Tafel equation ($\eta =b{\log }_{10}(j/j_0)$)

An activation-controlled large-overpotential relation $|\eta |=b{\log }_{10}(|j|/j_0)$. The Tafel slope $b$ uses volts per decade when the logarithm is base ten. Exchange current density and operating current density must use the same area convention.

The change in overpotential per decade of current density in the activation-controlled regime of a Tafel equation. In a single-step Butler-Volmer equation with constant transfer coefficient, the anodic slope is $b_a=RT\ln 10/({\alpha }_{a}nF)$, where $T$ is temperature, $R$ is the molar gas constant, $n$ is the number of transferred electrons and $F$ is the Faraday constant. The magnitude of the cathodic slope is $b_c=RT\ln 10/({\alpha }_{c}nF)$. Inferring one from the other requires the model's relation between the two coefficients; the equality ${\alpha }_a+{\alpha }_c=1$ applies to this effective single-step model and need not describe a multistep reaction.