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.

References

[1] T.A. Centeno, M. Hahn, J.A. Fernandez, R. Kotz, F. Stoeckli, Electrochem.Commun. 9 (2007) 1242e1246.

[2] J. Eskusson, A. Janes, A. Kikas, L. Matisen, E. Lust, J. Power Sources 196 (2011)4109e4116.

[3] H.K. Song, Y.H. Jung, K.H. Lee, L.H. Dao, Electrochim. Acta 44 (1999)3513e3519.

[4] H.K. Song, H.Y. Hwang, K.H. Lee, L.H. Dao, Electrochim. Acta 45 (2000)2241e2257.

[5] H.K. Song, J.H. Sung, Y.H. Jung, K.H. Lee, L.H. Dao, M.H. Kim, H.N. Kim,J. Electrochem. Soc. 151 (2004) E102eE109.

[6] J.H. Jang, S. Yoon, B.H. Ka, S.M. Oh, J. Korean Electrochem. Soc. 6 (2003)255e260.

[7] J.H. Jang, S.M. Oh, J. Electrochem. Soc. 151 (2004) A571eA577.[8] J.H. Jang, S. Yoon, B.H. Ka, Y.H. Jung, S.M. Oh, J. Electrochem. Soc. 152 (2005)

A1418eA1422.[9] S. Yoon, J.H. Jang, B.H. Ka, S.M. Oh, Electrochim. Acta 50 (2005) 2255e2262.

Sources 267 (2014) 411e420 419[10] J.H. Jang, A. Kato, K. Machida, K. Naoi, J. Electrochem. Soc. 153 (2006)A321eA328.

[11] J.H. Jang, K. Machida, Y. Kim, K. Naoi, Electrochim. Acta 52 (2006)1733e1741.

[12] J.H. Jang, S. Jeon, J.H. Cho, S.-K. Kim, S.-Y. Lee, E. Cho, H.-J. Kim, J. Han, T.-H. Lim, J. Electrochem. Soc. 156 (2009) B1293eB1300.

[13] H.D. Yoo, J.H. Jang, B.H. Ka, C.K. Rhee, S.M. Oh, Langmuir 25 (2009)11947e11954.

[14] J.H. Jang, S.M. Oh, J. Korean Electrochem. Soc. 13 (2010) 223e234.[15] H.D. Yoo, Y. Park, J.H. Ryu, S.M. Oh, Electrochim. Acta 56 (2011)

9931e9936.[16] R.S. Mikhail, S. Brunauer, E.E. Bodor, J. Colloid Interface Sci. 26 (1968)

45e53.[17] H.Y. Zhu, G.Q. Lu, N. Maes, E.F. Vansant, J. Chem. Soc. Faraday Trans. 93 (1997)

1417e1423.[18] P.W. Ruch, D. Cericola, M. Hahn, R. Kotz, A. Wokaun, J. Electroanal. Chem. 636

(2009) 128e131.[19] H.D. Yoo, Ph.D. Thesis, Seoul National University, 2011.[20] J.A. Macia-Agullo, B.C. Moore, D. Cazorla-Amoros, A. Linares-Solano, Carbon 42

(2004) 1367e1370.[21] N. Stribeck, X-Ray Scattering of Soft Matter, Springer, Berlin, 2007.[22] T. Kyotani, J. Chmiola, Y. Gogotsi, in: F. Beguin, E. Frackowiak (Eds.), Carbons

for Electrochemical Energy Storage and Conversion Systems, CRC press, NewYork, 2010, p. 105.

[23] J. Chmiola, G. Yushin, Y. Gogotsi, C. Portet, P. Simon, P.L. Taberna, Science 313(2006) 1760e1763.

[24] M.M. Hantel, T. Kaspar, R. Nesper, A. Wokaun, R. Kotz, Electrochem. Commun.13 (2011) 90e92.

[25] X. Andrieu, in: T. Osaka, M. Datta (Eds.), Energy Storage Systems for Elec-tronics, Gordon and Breach Science Publishers, 2000, p. 529.

[44] M.E. Suss, T.F. Baumann, M.A. Worsley, K.A. Rose, T.F. Jaramillo,M. Stadermann, J.G. Santiago, J. Power Sources 241 (2013) 266e273.

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

H.D. Yoo et al. / Journal of Power Sources 267 (2014) 411e420420[26] W.G. Pell, B.E. Conway, N. Marincic, J. Electroanal. Chem. 491 (2000) 9e21.[27] H.-Q. Li, J.-Y. Luo, X.-F. Zhou, C.-Z. Yu, Y.-Y. Xia, J. Electrochem. Soc. 154 (2007)

A731eA736.[28] C. Portet, P.L. Taberna, P. Simon, C. Laberty-Robert, Electrochim. Acta 49

(2004) 905e912.[29] M. Yao, K. Okuno, T. Iwaki, M. Kato, S. Tanase, K. Emura, T. Sakai, Electrochem.

Solid-State Lett. 10 (2007) A245eA249.[30] Y.J. Kim, Y. Masutzawa, S. Ozaki, M. Endo, M.S. Dresselhaus, J. Electrochem.

Soc. 151 (2004) E199eE205.[31] A. Denisenko, C. Pietzka, A. Chuvilin, U. Kaiser, H. Lu, W.J. Schaff, E. Kohn,

J. Appl. Phys. 105 (2009) 033702.[32] R. de Levie, Electrochim. Acta 8 (1963) 751e780.[33] H.-K. Song, J.H. Jang, J.J. Kim, S.M. Oh, Electrochem. Commun. 8 (2006)

1191e1196.[34] P.W. Ruch, R. Kotz, A. Wokaun, Electrochim. Acta 54 (2009) 4451e4458.[35] M. Hahn, O. Barbieri, R. Gallay, R. Kotz, Carbon 44 (2006) 2523e2533.[36] R. Mysyk, E. Raymundo-Pinero, F. Beguin, Electrochem. Commun. 11 (2009)

554e556.[37] D. Weingarth, A. Foelske-Schmitz, R. Kotz, J. Power Sources 225 (2013) 84e88.[38] X. Yang, C. Cheng, Y. Wang, L. Qiu, D. Li, Science 341 (2013) 534e537.[39] M.D. Stoller, R.S. Ruoff, Energy Environ. Sci. 3 (2010) 1294e1301.[40] D. Aurbach, M.D. Levi, G. Salitra, N. Levy, E. Pollak, J. Muthu, J. Electrochem.

Soc. 155 (2008) A745eA753.[41] J. Newman, J. Electrochem. Soc. 142 (1995) 97e101.[42] M. Eikerling, A.A. Kornyshev, E. Lust, J. Electrochem. Soc. 152 (2005) E24eE33.[43] H. Zheng, J. Li, X. Song, G. Liu, V.S. Battaglia, Electrochim. Acta 71 (2012)

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