Ab Initio Atomistic Thermodynamics for Fuel Cell Catalysis - Fuel Cell Catalysis: A Surface Science Approach - page 131

All deviations from ideal behavior, which are directly (electrostatically) or indirectly
(through the solvent) caused by ion - ion interactions are usually treated by scaling the
concentration with a so-called activity coefficient f i , which leads to the activity
a i ¼ f i c i [Atkins, 1990]. Inserting the activity into (5.2) gives

c 0 þ k B T ln ( f i )

c i

m i (T, a i ) ¼ m i (T, c 0 ) þ k B T ln (5 : 3)

In most electrochemical experiments, ion concentrations ,1 M are used, and the
last term in (5.3) contributes to the chemical potential by only a few percent.
However, at higher concentrations (.5 M), this might increase even up to 10%
[Bockris et al., 2000].
While different theoretical methods have been developed to calculate the deviations
from ideal behavior, i.e., the activity coefficient, for each ionic species separately
(anions: f a ; cations: f c ) [Bockris et al., 2000; Schmickler, 1996a, b; Abbas et al.,
2002], only the mean activity coefficient is experimentally accessible, which is usually

approximated by f + ¼

p . This is due to the fact that if only one of the ionic
species were to be added to the electrolyte, the change in Gibbs free energy would
result in an additional energy contribution from the interaction of the ionic species
with an overall charged (electrified) solution. Since these two energy contributions
cannot be separated unambiguously, and to avoid a charged electrolyte, one has to
add an entire salt molecule to the electrolyte at a time.
The second term on the right-hand side of (5.1) is the energy required to transfer the
charge q i associated with each particle of the ith species from a reference potential f ref
to the electrostatic potential of the bulk electrolyte (solution), f S . Since the reference
potential can be chosen freely, throughout this chapter we use f ref as energy zero for
the electrostatic potential. Further discussion on the importance of this aspect will be
provided later.

f a f c

5.2.2 The Non-Electrochemical Interface

Focusing on the example of a solid/gas interface, in the following, we will describe
how to evaluate the stability of non-electrochemical interfaces, which are not influ-
enced by a potential applied externally or caused by an inhomogeneous ion distri-
bution within the system. In the case that both the solid and the gaseous phase are
present in macroscopic quantities, we have already seen in the previous section that
each of these reservoirs is characterized by its chemical potential m i (T, p i ), which
for the non-electrochemical interface is a function of temperature and partial pressure.
If both reservoirs are brought into contact, different interfacial structures are
possible (Fig. 5.2):

† phase separation;
† formation of an ordered adsorbate layer;
† formation of a stable or metastable surface compound (e.g., surface oxide or
surface hydride);
† total phase mixing (e.g., bulk oxide or bulk hydride).