-
f porous carbon electrodes to predict rateoub
n Janeering, Science anogy and
measurement.
7 May 2014
Activated carbon
pores is proled byle capacitance plotsimpedance analysishat rate
capability isonic accessibility forcomplexity in pore
. All rights reserved.
1. Introduction
Electric double-layer capacitors (EDLCs) have been used as
ahigh-power energy storage device due to their unique
character-istics of high rate capability (
-
wercycle life (>100,000 cycles). At present, activated
carbons are themost popular EDLC electrodes due to their high
electrical conduc-tivity, large surface area and wide pore size
distribution [1].
In general, the rate capability of activated carbon electrodes
isgoverned by two factors: 1) ohmic resistance that determines
theohmic voltage drop and thus working voltage, and 2) ionic
acces-sibility into pores, by which utilizable capacitance is
determined.Commonly, dc methods are employed to assess the rate
capability;for instance, galvanostatic chargeedischarge cycling
with variedcurrent density. Here, the ohmic resistance (Rohm) can
be estimatedfrom the voltage drop at the beginning of current
reversal, whereasthe ion accessibility can be estimated from the
delivered capaci-tance values. Even if the dc methods can give
general informationon EDLC parameters, ac methods such as
electrochemical imped-ance spectroscopy (EIS) can provide more
detailed information; forinstance, pore structure of electrode
materials and kinetics indouble-layer charging/discharging
processes [2]. In the previousworks, ac impedance analysis based on
transmission-line modelwith pore size distribution (TLM-PSD) was
successfully utilized toassess the pore structure of carbon
materials [3e5]. Later on, theconcept of TLM-PSD has been
incorporated into complex capaci-tance analysis, which allows a
graphical analysis on capacitance,rate capability, and leakage
current [6e15]. Especially, it wasdemonstrated that the effect of
pore structure, electrode potential,and electrode thickness on rate
capability can be easily evaluatedby comparing the peak frequency
on imaginary capacitance plots.
The primary objective of this work is to establish an
analyticalmethod to correlate the ac method (impedance analysis)
with dcmethod (galvanostatic chargeedischarge cycling) for the
predictionof rate capability of EDLC systems. To this end,
experimental acimpedance data are analysed to obtain ohmic
resistance and ionicaccessibility for activated carbon electrodes.
Then, the utilizablecapacitance is calculated as a function of
operating time (top) orcurrent density (i) by using correlation
functions between ac and dcvariables. Finally, the transform
technique is validated bycomparing the rate capability predicted
from two methods.
2. Experimental details
2.1. Material characterizations
The samples were characterized by using a eld-emissionscanning
electron microscope (FE-SEM, JEOL JSM-6700F), nitro-gen adsorption
(Micromeritics, ASAP 2010), and small angle X-rayscattering (SAXS,
Bruker GADDS, CuKa, l 0.154056 nm). The ni-trogen adsorption data
was analysed by BarreteJoynereHalenda(BJH) andmodied micropore (MP)
[16,17] methods to characterizemesopores and micropores,
respectively.
2.2. Electrode preparation
For the electrochemical tests, the composite electrodes
wereprepared by coating the slurry of active material (RP20 or
MSP20),polytetrauoroethylene and carboxyl methyl cellulose(PTFE
CMC, 6:4 in mass ratio) binder, and conductive carbon(Super-P)
(8:1:1 inmass ratio in deionizedwater) on apiece of Al
foil(thickness 21 mm). The electrode plates were dried in
vacuumoven at 120 C for 12 h without pressing process. The
resultantthickness of the coated lm was approximately 40 2 mmwith
theactivemass loading of 1.5 0.1mg on the electrode area of 0.95
cm2.
2.3. Electrochemical measurements and impedance tting
For a 3-electrode cell test, a home-made cell comprising
poly-
H.D. Yoo et al. / Journal of Po412ethereethereketone (PEEK) body
and stainless steel (316L) currentcollectors was used. A spring was
attached to a current collector tokeep the positive, negative, and
reference electrodes be tightlycontacted to the current collectors.
O-rings (Viton) were used toensure the sealing at the joints of
current collectors and cell body.Positive and negative electrodes
were positioned to exactlyconfront each other, and the reference
electrode was just besidethem. Two pieces of separator was put
between positive, reference,and negative electrodes for all the
electrodes to be insulated oneanother. Activated carbon (RP20) were
utilized to prepare a refer-ence electrode [18] (coated lm on Al
foil, 1 mg on 0.6 cm2, 50 mmthickness) and a counter electrode
(sheet-type, 30 mg on 1.8 cm2,400 mm thickness). A porous glass bre
was used as the separator.The electrolytes were 1 M
tetraethylammonium tetrauoroborate(TEABF4) in acetonitrile (AN) or
propylene carbonate (PC). Imped-ance was measured at 0.0 V vs.
carbon over the frequency range of2 mHze100 kHz (Zahner, Im6e) with
a root mean square (rms)amplitude of 5 mV. For the complex
nonlinear least squares (CNLS)tting of the impedance data, the
TLM-PSD was coded in FORTRANto run in LEVM 8.09 software [19].
Modulus weighting (withrespect to calculated values) was adopted
for the CNLS tting.
For rate experiment, symmetric 2-electrode (CR2032 coin
type)cells were assembled by sandwiching two identical electrodes
andoperated in 0e3.5 V. Experimental conditions are same with the
3-electrode experiments, except for the electrode area (2.27
cm2).Galvanostatic chargeedischarge cycling was made with a
WBCS-3000 battery cycler (Wonatech Co.). Both of charging and
dis-charging current densities were varied from 0.5 to 40 mA
cm2.
3. Results and discussion
3.1. Characterization of activated carbons
As the EDLC electrodes, two different activated carbons
wereused; RP20 (Kuraray Chemical Co.) and MSP20 (Kansai Coke
andChemicals Co.). The former is produced by physical steam
activa-tion, whereas the latter by chemical activation using
potassiumhydroxide (KOH). As shown in the FE-SEM images (inset of
Fig. 1a),RP20 has a rougher morphology as compared with that for
MSP20.It is known that steam activation (RP20) leads to more
severemorphological change as compared with KOH activation
(MSP20)[20]. The particle diameter is similar for two carbons (~5
mm).
From the nitrogen adsorption isotherms, total pore
volumes(Vtotal) are calculated to be 0.77 cm3 g1 (RP20) and 0.98
cm3 g1
(MSP20) (Table 1). The adsorptionedesorption isotherms (Fig.
1a)also show that RP20 has a larger portion of mesopores and
macro-pores, while the micropores are dominant in MSP20. The BET
sur-face area (SBET) is larger for MSP20 due to the higher
population ofmicropores. In the BJH pore size distribution (Fig.
1b), RP20 shows alarger portion of meso- or macropore volume
between the di-ameters of 4e300 nm. The meso- and macro-pore volume
atD > 2 nm are 0.17 cm3 g1 for RP20 and 0.15 cm3 g1 for
MSP20,which is 22% and 15% of Vtotal, respectively. Accordingly,
the averagemesopore diameter (Dmeso) is calculated to be larger for
RP20(4.9 nm) as compared with that for MSP20 (2.8 nm). When
themicropore region (D
-
MP
H.D. Yoo et al. / Journal of Power Sources 267 (2014) 411e420
413Based on the above results, it is expected that RP20
exhibitshigher rate capability since it has larger pore size and
lower porecomplexity [22], but lower specic capacitance as its
surface area issmaller than that for MSP20. Meanwhile, if the
specic capacitanceis calculated with an assumption that the whole
surface is utilizedfor charge storagewith identical capacitance of
8 mF cm2 [23,24], it
Fig. 1. (a) N2 adsorption isotherms and pore size distribution
by (b) BJH and (c) modiedRP20 and MSP20 in the inset.is estimated
to be 120 F g1 (RP20) and 160 F g1 (MSP20) from theBET surface
areas. However, the calculated value is only a roughestimation
since the pore utilization and unit capacitance arestrongly
dependent on the used electrolyte and charge/dischargerate in
practical EDLCs.
3.2. Graphical analysis of EIS data: Nyquist plot and
complexcapacitance analysis
Fig. 2 displays the Nyquist plots that are obtained fromRP20
andMSP20 in 1.0 M TEABF4/AN and TEABF4/PC electrolyte, in which
asemicircle and a spike appear at the high and low frequency
region,respectively. Total impedance can be divided into three
compo-nents in the Nyquist plots; bulk electrolyte resistance
(x-interceptat the highest frequency region), interfacial impedance
betweenelectrode and bulk solution (semicircle at the middle
frequencyregion), and the impedance that is associated with
intra-particlepores (spike at the low frequency region) (Fig. 3).
The rst twoterms are mainly dependent on the electrolyte solution,
while thelast one (low frequency tails) is controlled by both
electrode ma-terials and electrolytes.
Table 1Pore properties derived from nitrogen adsorption
isotherms.
SBET/m2 g1a Vtotal/cm3 g1 Davg/nm Dmeso/nmb
RP20 1520 30 0.77 2.0 4.9MSP20 2060 40 0.98 1.9 2.8
a Measured by BrunaureEmmetteTeller (BET) method.b Measured by
BarreteJoynereHalenda (BJH) method.Previously, the semicircle at
the middle frequency region hasbeen assigned to the ion transport
processes [25e27] or the contactimpedance between electrode and
current collector [28,29]. As theresistances are larger in the
PC-based electrolyte for both elec-trodes in this work, the ion
transport processes seem to be domi-nant in our experiment, even if
the contribution from the electronic
methods for RP20 and MSP20. (d) SAXS patterns of RP20 and MSP20.
FE-SEM images ofcontact resistance cannot be neglected. The
semicircle has alsobeen assigned to the inter-particle ionic
impedance [25], but oursimulation shows that the inter-particle
ionic resistances aremerged in the sloped line at low frequencies
as additional poreresistances [9]. Practically, the process for the
semi-circle can beregarded as a simple resistance at lower
frequency than 10 Hz,while the typical EDLC charge/discharge
condition corresponds tothe frequency of 0.1 Hz.
Fig. 2. Nyquist plots of (a) RP20 and (b) MSP20 electrodes in AN
or PC electrolytes.Lines: CNLS tted results.
-
to be 42U cm2 and 75 F g1 for RP20, and 47U cm2 and 130 F g1
forMSP20. Here,mass (g) refers tomass of carbon only (i.e.without
themass of aluminium current collector). As higher rate capability
canbe assumed by smaller time constant (t) that is the product of
Resrand Cutil, it is predicted that the rate capability of RP20 (t:
2.6 s inAN and 4.7 s in PC) is higher as compared with that for
MSP20 (t:3.5 s in AN and 9.1 s in PC). Rate capability can be
predicted fromthis simple graphical analysis by using Resr and
Cutil values, butdetailed analysis, such as the separate discussion
on the effect ofion size and conductivity, is not available.
More detailed analysis on the capacitive parameters and
ratecapability can be performed by using the complex
capacitanceanalysis [7]. For this, the measured impedance (Z(f)
Z0(f) jZ00(f))is transformed into the complex capacitance (C(f)
C0(f) jC00(f)) bythe relation of C(f) 1/[juZ(f)]. The real part of
complex capacitance(C0(f)) represents the apparent capacitance
value as a function offrequency, while the imaginary part (C0(f))
is correlatedwith C0(f) byKronigeKramers (KeK) relations. When C0
0(f) is plotted as a func-tion of frequency in semi-log scale,
peak-shaped curves areappeared in the imaginary capacitance plot
(C00(f) vs. log f, Fig. 4aand b). Then, as suggested by the KeK
relations, total capacitance
H.D. Yoo et al. / Journal of Power Sources 267 (2014)
411e420414As a simple approach, capacitive electrochemical systems
can berepresented by a serial connection of equivalent series
resistance(Resr) and utilizable capacitance (Cutil), which
approximates thecapacitor behaviour at sufciently low frequencies.
In thisapproximation, Resr comprises 1) bulk electrolyte
resistance, 2)interfacial resistance, and 3) apparent resistance of
intra-particlepores (Fig. 3). The capacitive charge storage is
assumed to occuron electrochemically equivalent sites with
identical serial resis-tance. As the impedance of such circuit is
Resr j/(uCutil), where j isimaginary unit and u is angular
frequency (2pf), the Resr and Cutilcan be determined from the real
and imaginary part of experi-mental impedance data from the
perpendicular region in theNyquist plots (Fig. 2).
In the AN-based electrolyte (ionic conductivity 56 mS cm1 at25
C), from the impedance data at 10 mHz, the Resr and Cutil are
2 1 2
Fig. 3. Equivalent circuit model for the porous carbon
electrodes.calculated to be 21 U cm and 80 F g for RP20, and 17 U
cm and140 F g1 for MSP20. In the PC-based electrolyte
(ionicconductivity 13mS cm1 at 25 C), the Resr and Cutil are
calculated
Fig. 4. Imaginary capacitance plots of (a) RP20 and (b) MSP20
electrodes in AN or PC electelectrodes with an assumption of
log-normal distribution (Eq. (6)).(Ctot) can be calculated from the
peak area (Ap) as Ctot 1.466Ap[13]. In addition, the peak frequency
(fp) at the maximum C00(f)corresponds to the characteristic
frequency, which is inverselyproportional to the time constant (t)
of capacitive systems.Therefore, capacitance and rate capability
can be easily estimatedfrom this graphical analysis.
Fig. 4a and b presents the imaginary capacitance plots
obtainedfrom two activated carbon electrodes. The Ctot and fp
values aredetermined to be 83.2 F g1/70.7 mHz (RP20) and 140.4 F
g1/50.4 mHz (MSP20) in the AN-based electrolyte; and 79.2 F g1/34.9
mHz (RP20), and 143.0 F g1/16.6 mHz (MSP20) in the PC-based
electrolyte (Table 2). The Ctot values are comparable in
twoelectrolytes, but they were smaller than the estimations from
theBET surface area (i.e. 120 and 160 F g1 for RP20 and
MSP20,respectively; assuming 8 mF cm2 for carbon surface) for both
RP20(~69%) and MSP20 (~89%) because very small pores that are
notutilizable for ion adsorption are also detected by N2
molecules(BET). This nding supports that EDLC can be more properly
eval-uated by electrochemical method that utilizes actual ions as
theprobe molecule, compared to N2 adsorption method that uses N2
asthe probe molecule [5]. Meanwhile, the peak frequency
valuesrolytes with CNLS tted results. Ionic accessibility proles
for (c) RP20 and (d) MSP20
-
CTLMPSDf CtotZ
C0f ;aopaodln ao (5)
Based on Eq. (5), the ionic accessibility prole, p(ao), can
beobtained by de-convoluting the impedance data with
discreteFourier transform [7,33]. However, it has been reported
that thePSD of porous materials can be assumed to have log-normal
func-
wer Sources 267 (2014) 411e420 415indicate that rate capability
of RP20 is higher than that of MSP20 inboth electrolytes by a
factor of 1.4 (AN) and 2.1 (PC). This solvent-dependent rate
capability for two carbon electrodes can beascribed to the
difference in the solvated ionic diameter: ca. 1.2 nmfor AN and 1.4
nm for PC [30].
3.3. Ionic accessibility prole by CNLS tting
A schematic Nyquist plot is presented in Fig. 3a. At the
highfrequency limit, a resistive term appears due to ion transport
inbulk solution, which can be represented by a simple resistance
ofRbulk (Fig. 3b). The semicircle in the middle frequency region
isassigned to the ion migration across the
bulk-electrolyte/electrodeinterface, while the sloping spike at the
low frequency region is forthe combined effect of ion transport and
double-layer formationinside pores. As these processes are serially
connected, totalimpedance (Z(f)) is the sum of bulk resistance
(Rbulk), impedancefor the semicircle (Zinterface) and sloping spike
(Zintra-pore):
Zf Rbulk Zinterfacef Zintraporef (1)To simulate the interfacial
impedance (Zinterface), (R1Q1)(R2C2)
circuit (Fig. 3c) is used, where Q is the constant phase element
(CPE,ZCPE 1/[T(ju)p]) [31]. The R2C2 is added because the
depressedsemicircles are not successfully tted by the R1Q1 alone.
In thetting, p is ca. 0.9 for all the tted results and T is a
variable. For theZintra-pore, the cylindrical pore model is
utilized, in which theequivalent circuit follows the TLMwith
segmental ionic resistancesand surface capacitances in
intra-particle pores [32]. For a singlepore or uniform multiple
pores, the electrochemical characteristicswith ac signals
(CTLM(f,ao)) can be expressed as the product of totalcapacitance
(Ctot) and the characteristic function (C0(f,ao)) as:
CTLMf ;ao Ctot C0f ;ao (2)
C0f ;ao aojpf
p tanh
jpfpao
!(3)
ao 12k rCdl2
r(4)
Here, the ionic accessibility (ao) indicates the feasibility for
acsignal to penetrate into pores (radius: r, and length: l) when
theionic conductivity in pores is k and the capacitance per unit
area onpore surface is Cd (Eq. (4)). For a pore with an ao, the
frequencydependency of the capacitance utilization can be
represented by
Table 2Capacitive parameters derived from imaginary capacitance
plots.
fp/mHz Ctot/F g1 FWHM
RP20 1 M TEABF4/AN 71 83 1.331 M TEABF4/PC 35 79 1.36
MSP20 1 M TEABF4/AN 50 140 1.331 M TEABF4/PC 17 143 1.35
H.D. Yoo et al. / Journal of PoEq. (3).The uniform pore model
fails to analyse practical porous car-
bon electrodes since pore structures are signicantly
non-uniform, except for some highly ordered materials [3].
There-fore, it is necessary to consider the non-uniformity of pores
inmodelling the electrochemical characteristics of porous
carbonelectrodes. When p(ao) is the ionic accessibility prole as a
func-tion of ionic accessibility, the complex capacitance of
non-uniformmultiple pores (CTLM-PSD(f)), with total capacitance of
Ctot, is givenas follows [7]:tion (Eq. (6)) to reasonably t the
experimental EIS data, where ao*and s represent the characteristic
ionic accessibility and the degreeof distribution for the
electrode, respectively [3e5].
pao 12p
psexp
12s2
ln ao ln ao
2 (6)The experimental impedance data of RP20 and MSP20 elec-
trodes are CNLS tted by Eq. (1), assuming non-uniform
multiplepores with log-normal distribution (Eq. (6)). The
Zintra-pore(f) isrepresented as 1/[juCTLM-PSD(f)] (Eq. (5)). The
tted curves are in agood agreement with the experimental data as
shown in Nyquistplots (Fig. 2) and imaginary capacitance plots
(Fig. 4a and b). Fromthe optimized parameters (Table 3), the
electrochemical charac-teristics for intra-particle pores can be
separately analysed fromthat of the bulk electrolyte and interface
(Table 4).
When the tted parameters are compared with those from thecomplex
capacitance analysis, total capacitance values are similarwithin 1%
of difference. From the larger ao* values, higher ratecapability is
expected for RP20 in both electrolytes, which is inaccordance with
the expectation from the fp values in the graphicalanalysis.
Therefore, it can be concluded that the capacitance andrate
capability, which are the key parameters to characterize
elec-trochemical characteristics of porous carbon electrodes, can
besuccessfully analysed by graphical analysis with C00(f) vs. log f
plot,as conrmed by tted parameters.
The ionic accessibility prole, which enables the quanticationof
rate capability, is derived by the unique interpretation of
theimpedance data. The ionic accessibility prole is dened as
thedistribution density of capacitance existence with respect to
thenatural log of ionic accessibility (p(ao) vs. ln ao), which is
obtainedfrom Eq. (6) with the tted parameters ao* and s (Fig. 4c
and d). Thedistribution function, p(ao) d[C/Ctot]/d[ln ao], can be
interpretedas the distribution densities of surface existence
(d[S/Stot]/d[ln ao])if constant Cd is assumed over the entire
surface. As the ionicaccessibility prole of RP20 is shifted to the
higher ao direction, itcan be noticed that RP20 has more accessible
pores by ac signalscompared with MSP20. In other words, MSP20 has
smaller ao*,which is in accordance with the nitrogen adsorption
(larger portionof micropores) and SAXS analysis (higher complexity
of porousstructure) results. The smaller pore diameter, more
complex porestructure, and possibly longer average pore length of
MSP20 resultin the smaller ao* value. Of two electrolytes, the
AN-based oneprovides larger ao* due to higher ionic conductivity as
comparedwith the PC-based one. All the properties are colligated to
ao*, thecharacteristic ionic accessibility into pores, according to
Eq. (4). Thelarger values of s for RP20 reect that the pore
structure is morelargely distributed compared with MSP20.
Table 3TLM-PSD parameters obtained by tting the impedance data
to Eq. 1
Ctot/F g1 ao*/s0.5 s c2
RP20 ANa 82.1 0.2 1.21 0.09 1.22 0.07 7.2 103PC 79.0 0.1 0.68
0.01 1.15 0.03 9.1 103
MSP20 AN 139.0 0.2 0.56 0.02 0.73 0.03 7.9 103PC 141.5 0.2 0.273
0.001 0.622 0.009 4.2 103a All the electrolytes contain 1 M
TEABF4.
-
differential capacitance can be predicted to be more severe:150
F g1 (top: 1000 s) to 93 F g1 (10 s). Accordingly, the
ratecapability can be quantitatively determined for various
combina-tions of electrode materials and electrolytes. When the
operationtime of the EDLC cells are decreased from1000 s to 10 s,
the retainedcapacitances will be: RP20/AN (90.8%) >MSP20/AN
(85.8%) > RP20/PC (82.7%) >MSP20/PC (62.0%). In general, the
higher the ao* value,the more feasible is the operation at shorter
top. In addition to theeffect of ao*, the Cdiff,EIS(top) curves
change less steeper for RP20with respect to top, due to the larger
s values (1.2) than those ofMSP20 (0.6e0.7). Also, the smaller
value of s for MSP20 leads to thehigher susceptibility to the ionic
conductivity for the rate capability,which is evidenced by the
larger difference of Cdiff,EIS(top) curves by
ed by tting the impedance data to Eq. 1
R2/U cm2 T1/106 p1 C2/mF cm2
4.7 0.3 68 6 0.89 0.01 420 606.9 0.6 37 2 0.89 0.01 260 305.1
0.5 70 10 0.88 0.02 80 209.5 0.6 46 2 0.88 0.01 140 20
rs of 1st semicircle, and C2 for interfacial capacitance of 2nd
semicircle.
wer Sources 267 (2014) 411e4203.4. Differential and apparent
capacitances calculated from ionicaccessibility proles
From the ionic accessibility proles (Fig. 4c and d), the
ratecapability of two activated carbon electrodes can be predicted.
Tothis end, rstly, the utilization of cylindrical pores with an
ionicaccessibility of ao, at an operating ac frequency of fop, is
assumed tobe Re[C0(fop,ao)] based on the TLM (Eq. (3)). Then, with
a decreasein fop, the utilization of a single pore will gradually
increase from0 (high frequency limit) to 1.0 (low frequency limit).
Theoretically,the pore utilizationwill be 10%, 50%, and 90% at
fop/ao2 of 15.9, 0.991,and 0.294, respectively (Fig. S1).
As the porous carbon electrodes have non-uniform pores,
thedifferential specic capacitance of an electrode, as a function
of fop,can be calculated from the EIS data (Cdiff,EIS(fop))
according to thefollowing integral equation (Eq. (7)), where the
p(ao) represents theionic accessibility prole obtained from EIS
analysis, and Ctot theaverage total capacitance of an electrode in
the operating voltagerange.
Cdiff ;EISfop Ctot
Z
RehC0fop;ao
ipaodln ao (7)
If the capacitance is constant over the potential range, the
Ctotcan be determined from the Ctot value measured by single
EISanalysis at any potential. The most direct method for studying
thepotential-dependent quantities (e.g. capacitance) is
multipleimpedance measurement at every potential, which is not
practicalbecause each impedance measurement takes at least 2 h for
aparticular potential point. Alternatively, either cyclic
voltammetry(CV) at a slow scan rate or chargeedischarge cycling at
a slow ratecan be performed to measure Ctot. In this study, using
slowlyscanned CV, Ctot values are determined to be 120 F g1 for
RP20 (inAN and PC) and 160 F g1 and 150 F g1 for MSP20/AN and
MSP20/PC, respectively (Fig. 5). As the capacitance value is
potential-dependent, the measured Ctot are 1.1e1.5 times larger
than theCtot value obtained from EIS analysis at 0 V vs. carbon.
Usually thecapacitance of activated carbon electrodes is minimum at
the po-tential of zero charge (pzc, about 0 V vs. carbon) [34]. The
lowerspecic capacitance of MSP20 in PC compared to AN is due to
theshrinkage of the voltammogram at about
-
diff,di
te t
H.D. Yoo et al. / Journal of Powerconsidering that the symmetric
EDLC cell contains active mass ofboth electrodes (i.e. total mass
becomes 2 times of an electrode'smass) while the cell's capacitance
becomes half of an electrode'scapacitance due to the serial
connection.
Cdiff ;dischi 4 Qcell;dischi
Vop Vohm
(8)
As shown in Fig. 6a and b, the Cdiff,disch(top) values, which
weremeasured by the galvanostatic chargeedischarge of EDLC
cells,were well matched with the Cdiff,EIS(top) curves predicted by
the EISdata in half-cell tests. Here, the operational time is equal
to theexperimental discharging time. For example, the Cdiff of an
EDLCelectrode with RP20/AN was experimentally measured to be119 F
g1 (0.5 mA cm2), 110 (10 mA cm2), and 100 (40 mA cm2),which well
agrees with the expected values by EIS analysis. For four
Fig. 6. (a,b) Cdiff,EIS(top) proles (lines) with respect to the
operational time (top) and Cf 1; solid lines, f 0.492) with respect
to the current density (i) and the full-cell rakinds of EDLCs, the
deviation between experimental and predictedvalues was within 10%.
Therefore, it can be concluded that the ratecapability of
differential capacitance of EDLC cells can be quanti-tatively
predicted by the developed analysis technique of theimpedance data
for porous electrodes in half cell test.
Fig. 7. Chargeedischarge curves at various current density
(0.5e40 mA cm2) for (a)RP20 and (b) MSP20 electrodes in AN or PC
electrolytes.In addition to the differential specic capacitance of
an elec-trode (Cdiff), the apparent specic capacitance of EDLC
cells (Ccell)and its dependency on the current density are another
importantfactor in evaluating practical EDLC cells. The Ccell
represents thepractical utilizable capacitance of EDLC cells that
includes the effectof ohmic losses, whereas the Cdiff indicates the
characteristics ofelectrode materials. When charge/discharged at
various currents(i), the apparent specic capacitance of an EDLC
cell (Ccell,disch) iscalculated by dividing the discharging specic
capacity of sym-metric full-cell, Qcell,disch(i), by the operating
voltage (Vop, 3.5 V inthis work) as:
Ccell;dischi Qcell;dischiVop (9)
At slow current density (5 mA cm2), measured Ccell,disch(i)
sch(top) values from the full-cell rate test (points). (c,d)
Ccell,EIS(i) proles (dashed lines,est data (Ccell,disch(i),
points).
Sources 267 (2014) 411e420 417values for EDLC cells (points in
Fig. 6c and d) are close to onefourth of the Cdiff,disch(i) values
for single electrodes, as expectedwith negligible iR-drop. With
current increase, the Ccell,disch valuesare decreased by increased
ohmic drop (Vohm) as well as by thedecrease in Cdiff,disch. As a
result, the decrease with current is ex-pected to be larger for
Ccell,disch than Cdiff,disch. For example, whenthe discharge
current was increased from 0.5 mA cm2 to40 mA cm2, the Ccell,disch
was decreased by 74%, while thedecrease in Cdiff,disch was 42%. As
the iR-drop plays an importantrole, the effect of electrolytes on
rate capability was much largerfor the apparent capacitances
(Ccell,disch(i)). When the electrolytewas changed from AN to PC,
the Ccell,disch of RP20 was decreasedby 19% (40 mA cm2), while the
corresponding Cdiff,disch changewas 5%.
The apparent specic capacitance of an EDLC cell, Ccell,EIS,
alsocan be predicted quantitatively from the Cdiff,EIS(top) of an
electrodedetermined through the EIS analysis (Eq. (10)). In Eq.
(10), Cdiff,EI-S(top) was divided by 4 considering that the
symmetric EDLC cellcontains 2 times of active mass (i.e.mass of
activated carbon) whilethe capacitance itself becomes half due to
the serial connection. Forthis, the ohmic resistance of EDLCs and
operating time should bedetermined at various current
densities.
Ccell;EISi Qcell;EISiVop
Cdiff ;EIStop
4 Vop iRohm
Vop(10)
-
experimental values, which conrms that the appropriate
correc-tion factor is required to utilize EIS data for EDLC cells.
The MSP20/PC cell shows larger deviation (up to 33%) even if the
Rohm valuewascalibrated with f 0.492, which can be accounted for by
limitationin estimating the voltage drop, as described above.
Additionally, chargeedischarge curves can be directly
simulatedfrom the Cdiff,EIS(i) proles and calibrated Rohm values at
a currentdensity (Fig. 9), which are in agreement with
experimentally ob-tained curves except for MSP20/PC. Note that the
simulated curveswere solely obtained by EIS parameters and Ctot
parameter fromcyclic voltammetry. The simulated and experimental
voltage pro-les are matched within 3% deviation for RP20 cells, and
4% devi-ation for MSP20/AN cell. Due to the abnormal adhesion of
PC-solvated TEA ion in MSP20, much larger deviation (41%)
wasobserved for the MSP20/PC cell.
3.5. Applications of EIS analysis of EDLCs for the rate
capabilityprediction and design of capacitor cells
The rate capability from Cdiff,EIS(top) is expected to be
theintrinsic properties of activated carbon particles as the
extrinsicproperties are separated by tting analysis. In other
words, thisinformation is independent of the extrinsic parameters
of elec-trodes (i.e. due to the electrode preparation process), as
they are
werThe ohmic resistances of EDLC cells aremainly composed of
bulkresistance in organic electrolytes and resistive terms from
twoelectrodes. In the EIS analysis with a three electrode cell,
theinterfacial impedance (Zinterface) of a porous carbon electrode
wasrepresented by overlapped semicircles. However, as active
fre-quency of the semicircle (100 kHze10 Hz) is sufciently larger
thanthe operational condition (i.e. current density) of EDLCs(fop
< 0.5 Hz), the interfacial impedance (Zinterface) can be
regardedas a simple resistance, Rinterface. Therefore, the ohmic
resistance ofan EDLC cell (Rohm) can be calculated from the EIS
data as the sumof Rbulk and interfacial resistances of both
electrodes(Rinterface 2(R1 R2)), with an empirical correction
factor (f), as:
Rohm Rbulk 2R1 R2 f (11)If the fabrication condition of EDLC
cells is identical to that of
half-cell test, f will become unity. However, the effective bulk
re-sistances and interfacial resistances can be inuenced by
theelectrode fabricationmethods and cell geometry [39]. In such
cases,the correction factor f is expected to be determined
empiricallyand can be utilized in the prediction of the EDLC
performance fromEIS data according to the analysis technique
developed in thisstudy.
For each combination of porous carbons and electrolytes, theRohm
value was determined by plotting the ohmic voltage drops inthe
chargeedischarge data as a function of current density (Fig.
S2).Then, a linear correlation between Rohm values of
symmetricalEDLCs and EIS analysis results (Rbulk 2(R1 R2)) were
foundamong MSP20/AN, RP20/AN, and RP20/PC, and the correction
fac-tor f for the used EDLC cells was determined to be 0.492 (Fig.
S3).This result implies that the applied pressure was probably
higherfor the coin-type cell (EDLCs for charge/discharge) compared
to thehome-made test cell (half-cells for EIS analysis). Even
though theapplied pressure was not numerically determined, it can
beconcluded that the effect of cell fabrication method on the
ohmicresistance values was maintained similarly in this study
andtherefore the prediction of Rohm from impedance data is
possiblewith a predetermined correlation factor.
In the case of MSP20/PC, the voltage drop at the
charge/discharge reversal and resultantly calculated Rohm was much
largerthan that expected from the EIS result with f 0.492. This
seems tobe originated from the additional voltage drops at the
negativeelectrode, as experimentally conrmed only for the
charge/discharge reversal of MSP20/PC (Fig. 8). Previously, similar
phe-nomenon was reported for nanoporous activated carbon
electrodein TEABF4/PC electrolyte, which was explained by strong
adhesionof cations on nanopores [40]. Even though the effect of
abnormaladhesion cannot be fully predicted by EIS analysis, such
combina-tions of porous carbon and electrolytes with abnormal ohmic
dropwill be not suitable for practical applications as EDLC devices
withhigh efciency.
The operating time (top) that corresponds to the
charge/discharge at various current densities (i) could be
determined byutilizing Eq. (12). When top is large (slow
charge/dischargewith lowi), it will be inversely proportional to
the current density (i), wherethe voltage drop by ohmic drop is
negligible and Cdiff,EIS(top) isconstantlymaintained. In contrast,
with fast charge/discharge (highi), top decline with higher i
became more rapid due to both thesignicant ohmic drop and decrease
in Cdiff,EIS(top). The relationshipbetween top and i are
numerically calculated from Eq. (12b) andpresented in Fig. S4,
where Vop is 3.5 V and Rohm is determined byEq. (11) with f 0.492.
It is noted that at i< 10mA cm2, the top vs. iproles of
identical activated carbon is very similar, regardless of
H.D. Yoo et al. / Journal of Po418the used
electrolytes.Qcell;EISi Cdiff ;EIS
top
4 Vop iRohm i top Am (12a)
i VopRohm 4topm1A
.Cdiff ;EIS
top (12b)
Here, A is the apparent electrode area (e.g. 2.27 cm2 in this
rateexperiment) and m is the total active mass in a symmetric
EDLC.
Fig. 6c and d compared the apparent specic
capacitancescalculated from EIS data in comparison to the
experimental values.Solid lines in Fig. 6c and d represent thus
calculated Ccell,EIS(i)proles after calibrating the Rohm values
with the coefcient off 0.492. The Ccell,EIS(i) and Ccell, disch(i)
are matched within 6%deviation for RP20/AN, RP20/PC,
andMSP20/AN.When the effect ofcell fabrication and geometry was not
considered (dashed lines,f 1) the calculated values became more
deviated from the
Fig. 8. Potential proles of both electrodes during the
galvanostatic chargeedischargeof full cell (i 0.5 mA cm2). Grey:
cell voltage. Red and blue: potential of () and ()electrode,
respectively. (For interpretation of the references to colour in
this gurelegend, the reader is referred to the web version of this
article.)
Sources 267 (2014) 411e420derived solely from the intrinsic
parameters of intra-particle pores;
-
werthe precedent impedances that are subject to the
experimentalconditions are factored out by tting analysis. And it
will bepossible to distinguish intrinsic and extrinsic effects on
the net ratecapabilities of cells that are fabricated by different
methods.
The Cdiff,EIS(top) or Ccell,EIS(top) plots can be applied to
estimatethe rate capability of a specic cell or to design cells
according tothe desired specication (i.e. operational rate and
capacitance). If anEDLC cell is made of MSP20 (10 mg)j1 M TEABF4 in
AN j RP20(15 mg), the capacitance of positive (C(top)) and negative
(C(top))electrodes can be calculated by multiplying active mass to
theCdiff,EIS(top) proles in Fig. 6a and b. And the capacitance of
the full-cell (Cfc(top)) can be calculated according to the rate
conditions, byusing 1/Cfc(top) 1/C(top) 1/C(top).
On the other hand, the Cdiff,EIS(top) curve can be utilized to
designa cell with desired rate capability. When 1 Ah of capacity is
requiredat 40 mA cm2 for a 3 V operating symmetric full-cell
withRohm 15 U cm2, total active mass of porous carbons can be
esti-mated to be 55 g (RP20) or 41 g (MSP20) to fabricate the cell
withAN electrolyte from Eq. (8). If Rohm is reduced to 2 U cm2,
therequired mass becomes 45 g (RP20) or 33 g (MSP20). This
calcu-lation is also possible for the PC-based electrolyte at
variousdischarge rates utilizing the Cdiff,EIS(top) plots. It is
noteworthy that,
Fig. 9. Comparison of experimental and simulated (f 0.492)
galvanostatic voltageproles at i 20 mA cm2.
H.D. Yoo et al. / Journal of Powhile we try to balance the
active mass, the rate capability can bealso lowered with thickness
increase by several tens of mm [9],where the calculated active mass
by the impedance analysis shouldbe regarded as the minimum mass of
active materials under nothickness effect. Related future work is
to develop more sophisti-cated model that considers thickness
effect.
As this paper aims to represent fundamental ideas for
estima-tion of rate capability, the experiments are simplied. Even
if theprinciples will be the same as described in this paper, there
aresome specic details to consider before practical application.
(1)The rate capability depends on electrode thickness as well
aselectrode material [9,41e44], but the former effect is not
consid-ered in this study. As the effect of electrode thickness can
be ana-lysed by similar impedance analysis [9], more precise cell
designwill be possible through this approach.
(2) Also it is noteworthy that the ionic accessibility proles
areobtained from the impedance measurements at pzc, and thepossible
differences between the positive and negative electrodesare not
represented. If positive and negative electrodes are to bestudied
separately, impedance should bemeasured at the middle ofthe
operational potential range for positive and negative
electrodes,respectively. This approach can be a future extension of
this work.4. Conclusions
Through the impedance analysis, rate capabilities of
porouscarbon electrodes are quantitatively proled as ionic
accessibilityprole, which is described as the distribution of
capacitance withrespect to ionic accessibility (ao). The ionic
accessibility proles aretransformed into calculated specic
capacitance of an electrode(Cdiff,EIS(top)) with respect to
operational time (top). More practically,calculated apparent specic
capacitance of a cell (Ccell,EIS(i)) wasderived from the calculated
specic capacitance of an electrode(Cdiff,EIS(top)) and calibrated
Rohm. The calculated specic capaci-tance of an electrode
(Cdiff,EIS(top)) and of a cell (Ccell,EIS(i)) are in agood
agreement with the galvanostatic full-cell rate test results.This
conrms that the rate capabilities of porous carbons can
bequantitatively predicted by EIS analysis, considering both
intrinsic(e.g. Cdiff,EIS(top)) and extrinsic (e.g. Rohm) factors.
The calculatedspecic capacitance (Cdiff,EIS(top)) prole can be used
for assessingand designing EDLC cells.
The intrinsic and extrinsic factors that control the EDLC
char-acteristics are separated by their characteristic frequencies
orphase-shifts, and obtained quantitatively by tting the
impedancedata to appropriate equivalent circuits. This
separation-ability ofthe impedance analysis may lead to the
standardized evaluation ofporous carbons for EDLC electrodes.
The ionic accessibilities of porous carbons are represented
bycharacteristic ionic accessibility (ao*) and the degree of
distribution(s). The pore diameter, existence of subnano-pores or
large meso-pores, fractal dimension, and average pore length are
the factorsthat control the ao*. The smaller the s value, the
higher is thesusceptibility to the electrolyte properties (e.g.
ionic conductivity)for the rate capability. For an electrode with
small s (e.g. MSP20electrode), proper choice of electrolyte is
indispensable for the ratecapability.
Acknowledgement
This work was supported by the National Research Foundationof
Korea funded by the MEST (NRF-2010-C1AAA001-2010-0029065) and the
cooperative R&D program funded by the KoreaResearch Council
Industrial Science and Technology (B551179-10-01-00). This work was
also supported by the Korea CCS R&D Center(KCRC) grant funded
by the Korea Government (Ministry of Science,ICT & Future
Planning) (No. 2013038315).
Appendix A. Supplementary data
Supplementary data related to this article can be found at
http://dx.doi.org/10.1016/j.jpowsour.2014.05.058.
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Glossary
A: apparent electrode area (cm2)AN: acetonitrileAp: peak areaao:
penetrability coefcient (s0.5)ao*: characteristic penetrability
coefcient (s0.5)BF4
: tetrauoroborate anionC: complex capacitance (C0 jC00)C0: real
part of complex capacitance (Re[C])C00: imaginary part of complex
capacitance (Im[C])Cdiff,EIS: differential specic capacitance of an
electrode by EIS analysis (F g1)Ccell,EIS: apparent specic
capacitance of a symmetric full cell by EIS analysis (F g1)CNLS:
complex nonlinear least squaresCPE: constant phase
elementCTLM(f,ao): complex capacitance of a single TLM
elementCTLM-PSD: complex capacitance of non-uniformmultiple pores
described by TLM-PSDC0(f,ao): characteristic function of a single
TLM elementCtot: total capacitance of an electrode (F g1)Ctot : the
average total capacitance of anelectrode in theoperating voltage
range (Fg1)Cutil: utilizable capacitance (F g1)D: pore diameter
(nm)EIS: electrochemical impedance spectroscopy
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258e265.fop: operational frequency (Hz)fp: peak frequency (Hz)f:
correction factor of ohmic resistancei: current density (mA cm2)j:
imaginary unit (
1
p)
m: total active mass in a symmetric EDLCp(ao): ionic
accessibility prolePC: propylene carbonatepzc: potential of zero
chargeRn: interfacial resistance of nth semicircleCn: interfacial
capacitance of nth semicircleQn: CPE of nth semicircleRbulk: bulk
resistance (U cm2)Resr: equivalent series resistance (U
cm2)Rinterface: interfacial resistance (U cm2)Rohm: ohmic
resistance (U cm2)s: degree of distributionSBET: surface area
measured by BET methodTEA: tetraethylammonium cationTLM:
transmission-line modelTLM-PSD: transmission-line model with pore
size distributiontop: operational time (s)Vohm: ohmic voltage drop
(V)Vtotal: total pore volume (cm3 g1)u: angular frequency (rad
s1)Z: impedanceZinterface: interfacial impedanceZintra-pore:
impedance of intra-particle pores
Impedance analysis of porous carbon electrodes to predict rate
capability of electric double-layer capacitors1 Introduction2
Experimental details2.1 Material characterizations2.2 Electrode
preparation2.3 Electrochemical measurements and impedance
fitting
3 Results and discussion3.1 Characterization of activated
carbons3.2 Graphical analysis of EIS data: Nyquist plot and complex
capacitance analysis3.3 Ionic accessibility profile by CNLS
fitting3.4 Differential and apparent capacitances calculated from
ionic accessibility profiles3.5 Applications of EIS analysis of
EDLCs for the rate capability prediction and design of capacitor
cells
4 ConclusionsAcknowledgementAppendix A Supplementary
dataReferences