Relative stability and local curvature analysis in carbon nanotori

Abstract

We introduce a concise formalism to characterize nanometer-sized tori based on carbon nanotubes and to determine their stability by combining ab initio density functional calculations with a continuum elasticity theory approach that requires only shape information. We find that the high strain energy in nanotori containing only hexagonal rings is significantly reduced in nanotori containing also other polygons. Our approach allows to determine local curvature and link it to local strain energy, which is correlated with local stability and chemical reactivity.

Long-wavelength deformations and vibrational modes in empty and liquid-filled microtubules and nanotubes: A theoretical study

“…The reason is that the wall of the nanotube undergoes stretching along the outer and compression along the inner torus perimeter in this process. This amounts to a total in-plane strain energy [28]…”

A Simple Model for Relative Energies of All Fullerenes Reveals the Interplay between Intrinsic Resonance and Structural Deformation Effects in Medium-Sized Fullerenes

“…This detail will be relevant to our later discussion. From a practical point of view, we also note that this model for E D is demonstrated to be applicable to finite systems such as fullerenes and nanotubes, yielding reasonable deformation energies for these systems. , …”

“…With decades of scientific research into fullerenes, it comes as no surprise that such a desirable model has been attempted before, with IPR itself being one of the earliest. Models based on the motifs − and local curvatures , of fullerenes have been proposed; related isodesmic-type reactions have been explored; correlations between topological indicators and relative isomer energies have also been examined . These previously proposed models appear to be useful for the systems for which they are designed, but it is less clear how well they will perform for fullerenes outside of their intended range.…”

Simulation of the Behavior of Carbon Nanotori during Unfolding: A Study of Stability and Electronic Structure

“…The object of this study was carbon nanotorus (10,6) with the diameter of 20 nm and thickness of 1 nm. This torus was obtained as a result of defectless folding of chiral nanotube with corresponding geometry sizes into ring.…”

“…At present, there is no universal approach to numerically estimate the stability of toroidal carbon nanostructures. For example, Chuang et al [10], proposed to estimate the stability of carbon nanotori by two criteria: two types of curvature (the local mean curvature and the local Gaussian curvature) and curvature energy distribution. At the same time, each of the curvature parameters should be chosen on the basis of torus geometry characteristics, and the extremal values of the curvature energy do not always coincide with the extremal values of the Gaussian curvature.…”