4
1 Surface Thermodynamics of Solid Electrode
depicted in Fig. 1.1c. In the latter approach, two dividing surfaces at each boundary
must be taken into consideration in the sense of the Gibbs approach. Further disadvantage is that terms dependent on surface volume are present in the equations, and it
encounters difficulties in assigning values to these terms. As shown in Fig. 1.1a, the
extensive property in the real interface region should vary from the border of α phase
to that of β phase. On the other hand, in the Guggenheim approach, an averaged
value of the extensive property X
π maintains uniform in the surface phase with a
thickness of τ. Let the area of the surface or interface in the entire system be denoted
by A. The total volume of the system V is the sum of the volumes of α and β phases
and the volume of surface phase (π phase):
V = V
α
+ V
β
+ V
π
.
(1.1)
The volume V
π of the surface phase is given by
V
π
= τ A.
(1.2)
In the case of the Gibbs model, the surface phase has no volume, that is,
V = V
α
+ V
β
.
(1.3)
1.3 Surface Excess Quantities
In the Gibbs model, the surface excess quantity X
σ is given by
X
σ
= X − X
α
− X
β
,
(1.4)
where X is the sum of extensive quantity in the entire system, and X
α or X
β is the
extensive quantity of α or β phase. As examples, surface excess entropy S
σ , internal
energy U
σ , Helmholtz free energy F
σ , and Gibbs free energy G
σ can be written,
respectively, as follows:
S
σ
= S − S
α
− S
β
.
(1.5)
U
σ
= U − U
α
− U
β
.
(1.6)
F
σ
= F − F
α
− F
β
.
(1.7)
G
σ
= G − G
α
− G
β
.
(1.8)