Current Equations - Part 2
In a state of equilibrium between a metal electrode and a solution containing an electroactive solute there is no net current and the potential difference between the electrode and bulk solution phase can be called Dfeq. Yet there will be electron transfer processes taking place in opposite directions at equal rates. This is referred to as the equilibrium exchange current density.
The exchange current density is is function of the electrode material and the electroactive species in solution. According to activated complex theory the current density is an exponential function of the potential difference. For the reduction of the electron acceptor species A to the donator D, A+ + e- =D, at equilibrium the reduction and oxidation current densities are equal
which can also be written
.
If the concentrations of A and D are equal we can designate both the anodic and cathodic current densities by the equilibrium exchange current density i0.
In the non-equilibrium case we can write
or it can be simplified by substituting i0 in the equation
where h is the difference between the non-equilibrium potential difference and the equilibrium potential difference. This is called the overpotential h. This is known as the Butler-Volmer equation. Given the hyperbolic sine function
the current equation can also be written as
.