8
1 Surface Thermodynamics of Solid Electrode
dA = Nda.
(1.21)
In the case where a solid is subjected to partly plastic and elastic deformation, the
total strain may be divided into two contributions of plastic and elastic strains as
represented by
dA
A
=
adN + Nda
Na
=
dN
N
+
da
a
,
(1.22)
where
dN
N
and
da
a
are the contributions of plastic and elastic strains, respectively.
1.5 Major Parameters of Surface Thermodynamics
In the frame of the Gibbs model, the excess internal energy U
σ is a function of excess
entropy S
σ , surface area A, and excess moles of components n
σ
1 , . . . , n
σ
i :
U
σ
= U
σ
S
σ
, A, n
σ
1 , . . . , n
σ
i
.
(1.23)
The complete differential of U
σ is
dU
σ
=
∂U
σ
∂S σ
A,n
σ
1 ...n
σ
i
dS
σ
+
∂U
σ
∂A
S σ ,n
σ
1 ...n
σ
i
dA +
i
∂U
σ
∂n
σ
i
S σ ,A,n
σ
j =i
dn
σ
i .
(1.24)
Furthermore, from the thermodynamic relationships of
∂U
σ
∂S σ
A,n
σ
1 ...n
σ
i
= T
σ ,
∂U
σ
∂A
S σ ,n
σ
1 ...n
σ
i
= γ , and
∂U
σ
∂n
σ
i
S σ ,A,n
σ
j =i
= μ
σ
i , Eq. (1.24) can be described as follows:
dU
σ
= T
σ dS
σ
+ γ dA +
i
μ
σ
i dn
σ
i ,
(1.25)
where γ is the interfacial intensive parameter conjugate to the extensive parameter A.
The second term γ dA in the right-hand side of Eq. (1.25) corresponds to the reversible
work for creating new surface by dA under plastic deformation. In this book, γ is
named “surface tension” in order to distinguish from “surface stress” associated with
the reversible work for changing surface area by dA under elastic deformation. We
explain the relationship between surface tension and surface stress in Sect. 1.6 of
this chapter.
According to Euler’s theorem since U
σ is a homogeneous function of the first
order with respect to all variable:
1 Surface Thermodynamics of Solid Electrode
dA = Nda.
(1.21)
In the case where a solid is subjected to partly plastic and elastic deformation, the
total strain may be divided into two contributions of plastic and elastic strains as
represented by
dA
A
=
adN + Nda
Na
=
dN
N
+
da
a
,
(1.22)
where
dN
N
and
da
a
are the contributions of plastic and elastic strains, respectively.
1.5 Major Parameters of Surface Thermodynamics
In the frame of the Gibbs model, the excess internal energy U
σ is a function of excess
entropy S
σ , surface area A, and excess moles of components n
σ
1 , . . . , n
σ
i :
U
σ
= U
σ
S
σ
, A, n
σ
1 , . . . , n
σ
i
.
(1.23)
The complete differential of U
σ is
dU
σ
=
∂U
σ
∂S σ
A,n
σ
1 ...n
σ
i
dS
σ
+
∂U
σ
∂A
S σ ,n
σ
1 ...n
σ
i
dA +
i
∂U
σ
∂n
σ
i
S σ ,A,n
σ
j =i
dn
σ
i .
(1.24)
Furthermore, from the thermodynamic relationships of
∂U
σ
∂S σ
A,n
σ
1 ...n
σ
i
= T
σ ,
∂U
σ
∂A
S σ ,n
σ
1 ...n
σ
i
= γ , and
∂U
σ
∂n
σ
i
S σ ,A,n
σ
j =i
= μ
σ
i , Eq. (1.24) can be described as follows:
dU
σ
= T
σ dS
σ
+ γ dA +
i
μ
σ
i dn
σ
i ,
(1.25)
where γ is the interfacial intensive parameter conjugate to the extensive parameter A.
The second term γ dA in the right-hand side of Eq. (1.25) corresponds to the reversible
work for creating new surface by dA under plastic deformation. In this book, γ is
named “surface tension” in order to distinguish from “surface stress” associated with
the reversible work for changing surface area by dA under elastic deformation. We
explain the relationship between surface tension and surface stress in Sect. 1.6 of
this chapter.
According to Euler’s theorem since U
σ is a homogeneous function of the first
order with respect to all variable: