QM(DFT) and MD studies on formation mechanisms of C 60 fullerenes (original) (raw)
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Molecular Simulations Of The Formation Process Of Fullerene
The formation mechanism of fullerene, a new type of carbon molecule with hollow caged structure, was studied by using the molecular dynamics method with the simplified classical potential function. The clustering process starting from isolated carbon atoms was simulated under controlled temperature condition. Here, translational, rotational and vibrational temperatures of each cluster were controlled to be in equilibrium. The structures of clusters which were obtained after enough calculation depended on the controlled temperature T c , yielding the graphitic sheet for T c < 2600 K, fullerene-like caged structure for 2600 K < T c < 3500 K, and chaotic 3-dimensional structure for T c > 3500 K. Through the detailed trace of precursors, it was revealed that the key feature of the formation of the caged structure was the chaotic 3-dimensional cluster of 40 to 50 atoms which had large vibrational energy. In addition, when the precursors were kept under lower vibrational energy, the successive growth of 2-dimensional graphitic structure was observed. Since the time scale of the simulation was compressed, the annealing process of each cluster was virtually omitted. In order to examine this effect, an imperfect C 60 obtained from the similar simulation was annealed at 2500 K for 50 ns without collisions. The perfect Buckminsterfullerene C 60 was finally obtained after successive Stone-Wales transformations.
The Journal of Chemical Physics, 2000
The ring-collapse mechanism that suggests the reactions among the mono-to polycyclic carbon clusters has been analyzed using semiempirical AM1 and HF/6-31G* methods. The two cage structures D 2 ͑chiral͒ and T d ͑achiral͒ for the C 28 clusters are considered. Basing on the ring-stacking/circumscribing model and the ring-collapse mechanism various precursors are selected along with some appropriate carbon belts. Reactions between the precursors and the belts are found to be endoergic and lead to stable intermediates. All these stacking processes follow gradual and sequential paths. Various possible transition states structures ͑TSs͒ have been located and the barrier heights are found to be well within the earlier prescribed limits. Further, stacking the stable intermediates by suitable carbon belts generate the desired cage structures. The second step of the stacking resembles the annealing mechanism for the formation of the cage structures that is essentially an exoergic process. In this annealing process cascade-type bond formation is visualized. Finally, basing on the deformation energies of the precursors and the barrier heights, it is observed that monocyclic precursors are more suitable for the fullerene growth mechanism.
Molecular dynamics simulation of carbon nanostructures: The D5h C70 fullerene
Physica E: Low-dimensional Systems and Nanostructures, 2014
Molecular dynamics calculations can reveal the physical and chemical properties of various carbon nanostructures or can help to devise the possible formation pathways. In our days the most well known carbon nanostructures are the fullerenes and the nanotubes. They can be thought of as being formed from graphene sheets, i.e. single layers of carbon atoms arranged in a honeycomb lattice. Usually the nature does not follow the mathematical constructions. An ideal nanotube can be thought of as a hexagonal network of carbon atoms that has been rolled up to make a cylinder. There is not any theory of carbon nanotube formation which is based on this construction. Although the first time the C 60 and C 70 were constructed by laser irradiated graphite, the fullerene formation theories are based on various fragments of carbon chains, and networks of pentagonal and hexagonal rings. In the present article different initial patterns will be given for the formation of the C 70 fullerene with D 5h symmetry. The desired final structures are obtained in tight-binding molecular dynamics calculations.
Modelling of C 2 addition route to the formation of C 60
Nanotechnology, 2006
To understand the phenomenon of fullerene growth during its synthesis, an attempt is made to model a minimum energy growth route using a semi-empirical quantum mechanics code. C 2 addition leading to C 60 was modelled and three main routes, i.e. cyclic ring growth, pentagon and fullerene road, were studied. The growth starts with linear chains and, at n = 10, ring structures begins to dominate. The rings continue to grow and, at some point n > 30, they transform into close-cage fullerenes and the growth is shown to progress by the fullerene road until C 60 is formed. The computer simulations predict a transition from a C 38 ring to fullerene. Other growth mechanisms could also occur in the energetic environment commonly encountered in fullerene synthesis, but our purpose was to identify a minimal energy route which is the most probable structure. Our results also indicate that, at n = 20, the corannulene structure is energetically more stable than the corresponding fullerene and graphene sheet, however a ring structure has lower energy among all the structures up to n 40. Additionally, we have also proved that the fullerene road is energetically more favoured than the pentagon road. The overall growth leading to cage closure for n = 60 may not occur by a single route but by a combination of more than one route.
ACS Nano, 2009
Using density-functional tight-binding (DFTB)-based quantum chemical molecular dynamics at 2500 and 3000 K, we have performed simulations of benzene combustion by gradually reducing the hydrogen to carbon (H/C) ratio. The accuracy of DFTB for these simulations was found to be on the order of 7؊9 kcal/mol when compared to higher-level B3LYP and G3-like quantum chemical methods in extensive benchmark calculations. Ninety direct-dynamics trajectories were run for up to 225 ps simulation time, during which hydrocarbon cluster size, curvature, and C x H y composition, carbon hybridization type, and ring count statistics were recorded. Giant fullerene cage formation was observed only after hydrogen was completely eliminated from the reaction mixture, with yields of around 50% at 2500 K and 42% at 3000 K. Cage sizes are mostly in the range from 152 to 202 carbon atoms, with the distribution shifting toward larger cages at lower temperature. In contrast to previous simulations of dynamics fullerene assembly from ensembles of C 2 molecules, we find that the resulting cages show smaller number of attached carbon chains (antenna) surviving until cage closure. Again, no direct formation pathway for C 60 from smaller fragments was observed. Our results challenge the idealized picture of "ordered" growth of PAHs along a route involving only maximally condensed and fully hydrogenated graphene platelets, and favor instead fleeting open-chains with ring structures attached, featuring a large number of hydrogen defects, pentagons, and other nonhexagon ring species.
Simulating the structural diversity of carbon clusters across the planar-to-fullerene transition
Physical Review A
Together with the second generation REBO reactive potential, replica-exchange molecular dynamics simulations coupled with systematic quenching were used to generate a broad set of isomers for neutral C n clusters with n = 24, 42, and 60. All the minima were sorted in energy and analyzed using order parameters to monitor the evolution of their structural and chemical properties. The structural diversity measured by the fluctuations in these various indicators is found to increase significantly with energy, the number of carbon rings, especially 6-membered, exhibiting a monotonic decrease in favor of low-coordinated chains and branched structures. A systematic statistical analysis between the various parameters indicates that energetic stability is mainly driven by the amount of sp 2 hybridization, more than any geometrical parameter. The astrophysical relevance of these results is discussed in the light of the recent detection of C 60 and C + 60 fullerenes in the interstellar medium.
Microscopic mechanism of fullerene fusion
Physical Review B, 2004
Combining total energy calculations with a search of phase space, we investigate the microscopic fusion mechanism of C 60 fullerenes. We find that the ͑2+2͒ cycloaddition reaction, a necessary precursor for fullerene fusion, may be accelerated inside a nanotube. Fusion occurs along the minimum energy path as a finite sequence of Stone-Wales transformations, determined by a graphical search program. Search of the phase space using the "string method" indicates that Stone-Wales transformations are multistep processes, and provides detailed information about the transition states and activation barriers associated with fusion.
Increasing Stability of the Fullerenes with the Number of Carbon Atoms: The Experimental Evidence
The Journal of Physical Chemistry B, 2007
The values of the molar standard enthalpies of formation, ∆ f H m (C 76 , cr)) (2705.6 (37.7) kJ‚mol-1 , ∆ f H m (C 78 , cr)) (2766.5 (36.7) kJ‚mol-1 , and ∆ f H m (C 84 , cr)) (2826.6 (42.6) kJ‚mol-1 , were determined from the energies of combustion, measured by microcombustion calorimetry on a high-purity sample of the D 2 isomer of fullerene C 76 , as well as on a mixture of the two most abundant constitutional isomers of C 78 (C 2V-C 78 and D 3-C 78) and C 84 (D 2-C 84 , and D 2d-C 84). These values, combined with the published data on the enthalpies of sublimation of each cluster, lead to the gas-phase enthalpies of formation, ∆ f H m (C 76 , g)) (2911.6 (37.9) kJ‚mol-1 ; ∆ f H m (C 78 , g)) (2979.3 (37.2) kJ‚mol-1 , and ∆ f H m (C 84 , g)) (3051.6 (43.0) kJ‚mol-1 , results that were found to compare well with those reported from density functional theory calculations. Values of enthalpies of atomization, strain energies, and the average CC bond energy were also derived for each fullerene. A decreasing trend in the gas-phase enthalpy of formation and strain energy per carbon atom as the size of the cluster increases is found. This is the first experimental evidence that these fullerenes become more stable as they become larger. The derived experimental average CC bond energy E CC) 461.04 kJ‚mol-1 for fullerenes is close to the average bond energy E CC) 462.8 kJ‚mol-1 for polycyclic aromatic hydrocarbons (PAHs).
To understand the phenomenon of fullerene growth during its synthesis, an attempt is made to model a minimum energy growth route using a semi-empirical quantum mechanics code. C 2 addition leading to C 60 was modelled and three main routes, i.e. cyclic ring growth, pentagon and fullerene road, were studied. The growth starts with linear chains and, at n = 10, ring structures begins to dominate. The rings continue to grow and, at some point n > 30, they transform into close-cage fullerenes and the growth is shown to progress by the fullerene road until C 60 is formed. The computer simulations predict a transition from a C 38 ring to fullerene. Other growth mechanisms could also occur in the energetic environment commonly encountered in fullerene synthesis, but our purpose was to identify a minimal energy route which is the most probable structure. Our results also indicate that, at n = 20, the corannulene structure is energetically more stable than the corresponding fullerene and graphene sheet, however a ring structure has lower energy among all the structures up to n 40. Additionally, we have also proved that the fullerene road is energetically more favoured than the pentagon road. The overall growth leading to cage closure for n = 60 may not occur by a single route but by a combination of more than one route.