Simple Expressions for Contact Values of Density Profiles in a Planar Double Layer

Exact, or even accurate, results are very valuable for developing improved statistical mechanical theories of, for example, the double layer formed by the ions in an electrolyte near a charged electrode. In this paper we consider the primitive model of the double layer. For simplicity, we assume the electrolyte to be binary and symmetric. In our previous work, we proposed an exact local expression for the contact value of the total ion density, which is valid for all electrode charges, and local expressions for the individual ion density contact values for an electrode with a small charge. Previously, no local expression was known for the individual density contact values at high electrode charge. On the basis of our work and a recent paper by Lou and Lee [J. Chem. Theory Comput. 2009, 5, 1079-1083], we suggest local, empirical expressions for these contact values and test them by comparison with our extensive simulation results. The simulations are performed in the canonical ensemble with the 'charged sheets' method being utilized to treat long-range electrostatic interactions. The simulation results for the various contact quantities are seen to validate the empirical results for all electrode charges treated. The results are also likely to be (i) useful pointers for simulation of more complex, realistic models and (ii) relevant for expreriments in that most electrochemistry occurs near the electrode where the classical Gouy-Chapman-Stern theory may not be adequate.