Various magnetic resonance techniques have been used to characterize the fullerene-based materials. These techniques include nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), and muon spin resonance (/aSR). The major results obtained by magnetic resonance studies of fullerenes are reviewed in this chapter. In the early experimental studies of these materials, NMR was exploited to authenticate the C60 and C70 structures. More recently, NMR techniques have been applied to illuminate many important fullerene properties relating to bond lengths, molecular dynamics, dopant locations, stoichiometric characterization, determinations of the superconducting energy gap, and others. The EPR technique has provided a major tool for studying spin states and endohedrally doped fullerenes, molecular anions and paramagnetic doped fullerene systems. Finally, ju,SR has provided a special tool useful for illuminating special aspects of the superconductivity of doped fullerenes.
Nuclear magnetic resonance has provided a powerful tool for the study of C60, C70 and doped fullerenes [16.1]. Most of the nuclear resonance studies have been made on the 13C nucleus, which has a natural abundance of 1.1%, a nuclear spin of 1/2, and no electric quadrupole moment. The probability for m isotopic substitutions to occur on an nc atom fullerene C„c is given in Eqs. (4.8) and (4.9) of §4.5 and explicit values for these probabilities for the natural abundance of 13C in C60 and C70 are given in Table 4.25. Since the more abundant 12C nucleus (98.9%) has no nuclear spin, 12C is not a suitable nucleus for NMR studies. NMR studies on doped fullerenes have also been made on nuclei associated with various dopant species, such as 39K, 133Cs, and 87Rb.
In this section we review the major ways in which NMR has been used to gain new and in some cases unique knowledge about fullerenes and fullerene-related materials. Some of the main findings regarding the structure and properties of C60 have been achieved using NMR techniques.
16.1.1. Structural Information about the Molecular Species
NMR was one of the earliest spectroscopies used to show conclusively that the icosahedral structure for the C60 molecule was correct. The 60 carbon atoms in C60 are now known to be located at the vertices of a regular truncated icosahedron where every site is equivalent to every other site (see Fig. 3.1). Such a structure (with a single i3C nuclear substitution) is consistent with a single sharp line in the NMR spectrum [16.3-13]. For characterization purposes, the 13C NMR line for C60 in benzene solution is at 142.7 ppm (parts per million frequency shift relative to tetramethylsilane) [see Fig. 16.1(a)] [16.4,7], In contrast, C70 in benzene shows five lines at 150.7, 148.1, 147.4, 145.4 and 130.9 ppm in a 1:2:1:2:1 intensity ratio (see Fig. 16.1(b)), indicative of the five different site symmetries on the C70 rugby ball structure shown in Fig. 3.5 and discussed in §3.2 [16.4], NMR has also been useful for identifying the C76 molecule with a chiral structure (see §3.2), which explains the complicated NMR spectrum with 19 lines [16.14]. NMR techniques are also being applied to establish details about the shapes and chiralities of various higher-mass fullerenes C„c and the variety of isomers associated with each C„c molecule.
16.1.2. Bond Lengths
By determining the 13C-13C magnetic dipolar coupling in the NMR experiment, which depends on the inverse cube of the nearest-neighbor C-C distance ac_c [16.15], the C-C bond distances in C60 have been measured [16.16], Such measurements were made at 77 K on an isotopically enriched (6% 13C) sample using a Carr-Purcell-Meiboom-Gill sequence to yield a doublet in the wings of the central line of the Fourier transform of the 13C NMR signal [16.16], The strong central line in this spectrum is due to 13C nuclei with no nearest-neighbor 13C nuclei, while the doublet lines in the wings are due to 13C-13C neighbors. The doublet structure shows that there are two types of C-C bonds in a Qq molecule, and the frequency of the two doublet peaks gives the C-C distance through the (aC-c) 3 dependence of the magnetic dipolar coupling noted above, yielding ac_c distances of 1.45 ± 0.075 A and 1.40 ± 0.015 A for neutral C60 [16.16]. Such experiments have been important in establishing the small difference in the bond lengths of the single and double bonds in the neutral C60 molecule (see Fig. 3.1). The differences in the bond lengths decrease for the doped C60 anions (see Fig. 8.2 in §8.1). From these bond lengths the diameter of the C60 molecule has been calculated to be 7.1±0.07 A [16.16],
16.1.3. Structural Information about Dopant Site Locations
NMR provides a powerful tool for site identification of the dopant species. For this use of the NMR technique, the NMR resonance is typically probed with respect to a convenient dopant nucleus. Because of the distinct local environment of the NMR resonant nucleus for each distinct crystalline site, measurements of the chemical shift (Fig. 16.2) of the 39K NMR line in K3C60 show that there are two different 39K NMR lines corresponding to the two distinct chemical shifts (see Fig. 16.2) associated with each of the
Fig. 16.2. The room temperature 39K NMR spectrum of the K:!C(l0 superconductor referenced to KF in water solution, demonstrating the distinct chemical shifts for occupation of the tetrahedral and octahedral lattice sites in the superconducting KjQq compound. The integrated intensity plot indicates a 2:1 site occupation for the tetrahedral and octahedral sites [16.17].
two distinct tetrahedral and octahedral site locations of crystalline K3C60 (see §8.5.1). Measurements of the integrated NMR line intensities of the two lines provide information about the probability of occupation of the distinct sites in the crystalline structure. Specifically, experimental measurements of the integrated intensities of the two NMR features in Fig. 16.2 show a 2:1 occupancy probability for the tetrahedral to octahedral sites in K3C60 [16.17],
As another example of site specification, NMR has been used to show that specific species favor one of the distinct crystalline sites relative to other sites. For example, 133Cs NMR resonance studies have been carried out on CsRb2C60 and Cs2RbC60 [16.18] to show that since the Cs+ ion is larger than the Rb+ ion (see §8.5), the Cs+ ion favors the larger octahedral site relative to the smaller tetrahedral site in certain cases. For CsRb2C60, a single broad 133Cs NMR line is observed extending from -150 to -400 ppm frequency shift, indicative of a Cs+ ion that is preferentially in an octahedral site, while for Cs2RbC60 two 133Cs NMR lines are observed, consistent with occupation of both tetrahedral and octahedral sites by the Cs+ ion. Because of the large size of the Cs+ ion, it expands and distorts the lattice when occupying a tetrahedral site. The distortions implied by NMR spectra for these compounds are consistent with those implied by their corresponding x-ray spectra [16.19]. Also related to this work are NMR spectra taken on 60 and Rb2CsC60 by examining the 87Rb nucleus [16.20]. In this case three lines are observed: one for an Rb ion in an octahedral site, another for occupation of a tetrahedral site, and a third for an Rb ion in a distorted tetrahedral site [16.21].
NMR techniques have also been used to obtain information on the distinct site locations for the carbon atoms in doped C60. In this case the NMR measurements are done on the 13C nucleus and 13C magic angle rotation spectra for Rb3C60 show three distinct lines with intensities in ratios close to the expected values of 12:24:24, for the three distinct carbon sites on the C^q ion in the Fm3m (fee) structure of the doped Rb3C60 (see Fig. 7.3 in §7.1.2) [16.22].
The NMR technique has been used to study the molecular dynamics of Qq, C70, and doped fullerenes, by studying the linewidth and lineshapes of the NMR lines themselves and by studying the temperature dependence of the spin-lattice relaxation time Tx. At high temperatures, the molecules tend to rotate almost freely, giving rise to very narrow NMR linewidths (see Fig. 16.3) through the motional narrowing effect [16.23]. As T decreases, the molecular rotations become hindered (see §7.1) and the NMR lines
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