General solution to the electric double layer with discrete interfacial charges

We provide extensive molecular dynamics simulations of counterion and coion distributions near an impenetrable plane with fixed discrete charges. The numerical results are described by an explicit solution that distinguishes the plasma (3$\end{document}]]<A _c/σ>3) and the binding regime (A _c/σ3) where σ is the ion diameter and A _c eν (ν is the surface charge density). In the plasma regime, the solution consists of a product of two functions that can be computed from simpler models and reveals that the effects of the discreteness of the charge extends over large distances from the plane. The solution in the binding regime consists of a Stern layer of width σ and a diffuse layer, but contrary to standard approaches, the strong correlations between ions within the Stern layer and the diffuse layer require a description in terms of a displaced diffuse layer. The solution is found to describe electrolytes of any valence at all concentrations investigated (up to 0.4M) and includes the case of additional specific interactions such as van der Waals attraction and other generalizations. We discuss some open questions.