Chapter 5
Controversy of Thermodynamics
Associated with Surface Stress
and Surface Tension of Solid Electrode
Abstract The contradictory discussions made so far in the electrochemistry community for the thermodynamics associated with surface stress and surface tension of a
solid electrode have been reviewed. The reviewed subjects include the controversial
arguments for the validity of the Gibbs–Duhem equation derived from the excess
internal energy for a solid electrode and for the incompatibility of the Shuttleworth
equation with Hermann’s mathematical structure of thermodynamics. In addition,
the review is concerned with the thermodynamic issues for the application of the
Shuttleworth equation to a solid electrode and for the surface stress measurement by
a cantilever bending method.
Keywords Homogeneous thermodynamic function · Gibbs–Duhem equation ·
Shuttleworth equation · Hermann’s mathematical structure of thermodynamics ·
Gokhshtein equation
5.1 Introduction
There have been controversial arguments in the electrochemistry community for the
thermodynamics associated with surface stress and surface tension of a solid electrode. The Gibbs–Duhem equation for a solid electrode derived by several researchers
is not consistent with that derived from the excess internal energy of a solid electrode which is a homogeneous function of the first order with respect to all variables.
The contradictory discussions have been made for the validity of the Gibbs–Duhem
equation for a solid electrode in connection with the difference between surface
stress and surface tension. In addition, the derivations of the Shuttleworth equation,
which links surface stress to surface tension, have been argued from the viewpoint
of incompatibility with Hermann’s mathematical structure of thermodynamics. The
controversial discussions still continue up to now.
Reviewing the controversial arguments on the above subjects is essentially necessary to find a clue for solving the thermodynamic issues. Moreover, there have been
the thermodynamic issues arose for the application of the Shuttleworth equation
© Springer Nature Singapore Pte Ltd. 2020
M. Seo, Electro-Chemo-Mechanical Properties of Solid Electrode Surfaces,
https://doi.org/10.1007/978-981-15-7277-7_5
139
Controversy of Thermodynamics
Associated with Surface Stress
and Surface Tension of Solid Electrode
Abstract The contradictory discussions made so far in the electrochemistry community for the thermodynamics associated with surface stress and surface tension of a
solid electrode have been reviewed. The reviewed subjects include the controversial
arguments for the validity of the Gibbs–Duhem equation derived from the excess
internal energy for a solid electrode and for the incompatibility of the Shuttleworth
equation with Hermann’s mathematical structure of thermodynamics. In addition,
the review is concerned with the thermodynamic issues for the application of the
Shuttleworth equation to a solid electrode and for the surface stress measurement by
a cantilever bending method.
Keywords Homogeneous thermodynamic function · Gibbs–Duhem equation ·
Shuttleworth equation · Hermann’s mathematical structure of thermodynamics ·
Gokhshtein equation
5.1 Introduction
There have been controversial arguments in the electrochemistry community for the
thermodynamics associated with surface stress and surface tension of a solid electrode. The Gibbs–Duhem equation for a solid electrode derived by several researchers
is not consistent with that derived from the excess internal energy of a solid electrode which is a homogeneous function of the first order with respect to all variables.
The contradictory discussions have been made for the validity of the Gibbs–Duhem
equation for a solid electrode in connection with the difference between surface
stress and surface tension. In addition, the derivations of the Shuttleworth equation,
which links surface stress to surface tension, have been argued from the viewpoint
of incompatibility with Hermann’s mathematical structure of thermodynamics. The
controversial discussions still continue up to now.
Reviewing the controversial arguments on the above subjects is essentially necessary to find a clue for solving the thermodynamic issues. Moreover, there have been
the thermodynamic issues arose for the application of the Shuttleworth equation
© Springer Nature Singapore Pte Ltd. 2020
M. Seo, Electro-Chemo-Mechanical Properties of Solid Electrode Surfaces,
https://doi.org/10.1007/978-981-15-7277-7_5
139