Transition from C60 to C70
As mentioned above, there is some difficulty in accounting for a reaction pathway between C60 and C70, since both C60 and C70 have relative potential minima and both appear as relative maxima in the cohesive energy plot of Fig. 6.5. This cohesive energy plot implies that C60 and C70 are especially stable and the intermediate fullerenes C62,..., C68 are less stable. In Fig. 6.5 we see that C60 has the most pronounced local maximum in the cohesive energy and C70 has the second most pronounced local maximum [6.16]. The general upward background in Fig. 6.5 reflects an increase in binding energy of ~11 meV per C2 dimer addition. The limit nc -> oo corresponds to the binding energy of graphite. It should be noted that the binding energy for C, is 3.6 eV/C atom. According to Fig. 6.5 the cohesive energy of C70 is about 35 meV higher than that for C60. However, for each of the less stable fullerenes, as well as for the stable fullerenes, the sum of the cohesive energies for C„c and for C2 is less than that for C„c+2, thus leading to the C2 dimer absorption process. Thus, while the addition of one C2 dimer from C60 is relatively unfavorable by the C2 absorption pathway, the probability for the addition of a second C2 dimer at the opposite side of the fullerene is
enhanced before the first C2 dimer is desorbed. Physically, the absorption of two or more C2 dimers following the absorption of the first dimer is favorable since the C2 absorption partially relieves the strain introduced by the absorption of the first dimer. If two dimers are thus absorbed, then the probability of quickly adding three additional C2 dimers is enhanced, because the addition of five C2 dimers completes the ring of five additional hexagons needed to form C70.
The correlated addition of one or more C2 dimers provides an intuitive mechanism for relieving local strain. Thus, the correlated sequential addition of five C2 dimers is closely related to the addition of a ring of five hexagons, so that the sequential correlated C2 dimer addition process provides a mechanism for the catalytic self-assembly of rings at preferred locations on fullerene balls. Either the correlated absorption of five C2 dimers or the absorption of a whole ring of five hexagons provides a pathway for going from C60 to C70. This concept can be generalized to a growth process from one relative potential minimum to another on the cohesive energy £coh vs. nc plot in Fig. 6.5. The same type of correlated self-assembly process can also be envisaged for the decay of fullerenes in going between C70 and C60, under an emission process that could, for example, be initiated by ion or laser irradiation.
Mass spectrometry has provided an extremely valuable technique for the characterization of fullerene specimens regarding their mass distribution (§6.3), the detection of their various stable charge states (§6.3) and of metallofullerenes (§5.4 and §8.2), and the identification of the various oligomers in photopolymerized fullerenes (see §7.5.1). Mass resolution of ra/im > 106 can be achieved with presently available mass spectrometers, and signals from as few as 10 ions can be detected [6.25]. The high-mass resolution is exploited for the unambiguous identification of high-charge states of fullerenes, and high-resolution techniques have been extensively utilized in photofragmentation studies of fullerenes to detect isotopes for a given molecular species. The high sensitivity of mass spectrometry instruments provides quantitative information about very small samples, which is of great use in studying high-mass fullerenes (such as C84) and metallofullerenes [such as [email protected] (see §8.2)].
A variety of mass spectrometry instruments are used for the characterization of fullerenes, including quadrupole time-of-flight instruments and Fourier transform mass spectrometers. The specific instrument selection depends somewhat on the type of measurement to be performed and the sensitivity that is needed. In time-of-flight instruments, the mass m is proportional to the square of the time of flight t.
To steer, trap, manipulate, and detect the various molecules and clusters in a mass spectrometer, the fullerenes are normally charged either positively or negatively. Lasers are commonly used both to ionize fullerenes and to desorb fullerenes from the surfaces. Ionization capabilities to form positive ions are often provided in a mass spectrometer, although negative ions are also used. A variety of lasers are used for ionization purposes, such as Nd:YAG operating either on its fundamental frequency or on one of its harmonics (1064, 532, 355, 266 nm). Laser desorption is used to remove trace quantities of charged ions from a sample for mass spectral characterization. Single-photon ionization, however, requires high photon energies (hoj > 7.58 eV for C60 and 7.3 eV for C70 [6.26]). Other common modes of ionization include 252Cf plasma desorption, fast atom bombardment, and electrospray ionization [6.25,27].
Mass spectrometers are sensitive to the ratio M/q, rather than to M itself, where M and q denote the mass and number of charges per molecule or cluster. Thus high-resolution analysis is needed for measuring the expected 13C contributions to each peak, since isotopic distributions are often used to identify the particular charge state of a fullerene (e.g., C"}(f). The ability to charge the C60 beams both positively and negatively, without causing structural damage to the fullerenes, has been very important for the detection, characterization and properties measurements of C60 beams by mass spectroscopy techniques.
The stability of fullerenes is in part due to their high binding energies per carbon atom. The experimental value for the binding energy per carbon atom in graphite is 7.4 eV [6.11]. Total energy calculations using a local density approximation (LDA) and density functional theory [6.28] show that the binding energy of C60 per carbon atom is only reduced by about 9% relative to graphite. The corresponding calculation for C70 [6.28] gives a binding energy per carbon atom that is slightly higher (by about 20 meV) than for C60. These LDA calculations of the binding energy [6.28] predict trends similar to those calculated for the cohesive energy in Fig. 6.5 [6.16], although the quantitative predictions differ in detail.
A very impressive experimental confirmation of the stability of fullerenes comes from the production of fullerenes by laser ablation from graphite [6.29] or carbon-based polymer substrates [6.30,31]. From the time-of-flight mass spectrum of polyimide shown in Fig. 6.8 we see three characteristic regions: the low-mass region shown in (a), which is characteristic of the substrate; the low- to intermediate-mass spectra in (b) showing evidence for fullerene formation, but with masses less than C60; the intermediate-mass range (c) showing the highest intensity of fullerene products; and finally in (d) the high-mass region going out to high mass values and showing only a slow fall-off in intensity with increasing mass. Proof that the mass peaks are associated with pure carbon species comes from doing an analysis of each mass peak for its isotopic abundance composition, and the results provide good fits to theoretical predictions for the natural isotopic abundance (see §4.5) [6.26]. Carbon clusters are formed by laser ablation at high temperatures (>3000 K), and the energetic clusters are believed to cool by C2 emission (reduction of a fullerene by one hexagon face), consistent with the requirements of Euler's theorem. The release of C2 rather than individual carbon atoms is also favored by the high binding energy of C2 (3.6 eV). From the peak intensities of the mass spectra of Fig. 6.8, it is possible to
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