6. Electrochemical reaction kinetics

6.3. Overpotentials

We have already introduced the term overpotential* and defined this as the deviation from the equilibrium potential, \eta=E-E_{eq} . In electrochemical literature, it is customary to split overpotential into activation (or charge transfer) and concentration overpotentials. If an electrode reaction were reversible, i.e. infinitely rapid (ideally non-polarizable electrode) and mass transfer were also infinitely rapid, the electrode potential would stay at its thermodynamic equilibrium value as determined by the Nernst equation, and no overpotential would exist. Overpotential means that the higher the current we are drawing out of an electrochemical cell, the higher the voltage needed above its thermodynamic cell voltage. In the case of a battery, overpotential means that when current is flowing we cannot utilize its full thermodynamic voltage (terminal voltage), it is instead lowered by the amount of overpotentials.

Tafel equations actually define the activation overpotential \eta_a . Let’s write, for example, Equation (6.30) as

\displaystyle \eta_a=\frac{RT}{\alpha nF}\text{ln}\frac{i}{i_0} (6.35)

which shows that the lower i0 is, the higher \eta_a is. We found earlier that current with \chi kin = 0.1 is under mass transfer control; hence it represents pure concentration overpotential. Subtracting the overpotential of this curve from the rest of the curves in Figure 6.4, we obtain the i-\eta_a curves in Figure 6.5, in other words the activation overpotential is the deviation from the y axis, depending on the current.

The origin of the concentration overpotential is in concentration polarization. Since the surface concentration is lower than the bulk concentration, a higher voltage is needed to draw current out of the cell. Equation (6.27) can be rewritten in the following form:

\displaystyle\frac{i}{i_0}=\text{exp}\left[\alpha nf\eta_a+\text{ln}\frac{c_{\text{R}}^s}{c_{\text{R}}^b}\right]-\text{exp}\left[(\alpha-1)nf\eta_a+\text{ln}\frac{c_{\text{O}}^s}{c_{\text{O}}^b}\right] (6.36)

that shows that the concentration overpotential, \eta_c , is of the form

\displaystyle\eta_c=\frac{RT}{nF}\text{ln}\frac{c^s}{c^b} (6.37)

Figure 6.5. Current-overpotential curves after subtracting for the concentration overpotential. \chi kin = 10 - 104 , \alpha = 0.5, n = 1 or 2.

If an electrode reaction is accompanied by homogeneous reactions (e.g. EC/CE mechanism) they make their contribution, known as the reaction overpotential. When there is a phase formation on the electrode, such as the deposition of metal, the formation and growth of the phase nuclei cause the nucleation overpotential that depends on surface chemical issues, including the geometry of the nuclei. Reaction and nucleation overpotentials are not addressed in this book in a closer detail.

It is necessary to remember that in addition to overpotentials an electrochemical cell always has ohmic losses due to the limited conductivity of electrolytes (see Chapter 3 and 4).


*The expression overvoltage is also used widely.