Page 25 - Analytical Electrochemistry 2d Ed - Jospeh Wang

10 FUNDAMENTAL CONCEPTS

Let us see now what happens in a similar linear scan voltammetric experiment,
but utilizing a stirred solution. Under these conditions, the bulk concentration
(C b; t†) is maintained at a distance d by the stirring. It is not in¯uenced by the
O
surface electron transfer reaction (as long as the ratio of electrode area to solution
volume is small). The slope of the concentration±distance pro®le
‰ C b; t† C 0; t††=dŠ is thus determined solely by the change in the surface
O O
concentration (C 0; t†). Hence, the decrease in C 0; t† during the potential scan
O O
(around E ) results in a sharp rise in the current. When a potential more negative

than E by 118 mV is reached, C 0; t† approaches zero, and a limiting current (i )is

O l
achieved:
nFAD C b; t†
O
O
i ˆ 1-13†
l
d
The resulting voltammogram thus has a sigmoidal (wave) shape. If the stirring
rate (U) is increased, the diffusion layer thickness becomes thinner, according to
B
d ˆ 1-14†
U a
where B and a are constants for a given system. As a result, the concentration
gradient becomes steeper (see Figure 1-5, curve b), thereby increasing the limiting
current. Similar considerations apply to other forced convection systems, e.g., those
relying on solution ¯ow or electrode rotation (see Sections 3-6 and 4-5, respec-
tively). For all of these hydrodynamic systems, the sensitivity of the measurement
can be enhanced by increasing the convection rate.
Initially it was assumed that no solution movement occurs within the diffusion
layer. Actually, a velocity gradient exists in a layer, termed the hydrodynamic
boundary layer (or the Prandtl layer), where the ¯uid velocity increases from zero at
the interface to the constant bulk value (U). The thickness of the hydrodynamic
layer, d , is related to that of the diffusion layer:
H
1=3

D
d  d H 1-15†
n
2
where n is the kinematic viscosity. In aqueous media (with n ' 10 2 cm s 1 and
2
1
D ' 10 5 cm s ), d is 10-fold larger than d, indicating negligible convection
H
within the diffusion layer (Figure 1-6). The above discussion applies to other forced
convection systems, such as ¯ow detectors or rotating electrodes (see Sections 3-6
and 4-5, respectively). d values of 10±50 mm and 100±150 mm are common for
electrode rotation and solution stirring, respectively. Additional means for enhancing
the mass transport and thinning the diffusion layer, including the use of power
ultrasound, heated electrodes, or laser activation, are currently being studied (3,4a).
These methods may simultaneously minimize surface fouling effects, as desired for
retaining surface reactivity.