5.4 Stern Modification

The potential distribution in the vicinity of the electrode-electrolyte interface can be approximated by the electrical double layer model. However, experimental data show deviations from the predicted values for the double layer charge and capacitance [190]. It was observed that the Gouy-Chapmann model overestimates the interface charge, and thus the capacitance for high-concentration electrolytes. Stern recognized that the ions in the electrolyte exhibit a certain ionic radius and, therefore, cannot approach the electrode surface closer than their ionic radius allows. This distance of closest approach is called the Outer Helmholtz Plane (OHP) [192]. The shell of water molecules around an ion also contributes to the distance of the closest approach. An extensive amount of energy would be necessary to release the watermolecules from the aqueous shell of the ion. Therefore, close to the electrodes surface, a zone depleted of ionic charges will emerge and an additional constant contribution to the total capacitance will evolve. This so called Stern capacitance has a typical value of $20\,\frac{\mu\mathrm{F}}{\mathrm{cm}^{2}}$. However, additionally to the Gouy-Chapmann and Stern contributions to the potential profile, several other effects exist. In general this effects are small and can be ignored. Some of these effects are (shown in Fig. 5.2):

Figure 5.2: The different surface effects. The (non-) specific adsorbtion, due to (partial) release of the solvation shell and conjoint closer approach to the interface, the so called IHP, is depicted with blue circles. The effect of surface complexation, due to the high affinity of attracting counter ions, is shown by the green circle. The Stern layer ends at the OHP, the zone without counter ions exhibiting their full water shell (depicted with red circles, surrounded by small light blue circles), and is continued by the Gouy-Chapman layer.

• Specific Adsorbtion of Ions on the Surface. This is caused by (partially) freeing the ions from their solvation shell and thus allowing them to be closer to the interface than the OHP. This new radius of closest approach is called Inner Helmholtz Plane (IHP). The total model, handling IHP and OHP, is called Gouy-Chapman-Stern-Graham model [191].
• Non-Specific Adsorbtion. Here, the ions keep their solvation shell, but are adsorbed onto the surface due to distant coulombic attraction.
• Polarization of Solvent. In general, the effects of electric field weakening due to the dipole moment of the water molecules is handled by adjusting the relative permittivity. This works well for the bulk, but in the vicinity of the surface many water molecules are not able to adjust to the electric field. So the relative permittivity will not be the same as for the bulk and can cause differences in the results (e.g. potential and charge distribution). However, at high electric fields, the description of the dielectric constant can become more complicate, due to dielectric saturation^5.2.
• Surface Complexation. Many charged surfaces exhibit an increased attraction to counter ions and enable the formation of complex compounds at the surface, changing the potential in their neighborhood.

Footnotes

... saturation^5.2

Polar fluids experience at high electric fields a non linear decrease in their permittivity [195].