Stern combined the idea of both the Helmholtz-Perrin model as well as Gouy-Chapman model and proposed a new model for the electrical double layer, known as the Stern model. It describes that some ions are stuck to the electrode and the rest are scattered in thermal disarray.
According to the stern model, a part of the charge on the solution is stuck close to the electrode in the OHP. These charges are known as the Helmholtz-Perrin charge(qH). The remaining charge is diffusely scattered in the solution, and this is known as the Gouy-Chapman charge(qG). Thus, the stern charge(qS) is the sum of the Helmholtz-Perrin charge and Gouy-Chapman charge as shown below.
The potential varies linearly up to OHP and then decays gradually in the solution as shown in the following figure.
Since there is the separation of charges, there results in potential drops. According to stern mode, there are two potential drops. This can be represented mathematically as:
Moreover, due to different charge regions and the separation of potential regions, there results in the separation of differential capacities.
From this equation, we can say that the total differential capacity of the electrified interface is given by the Helmholtz and Gouy capacities in series.
Conditions of Stern Model
We can discuss two major conditions for the Stern model.
- At high concentrations, the value of CG increases while CH remains constant. Therefore, the total capacity at a higher concentration is equal to the H-P capacity. It means the charge is effectively squeezed in OHP or very near.
- At low concentrations, CG decreases while CH remains constant and the total capacity is equal to G-C capacity. It means the charges are scattered into the solution forming a diffuse region.
The Stern model works well for non-interacting ions i.e The condition for this model to succeed is that ions should not be in close proximity to the electrode and should not be adsorbed to the electrode.
Double layer model Vs Triple layer model
The major difference between the double-layer model and triple layer model is that there is adsorption of ions to the electrode surface, which creates a new layer known as the Inner Helmholtz Plane(IHP) in the triple-layer model, thus adding one more layer of charges than in the double-layer model. This can be illustrated by the following figure.