Limitations of the Poisson-Boltzmann theory

In the treatment of the diffuse electric double layer, several assumptions were made which lead to imperfections [60]  

Despite these strong assumptions, the Poisson-Boltzmann theory describes electric double layers surprisingly well. The reason is that errors lead to opposite effects and compensate each other. Including non-coulombic interactions leads to an increase of the ion concentration at the surface and a reduced surface potential. On the other hand, taking the finite size of the ions into account leads to a lower ion concentration at the surface and thus an increased surface potential. A reduction of the dielectric permittivity due to the electric field increases its range but at the same time reduces the surface potential because less ions dissociate or adsorb. 

Fortunately, there is a relatively simple semi-empirical extension of the Gouy-Chapman theory, which accounts for most experimental observations. This extension was proposed by Stern.7 

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