Contents
1 Surface Thermodynamics of Solid Electrode . . . . . . . . . . . . . . . . . . .
1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2 Definition of Surface Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3 Surface Excess Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.4 Surface Plastic and Elastic Strains . . . . . . . . . . . . . . . . . . . . . . .
7
1.5 Major Parameters of Surface Thermodynamics . . . . . . . . . . . . . .
8
1.6 Surface Tension and Surface Stress . . . . . . . . . . . . . . . . . . . . . . 13
1.7 Gibbs–Duhem Equation of Solid Surface . . . . . . . . . . . . . . . . . . 16
1.8 Electrified Interface and Electrocapillarity . . . . . . . . . . . . . . . . . 18
1.9 Electrocapillary Curves of Liquid and Solid Metal Electrodes . . . 24
1.10 Surface Stress versus Potential Curve of Solid Metal
Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Appendix 1: Derivation of the Tensor Equivalent of the Shuttleworth
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Appendix 2: Calculation of the Magnitude of Surface Elastic
Strain from the Curvature Change of Cantilever Bending . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2 Methods for Investigating Electro-Chemo-Mechanical
Properties of Solid Electrode Surfaces . . . . . . . . . . . . . . . . . . . . . . . 39
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Piezoelectric Detection of Differential Surface Stress . . . . . . . . . 40
2.3 Cantilever Bending Method for Measurement of Changes
in Surface Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.1 Relationship between Surface Stress and Curvature
of Cantilever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.2 Optical Detection of Curvature . . . . . . . . . . . . . . . . . . . . 51
vii
1 Surface Thermodynamics of Solid Electrode . . . . . . . . . . . . . . . . . . .
1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2 Definition of Surface Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3 Surface Excess Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.4 Surface Plastic and Elastic Strains . . . . . . . . . . . . . . . . . . . . . . .
7
1.5 Major Parameters of Surface Thermodynamics . . . . . . . . . . . . . .
8
1.6 Surface Tension and Surface Stress . . . . . . . . . . . . . . . . . . . . . . 13
1.7 Gibbs–Duhem Equation of Solid Surface . . . . . . . . . . . . . . . . . . 16
1.8 Electrified Interface and Electrocapillarity . . . . . . . . . . . . . . . . . 18
1.9 Electrocapillary Curves of Liquid and Solid Metal Electrodes . . . 24
1.10 Surface Stress versus Potential Curve of Solid Metal
Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Appendix 1: Derivation of the Tensor Equivalent of the Shuttleworth
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Appendix 2: Calculation of the Magnitude of Surface Elastic
Strain from the Curvature Change of Cantilever Bending . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2 Methods for Investigating Electro-Chemo-Mechanical
Properties of Solid Electrode Surfaces . . . . . . . . . . . . . . . . . . . . . . . 39
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Piezoelectric Detection of Differential Surface Stress . . . . . . . . . 40
2.3 Cantilever Bending Method for Measurement of Changes
in Surface Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.1 Relationship between Surface Stress and Curvature
of Cantilever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.2 Optical Detection of Curvature . . . . . . . . . . . . . . . . . . . . 51
vii