Chemistry Reference
In-Depth Information
R
ct
W
R
e
C
dl
2.6
Electrical equivalent circuit representing the model of
Ershler-Randles.
determined by transport phenomena in the electrolyte. This is based on the
fact that in electrochemical impedance spectroscopy, the amplitude of the
applied signal(s) is(are) small. The charge-transfer resistance for a reaction
is given by Equation 2.48.
Suppose that the envisaged reaction is a corrosion reaction, which means
that reactions of the type of Equation 2.47 occur simultaneously at the elec-
trode surface but belonging to two different redox systems; then
R
ct
can be
defined as a polarisation resistance:
T
ni
R
F
R
=
[2.48]
ct
0
where R is the universal gas constant (8.317 J mol
-1
K
-1
),
T
is the thermo-
dynamic temperature in K,
n
is the number of electrons exchanged in the
reaction, F is the Faraday constant (96485 C mol
-1
),
i
0
is the current density
at the equilibrium potential (in A m
-2
).
If the reaction rate is controlled by transport phenomena, then the result-
ing impedance can be explained by a component that depends on the
conditions of transport. The best-known example is the so-called Warburg
impedance
Z
W
, valid for semi-infinite diffusion
37,38
:
s
w
(
)
Z
=
1
-
j
[2.49]
W
where s is the Warburg coefficient:
R
F
T
1
1
Ê
Á
ˆ
˜
s=
+
[2.50]
n
22
2
•
-
12
•
-
12
c
D
c
D
O
O
R
R
where, if i represents O and R,c
i
•
is the bulk concentration of component
I
(mol m
-3
), and D
i
is the diffusion coefficient (m
2
s
-1
).
Another example of a transport-determined impedance is the one for
convective diffusion
39
, which is not explained here.
Figure 2.7 shows a Nyquist plot corresponding to the electrical equiva-
lent circuit of Fig. 2.6. The slope of the impedance can be explained by a
circuit, consisting of different resistive and capacitive components
37
.The
