Size effect in the characterization of microporous activated nanostructured carbon

Size effect in the characterization of microporous activated nanostructured carbon

Microporous and Mesoporous Materials 130 (2010) 21–25 Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepag...

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Microporous and Mesoporous Materials 130 (2010) 21–25

Contents lists available at ScienceDirect

Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso

Size effect in the characterization of microporous activated nanostructured carbon Szymon Łos´ a,*, Laurent Duclaux b, Wojciech Kempin´ski a, Maria Połomska a a b

´ , Poland Institute of Molecular Physics, Polish Academy of Science, ul. Smoluchowskiego 17, 60-179 Poznan Université de Savoie, 73376 Le Bourget du Lac Cedex, France

a r t i c l e

i n f o

Article history: Received 7 July 2009 Received in revised form 30 September 2009 Accepted 10 October 2009 Available online 23 October 2009 Keywords: Nanostructure Size-characterization Electron paramagnetic resonance Raman X-ray diffraction

a b s t r a c t Two kinds of microporous activated nanostructured carbons were studied by X-ray diffraction, Raman spectroscopy, electron paramagnetic resonance (EPR) spectroscopy and electrical conductivity measurement. They have different specific surface areas: 1500 m2/g (AC I) and 2500 m2/g (AC II). From X-ray diffraction analysis the average values of the nanodomain sizes of the AC I and AC II carbon particles are 1.7 nm and 1.5 nm, respectively. The Raman spectra and conductivity measurements have consistently confirmed the gradation of the crystallite sizes. It was observed also that the EPR spectra shapes and their temperature evolution between 300 K and 4 K were depending on the types of carbon sample. Room temperature spectra show dissimilar line-widths DB = 0.5 mT and 1.6 mT for AC I and AC II, respectively. The AC I carbon EPR spectra show: (a) a broadening at the beginning of the cooling process, similar to the EPR behavior of graphite and, subsequently, (b) a quick narrowing below 130 K. For the super-activated carbon (AC II), a monotonic narrowing process is observed on decreasing the temperature. These different behaviors were attributed to the size effect of graphenes in both activated carbons. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction Recently, microporous activated carbon (AC) turned out to be of interest for many researchers due to its potential of technical applications for gas adsorption [1,2], pollutant removal [3–5] and electrochemical double layer capacitors [6,7]. A great attention was focused on super AC of which a specific surface area (SSA) as high as 3000 m2/g, was calculated by the Brunauer, Emmett, and Teller (BET) method, yielding more than 5% of hydrogen adsorption at liquid nitrogen temperature [1]. However, the theoretically calculated SSA for a graphene plane is only 2600 m2/g, proving the difficulties to obtain real values of surface of nanoporous materials using only the BET method. Currently, microporous AC materials appear to be of interest due to their structure characterized by pore sizes and carbon particles sizes which are limited to nanometric dimensions. In activated carbon fibers (ACFs), the transition from conducting to insulating states was observed [8] and a new hexatic phase (with intermediate ordering between liquid and solid states) for the adsorbate in the porous structure [9] was detected. The bulk water properties are no more observed for water molecules trapped inside nanotubes of which the diameter sizes are below 5 nm [10]. Moreover, single graphite layers [11] or graphitic nanoparticles in ACF can behave as quantum dots [12]. The quantum dots matrix was proposed for modeling an ACF system in which the potential barriers between the nanographitic particles are not * Corresponding author. Fax: +48 618 684 524. E-mail address: [email protected] (S. Łos´). 1387-1811/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.micromeso.2009.10.007

well defined. To investigate the localized states in activated carbons which can define these barriers, the detailed studies of different AC are needed. From the structural analysis viewpoint, AC is a disordered material. Transmission electron microscopy studies [13] have shown that AC is a conglomerate of layered graphite planes with nanometric in-plane dimensions and diverse interlayer distances. The aim of this paper is an attempt to characterize the size effect by different techniques. It is expected that limiting the particles size to nanometric dimensions should lead to many changes in properties compared to an unconfined graphite plane. Indeed, the domains size limitation leads to modification of phonon spectra probed by Raman spectroscopy [14,15] and it should also affect the relaxation processes probed by EPR spectroscopy. Moreover, the boundary carbon atoms at zigzag shaped-edges contribute to the presence of a significant number of localized electrons [16–18]. These electrons can be at the origin of some specific properties in different graphitic carbon materials, as for the activated carbons which contains nanosized particles with open edges [19]. 2. Experimental 2.1. Samples Two kinds of microporous activated carbon samples: AC I and AC II, were studied. The first one (AC I) was prepared from a phenolic resin precursor by a typical steam activation. The second one (AC II), namely ‘‘Maxsorb”, was super-activated from a mixture of

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petroleum coke and an excess amount of potassium hydroxide [20]. The SSA of the AC I and AC II samples, determined by nitrogen adsorption (BET method) are reaching 1500 m2/g and 2500 m2/g, respectively [21]. In order to eliminate the oxygen surface groups generated by the activation process [20,21], the activated carbon samples (AC I and AC II) were annealed in a N2/H2 gas flow at 973 K. Activated carbons (typically 5 g) were heated (50 K/min) under a N2 atmosphere (flow: 280 mL/min) until they have reached 973 K and thereafter annealed at the latter temperature for 2 h under a reducing gas flow (N2/H2 mixture flow: 40 mL/ min) [21]. The reducing treatment operated with the aim of removing completely the oxygenated surface functionalities was successful, as the element analyses indicate the presence of 0.7 at.% and 0.4 at.% of oxygen in the treated AC I and AC II, respectively.

20000

15000

Intensity [a. u.]

22

002 10000

10. 11.

5000

AC I AC II 0 10

20

2.2. X-ray diffraction and Raman spectra

2.3. Electrical losses measurements The electrical conduction (electrical losses) vs. electric field frequency have been measured by a Multi-frequency RLC Meter HP 4275A. The AC materials were placed in a cylindrical capacitor of 3 mm diameter, with inner electrode of 1 mm diameter and 9 mm length. The electric field frequency range between 10 kHz and 10 MHz has been chosen. Measurements were carried out at room temperature. 2.4. Electron paramagnetic resonance The AC I and AC II samples were characterized by electron paramagnetic resonance (EPR) spectroscopy. The measurements have been carried out in the temperature range between 4.2 K and 300 K using an X-band spectrometer equipped with a helium cryostat. The samples have been outgassed at 450 K under 3.6  105 mbar vacuum prior to the EPR experiments. Samples (average mass 70 mg) were introduced into EPR silent tubes. 3. Results and discussion 3.1. X-ray diffraction, Raman and conductivity measurements X-ray diffraction [22] and Raman spectroscopy [14,15] are wellknown methods to estimate the crystallite sizes of carbon materials. The in-plane coherence length of the crystallites can be calculated from the X-ray powder diffraction data. The hk. bands (the weak 10. band and the still weaker 11. band) are the most intense reflections observed in the diffractograms of AC I and AC II (Fig. 1). The 002 line is very broad and quasi undetectable because of the very disordered turbostractic arrangements (quasi-two-dimensional arrangement) of the aromatic layers in the activated carbons resulting in uncorrelated graphitic planes along the c-axis. The

40

50

Fig. 1. The X-ray diffraction patterns for AC I and AC II carbon samples. The dots following the hk. symbols, which replace l (usually used in hkl symbols denoting directions in the k-space) are introduced in order to indicate the lack of regular arrangement along the corresponding third axis.

coherence length along the basal plane was estimated from the 10. bands using the Sherrer equation: La ¼ 0:89k=ðD2hcoshÞ where La, in-plane coherence length; k, X-ray wavelength; D(2v), peak width; h, diffraction angle. The calculated values of La are 1.7 and 1.5 nm for the AC I and AC II carbons, respectively. As low differences between the particles dimensions of the two carbon types were deduced from the coherence length calculation, the size of particles were also estimated from the Raman spectra. In the wave number range 800–2000 cm1 (Fig. 2), two characteristic bands are observed: a disordered band (D) close to 1300 cm1 and a graphite band (G) in the vicinity of 1600 cm1. Their intensity ratio can be used to estimate the sizes of the hexagonal arrangements within the particles [23]. The G peak is due to the bond stretching of the sp2 atoms, whereas the D peak originates from the breathing modes of A1g symmetry involving phonons near the K point of the Brillouin zone. This D peak is absent in a perfect graphite structure and becomes active only in the presence of disorder. Its intensity is proportional to the number of ordered rings. The G band is at the position reported in Ref. [15], but the D band is broaden. This suggests an increase in defects density and a considerably large reduction in particles dimensions [14]. As shown by Ferrari et al. [14], the ID/IG ratio for amorphous carbon (non graphitic carbon with La < 2 nm) follows the rule: ID =IG / L2a . Therefore, the characteristic grain sizes for AC I and AC II carbons are

0.008

Amplitude [a.u.]

The samples have been characterized by X-ray (Ka1 Molybdenum radiation, k = 0.70926 Å) diffraction in the transmission mode in sealed glass capillaries (1 mm in diameter) using an INEL diffractometer equipped with a curve detector (INEL CPS 120) and a 2 kW X-ray generator (U = 40 kV, I = 20 mA). The Raman spectra of the AC I and AC II samples were recorded by the Bruker IFS66FRA106 spectrometer. The samples were excited with a 1064 nm diode-pumped Nd:YAG laser of output power 50 mW. Raman studies were carried out at 180° geometry and recorded in the 100–3500 cm1 frequency range, collected with up to 10,000 scans and a 4 cm1 spectral resolution. For the 800– 2000 cm1 spectra range, the size of the nanoparticles can be estimated using an empirical formula [14,15].

30

2 θ [Deg]

AC I AC II

0.006

0.004

0.002

0.000 800

1000

1200

1400

1600

1800

2000

-1

K [cm ] Fig. 2. Raman spectra in the range between 800 cm1 and 2000 cm1 for AC I and AC II samples, recorded at room temperature.

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3.06 nm and 2.93 nm, respectively. The values of the grains sizes estimated from the Raman spectra are almost two times larger than their dimensions derived from the X-ray diffraction. These values are over-estimated due to the empirical origin of this estimation based on Raman spectra. However, the same ratio between the particles sizes for the two types of carbon samples is obtained by both methods. The graphene particles sizes of AC I are larger than those of AC II. In order to confirm the different particle size distribution between samples, the electrical conductance measurements (electrical losses) vs. electric field frequency have been performed. Each AC gives a significantly different response to the alternate electric field (Fig. 3.). For low frequencies (10 kHz and 20 kHz), the capacitors losses are beyond the capability of the instrument. For a higher rate, in every sample a minimum is observed at a different frequency. Further increase in frequency results in a slight rise in conductance. On the assumption that the electron mean free path is longer than the particles diameters, the electrons can freely

10

ACI ACII

8

ε'' [a. u.]

6

23

move along a graphene plane until they are scattered by a boundary wall [22] or a potential wall [11] between two grains. In the low frequency range m of the alternate electric field, a huge current loss occurs, as the time s of motion of an electron along the electric field direction is long (m  1/s). The losses are diminished by shortening this time (s). A minimum is obtained, whereas the applied electric field is able to change the electron direction just before the scattering process. Assuming the same electron velocity for both materials, the minima are reached at different frequencies as the average size of a nanocarbon unit for AC I is larger than that for AC II samples. The combined experiments: X-ray diffraction, Raman spectra and the electrical conductance investigation, have confirmed the nanoparticles size gradation between AC I and AC II samples. However, from X-ray diffraction characterization, the crystallites sizes were found lower by a factor of two than those calculated from Raman spectra. The disagreement between the results obtained by these two methods is weak taking into consideration the empirical origin of the relation (1) used for the Raman characterization. The crystallites dimensions obtained from X-ray diffractograms (1.7 nm and 1.5 nm mean in-plane sizes, for AC I and AC II samples, respectively) are more realistic, though the differences in average dimensions are small in comparison to the experimental accuracy. The disagreement between the crystallites size investigated by the three methods emphasizes the difficulties to obtain experimentally the absolute dimension value of nanocarbon units in activated carbon. The three different experimental methods have therefore consistently indicated larger crystallite sizes for AC I in comparison to AC II.

4

3.2. EPR 2

0 4

10

5

6

10

7

10

10

ν [Hz] Fig. 3. Dielectric loss factor of a cylindrical capacitor for AC I and AC II samples as a function of the measured electric field frequency.

The EPR spectra of every AC material reveals an asymmetric line centered on the spectral splitting factor value g = 2.0028 ± 0.0002. Its shape depends on the microwave power. At low-temperature and high power, the signal saturates. For graphite-like carbon materials the EPR signal originates from the delocalized p conducting electrons at the surface [24]. A scattering process (between electrons and phonons or electrons and particles boundary) determines the line shape.

5000

1500

experimental points Curie law

4500

Double Integral [a.u.]

4000

Amplitude [a. u.]

1000

500

3500 3000 2500 2000 1500 1000 0

50

100

150

200

250

300

T [K]

0 experimental points fit narrow component broad component very broad component

-500

-1000

-1500 31 8

32 1

32 4

32 7

33 0

33 3

B [mT] Fig. 4. The convolution and fitting result of typical EPR spectra recorded at 150 K for AC II. Insert shows the double integral of the total EPR spectrum vs. temperature and its relation to the Curie law.

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As was previously reported [25,26], the spectra can be fitted by three Lorentzian components. For example, the deconvolution of the EPR spectra for AC II at 150 K is revealed on Fig. 4. Each line has a different width and can be described as resulting from different paramagnetic electron states of the carbon particle. The very broad component can be ascribed to the paramagnetic centers created by atoms and molecules interacting with the graphitic surface. These hetero-atoms are the oxygenated surface groups which have mostly been removed after H2/N2 thermal treatment at 973 K so that the contribution of the very broad component to the paramagnetic susceptibility is negligible. Applying the thermal treatment described in reference [21], the concentration of the paramagnetic centers in the sample lowers significantly [25], which results in the vanishing of this very broad signal component. A high temperature treatment, which reduces the functional groups contamination, has a significant effect on the decrease in the line-width [25]. At room temperature, the EPR spectra of AC I and AC II reveal line-widths of 0.6 mT and 1.6 mT, respectively. During the cooling process, the line-width of the AC II EPR signal shows a monotonic decrease. The solid lines in Fig. 5 represent the quadratic dependences for the narrow and the broad components of the EPR signal from AC II. The line-width of the AC I sample shows a quite different behavior. This line broadens along as lowering the temperature from 300 K to 150 K (line-width increased from 0.5 mT to 3.6 mT). Below 150 K, a sudden narrowing of the EPR line of AC I is observed. The line-width reaches a value comparable to that measured for AC II well below 100 K. The line-width dependence on temperature results from a complex evolution of the spectra. Two other kinds of paramagnetic centers should be taken into careful consideration. They are revealed by broad and narrow components. Such centers have been brought out in a wide class of carbon materials, wherein small particles can be found: carbon black samples [27], ACF [26], graphene planes developed from nanodiamonds [22] and also AC [25]. For both kinds of paramagnetic centers located at the graphene planes the g-value is practically equal. Nevertheless, they are distinguishable by their corresponding line-widths. As the ratio of the line-widths is close to ten, the relaxation time of the localized paramagnetic centers is significantly longer than that of the delocalized ones due to the coupling strength. The presence of these two different centers was recently observed by applying the EPR pulse technique to ACF [28] where the observed magnetic recovery shows a com-

4.0

Broad Component of AC I Narrow Component of AC I Broad Component of AC II Narrow Component of AC II

3.5 3.0

ΔB [mT]

2.5 2.0 1.5 1.0 0.5 0.0 0

50

100

150

200

250

300

T [K] Fig. 5. Spectra components widths as a function of temperature T for AC I and AC II samples. A monotonic narrowing of the width for AC II, proportional to the square of temperature, is marked with the solid lines.

plex relaxation process in which a slow relaxation is seen on the background of a fast process. From the point of view of the structure, the AC should be treated as a highly defected material despite some similarities to graphite. The X-ray investigation shows a some correlation between the in-plane carbon atoms which explains the observation of resonance signals emerging from the delocalized p electrons. Taking into account the line-width, the broad component observed in both kinds of samples can be attributed to this type of paramagnetic center. For example, in thin HOPG (Highly Oriented Pyrolitic Graphite), where the skin depth is negligible, a single Lorentzian line is observed with a g-value of 2.0031 and a line-width of 0.5 mT at room temperature [29]. Such a width value results from a relaxation mechanism already observed in many carbon materials [24]. Next kind of paramagnetic centers to which the narrow component of EPR spectra is assigned, can be localized at the edge of a graphene layer. They are related to the states of polarized electrons in the vicinity of the boundaries of zigzag shape [16–18]. The presence of boundary states localized on inshore atoms was proposed for the first time on the basis of theoretical calculations and then supported by experimental results from scanning tunneling microscope studies [30–32]. The narrow component ascribed to these states is caused by a weak coupling between local phonons and in-plane phonons [33] giving the longest relaxation time of this third observed component. The proportion of these boundary states, compared to the other ones, is higher in nanostructured carbons. A higher ratio of boundary atoms number with respect to the total number of atoms is observed in materials with finer structures. From EPR spectra recorded at 4.8 K, 8% of the whole amount of the observed spins occupy boundary states in the AC I carbon samples. Taking into account the average in-plane distance between carbon atoms ðdC—C ¼ 0:141 nmÞ in a graphene) and the particle dimension of AC I (i.e., 1.7 nm), the ratio of the boundary atoms to the total of atoms is close to 43 at.% This value is much higher than that corresponding to the observed amount of localized states in the EPR spectra (8%). However, only every fifth boundary atom (or less) can supposedly gives an edge state [17]. The analysis of the intensity of the narrowest component for the AC II sample has led to similar value of the spin amount that might be localized at edge states. A tiny density of localized states was confirmed by the lack of the spin echo in the EPR pulse spectroscopy. The total double integral of spectra did not fulfill the Curie law due to the influence of the Pauli paramagnetism. The deconvolution of the whole EPR signal has not enabled us to separate the effects of the Pauli and the Langevin paramagnetism. In Fig. 5, the line-width analysis of broad and narrow components for AC II samples shows a monotonic quadratic narrowing as a function of decreasing temperature. The observed line-width vs. temperature relations for AC I samples are quite different. The width of the broad and narrow components behaves similar to that of the graphite monocrystal EPR signal [24] in the temperature range from 300 K to 130 K. Indeed, the HOPG EPR spectra are also broadened on cooling. However, the thermal variations of the spectra for AC I are much stronger here, showing a width ratio close to seven in the range from 130 K to room temperature. As a consequence, EPR spectra were hard to record in a proper way in the temperature of 130 K when spectra of HOPG are well recorded up to 77 K [24]. As reported in Ref. [24], the width of EPR signal can be governed by the scattering of conducting electrons on phonons. Taking into account the analogy between the graphite line and the broad component for AC II, the width of the spectra for AC II can be explained by a metallic relaxation mechanism [34,35]. This mechanism requires the assumption that the spectra widths depend on the electric properties. The resistivity of the metal falls off with decreasing

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temperature. This leads to narrowing of the line-width. Such dependence is observed only for AC II, where the quadratic monotonic narrowing suggests a flipping process [35]. The spectra broadening for AC I vs. decreasing temperature displays a rise in relaxation rate due to the growing number of the scattered electrons. As shown by the EPR pulse technique, the exited electron interacts with the carbon lattice causing its deformation. This can be described by two-level tunneling states TLS [28]. Such deformations could be localized at the edge of the lattice or are able to propagate through the lattice. At high temperatures, the lattice deformation leads to two characteristic Debye temperatures responsible for longitudinal (TL = 2480 K) and transverse (TT = 180.5 K) modes of vibrations [22]. Lowering the temperature results in a change of the phonons spectra. In particular, the transverse vibrations are strongly suppressed due to the low value of TT. In the AC case, this attenuation is reinforced by the size effect of small particles imposing a long wavelength limit. Moreover, the exclusion of the transverse mode is expected for a carbon crystallite size lower than a critical dimension. Thus, the differences in the behavior of EPR spectra could be brought about by the diversity of the particles lengths. The monotonic narrowing of the EPR signal for AC II presents an evidence for a size unit smaller than the critical one. For AC I, the narrowing process on cooling can be observed well below 130 K because the spontaneous excitation of the transverse mode is excluded by temperature. The temperature is not able to exclude the transverse mode for unlimited graphite sheet, but results in exclusion of transverse phonon mode for AC I. The smaller particles cause the entire exclusion transverse phonon mode like for AC II whereas for the larger particles of AC I, the narrowing process on cooling can be observed well below 130 K because the spontaneous excitation of the transverse mode is excluded by temperature. 4. Conclusions Two different AC samples were characterized from the point of view of their in-plane average sizes of the graphene planes within the basic structural units of ACs (crystallites made of the stacking of a few aromatic layers). Whereas the graphene sizes obtained from the empirical Raman method are charged by larger errors, the average in-plane size units obtained from the hk. X-ray diffraction line-widths are 1.7 nm and 1.5 nm for AC I and AC II samples, respectively. Although, the estimated particle sizes are quite similar, larger graphene dimensions were found for AC I than for AC II in agreement with the results obtained from three independent experiments: X-ray powder diffraction, Raman spectroscopy, and conductivity measurements. The low-temperature EPR signals of the two different AC samples have revealed an unexpected line-width temperature dependence. As cooling from room temperature to 4.2 K, AC spectra would be expected to broaden as HOPG graphite EPR signal in the same range of temperature. However, the AC I sample spectra showed such a behavior only at the beginning of the cooling process. Above 130 K, a quick process of line narrowing occurred subsequently, while for the sample AC II the narrowing was observed in the whole range of decreasing temperature. This narrowing phenomena probed by EPR technique was attributed to the differences in average sizes of the graphene planes of the two AC materials.

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In detailed analysis of the EPR spectra shapes, three different states in which electrons on graphene could be involved were taken into consideration. The very broad component of the EPR spectra was assigned to known states created by hetero-atoms interacting with carbon surface. The broad component was attributed to the delocalized p electrons. The narrow component was interpreted in terms of localized spin states due to the presence of edge electrons for which the content is expected to be inversely proportional to the size of the particle. The double integral of the EPR spectra vs. temperature was not found to fit well with the Curie law and the influence of both Pauli and Langevin paramagnetism was observed. References [1] P. Bénard, R. Chahine, Langmuir 17 (2001) 1950–1955. [2] W.-C. Xu, K. Takahashi, Y. Matsuo, Y. Hattori, M. Kumagai, S. Ishiyama, et al., Int. J. Hydrogen Energy 32 (2007) 2504–2512. [3] J. Guo, A.C. Lua, Mater. Lett. 55 (2002) 334–339. [4] F.-C. Wu, R.-L. Tseng, R.-S. Juang, Separ. Purif. Tech. 47 (2005) 10–19. [5] L. Donnaperna, L. Duclaux, R. Gadiou, M.P. Hirn, C. Merli, L. Pietrelli, J. Colloids Interf. Sci. 339 (2009) 275–284. [6] P. Azaïs, L. Duclaux, P. Florian, D. Massiot, M.-A. Lillo-Rodenas, A. LinaresSolano, et al., J. Power Sources 171 (2007) 1046–1053. [7] C. Schmitt, H. Pröbstle, J. Fricke, J. Non-Cryst. Solids 285 (2001) 277–282. [8] K. Koga, X.C. Zeng, H. Tanaka, Phys. Rev. Lett. 79 (1997) 5262–5265. [9] R. Radhakrishnan, K.E. Gubbins, M. S´liwin´ska-Bartkowiak, J. Chem. Phys. 116 (2002) 1147–1155. [10] N. Naguib, H. Ye, Y. Gogotsi, A.G. Yazicioglu, C.M. Megaridis, M. Yoshimura, Nano Lett. 4 (2004) 2237–2243. [11] J.C. Meyer, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, J. Both, S. Roth, Nature 440 (2007) 60–63. [12] M. Kempin´ski, W. Kempin´ski, J. Kaszyn´ski, M. S´liwin´ska-Bartkowiak, Appl. Phys. Lett. 88 (2006) 143103. [13] J.N. Rouzaud, C. Clinard, Fuel Process. Technol. 78 (2002) 229–235. [14] A.C. Ferrari, J. Robertson, Phys. Rev. B 61 (2000) 14095–14107. [15] P.K. Chu, L. Li, Mater. Chem. Phys. 96 (2006) 253–277. [16] K. Wakabayashi, M. Fujita, H. Asjiki, M. Sigrist, Physica B 280 (2000) 388–389. [17] K. Nakada, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B 54 (1996) 17954–17961. [18] K. Wakabayashi, M. Fujita, H. Ajiki, M. Sigrist, Phys. Rev. B 59 (1999) 8271– 8282. [19] T. Enoki, J. Phys. Chem. Solids 65 (2004) 103–108. [20] T. Otawa, Y. Nojima, T. Miyazaki, Carbon 35 (1997) 1315–1319. [21] P. Azaïs, Recherche des Causes du Vieillissement de Supercondensateurs a Electrolyte Organique à base de carbones actives, University of Orleans France, Ph.D. thesis, 2003. [22] O.E. Andersson, B.L.V. Prasad, H. Sato, T. Enoki, Y. Hishiyama, Y. Kaburagi, et al., Phys. Rev. B 58 (1998) 16387–16395. [23] F. Tuinstra, J.L. Koening, J. Chem. Phys. 53 (1970) 1126–1130. [24] G. Wagoner, Phys. Rev. 118 (1960) 647–653. [25] S. Łos´, M. Letellier, P. Azaïs, L. Duclaux, Chem. Solids 67 (2006) 1182–1185. [26] M. Kempin´ski, W. Kempin´ski, M. S´liwin´ska-Bartkowiak, Rev. Adv. Mater. Sci. 12 (2006) 72–77. [27] C.C. Liu, A.B. Walters, M.A. Vannice, Carbon 33 (1995) 1699–1708. [28] S. Lijewski, M. Wanecka, S.K. Hoffmann, M. Kempin´ski, W. Kempin´ski, M. S´liwin´ska-Bartkowiak, Phys. Rev. B 77 (2008) 014304. [29] J. Stankowski, L. Piekara-Sady, W. Kempin´ski, O. Huminiecki, P.B. Sczaniecki, Fullerene Sci. Technol. 5 (1997) 1203. [30] Z. Klusek, W. Kozłowski, Z. Waqar, S. Datta, J.S. Burnell-Gray, I.V. Makarenko, et al., Appl. Surf. Sci. 252 (2005) 1221–1227. [31] Z. Klusek, Z. Waqar, E.A. Denisov, T.N. Kompaniets, I.V. Makarenko, A.N. Titkov, et al., Appl. Surf. Sci. 161 (2000) 508–514. [32] Y. Niimi, T. Matsui, H. Kambra, K. Tagami, M. Tsukada, H. Fukuyama, Appl. Surf. Sci. 241 (2005) 43–48. [33] M. Igami, M. Fujita, S. Mizuno, Appl. Surf. Sci. 130 (1998) 870–875. [34] R.J. Elliott, Phys. Rev. 96 (1954) 266–279. [35] G. Feher, A.F. Kip, Phys. Rev. 98 (1955) 337–348.