi-empirical work of Fawcett and Henderson and the simulations of Boda and Henderson have shown that the contact value of the charge profile at low electrode charge is also given incorrectly by the GC theory, at least for a binary symmetric restricted primitive model electrolyte. In the present study we examine the contact values of the profiles of the double layer formed by the electrolyte species in a binary symmetric restricted primitive model electrolyte as a function of the electrode charge by means of simulation. It is difficult to extract detailed information from simulation values of the density and charge profiles at large electrode charge because the contact values of these profiles are dominated by the large quadratic term in the electrode charge. However, we find from our simulations for a fairly wide range of concentrations and electrode charges, that the product of the counterion and coion profiles is a sensitive probe with which to study the double layer because it is a direct test of the basis of the GC approximation that the counterion and coion profiles are exponentials of ±zeψ(x)/kT and so have a product that is identically one. We find that this product is not one or even a constant as the electrode charge is varied and, thus, the GC contact values do not agree even qualitatively with the simulation results. In contrast, the modified Poisson–Boltzmann theory is quite successful in accounting for the behavior of this product.