A modified Poisson–Boltzmann study of the singlet ion distribution at contact with the electrode for a planar electric double layer

Abstract

The properties of the singlet ion distributions at and around contact in a restricted primitive model double layer are characterized in the modified Poisson–Boltzmann theory. Comparisons are made with the corresponding exact Monte Carlo simulation data, the results from the Gouy–Chapman–Stern theory coupled to an exclusion volume term, and the mean spherical approximation. Particular emphasis is given to the behaviour of the theoretical predictions in relation to the contact value theorem involving the charge profile. The simultaneous behaviour of the coion and counterion contact values is also examined. The performance of the modified Poisson–Boltzmann theory in regard to the contact value theorems is very reasonable with the contact characteristics showing semi-quantitative or better agreement overall with the simulation results. The exclusion-volume-treated Gouy–Chapman– Stern theory reveals a fortuitous cancellation of errors, while the mean spherical approximation is poor.