Chapter 2. Arc discharge Fullerene Formation Mechanism
2.3 Free energy evolution from atomic carbon to buckyball fullerene during fullerene growth
2.4.1 Collision between carbon clusters
Collisions between fullerene cages were first tested using MD simulations with NVE ensemble to guarantee the conservation of energy in collisions. It was found that the collisions between fullerene cages seldom result in reaction or coalescence. For the most reactive fullerene cage C20, the two molecules with the opposite velocity of 0.002 Å/fs could only bond to each other with two carbon-carbon bonds after collision while no further coalescence happens (Fig. 2.10a).
In experiments and our subsequent MC model, 0.002 Å/fs (200 m/s) is already a very large initial velocity that most of time molecules cannot reach. When further increasing the velocity to 0.03 Å/fs, the two C20 molecules even bounced back and left each other (Fig. 2.10b). Two C30 fullerenes with less reactivity compared to C20 fullerenes also exhibited the same behaviors where at 0.002 and 0.02 Å/fs, they could only bond to each other but no further reactions and at 0.03 Å/fs, they bounced back (Fig. 2.10c-d). For the most stable C60 IPR fullerenes, it became even harder for the molecules to react with each other. In most cases, they would just have a simple collision and change the momentum to leave each other (Fig. 2.10e, g). It was only with low momentum that the two molecules could happen to bond together but there is still no tendency for the fullerenes to merge together (Fig. 2.10f).
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Figure 2.10 DFT-MD simulations of the collisions between (a-b) C20 and C20, (c-d) C30 and C30, (e) C60
and C60, and (f-g) C20 and C60, at different initial velocities which are labeled at the bottom of each figure.
The simulations were performed with NVE ensembles which means during the simulation the total energy was fixed.
Figure 2.11 (a-d) Snapshots of the DFT-MD simulations of the collisions between C28 ring and C34 ring, where in the system the carbon density is 10 times of that in graphite. During the simulation, the temperature decreased gradually from 3000 K to 2000 K (40 steps per K) with a 1 fs time step. Totally the simulation run for 40 ps, during which at ~ 5 ps the first polygon formed.
Our simulation results showed that the collisions between fullerenes would not lead to reactions, and therefore it is not the reason for the fullerene cages to grow larger. In the second step,
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simulations of collisions between rings were tested. In Fig. 2.11, it shows the process after a C28 monocyclic ring entangled with a C34 monocyclic ring. To mimic the cooling process in experiments, during the simulation, the temperature was gradually decreased from 3000 K to 2000 K, which corresponds to our previous result that the critical transition from ring to fullerene happens at 2500 K-3000K. At 5 ps (2725 K, Fig. 2.11b), there formed the first pentagon at the crossing point of the rings which agrees with the previous CNT growth assumption of pentagon-first135. After the formation of the first pentagon, around this polygon, there emerged more hexagons and pentagons (Fig. 2.11c). A sp2 carbon network was soon formed with many dangling carbon at the edge of the network being terminated by carbon chains/rings (Fig. 2.11d). This is a very stable structure and has been observed frequently in many MD simulations for the sp2 carbon materials growth, where within the network all the carbon atoms are sp2 bonded and the other atoms all forming sp carbon chains. Thus it is concluded that collisions between rings could result in reactions, and these reactions by forming a sp2 carbon network could be regarded as the nucleation of a fullerene structure.
Figure 2.12 (a-f) Snapshots of the DFT-MD simulations of the collisions between C42 non-IPR fullerene and two chains (C10 and C9) at 3500 K with NVT ensemble. The simulation totally run for 20 ps.
In the results of the last section, we showed that, at a stage with desired temperature during fullerene formation, the transition between chain/ring and fullerene could happen when crossing a relative low barrier. So in this period, there must exist both large quantities of chains/rings and fullerenes. What will happen when the two species collide with each other?
MD simulations of the collision between chain/ring and fullerene were performed and one of the trajectories is shown in Fig. 2.12. Two very special events were observed in this simulation.
At first, a C10 chain run towards a C42 non-IPR fullerene (Fig. 2.12a). There was no contact
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between the two molecules when the chain crossed from aside (Fig. 2.12b) until the chain left one carbon atom to the fullerene before passing away (Fig. 2.12c-d). During the exchange, the fullerene obtained an additional carbon atom to be an odd-member fullerene, which is not as stable as even-member IPR or non-IPR fullerene, and as we believed will soon transform into more favorable structure. It is interesting that the collision between chain/ring and fullerene could result in the addition of one or more carbon atoms to the fullerene cage, which has been reported to be able to lower the SW barrier and therefore anneal the fullerene structure197. Later in the simulation, another C9 chain was added to the system. It also run to the fullerene and finally attached to it until the end of the simulation (Fig. 2.12e-f). The attachment is very stable as it happened at the edge of a fused pentagon pair (Fig. 2.12e). It also got the attention because the addition of a carbon chain could actually also be seen as the addition of a carbon atom and therefore could attribute to the enlargement of the fullerene.
In the fullerene synthesis, when fullerene structures begin to emerge, there are mostly fullerenes, long carbon chains, and carbon rings existing in the system. As our simulations showed that fullerenes cannot react with other fullerenes, so the further growth and annealing of the fullerenes must depend on their collisions and reactions with long carbon chains and rings. In addition, the reactions between carbon chains/rings might be the beginning or the nucleation of the transformation from chains/rings to fullerene cages.