C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6

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Predicted mechanical properties of a coiled carbon nanotube

Jinhe Wang a, Travis Kemper b, Tao Liang b, Susan B. Sinnott b,*

a Laboratory of Nanotechnology, Shanghai Nanotechnology Promotion Center, Shanghai 200237, Chinab Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611-6400, USA

A R T I C L E I N F O

Article history:

Received 3 May 2011

Accepted 29 September 2011

Available online 6 October 2011

0008-6223/$ - see front matter � 2011 Elsevidoi:10.1016/j.carbon.2011.09.060

* Corresponding author.E-mail address: ssinn@mse.ufl.edu (S.B. S

A B S T R A C T

Nanostructured carbon materials continue to attract much interest for use in devices and

as fillers in composites. Here, classical molecular dynamics simulations are carried out

using many-body empirical potentials to contrast the mechanical properties of straight

and coiled carbon nanotubes. The specific properties of a coiled carbon nanotube (CCNT)

are investigated under compression, tension, re-compression, re-tension and pullout from

a polyethylene (PE) matrix. The stress–strain curves, spring constants, and yielding strains

under compression and tension are given for each system, and the corresponding reasons

for the differences in their behavior are discussed. They indicate that the interaction

between a CCNT and a PE matrix is stronger than the corresponding interactions between

CNTs and PE. Thus, the results indicate that CCNTs are good potential candidates for light-

weight, tough composites.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The addition of nanostructured materials, such as carbon

nanotubes (CNTs), to polymers offers a viable means of alter-

ing the mechanical [1–4], thermal [5–7] and electrical [8,9]

properties of polymer-based composite materials. The result-

ing properties include tensile strengths of 100–600 GPa, a den-

sity of around 1.3 g/cm3, elastic moduli of 200–5000 GPa and

fracture strains of 10–30% [10,11]. CNTs have desirable

mechanical properties that make them particularly attractive

for strengthening polymers [12,13]. For example, CNTs that

were added to a polystyrene (PS) matrix increased its micro-

hardness, improved its wear resistance and decreased its fric-

tion coefficient [13].

Nevertheless, there remain significant problems with the

incorporation of CNTs into polymer matrices. For instance,

they tend to agglomerate with one another and interact

weakly with the surrounding polymer. This results in poor

mechanical load transfer from the polymer to the CNT and

interfacial failure well below the strength of a CNT [11].

Therefore, there has been significant effort put into

er Ltd. All rights reservedinnott).

strengthening the polymer–CNT interface. For instance, CNTs

may be functionalized by chemical modification [14,15], ion

beam modification [16] and dispersed in solution with

peptides [17–19]. Unfortunately, these approaches may also

lead to the degradation of their integrity [20]. An alternative

solution is to mechanically impede interfacial failure by using

CNTs that are coiled rather than straight.

Coiled carbon nanotubes (CCNTs) were theoretically pro-

posed to exist by Ihara and co-workers in 1993 [21]. That same

year, some irregular spiral nanotubes were found mixed with

straight nanotubes produced by Jose-Yacaman et al. [22]. In

1994, Zhang et al. [23,24] experimentally synthesized regular

CCNTs. The coiled structure of the CCNTs can potentially al-

low them to anchor themselves into a polymer matrix, and

thus improve the overall strength and toughness of the

resulting composite.

Chen et al. [25] used atomic force microscope (AFM) canti-

levers to carry out a tensile test on an individual CCNT. They

found that it behaved like an elastic spring with a spring con-

stant of 0.12 N/m under strains that were less than or equal to

15%. In addition, Li et al. [26] added CCNTs to an epoxy resin,

.

C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6 969

and investigated the mechanical properties of the resulting

composite by nano-indentation and tensile tests. The results

showed that the hardness increased by 48%, elastic modulus

increased by 41%, and the tensile strength of the CCNT/epoxy

composite increased by 103%. This improvement was attrib-

uted to the fact that the CCNTs were well dispersed in the ma-

trix and formed a mechanical interlock with it.

Despite these promising reports, the theoretical mechani-

cal properties of CCNTs and the molecular scale mechanisms

by which CCNTs interact with polymer matrices remain to be

illuminated. Previous studies employed theoretical simula-

tions to investigate the interactions between CNTs and poly-

mers [27–30]. Here, we present the results of classical

molecular dynamics (MD) simulations of the mechanical

deformation of a CCNT, and compare the predictions to those

of comparable straight single-walled carbon nanotubes

(SWCNTs). We also examine and compare the forces needed

to pull a CCNT and SWCNT out of a polyethylene (PE) matrix.

The atomic-scale mechanisms that control the mechanical

responses of each of these nanostructures are also discussed.

2. Methodology

2.1. Computational details

The potential energy and total forces in the MD simulations

are determined using the second generation of the reactive

empirical bond-order (REBO) hydrocarbon potential [31,32]

for short-ranged interactions, and a standard Lennard-Jones

(LJ) potential for long-range interactions. The two potentials

are seamlessly connected by a cubic spline. The REBO hydro-

carbon potential developed by Brenner and co-workers is

based on Tersoff’s covalent bonding formalism, with addi-

tional terms that correct for over binding of radicals and non-

local environmental effects. The many-body nature of the

REBO potential allows the bond energy of each atom to de-

pend on its local environment, which allows for the forma-

tion and breaking of chemical bonds, unlike traditional

force fields [33,34]. This potential has been reliably applied

to carbon-based materials [35,36], including carbon nano-

tubes [37–40], hydrocarbons [41,42], and polymers [41,43].

In the simulations reported here, a Langevin thermostat

[44] is applied to selected atoms to maintain the temperature

of each system at around 300 K. The time step used is 0.2 fs

for all trajectories. Compression and tensile loading is carried

out at a constant strain rate of 1 m/s along the length of the

CNTs and CCNT. The short-range REBO outer cutoff is ex-

tended from 0.170 nm to 0.195 nm to allow for proper bond

elongation during tension simulations [32].

2.2. Details of the atomistic systems

The CCNT that is examined in the simulations is generated

from a CCNT unit cell with length of 14.995 nm. The unit cell

is composed of 360 carbon atoms and contains 10 sevenfold

carbon-atom rings on the inner surface and 10 fivefold car-

bon-atom rings on the outer surface. A spiral function is used

to fit the central line of the CCNT in order to find the values of

fit tube diameter (d) and coil diameter (D), as illustrated in

Fig. 1a; d and D are 0.8 nm and 2.0 nm, respectively (see

Fig. 1b). The CCNT examined here is obtained by multiplied

the unit cell along the length of the CCNT twice. The initial

CCNT structure is freely evolved in vacuum prior to the fol-

lowing applications and is found to be stable.

For comparison two different lengths of SWCNTs are also

created. The first (CNT-1) has the same length, of 4.5 nm, as

the CCNT (Fig. 1c). The second (CNT-2) possesses the same to-

tal length of the CCNT if it were to be uncoiled of 11 nm

(Fig. 1d). The left hand side (LHS) atoms of the CCNT and

CNT models are held fixed throughout the simulations and

are not allowed to evolve with time. In contrast, the atoms

on the right hand side (RHS) are not allowed to evolve in re-

sponse to the applied forces; rather they are manually moved

at a constant rate and are consequently termed ‘‘rigid and

moving’’ atoms. Thermostats are applied to atoms adjacent

to the rigid atoms on the LHS and the rigid and moving atoms

on the RHS. The thermostat atoms in these regions are al-

lowed to evolve according to calculated forces, while main-

taining the temperature of the system through the

application of random dissipative forces. The atoms in center

region are allowed to evolve in time without any additional

constraints; these are termed ‘‘active’’ atoms.

Crystalline PE with a density of 994.0 kg/m3 is used as the

polymer matrix for the CCNT-composite pull out simulations.

In particular, a PE slab with dimensions of 10.3 nm ·10.2 nm · 6.0 nm is constructed with periodic boundaries in

two directions to simulate an infinite surface. Two orienta-

tions of the PE chains perpendicular and parallel to the

surface are used to examine the influence of these two

extremes on the results.

The CCNT–polymer composite, which is illustrated in

Fig. 2, is constructed to have a density of 1002 kg/m3, with

the nanotube oriented perpendicular to the surface, with a

0.32 nm gap between the CCNTwalls and the polymer chains.

A 1.0 nm layer of atoms is fixed around the edges of the com-

posite supercell to mimic the influence of a more extensive

composite system than is present in the simulation cell dur-

ing the pullout simulations. A buffer of thermostat atoms is

then applied to maintain a constant temperature within the

active region of the composite. The relative number of fixed,

rigid and moving, thermostat and active atoms for the sys-

tems considered here is given in Table 1.

Various methods for calculating stress applied to a CNT

have been proposed [45,46]. In this work, the force and corre-

sponding displacement that keeps the CNT or CCNT com-

pressed or stretched at a constant rate of 1.0 m/s is

outputted every 0.20 ps during the simulation, and the raw

data is smoothed to obtain force vs. displacement curves.

Subsequent stress vs. strain curves are calculated using Eq.

(1) for the CNTs and Eq. (2) for the CCNT:

e ¼ F=ðpdtÞ ð1Þ

e ¼ F cos h=ðpdtÞ ð2Þ

In these equations, e is the stress, F is the force, d is the tube

diameter, and t is effective shell thickness, which is chosen to

be 0.34 nm (the interlayer spacing of multi-walled CNTs), and

h is the pitch angle of the CCNT.

Fig. 1 – Configuration of (a) CCNT unit cell, (b) CCNT, (c) CNT-1 and (d) CNT-2, in (b)–(d) the far left-hand side (LHS) and right-

hand side (RHS) atoms are rigid, the center region is active, and the buffer regions in between are thermostated as described

in the text.

Fig. 2 – Configuration of the CCNT in the PE matrix.

Table 1 – Number of atoms of each part in each model.

CCNT CNT-1 CNT-2 PE CCNT/PE

Total 1080 432 1080 80,640 79,162Active 719 240 792 49,280 48,914Thermostat 241 96 192 19,040 19,632Fixed 60 48 48 6160 10,496Rigid and moving 60 48 48 6160 120

970 C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6

3. Results

3.1. Single walled carbon nanotubes

The stress–strain curve and snapshots from the compression

simulation of CNT-1 are given in Fig. 3. As previously reported

[47–49], compression kinks develop within the body of the

nanotube. These points correspond to modulations within

the linear region of the stress–strain curve. Buckling occurs

at a strain of 4.3% with a maximum stress of 73 GPa. Fig. 4

shows the stress–strain curve and snapshots for CNT-2 under

compression. Comparing this curve with that of CNT-1, the

Fig. 3 – Stress strain curve for CNT-1 under compression, each snapshot (front view) corresponds to a failure point. The atoms

are colored according to strain.

Fig. 4 – Stress–strain curve for CNT-2 under compression. The two images belong to one strain point of 4%. The top image is a

front view where the colors represent the thermostats in a manner that is consistent with Fig. 1. The bottom image is an

upward view where the colors represent strains in a manner that is consistent with Fig. 3. (For interpretation of the references

to color in this figure legend, the reader is referred to the web version of this article.)

C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6 971

main difference is that the maximum total stress on CNT-2 is

substantially smaller than that on CNT-1. For instance, it is

34 GPa at a strain of 2.5%, which is much smaller than that

of CNT-1 and this results in different dimensionless quanti-

ties L/d (where L is the original length and d is the diameter

of the CNTs) [50]. Snapshots from the simulations illustrating

this point are given in Fig. 3. In this simulation CNT-1’s L/d is

relatively small. When compression occurs the active C atoms

in the middle part of CNT-1 are more likely to form small

buckles in different directions. When the buckles are formed

perpendicular to each other in two different directions (in this

case two buckles are formed in the x and y direction, respec-

tively), the buckles restrain each other’s further development

to bend and prevent the stress from increasing until the buck-

les increase, thus decreasing the stress. The final break occurs

in the compression direction.

In the case of CNT-2 compression, the L/d is much larger,

and the carbon atoms in the middle have more space to re-

lease their stress, as indicated in Fig. 4. Therefore, when the

small buckle appears, it is more likely to develop into a bend

and decrease the stress.

Under tensile strain the stress increases linearly until

breakage occurs, as illustrated in Fig. 5. Both CNT-1 and

CNT-2 have a tensile strength of about 100 GPa at a strain of

20%. The tensile strength is lower than in previously pub-

lished results [27] due to the choice of t used in Eq. (1). How-

ever, this result clearly illustrates that L/d does not strongly

influence the tensile strain results.

-5 0 5 10 15 20 25 30 35 40

0

20

40

60

80

100

120

Str

ess

(GP

a)

Strain (%)

CNT-1 CNT-2

Fig. 5 – Stress–strain curves for tensile test on CNT-1 and

CNT-2.

Fig. 7 – Compression snapshots of the CCNT in (a) region I,

(b) region II and (c) region III of Fig. 6.

972 C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6

3.2. Coiled carbon nanotube

3.2.1. CompressionIn Fig. 6 the curves of compression stress vs. strain of the

CCNT are shown, and snapshots at each regime are illustrated

in Fig. 7. From the stress–strain curve we can see that the

compressing stress increases linearly until it reaches a yield

point where the strain is 16% and the stress is 9.2 GPa. After

the initial linear regime, the stress undergoes a small de-

crease and then increases again after the compressing strain

passes 23%. Throughout the compression process analysis of

the bonding indicates that no covalent bonds are broken, so

no buckling of the CCNT is predicted to occur.

In the first regime, before the strain reaches 16%, the stress

is attributed to the compression of the six-carbon rings and

torsion of the C–C bonds. This is elastic deformation (region

I), and small structural changes can be seen in Fig. 7a. As

compression continues, an increasing number of C–C bonds

are aligned perpendicular to the compression axis, which

makes compression strain decrease. This is illustrated in

0 5 10 15 20 25 30 35 40-2

0

2

4

6

8

10

12

14

16

18

Str

ess

(GP

a)

Strain (%)

CCNT compression Number of covalent bond

1450

1500

1550

1600

1650

1700

1750

IIIIII Num

ber

Fig. 6 – Strain vs. stress curve for the CCNT. (I) First linear

regime; (II) yielding regime; (III) second linear regime.

Fig. 7b, where the pitch angle and the diameter of the middle

coil ring have slightly increased. This transformation leads to

the decrease of the stress (Part II on Fig. 6). When the strain

reaches 23%, the distance between the walls of the CCNT

rings is small enough to make the walls of the CCNT rings

push against each other and compress the rest of the CCNT

(see Fig. 7c, where the diameter of the middle coil ring is com-

pressed compared to the original). This results in the next in-

crease of the total force (Part III in Fig. 6).

In order to illustrate that before the strain reaches 16% the

deformation of the CCNT is elastic, we re-compressed a CCNT

that is pre-compressed to 16% and compare this to the total

force of the original one. Fig. 8 indicates that these two curves

match each other very well, which indicates that the pre-

compression is reversible and the deformation is elastic.

0 5 10 15 20 25 30 35 40

-2

0

2

4

6

8

10

12

14

16

18

20

Str

ess

(GP

a)

Strain (%)

Orignal CCNT compression CCNT re-compression

Fig. 8 – Comparison of original compression and re-

compression of an uncompressed CCNT.

0 10 20 30 40 50 602

4

6

8

10

12

14

16

18

20

CCNT tension Number of

covalent bonds

Strain (%)

Str

ess

(GP

a)

1592

1594

1596

1598

Num

ber

I II III

Fig. 9 – Tension simulation results.

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

18

Str

ess

(GP

a)

Strain (%)

CCNT tension CCNT re-tension

Fig. 11 – Stress–strain results of CCNT after subjected to

tension and relaxation followed by tension (re-tension).

C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6 973

3.2.2. TensionThe stress response to strain is predicted to have three re-

gions, which are indicated in Fig. 9. In the first region, the

stress increases continually until it reaches a point where

the stress and strain is about 14 GPa and 30%, respectively.

The stress begins to decrease when the strain passes 30%.

Fig. 9 also illustrates the number of covalent bonds vs. strain,

and indicates that no covalent bonds are broken until it

passes the yield point.

When the strain passes 30%, some covalent bonds are seen

to break, and the total stress decreases. These broken bonds

are shown in Fig. 10a; the color change of some central carbon

atoms illustrates the bonds that are broken. After the initial

covalent bonds break more covalent bonds in the central line

become strained and a stress concentration line is formed

(see Fig. 10b), which results in an increasing strain.

In order to evaluate the elasticity/recovery of the CCNT in

the elastic region, it is stretched and relaxed then stretched

again. Fig. 11 illustrates the way in which the response re-

mains consistent.

From the compression and tension analysis, the elastic

deformation regimes have been identified and are predicted

to be at strains below 16% for compression and below 30%

Fig. 10 – Snapshots during tensile deformation of the CCNT, whe

formed in this carbon atom (a) 30% strain (b) 40% strain. (For inte

reader is referred to the web version of this article.)

for tension, respectively. These regimes are meaningful for

fitting the spring constant of the CCNT according to the spring

equation (F = �kx). In order to best evaluate k, both compres-

sion and tension data are considered and the fitting result is

given in Fig. 12. The fitting line passes perfectly through the

origin, and the fitted spring constant is determined to be

10.1 N/m. Specifically, the spring constant is inversely propor-

tional to the number of coils in the spring, and the active re-

gion of the considered CCNT contains two coils [51].

Consequently, the spring constant is determined to be

20.2 N/m per coil. This differs from an experimentally deter-

mined spring constant of 0.12 N/m for an amorphous carbon

nano coil with approximately 10 coils, which corresponds to

1.2 N/m per coil [25]. The order of magnitude difference in

the spring constants can be attributed to the different geom-

etries and shear moduli of the materials that make up the

coils, on which the spring constant is also dependent [52,53].

3.2.3. Pullout from the PE matrixWith the PE chains oriented parallel to the CCNT, the CCNT is

pulled out from the matrix with a constant velocity. In Fig. 13

re the color of the carbon atom represents the bond number

rpretation of the references to color in this figure legend, the

-20 -10 0 10 20 30-20

-15

-10

-5

0

5

10

15

20

25 Force of compression and tension Fitted line

For

ce (

nN)

Strain (%)

Spring constant=10.1N/m

Fig. 12 – Spring constant of the CCNT.

0 2 4 6 8 10 12

-2

-1

0

1

2

3

Tota

l for

ce (

nN)

Displacement (Angstrom)

CCNT parallel pullout

Fig. 13 – Parallel model pullout simulation results for a CCNT

in a PE matrix.

0 1 2 3 4 5 6 7-1

0

1

2

3

4

5

Tota

l for

ce (

nN)

Displacement (Angstrom)

CCNT perpendicular pullout

Fig. 14 – Force on a CCNT as response to being pulled out of

the PE matrix at a constant rate.

Table 2 – Comparison of findings for SWCNTs and CCNTs.

CCNT SWCNT

CNT-1 CNT-2

Compression Stress (GPa) 9.2 73 34Strain (%) 16 4.3 2.5

Tension Stress (GPa) 14 90 85Strain (%) 30 15 15

Pullout force (nN) Perpendicular 1.5 0.1 [54]Parallel 0.15

974 C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6

the restoring force in response to the pullout can be seen to

fluctuate around 0.15 nN. This is comparable to previous

studies of SWCNT pullout from a PE matrix [54]. As is the case

for a SWCNT in a PE matrix, if the polymer chains are aligned

parallel to the CCNT, there are only weak van der Waal’s

forces acting to hold the CCNT in the polymer.

Conversely, if the PE chains are aligned perpendicular to

the CCNT the response is quite different, as illustrated in

Fig. 14. Initially, the force fluctuates around 1.5 nN as the

CCNT pushes PE chains out of the way. Once the end of the

CCNT is pulled over 0.5 nm out from the surface of the poly-

mer, the forces sharply increase. This is due to the CCNT

being caught on a non-terminating PE chain which passes

through its center and which it has to break to continue the

pull-out process.

4. Discussion

Table 2 organizes the maximum stresses and strains of the

SWCNT and CCNT during their elastic deformation in com-

pression and tension, and the pullout forces of the CCNT

and SWCNT from the crystalline PE matrix. It can be seen that

the CCNT is much less stiff than the SWCNT, since the com-

pressive and tensile yielding strain of the CCNT is about 4·and 2· that of the SWCNT, respectively. Another obvious dif-

ference is the pullout force required to pull these nanotubes

out of a PE matrix. In the case of a SWCNT, the pullout forces

are only about 0.1 nN, which is almost the same with that of

the CCNT when it is aligned parallel to the surrounding PE

chains. However, when the CCNT is perpendicular to the sur-

rounding PE chains, the pullout force is about 15 times of that

of a SWCNT.

5. Conclusions

In this work, the mechanical properties of a CCNT are pre-

dicted by classical molecular dynamics simulations, and com-

pared with the properties of SWCNTs. The simulation results

predict that the yielding stress and strain of the CCNT under

compression is 9.2 GPa and 16%, respectively. Before the

strain reaches 16%, the deformation of the CCNT is reversible.

The yield stress and strain of the CCNT under tension is pre-

dicted to be 14 GPa and 30%, respectively. Before the strain

reaches 20%, and the deformation of CCNT is reversible. Com-

pared with a SWCNT that has the same diameter, the CCNT is

much less stiff and has a much larger pullout force than a

SWCNT in a PE matrix. These results indicate that CCNTs

C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6 975

might be better candidates than regular single walled carbon

nanotubes to produce high-quality polymer composites.

Acknowledgements

JW acknowledges the financial support provided by Shanghai

Postdoctoral Science Foundation (11R21420900), Natural Sci-

ence Foundation of Shanghai (No. 11ZR1432100) and the Chi-

na Scholarship Council through the scholarship program in

2008, while TK, TL, and SBS acknowledge the support of the

National Science Foundation (grant number CHE-0809376).

We thank Vitor Coluci for providing the coiled nanotube unit

cells used in these simulations and for helpful discussions.

R E F E R E N C E S

[1] Yang Z, Dong B, Huang Y, Liu L, Yan F, Li H. A study on carbonnanotubes reinforced poly(methyl methacrylate)nanocomposites. Mater Lett 2005;59:2128–32.

[2] Tibbetts GG, McHugh JJ. Mechanical properties of vapor-grown carbon fiber composites with thermoplastic matrices. JMater Res 1999;14:2871–80.

[3] Jia ZJ, Wang ZY, Xu CL, Liang J, Wei BQ, Wu DH, et al. Study onpoly(methyl methacrylate)/carbon nanotube composites.Mater Sci Eng A-Struct Mater Prop Microstruct Process1999;271:395–400.

[4] Qian D, Dickey EC, Andrews R, Rantell T. Load transfer anddeformation mechanisms in carbon nanotube–polystyrenecomposites. Appl Phys Lett 2000;76:2868–70.

[5] Pham JQ, Mitchell C a, Bahr JL, Tour JM, Krishanamoorti R,Green PF. Glass transition of polymer/single-walled carbonnanotube composite films. J Poly Sci Part B Poly Phys2003;41:3339–45.

[6] Wei C, Srivastava D, Cho K. Thermal expansion and diffusioncoefficients of carbon nanotube–polymer composites. NanoLett 2002;2:647–50.

[7] Biercuk MJ, Llaguno MC, Radosavljevic M, Hyun JK, JohnsonAT, Fischer JE. Carbon nanotube composites for thermalmanagement. Appl Phys Lett 2002;80:67.

[8] Sandler J. Development of a dispersion process for carbonnanotubes in an epoxy matrix and the resulting electricalproperties. Polymer 1999;40:5967–71.

[9] Pumera M, Merkoci a, Alegret S. Carbon nanotube–epoxycomposites for electrochemical sensing.. Sensors Actuat BChem 2006;113:617–22.

[10] Breuer O, Sundararaj U. Big returns from small fibers: areview of polymer/carbon nanotube composites. PolymCompos 2004;25:630–45.

[11] Desai A, Haque M. Mechanics of the interface for carbonnanotube polymer composites. Thin Walled Struct2005;43:1787–803.

[12] Ci L, Bai J. The reinforcement role of carbon nanotubes inepoxy composites with different matrix stiffness. Comp SciTechnol 2006;66:599–603.

[13] Yang Z, Dong B, Huang Y, Liu L, Yan F-Y, Li H-L. Enhancedwear resistance and micro-hardness of polystyrenenanocomposites by carbon nanotubes. Mater Chem Phys2005;94:109–13.

[14] Hong CY, You YZ, Pan CY. A new approach to functionalizemulti-walled carbon nanotubes by the use of functionalpolymers. Polymer 2006;47:4300–9.

[15] Zhang W, Swager TM. Functionalization of single-walledcarbon nanotubes and fullerenes via a dimethylacetylenedicarboxylate-4-dimethylaminopyridine zwitterionapproach. J Am Chem Soc 2007;129:7714–5.

[16] Zhu YW, Cheong FC, Yu T, Xu XJ, Lim CT, Thong JTL, et al.Effects of CF4 plasma on the field emission properties ofaligned multi-wall carbon nanotube films. Carbon2005;43:395–400.

[17] Witus LS, Rocha JDR, Yuwono VM, Paramonov SE, WeismanRB, Hartgerink JD. Peptides that non-covalently functionalizesingle-walled carbon nanotubes to give controlled solubilitycharacteristics. J Mater Chem 2007;17:1909–15.

[18] Yokoi T, Iwamatsu S, Komai S, Hattori T, Murata S. Chemicalmodification of carbon nanotubes with organic hydrazines.Carbon 2005;43:2869–74.

[19] Liu P. Modifications of carbon nanotubes with polymers. EurPoly J 2005;41:2693–703.

[20] Haskins RW, Maier RS, Ebeling RM, Marsh CP, Majure DL,Bednar AJ, et al. Tight-binding molecular dynamics study ofthe role of defects on carbon nanotube moduli and failure. JChem Phys 2007;127:074708.

[21] Itoh S, Ihara S, Kitakami J. Toroidal form of carbon C360. PhysRev B 1993;47:1703–4.

[22] Jose-Yacaman M, Miki Yoshida M, Rendon L, Santiesteban JG.Catalytic growth of carbon microtubules with fullerenestructure. Appl Phys Lett 1993;62:202–4.

[23] Zhang XB, Zhang XF, Bernaerts D, Tendeloo GV, Amelinckx S,Landuyt JV, et al. The texture of catalytically growncoil-shaped carbon nanotubules. Eur Phys Lett 1994;27:141–6.

[24] Amelinckx S, Zhang XB, Bernaerts D, Zhang XF, Ivanov V,Nagy JB. A formation mechanism for catalytically grownhelix-shaped graphite nanotubes. Science 1994;265:635–9.

[25] Chen X et al. Mechanics of a carbon nanocoil. Nano Lett2003;3:1299–304.

[26] Li X, Lau K, Yin Y. Mechanical properties of epoxy-basedcomposites using coiled carbon nanotubes. Comp SciTechnol 2008;68:2876–81.

[27] Mokashi VV, Qian D, Liu YJ. A study on the tensile responseand fracture in carbon nanotube-based composites usingmolecular mechanics. Comp Sci Technol 2007;67:530–40.

[28] Zheng QB, Xia D, Xue QZ, Yan KY, Gao XL, Li Q.Computational analysis of effect of modification on theinterfacial characteristics of a carbon nanotube–polyethylenecomposite system. Appl Surf Sci 2009;255:3534–43.

[29] Wang Q. Buckling of carbon nanotubes wrapped bypolyethylene molecules. Phys Lett A 2011;375:624–7.

[30] St Dennis JE et al. Rod-like carbon nanostructures producedby the direct pyrolysis of alpha-cyclodextrin. Carbon2011;49:718–22.

[31] Brenner DW. Empirical potential for hydrocarbons for use insimulating the chemical vapor-deposition of diamond films.Phys Rev B 1990;42:9458–71.

[32] Brenner DW, Shenderova OA, Harrison JA, Stuart SJ, Ni B,Sinnott SB. A second-generation reactive empirical bondorder (REBO) potential energy expression for hydrocarbons. JPhys Condens Matter 2002;14:783–802.

[33] Mayo SL, Olafson BD, Goddard WA. Dreiding – a generic force-field for molecular simulations. J Phys Chem1990;94:8897–909.

[34] Rappe AK, Casewit CJ, Colwell KS, Goddard WA, Skiff WM.UFF, a full periodic-table force-field for molecular mechanicsand molecular-dynamics simulations. J Am Chem Soc1992;114:10024–35.

[35] Devine B et al. Multilevel computational analysis offluorocarbon polyatomic deposition on diamond. J PhysChem C 2010;114:12535–44.

976 C A R B O N 5 0 ( 2 0 1 2 ) 9 6 8 – 9 7 6

[36] Garrison BJ, Dawnkaski EJ, Srivastava D, Brenner DW.Molecular-dynamics simulations of dimer opening on adiamond (001)(2 · 1) surface. Science 1992;255:835–8.

[37] Garg A, Sinnott SB. Effect of chemical functionalization onthe mechanical properties of carbon nanotubes. Chem PhysLett 1998;295:273–8.

[38] Sinnott SB et al. Model of carbon nanotube growththrough chemical vapor deposition. Chem Phys Lett1999;315:25–30.

[39] Sinnott SB, Shenderova OA, White CT, Brenner DW.Mechanical properties of nanotubule fibers and compositesdetermined from theoretical calculations and simulations.Carbon 1998;36:1–9.

[40] Ni B, Sinnott SB. Chemical functionalization of carbonnanotubes through energetic radical collisions. Phys Rev B2000;61:16343–6.

[41] Sinnott SB, Colton RJ, White CT, Brenner DW. Surfacepatterning by atomically-controlled chemical forces –molecular-dynamics simulations. Surf Sci 1994;316:L1055–60.

[42] Qi LF, Sinnott SB. Polymerization via cluster solid surfaceimpacts: molecular dynamics simulations. J Phys Chem B1997;101:6883–90.

[43] Wijesundara MBJ, Hanley L, Ni B, Sinnott SB. Effects ofunique ion chemistry on thin-film growth byplasma-surface interactions. Proc Natl Acad Sci USA2000;97:23–7.

[44] Adelman SA, Doll JD. Generalized Langevin equationapproach for atom/solid-surface scattering: generalformulation for classical scattering off harmonic solids. JChem Phys 1976;64:2375–88.

[45] Lu JM, Wang YC, Chang JG, Su MH, Hwang CC. Molecular-dynamic investigation of buckling of double-walled carbonnanotubes under uniaxial compression. J Phys Soc Jpn2008;77:044603.

[46] Liu L, Zhao MH, Zhou QL, Chen X. Measuring elastic propertyof single-walled carbon nanotubes by nanoindentation: atheoretical framework. Mech Res Commun 2008;35:256–67.

[47] Yakobson BI, Brabec CJ, Bernholc J. Nanomechanics of carbontubes: instabilities beyond linear response. Phys Rev Lett1996;76:2511–4.

[48] Garg A, Han J, Sinnott SB. Interactions of carbon-nanotubuleproximal probe tips with diamond and graphene. Phys RevLett 1998;81:2260–3.

[49] Harrison JA, Stuart SJ, Robertson DH, White CT. Properties ofcapped nanotubes when used as SPM tips. J Phys Chem B1997;101:9682–5.

[50] Cao GX, Chen X. Mechanisms of nanoindentation on single-walled carbon nanotubes: the effect of nanotube length. JMater Res 2006;21:1048–70.

[51] Shigley JE. Mechanical engineering design. 4th ed. NewYork: McGraw Hill; 1983.

[52] Salvetat J, Briggs GAD, Bonard JM, Bacsa RR, Kulik AJ, StockliT, et al. Elastic and shear moduli of single-walled carbonnanotube ropes. Phys Rev Lett 1999;82:944–7.

[53] Wei XL, Liu Y, Chen Q, Wang MS, Peng LM. The very low shearmodulus of multi-walled carbon nanotubes determinedsimultaneously with the axial young’s modulus via in situexperiments. Adv Funct Mater 2008;18:1555–62.

[54] Frankland SJV, Harik VM. Analysis of carbon nanotube pull-out from a polymer matrix. Surf Sci 2003;525:103–8.