Environmental Engineering Reference
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oxide (PtO
2
). In the following, we shall derive the condition under which the bulk
oxide is the thermodynamically stable phase of the electrode.
For the non-electrochemical system of a Pt surface in contact with an O
2
atmos-
phere, the Pt
x
O
y
bulk electrode is only stable if
Pt
þ
y
g
bulk
Pt
x
O
y
, xg
bulk
2
m
O
2
(5
:
23)
which for the electrochemical system becomes
g
bulk
Pt
x
O
y
, xg
bulk
Pt
þ
y m
H
2
O
þ
2eDf
DG
H
2
O
(5
:
24)
O
2
where DG
H
2
O
O
2
1
2
O
2
out of liquid water (experi-
mentally, 2.46 eV [Atkins, 1990]). Here, we have made use of the fact that water is
the source of all the oxygen that, together with two electrons, is used to form the
bulk oxide. Referencing the chemical potential of water by Dm
H
2
O
¼
m
H
2
O
2
E
tot
is the Gibbs energy required to form
O
2
,
(5.24) can be rewritten as
h
i
2eDf
þ
DG
H
2
O
O
2
Dm
H
2
O
.
1
Pt
y
g
bulk
Pt
x
O
y
xg
bulk
2
E
tot
(5
:
25)
O
2
y
The expression in the square brackets is exactly the formation energy of the Pt bulk
oxide out of bulk platinum and molecular O
2
, which can easily be evaluated by
DFT calculations [Jacob, 2007b]. Together with the experimental value for DG
H
2
O
O
2
,
we can finally formulate the following stability ranges at which the three known Pt
bulk oxides are thermodynamically stable:
† a-PtO
2
:
þ
1
:
74 eV
2eDf, Dm
H
2
O
, 0eV
† b-PtO
2
:
þ
1
:
74 eV
2eDf, Dm
H
2
O
, 0eV
† PtO:
þ
1
:
97 eV
2eDf, Dm
H
2
O
, 0eV
(5
:
26)
Decomposition of the bulk oxide will occur if Dm
H
2
O
is too negative to fulfill these
conditions.
5.3.4 Pt Surface Oxidation
In this section, we will investigate the surface structure of the electrode in the potential
range before a surface or bulk oxide starts forming, and will restrict ourselves to
the adsorption of atomic oxygen only (not OH
-
) [Jacob and Scheffler, 2007].
Furthermore, in our simulations, we assume a single-crystal Pt(111) electrode,
which will be compared with the experimental CV curve (Fig. 5.9) for polycrystalline
Pt. This simplification is motivated by the fact that our interest here is to describe the
general behavior of the system only.
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