1.4 PEM Fuel Cell Electrochemistry
1.4.5 Cyclic Voltammetry
Cyclic voltammetry is the most useful technique in electrochemistry. It can rapidly provide qualitative information about electrochemical reactions, such as thermodynamics and kinetics.
In cyclic voltammetry, the potential of the working electrode is scanned linearly from an initial to a vertex value, and then the scan is reversed. The electrochemical response of the target species with applied potential during the forward and reverse scans can be obtained from the scan cycle. Figure 1.14 shows
a schematic illustration of the potential changes in cyclic voltammetric experiments.
Figure 1.14. Potential–time excitation signals in a cyclic voltammetric experiment [19].
(From Wang J. Analytical electrochemistry. ©2006 Wiley-VCH. Reproduced with permission.)
Assuming that a redox species exists only in oxidized form (O) in the solution, as the potential scans from being more positive than the thermodynamic potential of the redox species to being a negative potential, there is initially no Faradaic current flow. As the electrode potential approaches E0, reduction of O starts and the reduction current begins to flow. As the potential continues to become more negative, the cathodic current increases until it reaches a peak and then starts to decrease. At the peak current, the reaction speed is determined by the mass transfer rate of O to the electrode surface. The decline of the current after the peak is due to the expansion of the diffusion layer near the electrode surface. As time passes, the diffusion layer became much thicker, leading to a decrease in the cathodic current.
The current decline is t−12-dependent, in accordance with Equation 1.48 in Section 1.4.4. After the potential is scanned at least 90/n mV negative to the peak potential, the scan is reversed. In the reverse cycle, the reduced species R, formed in the forward potential sweep, is oxidized back to O. Again, an oxidation peak and a decline of the peak can be observed. The visually represented response of current versus potential is called a cyclic voltammogram.
Figure 1.15 shows a potential sweep cycle, the electrochemical response with the cycle, and the surface concentration profile in the potential sweep. A cyclic voltammogram can give information about the thermodynamic potential, diffusion coefficient, kinetics, and reversibility of the reaction.
The extent to which qualitative parameters can be extracted from the cyclic voltammogram is dependent on its reversibility. Different equations have been obtained for different systems.
Forward
24 X-Z. Yuan, C. Song, H. Wang and J. Zhang
Figure 1.15. Typical cyclic voltammogram for a reversible redox process [19]. (From Wang J., Analytical electrochemistry. ©2006 Wiley-VCH. Reproduced with permission.)
For a reversible system, the Randles–Sevcik equation gives the peak current (ip) for a reversible couple:
3
1/ 2 3/ 2 1/ 2 1/ 2
0.2263( )
p O O
i F n AD C v
= RT (1.49)
where F, R, and T have their usual meanings, n is the electron number, A is the electrode area, DO is the diffusion coefficient of O, CO is the concentration of O in the solution, and ν is the potential scan rate.
At 25°C, with A in cm2, DO in cm2/s, CO in mol/cm3, ν in V/s, and ip in A, the equation becomes
5 3/ 2 1/ 2 1/ 2
(2.69 10 )
p o O
i = × n AD C v (1.50)
Forward
The reversible electrochemical process is characterized by the following features:
1. The peak current is proportional to ν1/2, and ipc ipa =1. 2. The peak position does not change with the scan rate.
3. Peak separation between the cathodic peak potential and the anodic potential (ΔEp) is a constant given by the following equation:
, ,
0.059
p p a p c 2.3 E E E RT
nF n
Δ = − = = V (at 25°C) (1.51)
where Ep,aand Ep,care the anodic and cathodic peak potential, respectively. Thus, from a cyclic voltammogram, the electron number, diffusion coefficient, electrode area, and electroactive species concentration can be obtained.
The thermodynamic potential of the redox reaction can also be obtained by averaging the anodic peak potential and the cathodic peak potential. However, for a reversible system, kinetic parameters such as reaction rate cannot be obtained because the reaction rates for both forward and backward reactions are extremely fast.
For an irreversible system (O + ne–→R), the peak current is reduced and given by the following equation:
5 1/ 2 1/ 2 1/ 2
(2.99 10 ) ( )
p a o O
i = × n nα AD C v (1.52)
where α is the charge transfer coefficient and na is the electron number involved in the charge transfer step. The peak current is proportional to the square root of the scan rate. However, it is only about 80% of its reversible counterpart, assuming an α of 0.5. The αna value can be obtained from the peak separation between the peak potential and the half-wave potential (Ep/2). In the irreversible system,
Ep−Ep/ 2 =1.857RT αnaF =47.7
αna mV at 25°C (1.53)
The peak potential is dependent on the scan rate, as given in the following equation:
0
0 1/ 2
[0.78 ln 1/ 2 ln( a ) ]
p
a
RT k n Fv
E E
n F D RT
α
= −α − + (1.54)
where k0 is the electrochemical reaction rate. It can be seen clearly that a cathodic shift of Ep by an amount 1.15RT/αnaF or 30/αna mV can be obtained from the slope of Ep versus logν.
The relationship between the peak current and the peak potential is given by the following equation:
26 X-Z. Yuan, C. Song, H. Wang and J. Zhang
ip=0.227nFACk0exp[−αnaF
RT (Ep−E0)] (1.55)
The parameters αna and k0 can be obtained from the plot of ln(ip) versus Ep–E0 determined at different scan rates from the slope and intercept, respectively.
For a quasi-reversible process, both charge transfer and mass transfer affect the current. The shape of the cyclic voltammogram is a function of k0/ πaD(where a
= nFν/RT). The peak separation between the anodic and cathodic peaks can give information about k0.
The reversibility of electrochemical reactions is determined by the reaction rates: for a reversible reaction, k0 ≥ 0.3ν1/2 cm/s, for a quasi-reversible reaction, 0.3ν1/2 > k0 ≥ 2 × 10–5ν1/2 cm/s, while for an irreversible reaction, k0 < 2 × 10–5ν1/2 cm/s. Figure 1.16 shows the cyclic voltammograms for irreversible and quasi- reversible redox processes.
Figure 1.16. Cyclic voltammograms for irreversible (A) and quasi-reversible (B) redox processes [19]. (From Wang J. Analytical electrochemistry. ©2006 Wiley-VCH.
Reproduced with permission.)