1.7 Types and Structures of Capacitors .................................................. 32

1.7.1 Fixed Capacitors ..................................................................... 32

1.7.2
Variable Capacitors ................................................................ 32

1.7.3
Power Capacitors .................................................................... 33

1.7.4
High-Voltage Capacitors ....................................................... 33

1.7.5 Interference-Suppression Capacitors .................................. 33

1.7.6 Ferrodielectric Capacitors .....................................................34

1.7.7 Polar Polymer Dielectric Capacitors ....................................34

1.7.8 Linear and Nonlinear Capacitors ........................................34

1.8 Summary ..............................................................................................34

References ....................................................................................................... 35

2. Fundamentals of Electrochemical Double-Layer Supercapacitors..... 37

2.1 Introduction ......................................................................................... 37

2.2 Electrode and Electrolyte Interfaces and Their Capacitances ...... 38

2.2.1 Electric Double-Layer at Interface of Electrode and
Electrolyte Solution ................................................................ 39

2.2.2 Double-Layer Net Charge Density by Gouy–

Chapman–Stern (GCS) Modeling........................................ 45

2.2.3 Theoretical Differential Capacitance of Electric

Double-Layer .......................................................................... 47

2.2.4 Differential Capacitance of Entire Double-Layer .............. 48

2.2.5 Potential Drop Distribution within Electric Double-

Layer ........................................................................................ 50

2.2.6 Factors Affecting Double-Layer Capacitance .................... 51

2.2.7 Specific Adsorption of Ions and Effect on Double-Layer . 52

2.3 Electrode Potential and Double-Layer Potential Windows
Using Different Electrode Materials and Electrolytes...................54

2.3.1 Electrode Potential .................................................................54

2.3.2 Double-Layer Potential Ranges or Windows ..................... 56

2.4 Capacitance of Porous Carbon Materials......................................... 58

2.4.1 Carbon Particles and Their Associated Electrode Layers 59

2.4.2 Capacitances of Porous Carbon Materials and Their
Associated Electrode Layers ................................................ 61

2.5 Electrochemical Double-Layer Supercapacitors ............................. 62

2.5.1 Structure and Capacitance ................................................... 62

2.5.2 Equivalent Series Resistance (ESR) .....................................64

2.5.2.1 Thermal Degradation from ESR...........................65

2.5.3
Leakage Resistance ................................................................ 66

2.5.3.1 Self Discharge through Leakage Mechanisms .. 67

2.5.4 Supercapacitor Charging and Discharging ....................... 69

2.5.4.1 Charging at Constant Cell Voltage ...................... 69

2.5.4.2 Charging at Constant Cell Current ..................... 70

2.5.4.3 Discharging Supercapacitor Cell at

Constant Resistance ............................................... 72

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Contents