Electrocatalysis and Catalyst Screening from Density Functional Theory Calculations - Fuel Cell Catalysis: A Surface Science Approach - page 59

In practice, DG 0 will also depend on the coverage of the adsorbate, u. Since this
effect has direct implications for cyclic voltammetry, it will be discussed in more
detail in Section 3.3.1 on theoretical cyclic voltammograms.
To summarize the model described above, we highlight the close connection this
theoretical standard electrode provides between surface science and electrochemistry.
Neglecting the effect of the electrolyte, the left and central parts of Reaction (3.1) rep-
resent a typical surface reaction, where the change in energy is the dissociative adsorp-
tion energy. Such reactions have been studied extensively within surface science, both
experimentally and using DFT. The central and right part of Reaction (3.1), on the
other hand, represent a typical electrochemical reaction. Hence, by introducing this
theoretical counterpart to the standard hydrogen electrode, we have provided a close
link between surface science and electrochemistry.

3.3 CYCLIC VOLTAMMOGRAMS AND POURBAIX DIAGRAMS

3.3.1 Theoretical Cyclic Voltammograms

Cyclic voltammetry is perhaps the most important and widely used technique within
the field of analytical electrochemistry. With a theoretical standard hydrogen electrode
at hand, one of the first interesting and challenging applications may be to try to use it
to make theoretical cyclic voltammograms (CVs). In following, we set out to do this
by attempting to calculate the CV for hydrogen adsorption on two different facets of
platinum: the (111) and the (100) facets.
Cyclic voltammetry entails the measurement of current flowing through an elec-
trode during a linear sweep of its potential versus a known electrochemical reference,
such as the standard hydrogen electrode. In the following, we will construct a theor-
etical CV that only concerns adsorption and desorption of hydrogen. The process
we study is thus the reaction of protons from the aqueous solution with electrons in
the electrode, i.e., from the last to the second-to-last state in Reaction (3.1). This
reaction is generally believed to be fast, a conclusion supported both by experiments
[Markovic and Ross, 2002] and calculations [Sk ´ lason et al., 2007]. In the case that
the reaction is close to equilibrium at each electrode potential, the free energy for
the reaction must be zero:

DG(U, u) ¼ 0 (3 : 6)

Combining Equations (3.6) with (3.3), one obtains

U(u) ¼ DG 0 (u) = e (3 : 7)

This relation, analogous to the Nernst equation at pH ¼ 0, implies that there is a
relation between the coverage of hydrogen at the surface and the potential. Based
on this observation, the starting point for the derivation of a theoretical cyclic