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

TL;DR

This paper develops a continuum elastic model to explain why carbon onion shells are spherical, attributing their shape to the smoothing of pentagonal protrusions due to elastic energies.

Contribution

It introduces a novel elastic shell model for fullerenes that explains the sphericity of carbon onions by analyzing the energy of pentagonal protrusions.

Findings

Pentagonal protrusions are smoothed out in larger fullerenes.

The model predicts an upper size limit for free-standing fullerenes.

Sphericity results from elastic energy minimization.

Abstract

A continuum elastic model of fullerenes is presented by utilizing the analogy between the closed carbon cages and elastic shells. We derive expressions for the curvature related strain energies Ep of the pentagonal protrusions. We propose to explain the observed sphericity of the carbon onions shells as opposed to the predicted protrusions around the pentagonal defects on the basis of our continuum elastic model of fullerenes. In our model the energy inherent in the pentagonal protrusions Ep is due to the stretching and bending of the shell and shown to be a function of the structural parameters. It also defines the upper limit on the size of the free-standing fullerenes. Using Ep and the topological arguments, we show that the pentagonal protrusions will be smoothed out, resulting in spherical shells of the carbon onions denoted as C60@C240@C540@C960@C1500 ,... .