13416
J. Phys. Chem. 1996, 100, 13416-13420
Fullerene Derivatives in Poly(methyl methacrylate): An EPR and Zero-Field ODMR Study of Their Photoexcited Triplet States Giancarlo Agostini,† Carlo Corvaja,*,† Michele Maggini,‡ Luigi Pasimeni,† and Maurizio Prato§ Dipartimento di Chimica Fisica, Centro di Studio sugli Stati Molecolari Radicalici ed Eccitati del CNR, UniVersita` di PadoVa, Via Loredan, 2, 35131 PadoVa, Italy, Dipartimento di Chimica Organica, Centro Meccanismi di Reazioni Organiche del CNR, UniVersita` di PadoVa, Via Marzolo, 1, 35131 PadoVa, Italy, and Dipartimento di Scienze Farmaceutiche, UniVersita` di Trieste, Piazzale Europa 1, 34127 Trieste, Italy ReceiVed: February 21, 1996; In Final Form: May 28, 1996X
Samples of two fullerene derivatives, namely, C60C2H4N(CH3) and C60C2H4N(Ph2C6H4-4-OCH3) in poly(methyl methacrylate) (PMMA), were prepared either by solvent evaporation from CHCl3 solutions or by thermal polymerization of methyl methacrylate monomers containing the fulleropyrrolidines. In the first case PMMA behaves as a neutral polymeric matrix, while in the second the material swells by absorption of the solvent and its glass transition temperature is shifted up by 8 °C with respect to undoped material. Both pieces of evidence are typical of cross-linking between the polymer chains that involves fulleropyrrolidines. EPR and ODMR spectroscopies are applied to the study of the cross-linked species. It is found that its excited triplet state is characterized by unusually large electron dipolar splitting (| D| ) 248 × 10-4 cm-1). Calculations of D have been carried out using a model that considers 3C60 and the fullerene derivatives as a collection of fully localized double bonds. The experimental negative sign of D has been reproduced for 3C60, and a positive sign of D is expected for cross-linked fulleropyrrolidine affected by cross-links in the equatorial region. Such a sign reversal can explain the different spin polarization patterns exhibited by their EPR spectra.
1. Introduction The physical properties of C60 have been extensively investigated, and a variety of interesting superconducting,1 magnetic,2 electrical,3 and photochemical properties4 have been observed in different media.5 On the way to practical applications, the incorporation of C60 into polymeric matrices is highly desirable for the interesting properties of the resulting materials.6 The photophysical properties of fullerene-doped polymers are of particular interest. Enhanced photoconductivity in C60-doped polymers has been observed and attributed to excited charge transfer states.7,8 Neutral polymers such as poly(methyl methacrylate) (PMMA) have been shown to stabilize the electrontransfer products formed in the photophysics of C60 and C70.9 The ability to fabricate devices based on C60 is limited by the poor processability of the fullerene. To overcome this difficulty, a number of groups have prepared fullerene derivatives that are more soluble in common organic solvents.10 Others have made efforts to copolymerize C60 with polymers.6,11 The polymeric environment shows up its effect through the interaction of C60 with the functional groups of the polymer. During polymerization attention has been paid to avoid multiaddition to the fullerene nucleus, resulting in cross-linked materials that are rather intractable. However, when crosslinking occurs, materials acquire new properties and it seemed interesting to investigate the C60-based species that are responsible for cross-linking in host polymers.11,12 Here, we focus on the incorporation of fulleropyrrolidines 113 and 214 in PMMA (see Figure 1). Films of PMMA containing C60 have been previously prepared.15 However, the higher solubility of 1 and 2 with respect to unmodified C60 resulted in much more homogeneous samples. We report on the properties of long-lived triplet excited states †
Dipartimento di Chimica Fisica, Universita` di Padova. Dipartimento di Chimica Organica, Universita` di Padova. Dipartimento di Scienze Farmaceutiche, Universita` di Trieste. X Abstract published in AdVance ACS Abstracts, July 1, 1996. ‡ §
S0022-3654(96)00528-X CCC: $12.00
Figure 1. Fulleropyrrolidines 1 and 2 used in this study.
generated on fullerenes upon irradiation. Optical emission, EPR, and zero-field ODMR spectroscopies were used. Zero-field optically detected magnetic resonance (ZF-ODMR) experiments were carried out in which transitions were detected optically between sublevels of these triplets at zero external magnetic field as microwave-induced changes of the emission,16 whose dominant part comes from the fluorescence.17 2. Experimental Section Compounds 1 and 2 were prepared as already described.13,14 Glassy solutions in PMMA were prepared either by dissolving desired amounts of fullerene and polymer in CHCl3 and then drying from the solvent (PMMA/E) or by producing in situ polymerization of methyl methacrylate monomer solution containing fullerene, accomplished during a thermal cycle (PMMA/T). More specifically, samples in PMMA/T were prepared by dissolving 3 mg of 1 or 4.5 mg of 2 in 10 mL of previously distilled methyl methacrylate monomer (Aldrich, 99%) containing 2.5 mM of R,R′-azoisobutyronitrile (Janssen, 98%) as radical initiator in 1 cm diameter glass tubes. The solution was degassed through four freeze-pump-thaw © 1996 American Chemical Society
Fullerene Derivatives
Figure 2. Low-temperature (5 K) LFM EPR spectrum of 1 excited triplet in PMMA/E (b) and by comparison that observed in a toluene matrix (a).
cycles, and the tubes were sealed off under vacuum. The polymerization was initiated very slowly by keeping the tube at 40 °C for at least 5 days. Subsequently, the temperature was raised to 60 °C (2-3 days) and 80 °C (2-3) days. A final annealing at 125 °C for 1 night followed by slow cooling to room temperature completed the thermal treatment.18 A CW-EPR method was used to detect the spectra of the photoexcited paramagnetic states by light-modulation fieldmodulation (LFM) EPR detection. Incident light (360 < λ < 600 nm) chopped at 97 Hz was supplied by an OSRAM HBO 500 W high-pressure mercury lamp, while the signal was detected by the in-phase lock-in detection technique. Temperature was controlled by an Oxford ESR-900 helium continuous flow cryostat within an estimated error of (0.5 K. Fluorescence spectra, measured on dilute solutions (∼10-4 M), were recorded by using the same optical apparatus as used for ODMR experiments.19 The emission was collected by a HR 250 Jobin Yvon monochromator equipped with a grating (1200 g/mm) blazed at 500 nm and detected by a water-cooled EMI 9659B extended S20 photomultiplier. The excitation light (450 < λ < 580 nm) was supplied by a 250 W HLX OSRAM lamp. To obtain ODMR spectra, use was made of a helix reflection system. Microwaves were provided by a sweep oscillator (HP 8350B) and amplitude modulated by a pin diode at about 400 Hz. The emission was focused onto a Centronic OSI 5K silicon photodiode after passing through an Ealing cutoff filter at 645 nm. The synchronous change of the emission was measured by a lock-in amplifier and recorded while scanning the microwave frequency. In microwave-induced fluorescence spectra (MIF) the microwave frequency was fixed at a resonant transition while the emitted light at different wavelengths was scanned. Differential scanning calorimetric (DSC) measurements were made with a Perkin-Elmer DSC-4 instrument, equipped with a 3600 HP work station for data acquisition. 3. Results C60, C70, and some C60 derivatives are known to give spinpolarized excited triplet states by irradiation with visible light.20-22 The EPR spectrum of the excited triplet state of 1 in a PMMA/E matrix, recorded at 5 K, is shown in Figure 2b. The pattern, showing the A/E polarization for the low/high field EPR transitions typical of the C60 triplet state, is very similar to that
J. Phys. Chem., Vol. 100, No. 32, 1996 13417
Figure 3. EPR spectrum of 2 excited triplets in PMMA/T recorded at 115 K. The simulation (dashed line) was made by allowing for the superposition of spectra due to the species A and B whose magnetic and spin population parameters are collected in Table 1. Equal line widths for the x, y, and z components were used: 3.0 mT for A and 15 mT for B.
already obtained for 1 in a toluene matrix 23 (Figure 2a). Analogous spectra were recorded for 2 in PMMA/E and in toluene. For the PMMA/T matrix the EPR spectra of 1 and 2 are strikingly different from those in PMMA/E. The spectrum of 2 is reported in Figure 3. It consists of the superposition of the signals due to two triplet species, henceforth denoted by A and B, having different ZFS parameters. The signals from both species are emissive on the low-field side and absorptive on the high-field side (E/A pattern), thus displaying a reversed spin polarization compared to that of 3C60 in toluene and also to that of 1 and 2 in PMMA/E. Furthermore, one of the species (A) is characterized by an unusually large dipolar splitting, about 2 times larger than that measured for 3C60. The spectrum remains unchanged on increasing the temperature from 5 K up to 150 K. For 1 only the A species was observed.23 The fluorescence spectra of 1 in PMMA/E and PMMA/T, reported in Figure 4, consist of broad bands with maxima centered at 710 nm for PMMA/E and at 725 nm for PMMA/T, which do not display any resolved vibronic structure, even at 1.8 K. This contrasts with the fluorescence spectrum of 1 in methylcyclohexane at 77 K, which shows a well-resolved vibronic progression.24 The emission spectra of 2 in PMMA/E and in PMMA/T are very similar to those of 1. The values of the ZFS parameters were checked by ODMR. ODMR spectra of 1 and 2 in PMMA/T, recorded by detecting the emission light at λ > 645 nm are reported in Figure 5. They consist of three lines centered at 180, 659, and 844 MHz for 1 and at 198, 638, and 847 MHz for 2 corresponding, respectively, to the 2|E|, |D| - |E|,and |D| + |E| transitions. The values for 2 correspond to the ZFS parameters of species A obtained from the EPR spectra. The line shapes of the ODMR lines were nicely reproduced by Gaussian functions with a fwhm of 75 MHz.In PMMA/E the ODMR spectrum of 1 gives transitions at lower frequencies (see lower trace in Figure 5). The lines are also reproduced by Gaussian functions but with a smaller line width of 36 MHz. The MIF spectrum of 1 in PMMA/T is also reported in Figure 4. It is obtained by modulating microwaves matching the |D| - |E| transition. Its spectral profile coincides with the fluorescence spectrum, indicating that the triplet species observed by ODMR originates from the same excited singlet that emits the observed fluorescence.
13418 J. Phys. Chem., Vol. 100, No. 32, 1996
Agostini et al. TABLE 1: Magnetic Parameters and Triplet Spin Population Ratios of Compounds 1 and 2 Embedded in Different Matrices, Obtained from Simulated EPR and ODMR Spectrab compound
matrix
1 1 1 1 1
toluene PMMA/E PMMA/E PMMA/T PMMA/T
2
PMMA/T
2
PMMA/T
a
×10-4
species
A B
Da
Ea
px:py:pz
spectrum
-90 -96 95 +248 250 +248 +128 248
+14 +14 13 -35 30 -35 -48 33
0.85:1:0.03 0.80:1:0.03
EPR EPR ODMR EPR ODMR
0.85:1:0.03 0.6:1:0.03
EPR ODMR
cm-1. b
Note that from ODMR spectra only the absolute values of D and E are measured.
Figure 4. Emission spectra of 1 in PMMA/E (a, dashed line) and in PMMA/T (b, solid line) detected at 1.8 K. The lower trace (c) represents the MIF spectrum of 1 in PMMA/T, detected at the same temperature.
Figure 5. ZF-ODMR spectra of 1 in PMMA/E (a) and of 1 and 2 in PMMA/T (curves b and c, respectively) detected by collecting the light emitted with λ > 645 nm. Note the much narrower frequency range and line width of spectrum a.
The ZFS parameters and the relative triplet level populations, which will be discussed in the next section, are collected in Table 1 together with those measured for 1 in toluene. 4. Discussion 4.1. Simulation of EPR Spectra. For the simulation of our EPR spectra we have followed the procedure discussed by Gonen and Levanon.25 In this procedure the values of D and E, the population ratios px:py:pz of the three levels in zero field, and a set of line width parameters for the EPR transitions are required. In the present instance these line widths were assumed to be orientation independent. For 3C60 it has been recently found that EPR spectra can be reproduced by the two sets of parameters: (1) D > 0 and px, py < pz; (2) D < 0 and px, py > pz. The sign of D for 3C60 has been determined experimentally from ENDOR measurements and proven to be negative.26 Therefore, a negative sign of D
combined with px, py > pz has been used to simulate A/E polarized EPR spectra of 1 and 2 in PMMA/E. The D, E parameters and the ratios between pi (i ) x, y, z) employed in the simulations are reported in Table 1. To reproduce the E/A polarization pattern exhibited by the EPR spectra of 1 and 2 in PMMA/T, we have assumed a positive sign of D while leaving unaltered the population ratios (px, py > pz) found from a simulation of the EPR spectra of 1 in toluene. The experimental and calculated EPR spectra of the triplet state of 2 in PMMA/T, obtained by assuming D > 0 and E < 0, are reported in Figure 3, whereas the values of D, E, and the population ratios for 1 and 2 are collected in Table 1. In the case of 2 an additional triplet species appears, characterized by a smaller D value while carrying the same spin polarization. With increasing temperature, the spectral features of 1 and 2 both in PMMA/E and PMMA/T samples do not change significantly. The singularities of the powder spectrum do not shift in frequency, indicating that the Jahn-Teller dynamics observed in 3C6027 is absent as is expected owing to the reduced symmetry of adducts.28 4.2. Model Calculation of D. To unravel the origin of the sign reversal in the D parameter, we have performed a model calculation of D that makes use of the unpaired electron distribution of the triplet state. Calculation of spin density distribution of the C60 radical anion has been carried out for the nearly degenerate structures of D5d, D3d, and D2h symmetries. For all of them it was found that the spin densities are accumulated more or less in the vicinity of the equator.29 For 3C60 a spin density distribution, with a maximum at the equatorial plane and varying tentatively as sin2 θ (θ is the angle between the line connecting a C atom with the center of the sphere and the z axis), has been employed to reproduce the 13C nuclei modulation of the ESEEM signal in a sample of 13Cenriched C60 dissolved in toluene.30 This assumption receives strong support from recent CNDO/S-CI calculations of 3C60 spin density according to which more than 70% of the spin density is concentrated over the 28 atoms nearest the equatorial plane.26,31 When the substituents attached to the nitrogen atom are neglected, fulleropyrrolidine derivatives 1 and 2 have C2V symmetry deriving from the D2h structure after fusion at a 6-6 ring junction of C60. The equatorial plane is that bisecting the fullerene sphere, and it is normal to the C2 symmetry axis. The observation that there is no substantial variation in the D and E parameters in going from C60 to the fulleropyrrolidines also suggests that in the latter the spin distribution should be confined to the equatorial plane. We have adopted the same (2/π)sin2 θ distribution to make a simple calculation of D based on a model of fully localized C-C double bonds over the fullerene surface.30 The ZFS parameter D is obtained as a sum of the contributions from all
Fullerene Derivatives the C-C double bonds, where each double bond gives contribution through its ZFS principal values, weighted by the mean spin density over the bond and projected along the C2 z axis of fullerene. Two sets of calculated D and E values are available from the literature for the contributions due to unpaired electrons separated by a single π bond. For the excited triplet state of ethylene, D ) 0.1847 cm-1 and E ) 0.2248 cm-1,32 while D ) 0.1500 cm-1 and E ) 0.2000 cm-1 are the values giving the best fit of the experimental data relative to aromatic π molecules like naphthalene, anthracene, phenanthrene, and triphenylene.33 It should be noted that the C-C bond length in ethylene is 1.32 Å while the aromatic bond lengths are about 1.4 Å, and in C60 and its Diels-Alder adducts the double bonds are 1.39 Å on the average.34 For 3C60 the former set of data leads to the calculated value of D ) -0.0128 cm-1, while from the second set one obtains D ) -0.0106 cm-1. In both cases the experimental negative sign of D is reproduced and the absolute value is in very good agreement with the experimental value. After submission of the present paper, a report appeared on theoretical calculation of D for 3C60.35 The authors, using a semiempirical method, obtained a negative value that further supports our findings. The negative contribution to D is given mainly by the two bonds parallel to the z axis straddling the equatorial plane. If the triplet wave function is allowed to be confined near the poles, a positive sign of D is expected. In the case where the spin density is uniformly distributed over the five bonds at the pole opposite to the substituent, use of the parameters from ref 32 gives the result D ) +0.0309 cm-1 while those from ref 33 yield D ) +0.0264 cm-1, in good agreement with the experimental values obtained for samples of 1 and 2 in PMMA/ T. 4.3. Possible Structures of 1 and 2 Embedded in PMMA/ T. To account for the positive sign of D, we report two experimental observations we made on the behavior of the PMMA/T matrix doped with 1 or 2. First, we noted that samples of 1 or 2 in PMMA/T did not dissolve when immersed in CHCl3 as do the analogous preparations in PMMA/E or PMMA itself. Instead, the materials swell by absorption of solvent until the maximum swelling is reached, where the osmotic pressure of the solvent penetrating the polymer is balanced by the elastic deformation of the polymer due to the volume increase.36 Second, by differential scanning calorimetry (DSC) we measured the specific heat at constant pressure Cp against temperature for the same sample of PMMA/T containing 1, as used in magnetic resonance experiments, and by comparison with a sample of undoped PMMA/T. The results are reported in Figure 6 from which a shift of about 8 °C is measured for the glass transition temperature Tg. A change of Tg in a polymer is expected when the polymer becomes more rigid. The increase in the intermolecular forces in the glass state caused by crosslinking can increase the Tg by the amount observed experimentally.37 Accordingly, for 1 and 2 dissolved in PMMA/T, it is plausible that the C-C double bonds in the vicinity of the equatorial plane participate in cross-linking with PMMA polymer chains through their radical heads formed during polymerization. The addition of initiator radicals is ruled out on the basis of the higher concentration of MMA radical oligomers. In the cross-linking process triplet spin density is pushed out from the equator, the most reactive region,38 toward the poles of the fullerene sphere. The calculation of D supports this picture. On localization of the electronic triplet wave function near the poles, a D value is predicted that is larger than that observed for samples in
J. Phys. Chem., Vol. 100, No. 32, 1996 13419
Figure 6. Differential scanning calorimetry plots of Cp for the PMMA/T sample (dashed line) and for PMMA/T doped with 2. From the midpoints of the two curves a temperature shift of 8 °C was measured.
toluene and fairly close to that observed experimentally in PMMA/T. The sign of D is thereby reversed from negative to positive. The different magnitude of D for the triplet species A and B in the EPR spectrum of 2 in PMMA/T apparently reflects a difference in the triplet wave function for the two species formed by radical addition. Despite the uncontrolled conditions under which the crosslinked species are produced, two well-defined chemical species are generated as a result of multiple additions during the thermal cycle. These species are characterized by unusually large ZFS parameters compared to fullerenes, while the spin polarization patterns remain unaltered and the emission spectrum is slightly red-shifted. Although the triplet spin distribution is markedly changed, absorption and emission spectra still remain those of fullerenes. Work is now in progress to study multiple adducts produced under controlled conditions. 5. Conclusion It is shown that samples of PMMA prepared by radical thermal polymerization acquire new properties when the starting solution of the monomer contains fulleropyrrolidines like 1 and 2 compounds: (i) When immersed in CHCl3 the material swells but does not dissolve as does undoped PMMA; (ii) The glass transition temperature of the polymer is shifted toward higher temperatures by about 8 °C with respect to the undoped material. Both facts are typical of cross-linking between the polymer chains. The model calculation of the ZFS parameter D allows us to account for the drastic change in the values of D for fulleropyrrolidine excited triplet states from PMMA/E to PMMA/T matrices and the reversal in the spin polarization pattern exhibited by their EPR spectra. It is found that cross-linking gives rise to a new multiple adduct whose excited triplet state is characterized by well-defined dipolar splitting and spin polarization. Finally, it should be noted that cross-linking was not observed when C60 was used in place of 1 and 2. This fact can be attributed to the high tendency of C60 to aggregate into clusters, whereas fulleropyrrolidines 1 and 2 possess enhanced microscopic solubility.
13420 J. Phys. Chem., Vol. 100, No. 32, 1996 Acknowledgment. This work was supported by the Italian National Research Council (CNR) through the Centro Studi sugli Stati Molecolari Radicalici ed Eccitati and by the Ministero dell’Universita` e della Ricerca Scientifica e Tecnologica (MURST) through the Progetto Finalizzato “Materiali Speciali per Tecnologie Avanzate”. Many thanks to Professor G. Favero (Department of Inorganic, Metallorganic and Analitical Chemistry of the University of Padova) for the DSC measurements. References and Notes (1) Hebard, A. F.; Rosseninsky, M. J.; Haddon, R. C.; Murphy, D. W.; Glarum, S. H.; Palstra, T. T.; Ramirez, A. P.; Kortan, A. R. Nature 1991, 350, 600. (2) Stephens, P. W.; Cox, D.; Lauher, J. W.; Mihaly, L.; Wiley, J. B.; Allemand, P. M.; Hirsch, A.; Holczer, K.; Li, Q.; Thompson, J. D.; Wudl, F. Nature 1992, 335, 331. (3) Dubois, D.; Moninot, G.; Kutner, W.; Jones, M. T; Kadish, K. J. Phys. Chem. 1992, 96, 7137. (4) (a) Jehoulet, C.; Bard, A. J.; Wudl, F. J. Am. Chem. Soc. 1991, 113, 5456. (b) Arbogast, J. W.; Darmanian, A. P.; Foote, C. S.; Rubin, Y.; Diederich, F. N.; Alvarez, M. M.; Anz, S. J.; Whetten, R. L. J. Phys. Chem. 1991, 95, 11. (5) Fullerenes, Recent AdVances in the Chemistry and Physics of Fullerenes and Related Materials; Kadish, K. M., Ruoff, R. S., Eds.; The Electrochemical Society, Inc.: Pennington, NJ, 1994; Vols. 92-94. (6) Hirsch, A. AdV. Mater. 1993, 5, 859. (7) Wang, Y. Nature 1992, 356, 585. (8) Sariciftci, N. S.; Smilowitz, L.; Heeger, A. J.; Wudl, F. Science 1992, 258, 1474. (9) Gevaert, M.; Kamat, P. V. J. Phys. Chem. 1992, 96, 9883. (10) Hirsch, A. Synthesis 1995, 895. (11) (a) Hawker, C. J. Macromolecules 1994, 27, 4836. (b) Zhang, N.; Scricker, R.; Wudl, F.; Prato, M.; Maggini, M.; Scorrano, G. Chem. Mater. 1995, 7, 441. (12) Loy, D. A.; Assink, R. A. J. Am. Chem. Soc. 1992, 114, 3977. (13) Maggini, M.; Scorrano, G.; Prato, M. J. Am. Chem. Soc. 1993, 115, 9798. (14) Maggini, M.; Karlsson, A.; Pasimeni, L.; Scorrano, G.; Prato, M.; Valli, L. Tetrahedron Lett. 1994, 35, 2985. (15) Kost, A.; Tutt, L.; Klein, M. B.; Dougherty, T. K.; Elias, W. E. Opt. Lett. 1993, 18, 334. (16) Matsushita, M.; Frens, A. M.; Groenen, E. J. J.; Poluektov, O. G.; Schmidt, J.; Meijer, G.; Verheijen, M. A. Chem. Phys. Lett. 1993, 214, 349.
Agostini et al. (17) Van den Heuvel, D. J.; Chan, I. Y.; Groenen, E. J. J.; Matsushita, M.; Schmidt, J.; Meijer, G. Chem. Phys. Lett. 1995, 233, 284. (18) Dick, B. Chem. Phys. 1989, 136, 429. (19) Agostini, G.; Corvaja, C.; Giacometti, G.; Pasimeni, L. Chem. Phys. 1993, 173, 177. (20) Wasielewski, M. R.; O’Neill, M. P.; Lykke, K. R.; Pellin, M. J.; Gruen, D. M. J. Am. Chem. Soc. 1991, 113, 2774. (21) Terazima, M.; Hirota, N.; Shinohara, H.; Saito, Y. Chem. Phys. Lett. 1992, 195, 333. (22) Bennati, M.; Grupp, A.; Mehring, M.; Belik, P.; Gugel, A.; Mullen, K. Chem. Phys. Lett. 1995, 240 , 622. (23) Agostini, G.; Corvaja, C.; Pasimeni, L. Chem. Phys. 1996, 202, 349. (24) Williams, R. M.; Zwier, J. M.; Verhoeven, J. W. J. Am. Chem. Soc. 1995, 117, 4093. (25) Gonen, O.; Levanon, H. J. Phys. Chem. 1984, 88, 4223. (26) Groenen, E. J. J. Private communication. (27) Bennati, M.; Grupp A.; Mehring, M. J. Chem. Phys. 1995, 102, 9457. (28) Bennati, M.; Grupp, A.; Mehring, M.; Belik, P.; Gugel, A.; Mullen, K. Chem. Phys. Lett. 1995, 240, 622. (29) Koga, N.; Morokuma, K. Chem. Phys. Lett. 1992, 196 , 191. (30) Grupp, A.; Pfeuffer, J.; Mehring, M. Congr. Ampere, Proc., 27th 1994, 967. Physics and Chemistry of Fullerenes and DeriVatiVes; Kuzmany, H., Fink, J., Mehring, M., Roth, S., Eds.; World Scientific: Singapore, 1995; p 403. (31) Surjan, P. R.; Udvardi, L.; Nemeth, K. J. Mol. Struct. 1994, 311, 55. (32) (a) Gouterman, M.; Moffitt, W. J. Chem. Phys. 1959, 30, 1107. (b) Boorstein, S. A.; Gouterman, M. J. Chem. Phys. 1963, 39 , 2443. (33) van der Waals, J. H.; ter Maten, G. Mol. Phys. 1964, 8 , 301. (34) (a) Hedberg, K.; Hedberg, L.; Bethune, D. S.; Brown, C. A.; Dorn, H. C.; Johnson, R. D.; de Vries, M. Science 1991, 254 , 410. (b) Burgi, H. B.; Blanc, E.; Schwarzenbach, D.; Liu, S.; Lu, Y.; Kappes, M. M.; Ibers, J. A. Angew. Chem., Int. Ed. Engl. 1992, 31, 640. (c) Rubin, Y.; Khan, S.; Freedberg, D. I.; Yeretzian, C. J. Am. Chem. Soc. 1993, 115, 344. (35) Surjan, P. R.; Nemeth, K.; Bennati, M.; Grupp, A.; Mehring, M. Chem. Phys. Lett. 1996, 251, 115. (36) Mathauer, K.; Schmidt, A.; Knoll, W.; Wegner, G. Macromolecules 1995, 28 , 1214. (37) Aklonis, J. J.; MacKnight, W. J. Introduction to Polymer Viscoelasticity; J. Wiley: New York, 1983. (38) (a) Hirsch, A.; Lamparth, I.; Karfunkel, H. R. Angew. Chem. 1994, 106, 453. (b) Lamparth, I.; Maichle-Mossmer, C.; Hirsch, A. Angew. Chem., Int. Ed. Engl. 1995, 34, 1607.
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