Impedance spectroscopy study of a catechol-modified activated carbon electrode as active material in electrochemical capacitor

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Impedance spectroscopy study of a catechol-modi ﬁ ed activated carbon electrode as active material in electrochemical capacitor

C. Cougnon

^a^,^*

, E. Leb egue

^b

, G. Pognon

^b

aLaboratoire MOLTECH Anjou, UMR-CNRS 6200, Universite d'Angers, 2 Boulevard Lavoisier, 49045 Angers, France

bInstitut des Materiaux Jean Rouxel (IMN), Universite de Nantesn CNRS, 2 Rue de la Houssiniere, BP32229, 44322 Nantes Cedex 3, France

h i g h l i g h t s

A catechol-modiﬁed carbon electrode is studied by impedance spectroscopy.

The grafting of molecules increases the time constant of the carbon product.

The modiﬁed carbon is less successful for high rate applications than unmodiﬁed one.

a r t i c l e i n f o

Article history:

Received 20 June 2014 Received in revised form 26 September 2014 Accepted 15 October 2014 Available online 23 October 2014

Keywords:

Electrochemical capacitor Impedance

Activated carbon Diazonium salt Grafting

a b s t r a c t

Modified activated carbon (Norit S-50) electrodes with electrochemical double layer (EDL) capacitance and redox capacitance contributions to the electric charge storage were tested in 1 M H2SO4to quantify the benefit and the limitation of the surface redox reactions on the electrochemical performances of the resulting pseudo-capacitive materials. The electrochemical performances of an electrochemically anodized carbon electrode and a catechol-modified carbon electrode, which make use both EDL capacitance of the porous structure of the carbon and redox capacitance, were compared to the performances obtained for the pristine carbon. Nitrogen gas adsorption measurements have been used for studying the impact of the grafting on the BET surface area, pore size distribution, pore volume and average pore diameter.

The electrochemical behavior of carbon materials was studied by cyclic voltammetry and electrochemical impedance spectroscopy (EIS). The EIS data were discussed by using a complex capacitance model that allows deﬁning the characteristic time constant, the global capacitance and the frequency at which the maximum charge stored is reached. The EIS measurements were achieved at different dc potential values where a redox activity occurs and the evolution of the capacitance and the capacitive relaxation time with the electrode potential are presented. Realistic galvanostatic charge/discharge measurements performed at different current rates corroborate the results obtained by impedance.

1. Introduction

Activated carbons are considered as a material of choice for the preparation of electrochemical capacitors (ECs) due to attractive intrinsic properties such as conductivity, high speciﬁc surface area and a large panel of pore size distribution, ranging from micropores (<2 nm) to mesopores (between 2 and 50 nm)[1e4].

Due to the very high speciﬁc surface of activated carbons, capacitance values comprise between 100 and 300 F g¹ are customarily achieved, that offers potentialities for the electric

charge storage[5,6]. To exceed this value, a faradaic contribution to the charge storage can be added to the purely capacitive process [7,8]. In that case, the electrochemical charge storage can occurs through the presence of heteroatoms in the carbon structure [9e12], or from a thin electroactive organic layer deposited at the surface of the carbon by impregnation or chemical grafting [13e25]. Until now, most of patents and publications related to the use of carbonaceous materials modiﬁed with redox moieties mainly focus on the capacitance gain originating from the faradaic contribution and demonstrate that with selected electroactive molecules, the total capacitance can be doubled[26e28]. However, despite a recent academic and industrial interest, only few studies report on the impact of the grafting on the electrochemical performances of the resulting modiﬁed porous carbons [29,30]. At

*Corresponding author. Tel.:þ33 (0)2 41 73 52 66; fax:þ33 (0)2 41 73 54 05.

E-mail address:charles.cougnon@univ-angers.fr(C. Cougnon).

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Journal of Power Sources

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behavior of these systems and is well-suited for study separately the double-layer capacitance and the contribution of molecules to the charge storage, because these two processes occur at different frequencies[13]. In this connection, the major point of concern of the present study is devoted to quantify better benefits and limi- tations of the grafting of redox molecules on the performances of ECs. In this purpose, a catechol-modified carbon electrode (NS-CA) was obtained by anodic demethylation of dimethoxybenzene molecules attached on the surface of the activated carbon Norit by spontaneous reaction with the 3,4-dimethoxybenzenediazonium salt produced in situ. The grafting of dimethoxybenzene molecules and the electrochemical transformation of dimethoxy benzene-attached units into catechol were demonstrated by X- ray photoelectron spectroscopy (XPS) and the change in specific surface area when going from unmodified to modified carbon was determined by nitrogen gas adsorption measurements. The electrochemical performances of the NS-CA electrode were studied by cyclic voltammetry and EIS, and were compared to the unmodified carbon electrode (NS1). EIS results were confirmed by realistic galvanostatic charge/discharge measurements performed at different current rates. To precisely estimate the contribution of the catechol-attached molecules to the electric charge storage, the behavior of the NS-CA electrode was also compared to an unmodified carbon electrode having undergone the same anodic treatment than for the demethylation (NS2), for being in the closest possible experimental conditions.

2. Experimental

2.1. Material preparation

For the modification of the carbon powder with redox molecules, 400 mg of carbon Norit-S50 (NS) was dispersed in 50 mL of acetonitrile (HPLC grade) by sonication for 30 min and then 1.53 g of 3,4-dimethoxyaniline (0.3 eq. versus carbon) was added with 4 mL of tert-butylnitrite (0.9 eq. versus carbon) for producingin situ the 3,4-dimethoxybenzenediazonium salt. After stirring at 50C for 5 h, the reaction mixture was vacuumfiltered on a Teflonfiltration

room temperature and the operating pressure in the analysis chamber was kept below 10⁹torr. Powders were deposited onto a carbon tape and all spectra were recorded in the CEA (constant analyser energy) mode with an analyser pass energy of 20 eV. Data treatment was performed with CasaXPS software and all spectra were calibrated taking 284.5 eV (graphite like carbon) as a reference binding energy.

2.3. Preparation of working electrodes

Working electrodes were prepared by mixing the active material (NS or NS-DMB) with polytetraﬂuoroethylene (PTFE, 60 wt%

dispersion in water) used as binder and carbon black (superior graphite) used as conducting additive with a ratio of 75:10:15 (wt;

wt; wt) in a small volume of ethanol until a homogeneous carbon paste was obtained. The carbon paste was spread to obtain a thin ﬁlm which was dried at 80C for 1 h. A sample of some milligrams was pressed for 60 s at 1 MPa between two stainless steel grids (80 mesh, 0.127 mm, Alfa Aesar) used as current collector.

Prior to use, the working electrode based on the NS-DMB active material was electrochemically oxidized in 1 M H₂SO₄ by cyclic voltammetry, in order to restore the well-known redox activity of the catechol groups by ether cleavage of the dimethoxybenzene- attached molecules (Scheme 2) [23,31]. In addition, in order to compare the behaviors of unmodiﬁed and modiﬁed carbon electrodes, a pristine carbon Norit electrode (NS1) undergoes the same anodic treatment than for convert NS-DMB into NS-CA, except that no molecules are attached. The resultant anodized carbon electrode (NS2) serves as blank electrode for precisely estimate the impact of the attached molecules onto the performances of the NS-CA electrode.

2.4. Electrochemical measurements

Electrochemical measurements were achieved at room temperature in an aqueous sulfuric acid (1 M) electrolyte with a three- electrode cell composed of a working electrode in conjunction with a pristine carbon auxiliary electrode (prepared as mentioned in the

Scheme 1.Preparation of the carbonedimethoxybenzene composite.

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Section 2.3) and an Ag/AgCl system as reference electrode. A potentiostatjgalvanostat model VSP (from Bio-Logic) monitored by ECLab software was used. For the EIS study, the measurements were conducted at different dc potential values mentioned in the text with an ac potential amplitude of 5 mV and a frequency range of 100 kHze1 mHz. Galvanostatic charge/discharge measurements were conducted in 1 M H₂SO₄ from0.1 V to 0.6 V at different current rates comprise between 0.1 A g¹and 10 A g¹.

3. Results and discussion

3.1. Chemical and physical characterizations

In this work, the activated carbon Norit S50 was chemically modified by reaction with the dimethoxybenzenediazonium saltin situgenerated and the resultant carbon modified electrode was further electrochemically oxidized in 1 M H₂SO₄, in order to restore the well-known redox activity of catechol groups by ether cleavage of the dimethoxybenzene-attached molecules (see section2.3). The formation of the dimethoxybenzeneecarbon composite and the electrochemical transformation of dimethoxybenzene-attached units into catechol were confirmed by XPS analysis (Fig. 1).

Fig. 1(a) shows the XPS spectra of the C 1s core level for the NS-DMB product and the pristine activated carbon. In comparison with the C 1s XPS spectrum obtained with the unmodified carbon Norit, a broad shoulder emerges at 286 eV with the modified carbon powder beside the well-known photoelectron peak at 284.5 eV, which is due to sp2 CeC bonds in graphite-like carbon. From XPS data reported in standard literatures, this change in the C 1s core energy level give evidence of methyl ether groups after chemical modification[32,33]. Prior to use, the dimethoxybenzene-attached molecules are demethylated by electrochemical oxidation in acidic media for restoring the well-known redox properties of catechol units before being studied in the same medium. After a series of 20 CVs recorded in 1 M H2SO4at 10 mV s¹from0.1 V to 1.1 V vs.

AgjAgCl (Fig. 1(b)), the cyclic voltammetric response of the modi- ﬁed electrode stabilizes and shows a current envelope characteristic of a catechol-modiﬁed carbon electrode[30].

In spite of the complexity of the CVs obtained, the ﬁrst CV recorded shows an irreversible anodic shoulder at 1 V, which can be attributed to the demethylation step, associated with the appear- ance of a new reversible system located at 0.4 V, which can be attributed to the catechol response, in good agreement with the ether cleavage of the dimethoxybenzene-attached molecules[13].

To corroborate that dealkylated products are obtained after oxidation, a modiﬁed gold substrate was used for monitor the electrochemical conversion of dimethoxybenzene-attached molecules into catechol by XPS (Fig. 1(c)). The gold electrode was

obtained by physical vapor deposition of an adhesion layer (about 5 nm) of chromium on a glass support, followed by a 100 nm layer of gold. After modiﬁcation by electrochemical reduction of a 2 mM 3,4-dimethoxyaniline solution in acetonitrile þ0.1 M Bu₄NPF₆ containing 9 equivalents of tert-butylnitrite, XPS spectra of C 1s and O 1s core levels were recorded before and after ether cleavage by cyclic voltammetry in 0.1 M H₂SO₄.

Scheme 2.Preparation of NS-CA and NS2 electrodes by electrochemical oxidation of NS-DMB and NS1 electrodes.

Fig. 1.(a) XPS spectra of C 1s core level for NS1 and NS-DMB. (b) Thefivefirst (dashed line) and the twentieth (solid line) CVs recorded at 10 mV s¹in 1 M H2SO4on a dimethoxybenzene-modified carbon electrode. The current was normalized with respect to the mass of active material (without PTFE). (c) XPS spectra of C 1s and O 1s core levels for a dimethoxybenzene-modified gold substrate before and after electrochemical deprotection.

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of dimethoxybenzene-attached molecules into catechol.

In order to investigate the change in texture along with the chemical modiﬁcation, Fig. 2 shows the adsorptionedesorption isotherms of nitrogen at 77 K for pristine carbon Norit (NS1) and carbon Norit modiﬁed with dimethoxybenzene groups (NS-DMB).

Both samples are characterized by type I and type IV isotherms for low and high relative pressure (P/P0), respectively. Each isotherm shows a rapid increase in the adsorbed volume of gas nitrogen at low relative pressure and a distinct hysteresis loop which is indicative of microporous adsorbents, while a slightly tilted plateau in the intermediate and highP/P₀values can be attributed to the progressive adsorption of gas nitrogen in the mesoporous structure of the carbon. When going from pristine carbon to carbon modiﬁed by molecule attachment, a dramatic loss in the adsorbed volume is obtained at low relative pressure and the proﬁle of the hysteresis loop change, implying that the volume of gas nitrogen irreversibly condensed in the porosity increase. Note that the sloped plateau observed on the adsorption and desorption branches of the isotherm for the pristine carbon becomes more horizontal upon grafting, as it was previously observed with Black Pearl carbon grafted with catechol molecules[30].

For better understanding the effect of the molecule attachment on the texture of the Norit carbon, isotherms were further analyzed by determining the pore size distribution (Fig. 3) as well as the cumulated surface (inset inFig. 3). As regards the pore size distribution,Fig. 3shows that the pristine carbon Norit presents two types of pores: micropores with diameter between 1 and 2 nm and small mesopores between 2 and 4 nm. Following the attachment of dimethoxybenzene molecules, an important loss of the surface of the micropores (<2 nm) and of the small mesopores (<4 nm) is observed. The BET speciﬁc surface area is drastically reduced by

72%, from 1231 to 341 m²g¹, the pore volume decreases by 70%, from 0.647 to 0.194 cm³ g¹, while the average pore diameter slightly increases by 0.05 nm, from 1.22 to 1.27 nm. Such results are an indication that the grafting of dimethoxybenzene molecules on carbon mainly affects the microposity, in good agreement with the remarkable drop of the adsorbed volume in theﬁrst part of the nitrogen adsorption isotherm. Indeed, a fraction of the ultra- microporosity remains inaccessible by the molecules, and the accumulation of molecules at the entrance of such ultramicropores immediately block their surface, while for the mesopores, a progressive coverage of the inner pore surface is expected to give a more progressive blocking of their surface. Such “constriction” phenomenon allows to explain that the grafting of molecules causes a signiﬁcant drop of both the pore surface and the pore volume, while the average pore diameter slightly increase in the same time. These results are in good agreement with previous studies reported by Belanger et al., in which the authors examine in detail the effect of the grafting of different amount of anthraqui- none and catechol molecules on the pore size distribution of the Black Pearl carbon[29,30].

3.2. Cyclic voltammetry

Fig. 4shows typical CVs recorded in 1 M H₂SO₄with pristine activated carbon Norit electrode (NS1) and catechol-modiﬁed carbon Norit electrode (NS-CA), compared to the response of an un- modiﬁed carbon Norit electrode previously cyclized in 1 M H₂SO₄at 10 mV s¹from0.1e1.1 V (NS2), for being in the closest possible experimental conditions than for NS-CA (see Section2.3), except that no molecules are attached.

At relative low scan rate, the CV recorded on NS1 shows a nearly rectangular shape over the entire potential domain where no electrochemical decomposition of the electrolyte occurs, which is characteristic of a nearly pure capacitive behavior (i.e., the current intensity remains constant over the entire potential windows in which the charge is accumulated). When NS2 serves as working electrode, the CV retains a quasi-rectangular shape, whilst the current intensity is slightly increased over the entire potential domain scanned, compared to the currentepotential curve obtained for the non-oxidized pristine carbon electrode (NS1). In particular, the CV recorded on the electrochemically oxidized carbon electrode reveals a weak redox system centered at 0.37 V that can be assigned to the presence of oxygenated surface functional groups as quinone, phenolic or carbonyl oxygen, created during the anodic treatment[35].

Fig. 2.Adsorptionedesorption isotherms of nitrogen at 77 K for unmodiﬁed (dotted line) and dimethoxybenzene-modiﬁed carbons (solid line).

Fig. 3.Pore size distribution of unmodiﬁed (dotted line) and dimethoxybenzene- modiﬁed carbons (solid line). The inset shows the cumulated surface area vs. pore diameter.

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For the carbon electrode grafted with electroactive molecules, the CV is characterized by an intense reversible electrochemical system centered at 0.38 V, accompanied to a retarded current when the potential sweep is reversed. It is of interest to note the close proximity in potential of the electrochemical systems obtained for NS2 and NS-CA, suggesting that the oxygenated surface groups generated just by electrochemical oxidation resemble to the catechol group and can be probably associated with quinone/hydro- quinone structures.

FromFig. 4, it is clear that both the electrochemical and chemical activations are efﬁcient for enhanced the capacitance by addition of a faradaic contribution. For NS2, the slight increase in current over the entire potential window scanned demonstrates that the oxygenated surface groups produce a pseudo-capacitive response, while electroactive molecules attached are responsible to a battery-like behavior, producing a nearly constant potential charge process where the redox reaction occurs. The global speciﬁc capacitance values, determined by integrating the area under the CVs presented inFig. 4, are 120 F g¹for NS1, 140 F g¹for NS2 and 190 F g¹for NS-CA. When an activated carbon electrode is sub- jected to anodic treatment, previous works demonstrate that a change in the carbon porosity and an increase in the concentration of surface groups are responsible to the increase in capacitance [36e38], probably due to an improved wettability of the carbon network that increases the pores accessibility and favors the ions adsorption processes. When the carbon is grafted with redox molecules, an additional capacitance gain is obtained over a narrow potential window where the redox reaction occurs and a charge transportation resistance is responsible to the distorting shape of the CV. However, the enhanced global capacitance obtained with NS-CA proves that the faradaic contribution to the electric charge storage is coupled to the non-faradaic double-layer capacitance.

3.3. Electrochemical impedance spectroscopy 3.3.1. Nyquist plots

Fig. 5presents Nyquist plots for NS1, NS2 and NS-CA over the complete frequency range investigated, while the inset ofFig. 5is an enhancement of the high frequency parts of the spectra. EIS measurements shown atFig. 5were performed in 1 M H₂SO₄at 0 V vs. AgjAgCl between 100 kHz and 1 mHz, with an ac amplitude voltage of 5 mHz.

The Nyquist plots show three distinct regions: a vertical tail at low frequency, a semi-circle at high frequency and a not well expressed linear variation of the impedance in the middle frequency range. In the very high frequency domain, ions do not have the time to penetrate inside pores and only the external surface can be sensed. On the contrary, at very low frequencies, complete penetration of ions inside the porous structure of the activated carbon occurs, because the ac penetration length of ions becomes equal to the average pore length. In that case, charge saturation dominates and the electrode behaves as an ideally polarizable porous interface, yielding a vertical line in the Nyquist representation. In the intermediate frequency range, the resistance and capacitance are frequency dependent due to incomplete penetration of the electrolyte inside the porous structure. Between intermediate and low frequency domains, the impedance response shows a characteristic frequency corresponding to the low- frequency knee observed in the Nyquist plots. This characteristic frequency separates two different behaviors in term of ac signal penetration length and corresponds to the frequency at which the system passes from a resistive behavior to a purely capacitive one. It is of interest to note that the middle-frequency branch observed prior that the capacitive behavior prevails, signiﬁcantly change when going from unmodiﬁed carbon to grafted carbon (this point will be discussed in detail below).

With ECs based on activated carbons, high-frequency semi-cir- cles are commonly observed [39,40]. This semi-circle shifts the capacitive charge process toward the higher resistance and limits the response time of the ECs, especially for fast charge/discharge rates. So, efforts were made for reducing its impact on the global resistance of the cell, but the reasons why the high-frequency semi- circle is formed remains controverted. Different explanations were proposed in the literature in relationship with the interfacial electronic resistance [41e44], the porous structure of activated carbons [39,40]or the faradaic charge transfer associated to the adsorption of the electrolytes at the solidjliquid interface[45].

As regards the high-frequency behavior of the carbon electrodes tested, Nyquist plots demonstrate that the diameter of the semi- circle change with the nature of the treatment. When the carbon electrode is just oxidized in 1 M H2SO4(NS2), the semi-circle becomes smaller, compared to the pristine carbon (NS1), while it becomes larger after attachment of molecules (NS-CA). The smaller high-frequency semi-circle for NS2 implies that the anodic treatment in H2SO4facilitates efficient electrolyte ion diffusion inside the porous structure of the carbon. The reduced RC loop for NS2 Fig. 5.Nyquist plots obtained at 0 V in 1 M H2SO4for the unmodified carbon electrode (NS1), the electrochemically oxidized carbon electrode (NS2) and the catechol- modified carbon electrode (NS-CA). The inset shows the magnification of the high- frequency region of the impedance plots.

Fig. 4.CVs recorded at 2 mV s¹in 1 M H2SO4onto unmodiﬁed carbon electrode (NS1), electrochemically oxidized carbon electrode (NS2) and catechol-modiﬁed carbon electrode (NS-CA). The current was normalized with respect to the mass of active material (without PTFE).

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for ECs, because it allows preserving a good capacitance value under a high-rate of operation, but the speciﬁc energy density obtained remains insufﬁcient to be effectively used into high power applications.

3.3.2. Complex capacitance plots

The electric charge is ideally stored in a capacitance, but series resistance and frequency dispersion of the capacitance are always observed with supercapacitors and the low frequency capacitance is shifted toward the higher resistance values.

For taking account the deviation from the ideal behavior of a pure capacitor, the impedance of the whole system can be deﬁned by using a capacitanceC(u) that is frequency dependent[46,47]:

Z u

¼ ðjuCðuÞÞ¹

Because the complex impedance for non-ideal supercapacitors contains a real part,C(u) can be written in the complex form as follow:

C u

¼ ju Z⁰ u

þjZ⁰⁰ u1

¼C⁰ u

jC⁰⁰ u

whereC⁰(u^{) and}^C⁰⁰⁽u) represent the real part and the imaginary part ofC(u). In this complex capacitance modeling of impedance data, the behavior of the supercapacitor is considered as basically capacitive and the variations ofC(u) over a wide frequency range can be extracted from the impedance data as follow:

C u

¼ Z⁰⁰ u

ujZðuÞj²j Z⁰ðuÞ ujZðuÞj²

At very low frequencies, where the imaginary part of the impedance dominates, C⁰(u) tends to the capacitance value extracted from the cyclic voltammetry or current charge/discharge curves. On the contrary, in the high-frequencies domain, Z⁰(u⁾ dominates and the imaginary part of the impedance becomes negligible, because only the electrochemical processes occurring at the exterior surface of the porous carbon can be sensed. So, at these very high frequencies, all the energy received by the system dissipates in ohmic components. These losses in energy are described by the imaginary part of the capacitanceC⁰⁰(u), where the real part of the impedanceZ⁰(u^{) appears.}

Fig. 6presents an enhancement of the middle frequency part of Z⁰(u^{) and} ^Z⁰⁰⁽u) vs. frequency plots for the pristine carbon Norit electrode, in conjunction with the Bode-phase plot that gives the relative contributions of the real and imaginary parts of the impedance. Whenq¼ 45, the two plots cross at a characteristic frequency f0where Z⁰(u⁾¼Z⁰⁰(u^{) and} ^C⁰⁽u⁾¼C⁰⁰(u). So, the frequency at this point is commonly used as a factor of merit to compare the performances of supercapacitors, since a high value of f0reﬂects a high rate cyclability [48]. This remarkable frequency corresponds to a relaxation time tR ¼1/f0 at which the whole

system change from a resistive to a capacitive behavior as the frequency of the alternative input voltage signal decreases. Atf0, the system is as much capacitive as resistive and a maximum loss in energy by ohmic dissipation corresponds (i.e., maximum value of C⁰⁰(u)). In the other word,t^Rrepresents the minimum time needed to efﬁciently discharge all the energy accumulated in the device.

The inset ofFig. 6shows a zoom of the frequency domain where the crossing of theZ⁰(u^{) and}^Z⁰⁰⁽u) vs. frequency plots appears for the three different electrodes tested. When going from unmodiﬁed carbon to carbon Norit modiﬁed with redox molecules, the characteristic frequencyf₀becomes lower, while it is slightly shifted towards the higher frequencies when the carbon electrode is just electrochemically anodized in H2SO4. This opposite displacement of f₀ as the activation of the carbon is achieved chemically or electrochemically, is very instructive about the impact of these treat- ments on the performances of the ECs and relevant information can be drawn from these changes.

Since the capacitance can be extracted from the low frequency value ofC⁰(u) and that the relaxation timetRcan be derived from the frequency value at whichC⁰⁰(u) passes through a maximum, the frequency behavior of the electrodes can be advantageously study by using the complex capacitance modeling of impedance data[47].

Fig. 7presents the changes in the real part of the capacitance (C⁰) vs. frequency for the pristine carbon electrode (NS1) and for the grafted carbon electrode (NS-CA). In both cases,C⁰sharply increases in the middle frequency range and tends to be frequency inde- pendent at very low frequency where the whole porosity of the electrode becomes accessible to the electrolyte. In this low frequency domain, a plateau is obtained either with NS1 or NS-CA, indicating that the maximum of capacitance can be reached in both cases. Nevertheless,Fig. 7shows that huge differences exist in the shapes of theC⁰vs. frequency plots when going from unmodi- ﬁed carbon to grafted carbon, as well as with the potential at which the EIS measurement is achieved.

For NS-CA, the sharp increase inC⁰ occurs with an onset frequency shifted towards the lower frequencies, implying that the resistance of ions inside the porous structure of carbon increases.

This result agrees well with the slightly distorted CV obtained with NS-CA and is well supported by the strong decrease of the BET surface area upon grafting. As regarded the influence of the potential on the low-frequency value of the capacitance, a huge potential dependence of the capacitance is found with NS-CA, Fig. 6.Evolution of the real part and the imaginary part of the impedance vs. frequency for the unmodified carbon electrode (NS1) superimposed to the corresponding Bode-phase plot. The inset shows a zoom in the middle frequency region of the impedance plots for the unmodified carbon electrode (NS1), the electrochemically oxidized carbon electrode (NS2) and the catechol-modified carbon electrode (NS-CA).

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contrary to the unmodiﬁed carbon electrode whose the low- frequency capacitance does not change with the potential (for NS1, only theC⁰vs. frequency curve obtained at 0 V is showed for clarity).

When the impedance measurement is achieved at 0 V, the capacitance values are roughly the same for NS-CA and NS1, but a huge difference is obtained at a potential where the attached- molecules are redox actives. With NS-CA, the low frequencies value ofC⁰increases from 0 to 0.4 V, whilst it decreases from 0.4 to 0.6 V. Furthermore, it appears that the maximum charge stored in redox molecules is reached in a frequency range of 20 mHze5 mHz when the dc potential is within a potential domain where the faradaic charge storage occurs, while the maximum of capacitance is reached below approximately 0.1 Hz for NS1.

On the contrary, according to the results in inset ofFig. 7, the electrochemical anodization of the carbon electrode allows the capacitance occurring with an onset frequency shifted towards the higher frequencies in comparison with NS1, due to enhanced ionic transportation within the porosity, which probably results to a better wettability of the oxygenated carbon structure. We also conducted impedance measurements on NS2 at different potentials and the change in capacitance with the dc potential applied demonstrated that the oxygenated surface groups participate to the pseudo-capacitance.

A more explicit representation of the change in capacitance with the potential is given atFig. 8for the three carbon electrodes tested.

Within a potential domain where no faradaic reaction occurs (i.e., between0.1 and 0.1 V), the specific capacitance of NS-CA is lower than for NS1, implying a loss in the double-layer capacitance during the grafting. At 0 V, the specific capacitance of the pristine activated carbon Norit used in this study is found to be 110 F g¹and 90% of the maximum specific capacitance is reached below 50 mHz. When going from unmodified carbon to carbon Norit grafted with electroactive molecules, the double-layer capacitance decreases by 15%, from 110 to 84 F g¹, due to a dramatic decrease in the BET surface area, and an increase in the ionic resistance allows capacitance to be reached at lower frequencies (90% of the capacitance is reached below 20 mHz). Conversely, with NS2, a slightly higher specific capacitance is obtained over this potential domain, according to the previous discussion related to the cyclic voltammetric study: the specific capacitance is found to be 119 F g¹ and 90% of the maximum capacitance is reached below 50 mHz. On the contrary,

within a potential domain where redox reactions occurs (i.e., between 0.2 and 0.5 V), a sudden increase in capacitance is obtained, especially with NS-CA, which is due to the supplementary charge stored through redox surface reactions.

FromFig. 9, the energy dispersion in the system also changes with the potential at which the EIS measurements are achieved.

Contrarily to the real part of capacitance,C⁰⁰(u) passes through a maximum at a characteristic frequencyf0, due to a dual effect of resistive components which dissipate energy through ohmic loss and capacitive components which store electric energy. Forf>f0, the dispersed energy dramatically increases when approachingf0, because theﬁrst electric charges are stored in a EC where the ohmic behavior dominates and a main part of the energy received by the EC dissipates in resistive components. Conversely, whenf<f0, the capacitive behavior dominates and the dissipated energy through irreversible resistive processes rapidly decreases. According to our previous comments, a relaxation time constanttRcorresponds to the characteristic frequencyf0obtained for the maximum energy dispersion. For NS-CA, a rapid increase of the energy dispersion and a shift of the maximum value ofC⁰⁰towards the lower frequencies are observed from 0 to 0.4 V, followed by a decrease and a shift towards the higher frequencies when the EIS measurements are achieved at a dc potential where the attached molecules are in their oxidized form (from 0.4 to 0.6 V). Note that whatever the dc Fig. 8.Evolution of the speciﬁc capacitance vs. potential extracted from the low frequencies values of the impedance data for NS1, NS2 and NS-CA.

Fig. 9.Imaginary capacitance vs. frequency plots recorded at various potential comprised between 0 V and 0.6 V in 1 M H2SO4onto unmodiﬁed carbon electrode (NS1) and catechol-modiﬁed carbon electrode (NS-CA). The inset shows the evolution of the imaginary capacitance vs. frequency for the electrochemically oxidized carbon electrode (NS2).

Fig. 7.Real part of the capacitance vs. frequency plots recorded at various potential comprised between 0 V and 0.6 V in 1 M H2SO4onto unmodiﬁed carbon electrode (NS1) and catechol-modiﬁed carbon electrode (NS-CA). The inset shows the evolution of the real part of the capacitance vs. frequency for the electrochemically oxidized carbon electrode (NS2).

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potential value, the grafting of molecules makes the dispersed energy and the time constant higher, even when attached- molecules are not electroactive. When the EIS measurements are achieved at dc potentials where grafted molecules are electroactive, changes inC⁰⁰(u) vs. frequency plots are mainly due to the supplementary charge stored in the attached molecules. However, when molecules are not electroactive, the dispersed energy remains slightly shifted towards the lower frequencies, implying that the ionic transportation inside the porous structure of the carbon is hindered by molecules.

For NS2, the evolution of the energy dispersion with the potential follows the same trend, except that no signiﬁcant shift in frequency is observed. The fact that the increase in energy dispersion not come along with a decrease of the characteristic frequency proves that, in our experimental conditions, the supplementary charge stored in the pseudo-capacitance created by electrochemical anodization not affects the high-rate capability of the electrochemical capacitor.

3.3.3. Evolution of the relaxation time constant with the potential Fig. 10resumes the evolution of the relaxation time constanttR

with the dc potential at which the EIS measurement is achieved.

Note that the evolution of the time constant with the potential follows roughly the same proﬁle than that of the low-frequency capacitance vs. potential plot presented at Fig. 8. This is because capacitance changes with potential prevail at f0due to a strong potential dependence of the charge stored in redox moieties. As for the aforementioned capacitance vs. potential plot, two different domains can be distinguished over the entire potential windows investigated, depending that the redox moieties are electroactive or not.

the supplementary charge stored in the electroactive moieties produces an increase in the relaxation time constantt^R^{, making} longer the time needed to reaches the maximum charge stored.

With NS-CA, the huge increase in capacitance associated to the attached electroactive molecules, combined with a hindered ionic transportation within the porous structure of the carbon, produce a huge potential dependence of the time constant, while with NS2, the small increase in capacitance balanced by a decrease in ionic resistance contribute to maintain the time constant at a value close to the one obtained for the pristine carbon Norit. So, the aforementioned results imply that the modiﬁed carbon based on attached electroactive molecules may not sustain high cycling rates as unmodiﬁed one.

In order to assess the impact of a change in the relaxation time constant on the high-rate capability, realistic galvanostatic charge/

discharge measurements were performed at different current rates.

Charge/discharge experiments were conducted in 1 M H2SO4at 0.1 A g¹, 1 A g¹and 10 A g¹with NS-CA, NS1 and NS2 as working electrodes, in conjunction with a pristine carbon auxiliary electrode and the observed constant current charge/discharge behaviors are plotted in a series of graphs inFig. 11(a)e(c).Fig. 11(a) shows the voltage responses as a function of time for a low current rate of 0.1 A g¹. At such low current rate, NS-CA shows an important increase in the global speciﬁc capacitance, in accordance with an increase in chargeedischarge time compared to NS1 and NS2.

Compared to NS1, the capacitance gains extracted from the charge/

discharge curves are 159% for NS-CA and 45% for NS2. When the current rate of charge/discharge increases, the capacitance gain of NS-CA decreases, while that of NS2 remains unchanged (Fig. 11(b) and (c)). For instance, when the current rate passes from 0.1 A g¹to 10 A g¹, the capacitance gain with NS-CA decreases from 159 % to 79 %, while that obtained with NS2 passes from 45 % to 43 %.

Although the global capacitance observed with NS-CA remains superior to that of NS2 for charge/discharge currents comprised between 0.1 A g¹ to 10 A g¹, the global capacitance of NS-CA decreases clearly along with the current, while the global capacitance of NS2 remains practically unchanged. These results prove Fig. 10.Evolution of the relaxation time constant vs. potential for NS1, NS2 and NS-CA.

Fig. 11.Galvanostatic charge/discharge curves of unmodiﬁed carbon electrode (NS1), electrochemically oxidized carbon electrode (NS2) and catechol-modiﬁed carbon electrode (NS-CA) in 1 M H2SO4at a current of 0.1 A g¹(a), 1 A g¹(b) and 10 A g¹(c). The current was normalized with respect to the mass of active material (without PTFE).

(9)

that NS-CA operates efﬁciently at low charging/discharging current rates, whilst NS2 can operate until 10 A g¹with the same efﬁciency.

4. Conclusion

This paper presents the performances of ECs based on modified activated carbons making use both the double layer capacitance of the high specific surface area of the carbon and the redox capacitance providing from the surface redox reactions implying oxygenated groups created by electrochemical anodization or catechol-attached molecules. The impedimetric response of carbon electrodes was investigated over an extended frequencies domain, ranging from 100 kHz, where the electrodes behave as a resistive component, to 1 mHz, where the systems behave as a pure capacitance. The EIS measurements were achieved at different potential comprised between0.1 V and 0.6 V, where the surface redox reactions occur. The frequency behavior of the whole system was assumed to be mainly capacitive and the impedimetric responses were analyzed by using a complex capacitance model that allows defining the time constant, the global capacitance and the frequency at which the maximum charge stored is reached.

Results shown that the grafting of electroactive molecules is accompanied with a strong potential dependent capacitance, a dramatic decrease in surface BET and an increase in the ionic resistance, making longer the time needed to reaches the maximum charge stored. So, the carbon powder grafted with redox molecules appears no sustainable for high cycling rate applications compared to the pristine carbon. Galvanostatic cycling of supercapacitor cells at different current rates conﬁrm this assumption, showing the decrease of the capacitance gain for the carbon- molecules composite as the charging/discharging current rate increase.

Acknowledgments

This work was supported by the Centre National de la Recherche Scientiﬁque (CNRS-France) and the Region Pays de la Loire through the framework of PERLE 2 project.

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