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dc.contributor.authorCox, B.en
dc.contributor.authorHill, J.en
dc.identifier.citationNanomaterials, 2018; 8(8):624-1-624-12en
dc.descriptionPublished: 17 August 2018en
dc.description.abstractThe 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.en
dc.description.statementofresponsibilityBarry J. Cox and James M. Hillen
dc.publisherMDPI AGen
dc.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 (
dc.subjectcarbon nanocones; geometry; curvature effects; mathematical modelling; approximate formulaeen
dc.titleCarbon nanocones with curvature effects close to the vertexen
dc.typeJournal articleen
pubs.library.collectionMathematical Sciences publicationsen
dc.identifier.orcidCox, B. [0000-0002-0662-7037]en
Appears in Collections:Mathematical Sciences publications

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