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Modeling of carbon onions

Carbon onions
Since the discovery of fullerene molecules and subsequent carbon nanotubes, carbon nanomaterials with curved surface have gained great interests because of their novel mechanical and electronic properties. Carbon onions, which consist of concentric spherical graphitic sheets, are one important member of the fullerene family.
Consisting of concentric fullerene-like structures, carbon onions can be formed in a variety of harsh environments such as high energy electron irradiation of a carbon precursor, thermal annealing of diamond nanoparticles, carbon ion implantation, and arc discharge from a carbon target in water.
Onions like structures have also been observed in soot and interstellar dust. In each case, the formation of onions involves high-temperature heating of carbon precursors, but the nucleation mechanism and range of possible microstructures are poorly understood.
The formation mechanism of carbon onions has remained a mystery, several conceptual models have been proposed for how the onions nucleate and form a three-dimensional structure.
Shrinking hot giant model
Simulations have proven highly successful in understanding the formation mechanism of fullerenes, which nucleate by the shrinking hot giant model, whereby a cluster of atoms form large, closed, caged structures by the aggregation of atoms before shedding chains of sp-bonded atoms to form smaller, energetically favorable, fullerene structures. Multi walled carbon onions can be formed from a variety of precursors including amorphous carbon and nano diamond, but the key factors which control the carbon onion microstructure are temperature and annealing time.
Continuum model
Todt and others of Vienna University of Technology, Austria have made a Continuum modeling of Van der Waals interactions between carbon onion layers by deriving relations analytically considering the doubly-curved geometry of carbon onion layers. They report that the Van der Waals induced pressures on opposing faces of two adjacent onion layers are not equal and depend on radii of both layers. The curvature effects have no significant influence on the equilibrium interlayer distances, but they significantly change the results for the radial displacements and, consequently, for the membrane forces in the layers. They did Monte Carlo simulations of C60 in C180 and C60 in C240 and concluded that the derived van der Waals model represents the radial displacements and equilibrium interlayer distances better than the simplified models.

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