Energies of sp2 carbon shapes with pentagonal disclinations and elasticity theory

TL;DR

This paper combines numerical calculations and elasticity theory to analyze the energies of various sp2 carbon shapes with pentagonal disclinations, providing analytical expressions and confirming elasticity theory's effectiveness.

Contribution

It introduces a method to interpret fullerene energies using elasticity theory and derives analytical formulas validated by numerical results.

Findings

Elasticity theory accurately predicts fullerene energies.

Derived analytical expressions match numerical calculations.

Elasticity approach simplifies understanding of complex carbon structures.

Abstract

Energies of a certain class of fullerene molecules (elongated, contracted, and regular icosahedral fullerenes) are numerically calculated using a microscopic description of carbon-carbon bonding. It is shown how these results can be interpreted and comprehended using the theory of elasticity that describes bending of a graphene plane. Detailed studies of a wide variety of structures constructed by application of the same general principle are performed, and analytical expressions for energies of such structures are derived. Comparison of numerical results with the predictions of a simple implementation of elasticity theory confirms the usefulness of the latter approach.