Carbon Nanocones with Curvature Effects Close to the Vertex.

Barry Cox,James Hill

doi:10.3390/nano8080624

Abstract

The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing curvature, and all bond lengths and bond angles are assumed to be those for the planar graphene sheet. Clearly, curvature effects will become more important closest to the cone vertex, and especially so for the cones with the smaller apex angles. Here, we construct carbon nanocones which, in the assembled cone, are assumed to comprise bond lengths and bond angles that are, as far as possible, equal throughout the structure at the same distance from the conical apex. The predicted bond angles and bond lengths are shown to agree well with those obtained by relaxing the conventional rolled-up model using Lammps software (version: 11 September 2008). The major objective here is not simply to model physically realisable carbon nanocones for which numerical procedures are far superior, but rather, to produce an improved model that takes curvature effects close to the vertex into account, and from which we may determine an analytical formula which represents an improvement on the conventional rolled-up model.

Highlights

Conventional models for carbon nanocones propose a construction comprising a sheet of graphene with a section removed which is rolled and joined seamlessly to form a conical nanostructure [1]
The present authors proposed a polyhedral model [3,4] which properly incorporates a hexagonal framework in which the bond angles and bond lengths are all assumed to be identical in the cylindrical configuration, and by necessity, the sum of the bond angles is less than 360°
We propose a corresponding model for carbon nanocones, but in this case, it is not possible to produce a completely analogous model, since the present structure does not have precise equality of all bond lengths and bond angles since the curvature changes along the length of the nanocone and so too, does the angle sum of the three bond angles at each carbon atom

Summary

Introduction

Conventional models for carbon nanocones propose a construction comprising a sheet of graphene with a section removed which is rolled and joined seamlessly to form a conical nanostructure [1]. The conventional models for both carbon nanotubes and nanocones assume that they comprise rolled-up graphene sheets that are joined seamlessly to form complete structures, and any effects arising from the changing curvature and bond bending and distortion are completely ignored. The present authors proposed a polyhedral model [3,4] which properly incorporates a hexagonal framework in which the bond angles and bond lengths are all assumed to be identical in the cylindrical configuration, and by necessity, the sum of the bond angles is less than 360°. It is not expected that every point in the graphene lattice will be exactly congruent with all others

Methods

Results

Conclusion