Ab Initio Atomistic Thermodynamics for Fuel Cell Catalysis - Fuel Cell Catalysis: A Surface Science Approach - page 130

In this chapter, we will give a general description of electrochemical interfaces
representing thermodynamically closed systems constrained by the presence of a
finite voltage between electrode and electrolyte, which will then be taken as the
basis for extending the ab initio atomistic thermodynamics approach [Kaxiras et al.,
1987; Scheffler and Dabrowski, 1988; Qian et al., 1988; Reuter and Scheffler,
2002] to electrochemical systems. This will enable us to qualitatively and quantitat-
ively investigate and predict the structures and stabilities of full electrochemical
systems or single electrode/electrolyte interfaces as a function of temperature, activi-
ties/pressures, and external electrode potential.
The abilities of this approach will then be illustrated with two examples: (i) the
potential-induced lifting of the Au(100) surface reconstruction; and (ii) the electro-
chemical oxidation of Pt(111).

5.2 THEORY

5.2.1 Electrochemical Potentials

Before we will discuss the electrochemical system, it is important to define the prop-
erties and characteristics of each component, especially the electrolyte. In the follow-
ing, we assume macroscopic amounts of an electrolyte containing various ionic and
nonionic components, which might be solvated. In the case that this bulk electrolyte
is in thermodynamic equilibrium, each of the species present is characterized by its
electrochemical potential, which is defined as the free energy change with respect
to the particle number of species i:

m i (T, c i , f S ) ¼ @ G
@ N i

þ q i f S ¼ m i (T, c i ) þ q i f S (5 : 1)

T,c i ,N j

Here G is the Gibbs free energy of the system without external electrostatic potential,
and q i f S refers to the energy contribution coming from the interaction of an applied
constant electrostatic potential f S (which will be specified later) with the charge q i
of the species. The first term on the right-hand side of (5.1) is the usual chemical poten-
tial m i (T, c i ), which, for an ideal solution, is given by

c 0

c i

m i (T, c i ) ¼ m i (T, c 0 ) þ k B T ln

(5 : 2)

where m i is the chemical potential of species i at standard conditions, which for the
solvent and the solute (electrolyte/ions) are defined as follows:

† solvent: standard temperature and pure solvent, which means the absence of
electrolyte ions,
† solute (Henry's law standard state): standard temperature and concentration c 0
in the hypothetical state of an ideal solution (infinite dilution), which is reached
at lim c i ! 0 f i ¼ 1.