Environmental Engineering Reference
In-Depth Information
activation overpotential (V
act
) and current density. Setting RT/a
Rd,c
F equal to a
constant A, Eq.
3.26
becomes:
i
c
i
0
;
c
V
act
;
c
¼
A ln
ð
3
:
27
Þ
where the constant A (called Tafel constant) is higher when the electrochemical
reaction is slower, whereas i
0,c
is higher for a faster reaction.
Equation
3.27
can be written also in the form:
V
act
;
c
¼
a
þ
b log
ðÞ
ð
3
:
28
Þ
where
log i
ðÞ
and b
¼
2
:
3
RT
a
Rd
;
c
F
RT
a
Rd
;
c
F
a
¼
2
:
3
The plot of overpotential versus current density in log scale gives the param-
eters a, b, and i
0
(b is called the Tafel slope). Equation
3.28
, which is only valid for
i [ i
0
, suggests that the exchange current density i
0
can be also regarded as the
current density value at which the overpotential begins to exert its function to
make possible the electrochemical reaction, becoming different from zero.
The Tafel equation can be used to model the activation losses in polarization
curve, in fact assuming that these are the only losses in a fuel cell, the cell voltage
is given by:
E
¼
E
c
E
a
¼
E
V
act
;
c
V
act
;
a
ð
3
:
29
Þ
As seen before, in a hydrogen/oxygen fuel cell the anode polarization can be
neglected, then Eq.
3.29
for this type of fuel cell can be written:
E
¼
E
V
act
¼
E
RT
i
i
0
aF
ln
ð
3
:
30
Þ
For PEM fuel cells with platinum-based electrocatalysts a is about 0.5 for
hydrogen electrode, and comprised in the range 0.1-0.5 for oxygen electrode,
while typical values for the constant i
0
at 25C and ambient pressure are about
0.1 mA/cm
2
at the cathode and about 200 mA/cm
2
at the anode [
50
].
From the above consideration it is clear that the exchange current density is the
main factor affecting the activation overpotential, then the optimization of a PEM
fuel cell performance requires the maximization of i
0
. This can be obviously
accomplished by increasing the catalyst activity, that means to raise the surface
area, cell temperature, and reactant pressure (this last effect should also favor gas
adsorption on catalyst sites).
Equation
3.30
with the proper values of the parameters a and i
0
can be used to
fit the polarization curve in the region of low current, in particular the logarithmic
dependence of current on polarization can model the fast decrease of voltage
observed under 2 A (Fig.
3.5
). However, it cannot explain the shift from the OCV
value, for which a further interpretation is necessary.
