Contact value relations and density functional theory for the electrical double layer

The recently developed contact-corrected density functional theory is applied to an electric double layer containing a valence and size symmetric electrolyte. The restricted primitive model is used to describe the electrolyte, and a non-polarisable, smooth, planar, uniformly charged hard surface is used to model the electrode. Comparison with Monte Carlo simulation results for this system shows that the theory satisfies the first contact value relation in line with the premise of the approach. Additionally, the theory is found to satisfy the semi-empirical second contact value relation quite closely. This is a welcome result, since no reference is made to this second relation nor is the relation used in the theoretical development. The second contact relation is closely related to the anomalous positive temperature derivative of the double layer capacitance at low temperature, low ion concentration, and low electrode charge, and indeed, the contact-corrected density functional theory predicts this effect.     

Contact condition for the density profiles in spherical and cylindrical double layers

Exact sum rules involving the contact values of the density profiles and bulk osmotic pressure in spherical and cylindrical electric double layers are formulated. When the radius of curvature in these systems tends to infinity, the contact conditions reduce to the well-known contact condition in planar double layer due to Henderson, Blum, and Lebowitz (1979). However, unlike the latter relation, the contact conditions in the non-planar geometries are non-local, and require for their implementation full knowledge of the electrode–ion singlet distribution functions.