Page 128 - Analytical Electrochemistry 2d Ed - Jospeh Wang

4-5 WORKING ELECTRODES 113

where k is the speci®c heterogeneous rate constant. In the limit of purely kinetically
1
controlled process (k < 10 6 ms ) the current becomes independent of the
rotation speed:

i ˆ nFAkC 4-7†
l
Overall, the RDE provides an ef®cient and reproducible mass transport and hence
the analytical measurement can be made with high sensitivity and precision. Such
well-de®ned behavior greatly simpli®es the interpretation of the measurement. The
convective nature of the electrode results also in very short response times. The
detection limits can be lowered via periodic changes in the rotation speed and
isolation of small mass transport-dependent currents from simultaneously ¯owing
surface-controlled background currents. Sinusoidal or square-wave modulations of
the rotation speed are particularly attractive for this task. The rotation-speed
dependence of the limiting current (equation 4-5) can also be used for calculating
the diffusion coef®cient or the surface area. Further details on the RDE can be found
in Adam's book (17).
An extension of the RDE involves an addition of a concentric-ring electrode
surrounding the disk (and separated from it by a small insulating gap) (19). The
resulting rotating ring-disk electrode (RRDE), shown in Figure 4-9b, has been
extremely useful for elucidating various electrode mechanisms (through generation
and detection reactions at the disk and ring, respectively). Because of the electrode
rotation, the product of the disk reaction is hydrodynamically transported across the
insulating gap toward the ring where it can be detected. Such ``collection''
experiments rely on measurements of the collection ef®ciency (N), which is the
ratio of the ring and disk currents:

N ˆ i =i 4-8†
R D
and corresponds to the fraction of the species generated at the disk that is detected at
the ring. (The negative sign arises from the fact that the currents pass in opposite
directions.) Hence, the ``collection'' current is proportional to the ``generation''
current. The value of N re¯ects the dimensions of the electrodes and the gap. Such
experiments are particularly useful for detecting short-lived intermediate species,
generated at the disk and consumed before reaching the ring (i.e., EC mechanism).
Such consumption during the disk-to-ring transition time results in current ratios
smaller than the ``geometric'' N. The RRDE has also been useful for studying ion
transport (doping=undoping) in conducting polymer ®lms.

4-5.2.2 Carbon Electrodes Solid electrodes based on carbon are currently in
widespread use in electroanalysis, primarily because of their broad potential window,
low background current, rich surface chemistry, low cost, chemical inertness, and
suitability for various sensing and detection applications. In contrast, electron-
transfer rates observed at carbon surfaces are often slower than those observed at
metal electrodes. The electron-transfer reactivity is strongly affected by the origin