Page 46 - Analytical Electrochemistry 2d Ed - Jospeh Wang

2-1 CYCLIC VOLTAMMETRY 31

2-1.1.1 Reversible Systems The peak current for a reversible couple (at

25 C), is given by the Randles±Sevcik equation:
5 3=2 1=2 1=2
i ˆ 2:69 10 † n ACD v 2-1†
p
2
where n is the number of electrons, A is the electrode area (in cm ), C is the
3
1
2
concentration (in mol cm ), D is the diffusion coef®cient (in cm s ), and v is the
1
scan rate (in V s ). Accordingly, the current is directly proportional to concentra-
tion and increases with the square root of the scan rate. The ratio of the reverse-to-
forward peak currents, i =i , is unity for a simple reversible couple. As will be
p;r p;f
discussed in the following sections, this peak ratio can be strongly affected by
chemical reactions coupled to the redox process. The current peaks are commonly
measured by extrapolating the preceding baseline current.
The position of the peaks on the potential axis (E ) is related to the formal
p
potential of the redox process. The formal potential for a reversible couple is
centered between E p;a and E :
p;c
E p;a ‡ E p;c

E ˆ 2-2†
2
The separation between the peak potentials (for a reversible couple) is given by

0:059
DE ˆ E p;a E p;c ˆ V 2-3†
p
n
Thus, the peak separation can be used to determine the number of electrons
transferred, and as a criterion for a Nernstian behavior. Accordingly, a fast one-
electron process exhibits a DE of about 59 mV. Both the cathodic and anodic peak
p
potentials are independent of the scan rate. It is possible to relate the half-peak
potential (E p=2 , where the current is half of the peak current) to the polarographic
half-wave potential, E 1=2 :
0:028
E p=2 ˆ E 1=2 V 2-4†
n

(The sign is positive for a reduction process.)
For multielectron-transfer (reversible) processes, the cyclic voltammogram

consists of several distinct peaks if the E values for the individual steps are
successively higher and are well separated. An example of such a mechanism is the
six-step reduction of the fullerenes C 60 and C 70 to yield the hexaanion products C 6
60
6
and C . Such six successive reduction peaks are observed in Figure 2-4.
70
The situation is very different when the redox reaction is slow or coupled with a
chemical reaction. Indeed, it is these ``nonideal'' processes that are usually of
greatest chemical interest and for which the diagnostic power of cyclic voltammetry
is most useful. Such information is usually obtained by comparing the experimental