Shapes and energies of icosahedral fullerenes: Onset of ridge sharpening transition

TL;DR

This paper investigates the shape and energy transitions of icosahedral fullerenes, identifying size-dependent regimes and a shape transition in large fullerenes, supported by atomistic simulations and elastic theory.

Contribution

It provides a detailed atomistic and elastic theory analysis of fullerene shape regimes and confirms the shape transition in very large fullerenes, extending previous elastic predictions.

Findings

Three distinct shape regimes identified based on size.

Shape transition occurs in fullerenes larger than about 500,000 atoms.

Quantum effects may influence the shape transition, but it persists under various conditions.

Abstract

Shapes and energies of icosahedral fullerenes are studied on an atomically detailed level. The numerical results based on the effective binary carbon-carbon potential are related to the theory of elasticity of crystalline membranes with disclinations. Depending on fullerene size, three regimes are clearly identified, each of them characterized by different geometrical properties of the fullerene shape. For extremely large fullerenes (more than about 500000 atoms), transition of fullerene shapes to their asymptotic limit is detected, in agreement with previous predictions based on generic elastic description of icosahedral shells. Quantum effects related to delocalized electrons on the fullerene surface are discussed and a simple model introduced to study such effects suggests that the transition survives even in more general circumstances.