Surface tension and the potential of zero charge

Trasatti, in Advances in Electrochemistry and Electrochemical Engineering, Vol. 10, ed. by H. Gerischer and C. W. Tobias, Wiley Interscience, New York, 1977. 

For a z-z electrolyte define the excess distribution of the cations and anions through 5n+(x) = n+ x)— no and Sn-(x) = n (x) — n0. Show that 5n+(x) = dn (x) holds for the linear Gouy-Chapman theory, but not for the nonlinear version. 

Consider a point dipole with dipole moment m in an external electric field E oriented along the 2 axis. Choosing a suitable coordinate system, show that the average value of the dipole moment along the direction of the field is  

For mE C k.T the exponentials can be expanded. Show that in this limit  

The Thomas-Fermi model of a metal is similar to the Gouy-Chapman theory for electrolytes. In this model the surface-charge density o is 

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