# A Review of Geometry, Construction and Modelling for Carbon Nanotori

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Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

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School of Information Technology & Mathematical Sciences, University of South Australia, Mawson Lakes, SA 5006, Australia

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Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand

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Author to whom correspondence should be addressed.

Received: 3 April 2019 / Revised: 8 May 2019 / Accepted: 28 May 2019 / Published: 4 June 2019

(This article belongs to the Section Nanotechnology and Applied Nanosciences)

After the discovery of circular formations of single walled carbon nanotubes called fullerene crop circles, their structure has become one of the most researched amongst carbon nanostructures due to their particular interesting physical properties. Several experiments and simulations have been conducted to understand these intriguing objects, including their formation and their hidden characteristics. It is scientifically conceivable that these crop circles, nowadays referred to as carbon nanotori, can be formed by experimentally bending carbon nanotubes into ring shaped structures or by connecting several sections of carbon nanotubes. Toroidal carbon nanotubes are likely to have many applications, especially in electricity and magnetism. In this review, geometry, construction, modelling and possible applications are discussed and the existing known analytical expressions, as obtained from the Lennard-Jones potential and the continuum approximation, for their interaction energies with other nanostructures are summarised.