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Nanomaterials 2018, 8(8), 624;

Carbon Nanocones with Curvature Effects Close to the Vertex

School of Mathematical Sciences, University of Adelaide, Adelaide , SA 5005, Australia
School of Information Technology and Mathematical Sciences, University of South Australia, Adelaide, SA 5000, Australia
Author to whom correspondence should be addressed.
Received: 15 July 2018 / Revised: 7 August 2018 / Accepted: 14 August 2018 / Published: 17 August 2018
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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. View Full-Text
Keywords: carbon nanocones; geometry; curvature effects; mathematical modelling; approximate formulae carbon nanocones; geometry; curvature effects; mathematical modelling; approximate formulae

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Cox, B.J.; Hill, J.M. Carbon Nanocones with Curvature Effects Close to the Vertex. Nanomaterials 2018, 8, 624.

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