Environmental Engineering Reference
In-Depth Information
Vector field of the electric field
Charge: electron
-
cation
+
5
-
+
+
4
-
3
-
+
+
2
-
1
-
+
0123456
(V1, V2)
x
(10
-10
m)
Figure 10.21 Illustration of an electron distribution in ac and ions in solution
Example 2:
Using the Debye length,
d
c
, calculated above find the EDLC capaci-
tance for a symmetric carbon ultra-capacitor in organic electrolyte, given the mass
of AC,
M
AC
, on the electrode and the specific area,
S
A
, of carbon surface.
Given
M
AC
¼
72 g (effective considering total electrode film mass)
S
A
¼
1,620 m
2
/g of specific area in the carbon measured by BET method.
Solution:
Using the definition of capacitance when plate area is decomposed in this
case to a porous electrode having the given mass and specific area and using the
Debye length for charge separation distance (see graphics in Figure 10.21 showing
spacing of 2 nm as example), we obtain
37
:
5
ð
8
:
854
10
12
e
r
e
0
M
AC
S
A
d
c
Þð
72
Þð
1,620
Þ
6
:
67
10
9
C
elec
¼
¼
¼
5,806 F
¼
2,903 F, and since each electrode is only half the terminal voltage, or 1.35 V for
organic electrolyte, the terminal voltage is 2.7 V. Hence, this would be approxi-
mately a 3,000 F, 2.7 V ultra-capacitor.
For this electrode capacitance the cell effective capacitance is
C
eq
¼
C
elec
/2
To further illustrate the equivalent plate size of this production ultra-capacitor,
we put the separation distance and capacitance value into the formula for a classical
two-plate capacitor and solve for the area, getting:
6
:
67
10
9
d
c
C
elec
e
r
e
0
¼
ð
5,906
Þ
37
:
5
8
:
854
10
12
¼
1
:
186
10
5
m
2
A
¼
ð
10
:
25
Þ
A
¼
11
:
86 ha
A
30 acre
