Overvoltage and the Structure of the Electrical Double Layer at a Hydrogen Electrode

The theory of absolute reaction rates applied to electrode processes leads to the equation $$\mathrm{s=(kT/h)}\exp {\mathrm{(-\Delta F}}^{*}\mathrm{/RT)}\exp \mathrm{(\alpha V}\mathfrak{F}\mathrm{/RT)}$$ for the specific rate of discharge of ions. The question arises as to whether V should be the actual potential at the electrode or only the overvoltage. In the case of hydrogen ion discharge, it is found experimentally that the overvoltage should be used. On the other hand, the theory in its simplest form requires V to be the total potential. This paradox can be resolved by postulating the existence of two different electrical double layers at the electrode surface, and two corresponding energy barriers over which the protons must pass. Provided that the barrier nearer the electrode is the higher, the overvoltage is essentially established across this layer, while the variation in equilibrium potential caused by variations in the hydrogen ion concentration of the solution is established across the outer double layer. Since the rate of discharge is determined by the potential difference across the inner double layer, the rate is determined by the overvoltage, and not by the total potential. The nature of these two energy barriers is also discussed. Both barriers may correspond to transfer of protons from water molecule to water molecule, or one may correspond to the actual discharge process in which a neutral hydrogen atom is formed. It does not yet seem to be possible to decide between these two alternatives, either theoretically or experimentally, but it seems most probable that both barriers correspond to proton transfers from water molecule to water molecule.