Environmental Engineering Reference
In-Depth Information
When calculating the interfacial free energies of particular surface structures, we
are limited by the condition that the Pt bulk oxide is not the thermodynamically
stable phase of the bulk electrode. Since a-PtO 2 and b-PtO 2 are the most stable Pt
bulk oxides, this is fulfilled as long as Dm H 2 O , 1 : 74 eV 2eDf. Keeping this con-
dition in mind, similarly to the previous example, we again have to adapt (5.19) to the
actual system in order to evaluate the stability of different surface structures. As
already discussed for the Au(100) system, the exact evaluation of (5.19) requires a
self-consistent calculation of the Gibbs free energy G of the entire electrode/electro-
lyte interface, which is far beyond present computer resources. However, under the
following assumptions, the modeling can be drastically reduced:
The structure and energetics of any adsorbate (here oxygen) is not influenced by
the electrode potential, i.e., the adsorbed species have no surface dipole.
A fixed electrolyte, respectively double-layer structure is assumed, which
remains unchanged under potential variation.
The second assumption, which we have already made in the previous example,
again allows us to consider the direct electrolyte contributions to the interfacial
free energy as constant [see (5.20)]. Although the model constrained by these two
strong assumptions certainly does not correspond to a realistic system, it represents
the actual level at which electrochemical interfaces are usually calculated. However,
as a consequence, the last three terms of (5.19) now give constant contributions,
and the Gibbs free energy G becomes independent of the excess charges, respectively
electrode potential, finally leading to
g 00 ¼ g 0 þ q e (Df F = e) g þ K 0
(5 : 27)
where we have used g 0 from (5.20) and introduced the notation K 0 for all constant
contributions. Applied to our system of Pt in contact with the aqueous electrolyte,
this becomes
g 00 (T, a H 2 O , a Pt , Df) ¼ 1
A
G(T, a H 2 O , a Pt , N O , N Pt ) N Pt g bulk
(T, a Pt )
Pt
N O [Dm H 2 O (T, a H 2 O ) þ 2eDf]
(5 : 28)
The last term comes from the assumption that every oxygen atom adsorbing on the
surface originates from a water molecule of the bulk electrolyte reservoir:
O adsorbed þ 2H þ þ 2e ! H 2 O(l)
(5 : 29)
Since, by this reaction, two electrons are transferred from the reference electrode
(which, for comparison with the experimental CV curves, we assume to be a reversible
hydrogen electrode, giving f ref ¼ 0) to the electrode, the term N O (2eDf) appears
in (5.28).
In order to compare the stability of different oxygen overlayers, DFT calculations
were performed on the energetic and structures of oxygen at different coverages. Since
the electrode is present in the solid phase, it is reasonable to assume the T and a
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