J. Phys. Chem. B 2007, 111, 9031-9035
9031
Increasing Stability of the Fullerenes with the Number of Carbon Atoms: The Experimental Evidence Aaro´ n Rojas,*,† Melchor Martı´nez,† Patricia Amador,‡ and Luis Alfonso Torres† Departamento de Quı´mica del Centro de InVestigacio´ n y de Estudios AVanzados, AVenida Instituto Polite´ cnico Nacional 2508, Me´ xico D.F., C.P. 07360, Me´ xico, and Facultad de Ciencias Quı´micas, Beneme´ rita UniVersidad Auto´ noma de Puebla, AVenida San Claudio y 14 sur, Puebla Pue., C.P. 72570, Mexico ReceiVed: April 10, 2007; In Final Form: May 24, 2007
The values of the molar standard enthalpies of formation, ∆fHοm (C76, cr) ) (2705.6 ( 37.7) kJ‚mol-1, ∆fHοm (C78, cr) ) (2766.5 ( 36.7) kJ‚mol-1, and ∆fHοm (C84, cr) ) (2826.6 ( 42.6) kJ‚mol-1, were determined from the energies of combustion, measured by microcombustion calorimetry on a high-purity sample of the D2 isomer of fullerene C76, as well as on a mixture of the two most abundant constitutional isomers of C78 (C2V-C78 and D3-C78) and C84 (D2-C84, and D2d-C84). These values, combined with the published data on the enthalpies of sublimation of each cluster, lead to the gas-phase enthalpies of formation, ∆fHοm (C76, g) ) (2911.6 ( 37.9) kJ‚mol-1; ∆fHοm (C78, g) ) (2979.3 ( 37.2) kJ‚mol-1, and ∆fHοm (C84, g) ) (3051.6 ( 43.0) kJ‚mol-1, results that were found to compare well with those reported from density functional theory calculations. Values of enthalpies of atomization, strain energies, and the average C-C bond energy were also derived for each fullerene. A decreasing trend in the gas-phase enthalpy of formation and strain energy per carbon atom as the size of the cluster increases is found. This is the first experimental evidence that these fullerenes become more stable as they become larger. The derived experimental average C-C bond energy EC-C ) 461.04 kJ‚mol-1 for fullerenes is close to the average bond energy EC-C ) 462.8 kJ‚mol-1 for polycyclic aromatic hydrocarbons (PAHs).
Introduction It is well-known that during the high-temperature process to produce fullerenes, a larger quantity of C60 and C70 is formed in the carbon soot over other fullerenes. In fact C84, C78, and C761 are solvent-extractable fullerenes2,3 but are obtained in quantities of very few milligrams. This seems to be in conflict with estimations of the stability of these molecules, which have been carried out by theoretical gas-phase enthalpy of formation calculations. The results indicate an increase in stability as the number of carbon atoms increases in the fullerene.4 Nevertheless, these have not been experimentally confirmed for the higher fullerenes, even though experimental data of gas-phase enthalpies of formation are key values. These data are of great importance, both for experimental researchers who are interested in knowing the possibility of producing macroscopic amounts of the fullerenes beyond C60, and for theoreticians who need to validate their methodology for predicting the gas-phase enthalpy of formation of higher fullerenes, given that, regardless the size of the cluster, their computations are based on the available experimental data of gas-phase enthalpy of formation of C60.4 Given this perspective, the experimental measurements of the molar standard combustion energy and subsequent derivation of the standard and gas-phase enthalpies of formation of the higher fullerenes turn out to be essential. However, because these clusters are not available in large quantities with the purity required by conventional calorimetric techniques, it has only been possible to measure the standard energy of combustion * E-mail:
[email protected]. † Centro de Investigacio ´ n y de Estudios Avanzados. ‡ Beneme ´ rita Universidad Auto´noma de Puebla.
and to derive the standard enthalpy of formation of C60 and C70 by combustion calorimetry.5 The logical next step in the thermochemistry of these carbon allotropes is the quantification, by calorimetry, of those themochemical quantities on larger fullerenes, such as C76, C78, and C84. Such research would not be feasible without a reliable microcombustion procedure,6 which has already been tested by measuring the molar standard energy of combustion of C60 and C70 on samples of around 2 mg per experiment. Even on the small mass involved, the accuracy and precision of this technique appears comparable to the conventional ones, resulting in reliable standard enthalpies of combustion and formation. In this work, we have applied this technique to obtain the first experimental measurement of the molar standard energy of combustion and the derivation of the molar standard enthalpies of combustion and formation of purified and wellcharacterized samples of C76, C78, and C84, using less than 2 mg per combustion experiment. Furthermore, these results in combination with the published enthalpies of sublimation8 of these fullerenes permits us to derive the first experimental set of gas-phase enthalpies of formation as well as the enthalpies of atomization, the strain energies, and the average C-C bond energy of these carbon clusters. Experimental Methods Isolation and Purification of C76, C78, and C84. Analysis and isolation of the samples of fullerenes were achieved by HPLC from a commercially available higher fullerene mixture (MER corporation), using Develosil C30-UG-5 analytical and semipreparative columns,9 and a Waters 600 HPLC system equipped with a diode array detector working at 312 nm.
10.1021/jp0727906 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007
9032 J. Phys. Chem. B, Vol. 111, No. 30, 2007
Figure 1. Isomers of the higher fullerenes studied by microcombustion calorimetry. Isomer numbering follows reference 7.
Simultaneously to the chromatographic separation (Figure 2a), the identification of the higher fullerenes was carried out by UV-vis analysis (Figure 2b) following the nomenclature of Manolopoulus.7 The mobile phase utilized in both analytical and semipreparative HPLC was a 63:37 toluene/acetonitrile mixture. In the analytical procedure, the applied volume of the mixture of fullerenes in solution in each injection was 10 µL, and the flow rate of the mobile phase was 1 mL‚min-1, whereas for the semipreparative column, these parameters were 5 mL and 4.7 mL‚min-1, respectively. According to the UV-vis spectra, two fractions were found for the case of C78. The first one corresponds to the C2V(3)-C78 isomer, and the second one is attributed to an isomeric mixture of C2V(2)-C78 and D3-C78, in agreement with respect to the spectra reported by Jinno and co-workers.10 For the sample of C84, a posterior analysis of its spectrum in the region from 500 to 900 nm (see Figure 1 of the Supporting Information) indicated a mixture of the D2(22)-C84 and D2d(23)-C84 isomers. Once each fullerene was isolated, the toluene/acetonitrile mixture was evaporated in a rotary evaporator, followed by drying of the obtained crystals in a stove under a reduced pressure of ∼1 Pa and a temperature of 303.15 K for 48 h. After this, for total elimination of the solvent, the temperature was increased to 433.15 K for an additional period of 12 h. Simultaneously, a reference sample of C60 with a purity of 99.99% (Aldrich) was dissolved in the same toluene/acetonitrile mixture and subjected to the same treatment of drying described for the higher fullerenes. The combustion energy measured
Rojas et al. before and after for this fullerene was 26 069.5 kJ‚mol-1 and 26 065.6 kJ‚mol respectively, suggesting that the drying procedure does not affect the value of the energy of combustion of the cluster. UV-Vis Spectroscopy. Purified samples of the fullerenes C76, C78, and C84 were dissolved in toluene (spectroscopic grade), and the UV-vis measurements of these solutions were carried out with a Varian Cary 4000 spectrometer using a scan rate of 600 nm min-1 and a resolution of 2.0 nm. Figure 1 of the Supporting Information shows the UV-vis spectra of the fullerenes C76, C78, and C84 in the region of 300-900 nm and its respective amplification in the range of 500-900 nm, in excellent agreement with respect to those reported by Kikuchi and co-workers.11 The amplified spectrum of C78 shows the superimposed signals corresponding to the mixture of the isomers C2V(3)-C78, C2V(2)-C78, and D3-C78, in good agreement with the spectra of isolated and well-purified samples of these isomers reported by Kappes and co-workers12 and Diederich and co-workers.2b On the other hand, the amplified UV-vis spectrum of C84 shows the superimposed signals of the isomers D2(22)-C84 and D2d(23)-C84, which is in agreement with those reported by Dennis and co-workers,13 who isolated, purified, and characterized these isomers. IR Spectroscopy. Purified samples of C76 and C78 were prepared for analysis by drop-coating them onto a KBr window from a CS2 solution. Residual solvent was removed from the resulting film by drying under vacuum for 12 h at 433.15 K. For C84, a sample of this fullerene was ground thoroughly with KBr, and the resulting powder was compressed into a pellet using a hydraulic press. All IR spectra were recorded at room temperature using a Perkin-Elmer FT-IR spectrum GX spectrometer at 0.5 cm-1 of resolution and adding 64 scans to produce each spectrum. Figures 2, 3, and 4 of the Supporting Information show the IR spectra of C76, C78, and C84, respectively, showing for C76 the characteristic signals, in good agreement with the spectrum reported by Kappes and coworkers,14 whereas for C78, the spectrum shows the superimposed signals of the C2V(3)-C78 and C2V(2)-C78 isomers, also in agreement with those reported by Kappes and co-workers,12 who characterized purified samples of each isomer. Concerning C84, the IR spectrum shows the superimposed signals of the D2(22)-C84 and D2d(23)-C84 isomers, also in agreement with the spectrum of each isolated fullerene reported by Dennis and co-workers.15
Figure 2. (a) HPLC chromatogram and (b) UV-vis spectra for fullerenes isolated. For details, see the Experimental Methods.
Stability of Fullerenes and Number of Carbon Atoms
J. Phys. Chem. B, Vol. 111, No. 30, 2007 9033
TABLE 1: Thermodynamic and Energetic Quantities (in kJ‚mol-1) Measured and Derived for the Fullerenes at 298.15 K and 101.325 kPa ∆cUοm
(cr) ) ∆cHοm (cr)a ∆fHοm (cr) ∆subHοm8 ∆fHοm (g) ∆fHοm (g) theor.4
∆fHοm (g) × C atom ∆aHοm ETR/βc Eπ(res)h Estrainh Estrain × C atom
∆fHοm (g) from eq 6 ∆fHοm (g) Theoretical4a
C60
C70
C76
C78
C84
-25 903.7 ( 42.0 2293.1 ( 44.8 182.0 ( 3.0 2475.1 ( 44.9
-30 083.0 ( 32.7 2537.4 ( 37.5 200.0 ( 6.0 2737.4 ( 37.9 2751.8 D5h
-32 612.3 ( 32.1 2705.6 ( 37.7 206.0 ( 4.0 2911.6 ( 37.9 2925.0 D2
-35 881.4 ( 36.5 2826.6 ( 42.6 225.0 ( 6.0 3051.6 ( 43.0 2998.8 D2(22) 2997.4 D2d(23)
41.3 ( 0.7 40 525.7 ( 52.1 1.643d 571.1 1539.9 25.7
39.1 ( 0.5 47 430.2 ( 48.9 2.036e 712.0 1692.0 24.2
38.3 ( 0.5 51 556.1 ( 50.5 2.207f 773.9 1777.5 23.4
-33 460.2 ( 30.6 2766.5 ( 36.7 213.0 ( 6.0b 2979.3 ( 37.2 2967.3 C2V(2) 2939.7 C2V(3) 2981.1 D3 38.2 ( 0.5 52 921.8 ( 50.6 2.275f 798.5 1819.5 23.3
36.3 ( 0.5 57 149.5 ( 56.7 2.465g 867.1 1809.9 21.5
C80
C82
C86
C88
C96
2992.3 3031.7 D2
3042.5 3012.9 C2(3)
3143.0 3076.9 C2(17)
3193.3 3117.9 C2(7)
3394.2 3325.4 D6h(184)
a Dispersions are twice the overall uncertainty; see ref 6. b Derived by least-squares analysis fitting of ∆subHοm8 data as a function of the number of carbon atoms. c β ) 362.2 kJ‚mol-1.21 d See ref 22. e See ref 23. f Derived by least-squares analysis fitting of ETR data as a function of the number of carbon atoms. g Average ETR of C84-D2(22) and C84-D2d(23) isomers.24 h Calculated as is explained in the text.
Microcombustion Calorimetry. The massic energy of combustion, ∆cuο (cr), of each purified fullerene was measured with a microbomb set, associated with a Setaram C80 Calvet calorimeter operating in isothermal mode.6 The sensors of the calorimeter are two fluxmeters with a detection limit in power of 2 µW and a calorimetric resolution of 0.1 µW, which are assembled inside a calorimetric block with a temperature control of at least (0.001 K. The samples of the fullerenes were burned in an oxygen atmosphere at 3.04 MPa and T ) 303.15 K. Flushing and filling of oxygen in both measurement and reference microbombs was done as have been described in detail previously.6 The calorimetric constant, km, of the measurement microbomb was determined by eight combustion experiments using approximately 4 mg of a standard reference sample of NIST 39j benzoic acid, providing an average value of km ) (1.013211 ( 0.00026). The electric firing energy required for ignition of the sample was independently determined also by using the C80 calorimeter. From eight experiments, the average value was (1.346 ( 0.037) Joules, which was taken into account in the calculation of the calorimetric constant of the microbomb and in the computation of the energy of combustion of each fullerene. The mass of all the substances involved in each combustion experiment was measured using a Mettler-Toledo UMX2 microbalance sensitive to 0.1 µg (precision: ( 0.1 µg), and the corrections for apparent mass to mass were applied. These corrections, as well as corrections to the standard state, and calculations of the thermochemical quantities were performed with computer software written in the laboratory and with assistance from ref 16. Densities, massic heat capacities, and data of (∂U/∂P)T for the fullerenes and others substances are supplied in the Supporting Information. All calculations of the molar masses are based on data of atomic masses recommended by the IUPAC.17 Detailed quantities of mass and energy involved in each combustion experiment of the higher fullerenes at 303.15 K are also given in the Supporting Information. The molar standard enthalpies of combustion at 298.15 K, ∆cHοm (cr, 298.15 K), shown in Table 1, were derived from
the standard enthalpies of combustion at 303.15 K using the correction
∆cHοm (cr, 298.15 K) ) ∆cHοm (cr, 303.15 K) -
303.15 K ∆Cp,m dT ∫298.15 K
where the value of ∆Cp,m for the combustion process was calculated from data of heat capacity of each solid fullerene reported in the Supporting Information and the molar heat capacities at constant pressure of (29.387 ( 0.003) J‚K-1‚mol-1 and (37.220 ( 0.002) J‚K-1‚mol-1, respectively, for O2 (g) and CO2 (g) at 300 K.18 For the fullerenes, the derived molar standard enthalpy of formation, ∆fHοm (cr), as well as the enthalpy of atomization, ∆aHοm, were calculated using the standard enthalpies of formation of -(393.51 ( 0.13) kJ‚mol-1 for CO2 (g) and (716.68 ( 0.44) kJ‚mol-1 for C (g).18 For C78, the value of the molar standard enthalpy of sublimation of (213.0 ( 6.0) kJ‚mol-1, reported in Table 1, was estimated by least-squares fitting of ∆subHοm data versus the number of carbon atoms, for C60, C70, C76 and C84, then interpolating. The uncertainty associated with the average results of energy and enthalpy of combustion in Table 1 represents twice the overall uncertainty, σ (∆cUο)Σ, and includes the uncertainties in the calibration and the combustion energies of the auxiliary materials.19 Quantification of CO2. To quantify the amount of CO2 released in a combustion experiment and to verify the total oxidation of each sample of fullerene, we developed a system for the absorption of carbon dioxide. For this, LiOH (cr) and P2O5 (cr) were used as effective CO2 absorbent and drying agents, respectively.20 After each experiment, the valve of the microbomb was connected to a set of three absorption tubes, attached to each other with Teflon tubing and Swagelok caps, and the combustion gases were slowly discharged throughout. The first tube constructed of stainless steel and containing P2O5 (cr) was located between the microbomb and the measurement tube and served to absorb all water vapor coming out with the gaseous products of the combustion. The second one was the measurement tube, manufactured from Pyrex glass and filled
9034 J. Phys. Chem. B, Vol. 111, No. 30, 2007
Rojas et al. The usual way to establish the relative stability of the fullerenes is to compute the gas-phase enthalpy of formation per carbon atom and to compare between clusters.4,5c-f From the data in Table 1, a decreasing trend of this value as the number of carbon atoms increases in the molecule is evident, meaning that less energy to include each carbon atom is necessary as the fullerene becomes larger. On the other hand, the enthalpy of atomization of a fullerene formed by n carbon atoms is calculated considering the reaction
Cn (g) ) nC (g)
(2)
∆aHοm ) n∆f Hοm (C, g) - ∆f Hοm (Cn, g)
(3)
and using the equality Figure 3. Correlation between the ∆aHοm of the fullerenes and their number of C-C bonds.
with LiOH (cr) and P2O5 (cr), where the reaction CO2 (g) + 2LiOH (cr) ) Li2CO3 (cr) + H2O (l) takes place. The mass of carbon dioxide product of the combustion was then determined by the difference in the mass of the measurement tube, detected on a micro 4503 Sartorious balance with a sensitivity of 1 µg, before and after the discharge of the gases. At the outlet of the CO2 analysis tube, another stainless steel tube containing a mixture of LiOH (cr) and P2O5 (cr) guaranteed no contamination with carbon dioxide or water vapor coming from the atmosphere. The true mass of carbon dioxide m (CO2), recovered after absorption was calculated as m (CO2) ) µ·∆m, where ∆m is the increase in mass of the measurement tube and µ is a factor of correction for the increase in the volume of the solid absorbent and the consequent decrease of the mass of gas inside the tube after absorption. The value of µ considered in this work was 1.000 54, calculated by Sabbah and Guardado20 for the system O2-LiOH-P2O5. Throughout the set of experiments, the mass of this recovered gas was 99.9% of the theoretical one, confirming complete combustion and allowing us to relate the energy of combustion results to the mass of fullerene weighted in the microbalance. Results and Discussion The resulting molar standard energies of combustion ∆cUοm (cr) and derived molar standard enthalpies of combustion ∆c Hοm (cr) at 298.15 K are listed in Table 1 and are related to the reaction
Cn (cr) + nO2 (g) ) nCO2 (g)
(1)
The standard molar enthalpies of formation, ∆fHοm (cr), at 298.15 K are calculated from eq 1 using the standard enthalpies of formation of the CO2 (g).18 For each one of the fullerenes studied, the respective molar standard enthalpies of sublimation, ∆subHοm, at 298.15 K have been reported by Piacente and co-workers.8 The molar gas-phase enthalpy of formation, ∆fHοm (g), was calculated combining those values with each experimental standard enthalpy of formation determined in this work. For C60 and C70, the ∆fHοm (g) was calculated from the results of standard enthalpy of formation previously reported6 and their respective enthalpies of sublimation.8 As shown in Table 1 and taking into account the uncertainty associated with the experimental results of gas-phase enthalpy of formation, there is good agreement between these and those obtained from density functional theory calculations4a for all the fullerenes studied.
where ∆fHοm (C, g) was taken from reference 18. The resulting values of enthalpies of atomization, shown in Table 1, are useful to elucidate the energetic characteristics of the fullerenes. An equation relating the enthalpy of atomization and the C-C bond energy has been proposed by Kiyobayashi:21
∆Haο ) nc-cEc-c + Eπ(res) - Estrain
(4)
where nc-c is the number of C-C bonds, calculated as nc-c ) 3n/2, and Ec-c is the C-C bond energy; and Eπ(res) and Estrain are, respectively, the resonance and strain energies. A straight-line fitting (Figure 3) of the enthalpy of atomization data, derived in this work, as function of nc-c, leads to the linear equation
∆aHοm/(kJ‚mol-1) ) 461.04nc-c - 982.70
(5)
indicating an average value of Ec-c in fullerenes of 461.04 kJ‚mol-1, which is very close to the average C-C bond energy of 462.8 kJ‚mol-1 calculated specifically for polycyclic aromatic hydrocarbons (PAHs);21 whereas the difference (Eπ - Estrain) is negative, indicating that there is a more important energetic contribution of the average Estrain than of the average Eπ(res) in the fullerenes. It is convenient, then, to separately quantify the strain and the resonance energies, revealing the factors responsible for the stability of each cluster. The Eπ(res) is calculated from the approximation Eπ(res) ) γETR.21 In this equality, ETR is the topological resonance energy, whose value in units of the resonance integral β have been determined for C6022 and C70,23 and estimated for C84;24 and γ ) (1-2.418/n) is the resonance energy diminution factor.25 Once Eπ(res) is calculated, the important quantity Estrain can be easily derived from eq 4; those results are also shown in Table 1. Comparing with the gas-phase enthalpy of formation of each cluster shows that it is notable that ∼60% of the energy involved in the formation of the fullerene must be spent in stabilizing the strain energy, which for the clusters studied has a maximum at C78. In contrast, it is clear that there is a decrease in the Estrain per carbon atom as the size of the cluster increases. Additionally, the derived linear eq 5 can be related to the gas-phase enthalpy of formation through eq 3, leading to an expression solely based on the number of carbon atoms to predict the gas-phase enthalpy of formation of fullerenes, for which the isolated pentagon rule is satisfied (n g 60).
∆f Hο[Cn (g)]/(kJ‚mol-1) ) 25.12n + 982.70
(6)
Comparison of the gas-phase enthalpies of formation, calculated from eq 6, with respect to the theoretical ones calculated
Stability of Fullerenes and Number of Carbon Atoms by DFT method4a for the more stable isomers of C80, C82, C86, C88, and C96 is also shown in Table 1. Conclusions To conclude, the gas-phase enthalpies of formation, enthalpies of atomization and strain energies of C76, C78, and C84 were derived from direct calorimetric measurements. This constitutes the first experimental thermochemical data set of these quantities for fullerenes beyond C60 and C70. The results indicate that an increase in the carbon atom number is associated with a lower energy in the formation of the corresponding cluster as well as a lower strain energy, suggesting that the higher fullerenes are stable enough to be isolated or chemically synthesized.26 Therefore, the relative amount of each fullerene extractable from carbon soot depends, rather, on the kinetics of the process of formation of the cluster.24,27,28 The proposed eq 6, derived from experimental data, can predict the gas-phase enthalpy of formation of fullerenes not yet isolated, with results in agreement with respect to DFT calculations. The remaining challenge now is to measure the standard energy of combustion and derive the standard enthalpies of formation of each of the most abundant isomers of C78 and C84 and also of those fullerenes that are even harder to isolate, such as C82 and C96, in the quantities required for calorimetric experiments. Acknowledgment. The authors are grateful to the CONACYT (Mexico) for financial support (Project P47679-Q) and the scholarship of M. Martı´nez. Supporting Information Available: UV-vis and IR spectra of the fullerenes studied. Detailed quantities of mass and energy involved in each combustion experiment on the fullerenes. This material is available free of charge via the Internet at htpp:// pubs.acs.org. References and Notes (1) Kra¨tschmer, W.; Lamb, L. D.; Fostiropoulous, K.; Huffmann, D. R. Nature 1990, 347, 354. (2) (a) Ettl, R.; Chao, I.; Diederich, F.; Whetten, R. L. Nature 1991, 353, 149. (b) Diederich, F.; Whetten, R. L.; Thilgen, C.; Ettl, R.; Chao, I.; Alvarez, M. M. Science 1991, 254, 1768. (c) Diederich, F.; Ettl, R.; Rubin, Y.; Whetten, R. L.; Beck, R.; Alvarez, M. M.; Anz, S.; Sensharma, D.; Wudl, F.; Khemani, K. C.; Koch, A. Science 1991, 252, 548. (3) Kikuchi, K.; Nakahara, N.; Wakabayashi, T.; Suzuki, S.; Shiromaru, H.; Miyake, Y.; Saito, K.; Ikemoto, Y.; Kaimosho, M.; Achiba, Y. Nature 1992, 357, 142. (4) (a) Cioslowski, J.; Rao, N.; Moncrieff, D. J. Am. Chem. Soc. 2000, 122, 8265. (b) Tseng, S. P.; Shen, M. Y.; Yu, C. H. Theor. Chim. Acta
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