Potential Relations and Mass Transport

In the above, we assumed that the surface concentrations, Cqx and CRed, do not depend on the current that flows at the electrode. Then, the reduction current increases exponentially to infinity with the negative shift of the potential, while the oxidation current tends to increase exponentially to infinity with the positive shift of the potential (Fig. 5.3). However, in reality, such infinite increases in current do not occur. For example, when a reduction current flows, Ox at the electrode surface is consumed to generate Red and the surface concentration of Ox becomes lower than that in the bulk of the solution. Then, a concentration gradient is formed near the electrode surface and Ox is transported from the bulk of the solution toward the electrode surface. Inversely, the surface concentration of Red be- 

Kf=nFAD0x/S and Kd= nFADRed/S Kf and Kt, are constant if S is constant. 3) From Eq. (5.4), which applies to a reversible electrode process, Cox approaches zero at E Eeq, while approaches zero at E Eeq. If we express the currents under these conditions by ig and i i, respectively, 

3) If the thickness of the diffusion layer (d) is time-independent, a steady limiting current is obtained. However, if the electrode reaction occurs at a stationary electrode that is kept at a constant potential, the thickness of the diffusion layer increases with time by the relation S (7iDt)1/2, where t is the time after the 

The current-potential relation in Eq. (5.9) is shown by curves 1 to 3 in Fig. 5.6. Curve 2 is for CRed=0 and curve 3 is for COx=0. The curves are S-shaped and the currents at potentials negative enough and positive enough are potential-indepen-dent, being equal to ig and igi, respectively. These currents are called limiting currents and are proportional to the bulk concentrations of Ox and Red, respectively [Eqs (5.7) and (5.8)]. The potential at i = (ig + ibi)/2 is equal to E1/2 in Eq. (5.10) and is called the half-wave potential. Apparently from Eq. (5.10), the half-wave potential is independent of the concentrations of Ox and Red and is almost equal to the standard redox potential E°, which is specific to each redox system. From the facts that the limiting current is proportional to the concentration of the electroactive species and that the half-wave potential is specific to the redox system under study, the current-potential relation can be used both in quantitative and qualitative analyses. 

Curves 4 and 4 in Fig. 5.6 show an example of the current-potential relation obtained for an irreversible electrode process. For a reversible electrode process, the reduction wave appears at the same potential as the oxidation wave, giving an oxidation-reduction wave if both Ox and Red exist in the solution (curves 1, 2 and 3 in Fig. 5.6). For an irreversible process, however, the reduction wave (curve 4) is clearly separated from the oxidation wave (curve 4 ), although the limiting currents for the two waves are the same as those in the reversible process. The cur-rent-potential relation for the irreversible reduction process can be expressed by 

---