The Butler—Volmer and Tafel equations

Substituting j0 in eqn. (76) into eqn. (74) with r = E Ee gives the Butler—Volmer equation 

Equation (80) relates the current density that flows through the electrode—electrolyte interface due to the electrode reaction to the overpotential in terms of two kinetic parameters, the exchange current density, j0, and the transfer coefficient, a. 

In deriving eqn. (80), limitations due to mass transport at the interface were not considered. Strictly speaking, this is not realistic and as the reaction rate increases with overpotential in each direction a variation of the concentrations of reactant and product at the surface operates and concentration polarization becomes more important. Each exponential expression in eqn. (80) must be multiplied by the ratio of surface to bulk concentrations, ci s/ci b. The effect of mass transfer in electrode kinetics has been discussed in Sect. 2.4. 

As seen in Sect. 3.1, the transfer coefficient 0 a 1, introduced in electrokinetics by Erdey-Gruz and Volmer [32b] for the hydrogen electrode reaction, measures the symmetry of the free energy curves at this intersection in the transition state. In Fig. 5, it can be seen that the transfer coefficient determines the rate at which j grows exponentially with 77 for a constant n. 

At high negative overpotentials, 17 0, the anodic reaction can be neglected, and from eqn. (80) 

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