24
1 Surface Thermodynamics of Solid Electrode
sides of Eq. (1.124) and confirmed the validity of Eq. (1.124). The piezoelectric technique for detecting the derivative of surface stress change is explained in Sect. 2.2
of Chap. 2. The electro-chemo-mechanical properties of solid electrode surfaces are
directly associated with the thermodynamic equations of the solid electrode surfaces.
It is emphasized that the potential- or charge-induced surface stress change and the
surface elastic strain-induced potential or charge change are linked with Eqs. (1.119)
and (1.124).
1.9 Electrocapillary Curves of Liquid and Solid Metal
Electrodes
In the simplest model of an electrified metal/solution interface, a layer of solvation
ions on the outer Helmholtz plane (OHP) constitutes the entire excess charge in the
solution side which has a sign opposite to that on the metal side; i.e., two layers
of excess charge (electric double layer) behave like a parallel-plate condenser. The
OHP is defined as the location of centers of solvation ions which can approach most
closely to the metal side. Since the electric double-layer capacity c o in the simplest
model is independent of potential, the surface charge density q on the metal side is
given by
q = c o
E − E pzc
,
(1.125)
where E pzc is the potential at which q becomes zero, i.e., the potential of zero charge.
For a liquid metal electrode such as mercury, the changes in surface tension can be
obtained by the integration of the Lippmann equation of Eq. (1.109) with respect to
potential:
γ − γ pzc = −
1
2
c o
E − E pzc
2 = −
q
2
2c o
,
(1.126)
where γ pzc is the surface tension at E pzc and γ takes a maximum at q = 0, i.e., at
E pzc .
The solid curve in Fig. 1.4 illustrates the electrocapillary curve (γ vs. E curve)
calculated from Eq. (1.126) by using c o = 0.20 F m
−2 and γ pzc = 0.426 J m
−2 . The
electrocapillary curve is a perfect parabola symmetrical at E pzc . The value of γ pzc
= 0.426 J m
−2 corresponds to that of γ pzc for the mercury electrode in 0.01 M KF
solution [28]. The maximum of the electrocapillary curve at E pzc is named “electrocapillary maximum (ecm).” However, the electrocapillary curve obtained experimentally deviates inwards from a parabolic shape, particularly in the potential region
more positive than E pzc as shown in the dotted curve of Fig. 1.4. The dotted curve
was calculated by changing c o from 0.20 to 0.30 F m
−2 at E > E pzc . The increase in
c o enhances the inward deviation of the electrocapillary curve. The deviation of the
1 Surface Thermodynamics of Solid Electrode
sides of Eq. (1.124) and confirmed the validity of Eq. (1.124). The piezoelectric technique for detecting the derivative of surface stress change is explained in Sect. 2.2
of Chap. 2. The electro-chemo-mechanical properties of solid electrode surfaces are
directly associated with the thermodynamic equations of the solid electrode surfaces.
It is emphasized that the potential- or charge-induced surface stress change and the
surface elastic strain-induced potential or charge change are linked with Eqs. (1.119)
and (1.124).
1.9 Electrocapillary Curves of Liquid and Solid Metal
Electrodes
In the simplest model of an electrified metal/solution interface, a layer of solvation
ions on the outer Helmholtz plane (OHP) constitutes the entire excess charge in the
solution side which has a sign opposite to that on the metal side; i.e., two layers
of excess charge (electric double layer) behave like a parallel-plate condenser. The
OHP is defined as the location of centers of solvation ions which can approach most
closely to the metal side. Since the electric double-layer capacity c o in the simplest
model is independent of potential, the surface charge density q on the metal side is
given by
q = c o
E − E pzc
,
(1.125)
where E pzc is the potential at which q becomes zero, i.e., the potential of zero charge.
For a liquid metal electrode such as mercury, the changes in surface tension can be
obtained by the integration of the Lippmann equation of Eq. (1.109) with respect to
potential:
γ − γ pzc = −
1
2
c o
E − E pzc
2 = −
q
2
2c o
,
(1.126)
where γ pzc is the surface tension at E pzc and γ takes a maximum at q = 0, i.e., at
E pzc .
The solid curve in Fig. 1.4 illustrates the electrocapillary curve (γ vs. E curve)
calculated from Eq. (1.126) by using c o = 0.20 F m
−2 and γ pzc = 0.426 J m
−2 . The
electrocapillary curve is a perfect parabola symmetrical at E pzc . The value of γ pzc
= 0.426 J m
−2 corresponds to that of γ pzc for the mercury electrode in 0.01 M KF
solution [28]. The maximum of the electrocapillary curve at E pzc is named “electrocapillary maximum (ecm).” However, the electrocapillary curve obtained experimentally deviates inwards from a parabolic shape, particularly in the potential region
more positive than E pzc as shown in the dotted curve of Fig. 1.4. The dotted curve
was calculated by changing c o from 0.20 to 0.30 F m
−2 at E > E pzc . The increase in
c o enhances the inward deviation of the electrocapillary curve. The deviation of the