First-Principles Simulation of the Active Sites and Reaction Environment in Electrocatalysis - Fuel Cell Catalysis: A Surface Science Approach - page 110

A “displacement free energy” DG disp can then be defined as

DG disp (pH, U) ¼ G OH (ad) (U) þ eU þ G H 2 O (aq) G H 2 O (ad) (U) G OH (aq) ( pH) (4 : 9)

where the free energy of the hydroxyl ion in solution, G OH (aq) , is a function of the
solution pH, and the free energies of the adsorbed hydroxyl and water species,
G OH (ad) (U) and G H 2 O (ad) , are functions of the electrode potential. This displacement
free energy is a thermodynamic descriptor for ion adsorption at the electrochemical
interface.
Reaction (4.8) may be restated as the sum of two reactions:

H 2 O ! OH þ H þ þ e (4 : 10)

OH (aq) þ H (aq) ! H 2 O (aq)

(4 : 11)

As Reaction (4.11) can be assumed to be at equilibrium, the free energy change of
reaction is zero, and the values of DG disp (Reaction 4.8), and of the free energy of
the water oxidation reaction (4.10) are equivalent. This is, of course, necessary,
because the Born - Haber paths from reaction to product must be thermodynamically
equivalent (water dissociation, or a solution phase exchange, coming from the same
reactant and leading to the same product states are therefore the same). For a general
displacement reaction, however, the similarities to an interfacial electrochemical
reaction are not as clear. This exercise serves, therefore, to illustrate that the double-
reference method can be used to consider the potential dependence of water displace-
ment at the surface by other solution phase species.
As is evident for water/hydroxyl exchange, the calculation of relative binding
energies at the electrode surface is complicated by the need to consider the effects of
the electrified interface on binding characteristics as well as the requirement that
solution phase free energies of the various species be determined. For illustrative
purposes, a rough approximation to the solution phase free energies can be generated
by simply calculating the energy of a solute molecule in a periodic unit cell with a
locally optimized solvation structure. In the future, ensemble averages could be
taken from ab initio molecular dynamical simulations. The static approach with a
locally optimized solvation shell is illustrated in Fig. 4.9 for the displacement of an
adsorbed water molecule with an adsorbed oxygen molecule on the Pt(111) surface.
The free energy of the solution phase species may be improved by combining the
calculation of the gas phase free energy with experimental solvation free energies, or
by more rigorous calculation of solvation free energies [Pliego and Riveros, 2000].
Although the energy value of the solution phase species affects the absolute value of
the displacement energy, it does not alter the trend of the displacement energy with
electrode potential, because the solution phase species are taken to reside beyond the
region of potential drop at the interface (beyond the OHP). In other words, the
energy of the solution phase species serves as a reference energy, which is independent
of the electrochemical potential. A negative substitution energy implies an energy state
for the adsorbed ion that is lower than its solution state (and hence thermodynamically
favors adsorption), whereas a positive substitution energy implies a higher energy state
for adsorption.