# Constant work function although changing Fermi energy

I'm working with the following book “Interfacial Electrochemistry” (2nd Edition) written by Wolfgang Schmickler and Elizabeth Santos and I'm trying to understand the process described in section "Absolute electrode potential". You can find the chapter here.

There the work function is defined as follows:

For electrons in a metal the work function Phi is defined as the minimum work required to take an electron from inside the metal to a place just outside. [...] The work function is the negative of the Fermi level, provided the reference point for the latter is chosen just outside the metal surface.

“Just outside” means (mentioned in an earlier chapter):

A postion very close to the surface, but so far away that the image interaction with the phase can be ignored.

The process I'm refering to is described on page 31:

[...] let us first consider two metals, I and II, of different chemical composition and different work functions ΦI and ΦII. When the two metals are brought into contact, their Fermi levels must become equal. Hence electrons flow from the metal with the lower work function to that with the higher one, so that a small dipole layer is established at the contact, which gives rise to a difference in the outer potentials of the two phases (see Fig. 4.1).

I don't understand the last half sentence. Why do the outer potentials change and not the work functions? E.g. I'm decreasing the Fermi Level of metal 1, hence (according to the definition) I'm increasing the work function.

These work functions and outer potentials are relative to the adjoining surfaces. The electrons flow to the metal with the lower Fermi energy and build a dipole at the interface. This could have impact on the work function.

Because of the same reason I could understand why the outer potentials change after joining the metals. I just don't get why the work function stays the same.

Thanks for your help!

By analogy, consider two separate waterfalls, one with a height $$h_1$$ and one with a height $$h_2$$ relative to the same zero point in potential energy. The potential energies for water going over the waterfalls are different. Now, put the waterfalls in contact such that their starting (top) points are at the same height. This is equivalent to putting the Fermi energies at the same position. For the water (electrons) to reach the same zero potential (vacuum level), the water in the shorter waterfall must drop through an additional (gravitational) potential energy. The individual potential energy differences for water falling from the tall or short waterfall remain the same as the initial condition. So too, the work functions for each metal remain fixed when the metals contact each other at the same Fermi energy. It is only that, an electron flowing from the material with the lower work function to the material with the higher work function must go through an additional potential energy difference.