Electrocatalysis and Catalyst Screening from Density Functional Theory Calculations - Fuel Cell Catalysis: A Surface Science Approach - page 71

Figure 3.10 Calculated current density based on Equation (3.5) (solid curves) and experimen-
tal current density from [Stamenkovic et al., 2007a] (dashed curves).

In the water/OH layer, there is a perfect one-to-one ratio between water and
OH , giving a coverage of monolayer (ML) of OH . Going beyond

3 ML of OH,
we have to replace a water22OH bond with an OH22OH bond. In the following, we
estimate the OH22OH interaction energy at a coverage of

1
3

1

1

3 ML of OH, without the
presence of water, and compare this energy with the corresponding result for
the OH/water layer (Fig. 3.11). Since the step is high, about 0.3 V, it is reasonable
to assume that the coverage never will be larger than 3 ML at potentials around U ¼
0.9 V. Although there is no consensus in the literature regarding the coverage of
OH during water splitting, we note that our maximum coverage of

1

3 ML is in good
agreement with the maximum coverage observed by [Stamenkovic et al., 2007a].
We include the configurational entropy of noninteracting particles, DS ¼ k B
ln[(1 2 u OH )/u OH ], for 0 , u OH , 3 . This expression assumes that OH molecules
do not interact, which we expect to be a good assumption, since all OH only have
water as nearest neighbors as long as the coverage is smaller than

1

3 ML [Karlberg
and Wahnstrom, 2005]. We can therefore write the potential and coverage dependence
of the reaction free energy of Reaction (3.17) as

eU

1 u OH
u OH

DG(u OH , U) ¼ DG OH k B ln (3 : 22)

1

Here DG OH is calculated for the standard condition of

3 ML OH and 1/3ML H 2 O.
Assuming that Reaction (3.18) is in equilibrium for all potentials [DG(U, u OH ) ¼ 0],
and, furthermore, that the excess barrier for water splitting is small, this leads to the
following expression for the coverage:

u OH ¼ 1
3

1
1 þ exp[(DG OH eU) = k B T]

(3 : 23)