Butler-Volmer Equation
High-Field Approximation
As the overpotential becomes more negative the reverse or anodic current becomes less significant so that the total or net current density approaches the condition of purely cathodic current.
In Figure 1 the solid red line is a plot of the net current density and the dotted blue line is a plot of cathodic current density alone. It is apparent that they tend to merge at high overpotential.
Figure 1.
Table 1 demonstrates quantitatively how small the difference between the total and cathodic becomes at an overpotential of 1.5V for a system with a=.5, i0=1x10-5 A cm-2, 25° C.
Table 1.
Low-field approximation
At very low overpotential the Butler-Volmer equation reduces to
.
The linear low-field approximation is plotted along with the total current density in Figure 2. The dotted blue line is the plot of the linear approximation.
Figure 2.