Galvani Potential Between Two Metals
First, consider the Galvani potential between two metals. When two metals are electrically isolated from each other, an arbitrary potential difference may exist between them. However, when two different metals are brought into electronic contact, electrons will flow from the metal with a lower work function to the metal with the higher work function until the electrochemical potential of the electrons in the bulk of both phases are equal. The actual numbers of electrons that passes between the two phases is small, and the occupancy of the Fermi levels is practically unaffected. Rather, this small increase or decrease in charge results in a shift in all the energy levels in the metals. An electrical double layer is formed at the interface between the two phases.
The equality of the electrochemical potential between the two different phases in contact can be written as:
where:
- is the electrochemical potential
- j denotes the species which are the carrier of electrical current in the system (which are electrons in metals)
- (1) and (2) denote phase 1 and phase 2, respectively.
Now, the electrochemical potential of a species is defined as a sum of its chemical potential and the local electrostatic potential:
where:
- μ is the chemical potential
- z is the electrical charge carried by a single charge carrier (unity for electrons)
- F is the Faraday constant
- Φ is the electrostatic potential
From the two equations above:
where the difference on the left-hand side is the Galvani potential difference between the phases (1) and (2). Thus, the Galvani potential difference is determined entirely by chemical identity of the two phases; specifically by the difference of the chemical potential of the charge carriers in the two phases.
The Galvani potential difference between an electrode and electrolyte (or between other two electrically conductive phases) forms in an analogous fashion, although the chemical potentials in the equation above may need to include all species involved in the electrochemical reaction at the interface.
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