Electrochemical Characteristics and Impedance Spectroscopy Studies of Carbon-Carbon Supercapacitors

Transcription

1 A292 Journal of The Electrochemical Society, 50 3 A292-A /2003/50 3 /A292/9/$7.00 The Electrochemical Society, Inc. Electrochemical Characteristics and Impedance Spectroscopy Studies of Carbon-Carbon Supercapacitors P. L. Taberna, P. Simon,*,a,z and J. F. Fauvarque Conservatoire National des Arts et Metiers, Laboratoire d Electrochimie Industrielle, Paris, France This paper presents the results obtained on the electrochemical behavior of electrochemical capacitors assembled in nonaqueous electrolyte. The first part is devoted to the electrochemical characterization of carbon-carbon 4 cm 2 cells systems in terms of capacitance, resistance, and cyclability. The second part is focused on the electrochemical impedance spectroscopy study of the cells. Nyquist plots are presented and the impedance of the supercapacitors is discussed in terms of complex capacitance and complex power. This allows the determination of a relaxation time constant of the systems, and the real and the imaginary part of the complex power vs. the frequency plots give information on the supercapacitor cells frequency behavior. The complex impedance plots for both a supercapacitor and a tantalum dielectric capacitor cells are compared The Electrochemical Society. DOI: 0.49/ All rights reserved. Manuscript submitted February 9, 2002; revised manuscript received August 3, Available electronically January 3, * Electrochemical Society Active Member. a Present address: Centre Interuniversitaire de Recherche et d Ingénierie des Matériaux, LCMIE, 3400 Toulouse, France. z simon@chimie.ups-tlse.fr Much work has been done for the last ten years on supercapacitors, as their electrochemical properties make these systems act as intermediate power and energy sources between electrochemical batteries and dielectric capacitors. -3 As compared to dielectric capacitors, supercapacitors can supply high power during several seconds. These characteristics, associated with good cyclability, make them useful in power electronic systems and promising systems in many applications in which supercapacitors are or could be used: automotive, spatial, military, etc. Three different types of supercapacitors are described in the literature: carbon-carbon, 4,5 metal oxide, 6,7 and electronically conducting polymers. 8-0 Carbon-carbon supercapacitors use the cheapest technology due to the low price of activated carbon. These systems function on the basis of the Gouy-Chapmann and Stern-Geary electrochemical double-layer theory. The charge is stored through the adsorption of the electrolyte ions on large-surface-area activated carbon 2300 m 2 /g. There is no charge-transfer reaction occurring during the charge-discharge process. Cyclability of these supercapacitors is then very high 00,000 cycles. Both nonaqueous and aqueous electrolyte can be used. Organic electrolyte leads to a larger electrochemical window than the aqueous one: it is then possible to increase the voltage up to 3 V. Supercapacitor voltage is limited to V with aqueous electrolyte-based supercapacitors. 2 This paper first describes the electrochemical characteristics of supercapacitor cells and presents the results obtained from the galvanostatic charge-discharge plots in terms of specific capacitance and specific resistance evolution during cycling tests. The second part of this paper is devoted to the frequency behavior study of supercapacitor cells. Electrochemical impedance spectroscopy plots of a tantalum dielectric capacitor are also presented and discussed. Experimental Electrochemical apparatus. Galvanostatic cycling tests were carried out with a VMP potentiostat Biologic Technologies, able to record one point every 20 ms. Electrochemical impedance spectroscopy EIS measurements were carried out with a Schlumberger Solartron 255 frequency response analyzer and a potentiostat Schlumberger Solartron 286 controlled by a computer with the software ZPlot. The frequency range studied was 0 khz to 0 mhz. All the measurements were made at the rest potential of the cell. The V signal amplitude applied was 5 mv. Electrodes. Electrodes are constituted by expanded aluminum 5005 current collectors laminated to 50 m thick and active material is an activated carbon-based paste. The collectors are mechanically polished with 80-grade glass paper. A conducting paint is applied on the aluminum current collectors using the spray technique. The conducting paint is polyurethane-based containing 7.6% tri-isocyanate hardener and 2.4% polyalcohol base, charged with 30 wt % acetylene black. Current collectors are dried several days under vacuum after painting. Active material is a mixture of 95% activated carbon PICACTIF SC with high specific surface area 2300 m 2 /g and 5% organic binder carboxy-methylcellulose and poly tetrafluoroethylene. 3,4 After drying, active material is laminated onto 4 cm 2 treated aluminum current collectors. 4 cm 2 supercapacitors cells. Two-electrode supercapacitors cells were built by assembling two 4 cm 2 electrodes between poly- tetrafluoroethylene PTFE plates. Two 25 m thick PTFE sheets were used as the separator. The system was kept under pressure with stainless steel clamps 6 kg/cm 2. Two-electrode cells were set in a sealed plexiglass box to ensure air tightness for the cells to be tested outside the glove box. This assembly ensures a relative tightness for about 2 weeks, the water content becoming then too high to keep constant the characteristics of the cells. Results and Discussion Cycling performances. The test cells were galvanostatically cycled at 20 ma/cm 2 between 0 and 2.3 V for long cycling over 0,000 cycles and between 0 and 3 V for short cycling about 2000 cycles. The electrolyte used was acetonitrile AN with.5 M tetraethylammonium tetrafluoroborate dried salt. The interest in ANbased electrolytes is due to their high conductivity 55 ms/cm with NEt 4 BF 4.5 M. 5 Figure presents a galvanostatic cycle between 0 and 2.3 V for a two-electrode 4 cm 2 cell containing 5 mg/cm 2 of active material for each electrode. The cell capacitance is deduced from the slope of the discharge curve with C I dv dt where C is the capacitance of the cell in farads, I the discharge current in amperes A, and dv/dt the slope in volts per second V s. In a symmetrical system, the specific capacitance C mac in farads per gram of activated carbon F g is related to the capacitance of the cell C by C mac 2C m AC 2

2 Journal of The Electrochemical Society, 50 3 A292-A A293 Figure. Charge-discharge curve for 4 cm 2 cell assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon between 0 and 2.3 V with cycling current density of 20 ma/cm 2. Figure 3. Evolution of the ESR for 4 cm 2 cell assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon between 0 and 2.3 V with cycling current density of 20 ma/cm 2. where m AC is the weight g per electrode of activated carbon. Figure 2 presents the specific capacitance change with the cycle number at I 20 ma cm 2. The activated carbon specific capacitance was about 00 F/g in this supercapacitor. This value is close to the one previously reported in the literature for this carbon. 3 In Fig. 2 it can be seen that the specific capacitance was constant at 95 F/g after a small decrease during the first 000 cycles. The pore accessibility of the active material was then not modified by electrochemical redox reactions involving, for example, functional surface groups, impurities, or electrolyte redox couples. The dependence of the equivalent series resistance ESR of the cell on the cycling number is presented in Fig. 3. The VMP Biologics cycling potentiostat used records one point every 20 ms 50 Hz. The ESR measured is then ESR 50 Hz V/ I where V is the voltage drop at beginning of the discharge in volt V, and I I charge I discharge in amperes A. Figure 3 confirms the absence of faradaic reactions. ESR was found to be stable over the cycling test at around cm 2. Cycling experiments were also carried out between 0 and 3 V in order to characterize the electrochemical behavior of the cells at higher voltage. Figure 4 presents the cell voltage change vs. time during cycling at 20 ma cm 2. The time dependence of the potential is linear, traducing the absence of major faradaic processes, 3 but at the same time, ESR slowly increases during cycling, as can be seen in Fig. 5. This can be attributed to slow kinetics faradaic reactions linked to the positive current collector corrosion and/or to the electrolyte oxidation. Maximum specific energy and power can be estimated at 2.3 V from the previous characteristics using Eq. 4 and 5, respectively. P max V 2 4 ESR m AM 4 E max 2 C V 2 m AM where m AM is the total active material weight on the two electrodes 30 mg cm 2. Calculations give P max 44 kw/kg and E max 7 Wh/kg of active material for the cell. Electrochemical impedance spectroscopy measurements. The impedance of an electrochemical system is measured by applying a low-amplitude alternative voltage V to a steady-state potential V s, with V( ) V max e j t, where is the pulsation and V max the signal amplitude. This input signal leads to a sinusoidal output current I, with I( ) I max e j( t ), where is the phase angle of the current vs. the voltage and I max the signal amplitude. The electrochemical impedance Z( ) is defined as b Z( ) V/ I Z( ) e j Z jz, where Z and Z are the real part and the imaginary part of the impedance, respectively, defined as Z 2 Z 2 Z( ) 2. 5 Scheme. Figure 2. Evolution of the activated carbon specific capacitance for 4 cm 2 cell assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon between 0 and 2.3 V with cycling current density of 20 ma/cm 2. One of the simplest ways to describe the supercapacitor frequency behavior is to associate a serial resistance R s and a capacitance C, as presented in Scheme. It is then possible to define the impedance of the circuit as b In the following equations, the function F of the variable will be noted as F( ).

3 A294 Journal of The Electrochemical Society, 50 3 A292-A Scheme 2. The impedance of this equivalent circuit is then Z R jc 9 Figure 4. Charge-discharge curve for 4 cm 2 cell assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon between 0 and 3 V with cycling current density of 20 ma/cm 2. leading to Z R s jc Z jr sc jc The admittance is defined as A /Z and can be calculated from Eq A jc jr sc R s 2 C The expression of the admittance clearly shows that when 0 then A jc, i.e., A tends to the admittance of a capacity. More complex models are described in the literature, as for example, the transmission line model TLM. 6 Some authors take into account the size and shape of the pores pore size distribution to fit the Nyquist plot TLM-PSD model. 7,8 An alternative approach is to describe the supercapacitor by using resistance and capacitance that are functions of the pulsation and noted as R( ) and C( ) The whole system can be identified as a supercapacitance K, that by analogy with a capacitance, leads to and Z R jc jk 0 C K jr C C K 2 R 2 C 2 ic 2 R 2 R 2 C 2 2 Equation 2 defines a real part and an imaginary part for the supercapacitance K. It is then possible to write Eq. 2 in the complex form K C jc 3 where C C 2 R 2 C 2 4 C C 2 R 2 R 2 C 2 5 From Eq. 4 and 5, it can be seen that C is the capacitance of the supercapacitor, varying with frequency, and C is the imaginary part of the supercapacitance, where the resistance R appears. It then describes the losses in the supercapacitor, by analogy with the work published earlier. 9-2 An alternative approach is to consider the supercapacitor as a whole by using the impedance data Z j C 6 The impedance Z( ) can be written under its complex form Z Z jz 7 Equations 6 and 7 lead to Eq. 8 C jz Z Z jz Z 2 8 Figure 5. Evolution of the ESR for 4 cm 2 cell assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon between 0 and 3 V with cycling current density of 20 ma/cm 2. It is then possible to define C C jc leading to 8a

4 Journal of The Electrochemical Society, 50 3 A292-A A295 C C Z Z 2 Z Z where C ( ) is the real part of the capacitance C( ). The lowfrequency value of C ( ) corresponds to the capacitance of the cell that is measured during constant-current discharge, for example. C ( ) is the imaginary part of the capacitance C( ). It corresponds to an energy dissipation by an irreversible process that can lead to a hysteresis, e.g., the dielectric losses in water occuring during the rotation or the movement of the molecules are the reason for 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 has simplified the understanding from the electrical point of view. Complex power has been defined to have similar equations S 2 V I 2 where S( ) is the apparent power in volt-amperes VA, I*( ) the conjugated form of the intensity I( j ) A, and V( j ) the complex voltage V, the latter two varying according to j. Equation 2 leads to the following expression S V rms I rms e j 22 Figure 6. Nyquist plots for 4 cm 2 cells assembled with two electrodes containing PICACTIF SC activated carbon in AN with.5 M NET 4 BF 4. Frequency range studied: 0 khz to 3 mhz. where V rms V max /& and I rms I max /&, and V max and I max are the maximal amplitude of the electric signal. The complex power also has another classical form S jq j V 2 rms Z 30 S P jq 23 or else This equation comes directly from the definition of a complex number. 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 of the complex power. Equations 22 and 24 are used to establish the relation 25 Z V rms I rms 24 and the complex power S( j ) can be written S V 2 rms / Z e j 25 leading to Eq. 26 and 27 P V rms / Z cos W 26 Q V rms / Z sin VAR 27 Equations 26 and 27 can also be written with complex capacitance from Eq. 9 and 20 that leads to the following expressions P C V rms 2 28 Q C V rms 2 29 The interest of these equations is to work directly with power values. It is generally easier to understand the physical sense, especially when the system studied supercapacitor is a power source. Applications to electrochemical impedance measurements. Ideal capacitance has no real part as there is only a reactive contribution to the power. Equations 23 and 25 have then the following forms 2 S j C V rms 3 Ideal resistance has no imaginary part as this component only dissipates energy. The complex power takes the well-known form S V 2 rms 32 Z with Z R. S decreases when R increases. Supercapacitors oscillate between two states: resistance at high frequencies and capacitance at low frequencies. Between these two states it behaves like a resistance-capacitance RC transmission line circuit. 6,7,8 Figure 6 presents the Nyquist plot of a two-electrode supercapacitor cell assembled with AN.5 M Net 4 BF 4 electrolyte. At high frequencies 0 khz, supercapacitors behave like a resistance R. At low frequency, the imaginary part of the impedance sharply increases and the plot tends to a vertical line characteristic of capacitive behavior. In the middle frequency range, the influence of electrode porosity and thickness on the migration rate of the ions from the electrolyte inside the electrode can be seen. 23 This shifts the low-frequency capacitive behavior along the real axis toward more resistive values. The thicker the electrodes, the larger the shift. The plot is quite linear in this frequency range. The crossing of this line with the low-frequency vertical line defines the knee frequency: below this frequency, the whole capacitance is reached. For higher values, the capacitance strongly depends on the frequency. 9 Figure 7a presents the real part of capacitance (C ) change vs. frequency, according to Eq. 9. The capacitance change is the one commonly described in the literature, 2 according to our previous comments: when the frequency decreases, C sharply increases,

5 A296 Journal of The Electrochemical Society, 50 3 A292-A Figure 8. Normalized reactive power Q / S and reactive power P / S vs. frequency plots for 4 cm 2 cells assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon in AN with.5 M NET 4 BF 4. Figure 7. Evolution of the a real part and b imaginary capacitance vs. frequency for 4 cm 2 cells assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon in AN with NET 4 BF 4.5 M. then tends to be less frequency dependent. This is characteristic of the electrode structure and the electrode/electrolyte interface. Figure 7b presents the evolution of C vs. frequency, accord to Eq. 20. The imaginary part of the capacitance goes through a maximum at a frequency f 0, defining a time constant as 0 /f 0 0 s. This time constant has earlier been described as a dielectric relaxation time 24 characteristic of the whole system. It can be seen in Fig. 6 that half of the low-frequency capacitance (C LF ) is reached at 0. For shorter times, C C LF /2, and C C LF /2 for longer times. This relaxation time corresponds to what Miller explained as the supercapacitor factor of merit. 25 A more explicit presentation of this time constant can be given. Figure 8 presents the normalized imaginary part Q / S and real part P / S of the complex power vs. frequency. The normalized active power corresponds to the power dissipated into the system. The impedance behavior of a supercapacitor varies from a pure resistance at high frequency to a pure capacitance at low frequency, as shown in Fig. 6. All the power is dissipated (P 00%) at high frequency, when the supercapacitor behaves like a pure resistance R, as can be seen in Fig. 8. From Eq. 26, the real part of the complex power P dissipated in a pure capacitance is zero ( 90 ). This is what is observed in Fig. 8, where P / S decreases when f decreases. The normalized imaginary part of the power Q / S increases when the frequency is decreased. It was a predictable behavior because Eq. 30 shows that pure capacitance exhibits only reactive power Q. The maximum of Q / S is then reached at low frequency when the supercapacitor behaves like a pure capacitance. The crossing of the two plots appears when P Q, i.e., when 45 and P / S Q / S /&, corresponding to the time constant 0, defining the frontier between the resistive and the capacitive behavior. These representations can be useful to characterize the supercapacitor cells from an electrical point of view. Equations 9, 20, 26, and 27 are used to characterize the influence of various parameters on the time constant, namely, the nature of the electrolyte solvent and the active material weight in the electrodes. The last example compares the carbon-carbon supercapacitor with a tantalum dielectric capacitor. Influence of the solvent. Figure 9 presents the Nyquist plot for two supercapacitor cells assembled with two different electrolytes: NEt 4 BF 4 in AN and in propylene carbonate PC. As expected, Nyquist plots are very different from one system to another. The resistance of the cells at high frequency traduces the high conductivity of the AN-based electrolyte 55 compared to 3 ms cm form NEt 4 BF 4 in PC. 5 At low frequency, each capacitor behaves like a pure capacitance, characterized by the vertical line parallel to the imaginary axis. A huge difference can be seen at medium frequencies, where the low-frequency capacitive behavior is largely shifted Figure 9. Nyquist plots for 4 cm 2 cells assembled with two electrodes containing 5 mg/cm 2 PICACTIF SC activated carbon in AN and PC with.5 and.0 M NET 4 BF 4, respectively.

6 Journal of The Electrochemical Society, 50 3 A292-A A297 Figure 0. Evolution of the a real part and b imaginary capacitance vs. frequency for 4 cm 2 cells assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon in AN and PC with.5 and.0 M NET 4 BF 4, respectively. along the real axis toward more resistive values for the cell assembled with PC-based electrolyte. This is obviously linked to the huge difference in the viscosity and in the dielectric constant existing between the two solvents, 26 leading to a difference in the electrolyte penetration inside the porous structure of the electrode. Best results are then obtained in AN-based electrolyte. Figure 0a presents the real part of the capacitance (C ) for the Figure 2. a Nyquist plots for 4 cm 2 cells assembled with two electrodes containing 5.0 and.3 mg/cm 2 PICACTIF SC activated carbon in AN.5 M NET 4 BF 4 and b, bottom high-frequency range enhancement. Figure. Normalized reactive power Q / S and active power P / S vs. frequency plots for 4 cm 2 cells assembled with two electrodes containing 5 mg/cm 2 of PICACTIF SC activated carbon in AN and PC with.5 and.0 M NET 4 BF 4, respectively. two cells. The low-frequency value of the capacitance is roughly the same around 2 F, as the active material weight in the cells was kept constant. The huge frequency dependence of the capacitance indicates that the whole electrode porosity was not reached in both cases. The time constants are very different, as can be seen in Fig. 0b: 0 and 48 s, respectively, when using AN and PC. The cell using AN is able to deliver its stored energy five times faster, meaning at higher power. Figure presents the evolution of both the normalized imaginary part Q / S and real part P / S of the complex power vs. frequency. That confirms previous observations: the pure capacitive behavior ( Q 95% S ) is reached at higher frequency for the AN-based cell 25 mhz as compared to the PC-based cell 6 mhz, traducing the great influence of the solvent on the performances of the cell.

7 A298 Journal of The Electrochemical Society, 50 3 A292-A Figure 4. Normalized reactive power Q / S and active power P / S vs. frequency plots for 4 cm 2 cells assembled with two electrodes containing 5.0 and.3 mg/cm 2 PICACTIF SC activated carbon in AN with.5 M NEt 4 BF 4. electrode porosity. The low-frequency capacitance values are 2 and.4 F for the cells containing 20 and 90 mg, respectively, of activated carbon. Figure 3b plots the C dependence on frequency. The plot gives the time constant of the cells, 0 s for the high activated carbon content and 4.8 s for the lowest one. Faster discharge time can then be reached with the low-carbon cell, meaning that discharged power is more important in this case. Figure 4 presents normalized imaginary part Q / S and real part P / S of the complex power vs. frequency for the two cells. The similar shape for the two plots shows that the two systems have close electrochemical properties, as they only differ in the amount of activated carbon. The change in active material weight from 5.0 to.3 mg/cm 2 has a less pronounced influence on the complex power behavior as compared to the nature of the solvent cf. Fig.. Comparison between tantalum capacitor and carbon-carbon supercapacitor. The last part of this paper compares two different systems, a tantalum dielectric capacitor Ta anda4cm 2 supercapacitor cell. The Ta capacitor was composed of three capacitors assembled in parallel. Each capacitor was 68 F, 6 V; the stack was then 204 F, 6 V. Figure 3. Evolution of the a real part and b imaginary capacitance vs. frequency for 4 cm 2 cells assembled with two electrodes containing 5.0 and.3 mg/cm 2 PICACTIF SC activated carbon in AN with.5 M NEt 4 BF 4. Influence of the active material content. Figure 2a presents the Nyquist plot for two supercapacitors assembled with different active material weight, 20 and 90 mg, respectively. Figure 2b is the high-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 resistance is slightly decreased when less active material is used. That was an expected result, as the electrode thickness is less in this case. The most important difference occurs in the middle frequency range, i.e., where the electrode thickness and porosity effects can be seen. When the electrode thickness increases with higher active material amount, the shift toward more positive resistance values increases. This is in agreement with our previous observations. Figure 3a presents the change in the real part of the capacitance C vs. frequency. C sharply increases between Hz and 50 mhz and tends to be less frequency dependent for the cell containing 90 mg of activated carbon. The capacitance is around.5 F for this cell. The whole capacitance is not reached at 2 mhz, even for the cell using less active material. This is due to the increase of the electrode thickness: the ions from the electrolyte have not reached the whole Figure 5. Nyquist plots of a4cm 2 cell carbon-carbon supercapacitor in AN with.5 M NEt 4 BF 4 electrolyte and with a Ta dielectric capacitor.

8 Journal of The Electrochemical Society, 50 3 A292-A A299 Figure 7. Normalized reactive power Q / S and active power P / S vs. frequency plots for 4 cm 2 cell carbon-carbon supercapacitor in AN with.5 M NEt 4 BF 4 and with a Ta dielectric capacitor. Figure 6. Evolution of the a real part and b imaginary capacitance vs. frequency for 4 cm 2 cell carbon-carbon supercapacitor in AN with.5 M NEt 4 BF 4 and with a Ta dielectric capacitor. Figure 5 presents the Nyquist plot for the two systems. The pure capacitive behavior of the Ta capacitor can be seen as its plot consists of a vertical line. ESR is very low, around 0.. The Nyquist plot of the supercapacitor was the same as the one previously observed. Figure 6a gives the capacitance C evolution with frequency. The difference is important from one system to the other. The capacitance of the Ta capacitor was constant at 20 F at high frequency, i.e., 000 Hz, while at the same time the capacitance of the carbon-carbon system was first very low and then strongly frequency dependent. This is obviously linked to the basic difference in the capacitors nature. Figure 6b presents the evolution of the imaginary part of the capacitance C vs. frequency. The two time constants were found to be very different, from 50 s to 0 s, respectively, for the Ta and carbon-carbon systems. The minimum discharge time is higher for the Ta system, leading to a power capacitor, as compared to the carbon-carbon system. This huge difference can be again explained by the difference in the nature of the two systems. Figure 7 presents the normalized imaginary part Q / S and real part P / S of the complex power vs. frequency plots for both the Ta capacitor and carbon-carbon supercapacitor. This plot provides information regarding the difference in the way to change from resistive to capacitive behavior for the two systems: the change occurs roughly from 20 khz resistive downto2khz capacitive, i.e., over one order of magnitude. For the carbon supercapacitor, it is visible from 0 Hz resistive to lower than 0 mhz: it spreads over three orders of magnitude. The use of a Ta capacitor can be achieved with high efficiency at frequencies as high as Hz ( Q 0.95 S ), while the carbon-carbon supercapacitor assembled with 5.0 mg cm 2 of active material is not able to work at the same efficiency before 20 mhz. Conclusions This paper presents the results obtained with carbon-carbon supercapacitors 4 cm 2 cells in organic electrolyte. The first part of the paper is devoted to basic performance and cycling results. The specific capacitance of the activated carbon used in this work PICAC- TIF SC from the Pica Company was found to be 95 F g at 20 ma cm 2 constant current cycling. The series resistance was cm 2. The use of treated-aluminum current collectors allowed a nominal voltage of 2.3 V to be reached during cycling. The characteristics of the cell were very stable during galvanostatic cycling, up to 0,000 cycles at 20 ma cm 2. The frequency behavior of the cells was then studied by using complex capacitance and complex power equations. It was then possible to define a relaxation time constant 0. This time constant corresponds to the value of 45 for the phase angle. It represents a transition for the supercapacitor between a resistive behavior for frequency higher than / 0 and a capacitive behavior for frequency lower than / 0. The time constant 0 was found to be 0 s for a standard 4 cm 2 cell assembled with 5.0 mg/cm 2 of activated carbon symmetrical cell. Complex power normalized imaginary part Q / S and real part P / S vs. frequency plots were proposed as a complementary presentation of the impedance response of the supercapacitor cells Z f (Z ). These plots allow an overview of the whole frequency behavior of the supercapacitors, ranging from a pure resistance at high frequency to a pure capacitance at low frequency. The influence of several parameters on the time constant 0 values was characterized. 0 increases from 0 to 48 s when the solvent was changed from AN to PC, leading to a sharp decrease of the cell power. On the contrary, and as it was expected, the decrease of the activated carbon weight in the electrodes led to a decrease of 0 from 0 to 4.8 s, increasing the cell power. These plots were also used to compare two different systems, a dielectric Ta capacitor 204 F, 6 V and a standard 4 cm 2 cell carbon-carbon supercapacitor 2 F, 2.3 V. The 0 time constants were found equal to 50 s and 0 s, respectively, for the Ta and the carbon-carbon systems. Finally, the complex power plot revealed the huge difference in the time needed for the Ta capacitor to pass from pure resistive ( Q 0) to pure capacitive behavior ( P 0) as compared to the carboncarbon supercapacitor. Acknowledgments The authors thank the Délégation Générale pour l Armement for financial support of this work. CNAM assisted in meeting the publication costs of this article.

9 A300 Journal of The Electrochemical Society, 50 3 A292-A References. A. Burke, J. Power Sources, 9, R. Kötz and M. Carlen, Electrochim. Acta, 45, A. Nishino, J. Power Sources, 60, T. Morimoto, K. Hiratsuka, Y. Sanada, and K. Kurihara, J. Power Sources, 60, A. Du Pasquier, J. A. Shelburne, I. Plitz, F. Badway, A. S. Gozdz, and G. Amatucci, in Proceedings of the th International Seminar on Double-Layer Capacitors and Similar Energy Storage Devices, Deerfield Beach, FL, December 3-5, Q. L. Fang, D. A. Evans, S. L. Roberson, and J. P. Zheng, J. Electrochem. Soc., 48, A I. D. Raistrick and R. T. Sherman, in Electrode Materials and Processes for Energy Conversion and Storage, S. Srinivasan, S. Wagner, and H. Wroblowa, Editors, PV 87-2, p. 582, The Electrochemical Society Proceedings Series, Pennington, NJ A. Laforgue, P. Simon, J. F. Fauvarque, J. F. Sarrau, and P. Lailler, J. Electrochem. Soc., 48, A M. Mastragostino, C. Arbizzani, R. Paraventi, and A. Zanelli, J. Electrochem. Soc., 47, A. Di Fabio, A. Giorgi, M. Mastragostino, and F. Soavi, J. Electrochem. Soc., 48, A A. Bard and L. R. Faulkner, Electrochemical Methods, John Wiley and Sons, New York S. Yoon, J. Lee, T. Hyeon, and S. M. Oh, J. Electrochem. Soc., 47, J. Gamby, P. L. Taberna, P. Simon, J. F. Fauvarque, and M. Chesneau, J. Power Sources, 0, A. Laforgue, P. Simon, C. Sarrazin, and J. F. Fauvarque, J. Power Sources, 80, A. Yoshida, S. Nonaka, I. Aoki, and A. Nishino, J. Power Sources, 60, D. Qu and H. Shi, J. Power Sources, 74, H. K. Song, Y. H. Jung, K. H. Lee, and Le H. Dao, Electrochim. Acta, 44, H. Keiser, K. D. Beccu, and M. A. Gutjahr, Electrochim. Acta, 2, M. Keddam and H. Takenouti, in Electrochemical Capacitors II, F. M. Delvick, D. Ingersoll, X. Andriev, and K. Naoi, Editors, PV 96-25, p The Electrochemical Society Proceedings Series, Pennington, NJ A. Frichet, P. Gimenez, and M. Keddam, Electrochim. Acta, 38, M. Guo, P. Diao, and R. Tong, J. Chin. Chem. Soc. (Taipei), 47, G. L. Johnson, Solid State Tesla Coil, Chap available at gjohnson/ 23. B. E. Conway, Electrochemical Supercapacitors: Scientific, Fundamentals and Technological Applications, pp. 377, Plenum, New York K. S. Cole and R. H. Cole, J. Chem. Phys., 9, J. Miller, in Proceedings of the 8 th International Seminar on Double-Layer Capacitors and Similar Energy Storage Devices, Deerfield Beach, FL, Dec 7-9, B. E. Conway, Electrochemical Supercapacitors: Scientific, Fundamentals and Technological Applications, pp. 366, Plenum, New York 999.