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A continuum elastic model of fullerenes is presented by utilizing the analogybetween the closed carbon cages and elastic shells. We derive expressions forthe curvature related strain energies Ep of the pentagonal protrusions. Wepropose to explain the observed sphericity of the carbon onions shells asopposed to the predicted protrusions around the pentagonal defects on the basisof our continuum elastic model of fullerenes. In our model the energy inherentin the pentagonal protrusions Ep is due to the stretching and bending of theshell and shown to be a function of the structural parameters. It also definesthe upper limit on the size of the free-standing fullerenes. Using Ep and thetopological arguments, we show that the pentagonal protrusions will be smoothedout, resulting in spherical shells of the carbon onions denoted asC60@C240@C540@C960@C1500 ,... .

Continuum elastic model of fullerenes and the sphericity of the carbon onion shells