108
Electrochemical Supercapacitors for Energy Storage and Delivery
1.2
1.0
Pseudocapacitance
0.8
–2
0.6
Double-layer capacitance
F.cm
0.4
tal Capacitance,
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
–0.2
–0.4
o
T
–0.6
–0.8
–1.0
–1.2
Electrode Potential, V
FIGURE 3.2
Calculated total capacitance as function of electrode potential. The following parameters
are used for calculation: n = 1, d = 1 × 10 –4 cm, C = 1 × 10–2 mol/cm, E
o
/
o
O R
= 0.3 V, and
O x
x
d
o
C
C = 0.5.
O
/ O
x
x
3.2.2 Pseudocapacitance Induced by Underpotential Deposition
Underpotential deposition (UPD) of H + and other metals such as Pd and Cu
on polycrystalline materials such as gold and platinum has been used as
an example system in developing pseudocapacitance theory and practice [2].
For example, the reaction of H + on a Pt electrode surface, shown by the surface cyclic voltammogram in Figure 3.3, can be written as
H + + e – + Pt ↔ Pt – H ads
(3.II)
Reaction (3.II) is a reversible redox reaction with H + residing in the electrolyte solution and the H atom on the Pt surface. If the entire Pt surface is
completely covered by a monolayer of H atoms, the saturated surface concentration of Pt – H ads can be expressed as Γ
o
Pt (mol/cm 2 ). If the Pt surface
is not completely covered by Pt – H ads , the surface concentration of Pt – H ads
can be expressed as Γ Pt H (mol/cm 2 ), and the Pt surface not occupied by
−
Pt
−
adsorbed H atoms can be written as Γ Pt = Γ
o
− Γ Pt H (mol/cm 2 ). Due to the
reversibility of the electrochemical Reaction (3.II), a Nernst form similar to
Equation (3.1) may apply:
Electrochemical Supercapacitors for Energy Storage and Delivery
1.2
1.0
Pseudocapacitance
0.8
–2
0.6
Double-layer capacitance
F.cm
0.4
tal Capacitance,
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
–0.2
–0.4
o
T
–0.6
–0.8
–1.0
–1.2
Electrode Potential, V
FIGURE 3.2
Calculated total capacitance as function of electrode potential. The following parameters
are used for calculation: n = 1, d = 1 × 10 –4 cm, C = 1 × 10–2 mol/cm, E
o
/
o
O R
= 0.3 V, and
O x
x
d
o
C
C = 0.5.
O
/ O
x
x
3.2.2 Pseudocapacitance Induced by Underpotential Deposition
Underpotential deposition (UPD) of H + and other metals such as Pd and Cu
on polycrystalline materials such as gold and platinum has been used as
an example system in developing pseudocapacitance theory and practice [2].
For example, the reaction of H + on a Pt electrode surface, shown by the surface cyclic voltammogram in Figure 3.3, can be written as
H + + e – + Pt ↔ Pt – H ads
(3.II)
Reaction (3.II) is a reversible redox reaction with H + residing in the electrolyte solution and the H atom on the Pt surface. If the entire Pt surface is
completely covered by a monolayer of H atoms, the saturated surface concentration of Pt – H ads can be expressed as Γ
o
Pt (mol/cm 2 ). If the Pt surface
is not completely covered by Pt – H ads , the surface concentration of Pt – H ads
can be expressed as Γ Pt H (mol/cm 2 ), and the Pt surface not occupied by
−
Pt
−
adsorbed H atoms can be written as Γ Pt = Γ
o
− Γ Pt H (mol/cm 2 ). Due to the
reversibility of the electrochemical Reaction (3.II), a Nernst form similar to
Equation (3.1) may apply: