Electrocatalysis and Catalyst Screening from Density Functional Theory Calculations - Fuel Cell Catalysis: A Surface Science Approach - page 68

Figure 3.8 Plots of the heights of the steps in Fig. 3.5 divided by the electron charge in order
to get a potential. Via the relations in Fig. 3.7, these steps are all functions of E O . On the vertical
axis is the highest potential at which a step in the ORR is downhill in free energy, depicted as a
function of the binding of O . The step that first becomes uphill in free energy defines U ORR

Max
(DE O )U. Steps 1 and 4 (lines labeled DG 1 and DG 4 , respectively) define the lower “volcano”
and thereby U ORR

Max

(DE O ). Pt is the pure metal closest to the top.

different intermediates, it is possible to obtain a quantitative version of the Sabatier
principle, stating at which value of the “descriptor,” in this case E O , the best tradeoff
is obtained. We note that the binding of OH would have served as an equally valid
descriptor.
Whereas U ORR

Max is relatively easy to determine from the calculated binding energies,
it is not easy to measure experimentally, since the measured potentials are always
related to a specific current. Therefore, in order to compare directly with experiment,
we have to calculate polarization curves, i.e., the current. The link between U ORR

Max

and

the current is the Tafel equation,

j c ¼ j 0 exp(ahe = k B T) (3 : 19)

where j c is the cathode current density, j 0 is the exchange current, his the overpoten-
tial, and ais the transfer coefficient. We will here only consider a¼ 1, but the model
could be constructed for other values of a. The overpotential is written as h; U 0 2 U
in order to rewrite the Tafel equation as

¼ j limit exp a(U Max

j c ¼ j 0 exp a(eU 0 eU)
k B T

ORR eU)
k B T

(3 : 20)