Simple extension of the Gouy–Chapman theory including hard sphere effects.: Diffuse layer contribution to the differential capacity curves for the electrode ∣ electrolyte interface

An extension of the Gouy–Chapman theory based on a field theoretical approach including the hard sphere effect is presented. This approach focuses on the influence of ions on the properties of the electrode ∣ electrolyte interface. The Hamiltonian consists of the electrostatic energy and the Helmholtz free energy function for the hard sphere mixtures. The calculated differential capacity curves depend on the ionic sizes and concentration. In dilute electrolytes, close to the potential of zero charge we observe the Gouy–Chapman minimum which becomes a maximum when the concentration of electrolyte increases. This minimum is surrounded by two maxima. The capacity at these maxima depends on the size of ions and their concentration in the solution. At high charge densities the ionic density becomes constant and the capacity depends only on the size of the counterion which counterbalances the charge on the electrode, being independent of its concentration. These features are observed on the capacity curves obtained for various electrolytes on various metals.