Environmental Engineering Reference
In-Depth Information
net current is observed through the external circuit and the rates of forward and
backward reactions are equal. It can be considered as the rate of electrochemical
forward and backward reactions at equilibrium, and can be regarded as analogous
to the rate constant of chemical reactions. Moreover in equation
3.23
:E
E
¼
over potential
a
Rd
is the charge transfer coefficient for the reduction reaction, which repre-
sents the fraction of overpotential necessary to move from the equilibrium con-
dition. It is comprised in the range 0 to 1.0 and depends on the reaction involved
and electrode material
a
Ox
= charge transfer coefficient for the oxidation reaction
F = Faraday, R = universal gas constant, T = absolute temperature.
Equation
3.23
evidences that some difference between equilibrium and actual
potential (E - E =0) is necessary to realize an electrochemical reaction and to
observe a current density through the external circuit. The overpotential in this
equation is called activation polarization, it is present at both anode and cathode of
a fuel cell and is correlated with electrode kinetics. The activation polarization is
associated with the energy required to break and reform the chemical bonds
involved in the transformation of reactants into products. The consequent reduc-
tion of energy available to produce useful power is related to the reaction rate, in
particular higher electrode kinetics imply lower activation losses. A measure of the
electrode activity in the specified electrochemical reaction is given by the
exchange current density i
0
(higher i
0
means higher electrode activity). In
hydrogen/oxygen fuel cells the reduction reaction at cathode is much slower than
the anodic oxidation, in particular the cathode exchange current density is several
order of magnitude lower with respect to the anodic exchange current density. This
means that the overpotential on the cathode is much larger than that on the anode,
then the Butler-Volmer equation, which is valid for both anode and cathode of a
fuel cell, can be written solely for the cathode reaction:
exp
a
Rd
;
c
FE
c
E
c
a
Ox
;
c
FE
c
E
c
i
c
¼
i
0
;
c
exp
ð
3
:
24
Þ
RT
RT
and assuming valid the ''high polarization'' approximation (E
c
much lower than
E
c
, cathode overpotential is negative), the second term of Eq.
3.24
can be
neglected [
47
], obtaining:
i
c
¼
i
0
;
c
exp
a
Rd
;
c
FE
c
E
c
ð
3
:
25
Þ
RT
From Eq.
3.25
the cathode activation overpotential can be derived:
RT
a
Rd
;
c
F
ln
i
c
i
0
;
c
E
c
E
c
¼
ð
3
:
26
Þ
Equation
3.26
, derived by electrode kinetics, has the same form of an empirical
equation proposed by Tafel
[
48
,
49
], which
gives the relationship between
