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Increase in Capacitance by Subnanometer Pores in
Carbon
Nicolas Jäckel, Patrice Simon, Yury Gogotsi, Volker Presser
To cite this version:
Nicolas Jäckel, Patrice Simon, Yury Gogotsi, Volker Presser. Increase in Capacitance by Subnanome-
ter Pores in Carbon. ACS Energy Letters, American Chemical Society 2016, 1 (6), pp.1262-1265.
�10.1021/acsenergylett.6b00516�. �hal-01528359�
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Eprints ID : 16683
To link to this article : DOI:10.1021/acsenergylett.6b00516
URL : http://dx.doi.org/10.1021/acsenergylett.6b00516
To cite this version : Jäckel, Nicolas and Simon, Patrice and
Gogotsi, Yury and Presser, Volker Increase in Capacitance by
Subnanometer Pores in Carbon. (2016) ACS Energy Letters, vol. 1
(n° 6). pp. 1262-1265. ISSN 2380-8195
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Increase in Capacitance by Subnanometer
Pores in Carbon
E
lectrical double-layer capacitors (EDLCs, also known as
supercapacitors or ultracap acitors) store energy by
electrosorption of ions at the electrode/electrolyte
interface.
1
To achieve a high-energy storage capacity, electrodes
with a high surface area and well-developed pore structure in
the range from several Angstroms to several tens of nanometers
are required.
2
However, neither natural precursor-derived
carbons nor templated carbon materials present an ideal,
infinitesimally narrow pore size dispersion.
3
In EDLCs, the use of salt dissolved in an organic or aqueous
solvent makes it important to consider the solvation shell
around the ions. The bare ion size is usually below 1 nm,
whereas the solvation shell can increase the size significantly.
3
Several studies have provided strong evidence of ion desolva-
tion during electrosorption, which is the only way to explain
why carbon materials with pore sizes smaller than the solvated
ion but larger than the bare ion have high charge storage
capacities.
4−8
A maximized capacitance (normalized by the
surface area) was found in experimental and theoretical studies
when matching the pore size with the ion size.
9
This effect
seems to be universally applicable for solvent-containing and
solvent-free electrolytes (ionic liquids), while important
secondary differences are to be considered for the latter. For
example, the oscillatory dependency of capacitance on pore size
predicted for neat ionic liquids and ideal carbons with slit pores
is lost when introducing a solvent, where a single maximum is
observed when the ion size and the pore size are identical.
10,11
This Viewpoint clarifies the correlation between capacitance
and pore size, which is of high practical importance for the
design of advanced carbon electrode materials. Two extreme
cases are obvious: excessively large pores, accompanied by large
pore volumes and limited specific surface area, will lead to a low
energy storage capacity, whereas very small pores will limit the
ion access due to steric effects (
Figure 1), in addition to
i
mposing obstacles to ion transport.
1 2,13
Yet, fo r the
intermediate range, down to the point when the pores are
too small for the bare ion to fit, there is no consent in the
literature about the correlation between the pore size and the
corresponding area-normalized capacitance. For example, there
h as been criticism about the method of surface area
determination and normalization, especially considering the
inadequacy of the Brunauer−Emmett−Teller (BET) model for
microporous carbons.
14,15
Benchmarking various kinds of
carbons, including carbon monoliths, a “regular pattern” was
presented, suggesting that the area-normalized capacitance does
not depend on the pore size.
14,16
This lack of dependence can
be explained by neither the ab initio or molecular dynamics
models
17,18
nor geometric considerations as when the pore
diameter increases by 50−90%, there is still just one ion in each
pore contributing to charge storage and the remaining surface
a rea and pore volume remain unused , decreasing the
capacitance normalized by the pore surface or volume.
Recently, we developed a model for understanding the
capacitance of microporous carbons, taking into account the
entire measured pore size distribution, and have established a
comprehensive data set of electrochemical measurements.
6
Density functional theory (DFT) kernels were used, which are
currently the most advanced methodology to extract porosity
data from gas sorption isotherms for meso- and microporous
carbons and effectively avoid the fundamental limitations of the
BET theory.
19
Activated carbon showed the highest specific
surface area (SSA), followed by two different titanium carbide-
derived carbons (CDCs),
20
activated carbon black (CB), and
carbon onions.
21
Yet, wh en normalizing electrochemical
performance data on porosity values, we first have to consider
differences between dry powder and film electrodes.
6
Then, we
have to assess the differences in pore size distributions; these
are shown in Figure 2A normalized to 100% for th e
aforementioned carbon materials. Many carbons display a
significant dispersion width; this is why the often-used volume-
weighted average pore size d
50
does not fully capture the pore
size distribution width, as we show by adding values for d
25
and
d
75
, representing the pore width encompassing 25 and 75% of
the total pore volume, respectively (Table 1, Figure 2A).
More differences in the surface area of the different electrode
materials become evident when we calculate the electrochemi-
cally active surface, that is, the ion-accessible surface area
(Table 1 , Figure 2B). Taking into account the bare ion size of
BF
4
−
(0.45 nm) and TEA
+
(0.67 nm), pores smaller than these
Figure 1. Electrosorption of specific ions with a finite size is only
possible if the pore size is at least equal to the ion size. Therefore,
the specific surface area of pores smaller than the bare ion size is
inaccessible for energy storage. Larger pores can adsorb more than
one ion per pore.
Viewpoint
values are inaccessible to the ions.
7
The result is a further
reduction of the specific surface area, and we have to consider
different cutoff values for the positively (cutoff pore size of 0.4
nm) and negatively (cutoff at 0.6 nm) polarized electrodes. In
the case of CDC, only about 40− 50% of the total SSA is
accessible to TEA
+
compared to about 70% for activated carbon
and
carbon black (Figure 2A).
The reported electrochemical measurements using a three-
electrode configuration (for experimental methods see the
Supporting Information) showed a nonlinear correlation of
SSA
and gravimetric capacitance measured in F ·g
−1
(Table 1)
for 1 M TEA-BF
4
in acetonitrile (ACN) or propylene carbonate
(PC ).
6
A very high Coulomb ic efficiency (up to 99%)
underlines the absence of significant Faradaic reactions in the
chosen potential window (Table 1). When we normalize the
measured electrode capacitance by the surface area accessible to
cations or anions at +1 and −1 V vs carbon, respectively, we see
a clear difference between positive and negative polarization
(
Figure 3, Table 1). Instead of just discussing the electro-
chemical data in the context of average pore width (d
50
), we
added error bars for the x-axis, which spread between d
25
and
d
75
(Figure 3). Even when considering pore size dispersity, we
still see a clear trend of increased normalized capacitance in
subnanometer pores, which is significantly larger for negative
polarization (i.e., electrosorption of the larger TEA
+
cation).
The
more effective use of available pores in the case of
matching sizes results in a strong increase in capacitance, which
was already shown by a geometric model of Huang et al. (ref
22; see also the data line in Figure 3). For larger pore sizes, in
Figure 2. (A) The cumulative pore size distribution of electrodes was derived by combining CO
2
and N
2
sorption and normalizing all data to
100%. (B) Porosity analysis of different carbon electrode materials using a DFT model. Data are normalized for SSA of electrodes containing
10 mass% PTFE as 100% and the calculated accessible surface area for BF
4
−
anions (0.4 nm, BF
4
−
accessible) and TEA
+
cations (0.6 nm, TEA
+
accessible).
Table 1. Combined NLDFT Model for CO
2
Sorption for Pores Smaller than 0.9 nm and QSDFT Model for N
2
Sorption for
Pores Larger than 0.9 nm
a
Material
DFT
SSA
(m
2
·
g
−1
)
d
50
(d
25
−d
75
) pore
width (nm)
capacitance at
+1 V in ACN
(F·g
−1
)
Coulomb
efficiency
(%)
capacitance
at +1 V in
PC (F·g
−1
)
Coulomb
efficiency
(%)
capacitance at −1 V
in ACN (F·g
−1
)
Coulomb
efficiency
(%)
capacitance at −1 V
in PC (F·g
−1
)
Coulomb
efficiency
(%)
AC 1839 1.3 (0.8−1.8) 113 96 115 99 103 99 102 99
CB 1097 15 (5−19) 99 99 99 99 88 99 87 99
OLC 232 9.5 (6−14) 20 98 20 99 16 99 16 99
CDC600 934 0.64 (0.53−0.93) 127 97 132 98 121 98 119 99
CDC1000 967 0.90 (0.62−1.4) 101 97 100 98 98 98 96 99
a
The average pore size relates to the volume-weighted arithmetic mean value d
50
with the standard deviation from d
25
to d
75
. Capacitance values were
recorded at +1 V vs carbon and −1 V vs carbon in a three-electrode setup (half-cell).
Figure 3. Capacitance of porous carbons normalized to the
accessible surface area for each ion in both solvents. The regular
pattern average of 0.95 F m
−2
from ref 15 is added, and data for the
Huang model is from ref 17.
particular, for mesopores, the capacitance converges toward an
average value below 0.1 F·m
−2
, which aligns well with the
“regular pattern” value reported by Centeno et al. (ref
15) and
with the calculated value limiting the double-layer capacitance
at the planar carbon interface (or larger than the few-nm pores;
ref 17).
For electrolytes with significant differences between the size
of anions and cations, our data clearly show the importance of
differentiating between ion electrosorption during positive or
negative polarization with use of half-cell measurements (
Figure
3). With a larger size of TEA
+
, and smaller corresponding
surface area accessible to the cations, the values of areal
capacitance during negative polarization are significantly larger
than those for BF
4
−
electrosorption (i.e., positive polarization).
A
ccordingly, adva nced EDLC cell design could achieve
performance enhancement by developing nanoporous carbon
with slightly different pore sizes for the positive and negative
electrodes.
23,24
In summary, our data analysis clearly supports the increase in
surface-normalized capacitance when most of the pores are
below 1 nm, in agreement with previous studies (e.g., see refs 7
and 25). This was shown for carbons with very different pore
structures considering the complexity of pore size dispersity
and for two different solvents (i.e., PC and ACN). This effect is
seen at different amplitudes for positive and negative
polarization, with a smaller increase for BF
4
−
within the range
of investigated pore sizes.
Nicolas Ja
ckel
†,‡
Patrice Simon*
,§,∥
Yury Gogotsi*
,⊥
Volker Presser*
,†,‡
†
INM - Leibniz Institute for New Materials, 66123
Saarbru
cken, Germany
‡
Department of Materials Science and Engineering, Saarland
University, 66123 Saarbru
cken, Germany
§
Universite
Paul Sabatier, CIRIMAT UMR, CNRS 5085, 5085,
31062 Toulouse Cedex 4, France
∥
Re
seau sur le Stockage Electrochimique de l′Energie, RS2E FR
CNRS 3459, 80039 Amiens Cedex, France
⊥
Department of Materials Science and Engineering, and A. J.
Drexel Nanotechnology Institute, Drexel University,
Philadelphia, Pennsylvania 19104, United States
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail: simon@chimie.ups-tlse.fr (P.S.).
*E-mail: gogotsi@drexel.edu (Y.G.).
*E-mail: volker.presser@leibniz-inm.de (V.P.).
■
ACKNOWLEDGMENTS
The authors thank Dr. Weingarth, Dr. Aslan, Anna Schreiber,
Jeon
Jeongwook (all at INM), and Katherine Van Aken (Drexel
University) for their technical support and helpful discussion.
N.J. and V.P. also thank Prof. Eduard Arzt (INM) for his
continuing support. Y.G. was supported by the Fluid Interface
Reactions, Structures and Transport (FIRST) Center, an
Energy Frontier Research Center funded by the U.S.
Department of Energy, Office of Science, Office of Basic
Energy Sciences.
■
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