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Type: Journal article
Title: Carbon nanocones with curvature effects close to the vertex
Author: Cox, B.
Hill, J.
Citation: Nanomaterials, 2018; 8(8):624-1-624-12
Publisher: MDPI AG
Issue Date: 2018
ISSN: 2079-4991
Statement of
Barry J. Cox and James M. Hill
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.
Keywords: carbon nanocones
curvature effects
mathematical modelling
approximate formulae
Description: Published: 17 August 2018
Rights: © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
DOI: 10.3390/nano8080624
Grant ID:
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