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.