Energy-Minimization Models for Hybrid Carbon Nanotori Production

The merging of carbon nanostructures has been extensively studied due to their outstanding properties. However, prior research neglected the rotational curvature through merging process, consequently restricting their advantages in the production of complex hybrid nanostructures in three-dimensional (3D). This paper addresses a novel energy minimization approach that includes the effects of the axial and rotational curvatures to model the hybrid carbon nanotori (CNTRs), providing a more complete foundation for the formation of stable CNTRs structures with different radii and curvature features. Two methodologies in energy minimization were used, namely elastic energy for 2D merging and the Willmore energy approach for 3D merging. The results confirm that both models in two-dimensional (2D) and 3D scenarios produce efficient and smooth joining curves. First model produces a minimum mean curvature around 0.15 and a total bending energy reduction of 18% which supports the stability of the configuration at the joining. While the second model uses zero mean curvature for the join. Moreover, the rotational curvature implication enhancing stability throughout the 3D connection process. By addressing the limitations of prior studies, this study develops an effective framework in production of stable hybrid nanostructures for future applications.