Experimental investigations of carbon nanotubes have revealed that they can collapse into nanoribbons that have a dumb-bell shape cross-section. Due to the extreme exibility of single-atom thick graphene sheets, if the tube is large enough self-induced Van der Waals forces acting on the at surfaces of the ribbon will be large enough to hold the nanotube in the collapsed (ribbon) configuration. Energetically, the additional strain (bending) energy stored in the collapsed state is offset by the decrease in energy of the Van der Waals interactions. Because Van der Waals forces are short ranged, one nds that tubes of great enough diameter are bistable. Here we investigate the natural of this bistability by investigating how the energy stored in the tube changes as it is compressed by at rigid indenters of various widths. The nanotube is assumed to deform uniformly along its length and the cross-section is modeled using inextensible, non-linear beam theory (Euler’s Elastica). We nd that the in ated (tube) conguration is always stable but that the energy barrier against decreases with increasing tube radius. Additionally, the energy difference between the in ated and collapsed states decreases nearly linear with increasing radius and for tubes with radius greater than 26 A the collapsed state is energetically favored.

1.
Chopra
N.
,
Benedict
L.
,
Crespi
V.
,
Cohen
M.
,
Louie
S.
, and
Zettl
A.
,
1995
. “
Fully collapsed carbon nanotubes
.”
Nature
,
377
, p.
135
135
.
2.
Chopra
N.
,
Ross
F.
, and
Zettl
A.
,
1996
. “
Collapsing carbon nanotubes with an electron beam
.”
Chemical Physics Letters
,
256
, pp.
241
245
.
3.
Arroyo
M.
, and
Belytschko
T.
,
2003
. “
A nite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes
.”
Mechanics of Materials
,
35
, pp.
193
215
.
4.
Zang
J.
,
Treibergs
A.
,
Han
Y.
, and
Liu
F.
,
2004
. “
Geometric constant de ning shape transitions of carbon nanotubes under pressure
.”
Physical Review Letters
,
92
, p.
105501
105501
.
5.
Frisch-Fay, R., 1962. Flexible Bars. Butterworths.
6.
Gao
G.
,
Cagin
T.
, and
Goddard
W.
,
1998
. “
Energetics, structure, mechanical and vibrational properties of single-walled carbon nanotubes
.”
Nanotechnology
,
9
, p.
184
184
.
7.
Margenau, R., and Kestner, N. R., 1971. Theory of Inter-molecular Forces. Pergamon.
8.
Carlos
W. E.
, and
Cole
M. W.
,
1980
. “
Interaction between a He atom and a graphite surface
.”
Surface Science
,
91
, pp.
339
357
.
9.
Crowell
A. D.
, and
Brown
J. S.
,
1982
. “
Laterally averaged interaction potentials for 1H2 and 2H2 on the (0001) graphite surface
.”
Surface Science
,
123
, pp.
296
304
.
10.
Dym, C. L., 1974. Stability Theory and Its Applications to Structural Mechanics. Dover.
11.
Tang
T.
,
Jagota
A.
,
Hui
C.-Y.
, and
Glassmaker
N. J.
,
2005
. “
Collapse of single-walled carbon nanotubes
.”
Journal of Applied Physics
,
97
, p.
074310
074310
.
12.
Umeno
Y.
,
Kitamura
T.
, and
Kushima
A.
,
2004
. “
Theoretical analysis on electronic properties of zigzag-type single-walled carbon nanotubes under radial deformation
.”
Computational Materials Science
,
30
, pp.
283
287
.
13.
Mehl
M. J.
, and
Papaconstantopoulos
D. A.
,
1996
. “
Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals
.”
Physical Review B
,
54
, pp.
4519
4530
.
14.
Liu
B.
,
Yu
M.-F.
, and
Huang
Y.
,
2004
. “
Role of lattice registry in the full collapse and twist formation of carbon nanotubes
.”
Physical Review B
,
70
, p.
161402
161402
.
15.
Brenner
D. W.
,
Shenderova
O. A.
,
Harrison
J. A.
,
Stuart
S. J.
,
Ni
B.
, and
Sinnott
S. B.
,
2002
. “
A second-generation reactive empirical bond order (rebo) potential energy expression for hydrocarbons
.”
Journal of Physics: Condensed Matter
,
14
, pp.
783
802
.
16.
Benedict
L.
,
Chopra
N.
,
Cohen
M.
,
Zettl
A.
,
Louie
S.
, and
Crespi
V. H.
,
1998
. “
Microscopic determination of the interlayer binding energy in graphite
.”
Chemical Physics Letters
,
286
, pp.
490
496
.
17.
Tang
T.
,
Jagota
A.
, and
Hui
C.-Y.
,
2005
. “
Adhesion between single-walled carbon nanotubes
.”
Journal of Applied Physics
,
97
, p.
074304
074304
.
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