Low-dimensional nanomaterials are attractive for various applications, including damage repair, drug delivery, and bioimaging. The ability to control the morphology of nanomaterials is critical for manufacturing as well as for utilizing them as functional materials or devices. However, the manipulation of such materials remains challenging, and effective methods to control their morphology remain limited. Here, we propose to mimic a macroscopic biological system—the gut—as a means to control the nanoscale morphology by exploiting the concept of mismatch strain. We show that, by mimicking the development of the gut, one can obtain a controlled wavy shape of a combined carbon nanotube and graphene system. We show that the scaling laws that control the formation of the gut at the macroscale are suitable for ultrasmall-diameter carbon nanotubes with a diameter smaller than 7 Å but do not account for the morphology of systems with larger diameter nanotubes. We find that the deviation is caused by cross-sectional buckling of carbon nanotube, where this behavior relates to the different constitutive laws for carbon nanotube and graphene in contrast to the macroscale biological system. Our study illustrates the possibility of downscaling macroscale phenomena to the nanoscale using continuum mechanics theory, with wide-ranging applications in nanotechnology.

References

References
1.
Geim
,
A. K.
, and
Novoselov
,
K. S.
,
2007
, “
The Rise of Graphene
,”
Nature Mater.
,
6
, pp.
183
191
.10.1038/nmat1849
2.
Iijima
,
S.
,
1991
, “
Helical Microtubules of Graphitic Carbon
,”
Nature
,
354
, pp.
56
58
.10.1038/354056a0
3.
Castro Neto
,
A. H.
,
Guinea
,
F.
,
Peres
,
N. M. R.
,
Novoselov
,
K. S.
, and
Geim
,
A. K.
,
2009
, “
The Electronic Properties of Graphene
,”
Rev. Mod. Phys.
,
81
, pp.
109
162
.10.1103/RevModPhys.81.109
4.
Balandin
,
A. A.
,
Ghosh
,
S.
,
Bao
,
W. Z.
,
Calizo
, I
.
,
Teweldebrhan
,
D.
,
Miao
,
F.
, and
Lau
,
C. N.
,
2008
, “
Superior Thermal Conductivity of Single-Layer Graphene
,”
Nano Lett.
,
8
, pp.
902
907
.10.1021/nl0731872
5.
Lee
,
C.
,
Wei
,
X. D.
,
Kysar
,
J. W.
, and
Hone
,
J.
,
2008
, “
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
,”
Science
,
321
, pp.
385
388
.10.1126/science.1157996
6.
Yu
,
M.-F.
,
Lourie
,
O.
,
Dyer
,
M. J.
,
Moloni
,
K.
,
Kelly
,
T. F.
, and
Ruoff
,
R. S.
,
2000
, “
Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load
,”
Science
,
287
, pp.
637
640
.10.1126/science.287.5453.637
7.
Yao
,
Z.
,
Postma
,
H. W. C.
,
Balents
,
L.
, and
Dekker
,
C.
,
1999
, “
Carbon Nanotube Intramolecular Junctions
,”
Nature
,
402
, pp.
273
276
.10.1038/46241
8.
Li
,
D.
,
Windl
,
W.
, and
Padture
,
N. P.
,
2009
, “
Toward Site-Specific Stamping of Graphene
,”
Adv. Mater.
,
21
, pp.
1243
1246
.10.1002/adma.200802417
9.
Cai
,
D.
,
Ren
,
L.
,
Zhao
,
H.
,
Xu
,
C.
,
Zhang
,
L.
,
Yu
,
Y.
,
Wang
,
H.
,
Lan
,
Y.
,
Roberts
,
M. F.
,
Chuang
,
J. H.
,
Naughton
,
M. J.
,
Ren
,
Z.
, and
Chiles
,
T. C.
,
2010
, “
A Molecular-Imprint Nanosensor for Ultrasensitive Detection of Proteins
,”
Nature Nanotechnol.
,
5
, pp.
597
601
.10.1038/nnano.2010.114
10.
Yan
,
R.
,
Park
,
J.-H.
,
Choi
,
Y.
,
Heo
,
C.-J.
,
Yang
,
S.-M.
,
Lee
,
L. P.
, and
Yang
,
P.
,
2011
, “
Nanowire-Based Single-Cell Endoscopy
,”
Nature Nanotechnol.
,
7
, pp.
191
196
.10.1038/nnano.2011.226
11.
Liu
,
Z.
,
Chen
,
K.
,
Davis
,
C.
,
Sherlock
,
S.
,
Cao
,
Q.
,
Chen
,
X.
, and
Dai
,
H.
,
2008
, “
Drug Delivery With Carbon Nanotubes for In Vivo Cancer Treatment
,”
Cancer Res.
,
68
, pp.
6652
6660
.10.1158/0008-5472.CAN-08-1468
12.
Xu
,
Z. P.
, and
Buehler
,
M. J.
,
2010
, “
Geometry Controls Conformation of Graphene Sheets: Membranes, Ribbons, and Scrolls
,”
ACS Nano
,
4
, pp.
3869
3876
.10.1021/nn100575k
13.
Kratz
,
K.
,
Narasimhan
,
A.
,
Tangirala
,
R.
,
Moon
S.
,
Revanur
,
R.
,
Kundu
,
S.
,
Kim
,
H. S.
,
Crosby
,
A. J.
,
Russell
,
T. P.
,
Emrick
,
T.
,
Kolmakov
,
G.
, and
Balazs
,
A. C.
,
2012
, “
Probing and Repairing Damaged Surfaces With Nanoparticle-Containing Microcapsules
,”
Nature Nanotechnol.
,
7
, pp.
87
90
.10.1038/nnano.2011.235
14.
Taber
,
L. A.
,
2004
,
Nonlinear Theory of Elasticity: Applications in Biomechanics
,
World Scientific
,
Singapore
.
15.
Savin
,
T.
,
Kurpios
,
N. A.
,
Shyer
,
A. E.
,
Florescu
,
P.
,
Liang
,
H.
,
Mahadevan
,
L.
, and
Tabin
,
C. J.
,
2011
, “
On the Growth and Form of the Gut
,”
Nature
,
476
, pp.
57
62
.10.1038/nature10277
16.
Zhao
,
X.
,
Liu
,
Y.
,
Inoue
,
S.
,
Suzuki
,
T.
,
Jones
,
R. O.
, and
Ando
,
Y.
,
2004
, “
Smallest Carbon Nanotube is 3 Angstrom in Diameter
,”
Phys. Rev. Lett.
,
92
, p.
125502
.10.1103/PhysRevLett.92.125502
17.
Stuart
,
S. J.
,
Tutein
,
A. B.
, and
Harrison
,
J. A.
,
2000
, “
A Reactive Potential for Hydrocarbons With Intermolecular Interactions
,”
J. Chem. Phys.
,
112
, pp.
6472
6486
.10.1063/1.481208
18.
MacKerell
, Jr.,
A. D.
,
Bashford
,
D.
,
Bellott
,
M.
,
Dunbrack
, Jr.,
R. L.
,
Evanseck
,
J. D.
,
Field
,
M. J.
,
Fischer
,
S.
,
Gao
,
J.
,
Guo
,
H.
,
Ha
,
S.
,
Joseph-McCarthy
,
D.
,
Kuchnir
,
L.
,
Kuczera
,
K.
,
Lau
,
F. T. K.
,
Mattos
,
C.
,
Michnick
,
S.
,
Ngo
,
T.
,
Nguyen
,
D. T.
,
Prodhom
,
B.
,
Reiher
, III,
W. E.
,
Roux
,
B.
,
Schlenkrich
,
M.
,
Smith
,
J. C.
,
Stote
,
R.
,
Straub
,
J.
,
Watanabe
,
M.
,
Wiórkiewicz-Kuczera
,
J.
,
Yin
,
D.
, and
Karplus
,
M.
,
1998
, “
All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins
,”
J. Phys. Chem. B
,
102
, pp.
3586
3616
.10.1021/jp973084f
19.
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
,”
J. Phys. Condens. Matter
,
14
, pp.
783
802
.10.1088/0953-8984/14/4/312
20.
Qin
,
Z.
,
Qin
,
Q. H.
, and
Feng
,
X. Q.
,
2008
, “
Mechanical Property of Carbon Nanotubes With Intramolecular Junctions: Molecular Dynamics Simulations
,”
Phys. Lett. A
,
372
, pp.
6661
6666
.10.1016/j.physleta.2008.09.010
21.
Qin
,
Z.
,
Feng
,
X. Q.
,
Zou
,
J.
,
Yin
,
Y.
, and
Yu
,
S.-W.
,
2007
, “
Superior Flexibility of Super Carbon Nanotubes: Molecular Dynamics Simulations
,”
Appl. Phys. Lett.
,
91
, p.
043108
.10.1063/1.2760039
22.
Nair
,
R. R.
,
Wu
,
H. A.
,
Jayaram
,
P. N.
,
Grigorieva
,
I. V.
, and
Geim
,
A. K.
,
2012
, “
Unimpeded Permeation of Water Through Helium-Leak-Tight Graphene-Based Membranes
,”
Science
,
335
, pp.
442
444
.10.1126/science.1211694
23.
Medhekar
,
N. V.
,
Ramasubramaniam
,
A.
,
Ruoff
,
R. S.
, and
Shenoy
,
V. B.
,
2010
, “
Hydrogen Bond Networks in Graphene Oxide Composite Paper: Structure and Mechanical Properties
,”
ACS Nano
,
4
, pp.
2300
2306
.10.1021/nn901934u
24.
Compton
,
O. C.
,
Cranford
,
S. W.
,
Putz
,
K. W.
,
An
,
Z.
,
Brinson
,
L. C.
,
Buehler
,
M. J.
, and
Nguyen
,
S. T.
,
2012
, “
Tuning the Mechanical Properties of Graphene Oxide Paper and Its Associated Polymer Nanocomposites by Controlling Cooperative Intersheet Hydrogen Bonding
,”
ACS Nano
,
6
, pp.
2008
2019
.10.1021/nn202928w
25.
Nair
,
A. K.
,
Qin
,
Z.
, and
Buehler
,
M. J.
,
2012
, “
Cooperative Deformation of Carboxyl Groups in Functionalized Carbon Nanotubes
,”
Int. J. Solids Struct.
,
49
, pp.
2418
2423
.10.1016/j.ijsolstr.2012.05.002
26.
Paul
,
D. R.
,
2012
, “
Creating New Types of Carbon-Based Membranes
,”
Science
,
335
, pp.
413
414
.10.1126/science.1216923
27.
Wang
,
L.
,
Zheng
,
Q.
,
Liu
,
J. Z.
, and
Jiang
,
Q.
,
2005
, “
Size Dependence of the Thin-Shell Model for Carbon Nanotubes
,”
Phys. Rev. Lett.
,
95
, p.
105501
.10.1103/PhysRevLett.95.105501
28.
Huang
,
Y.
,
Wu
,
J.
, and
Hwang
,
K. C.
,
2006
, “
Thickness of Graphene and Single-Wall Carbon Nanotubes
,”
Phys. Rev. B
,
74
, p.
245413
.10.1103/PhysRevB.74.245413
29.
Yakobson
,
B. I.
,
Brabec
,
C. J.
, and
Bernholc
,
J.
,
1996
, “
Nanomechanics of Carbon Tubes: Instabilities Beyond Linear Response
,”
Phys. Rev. Lett.
,
76
, pp.
2511
2514
.10.1103/PhysRevLett.76.2511
30.
Pantano
,
A.
,
Parks
,
D. M.
, and
Boyce
,
M. C.
,
2004
, “
Mechanics of Deformation of Single- and Multi-Wall Carbon Nanotubes
,”
J. Mech. Phys. Solids
,
52
, pp.
789
821
.10.1016/j.jmps.2003.08.004
31.
Li
,
X. Y.
,
Yang
,
W.
, and
Liu
,
B.
,
2007
, “
Bending Induced Rippling and Twisting of Multiwalled Carbon Nanotubes
,”
Phys. Rev. Lett.
,
98
, p.
205502
.10.1103/PhysRevLett.98.205502
32.
Gao
,
G. H.
,
Cagin
,
T.
, and
Goddard
,
W. A.
,
1998
, “
Energetics, Structure, Mechanical and Vibrational Properties of Single-Walled Carbon Nanotubes
,”
Nanotechnology
,
9
, pp.
184
191
.10.1088/0957-4484/9/3/007
33.
Qin
,
Z.
,
Kreplak
,
L.
, and
Buehler
,
M. J.
,
2009
, “
Hierarchical Structure Controls Nanomechanical Properties of Vimentin Intermediate Filaments
,”
PLoS ONE
,
4
, p.
e7294
.10.1371/journal.pone.0007294
34.
Qin
,
Z.
, and
Buehler
,
M. J.
,
2010
, “
Molecular Dynamics Simulation of the Alpha-Helix to Beta-Sheet Transition in Coiled Protein Filaments: Evidence for a Critical Filament Length Scale
,”
Phys. Rev. Lett.
,
104
, p.
198304
.10.1103/PhysRevLett.104.198304
35.
Buehler
,
M. J.
,
2010
, “
Tu(r)ning Weakness to Strength
,”
Nano Today
,
5
, pp.
379
383
.10.1016/j.nantod.2010.08.001
36.
Buehler
,
M. J.
,
2010
, “
Strength in Numbers
,”
Nature Nanotechnol.
,
5
, pp.
172
174
.10.1038/nnano.2010.28
37.
Buehler
,
M. J.
,
Kong
,
Y.
,
Gao
,
H. J.
, and
Huang
,
Y.
,
2006
. “
Self-Folding and Unfolding of Carbon Nanotubes
,”
ASME J. Eng. Mater. Technol.
,
128
(
1
), pp.
3
10
.10.1115/1.1857938
38.
Zhou
,
W.
,
Huang
,
Y.
,
Liu
,
B.
,
Hwang
,
K. C.
,
Zuo
,
J. M.
,
Buehler
,
M. J.
, and
Gao
,
H.
,
2007
, “
Self Folding of Single- and Multi-Wall Carbon Nanotubes
,”
Appl. Phys. Lett.
,
90
, p.
073107
.10.1063/1.2535874
39.
Cranford
,
S.
,
Sen
,
D.
, and
Buehler
,
M. J.
,
2009
, “
Meso-Origami: Folding Multilayer Graphene Sheets
,”
Appl. Phys. Lett.
,
95
, p.
123121
.10.1063/1.3223783
You do not currently have access to this content.