2
1 Surface Thermodynamics of Solid Electrode
(surface stress vs. potential or surface tension vs. potential) derived for the electrified interface of a solid electrode is different from that (surface tension vs. potential)
derived for the electrified interface of a liquid electrode. The comparison between
the electrocapillary curves obtained experimentally for the electrified interfaces of
gold (solid) and mercury (liquid) electrodes is necessitated to confirm the difference between electrocapillary curves derived thermodynamically for the electrified
interfaces of solid and liquid electrodes.
It is noticed that the term “solid electrode” used in this book represents simply
the case where a solid electron-conductor such as metal is immersed in a liquid
ionic-conductor (i.e., electrolyte solution). The term “surface” is usually used for
the termination of a solid or liquid phase faced to vacuum. On the other hand, the
boundary between two phases (e.g., solid and liquid) is named “interface.” Nevertheless, it is reminded that the term “electrode surface” in this book is used for the
electrode/solution interface unless otherwise noticed. We start this chapter from the
definition of a surface phase.
1.2 Definition of Surface Phase
There are two approaches to define thermodynamically the interface region as a
surface phase [1, 2]. Figure 1.1 is useful to explain the definition of a surface phase [3].
Figure 1.1a shows schematically the variation of extensive property X as a function
of distance z across the interface region between bulk α (e.g., solid) and β (e.g.,
liquid) phases contacted each other. In Fig. 1.1a, it is assumed that the x-y plane of a
rectangular prism consisting of α and β phases is flat and has a homogeneous property.
One approach for the definition of a surface phase has been achieved by Gibbs [1]
who replaces a real interface region by a dividing surface as a two-dimensional
surface phase. As depicted in Fig. 1.1b, the two-dimensional surface phase (σ phase)
is defined by the requirement of surface discontinuity that the extensive property
under consideration should maintain a uniform value in each bulk phase up to the
dividing surface (perpendicular line: DS) and the net value of extensive property
corresponding to the areas with plus sign (β phase) and minus sign (α phase) is fixed
as a surface excess of the extensive property at the dividing surface. The net value of
a certain property at the dividing surface can be made zero by choosing the position
of the dividing surface to equate the area of plus sign to that of minus sign. However,
the net values of the other properties are not zero at the dividing surface chosen
above. The demerit of this approach is that the net value of the extensive property at
the dividing surface depends on the position of the dividing surface. Nevertheless,
as explained later in the section of surface excess quantities, this issue is solved by
adoption of the surface excess quantities of other components relative to a specified
component (i.e., relative surface excess quantity) since the relative surface excess
quantity is independent of the position of the dividing surface.
An alternative approach has been made by Guggenheim [2] in which the surface
phase is defined as a three-dimensional phase (π phase) with a thickness of τ as
1 Surface Thermodynamics of Solid Electrode
(surface stress vs. potential or surface tension vs. potential) derived for the electrified interface of a solid electrode is different from that (surface tension vs. potential)
derived for the electrified interface of a liquid electrode. The comparison between
the electrocapillary curves obtained experimentally for the electrified interfaces of
gold (solid) and mercury (liquid) electrodes is necessitated to confirm the difference between electrocapillary curves derived thermodynamically for the electrified
interfaces of solid and liquid electrodes.
It is noticed that the term “solid electrode” used in this book represents simply
the case where a solid electron-conductor such as metal is immersed in a liquid
ionic-conductor (i.e., electrolyte solution). The term “surface” is usually used for
the termination of a solid or liquid phase faced to vacuum. On the other hand, the
boundary between two phases (e.g., solid and liquid) is named “interface.” Nevertheless, it is reminded that the term “electrode surface” in this book is used for the
electrode/solution interface unless otherwise noticed. We start this chapter from the
definition of a surface phase.
1.2 Definition of Surface Phase
There are two approaches to define thermodynamically the interface region as a
surface phase [1, 2]. Figure 1.1 is useful to explain the definition of a surface phase [3].
Figure 1.1a shows schematically the variation of extensive property X as a function
of distance z across the interface region between bulk α (e.g., solid) and β (e.g.,
liquid) phases contacted each other. In Fig. 1.1a, it is assumed that the x-y plane of a
rectangular prism consisting of α and β phases is flat and has a homogeneous property.
One approach for the definition of a surface phase has been achieved by Gibbs [1]
who replaces a real interface region by a dividing surface as a two-dimensional
surface phase. As depicted in Fig. 1.1b, the two-dimensional surface phase (σ phase)
is defined by the requirement of surface discontinuity that the extensive property
under consideration should maintain a uniform value in each bulk phase up to the
dividing surface (perpendicular line: DS) and the net value of extensive property
corresponding to the areas with plus sign (β phase) and minus sign (α phase) is fixed
as a surface excess of the extensive property at the dividing surface. The net value of
a certain property at the dividing surface can be made zero by choosing the position
of the dividing surface to equate the area of plus sign to that of minus sign. However,
the net values of the other properties are not zero at the dividing surface chosen
above. The demerit of this approach is that the net value of the extensive property at
the dividing surface depends on the position of the dividing surface. Nevertheless,
as explained later in the section of surface excess quantities, this issue is solved by
adoption of the surface excess quantities of other components relative to a specified
component (i.e., relative surface excess quantity) since the relative surface excess
quantity is independent of the position of the dividing surface.
An alternative approach has been made by Guggenheim [2] in which the surface
phase is defined as a three-dimensional phase (π phase) with a thickness of τ as