286
Electrochemical Supercapacitors for Energy Storage and Delivery
i E
( )
C E
sp ( ) =
(7.7)
mν
Using Equation (7.7), the specific capacitance can be obtained at any potential
point studied, as shown in Figure 7.6. However, this specific capacitance is
taken only at a specified electrode potential. To determine the specific capacitance in the potential range of E 1 to E 2 , integration is needed. An approximation method can be expressed as
n E
( )
1
2 i E
( )
C sp =
i
(7.8)
mν ∑ n
j=1( )
E 1
where n is the number of data points collected in the CV measurement. It can
be seen that the larger the n, the more accurate the obtained C sp should be.
The other way is to calculate C m is using the measured charge quality Q,
which is the total charge transferred during the forward or backward direction CV scanning in the electrode potential range of E 1 to E 2 . If E 1 is the initial
electrode potential, as shown in Figure 7.6, and E 2 is the end potential, C m can
be expressed as
Q
C m =
(7.9)
E 2 − E 1
Note that from the CV curve in Figure  7.6 the charge Q can be obtained
through integration, as expressed by
t E
( )
2
Q = ∫ i ( )
Ed t
(7.10)
t=0( )
E 1
Practically, this charge quantity can be obtained easily by measuring the
areas under the CV trace scan or by using CV software. The specific capacitance can be obtained by
t E
( )
2
1
C sp =
∫ i E
( )dt
(7 .11)
m E 2 − E 1 t=0(E 1)
Note that both Equations (7.8) and (7.11) are obtained from data collected during forward potential scanning. The same calculation can also be carried out