28 Electrocatalysis and the splitting of water
last step that becomes at for RuO2 is the third which includes the formation
of OOH. For RuO2 it was therefore concluded that the third step is potential
determining, since the binding to OOH is slightly too weak. It should be
noted that energy barriers for each step are not directly taken into account.
The thermodynamic analysis was also extended to predicting a volcano shaped
activity plot based on a single descriptor, the binding to oxygen. This was
justied based on the apparent correlation between binding energies for similar
intermediates. Later it has been found that Brøndsted-Evans-Polanyi relations
exists for the oxygen intermediates of OER on several surfaces, such as metals
and oxides 91. These relations correlate the energy of formation for transition
states to the overall thermodynamic change in free energy of a reaction step
92, 93. In other words, the energy barriers associated with a reaction can be
described as a linear function of the change in free energy. With the DFT
method and thermodynamic analysis in place a natural step forward was to
extend the calculations to a large variety of materials. From such calculations
universal scaling relations emerged 56,9497. Scaling relations provide a simple
correlation between the binding energy of similar adsorbates independently from
the surface. In this way the binding energies of OH or OOH are correlated
to the binding energy of O. By averaging over a large number of oxides it was
found that the adsorption energy of OOH, E*OOH, could be described as a
function of E*OH in the following equation:
E*OOH = E*OH + 3:2 eV (2.22)
Independently of the nature of the oxides there is a constant oset of 3.2 eV
between step 1 (equation 2.14) and step 3 (equation 2.16) in the reaction mechanism.
For the ideal catalyst this dierence is 2.46 eV, since two electrons and
protons are transferred from step 1 to 3. The discrepancy between the ideal
catalyst and the best possible catalyst following these scaling relations is 0.74
eV or 0.37 eV per step which is close to the predicted overpotential of RuO2.
Notice that even though the oset is the same for all of the oxides it doesn't
mean that they are all as good as RuO2. The predicted overpotential of 0.37 V
only results from optimal splitting of the 3.2 eV oset into two steps and therefore
the 0.37 V is a minimum overpotential. For OER catalysis it is therefore
seemingly impossible to nd a simple surface with the ideal binding energies to
all intermediates. This limitation is shown in gure 2.7, where the theoretically
predicted overpotential is shown for various oxides as a function of a single descriptor
94. The descriptor in this case is the dierence in Gibbs free energy
for O and OH adsorption. While these theoretically predicted overpotentials
relate to a thermodynamic allowance of the reaction, the comparison to experimental
current densities is not straightforward. However, the trends found from
such analyses are in good agreement with experiments and, in fact, the overpotential
needed to drive 10 mA/cm2 on at surfaces match to the theory within
100-200 mV for most materials 75, 94.