Electrocapillary equation relative surface excess

Returning now to the electrocapillary equation, (13.1.31), we find that the relative surface excess of potassium ion at the interface considered there is given by (1, 6-8)... 

If the concept of partial charge is introduced into the electrocapillary equation one gets the following result for the relative surface excess of the adsorbed ion ... 

These equations clearly show that the the slope of the electrocapillary curve of nonpolarized interface does not give the surface charge density but the relative surface excess of ionic components, as defined by Eq. (18) for case Ilb. In other words, the electrocapillary maximum potential does not correspond to the potential of zero charge . An approach to investigate the surface charge density and the double layer structure may be predicted as follows. When the values of the second terms of the right-hand sides of Eq. (18) (that is, the and Tnb values), are known or estimated on reasonable argument, Fd and F(so that by Eq. (19)) can be found from the slope... 

Relationship (19.4), known as Lippmann equation, permits the evaluation of the excess of charge at the electrode surface from the electrocapillary curve y — y 4 )- Fot interfaces relatively simple such as the mercury/lM aqueous KCl interface, Eqn (19.4) results in a parabola with a maximum at dy/d0 = 0, i.e., for null charge at the electrode surface. This condition corresponds to the potential of zero charge (Pp ) for the electrode in the electrolyte solution. 

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