Tafel equation

The Tafel equation relates the rate of an electrochemical reaction to the overpotential. Where an electrochemical reaction occurs in two "half reactions" on separate electrodes, the Tafel equation is applied to each electrode separately. The Tafel equation was first deduced experimentally and was later shown to have a theoretical justification. On a single electrode the Tafel equation can be stated simply as

$$ V=A\times ln\left(\frac{i}{i_0}\right) $$

where $$V$$ is the overpotential, $$A$$ is the so called "Tafel slope", $$i$$ is the current, and $$i_0$$ is the so called "exchange current". This equation assumes that the reverse reaction rate is negligible compared to the forward reaction rate.

The Tafel slope is measured experimentally however it can be shown theoretically when the dominant reaction mechanism involves the transfer of a single electron that

$$ \frac{kT}{e} < A $$

where A is defined as

$$ A = \frac{kT}{e\alpha}$$

where $$k$$ is Boltzmann's constant, $$T$$ is the thermodynamic temperature, $$e$$ is the elementary electric charge, and $$\alpha$$ is the so called "charge transfer coefficient" the value of which must be between 0 and 1.

The exchange current is the rate of reaction at the reversible potential (when overpotential is zero by definition). At the reversible potential the reaction is in equilibrium meaning that the forward and reverse reactions progress at the same rates. This rate is the exchange current.