6.4.4. Fragmentation of C60 by Energetic Ions
We now describe a very different fragmentation study, where C60 is the target rather than the projectile. Under the influence of heavy-ion irradiation, it has been shown that C60 breaks up into individual carbon atoms [6.55], In these experiments C60 films were exposed to 320-keV Xe ion irradiation for which the mean projected ion penetration depth Rp and the half-width at half-maximum intensity ARp are Rp ± ARp = 120 ± 18 nm, and the Xe ion implantation was carried out at both room temperature and 200°C for ion doses in the range 1012 to 1016 Xe/cm2. Monitoring the effect of the implantation by resistance measurements on the C60 film [see Fig. 6.16(a)], it was found that the onset for conduction occurred at a dose of 2.5 x 1012 Xe/cm2, several orders of magnitude less than the onset for fused quartz, irradiated with 100-keV carbon atoms [6.55,56], although in both cases the temperature dependence of the resistance of the irradiated sample followed a logfl vs. (1/T)1/4 law, characteristic of the 3D variable-range hopping transport mechanism [6.57]. Writing the functional dependence of the electrical resistance R for this regime as
where y is a numerical factor, N is the concentration of hopping centers, and £ is the average size of a hopping center, and noting that the hopping center density is proportional to the dose D, then N can be written as
Fig. 6.16. (a) Resistance vs. dose for 320-keV Xe irradiation of Cm at room temperature (filled circles) and at 200°C (open circles) and for 100-keV C irradiation of fused quartz at room temperature (filled triangles) and at 200°C (open triangles). In (b) the data of (a) are replotted as log10(resistance) vî. (dose)-"3 for 100-keV C implanted fused quartz (circles) and 320-keV Xe implanted C60 (squares). Both implantations are at 200° C. The straight lines are least squares linear fits to the data [6.55].
where W is the thickness of the implanted region, yielding a prediction that logi? ~ £>~1/3. We see from Fig. 6.16(b) that this hypothesis is well supported by the experiments for 320-keV Xe implantation into C60 and for 100-keV C implantation into fused quartz. From the slopes of the lines in Fig. 6.16(b), the magnitude of £ can be determined. For both the C60 and the fused quartz, the hopping center is found to be a single carbon atom of size ~1 A [6.55]. The observation that the irradiation dose onset for conduction is about 60 times lower for C60 than for ion-implanted diamond [6.56,58] suggests that the fragmentation of C60 by heavy Xe ions breaks up the C60 molecule into 60 individual carbon atoms. This hypothesis is supported by the magnitude of the thermal spike associated with the ion implantation [6.56], yielding a kinetic energy of 16 eV per carbon atom, far greater than the binding energy of carbon in the solid state (7.4 eV/C atom in graphite) [6.55]. The results obtained for Xe irradiation are consistent with those for proton irradiation of C60 films where disintegration of the C60 by protons of 100 keV was reported [6.59],
The tendency of C60 to fragment upon ion irradiation suggests that ion implantation is not an attractive method for the doping of C60. These results also indicate that the abundance of fullerenes in the interstellar space may be low because of their tendency to disintegrate upon exposure to heavily damaging energetic particles in space [6.55],
Molecular dynamics simulations combined with tight-binding total energy calculations have been used to simulate the fragmentation process [6.60-62] of C60 and C70 by calculating bond lengths, the number of nearest-neighbors per carbon atom, the heat capacity, and the binding energy as a function of temperature. Bond breaking (or melting) is observed in these simulations between 3000 and 4000 K for both C60 and C70, below that for diamond (4100 K). The bond breaking of fullerenes is already anticipated by T ~ 3000 K because of large bond distortions shown in the molecular dynamics simulations. A decrease in the average number of nearest-neighbors (below 3) appears by 4000 K. Once a single bond is broken, stress accumulates near the broken bond, leading rapidly to further bond breaking at neighboring bonds. The bond breaking occurs preferentially at single bond sites. At melting, a latent heat of 1.65 eV and 1.29 eV is found for C60 and C70, respectively [6.60], which is somewhat higher than for graphite (1.085 eV).
Not only the fragmentation but also the growth of fullerenes has been modeled using molecular dynamic simulations. The ab initio molecular dynamics method used in these simulations is called the Car-Parrinello method [6.63], in which the electronic interactions are treated in the den sity functional formalism, while the atoms follow Newtonian dynamics with forces derived directly from the local density equations. The electronic and ionic subsystems evolve simultaneously, allowing study of time-dependent simulations at finite temperature and of geometry optimization based on simulated annealing.
These molecular dynamics simulations have provided a number of insights into the growth process for fullerenes [6.60-62] and for tubules [6.64]. Simulations of a C20 unit showed the dodecahedron cage structure to have the lowest energy, with the corannulene C20 cluster (found in the C60 molecule) as discussed in §3.1 to be higher in energy by 0.75 eV, and the ring structure to have an energy higher by 2.65 eV than the cage structure [6.61]. However, when entropy is taken into account, the free energy at elevated temperatures (>1500 K) shows the opposite order, with the C20 ring structure having the lowest free energy, the corannulene C20 the second lowest free energy, and the C20 dodecahedron cage molecule having the highest free energy of the three configurations. Such calculations thus provide insight into reasons why mass spectra for nc ~ 20 are interpreted in terms of the ring configuration [6.61].
Molecular dynamic simulations have been informative about the formation of defective C60 structures and the identification of the most likely defects (two adjacent pentagons) [6.5,10,65-68], Simulations of the growth and annealing of C60 from the gas-phase are impeded by the inability of today's computers to simulate the long cooling times needed to reach equilibrium. Some molecular dynamic simulations [6.5] show that as a plasma of 60 carbon atoms is cooled from 7000 K, dimers form first, then chains, and finally polycyclic rings are formed. Only when the system is cooled to ~3000 K is a cage structure formed, and this structure is predominantly made of hexagonal and pentagonal faces, although the cage structure according to this model is a highly defective form of C60 [6.5,6,69,70].
Molecular dynamics simulations have also been informative for studying the local stability and reactivity of fullerenes. For example, scenarios for the absorption of a C2 cluster by C60 have been identified, although no route could be found for the absorption of a C3 cluster [6.61], as might be expected from Euler's theorem. As another example, molecular dynamic simulations have been used to compute the heats of reactions of fullerenes with small C2 or C3 clusters, showing for example that energy is required for C, emission in the reaction Cgg + 13.6 eV —> C^ + C2 or, as another example, C58 + C62 2C60 + 4.6 eV, reaffirming the high stability of C60 [6.61],
The energies for fragmentation of C60 and C70 by C2 emission were also calculated [6.71], yielding C60+ 11.8 eV C5g+ C2 and C70+ 11.5 eV C68+ C2, respectively, in good agreement with the work of others [6.61,72].
In addition to these examples, molecular dynamics simulations have been widely used for the interpretation of specific experiments, such as nuclear magnetic resonance (NMR) dynamical studies [6.73], optimization of bond lengths for fullerenes [6.74,75] and carbon nanotubes, temperature dependence of bond lengths for fullerenes [6.61], the energy partition between C£0 and a diamond (111) surface upon collision [6.76], and vibrational modes of fullerenes [6.77,78], to mention a few explicit examples.
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