Journal of the Electrochemical Society 150-3 A292-A300 2003

Journal of The Electrochemical Society, 150 ~3! A292-A300 ~2003!0013-4651/2003/150~3!/A292/9/$7.00 © The Electrochemical Society, Inc.

A292

Electrochemical Characteristics and Impedance SpectroscopyStudies of Carbon-Carbon SupercapacitorsP. L. Taberna, P. Simon,* ,a,z and J. F. Fauvarque

Conservatoire National des Arts et Metiers, Laboratoire d’Electrochimie Industrielle, 75003 Paris, France

This paper presents the results obtained on the electrochemical behavior of electrochemical capacitors assembled in nonaqueouselectrolyte. The first part is devoted to the electrochemical characterization of carbon-carbon 4 cm2 cells systems in terms ofcapacitance, resistance, and cyclability. The second part is focused on the electrochemical impedance spectroscopy study of thecells. Nyquist plots are presented and the impedance of the supercapacitors is discussed in terms of complex capacitance andcomplex power. This allows the determination of a relaxation time constant of the systems, and the real and the imaginary part ofthe complex powervs. the frequency plots give information on the supercapacitor cells frequency behavior. The complex imped-ance plots for both a supercapacitor and a tantalum dielectric capacitor cells are compared.© 2003 The Electrochemical Society.@DOI: 10.1149/1.1543948# All rights reserved.

Manuscript submitted February 19, 2002; revised manuscript received August 31, 2002. Available electronically January 31, 2003.

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Much work has been done for the last ten years on supercaptors, as their electrochemical properties make these systems aintermediate power and energy sources between electrochembatteries and dielectric capacitors.1-3 As compared to dielectric capacitors, supercapacitors can supply high power during severalonds. These characteristics, associated with good cyclability, mthem useful in power electronic systems and promising systemmany applications in which supercapacitors are or could be uautomotive, spatial, military, etc.

Three different types of supercapacitors are described in theerature: carbon-carbon,4,5 metal oxide,6,7 and electronically conducting polymers.8-10

Carbon-carbon supercapacitors use the cheapest technologto the low price of activated carbon. These systems function onbasis of the Gouy-Chapmann and Stern-Geary electrochemdouble-layer theory.11 The charge is stored through the adsorptionthe electrolyte ions on large-surface-area activated carbon~2300m2/g!. There is no charge-transfer reaction occurring duringcharge-discharge process. Cyclability of these supercapacitothen very high~.100,000 cycles!. Both nonaqueous and aqueoelectrolyte can be used. Organic electrolyte leads to a larger elechemical window than the aqueous one: it is then possible tocrease the voltage up to 3 V. Supercapacitor voltage is limited towith aqueous electrolyte-based supercapacitors.12

This paper first describes the electrochemical characteristicsupercapacitor cells and presents the results obtained from thevanostatic charge-discharge plots in terms of specific capacitand specific resistance evolution during cycling tests. The secpart of this paper is devoted to the frequency behavior studysupercapacitor cells. Electrochemical impedance spectroscopyof a tantalum dielectric capacitor are also presented and discus

Experimental

Electrochemical apparatus.—Galvanostatic cycling tests wercarried out with a VMP potentiostat~Biologic Technologies!, able torecord one point every 20 ms. Electrochemical impedance speccopy ~EIS! measurements were carried out with a SchlumberSolartron 1255 frequency response analyzer and a potentiSchlumberger Solartron 1286 controlled by a computer withsoftware ZPlot. The frequency range studied was 10 kHz to 10 mAll the measurements were made at the rest potential of the cell.DV signal amplitude applied was65 mV.

Electrodes.—Electrodes are constituted by expanded alumin5005 current collectors laminated to 150mm thick and active mate-

* Electrochemical Society Active Member.a Present address: Centre Interuniversitaire de Recherche et d’Inge´nierie des

Materiaux, LCMIE, 31400 Toulouse, France.z E-mail: [email protected]

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rial is an activated carbon-based paste. The collectors are meccally polished with 180-grade glass paper. A conducting painapplied on the aluminum current collectors using the spray tenique. The conducting paint is polyurethane-based containing 7tri-isocyanate hardener and 2.4% polyalcohol base, charged witwt % acetylene black. Current collectors are dried several daysder vacuum after painting.

Active material is a mixture of 95% activated carbon PICACTSC with high specific surface area~2300 m2/g! and 5% organicbinder @carboxy-methylcellulose and poly~tetrafluoroethylene!#.13,14

After drying, active material is laminated onto 4 cm2 treated alumi-num current collectors.

4 cm2 supercapacitors cells.—Two-electrode supercapacitorcells were built by assembling two 4 cm2 electrodes between poly~tetrafluoroethylene! ~PTFE! plates. Two 25mm thick PTFE sheetswere used as the separator. The system was kept under pressurstainless steel clamps~16 kg/cm2!. Two-electrode cells were set insealed plexiglass box to ensure air tightness for the cells to be teoutside the glove box. This assembly ensures a relative tightnesabout 2 weeks, the water content becoming then too high to kconstant the characteristics of the cells.

Results and Discussion

Cycling performances.—The test cells were galvanostaticalcycled at620 mA/cm2 between 0 and 2.3 V for long cycling~over10,000 cycles! and between 0 and 3 V for short cycling~about 2000cycles!. The electrolyte used was acetonitrile~AN! with 1.5 M tet-raethylammonium tetrafluoroborate dried salt. The interest in Abased electrolytes is due to their high conductivity~55 mS/cm withNEt4BF4 1.5 M!.15

Figure 1 presents a galvanostatic cycle between 0 and 2.3 Va two-electrode 4 cm2 cell containing 15 mg/cm2 of active materialfor each electrode. The cell capacitance is deduced from the slopthe discharge curve with

C 5I

S dV

dt D@1#

where C is the capacitance of the cell in farads,I the dischargecurrent in amperes~A!, anddV/dt the slope in volts per second~Vs21!.

In a symmetrical system, the specific capacitanceCmACin farads

per gram of activated carbon~F g21! is related to the capacitance othe cellC by

CmAC5

2C

mAC@2#

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Journal of The Electrochemical Society, 150 ~3! A292-A300 ~2003! A293

wheremAC is the weight~g! per electrode of activated carbon.Figure 2 presents the specific capacitance change with the c

number atI 5 620 mA cm22. The activated carbon specific capacitance was about 100 F/g in this supercapacitor. This valuclose to the one previously reported in the literature for tcarbon.13 In Fig. 2 it can be seen that the specific capacitanceconstant at 95 F/g after a small decrease during the first 1000 cyThe pore accessibility of the active material was then not modiby electrochemical redox reactions involving, for example, futional surface groups, impurities, or electrolyte redox couples.dependence of the equivalent series resistance~ESR! of the cell onthe cycling number is presented in Fig. 3. The VMP Biologics ccling potentiostat used records one point every 20 ms~50 Hz!. TheESR measured is then

ESR50 Hz 5 DV/DI @3#

whereDV is the voltage drop at beginning of the discharge in v~V!, and DI 5 uI chargeu 1 uI dischargeu in amperes~A!. Figure 3 con-firms the absence of faradaic reactions. ESR was found to be sover the cycling test at around 1V cm2.

Cycling experiments were also carried out between 0 and 3 Vorder to characterize the electrochemical behavior of the cellhigher voltage. Figure 4 presents the cell voltage changevs. timeduring cycling at620 mA cm22. The time dependence of the potential is linear, traducing the absence of major faradaic proces

Figure 1. Charge-discharge curve for 4 cm2 cell assembled with two electrodes containing 15 mg/cm2 of PICACTIF SC activated carbon betweenand 2.3 V with cycling current density of620 mA/cm2.

Figure 2. Evolution of the activated carbon specific capacitance for 4 c2

cell assembled with two electrodes containing 15 mg/cm2 of PICACTIF SCactivated carbon between 0 and 2.3 V with cycling current density of620mA/cm2.


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but at the same time, ESR slowly increases during cycling, as caseen in Fig. 5. This can be attributed to slow kinetics faradaic retions linked to the positive current collector corrosion and/or toelectrolyte oxidation. Maximum specific energy and power canestimated at 2.3 V from the previous characteristics using Eq. 45, respectively.

Pmax 5V2

4 3 ~ESR! 3 mAM@4#

Emax 51

2

C 3 V2

mAM@5#

wheremAM is the total active material weight on the two electrod~30 mg cm22!. Calculations givePmax 5 44 kW/kg and Emax

5 17 Wh/kg of active material for the cell.

Electrochemical impedance spectroscopy measurements.—Theimpedance of an electrochemical system is measured by applyilow-amplitude alternative voltageDV to a steady-state potentialVs,with DV(v) 5 DVmaxe

jvt, wherev is the pulsation andDVmax thesignal amplitude. This input signal leads to a sinusoidal output crent DI , with DI (v) 5 DI maxe

j(vt1w), wherew is the phase angleof the currentvs. the voltage andDI max the signal amplitude. Theelectrochemical impedanceZ(v) is defined asb Z(v) 5 DV/DI5 uZ(v)ue2jw 5 Z8 1 jZ9, whereZ8 and Z9 are the real part andthe imaginary part of the impedance, respectively, defined asZ82

1 Z92 5 uZ(v)u2.

Scheme 1.

One of the simplest ways to describe the supercapacitor frequbehavior is to associate a serial resistanceRs and a capacitanceC, aspresented in Scheme 1. It is then possible to define the impedanthe circuit as

b In the following equations, the functionF of the variable~v! will be noted asF(v).

Figure 3. Evolution of the ESR for 4 cm2 cell assembled with two elec-trodes containing 15 mg/cm2 of PICACTIF SC activated carbon betweenand 2.3 V with cycling current density of620 mA/cm2.


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Journal of The Electrochemical Society, 150 ~3! A292-A300 ~2003!A294

Z 5 Rs 11

jC 3 v@6#

leading to

Z 51 1 jRsC 3 v

jC 3 v@7#

The admittance is defined asA 5 1/Z and can be calculated fromEq. 7

A 5 jC 3 v 3 F 1 2 jRsC 3 v

1 1 Rs2C2 3 v2G @8#

The expression of the admittance clearly shows that whenv → 0thenA → jCv, i.e., A tends to the admittance of a capacity.

More complex models are described in the literature, as forample, the transmission line model~TLM !.16 Some authors take intoaccount the size and shape of the pores~pore size distribution! to fitthe Nyquist plot~TLM-PSD model!.17,18

An alternative approach is to describe the supercapacitor bying resistance and capacitance that are functions of the pulsativand noted asR(v) andC(v)

Figure 4. Charge-discharge curve for 4 cm2 cell assembled with two electrodes containing 15 mg/cm2 of PICACTIF SC activated carbon betweenand 3 V with cycling current density of620 mA/cm2.

Figure 5. Evolution of the ESR for 4 cm2 cell assembled with two electrodes containing 15 mg/cm2 of PICACTIF SC activated carbon betweenand 3 V with cycling current density of620 mA/cm2.


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Scheme 2.

The impedance of this equivalent circuit is then

Z 5 R~v! 1 F 1

jC~v! 3 vG @9#

The whole system can be identified as a supercapacitanceK, that byanalogy with a capacitance, leads to

Z 5 R~v! 1 F 1

jC~v! 3 vG 51

jKv@10#

and

K 5 F C~v!

1 1 jR~v! 3 C~v! 3 vG @11#

K 5 F C~v!

1 1 R2~v! 3 C2~v! 3 v2G2 F iC2~v! 3 R~v! 3 v

1 1 R2~v! 3 C2~v! 3 v2G @12#

Equation 12 defines a real part and an imaginary part for the sucapacitanceK. It is then possible to write Eq. 12 in the compleform

K 5 C8 2 jC9 @13#

where

C8 5 F C~v!

1 1 R2~v! 3 C2~v! 3 v2G @14#

C9 5 F C2~v! 3 R~v! 3 v

1 1 R2~v! 3 C2~v! 3 v2G @15#

From Eq. 14 and 15, it can be seen thatC8 is the capacitance of thesupercapacitor, varying with frequency, andC9 is the imaginary partof the supercapacitance, where the resistanceR appears. It then de-scribes the losses in the supercapacitor, by analogy with the wpublished earlier.19-21

An alternative approach is to consider the supercapacitor awhole by using the impedance data

Z~v! 51

j v 3 C~v!@16#

The impedanceZ(v) can be written under its complex form

Z~v! 5 Z8~v! 1 jZ9~v! @17#

Equations 16 and 17 lead to Eq. 18

C~v! 51

v 3 ~ jZ8~v! 2 Z9~v!!5

2~Z9~v! 1 jZ8~v!!

vuZ~v!u2

@18#

It is then possible to define

C~v! 5 C8~v! 2 jC9~v! @18a#

leading to


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C8~v! 52Z9~v!

vuZ~v!u2 @19#

C9~v! 5Z8~v!

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where C8(v) is the real part of the capacitanceC(v). The low-frequency value ofC8(v) corresponds to the capacitance of the cthat is measured during constant-current discharge, for exampl

C9(v) is the imaginary part of the capacitanceC(v). It corre-sponds to an energy dissipation by an irreversible process thalead to a hysteresis,e.g., the dielectric losses in water occurinduring the rotation or the movement of the molecules are the reafor food and drink getting hot in a microwave oven.22

These relations are discussed later in this paper.

Complex power.—Complex writing of the impedance equations hsimplified the understanding from the electrical point of view. Coplex power has been defined to have similar equations

S~v! 51

2DV~v! • DI !~v! @21#

whereS(v) is the apparent power in volt-amperes~VA !, DI * (v)the conjugated form of the intensityDI ( j v) ~A!, andDV( j v) thecomplex voltage~V!, the latter two varying according toj v.

Equation 21 leads to the following expression

S~v! 5 DVrms • DI rmse2j w @22#

whereDVrms 5 DVmax/& and DI rms 5 DI max/&, andDVmax andDI max are the maximal amplitude of the electric signal.

The complex power also has another classical form

S~v! 5 P~v! 1 jQ~v! @23#

This equation comes directly from the definition of a complex nuber. P is called the active power~watt! and Q the reactive power~volt-ampere-reactive, VAR!.

The impedance data can be used to apply the definition ofcomplex power. Equations 22 and 24 are used to establish thetion 25

uZ~v!u 5DVrms

DI rms@24#

and the complex powerS( j v) can be written

S~v! 5 @DVrms2 /uZ~v!u# 3 e2j w @25#

leading to Eq. 26 and 27

P~v! 5 @DVrms2 /uZ~v!u# 3 cosw ~W! @26#

Q~v! 5 2@DVrms2 /uZ~v!u# 3 sinw ~VAR! @27#

Equations 26 and 27 can also be written with complex capacitafrom Eq. 19 and 20 that leads to the following expressions

P~v! 5 vC9~v!uDVrmsu2 @28#

Q~v! 5 2vC8~v!uDVrmsu2 @29#

The interest of these equations is to work directly with powvalues. It is generally easier to understand the physical sense,cially when the system studied~supercapacitor! is a power source.

Applications to electrochemical impedance measurements.—Idealcapacitance has no real part as there is only a reactive contribto the power. Equations 23 and 25 have then the following form


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or else

S~v! 5 2j vCDVrms2 @31#

Ideal resistance has no imaginary part as this componentdissipates energy. The complex power takes the well-known for

S~v! 5DVrms

2

uZ8u@32#

with Z8 5 R. S decreases whenR increases.Supercapacitors oscillate between two states: resistance at

frequencies and capacitance at low frequencies. Between thesestates it behaves like a resistance-capacitance~RC! transmission linecircuit.16,17,18

Figure 6 presents the Nyquist plot of a two-electrode supepacitor cell assembled with AN1 1.5 M Net4BF4 electrolyte. Athigh frequencies~10 kHz!, supercapacitors behave like a resistanR. At low frequency, the imaginary part of the impedance sharincreases and the plot tends to a vertical line characteristic ofpacitive behavior. In the middle frequency range, the influenceelectrode porosity and thickness on the migration rate of the ifrom the electrolyte inside the electrode can be seen.23 This shiftsthe low-frequency capacitive behavior along the real axis towmore resistive values. The thicker the electrodes, the larger the sThe plot is quite linear in this frequency range. The crossing of tline with the low-frequency vertical line defines the ‘‘knee frquency:’’ below this frequency, the whole capacitance is reachFor higher values, the capacitance strongly depends onfrequency.19

Figure 7a presents the real part of capacitance (C8) changevs.frequency, according to Eq. 19. The capacitance change is thecommonly described in the literature,21 according to our previouscomments: when the frequency decreases,C8 sharply increases

Figure 6. Nyquist plots for 4 cm2 cells assembled with two electrodes cotaining PICACTIF SC activated carbon in AN with 1.5 M NET4BF4 . Fre-quency range studied: 10 kHz to 13 mHz.


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then tends to be less frequency dependent. This is characteristhe electrode structure and the electrode/electrolyte interface.

Figure 7b presents the evolution ofC9 vs. frequency, accord toEq. 20. The imaginary part of the capacitance goes through a mmum at a frequencyf 0 , defining a time constant ast0 5 1/f 0

5 10 s. This time constant has earlier been described as a dielerelaxation time24 characteristic of the whole system. It can be sein Fig. 6 that half of the low-frequency capacitance (CLF) is reachedat t0 . For shorter times,C8 , CLF/2, andC8 . CLF/2 for longertimes. This relaxation time corresponds to what Miller explainedthe supercapacitor factor of merit.25

A more explicit presentation of this time constant can be givFigure 8 presents the normalized imaginary partuQu/uSu and realpart uPu/uSu of the complex powervs. frequency. The normalizedactive power corresponds to the power dissipated into the sysThe impedance behavior of a supercapacitor varies from a pursistance at high frequency to a pure capacitance at low frequencshown in Fig. 6. All the power is dissipated (P 5 100%) at highfrequency, when the supercapacitor behaves like a pure resistanR,as can be seen in Fig. 8. From Eq. 26, the real part of the compowerP dissipated in a pure capacitance is zero (w 5 90°). This iswhat is observed in Fig. 8, whereuPu/uSu decreases whenf de-creases. The normalized imaginary part of the poweruQu/uSu in-creases when the frequency is decreased. It was a predictable bior because Eq. 30 shows that pure capacitance exhibitsreactive powerQ. The maximum ofuQu/uSu is then reached at lowfrequency when the supercapacitor behaves like a pure capacitThe crossing of the two plots appears whenuPu 5 uQu, i.e., whenw 5 145° and uPu/uSu 5 uQu/uSu 5 1/&, corresponding to thetime constantt0 , defining the frontier between the resistive and t

Figure 7. Evolution of the~a! real part and~b! imaginary capacitancevs.frequency for 4 cm2 cells assembled with two electrodes containingmg/cm2 of PICACTIF SC activated carbon in AN with NET4BF4 1.5 M.


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capacitive behavior. These representations can be useful to chterize the supercapacitor cells from an electrical point of view.

Equations 19, 20, 26, and 27 are used to characterize the ience of various parameters on the time constant, namely, the nof the electrolyte solvent and the active material weight in the etrodes. The last example compares the carbon-carbon supercapwith a tantalum dielectric capacitor.

Influence of the solvent.—Figure 9 presents the Nyquist plot for twsupercapacitor cells assembled with two different electrolyNEt4BF4 in AN and in propylene carbonate~PC!. As expected, Ny-quist plots are very different from one system to another. The retance of the cells at high frequency traduces the high conductivitthe AN-based electrolyte~55 compared to 13 mS cm21 for 1 MNEt4BF4 in PC!.15 At low frequency, each capacitor behaves likepure capacitance, characterized by the vertical line parallel toimaginary axis. A huge difference can be seen at medium frequcies, where the low-frequency capacitive behavior is largely shif

Figure 8. Normalized reactive poweruQu/uSu and reactive poweruPu/uSu vs.frequency plots for 4 cm2 cells assembled with two electrodes containingmg/cm2 of PICACTIF SC activated carbon in AN with 1.5 M NET4BF4 .

Figure 9. Nyquist plots for 4 cm2 cells assembled with two electrodes cotaining 15 mg/cm2 PICACTIF SC activated carbon in AN and PC with 1.and 1.0 M NET4BF4 , respectively.


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along the real axis toward more resistive values for the cell assembled with PC-based electrolyte. This is obviously linked to thehuge difference in the viscosity and in the dielectric constant existing between the two solvents,26 leading to a difference in the elec-trolyte penetration inside the porous structure of the electrode. Beresults are then obtained in AN-based electrolyte.

Figure 10a presents the real part of the capacitance (C8) for the

Figure 10. Evolution of the~a! real part and~b! imaginary capacitancevs.frequency for 4 cm2 cells assembled with two electrodes containing 15mg/cm2 of PICACTIF SC activated carbon in AN and PC with 1.5 and 1.0 MNET4BF4 , respectively.

Figure 11. Normalized reactive poweruQu/uSu and active poweruPu/uSu vs.frequency plots for 4 cm2 cells assembled with two electrodes containing 15mg/cm2 of PICACTIF SC activated carbon in AN and PC with 1.5 and 1.0 MNET4BF4 , respectively.


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two cells. The low-frequency value of the capacitance is roughlysame~around 2 F!, as the active material weight in the cells wakept constant. The huge frequency dependence of the capaciindicates that the whole electrode porosity was not reached incases.

The time constants are very different, as can be seen in Fig.10 and 48 s, respectively, when using AN and PC. The cell usingis able to deliver its stored energy five times faster, meaninghigher power. Figure 11 presents the evolution of both the normized imaginary partuQu/uSu and real partuPu/uSu of the complexpowervs. frequency. That confirms previous observations: the pcapacitive behavior (uQu > 95%uSu) is reached at higher frequencfor the AN-based cell~25 mHz! as compared to the PC-based cell~6mHz!, traducing the great influence of the solvent on the perfmances of the cell.

Figure 12. ~a! Nyquist plots for 4 cm2 cells assembled with two electrodecontaining 15.0 and 11.3 mg/cm2 PICACTIF SC activated carbon in AN 1.5M NET4BF4 and ~b, bottom! high-frequency range enhancement.


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Influence of the active material content.—Figure 12a presents theNyquist plot for two supercapacitors assembled with different activmaterial weight, 120 and 90 mg, respectively. Figure 12b is thhigh-frequency zoom of the plot. The difference in the active material amount in the cells leads to a difference in the electrode thickness from one cell to the other. The high-frequency resistanceslightly decreased when less active material is used. That wasexpected result, as the electrode thickness is less in this case. Tmost important difference occurs in the middle frequency range,i.e.,where the electrode thickness and porosity effects can be seeWhen the electrode thickness increases~with higher active materialamount!, the shift toward more positive resistance values increaseThis is in agreement with our previous observations.

Figure 13a presents the change in the real part of the capacitanC8 vs. frequency.C8 sharply increases between 1 Hz and 50 mHzand tends to be less frequency dependent for the cell containingmg of activated carbon. The capacitance is around 1.5 F for this ceThe whole capacitance is not reached at 12 mHz, even for the cusing less active material. This is due to the increase of the electrothickness: the ions from the electrolyte have not reached the who

Figure 13. Evolution of the~a! real part and~b! imaginary capacitancevs.frequency for 4 cm2 cells assembled with two electrodes containing 15.0 and11.3 mg/cm2 PICACTIF SC activated carbon in AN with 1.5 M NEt4BF4 .


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electrode porosity. The low-frequency capacitance values are 21.4 F for the cells containing 120 and 90 mg, respectively, of avated carbon. Figure 13b plots theC9 dependence on frequency. Thplot gives the time constant of the cells, 10 s for the high activacarbon content and 4.8 s for the lowest one. Faster dischargecan then be reached with the low-carbon cell, meaning thatcharged power is more important in this case.

Figure 14 presents normalized imaginary partuQu/uSu and realpart uPu/uSu of the complex powervs. frequency for the two cells.The similar shape for the two plots shows that the two systems hclose electrochemical properties, as they only differ in the amounactivated carbon. The change in active material weight from 15.11.3 mg/cm2 has a less pronounced influence on the complex pobehavior as compared to the nature of the solvent~cf. Fig. 11!.

Comparison between tantalum capacitor and carbon-carbsupercapacitor.—The last part of this paper compares two differesystems, a tantalum dielectric capacitor~Ta! and a 4 cm2 superca-pacitor cell. The Ta capacitor was composed of three capacassembled in parallel. Each capacitor was 68mF, 16 V; the stack wasthen 204mF, 16 V.

Figure 14. Normalized reactive poweruQu/uSu and active poweruPu/uSu vs.frequency plots for 4 cm2 cells assembled with two electrodes containin15.0 and 11.3 mg/cm2 PICACTIF SC activated carbon in AN with 1.5 MNEt4BF4 .

Figure 15. Nyquist plots of a 4 cm2 cell carbon-carbon supercapacitor in ANwith 1.5 M NEt4BF4 electrolyte and with a Ta dielectric capacitor.


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Figure 15 presents the Nyquist plot for the two systems. The pcapacitive behavior of the Ta capacitor can be seen as its plotsists of a vertical line. ESR is very low, around 0.1V. The Nyquistplot of the supercapacitor was the same as the one previouslyserved. Figure 16a gives the capacitanceC8 evolution with fre-quency. The difference is important from one system to the otThe capacitance of the Ta capacitor was constant~at 210mF! at highfrequency,i.e., 1000 Hz, while at the same time the capacitancethe carbon-carbon system was first very low and then stronglyquency dependent. This is obviously linked to the basic differencthe capacitors nature.

Figure 16b presents the evolution of the imaginary part ofcapacitanceC9 vs. frequency. The two time constants were foundbe very different, from 50ms to 10 s, respectively, for the Ta ancarbon-carbon systems. The minimum discharge time is 23 105

higher for the Ta system, leading to a power capacitor, as compto the carbon-carbon system. This huge difference can be agaiplained by the difference in the nature of the two systems.

Figure 17 presents the normalized imaginary partuQu/uSu andreal partuPu/uSu of the complex powervs. frequency plots for boththe Ta capacitor and carbon-carbon supercapacitor. This plotvides information regarding the difference in the way to chanfrom resistive to capacitive behavior for the two systems: the chaoccurs roughly from 20 kHz~resistive! down to 2 kHz~capacitive!,i.e., over one order of magnitude. For the carbon supercapacitor,visible from 10 Hz~resistive! to lower than 10 mHz: it spreads ovethree orders of magnitude. The use of a Ta capacitor can be achwith high efficiency at frequencies as high as 63 103 Hz (uQu5 0.953 uSu), while the carbon-carbon supercapacitor assembwith 15.0 mg cm22 of active material is not able to work at the samefficiency before 20 mHz.

Figure 16. Evolution of the~a! real part and~b! imaginary capacitancevs.frequency for 4 cm2 cell carbon-carbon supercapacitor in AN with 1.5NEt4BF4 and with a Ta dielectric capacitor.


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Conclusions

This paper presents the results obtained with carbon-carbonpercapacitors 4 cm2 cells in organic electrolyte. The first part of thpaper is devoted to basic performance and cycling results. Thecific capacitance of the activated carbon used in this work~PICAC-TIF SC from the Pica Company! was found to be 95 F g21 at 620mA cm22 constant current cycling. The series resistance was 1Vcm2. The use of treated-aluminum current collectors allowednominal voltage of 2.3 V to be reached during cycling. The charteristics of the cell were very stable during galvanostatic cycling,to 10,000 cycles at620 mA cm22.

The frequency behavior of the cells was then studied by uscomplex capacitance and complex power equations. It was thensible to define a relaxation time constantt0 . This time constantcorresponds to the value of145° for the phase anglew. It representsa transition for the supercapacitor between a resistive behaviofrequency higher than 1/t0 and a capacitive behavior for frequenclower than 1/t0 . The time constantt0 was found to be 10 s for astandard 4 cm2 cell assembled with 15.0 mg/cm2 of activated carbon~symmetrical cell!. Complex power normalized imaginary pauQu/uSu and real partuPu/uSu vs. frequency plots were proposed ascomplementary presentation of the impedance response of thepercapacitor cellsZ9 5 f (Z8). These plots allow an overview of thwhole frequency behavior of the supercapacitors, ranging frompure resistance at high frequency to a pure capacitance at lowquency. The influence of several parameters on the time constat0

values was characterized.t0 increases from 10 to 48 s when thsolvent was changed from AN to PC, leading to a sharp decreasthe cell power. On the contrary, and as it was expected, the decrof the activated carbon weight in the electrodes led to a decreast0 from 10 to 4.8 s, increasing the cell power. These plots were aused to compare two different systems, a dielectric Ta capacitor~204mF, 16 V! and a standard 4 cm2 cell carbon-carbon supercapacitor~2F, 2.3 V!. The t0 time constants were found equal to 50ms and 10s, respectively, for the Ta and the carbon-carbon systems. Finthe complex power plot revealed the huge difference in the tneeded for the Ta capacitor to pass from pure resistive (uQu 5 0) topure capacitive behavior (uPu 5 0) as compared to the carboncarbon supercapacitor.

Acknowledgments

The authors thank the ‘‘De´legation Generale pour l’Armement’’for financial support of this work.

CNAM assisted in meeting the publication costs of this article.

Figure 17. Normalized reactive poweruQu/uSu and active poweruPu/uSu vs.frequency plots for 4 cm2 cell carbon-carbon supercapacitor in AN with 1M NEt4BF4 and with a Ta dielectric capacitor.


ccand

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