Pine Research MSR 636A, User Manual, Page: 142 / 176

136
The diffusion layer is much thinner than the hydrodynamic layer. The diffusion
layer thickness (
δ
F
) can be approximated as follows,
2 / 1 6 / 1
  ω v D 1.61 δ 1/3
F
F
in terms of the diffusion coefficient ( D
F
) of the molecule or ion. For a molecule or
ion with a typical diffusion coefficient ( D
F
 10
-5
cm
2
/sec) in an aqueous solution,
the diffusion layer is about twenty times thinner than the stagnant layer
(
δ
F
 0.05 δ
H
).
The first mathematical treatment of convection and diffusion towards a rotating
disk electrode was given by Levich. Considering the case where only the oxidized
form of a molecule (or ion) of interest is initially present in the electrochemical cell,
the cathodic limiting current (i
LC
) observed at a rotating disk electrode is given by
the Levich equation,
[2,9]
i
LC
= 0.620 n F A D
2/3
ν
– 1/6
C
O
ω
1/2
in terms of the concentration ( C
O
) of the oxidized form in the solution, the Faraday
constant ( F = 96485 coulombs per mole), the electrode area ( A ), the kinematic
viscosity of the solution ( ν ), the diffusion coefficient ( D ) of the oxidized form, and
the angular rotation rate ( ω ). Alternatively, when the solution initially contains
only the reduced form, the Levich equation for the anodic limiting current (i
LA
)
can be written as
i
LA
= 0.620 n F A D
2/3
ν
– 1/6
C
R
ω
1/2
where the concentration term ( C
R
) is for the reduced form rather than the
oxidized form.
10.4.1 Levich Study
A Levich study is a common experiment performed using a rotating disk electrode
in which a series of voltammograms is acquired over a range of different rotation
rates. For a simple electrochemical system where the rate of the half reaction is
governed only by mass transport to the electrode surface, the overall magnitude
of the voltammogram should increase with the square root of the rotation rate
(see Figure 10.7, left).
The currents measured during a Levich study are usually plotted against the
square root of the rotation rate on a graph called a Levich plot. As predicted by
the Levich equation, the limiting current (see red circles on Figure 10.7, right)
increases linearly with the square root of the rotation rate (with a slope of
0.620 n
F A D
2/3
ν
–1/6
C
) and the line intercepts the vertical axis at zero. It is common to