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Type: Journal article
Title: Determination of join regions between carbon nanostructures using variational calculus
Author: Baowan, D.
Cox, B.
Hill, J.
Citation: Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2013; 54(4):221-247
Publisher: Australian Mathematical Society
Issue Date: 2013
ISSN: 1446-1811
Statement of
D. Baowan, B. J. Cox And J. M. Hill
Abstract: We review the work of the present authors to employ variational calculus to formulate continuous models for the connections between various carbon nanostructures. In formulating such a variational principle, there is some evidence that carbon nanotubes deform as in perfect elasticity, and rather like the elastica, and therefore we seek to minimize the elastic energy. The calculus of variations is utilized to minimize the curvature subject to a length constraint, to obtain an Euler–Lagrange equation, which determines the connection between two carbon nanostructures. Moreover, a numerical solution is proposed to determine the geometric parameters for the connected structures. Throughout this review, we assume that the defects on the nanostructures are axially symmetric and that the into-the-plane curvature is small in comparison to that in the two-dimensional plane, so that the problems can be considered in the two-dimensional plane. Since the curvature can be both positive and negative, depending on the gap between the two nanostructures, two distinct cases are examined, which are subsequently shown to smoothly connect to each other.
Keywords: variational calculus
carbon nanotubes
C60 fullerenes
Rights: © Australian Mathematical Society 2013
DOI: 10.1017/S1446181113000217
Grant ID: ARC
Appears in Collections:Aurora harvest 4
Mathematical Sciences publications

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