Environmental Engineering Reference
In-Depth Information
FIGURE 2.14
FE-SEM nanotomography of a porous carbon (PC-CTAB) (dimensions: 500 × 500 × 700 nm). Gray areas represent
the compact carbon domains.
2.3.3 Electrochemical Properties of Nanoporous Carbon
Applying a potential to a carbon electrode in an electrochemical cell induces the following
processes: (i) charging of the electrochemical double layer; (ii) electron transfer to a surface
and/or solution species through a Faradaic reaction. By measuring the current-potential
relationship, it is possible to evaluate both effects.
2.3.3.1 Double-Layer Capacitance
The irst process is related with the differential capacitance of the electrode, deined by
dQ
dE
Cd
=
(2.2)
where
Cd
is the differential capacitance (F),
Q
the electrical charge (C),
A
the surface area,
and
E
(V) the electrode potential. Since porous carbons are conductors with large speciic
surfaces (
S
sp
> 100 m
2
/g), they can have large capacitances due to the relationship
Cd
=
Cd
a
S
=
Cd
a
mS
sp
(2.3)
where
Cd
a
is the areal capacitance (F/cm
2
),
S
the surface area (cm
2
),
S
sp
the speciic surface
(m
2
/g), and
m
the material mass.
As an example, an electrode of geometrical area 0.071 cm
2
(3-mm-diameter disc) covered
with 1 mg of a carbon with
S
sp
= 500 m
2
/g, which has an areal capacitance (
Cd
a
) of 20 μF/
cm
2
, will have a capacitance of 1 F.
The capacitance can be measured by cyclic voltammetry (CV) or by electrochemical imped-
ance spectroscopy (EIS). CV applies a potential scan to the working electrode, measuring the
current. This measurement gives an accurate idea of the accessible surface for any electro-
chemical process in aqueous media. The differential capacitance is calculated as
d
d
Q
E
d
d
Q
t
d
d
t
E
Cd
== =
iv
(2.4)
where
t
is the time,
i
the current, and
v
the scan rate.
