Chapter 2. Arc discharge Fullerene Formation Mechanism
2.3 Free energy evolution from atomic carbon to buckyball fullerene during fullerene growth
2.4.2 Transformation between non-IPR and IPR fullerenes
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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.
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Figure 2.13 (a) MEP for the SW transition in C60 fullerene with the optimized atomic structures of the initial non-IPR C60 fullerene, the transition state, and the final IPR C60 fullerene. (b) Evolution of the free energy barrier and reaction free energy of the transition from non-IPR C60 to IPR C60 fullerene with the increase of temperature.
Therefore, according to our atomic simulation result of the collision between carbon chain and fullerene (Section 2.4.1), we proposed another potential route for the SW transition from non- IPR fullerene to IPR fullerene. In the first step, we consider the collision between a non-IPR C60 fullerene with a C9 chain. During the collision, the carbon atom at the end of the chain will be passed to the SW site of the fullerene to be a dangling carbon and the carbon chain will leave with the loss of a single carbon atom (Fig. 2.14a). This reaction is with a very high reaction energy of 3.46 eV, and therefore we take it to be very similar to the reaction barrier (no additional barrier because the reaction involves only the straight break of a carbon-carbon bond at the end of the chain). Thus, with such a moderate barrier, the reaction could happen at high temperature and with a kinetic energy conversion from collision, which was also demonstrated by our MD simulation.
In the second step, the non-IPR to IPR transition takes place with the assistance of the dangling carbon from the chain with a reaction energy of -1.2 eV and an energy barrier of 1.47 eV (Fig.
2.14b and d). For such a barrier, the reaction could easily happen at experimental conditions.
To be noted, even when the dangling carbon was added to a random position, through diffusion the dangling carbon could still move to the SW site, and the reaction could still happen, since the diffusion barrier of the additional carbon on a non-IPR C60 fullerene is only 0.9 eV.
Once the IPR C60 fullerene is formed, we take away the additional dangling carbon by its collision with another C8 chain (Fig. 2.14c). So after three steps, the only change is the transition of the fullerene structure. The carbon chain can be regarded as a catalyst, and its participation help reduce the transition barrier.
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Figure 2.14 Potential transition path from non-IPR to IPR C60 fullerene with the help of an additional carbon atom from a C9 chain. The path consists of three reaction steps: (a) addition of a carbon atom from a C9 chain to non-IPR C60 fullerene; (b) transition from non-IPR to IPR C60 fullerene with the additional carbon; (c) leaving of the additional carbon from the IPR C60 fullerene to a C8 carbon chain.
(d) MEP of the transition from non-IPR to IPR C60 fullerene with the help of the additional carbon, and the initial, transition, and final atomic structures.
There are also reports arguing about the direct addition of a dangling carbon to the non-IPR fullerene for the reduction of the SW transition barrier197. We have also researched on this. The addition of a single carbon atom to the non-IPR fullerene would greatly reduce the reaction energy of the first step (Fig. 2.15a). However, at the third step, the releasing of a single carbon atom to the system is with a very high energy penalty (Fig. 2.15c). More importantly, according to the free energy calculations shown before, in experimental conditions, when the fullerene structures start to form at around 3000 K, there is very little chance for atomic carbon to exist.
Therefore, we believe this transition path with the direct addition of atomic carbon is not possible.
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Figure 2.15 Potential transition path from non-IPR to IPR C60 fullerene with the help of an additional carbon atom. The path consists of three reaction steps: (a) addition of a carbon atom to non-IPR C60
fullerene; (b) transition from non-IPR to IPR C60 fullerene with the dangling carbon; (c) leaving of the additional carbon from the IPR C60 fullerene.
The second event happened in the MD simulation where a carbon chain could attach to a fullerene for a relative long time period also reminded us a second possible route for the easy SW transition. As shown in Fig. 2.16, we considered the route that the SW transition happens with the assistance of a carbon chain attached to the fullerene like a tail. In the first step, a C9
carbon chain collided with a non-IPR C60 fullerene (Fig. 2.16a). After the collision, the chain was attached to the fullerene with a -2.53 eV reaction energy. With a direct formation of carbon- carbon bond, the reaction is therefore with no energy barrier, and the reaction could happen easily, as also demonstrated by our MD simulation before.
In the second step, the non-IPR fullerene was transformed into an IPR fullerene with the help of the carbon chain (Fig. 2.16b). Technically, the calculation of the transition barrier for this reaction is not easy. We could not get the converged result using VASP version NEB calculation.
Thus based on the NEB calculation, we further optimized the transition state using Gaussian with the same DFT-PBE method. The barrier and the transition state were finally obtained (Fig.
2.16d). The barrier is 3.61 eV, higher than that of the first route we proposed, but already reduced a lot compared with the conventional SW transition barrier.
The last step of this path is just the releasing of the carbon chain after the annealing of the non- IPR fullerene to IPR fullerene (Fig. 2.16c). The reaction energy is 2.23 eV. Because this reaction is simple with only the break of a carbon-carbon bond, no additional barrier is considered and therefore the reaction barrier is 2.23 eV, which is easy to overcome at the growth condition.
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Figure 2.16 Potential transition path from non-IPR to IPR C60 fullerene with the help of an additional C9
carbon chain. The path consists of three reaction steps: (a) addition of a C9 chain to non-IPR C60 fullerene;
(b) transition from non-IPR to IPR C60 fullerene with the additional carbon chain; (c) leaving of the additional carbon chain from the IPR C60 fullerene. (d) MEP of the transition from non-IPR to IPR C60
fullerene with the help of the additional carbon chain, and the initial, transition, and final atomic structures. The NEB calculations of the SW transition with additional carbon chain using VASP were not able to converge (DFT1 and DFT2). So the final transition state was obtained with Gaussian’s optimization (Opt-TS3) also using DFT-PBE method.
Comparing the two newly proposed SW transition routes and the conventional one, both of the new routes greatly reduce the energy barrier (Fig. 2.17a-d). If only consider the transition step (Fig. 2.17a), the route with the additional dangling carbon is more favorable since the barrier (1.47 eV) is lower than that with the additional carbon chain (3.61 eV). However, taking all the three steps into consideration including the addition of the adatom/ad-chain and the releasing of the adatom/ad-chain (Fig. 2.17e), it is obvious that the reaction path with the additional chain (red) is the real MEP.
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Therefore, we propose a reasonable route for the annealing and formation of fullerene by the collision between fullerene and carbon chain/ring. The addition of the carbon chain/ring could be regarded as the same as the addition of a dangling carbon which could reduce the SW transition barrier. In addition, the collisions could also lead to the growth of fullerene by addition of carbon atoms from carbon chains/rings.
Figure 2.17 (a) Comparison of the MEPs for the SW transition by (b) conventional rotation of carbon- carbon bond (black), (c) with the addition of a carbon chain (red), and (d) with the addition of a dangling carbon (blue). (e) Energy profile for the two SW transition paths with additional dangling carbon (black) and with additional carbon chain (red).
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