MATHEMATICAL MODELLING FOR JOINING CARBON NANOSTRUCTURES: FULLERENE AND TORUS

Abstract

Dierent congurations of carbon nanostructures, includ-
ing carbon nanotori and carbon fullerenes, have been identied using
experimental techniques. These structures are used at the nanoscale in
many dierent elds, and their inclusion may lead to novel combina-
tions with improved features and applications. In this study, a carbon
fullerene and nanotorus combination was identied. Two dierent ap-
proaches that depend on energy minimization were used to predict the
conjoining curves. The primary model targets the reduction of elastic
energy focusing on axial curvature alone, but the alternative model in-
corporates the Willmore energy, that accounts both the rotational and
the axial curvatures. Due to the catenoid status as an optimal min-
imiser of this energy, a segment of it employed to facilitate the fusion
of two nanostructures. Our ndings reveal that both proposed models
successfully identify the junction area among nanostructures, allowing
for the creation of integrated nanostructures through either method.