3 independently observed that capacitance was not a constant and that it depended on the applied potential and the ionic concentration. According to this theory counterions that are not strongly bound to the surface, unlike the potential-determining ions, form not a plane but diffuse layer. The Gouy-Chapman model made significant improvements by introducing a diffuse model of the double layer. In this model the charge distribution of ions as a function of distance from the metal surface allows Maxwell-Boltzmann statistics to be applied. Thus the electric potential decreases exponentially away from the surface of the fluid bulk (Figure 1.2) [1].
1.2. Scheme of Gouy-Chapman construction of double layer
Gouy-Chapman model give such conclusions as :) The concentration of counterions decreases with increasing distance from the surfaceand the thickness of the diffusion layer decreases in inverse proportion;) Ions, which is more have greater effect on increasing the thickness of the diffusion layer at the same concentration [3].
1.3 Stern Theory
Gouy-Chapman model fails for highly charged double layers. In 1 924 Otto Stern suggested theory combining Helmholtz with Gouy-Chapman. In Stern s model, some ions adhere to the electrode as suggested by Helmholtz, giving an internal Stern layer, while some form a Gouy-Chapman diffuse layer. to Stern theory formation of a counterions layer determined not only by their electrostatic interaction with the charged surface, but also by adsorption. The theory also takes into account that no matter how small counterions are, they still have a finite size and consequently ions closest approach to the electrode is on the order of the ionic radius [3]. The ratio between the electrostatic and adsorption forces determines the concentration and even charge of the ion at the surface. Electric double layer structure in accordance with the theory of Stern shown in Figure 1.3.
1.3. Electric double layer structure according to the theory of Stern
The Stern model had its own limitations, effectively modeling ions as point charges, assuming all significant interactions in the diffuse layer are Coulombic, assuming dielectric permittivity to be constant throughout the double layer and that fluid viscosity is constant above the slipping plane. theory provided an explanation for the phenomenon of surface overcharging.
. 4 Grahame Theory
. C. Grahame modified Stern theory in 1947. [9] He proposed that some ionic or uncharged species can penetrate the Stern layer, although the closest approach to the electrode is normally occupied by solvent molecules. This could occur if ions lose their solvation shell as they approach the electrode. He called ions in direct contact with the electrode specifically adsorbed ions raquo ;. This model proposed the existence of three regions. The inner Helmholtz plane (IHP) plane passes through the centres of the specifically adsorbed ions. The outer Helmholtz plane (OHP) passes through the centres of solvated ions at the distance of their closest approach to the electrode. Finally the diffuse layer is the region beyond the outer Helmholtz plane (OHP).
. 5 Bockris/Devanthan/Mьller Theory
1 963 J. O'M. Bockris, MAV Devanthan and K. Alex Mьller proposed the BDM model of the double-layer that included the action of the solvent in the interface. They suggested that the attached molecules of the solvent, such as water, would have a fixed alignment to the electrode surface. This first layer of solvent molecules displays a strong orientation to the electric field depending on the charge. This orientation has great influence on the permittivity of the solvent that varies with field strength. The inner Helmholtz plane (IHP) passes through the centers of these molecules. Specifically adsorbed, partially solvated ions appear in this layer. The solvated ions of the electrolyte are outside the IHP. Through the centers of these ions pass the outer Helmholtz plane (OHP). The diffuse layer is the region beyond the OHP. The BDM model now is most commonly used [1] .Figure 2.4. depicted scheme of DL according Bockris/Devanthan/Mьller theory.
Figure 2.4. Schematic representation of a double layer on an electrode (BMD) model. 1. Inner Helmholtz plane, (IHP), 2. Outer Helmholtz plane (OHP), 3. Diffuse layer, 4. Solvated ions (cations) 5. Specifically adsorbed ions (redox ion, which contributes to the pseudocapacitance), 6. Molecules of the electrolyte solvent
1.6 Trasatti/Buzzanca Theory
Further research with double layers on ruthenium ...
