The Torus Site


A planar graphene monolayer can be bent to a nanotube and then to a torus.


  • Types of Tori:
    • Polygonal tori
      contain also non-hexagonal rings.
      Polygonal tori can further be classified by their rotational symmetry, the length of the nanotube segments and the height along the torus axis.


The following information about specific tori corresponds to the publication
Chern Chuang, Jie Guan, David Witalka, Zhen Zhu, Bih-Yaw Jin, and David Tománek,
"Relative Stability and Local Curvature Analysis in Carbon Nanotori", Phys. Rev. B 91,165433 (2015).

The curvature energy is an estimate of the formation energy of the particular isomer with respect to graphite. This estimate, provided by Chern Chuang, Jie Guan and David Witalka, is based on the local curvature.

  • Polygonal Tori:
    Rotational Symmetry Series
 n is the rotational symmetry index
Family 1

n=4
n=5
n=6
n=7
n=8
n=9
n=10
n=11
n=12
n=13

Family 2

n=4
n=5
n=6
n=7
n=8
n=9
n=10
n=11
n=12
n=13



  • Polygonal Tori:
    Nanotube Segment Length Series
 L is the nanotube segment length index

L1
L2
L3
L4
L5
L6
L7
L8

L9
L10
L11
L12
L13
L14
L15 		 



  • Polygonal Tori:
    Torus Height Series
 H is the height index

H1
H2
H3
H4
H5
H6
H7
H8

H9
H10
H11
H12
H13
H14
H15 		 

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The web resource at http://www.nanotube.msu.edu/torus/ has been provided by David Tomanek and David Witalka at the Michigan State University Computational Nanotechnology Lab. It is linked to the Supplementary Information provided with the monograph Guide through the Nanocarbon Jungle: Buckyballs, Nanotubes, Graphene, and Beyond.

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Last update:   2020.07.24 (Friday) 10:07:12 EDT.
Web page constructed and maintained by David Witalka.