Environmental Engineering Reference
In-Depth Information
As seen in Figure 10.19 the ions in meso and macro pores will accumulate into
layers resulting in an electric field within the electrolyte. This phenomenon results in
the EDLC having a capacitance that is somewhat voltage dependent. The electric field
across an isotropic dielectric is linear, but when in the presence of distributed charge
within the electrolyte, it obeys the Poisson equation. As the capacitor is charged, the
electrolyte becomes depleted of ions and further layering is slowed down.
To illustrate an ultra-capacitor's energy storage mechanism, consider a popular
production cell rated 2,700 F, 2.5 V (2.7 V maximum), 625 A pulse discharge and
having an internal resistance of 1 m
W
25%. The capacitance dispersion on ultra-
capacitors is typically
10%,
þ
30% of rated, and its operating temperature is
40
to
þ
70
C. The production cell has a mass of 725 g in a 0.6 L prismatic package.
From these data its energy rating, gravimetric energy and power density, and
volumetric energy density are determined:
2
1
2
CV
2
mx
¼
2,700
ð
2
:
5
Þ
E
c
¼
¼
8,400 J
ð
10
:
21
Þ
2
Charge separation distance,
d
, can be approximated using the facts listed and
substituting into (10.21). Before proceeding we note that from the ultra-capacitor
construction that the terminal capacitance used to calculate the stored energy is
actually the equivalent of two electrolytic double layer capacitors, 2
C
eq
, connected
in series, each having the charge separation distance
d
. Using this new insight into
the ultra-capacitor, we approximate the ionic separation distance,
d
,as
e
r
e
0
r
e
m
c
2
C
eq
d
¼
ð
10
:
22
Þ
where the dielectric constant
e
r
¼
~3, permittivity
e
0
¼
8.854
10
12
F/m, specific
area density
r
e
¼
2,000 m
2
/g and cell mass
m
c
¼
725 g. The capacitance
C
for this
unit is given as 2,700 F. From this, (10.22) predicts that
3
ð
8
:
854
10
12
Þ
2,000
ð
725
Þ
2
ð
2,700
Þ
d
¼
¼
3
:
57 nm
ð
10
:
23
Þ
For this relatively crude illustration, (10.23) yields an ionic separation of just
36
˚
. If the activated carbon pore size is
<
2.0 nm, then only aqueous electrolytes
will enable the EDLC effect because organic electrolytes have ions with diameters
that are too large. When the pore size is
>
2 nm, both aqueous and organic elec-
trolytes in the activated carbon electrode structure will exhibit the EDLC effect.
There is considerable research at present into the ion kinetics and adsorption
effect that leads to electronic double layer capacitance (EDLC) in aqueous and
organic electrolytes. Figure 10.20 is a taxonomy of energy storage technologies that
is a useful guide to where in this overall picture the EDLC resides. Our focus will
be on electrochemical capacitors of symmetric design in organic electrolyte.
