Chapter 2. Arc discharge Fullerene Formation Mechanism
2.3 Free energy evolution from atomic carbon to buckyball fullerene during fullerene growth
2.4.3 Fullerene decomposition at high temperature
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Figure 2.18 DFT-MD simulation of the decomposition of a C30 fullerene at 5000 K with a time step of 0.5 fs. The simulation run for 16.8 ps and the originally perfect C30 fullerene finally decomposed into carbon chains. Left axis denotes the MD energy (grey line), and the black line is the smoothed line of the MD energy showing the energy tendency. Right axis (red dots) represents the energy of the DFT optimized intermediate structures, where some representatives of the optimized structures are shown with the label of their step number.
The figure clearly shows the decomposition process. Through the early bond rotation and breaking, there formed one or two large holes in the fullerene. With the increasing of the hole size, the fullerene cage structure changed to a basket (configuration at step 13800) -- a bowl structure with a handle. Later with the further increase of energy, the curved bowl became smaller and gradually flattened to be a simple sp2 network but still with a handle (configuration at step 15000). After more polygons merging into large rings or some dangling carbon chains, a bicyclic ring with a square in the center and two dangling carbon chains formed and was with the highest energy among all the configurations. When the bicyclic ring transformed into a big monocyclic ring (with a carbon chain attached), the energy decreased to the lowest, and further increased when the ring decomposed into chains.
The process corresponds to our previous free energy calculation that during the transition from monocyclic ring to fullerene, both monocyclic ring and fullerene are in the local energy minimum, and the transition need to cross a barrier. Here with the simulation result, if we take the decomposition process as the reversed formation, we could identify the transition barrier from ring to fullerene to be 4.33 eV, where the transition structure is a bicyclic ring with a square in the center and two dangling carbon chains. This process agrees quite well with Goddard’s ring fusion spiral zipper model in which they claimed that the formation of the fullerene started from the merging of two monocyclic rings201. In our simulation, at high temperature, as the kinetic energy quickly transformed into the energy of the configuration, the cluster evolution could not go exactly along the MEP, i.e. forming exactly a bicyclic ring without dangling carbon chains as transition state. But it is already very close to that, and the resulting transition barrier should be very similar to the real one. Most importantly, our simulation, if see inversely, showed the process how the ring weaving into a fullerene: it first wove into a bowl with a handle, and then gradually closed the open edge with the weaving of the handle.
Currently, the energy barrier is from the 0 K energies of the configurations by DFT calculations.
We further considered the temperature effect on this transition barrier using previously introduced “Thermo” code to calculate the free energy barrier. The result is shown in Fig. 2.19.
It was found that with the increase of the temperature, the transition barrier increases and the
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transition structure would also change from initial bicyclic ring to polycyclic ring. This also agrees with our previous calculation of the free energy evolution of the carbon clusters that with the decrease of the temperature during the fullerene formation, the barrier will decrease.
Figure 2.19 Free energy plot of the decomposition path of C30 fullerene using the data of a dozen of critical structures.
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Figure 2.20 Energy evolutions of the 15 decomposition trajectories of (a) C30, (b) C50, and (c) C60
fullerene at 5000 K using DFTB-MD with a time step of 0.5 fs. The grey lines represent the original energy fluctuation while the bold colored lines are the corresponding smoothed energy lines showing the energy tendencies.
The DFT-MD simulations are very time and resource consuming, and are only applicable for small systems. To have more trajectories and to simulate the decomposition of larger fullerenes, we performed 15 DFTB-MD simulations for each of the C30, C50, C60 fullerenes at 5000 K. The MD energy fluctuations (grey lines) are shown in Fig. 2.20a, b, and c for C30, C50, and C60
fullerenes respectively, where the corresponding smoothed energy lines in bold color are denoted to clearly show the energy tendencies. It was found that most of the C30 decompositions could happen at the beginning of the simulations, several of the C50 decompositions took longer time to start, and the decompositions of C60 fullerenes would take longer and longer time. This agrees with the stabilities of the three kinds of fullerenes as C60 is the most stable and therefore takes longer time to decompose while C30 is the most reactive and can decompose very soon.
Figure 2.21 Analysis of one DFTB-MD trajectory for C60 decomposition. The purple line is the smoothed MD energy of the trajectory. The representative structures shown in the figure are optimized using DFT calculation with their step number labeled.
The decomposition procedures of fullerenes in DFTB-MD simulations are very similar to that in DFT-MD simulation. Here we introduced one trajectory of the C60 decompositions with a steady intermediate stage as shown in Fig. 2.21. The decomposition of C60 also started with the bond rotation, and it changed the IPR fullerene into a non-IPR fullerene first during step 1430 to step 1690. Later it evolved to a large basket (step 8880) which was then healed to a defective
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but complete fullerene cage (step 18750) and the open edge closed. This resulted in a relative steady stage, and the decomposition suspended. It was until step 4000 the decomposition restarted and formed the basket structure (step 42990) again. The basket then opened wider up, and became a large bowl with dangling carbon chains. At last we found a carbon chain network with a pentagon at the center, reminding us of the pentagon-first theory again.
The atomic simulations provide us more insight into the fullerene formation process. During the synthesis, it is hard to observe reactions between fullerenes, while the collisions between rings could result into the transformation of fullerenes from rings, and the collisions between rings/chains and fullerenes could help transfer carbon atoms from rings/chains to fullerenes and contribute to the growth and annealing of the fullerenes. Especially the transition from non-IPR fullerene to IPR fullerene could be realized with the help of the carbon chains/rings. In addition, through the MD simulation of the fullerene decomposition process, the reversed process, fullerene formation, was studied. A formation barrier of 4.33 eV was identified from the initial local-minimum-energy structure--carbon monocyclic ring, to the transition state structure-- bicyclic ring, and finally to the final structure--fullerene. The transition from carbon ring to fullerene was also observed where intermediate—basket and bowl-like structures were formed.