Influence of particle size on rate performance of mesoporous carbon electric double-layer capacitor (EDLC) electrodes

Article abstract of DOI:10.1149/1.3490638

Herein, mesoporous carbon materials with different particle sizes were prepared using the direct templating method. To control particle size, the concentration of surfactant/silicate dissolved in aqueous solution was varied. According to a decrease in the concentration, a larger surface area and a smaller particle size were observed, whereas pore size and connectivity remained invariant. From the investigation of electric double-layer capacitor performance, specific capacitance was proportional to surface area. From electrochemical impedance spectroscopy analysis, a resistance relevant to pseudocapacitive faradaic reaction on electrode surface became larger, but a decrease in the total electrolyte resistance in pores was observed as a function of particle size decrease. This contradictory behavior of two resistances resulted in an existence of optimal particle size for the minimum equivalent series resistance (1.40 ω cm²), which was comparable with the ordered mesoporous carbon electrode from the MCM-48 template.

Full text of DOI:10.1149/1.3490638

Journal of The Electrochemical Society, 157 ͑11͒ A1229-A1235 ͑2010͒
A1229
0
013-4651/2010/157͑11͒/A1229/7/$28.00 © The Electrochemical Society
Influence of Particle Size on Rate Performance of Mesoporous
Carbon Electric Double-Layer Capacitor (EDLC)
Electrodes
a, ,z
b,
a
c
Songhun Yoon, * Seung M. Oh, * Chul Wee Lee, and Jae-Won Lee
a
Green Chemical Technology Division, Korea Research Institute of Chemical Technology, Daejeon 305-
6
00, Korea
b
Research Center for Energy Conversion and Storage, School of Chemical Engineering and Institute of
Chemical Process, College of Engineering, Seoul National University, Seoul 151-744, Korea
c
Korea Institute of Ceramic Engineering and Technology, Seoul 153-801, Republic of Korea
Herein, mesoporous carbon materials with different particle sizes were prepared using the direct templating method. To control
particle size, the concentration of surfactant/silicate dissolved in aqueous solution was varied. According to a decrease in the
concentration, a larger surface area and a smaller particle size were observed, whereas pore size and connectivity remained
invariant. From the investigation of electric double-layer capacitor performance, specific capacitance was proportional to surface
area. From electrochemical impedance spectroscopy analysis, a resistance relevant to pseudocapacitive faradaic reaction on
electrode surface became larger, but a decrease in the total electrolyte resistance in pores was observed as a function of particle
size decrease. This contradictory behavior of two resistances resulted in an existence of optimal particle size for the minimum
2
equivalent series resistance ͑1.40 ⍀ cm ͒, which was comparable with the ordered mesoporous carbon electrode from the
MCM-48 template.
©
2010 The Electrochemical Society. ͓DOI: 10.1149/1.3490638͔ All rights reserved.
Manuscript submitted June 23, 2010; revised manuscript received August 9, 2010. Published September 25, 2010.
The template preparation of mesoporous carbon materials has
CTAB/TEOS/NaOH/H O was 2/1/1/200. Here, CTAB concentra-
2
1-3
been vastly investigated. As the templates, various templates such
as ordered mesoporous silica, spherical silica particles, polymer
tion was varied from 10 to 0.01 wt %. This solution was stirred at
40°C for 2 h to produce the CTAB/silicate rod-shaped micelles that
2
-6
11,12
beads, and even the surfactant have been utilized. The mesopo-
rous carbons prepared by a template method have exhibited out-
standing performance when they were applied into various fields
such as gas separation, water purification, catalyst support, adsor-
play the role of template.
Another solution of resorcinol ͑R͒ and
formaldehyde ͑F͒ was prepared with Na CO as a catalyst at the
2
3
molar ratio of R/F/Na CO /H O = 10/20/1/100. After this solution
2
3
2
was reacted for several 10 min, the oligomeric phase of resorcinol–
7
-9
13
bents, and electrode materials for charge storage. Especially, as
electrode materials for energy conversion and storage devices such
as electric double-layer capacitors ͑EDLCs͒, lithium-ion batteries,
and fuel cells, mesoporous carbon electrodes have displayed im-
proved rate performance, which was certainly due to the well-
formaldehyde ͑RF͒ was formed. Two solutions ͑the template and
RF solutions͒ were mixed at the molar ratio of R/TEOS = 1/1,
stirred vigorously, and then aged at 85°C for a week. The obtained
precipitate was filtrated, dried in air at 85°C, and then heat-treated at
1
000°C under Ar atmosphere for 1 h to remove CTAB and to car-
1
,2
developed mesoporosity and the high pore connectivity. This char-
acteristic pore structure enabled electrolytes or ions to transport
bonize the RF gel. As the final step, the silica included in the com-
posite was removed by HF and porous carbon was acquired.
6,7,9
quickly through interconnected mesopores.
In our previous pa-
Pore size distribution ͑PSD͒ was analyzed by N adsorption mea-
2
pers, the pore formation mechanism and the effect of carbonization
surement ͑Micromeritics ASAP 2010͒. The external morphology of
carbon was examined using a scanning electron microscope ͑JEOL
JSM-840A͒, whereas the pore image was scanned by a transmission
electron microscope ͑TEM, JEOL JEM-2010͒. The X-ray diffraction
patterns were obtained with a Rigaku D/Max-3C diffractometer
6
temperature have been clarified in the direct templating method.
Even with the ordered structure collapsed, the high rate performance
was still maintained in the prepared mesoporous carbon electrodes.
Furthermore, the reaction time influence of the silicate/surfactant on
10
pore structure was investigated.
equipped with
a rotating anode and Cu K␣ radiation ͑␭
As an extension of our previous work, the concentration of the
surfactant/silicate is varied to control the carbon particle size. After
the addition of the carbon precursor to the template solution, meso-
porous carbons are obtained from aging, carbonization, and silica
etching. Using morphological and sorption analysis, the pore struc-
ture of the as-prepared mesoporous carbons is characterized. The
performance of EDLC is investigated using cyclic voltammetry
=
0.15418 nm͒.
Electrochemical characterization.— To prepare the EDLC elec-
trode, a mixture of prepared carbon and polytetrafluoroethylene
binder, Ketjenblack ECP-600JD ͑10:1:1 in weight ratio͒ was dis-
persed in isopropyl alcohol and was coated on 1 ϫ 1 cm stainless
steel Exmet as the current collector. The electrode resistance was
͑
CV͒ and electrochemical impedance spectroscopy ͑EIS͒. From the
7
comparison between the physical and electrochemical analyses, the
influence of particle size ͑pore length͒ on the rate performance of
EDLC electrodes is clarified.
negligible when 10 wt % conducting materials was added. The
resulting electrode plate was pressed and dried under vacuum at
1
20°C for 12 h.
The electrochemical performance of the composite carbon elec-
trodes was analyzed with a three-electrode configuration in an aque-
Experimental
ous 2 M H SO electrolyte. A Pt flag and a saturated calomel elec-
2
4
Materials.— In Fig. 1, a schematic description of the particle
trode ͑SCE͒ were used as the counter and reference electrodes,
respectively. The interelectrode gap between the working and refer-
ence electrodes was fixed as 0.4 cm. EIS and CV were conducted by
Iviumstat of Ivuim Technology. AC impedance spectra were re-
size control is displayed, which is similar to our previous direct
6
templating method. After dissolving cetyltrimethylammonium bro-
mide ͑CTAB͒ and sodium hydroxide in deionized water, tetraethyl
orthosilicate ͑TEOS͒ as silica source was added. The molar ratio of
corded at open-circuit voltage at 10 mV magnitude from 0.05 to
5
1
0
Hz. CV was carried out in the potential range of 0.0–0.7 V ͑vs
−
1
SCE͒ with a scan rate of 5 mV s . For the nonlinear least-squares
NLLS͒ fitting of ac impedance spectra, a program of Equivalent
Circuit Ver. 3.95 by EG&G PARC was used.
͑
*
Electrochemical Society Active Member.
E-mail: yoonshun@krict.re.kr
z
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A1230
Journal of The Electrochemical Society, 157 ͑11͒ A1229-A1235 ͑2010͒
Porous carbon
SSM
CTAB in solution
CTAB
Low concentration
TEOS
1
2
3
) RF adding
) carbonization
) silica etchig
Figure 1. ͑Color online͒ Schematic expla-
nation of synthesis process.
pH >14
High concentration
Results and Discussion
particle agglomeration was observed and nonporous carbon particles
appeared at 0.1%. The concentration dependency of the prepared
mesoporous carbons was similar to the mesoporous silica, which
Morphological and nitrogen sorption analysis.— In Fig. 2,
SEM images of as-prepared mesoporous carbons are displayed ac-
cording to CTAB/silicate concentration. The particle size was varied
a little from 10 to 5% concentration change, but its abrupt decrease
was observed at 2%. For the 1% case, nanosized carbon rods of
14
was reported. Hence, the morphological change in as-prepared car-
bon materials indicated that the added surfactant/silicate played the
6,9,10
role of the template for carbon preparation.
The pore morphology was investigated by TEM analysis ͑Fig. 3͒,
where a high population of pores ͑lighter image͒ is identified. As
seen, the pore morphology ͑diameter and shape͒ seemed invariant,
irrespective of surfactant concentration. For 1 and 0.5% carbon, car-
bon nanorods with mesopores were obtained. As described in the
previous paper, the observed wormholelike pores were characteristic
to mesoporous carbon materials prepared by direct templating
1
00–200 nm in diameter were observed. At 0.5% concentration,
6
,9
preparation.
Figure 4 shows the change in N sorption profiles for the pre-
2
pared carbons according to concentration. Here, characteristic H2-
1
5
type hysteresis defined from IUPAC was commonly observed.
This hysteresis at 0.6 P/P was relevant to the mesopores in carbon
0
materials. In addition, the abrupt increase in volume adsorbed near
saturation pressure ͑P/P ϳ 1͒ started at 2% and becomes larger at
0
1
%, which was probably due to large mesopores between interpar-
ticles, which was confirmed in Fig. 2c and d.
These sorption profiles are utilized in two ways: An estimation of
PSD and a calculation of pore connectivity. Figure 5 shows the PSD
calculated from the adsorption branch of Fig. 4 using the Barrett–
1
5
Joyner–Halenda ͑BJH͒ method. For all carbon materials, pores
ranging from 1 to 10 nm were dominant and their average pore
diameter remained almost the same. The average pore diameters are
listed in Table I. From our preliminary experiment, it was revealed
that pore diameter depended on silicate reaction time and carboniza-
6
,10
tion temperatures.
Therefore, the invariant pore diameter in Fig.
5
was attributable to the same CTAB/silicate reaction time ͑2 h͒ and
carbonization temperature ͑1000°C͒. With the change in surfactant
concentration in our experiment, only the particle size of mesopo-
rous carbons was varied, as shown in Fig. 2. Although a threshold of
pore volume distribution ͑dV/dD͒ located from 6 to 10 nm diameter
was observed for the 10 and 5% cases, its corresponding pores were
less populated than peak pores of 3 nm and its contribution in the
total pores is disregarded. A larger Brunauer, Emmett, and Teller
͑
BET͒ surface area ͑ABET͒ was observed with decreasing concentra-
Figure 2. Field-emission-scanning electron microscopy images of various
carbons. ͑a͒-͑f͒ are 10, 5, 2, 1, 0.5, and 0.1 wt % surfactant concentration,
respectively.
tion, which was a direct result of the increase in particle size ͑Table
I͒.
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Journal of The Electrochemical Society, 157 ͑11͒ A1229-A1235 ͑2010͒
A1231
baseline to individual desorption data ͑x͒ and a length to acquired
adsorption data ͑y͒. From the inset of Fig. 4, F͑P͒/f͑P͒ can be
obtained from the ratio of x and y; F͑P͒/f͑P͒ = x/y. The f͑P͒ can
be calculated from the following equation
ϱ
ϱ
V͑D͒
D
V͑D͒
D
f͑P͒ =
dD/
dD
͓1͔
͵
2
͵
2
ء
D
0
Here, D and V͑D͒ are the diameter of pore ͑dV/dD͒ and the pore
diameter where condensation happens, respectively. From dV/dD
1
6
and D in Fig. 5, f͑P͒ can be obtained.
Two parameters such as L and Z are used for pore connectivity
1
7
description. Here, L and Z are the characteristic average nominal
linear dimension and coordination number, respectively. Physically,
Z can be interpreted as the number of body ͑pore͒ meeting at a node
and so it is proportional to the connectivity of pores. After obtaining
f and F using the above method, Z and L are calculated by NLLS
using the generalized scaling equation expressed in the following
equation
L
␤/␯ZF = h͓͑Zf − 1.5͒L1/␯
͔
͓2͔
Here, ␤ and ␯ are 0.41 and 0.88, respectively.
In Fig. 6a, the relationship between F͑P͒ and f͑P͒ was obtained
from the sorption profiles of Fig. 4. As seen, the characteristic per-
colation for a finite system was observed for all carbons. The per-
colation threshold ͑f ͒ was similar about 0.5, irrespective of concen-
c
tration change. Here, fc can be roughly estimated from the f͑P͒
value showing the same value of F͑P͒ and f͑P͒. This similar fc
indicates a similar connectivity for all carbon materials. To calculate
Z and L, an NLLS fitting was conducted, as shown in Fig. 6b, where
the typical result for 1% carbon is displayed. The empty circle rep-
resents the sampled data and the solid line that correspond to the
2
−3
best fitting result ͑␹ Ͻ 10 ͒. Table I lists the best-fitted values for
Z and L. Z remained similar, irrespective of surfactant concentration,
indicative of a similar pore connectivity for all carbons. In our pre-
liminary experiment, Z was varied according to the change in reac-
tion time of silicate/surfactant before RF addition, indicative of pore
connectivity variation.
From the above physical analysis, therefore, it was concluded
that the pore size and its connectivity remained invariant, agreeing
with the decrease in the surfactant concentration, whereas the par-
ticle size and concomitant surface area were varied. The pore length
of the mesoporous carbons became shorter with particle size de-
crease. Using the prepared carbons, EDLC electrodes were fabri-
cated, and their performance was investigated. Because the other
pore structure parameters remained invariant for all carbon materi-
als, the independent investigation of the pore length effect on rate
performance was possible in our EDLC electrodes.
Comparison of supercapacitor performances.— In the previous
literatures, mesoporous carbon electrodes for EDLC electrode mate-
rials have exhibited an improved rate performance, which was at-
Figure 3. TEM images of various carbons. ͑a͒-͑c͒ are 10, 1, and 0.5 wt %
surfactant concentration, respectively.
2
,5-7,9
tributable to their characteristic pore structures.
Pore features
such as size, connectivity, and length can be the crucial factors de-
termining the rate performance of EDLC because electrolyte trans-
ports through the pores of carbon electrodes. However, it was diffi-
cult to investigate pore structure effect systematically because the
independent control of pore diameter, connectivity, and length is
required in porous carbon preparation. In our experiment, however,
only pore length ͑particle size͒ was varied with the other structure
factors invariant. Using the prepared mesoporous carbon materials,
the relationship between pore length and rate performance was in-
vestigated.
From the sorption profile analysis, the hysteresis during adsorp-
tion and desorption can be utilized for the estimation of the pore
connectivity, which is relevant to the percolation of gas filled in
1
6-19
pores.
During adsorption, the pores were filled with a liquidlike
condensed phase of gas at the condensation pressure at pore diam-
ء
ء
eter ͑D ͒. Here, D is an increasing function of pore size and is
15
expressed by the Kelvin–Halsh equation. In desorption, the vapor-
ization of N gas cannot follow the decreasing order of pore size due
2
15
to the complicated pore connection. In the percolation theory, two
important variables such as f and F are utilized for connectivity
estimation. Here, f and F are bond occupation probability and per-
Figure 7 displays capacitance vs voltage profiles for the carbon
electrodes. Here, these profiles were derived by dividing the current
−
1
colation probability, respectively. From N sorption hysteresis, f and
in the cyclic voltammograms by a scan rate of 5 mV s . As seen,
the rectangular characteristic for EDLC was observed and specific
capacitance became larger with a decrease in concentration, indica-
tive of the proportionality between the surface area and the specific
2
F are the function of gas pressure and were obtained according to
the literature. First, the ratio between F͑P͒ and f͑P͒ is estimated
graphically from the ratio between a length from the desorption
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A1232
Journal of The Electrochemical Society, 157 ͑11͒ A1229-A1235 ͑2010͒
Figure 4. N2 sorption profiles for pre-
pared carbons at the reaction time of ͑a͒
0, ͑b͒ 5, ͑c͒ 2, and ͑d͒ 1%.
1
capacitance. In addition, an abnormal increase in cathodic peak was
observed at 0.2 V vs SCE for a 2 wt % carbon electrode. Although
the reason is not clear, it is probable that the more etching of carbon
surface by HF can happen due to the variable etching time. This
resulted in the difference of surface functionality of porous carbon
and gave rise to higher pseudocapacitive peaks at 0.2 V vs SCE.
However, the observed smaller increase in a pseudocapacitive peak
seems to influence the electrolyte transport property within carbon
pores a little, which is proven in the following EIS experiment.
In Fig. 8, the EIS data as a Nyquist plot for the carbon electrodes
are shown. Here, characteristic impedance spectra for EDLC were
observed at 0.2 V vs SCE to minimize the pseudocapacitive effect
cally, the total impedance of the electrolyte ͓Z ͑f͔͒ can be expressed
e
from the impedance of one pore ͓Z ͑f͔͒ based on the transmission
p
1
0,19,24
line model
Zp͑f͒
1
Rp
Rt
ͱ
ͱ
coth͓ ␶␲fj͔
Ze͑f͒ =
=
coth͓ ␶␲fj͔ =
Np
mn ͱ␶␲fj
ͱ␶␲fj
͓
4͔
Here, N , m, n, and R are the total number of pores in the elec-
p
t
trodes, the number of pores in one particle, the number of particles
in the porous materials, and the total electrolyte resistance in the
pores, respectively. Equation 4 is valid for a very thin electrode
because the electrolyte resistance at the interparticle pores can be
disregarded and the overall intraparticle pores are assumed to be
7
from quinine/hydroquinone surface funtionality. At a very high fre-
quency in Fig. 8, the intercept Zreal was consistent for every elec-
trode, which reflected the same cell structure. Physically, this inter-
cept Zreal corresponds to the bulk resistance ͑Rbulk͒, which is
relevant to the bulk electrolyte transport between the reference and
1
0,19
arranged in parallel connections.
In the CDC expression, Eq. 4
has an identical mathematical form with a finite length diffusion. In
this expression, a tangent-hyperbolic function of CDC symbol ͑T͒ in
7-9,19
23
working electrodes.
In the high frequency region, a semicircle
the admittance form is given as
was observed for all electrodes and it became larger with decrease in
ء
ͱ
ͱ
T ; Y ͑␻͒ = Y j␻ tanh͓B jw͔
͓5͔
concentration. This semicircle resistance ͑R ͒ included various elec-
o
s
trochemical processes such as an ionic transfer from bulk solution to
electrode and a slight faradaic reaction from charge-transfer reaction
Using Eq. 3 and 5 and an equivalent circuit in Fig. 9, NLLS fittings
of EIS data in Fig. 8 were conducted. The best-fitted results are
20,21
at a functional group of carbon surface.
As seen in Fig. 7, the
2
displayed in the solid line in Fig. 8 and listed in Table I ͑␹
faradaic reaction from the quinine/hydroquinone reaction became
more distinct with concentration decrease, which resulted in higher
charge-transfer reaction and in the concomitant larger semicircle in
−3
Ͻ 10 ͒. In this table, the fitted value of R
͑ϳ0.6 ⍀͒ was similar
bulk
to the calculated one using bulk electrolyte conductivity and elec-
trode distance ͑0.58 ⍀͒. In addition, R became larger and the
7
2
2
s
Fig. 8. Also, the particle decrease with decreasing concentration
can result in larger ionic transfer resistance from the bulk to the
electrochemical time constant for the semicircle ͑␶ ͒ was decreased,
s
21
which was possibly relevant to the increase in faradaic reaction. Rt
and ␶ can be estimated and are listed in Table I. According to con-
centration decrease, R and ␶ became smaller, Theoretically, R has
electrode phase. In the equivalent circuit in Fig. 9, this semicircle
can be described as a parallel connection of R and Q , the circuit
s
s
t
t
description code ͑CDC͒. Here, Q is a constant phase element ex-
s
10,19,20,24
23
the following relationship with physical parameters
pressed as an admittance form by Boukamp
ء
n
Rp
4␳ l
p p
Q ; Y ͑␻͒ = Y ͑j␻͒
͓3͔
s
o
Rt =
=
͓6͔
2
Np ␲D N
p
Here, ␻ = 2␲f. For n = 1 and n = 0.5, Q represents an ideal ca-
s
pacitance and a Warburg impedance, respectively. Another interest-
ing trend in Fig. 8 is the slope change from 45° to vertical as a
function of the frequency decrease. At this slope change, theoreti-
Here, Rp, ␳p, lp, and Dp are electrolyte resistance within one pore,
resistivity of electrolyte in pores, pore length, and pore diameter,
2
p
10,19,23
respectively; R = 4␳ l /͑␲D ͒.
Pore volume for double-
p
p
p
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Journal of The Electrochemical Society, 157 ͑11͒ A1229-A1235 ͑2010͒
A1233
0.05
10 %
5
%
2
%
%
Figure 6. ͑a͒ The relationship between bond occupation probability ͓f͑P͔͒
and percolation probability ͓F͑P͔͒. Circle, reversed triangle, rectangle, and
diamond are 10, 5, 2, and 1% concentration of carbons, respectively. ͑b͒
NLLS fitting using universal scaling function for carbon of 1% concentration
sorption data. The empty circle and solid line are the obtained data and the
best-fitted line, respectively.
1
0
2
4
6
8
10
12
14
D/nm
Figure 5. The PSDs calculated by BJH method in N adsorption branch. The
2
concentration is given in the inset.
cally explained under condition of the invariant D and pore con-
p
nectivity ͑Z͒. One can expect that lower pore connectivity can give
rise to a poor electrolyte transport and a larger electrolyte resistance
in pores, although its mathematical form is hard to be derived. How-
ever, Z was nearly invariant irrespective of concentration change,
indicative of a trivial influence of Z on R . In Fig. 9, l decreases and
layer charging is hard to be considered for the above relationship
because the interparticle pore volume is not negligible in the total
pore volume. Similar to Eq. 5, ␶ can be expressed as
2
0,24
t
p
2
N increases according to the smaller particles. Hence, it is reason-
␳
l C
p
p p
d
␶
= R ϫ C = 4
͓7͔
able that R and ␶ became smaller with decrease in particle size,
p
p
t
Dp
which was confirmed in our experiment.
Here C and C are the double-layer capacitance in one pore and the
In a practical point of view in EDLC, equivalent series resistance
͑ESR͒ has been used as a representative parameter determining rate
p
d
1
0
double-layer capacitance per area, respectively; C = C ␲D l . In
p
d
p p
1
0
Fig. 9b, the dependency of l and N on particle size was schemati-
performance and it can be expressed as
p
p
Table I. Change of surface area and supercapacitor performances according to decrease in concentration.
Physical properties
EIS fitting results
͑
Q /⍀͒
T/⍀
s
Concentration
%͒
A
D
Rbulk
͑⍀͒
Rs
͑⍀͒
␶s
͑s͒
Rt
͑⍀͒
␶p
͑s͒
R + R /3
ESR
͑⍀ cm ͒
BET
−1
s
t
2
2
͑
͑m g ͒ ͑nm͒
Z
L
Yo
n
Yo
B
͑⍀͒
1.7 ϫ 10−
1
0.46 0.50 1.1
0.40 0.47 1.9
0.55 0.36 0.65 0.13
0.56 0.32 0.57 0.09
0.25
0.22
0.45
0.53
0.38
0.57
1.53
1.62
1.40
1.66
1
5
2
1
0
526
527
541
620
3.0
2.8
3.1
2.9
6.8 3.89 0.63 0.08
2.0
1
−
−
−
2
3
4
−3
−4
−4
6.5 4.20 0.56 0.14 1.4 ϫ 10
5.7 3.23 0.64 0.16 1.5 ϫ 10
6.2 3.10 0.52 0.38 5.0 ϫ 10
0.5 2.0 ϫ 10
0.7 2.4 ϫ 10
0.7 1.9 ϫ 10
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A1234
Journal of The Electrochemical Society, 157 ͑11͒ A1229-A1235 ͑2010͒
1
00
5
0
0
-
50
-
100
150
-
0
.0
0.2
0.4
0.6
0.8
Voltage/V vs. SCE
Figure 7. Capacitance vs voltage profiles that were recorded under
−
1
5
mV s scan rate. Solid, dotted, dashed, and dashed–dotted lines are car-
bon electrodes of 10, 5, 2, and 1% concentration, respectively.
Rt
ESR =
Rk = Relectrode + Rbulk + R + R
= Rbulk + R +
electrolyte s
͚
s
3
k
͓
8͔
Figure 9. ͑Color online͒ ͑a͒ Equivalent circuit describing the electrochemi-
cal processes in Fig. 8. ͑b͒ A schematic explanation of pore parameter change
for decrease in particle size in the prepared mesoporous carbons.
Here, Relectrode and Relectrolyte are the electrical resistance of electrode
and the total electrolyte resistance of electrode, respectively;
1
0,18,20
Relectrode = R /3.
Relectrode is very small and negligible when
t
7,10
enough conducting agent was added into the electrode.
Because Rbulk can be much smaller if the distance between work-
make a significant contribution on ESR. In Table I, the sum of Rs
ing and reference electrodes is minimized, the other two resistances
and R /3 was listed. This sum has a minimum value at the 2%
t
1
1
0
.5
.0
.5
.0
1.5
1.0
0.5
0.0
(
a)
c)
(b)
0
0
.5
1.0
1.5
2.0
0.5
1.0
1.5
2.0
Figure 8. Nyquist plots ͑empty circles͒
with concentration change and the best-
fitted results using equivalent circuit in
Fig. 9 ͑solid lines͒. ͑a͒-͑d͒ are 10, 5, 2, and
Zreal/
Zreal/
1
.5
.0
.5
.0
1.5
1.0
0.5
0.0
1
% concentration.
(
(d)
1
0
0
0
.5
1.0
1.5
2.0
0.5
1.0
1.5
2.0
Zreal/
Zreal/
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Journal of The Electrochemical Society, 157 ͑11͒ A1229-A1235 ͑2010͒
concentration case due to the optimal values of R and R . After the
A1235
s
t
Acknowledgments
normalization of R + R /3 using the apparent electrode area
s
t
2
͑
2 cm ͒ of both external electrode sides, the calculated ESR was
obtained as listed in Table I. The measured ESR of the 2% carbon
electrode was 1.40 ⍀ cm , which was the smallest when compared
This research was supported by a grant from the Fundamental
R&D Program for Core Technology of Materials funded by the Min-
istry of Knowledge Economy ͑TS107–17–1͒, Republic of Korea.
2
with the other carbons in Table I. This indicated the best rate capa-
Korea Research Institute of Chemical Technology assisted in meeting the
publication costs of this article.
bility for the 2 wt % carbon electrode. Although R became smaller
t
with shorter pore length, Rs increased unexpectedly, which was
probably associated with the change in external pore volume and
surface functionality with decreasing concentration. This contradic-
tory tendency between R and R can result in the existence of opti-
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