Helmholtz double layer current density

It is to be noted that the Helmholtz double layer plays a significant role in concentration polarization since the concentration of the ions on the electrode surface, and the diffusion of ions from the bulk of the solution into the Helmholtz plane are contributing factors to the limiting current density. This situation may be visualized as shown below ... 

For intermediate ionic strengths, because of higher repulsion, no current maxima occur, i.e., the current density depends mainly on the amount of DNA molecules screened by counterions and their mobility inside the loose adsorption layer. Therefore surface denaturation, ° ° favored by the energy of adsorption, seems unlikely, whereas the high field strength ( 10 V cm ) in 1 M salt solution is effective just in the Helmholtz double layer region (<0.5 nm), i.e., this concerns a small part of the few segments adsorbed and influences merely less than 1 % of the whole DNA molecule, which extends over the diffuse double layer into the bulk of solution. ... 

If the repulsion between the ion and the electrode is small, the discharge occurs in the Helmholtz double layer, i.e., in the first layer of solvent molecules attached to the metal surface. In this layer befor discharge the ion is making vibrations with a low frequency <<1) in a direction x normal to the metal surface. The current density equation (108.IV) then becomes... 

If the repulsion between the ion and the electrode is strong, the discharge may occur at a distance x of the metal surface which is greater than the tickness of the Helmholtz double layer (x>d 1A), Before discharge the ion approaches the electrode by a translation motion with a mean velocity v which is influenced by the electric field. Then, the current density equation can be written as... 

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