290
Electrochemical Supercapacitors for Energy Storage and Delivery
pseudosupercapacitor, the electrode capacitance (C m ) can be treated as the
sum of two capacitances connected in parallel:
C m = C dl + C pc
(7.17)
According to the definition of capacitance and Equation (7.1), Equation (7.17)
can be alternatively expressed as
i E
( )+ i ( )
dt
dt
dl
pc E
C = i ( )
+ i E
m
d l E
p c ( )
=
(7.18)
dE
dE
ν
Equation (7.18) suggests that the momentary current recorded on the active
layer-coated electrode of the pseudosupercapacitor is the sum of the doublelayer charging or discharging current (i dl (E)) and the electrochemical reaction current (i pc (E)). Note that both currents are functions of the electrode
potential. As shown in Figure 7.5, the background current is the double-layer
charging or discharging current, and the redox wave current is the electrochemical reaction current of the Fe(II)/Fe(III) center assigned to Reaction
(7.I) [6]:
–
Fe(II)-N x /C ↔ Fe(III)-N x /C + e
(7.I)
The charge quantity of the background current (Q dl ) during the positive
potential CV (Figure 7.5) scan direction in the range of (E 2 – E 1 ) can be calculated by measuring the area under the CV trace. Then, for the redox peak
observed near 0.67 V (versus RHE), the charge transfer Q pc (measured by
subtracting background current) can be determined and the entire or apparent electrode capacitance can be calculated according to
Q + Q
dl
pc
C m =
(7.19)
E 2 − E 1
For example, the Q dl in Figure 7.5 can be measured to be 2.90 × 10 –3 C and the
Q pc to be 4.40 × 10 –4 C, respectively, in the potential scan range |E 2 – E 1 | of
0.95 V. According to Equation (7.19), the capacitance (C m ) of the electrode layer
can be calculated at 3.44 × 10 –3 F. Due to the total weight of the active material (m) of 3.0 × 10 –5 g, according to Equation (7.4), the specific capacitance of
the active electrode material (C sp ) can be calculated as 115 F.g –1 . Note that this
value reflects only the apparent specific capacitance for the entire electrode
layer rather than the individual material’s specific capacitance.
Using the CV data in Figure 7.5, the individual specific capacitance of
an electrode material can be estimated. For example, the electrode layer in
Figure 7.5 is composed of two materials, the carbon support particles and
Electrochemical Supercapacitors for Energy Storage and Delivery
pseudosupercapacitor, the electrode capacitance (C m ) can be treated as the
sum of two capacitances connected in parallel:
C m = C dl + C pc
(7.17)
According to the definition of capacitance and Equation (7.1), Equation (7.17)
can be alternatively expressed as
i E
( )+ i ( )
dt
dt
dl
pc E
C = i ( )
+ i E
m
d l E
p c ( )
=
(7.18)
dE
dE
ν
Equation (7.18) suggests that the momentary current recorded on the active
layer-coated electrode of the pseudosupercapacitor is the sum of the doublelayer charging or discharging current (i dl (E)) and the electrochemical reaction current (i pc (E)). Note that both currents are functions of the electrode
potential. As shown in Figure 7.5, the background current is the double-layer
charging or discharging current, and the redox wave current is the electrochemical reaction current of the Fe(II)/Fe(III) center assigned to Reaction
(7.I) [6]:
–
Fe(II)-N x /C ↔ Fe(III)-N x /C + e
(7.I)
The charge quantity of the background current (Q dl ) during the positive
potential CV (Figure 7.5) scan direction in the range of (E 2 – E 1 ) can be calculated by measuring the area under the CV trace. Then, for the redox peak
observed near 0.67 V (versus RHE), the charge transfer Q pc (measured by
subtracting background current) can be determined and the entire or apparent electrode capacitance can be calculated according to
Q + Q
dl
pc
C m =
(7.19)
E 2 − E 1
For example, the Q dl in Figure 7.5 can be measured to be 2.90 × 10 –3 C and the
Q pc to be 4.40 × 10 –4 C, respectively, in the potential scan range |E 2 – E 1 | of
0.95 V. According to Equation (7.19), the capacitance (C m ) of the electrode layer
can be calculated at 3.44 × 10 –3 F. Due to the total weight of the active material (m) of 3.0 × 10 –5 g, according to Equation (7.4), the specific capacitance of
the active electrode material (C sp ) can be calculated as 115 F.g –1 . Note that this
value reflects only the apparent specific capacitance for the entire electrode
layer rather than the individual material’s specific capacitance.
Using the CV data in Figure 7.5, the individual specific capacitance of
an electrode material can be estimated. For example, the electrode layer in
Figure 7.5 is composed of two materials, the carbon support particles and