In 1910 and 1913, Gouy and Chapman both observed that capacitance was not a constant and it depended on the applied potential. Gouy suggested that the counter ions are not rigidly held, but tend to diffuse into the liquid phase until the counter potential set up by this departure restricts this tendency. (LucaRighetto, 1995)The kinetic energy of the counter ions will, in part, affect the thickness of the resulting diffuse double layer. Gouy and Chapman developed the theories by adding the diffuse layer, the detail structure is shown in Fig 3(b). The change in concentration of the counter ions near a charge surface follows the Boltzman distribution (Stojek, 2002).
The concentration of the oppositely charged ions decreasing with distance from the surface, this is called the diffuse double layer.
Although this theory considered the ion diffusion, it is still not entirely accurate. In the experiment, the double layer thickness is generally found to be greater than calculated valve. This may result by the Boltzman distribution cause this equation made an assumption on the molar concentration, the approximation is applicable for bulk solution but not to be true near a charge surface.