Environmental Engineering Reference
In-Depth Information
E
Pt(H
2
O)
=
Pt
-
OH
ads
agrees well with voltammetric measurements of the potential corre-
sponding to similar partial coverage by OH
ads
on a Pt surface in contact with aqueous
electrolytes free of strongly adsorbed anions. It can be readily seen that it is the value of
the cathode potential with respect to E
Pt(H
2
O)
=
Pt
-
OH
ads
(not with respect to E
O
2
=
H
2
O
) that
determines the value of 1 2 u
OH
in (1.10). Consequently, to “ignite” the ORR current at
Pt, a key requirement is seen to be a pre-exponential factor in (1.10) significantly larger
than zero, which requires, in turn that u
ox
be lowered significantly under 1 by bringing
E
cath
close to E
Pt(H
2
O)
=
Pt
-
OH
ads
, i.e., down from E
O
2
=
H
2
O
by almost 400 mV.
Can this demand for a significant number of metal active sites be further quantified
by a general expression in terms of cathode potential demand? The answer is, in
principle, yes, although the dependence of the relative populations of metal surface
sites and oxidized surface sites on cathode potential could depend on
E
E
Pt(H
2
O)
=
Pt
-
OH
ads
in a somewhat different way, depending on the degree to which the
free energy of oxygen chemisorption is coverage-dependent. In the simplest case of
noninteracting adsorbed species, where the relative populations are determined by a
Nernst-type relationship with one electron assumed to be required for conversion of
a metal site to an oxide-covered site (and vice versa), the expression for the surface
population ratio will be
u
OH
1
u
OH
¼
exp
F
RT
E
E
Pt(H
2
O)
=
Pt
-
OH
ads
(1
:
11)
A more spread-out dependence of OH
ads
on E
E
Pt(H
2
O)
=
Pt
-
OH
ads
will occur when
interaction energies between chemisorbed species become significant; however, it is
always the potential difference E
E
Pt(H
2
O)
=
Pt
-
OH
ads
that determines the availability
of active metal sites, reflected by the 1 2 u
OH
term in the pre-exponential factor.
The pre-exponential factor can consequently be expressed directly as a function
of E
E
Pt(H
2
O)
=
Pt
-
OH
ads
by replacing the 1 2 u
OH
term in (1.10) by a term derived
from (1.11), to yield
exp
DH
act
RT
exp
E
E
O
2
=
H
2
O
b
int
1
Z
þ
1
J
ORR
(E)
¼
kP
O
2
N
total
(1
:
12)
where
F
RT
E
E
Pt(H
2
O)
=
Pt
-
OH
ads
Z
¼
exp
(1
:
13)
Equation (1.12) describes an ORR rate dependence on potential that derives from two
different redox potentials, one affecting the exponential part of the expression and the
other affecting the pre-exponential part. The term depending on E
E
O
2
=
H
2
O
reflects
the lowering of the activation energy at an active metal site by an increase in cathode
overpotential, whereas the term depending on (E
E
Pt(H
2
O)
=
Pt
-
OH
ads
) describes the
fraction of active metal sites, (1/Z
þ
1), at some value of E. Equation (1.12) suggests
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