The point ion modified Poisson-Boltzmann theory for a planar electric double layer with different permittivities for the electrode, inner layer and diffuse layer

The planar electric double layer is modelled by an electrode, inner layer and diffuse layer whose constant permittivities differ. A point ion modified Poisson-Boltzmann analysis is made of the model with the ions in the diffuse layer having a distance of closest approach to the electrode, which is greater than the inner layer thickness and mimics the ion radius of a primitive model electrolyte. Comparisons are made with existing Monte Carlo simulations for uncharged and charged electrodes. For 1:1 and 2:1 electrolytes with a charged electrode, the modified Poisson-Boltzmann theory successfully predicts the singlet ion normalised density functions and the mean electrostatic potential. With the uncharged electrode, the neglect of ion size is more critical and the theoretical predictions are now poor at the higher concentrations.