Journal of Power Sources 154 (2006) 314–320

On the specific double-layer capacitance of activated carbons,

in relation to their structural and chemical properties
T.A. Centeno a , F. Stoeckli b,∗
a Instituto Nacional del Carbon-CSIC, Apartado 73, E-33080 Oviedo, Spain
b Institut de Chimie de l’Université, Av. de Bellevaux 51, CH-2000 Neuchâtel, Switzerland

Received 30 November 2004; received in revised form 21 February 2005; accepted 9 April 2005
Available online 9 June 2005

Abstract

Twelve well-characterized activated carbons with average micropore widths between 0.7 and 2 nm, total surface areas of 378–1270 m2 g−1
and specific capacitances C up to 320 F g−1 have been investigated, using H2 SO4 2 M as electrolyte. Some of the carbons have also been
oxidized with (NH4 )2 S2 O8 , which leads to specific oxygen contents between 0.4 and 7.1 ␮mol m−2 of carbon surface area. It appears that
Co , the limiting capacitance at a current density of 1 mA cm−2 of electrode surface, does not depend significantly on the oxygen content. An
empirical equation is proposed to describe the decrease of C with increasing current density d (1–70 mA cm−2 of electrode surface), as a
function of the oxygen content.
As suggested by different authors, Co can be expressed as a sum of contributions from the external surface area Se and the surface of
the micropores Smi . A closer investigation shows that Co /Smi increases with the pore size and reaches values as high as 0.250–0.270 F m−2
for supermicropores. It is suggested that the volume Wo∗ of the electrolyte found between the surface layers in pores wider than 0.7–0.8 nm
contributes to Co . However, this property is limited to microporosity, like the enthalpy of immersion of the carbons into benzene. The latter
is also correlated to Co , which provides a useful means to identify potential supercapacitors.
© 2005 Elsevier B.V. All rights reserved.

Keywords: Electrochemical capacitor; Activated carbon; Microporosity; Surface area; Surface oxygen; Calorimetry

1. Introduction immersion calorimetry [16], suggest that the pore widths cor-
respond to these dimensions.
Activated carbons [1] are used mainly in filtration technol- Observations in high resolution electron microscopy
ogy, but in recent years they have also found applications in [10–12] (bright- and dark-field techniques) show that micro-
electrical energy storage, as double-layer capacitors (see, for pores are locally slit-shaped, at least for widths L and
example, reviews [2,3] and Refs. [4–10]). This type of car- extensions up to 1–1.2 nm. Larger micropores, often called
bon is characterized by a developed microporous structure ‘supermicropores’ have more complicated and cage-like
and a correspondingly large surface area. A number of stud- structures. The upper limit for microporosity is around
ies based on direct and indirect observations [1,11–15] show 2–2.5 nm, where capillary condensation begins and a num-
that the material consists of interconnected cavities between ber of specific properties disappear (for example, the energy
twisted graphitic (or aromatic) sheets. Classical techniques of adsorption of the vapour and the liquid phases). Depend-
based on the adsorption of molecules of variable dimensions ing on the precursor material and the activation process [1],
(0.4–1.5 nm), either from the vapour phase or monitored by the micropore volume Wo can be as high as 0.8–1 cm3 g−1 .
For commercial activated carbons, the surface area of the
micropore walls, Smi , is in the range of 700–1000 m2 g−1 ,
∗ Corresponding author. Tel.: +41 32 718 2400; fax: +41 32 718 2511. but in special cases it can reach 1200–1400 m2 g−1 (this
E-mail address: fritz.stoeckli@unine.ch (F. Stoeckli). limit seems realistic for activated carbons, if one keeps in

0378-7753/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.jpowsour.2005.04.007
 T.A. Centeno, F. Stoeckli / Journal of Power Sources 154 (2006) 314–320 315

mind the fact that graphene sheets have a maximum sur- sis is on the role of microporosity and therefore a selec-
face area of 2600 m2 g−1 and that they usually come in pairs tion of well-characterized carbons [19–21] has been con-
or larger stacks). The total surface area can be assessed sidered, with average pore widths Lo between 0.75 and
directly by the selective adsorption of sparingly soluble 2 nm.
molecules, such as phenol and caffeine from aqueous solu- As a first step (Section 3.1), we outline an approach, which
tions [17–19]. In this case, adsorption is limited to a mono- offers the possibility to predict with reasonable accuracy Co ,
layer, as opposed to vapour adsorption, where the entire the limiting capacitance of carbon electrodes at low den-
micropore volume is filled. The latter process is described sity currents (d ∼ 1 mA cm−2 of electrode). It appears that
by Dubinin’s classical theory [1,13,19]. The value of Smi the volume Wo∗ also plays an important role, beside Smi and
is also confirmed by the cumulative surface area of the Se , and it follows that reasonable predictions can be made
micropore walls calculated from the pore size distribution for Co with the help of these three structural characteristics.
obtained by various techniques [19–21] including modelling Secondly (Section 3.2), an equation is proposed to describe
of adsorption. the variation of C with increasing current density (up to
Depending on their accessible width L, micropores can 70 mA cm−2 of electrode) and the oxygen content of the car-
accommodate a variable number of layers of adsorbate bon [O]. Finally (Section 3.3), it will be shown that that an
between their walls. For a typical molecule, such as water, empirical, but interesting correlation exists between Co and
nitrogen or benzene, micropores wider than 0.7–0.8 nm will the enthalpy of immersion of the carbons into inert liquids,
accommodate between two and five–six layers, the upper such as benzene. This observation can be used to assess the
limit corresponding to supermicropores (L ∼ 2.5 nm). The suitability of an unknown carbon to be used as a capacitor.
layers which are not in direct contact with the surface (up to
four layers) define a ‘core’ with a volume Wo∗ with properties
strictly limited to microporosity. For example, as discussed 2. Experimental
elsewhere [21], immersion calorimetry suggests that adsorp-
tion by microporous carbons can be formally divided into 2.1. Materials
three distinct contributions, namely from the first layers in
the micropore walls and on the external surface Se found in The study is based on a broad spectrum of microporous
pores larger than 2 nm (meso- and macropores [22]), as well carbons obtained by steam activation around 800 ◦ C of ligno-
as from the volume Wo∗ . As shown below, a similar approach cellulosic precursors (series BV, AZ46), of anthracites (CMS
can probably be applied to the description of the capacitance and DCG-5) and a carbon black (XC-72-17). A KOH acti-
Co of microporous carbons. vated petroleum pitch (PX-21) was also included in the study,
Depending on the development of the microporous tex- in view of its high capacitance under the given experimental
ture, one may obtain with aqueous electrolytes specific capac- conditions (322 F g−1 of carbon at low current density). The
itances C for carbon electrodes in aqueous media in the solids have been well characterized by a variety of techniques,
range of approximately 50–300 F g−1 of carbon. Attempts such as vapour adsorption [1,13,19], immersion calorimetry
have been made to correlate this property with the microp- into liquids with different molecular sizes [16,21], the selec-
orous and external surface areas Smi and Se , as well as SBET tive adsorption of phenol from aqueous solutions [17,18]
[2,4,5,7–10]. The latter is derived from the BET theory [22], and, in some cases, by the analysis of the CO2 isotherm
but it is often unrealistic, as it is the monolayer equivalent of with the help of model isotherms obtained by Monte Carlo
the adsorbate filling the micropores. simulations (CMS, DCG-5 and XC-72-17) [20]. The latter
As shown elsewhere [13,21], SBET corresponds to the technique assumes slit-shaped micropores, which is a reason-
total surface area Smi + Se only for microporous carbons with able model for pore widths up to approximately 1.2–1.5 nm.
average pore widths Lo around 1 nm. It follows that specific Beyond, for the cage-like supermicropores, one must use an
properties, such as enthalpies of immersion, oxygen contents equivalent width equal to 2000Wo (cm3 g−1 )/Smi (m2 g−1 )
or capacitances C expressed in units per square metre of BET [19].
surface area, can be misleading for carbons with a large pro- The external (non-porous) surface area Se can be deter-
portion of supermicropores. Since C depends on the actual mined accurately from a classical comparison plot based on
surface area of a carbon, it is necessary to use the correct val- the adsorption of a vapour, such as N2 [22,23], C6 H6 [24]
ues of Smi and Se . On the basis of Qu and Shi’s work [9,10], or CH2 Cl2 [25] on the given carbon and on a non-porous
it appears that using these parameters separately improves reference (usually a carbon black). The foregoing techniques
the situation. However, they are still not sufficient to allow lead therefore to reliable values of the micropore surface area
reliable predictions of the capacitances of a range of typical Smi and the external surface Se (the corresponding values are
activated carbons at low density currents. given in Table 1).
The aim of this paper is to suggest further correlations The amount and the type of oxygen found on the surface
between structural and chemical characteristics of activated was determined by TPD [26,27] and/or a technique based on
carbons and their capacitance C, in view of practical applica-
i H(H2 O), the enthalpy of immersion of the carbons into
tions, such as the optimization of capacitors. The empha- water [28]. As discussed elsewhere [26], for the oxidized
316 T.A. Centeno, F. Stoeckli / Journal of Power Sources 154 (2006) 314–320

Table 1
Structural, chemical and electrochemical characteristics of the activated carbons
Carbon CMS CMS-H2 DCG-5 XC-72-17% BV46 BV46-ox PX-21 M-30 AZ46-0 AZ46-3 AZ46-5 AZ46-10
Wo (cm3 g−1 ) 0.25 0.25 0.54 0.13 0.40 0.42 1.20 0.7 0.33 0.32 0.32 0.33
Wo∗ (cm3 g−1 ) 0.01 0.01 0.20 0.04 0.15 0.19 0.79 0.33 0.10 0.07 0.06 0.05
Eo (kJ mol−1 ) 26.1 26.2 21.2 21.3 21.4 19.8 17.5 19.6 22.6 23.5 23.9 24.5
Lo (nm) 0.75 0.73 1.1 1.1 1.1 1.29 ∼2 1.33 0.96 0.89 0.86 0.82
Smi (m2 g−1 ) 625 685 982 259 727 651 1166 1050 668 719 744 805
Se (m2 g−1 ) ∼20 28 40 119 110 112 104 50 140 131 117 115
−
i H[C6 H6 ] (J g−1 ) 95.1 92.0 146.0 54.0 131.4 134.0 268.9 219.0 110.0 114.4 112 112
[O] (mmol g−1 ) 1.31 1.2 2.2 0.2 0.32 3.26 8 1.3 0.81 4.50 5.31 6.56
[O] (␮mol m−2 ) 1.96 1.68 2.15 0.53 0.38 4.27 6.30 1.20 1.00 5.30 6.17 7.13
Charge–discharge, C (F g−1 )
1 mA cm−2 115 104 169 38 142 155 322 204 126 150 153 144
10 mA cm−2 108 95 153 37 133 137 265 180 115 132 102 93
50 mA cm−2 95 52 138 33 123 122 206 160 105 88 98 30
70 mA cm−2 91 – 129 – 120 112 171 146 102 62 69 –
Votammetry
5 mVs−1 115 104 160 43 147 148 263 193 124 147 141 121
20 mVs−1 105 77 130 41 129 134 165 152 113 94 106 97
50 mVs−1 84 47 85 35 107 106 84 – 90 49 71 39
Wo∗ = Wo − 3.5 × 10−4 Smi .

carbons of the present series, the surface oxygen is evenly dis- was used as electrolyte. The capacitance C was determined
tributed between the main chemical functions, namely acidic, by galvanostatic charge–discharge voltage cycles from 0 to
phenolic and inert groups (e.g. carbonyl). For example, in 0.8 V at current density d of 1, 10, 50 and 70 mA cm−2 of
the case of carbons of series AZ46, there exists a linear rela- electrode surface. The specific capacitance C (F g−1 ) of a
tionship between the surface acidity (meq. NaOH g−1 ) and single electrode has been calculated by using the expression
the total oxygen content. As shown by immersion calorime-

td
try into water, following the preadsorption of n-nonane, C = 2I (1)
the oxygen-containing complexes are distributed relatively mc
Vd
evenly over the microporous structure [19,29]. This hypoth- where I is the current,
td the time spent during the dis-
esis is also confirmed by the modelling of water adsorption charge,
Vd the voltage decrease in the discharge and mc
in typical PSDs [30] and it follows that the chemistry of the is the weight of carbon loaded in the composite electrode
external surface is not distinct from that found in the micro- [9]. From these data, it is possible to calculate the capac-
pores. itances either in F g−1 or F cm−3 for the actual capacitor
These techniques provide a reliable structural character- (carbon + carbon black + binder, etc.). Voltammetry experi-
ization of the material and, in particular, a reliable assess- ments at scan rates of 5, 20 and 50 mV s−1 were also used for
ment of the microporous and external surface areas, Smi and estimating the specific capacitance of each electrode accord-
Se . Moreover, as seen in Table 1, the 12 carbons cover a ing to
wide range of pore sizes (0.7–2 nm) and of oxygen con-
tents (0.2–6.6 mmol g−1 or 0.4–7.1 ␮mol m−2 ). This includes qa + |qc |
C= (2)
most commercial activated carbons (oxygen contents below mc
V
1 ␮mol m−2 ), as well as their oxidized forms, which jus- where qa and qc are the anodic and cathodic voltammet-
tifies an analysis leading to the correlations presented ric charges on positive and negative sweeps and
V is the
below. potential range of CV (0.8 V) [31]. As shown in Table 1, a
satisfactory agreement was found between the data obtained
2.2. Electrochemical characteristics by both techniques, but our correlations are based exclusively
on the first technique, which appears to be more accurate.
The electrochemical measurements were carried out in
a potentiostat–galvanostat Autolab-Ecochimie PGSTAT30. 3. Results and discussion
Sandwich-type capacitors were prepared with two carbon
pellets (8 mm in diameter) separated by glassy fibrous 3.1. Limiting capacitance Co at 1 mA cm−2 and
paper and placed inside a Swagelok-cell. The electrodes structural properties of the carbons
(11–12 mg) were obtained by pressing a mixture of 75 wt%
of carbon, 20 wt% of polyvinylidene fluoride and 5 wt% of As shown by Qu and Shi [9,10], who investigated the
carbon black (Super P). Two molar H2 SO4 aqueous solution double-layer capacitance at low current density for more than
 T.A. Centeno, F. Stoeckli / Journal of Power Sources 154 (2006) 314–320 317

30 carbons (activated microbeads and fibers), SBET is often cellulosic) and known chemical treatments. Consequently,
larger than Smi + Se , which is not surprising [21]. These dif- we shall use only the data of Table 1, in order to exam-
ferent areas were obtained, respectively, from the analysis of ine the role of structural and chemical properties on Co
the nitrogen isotherm with the BET model, the DFT tech- and C.
nique and comparison plots. The specific capacitance at low First of all, one may assume that the contribution from
current densities, Co , in F m−2 of carbon surface area and the external surface area, cext , is relatively constant for clas-
given by the ratio sical activated carbons, often of similar origin. Moreover, as
shown by immersion calorimetry [19] and confirmed by the
Co (F g−1 )
Co (F m−2 ) = (3) modeling of water adsorption isotherms [29,30], the oxygen-
SBET (m2 g−1 ) containing complexes are distributed over the entire micro-
pore system, and not limited to the external surface Se . This
varies between 0.06 and 0.22 F m−2 for a 5 M KOH elec- means also that the Se will not be the main cause for a decrease
trolyte. On the other hand, for highly activated carbon fibers in C with increasing current density.
with BET surface areas between 2700 and 3200 m2 g−1 and Frakowiak et al. [2] report values between 0.1 and
a 1 M H2 SO4 electrolyte [5], one obtains values as low as 0.16 F m−2 obtained with 6 M KOH for mesoporous car-
0.07–0.11 F m−2 . However, the average micropore sizes and bon nanotubes and a carbon template without microporosity.
volumes suggest much smaller real surfaces. This is a plausible range for cext and using, for example,
A closer examination of Shi’s data shows that a bet- 0.14 F m−2 , it appears that for the carbons of Table 1 cmi
ter correlation is obtained for Co if one use Stot = Smi + Se . varies from 0.15 F m−2 (CMS-H2) to 0.26 F m−2 (PX-21).
This leads to an average capacitance of 0.138 ± 0.038 F m−2 The data of Qu and Shi [9] show a similar trend, which sug-
(standard deviation for 30 values). For our carbons and 2 M gests that cmi may be a function of the average micropore
H2 SO4 (Table 1), Stot leads to 0.172 ± 0.038 F m−2 . These width Lo . Fitting the data of Table 1 to a simple three-
values are similar, but in view of their scatter, they are only parameter equation leads to the correlation (R = 0.980, see
indicative for the whole spectrum of activated carbons. The Fig. 1)
recent data of Gryglewicz et al. [4] for 1 M H2 SO4 and 6 M
KOH electrolytes lead, respectively, to 0.127 ± 0.028 and
Co (F g−1 ) = (0.096 + 0.081Lo )Smi + 0.124Se (5)
0.095 ± 0.024 F m−2 . Although no estimate is given by these
authors, the simple relation L (nm) = 2000Vmi (cm3 g−1 )/Smi
It covers the range 0.7–0.8 nm < Lo < 2 nm, where the lower
(m2 g−1 ) [19] suggests average micropore widths of 0.72 nm
bound corresponds typically to two layers in the micropores,
for all carbons, which is surprising.
one on each wall. For Lo = 0.75 nm, cmi = 0.156 F m−2 against
It was first suggested by Shi that Co , the capacitance at
0.258 F m−2 for cage-like supermicropores with Lo = 2 nm.
low current density, results from separate contribution from
Beyond, one may expect a rapid decrease and the surface
Smi and Se ,
acquires the properties of an external surface. One reason is
Co (F g−1 ) = cmi Smi + cext Sext (4) the rapid decrease of the force field in pores beyond 2 nm. This
is clearly the case for adsorption, where Dubinin’s theory for
For the aqueous KOH electrolyte used by Shi, parameters cmi the volume filling of micropores (TVFM) is no longer valid
and cext are, respectively, 0.195 and 0.74 F m−2 for activated beyond 2–2.5 nm.
microbeads and 0.145 and 0.075 F m−2 for activated fibers (it
should be noted that the value of 0.74 F m−2 is unusually high,
since the external surface area of the two types of carbons are
similar). Our own data (Table 1), based on 2 M H2 SO4 , leads
to cmi = 0.20 F m−2 and cext = 0.022 F m−2 (R = 0.916).
These results show that Shi’s Eq. (4) provides a bet-
ter description for Co , but parameters cmi and cext depend
both on the electrolyte, which is not too surprising, and
other factors. The latter may include experimental condi-
tions, as well as structural and chemical properties of the
carbons, as suggested by different authors. For example,
Gryglewicz et al. [4] suggest that for activated carbons
with highly developed surface areas and a low mesopore
fraction, the double-layer capacitance also depends on the
pore size distribution. It follows that a closer examination
of the parameters leading to a further improvement of Eq.
(4) should be based on clearly defined experimental con-
ditions, using sets of well-characterized carbons, ideally of Fig. 1. Correlation between the calculated and experimental capacitances
the same type (activated carbons), of the same origin (ligno- Co (F g−1 ) at 1 mA cm−2 of electrode, using Eqs. (5) (
) and (8) ().
318 T.A. Centeno, F. Stoeckli / Journal of Power Sources 154 (2006) 314–320

A possible explanation for the increase of Co with Lo is single layer. After regrouping one obtains
a contribution to cmi from the layers found between the sur-
face layers. Their number varies between 0 and 3–4 and their Co (F g−1 ) = (0.095 + 0.079Lo )Smi + 0.134Se (10)
contribution is a specific property, possibly limited to micro-
pores. As discussed elsewhere [21], immersion calorimetry which is practically Eq. (5). However, the latter has been
suggests that liquid adsorption in microporous carbons can obtained with only three adjustable parameters.
be divided into three contributions, namely from the surface Eqs. (8) and (10) may provide, formally at least, a good
areas Smi and Se , and from the volume Wo∗ . The latter is estimate of Co for activated carbons with micropores and
defined as the volume of liquid found between the layers in supermicopores, thus covering practically the whole range
contact with the micropore walls, given by of commercially available carbons. However, more data will
be needed for carbons with average pore sizes Lo between
Wo∗ = Wo − cSmi (6) 1.5 and 2.5 nm, based preferably on activation series. It is
also likely that parameters c1 –c4 depend on the experimental
In the case of benzene, it is found that c corresponds to a conditions and on the electrolyte (in the present case, 2 M
monolayer thickness of 0.41 nm, which is reasonable for this H2 SO4 ).
molecule lying flat on a graphitic surface [21,22]. As sug- Inspection of the data of Table 1 shows that within the
gested by Eq. (5), Co depends on Lo and therefore on Wo∗ , experimental uncertainty on Co (±10%), this quantity does
which leads to not depend on the amount of oxygen present on the sur-
face. For example, in the case of series BV and AZ46,
Co (F g−1 ) = c1 Smi + c2 Sext + c3 (Wo − c4 Smi ) (7) where [O] varies, respectively, from 0.38 to 4.27 and 1 to
The data for the 12 carbons of Table 1 lead to the correlation 7.13 ␮mol m−2 . This means that the limiting capacitance Co
(R = 0.982, see Fig. 1) can be assessed on the basis of the structural parameters
Smi , Se and Wo∗ alone (at this stage, we cannot explain the
Co (F g−1 ) = 0.150Smi + 0.134Sext relatively low value of Co = 126 F g−1 observed for carbon
AZ46-0, whereas the structural parameters of the carbons in
+158(Wo − 3.5 × 10−4 Smi ) (8) this series are similar).
Parameter c4 = 3.5 × 10−4 cm3 nm−1 corresponds to an aver-
age monolayer thickness of 0.35 nm for the electrolyte (in the 3.2. Variation of C with current density and oxygen
present case, H2 SO4 2 M), which is reasonable. However, it content
is likely that other electrolytes may lead to different values
for parameters c1 –c4 . As shown in the table and reported by different authors,
The value of Wo∗ (see Table 1) is practically zero for the car- for example [7,9], C decreases generally with increasing elec-
bons with average micropore width Lo < 0.7–0.8 nm (CMS) it trode current density d (1–70 mA cm−2 in the present case).
increases with Lo , as more electrolyte can be accommodated This pattern reflects a large resistance in pores due to the hin-
between the layer directly in contact with the micropore walls. dering of ion transfer in the randomly connected micropores.
The contribution of Wo∗ to Co varies between 0 and 40% (car- Ionic motion in such small pores may be so slow that the total
bon PX-21). microporous surface may not be utilized for charge storage
It should also be pointed out that a contribution of at high current [2].
158 F cm−3 to the capacitance Co seems plausible, as long It has been reported [32] that the resistance is also an
as it is limited to the one to four intermediate layers increasing function of the degree of oxidation of the carbon
found inside micropores. This is suggested, for example, and suggests that the imparted polarity may hinder the motion
by the value of 460 F cm−3 for the layers which are in of ionic species in the micropores. Our preliminary experi-
direct contact with the surface, as obtained for carbon CMS ments suggest a somewhat faster decrease of C at higher elec-
(Co = 115 F g−1 and Wo = 0.25 cm3 g−1 ). The micropores of trode current densities, as the oxygen content [O] increases.
this solid (Lo = 0.75 nm) can accommodate only two layers This is clearly illustrated by Fig. 2(a and b), showing the vari-
of 0.35 nm. ation of the relative capacitance C/Co for carbons AZ46-0,
Eqs. (8) and (5) are obviously related, as shown by simple AZ46-3 and AZ46-10, where the oxygen content increases
algebra. With the definition of Wo∗ (Eq. (6)) and the fact that from 0.81 to 6.56 mmol g−1 or from 1 to 7.13 ␮mol m−2
for slit-shaped micropores Wo (cm3 g−1 ) = Smi (m2 g−1 )Lo of total surface Smi + Se . The same pattern is observed for
(nm)/2000 [19], Eq. (8) becomes carbons BV46 and BV46-ox (0.38 and 4.27 ␮mol [O] m−2 ,
respectively). Since the carbons of these series have very
Co (F g−1 ) = [0.150 + 0.079(Lo − 0.70)]Smi + 0.134Se similar structural characteristics, there is little doubt about
(9) the influence of oxygen on the capacitance, even at moder-
ate current densities. However, it should be pointed out that
0.70 nm is the lower bound for Lo , as it represents the mini- the amounts of oxygen [O] are much higher than is found in
mum average pore width in which the walls are covered by a standard activated carbons.
 T.A. Centeno, F. Stoeckli / Journal of Power Sources 154 (2006) 314–320 319

Fig. 3. Correlation between the calculated and experimental capacitances C

(F g−1 ) for the carbons of Table 1 at electrode current densities d of 1, 10,
50 and 70 mA cm−2 , using Eq. (11). Co is the capacitance for 1 mA cm−2 .

influence of the different oxygen-containing surface com-

plexes requires a further study, but Eq. (11) suggests inter-
esting trends. Moreover, this expression provides a useful
correlation for the evaluation of the performance of a given
carbon to be used for electrochemical applications (capaci-
tors and energy storage devices). Like Eqs. (8) and (10), Eq.
(11) also covers a wide range of active carbons and it pro-
vides a useful tool for the prediction of their performances as
capacitors.

3.3. Correlation between Co and the enthalpy of

immersion
i H(C6 H6 )

Fig. 2. (a and b) Variation of the relative capacitance C/Co with the cur- Finally, it is worthwhile, from a practical point of view,
rent density d for carbons AZ46-0 (), AZ46-3 (), AZ46-10 (䊉) (a), and to mention that the limiting capacitance Co is related to the
BV46 (), BV46-ox () (b). The data were obtained by the galvanostatic enthalpy of immersion of the corresponding carbon into a
charge–discharge technique.
non-specific liquid, such as benzene (see Table 1). As illus-
trated by Fig. 4, one obtains a relatively good correlation for
At this stage of our research, the data for the capacitance C the 12 carbons of Table 1 and another 8 carbons currently
determined by the galvanostatic charge–discharge technique,
the current density d and the total oxygen content [O] of the
carbons suggest the following overall, but provisional and
empirical expression, with a correlation coefficient of 0.975
(see Fig. 3)
C (F g−1 ) = Co exp[−5.32 × 10−3 d(1 + 0.0158[O]2 )]
(11)
Co is the value for a current density d of 1 mA cm−2 of elec-
trode and [O] is given in mmol g−1 . The use of the total
oxygen content in Eq. (11) may be questioned, since the
mobility may depend on the different types of surface groups
(in particular acids). However, for most of the carbons used
in this study, there exists a linear relation between the acidity
(meq. NaOH g−1 ) and the total oxygen content [O] [27]. It Fig. 4. Empirical correlation between Co , the capacitance C (F g−1 ) at
appears that three types of oxygen atoms (acidic, basic and 1 mA cm−2 and the enthalpy of immersion
i H(C6 H6 ) (J g−1 ) at 293 K
inert) are evenly distributed in these carbons. Obviously, the for 20 microporous carbons.
320 T.A. Centeno, F. Stoeckli / Journal of Power Sources 154 (2006) 314–320

under investigation, Acknowledgement

Co (F g−1 ) = −k
i H(C6 H6 ) (J g−1 ) The authors wish to thank Professor C. Moreno-Castilla

−1
(k = 1.15 ± 0.10 F J ) (12) (University of Granada) for the gift of carbons of series AZ
and BV.
A similar correlation (k = 1.2 F J−1 ) is found for immersion
into the electrolyte solution itself (2 M H2 SO4 aq.), but indi-
vidual deviations exist, due to specific chemical reactions References
of the acid with surface groups and to the relatively strong
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