16 October 1998

Ž .Chemical Physics Letters 295 1998 273–278

Effect of chemical functionalization on the mechanical propertiesof carbon nanotubes

Ajay Garg, Susan B. Sinnott )

The UniÕersity of Kentucky, Department of Chemical and Materials Engineering, Lexington, KY 40506-0046, USA

Received 1 July 1998; revised 1 July 1998

Abstract

Ž .Carbon nanotubes CNTs have been proposed as ideal fibers for the manufacture of the next generation of compositematerials. To ultimately increase the interaction of the CNTs with polymer matrices, researchers have attached chemicalfunctional groups to the nanotube walls. The effects of covalent chemical attachments on the mechanical properties of

Ž .single-walled CNTs are examined with classical molecular dynamics simulations. The maximum compressive bucklingforce for various functionalized and non-functionalized CNTs is calculated. It is found that covalent chemical attachmentsdecrease the maximum buckling force by about 15% regardless of tubule helical structure or radius. q 1998 Published byElsevier Science B.V. All rights reserved.

There has been intense interest in carbon nano-Ž .tubules CNTs since their discovery by Iijima in

w x1991 1 in large part because they posses uniquew xstructural and electronic properties 2–4 . Recently,

new methods have been developed to produce CNTsw xin gram-scale quantities 5,6 thus further increasing

their potential use in numerous applications. Depend-ing on the synthesis conditions, nanotubules can be

Ž . w xsingle-walled a single tubule or multi-walled 1,7Ž2–50 tubules positioned concentrically within one

.another . The helical symmetry of the carbon atomsaround the axis of the cylinder is denoted by two

Ž .integers m,n that indicate the number of latticevectors in the graphite plane used to make the tubulew x8 . Various helical structures are possible, such as

) Corresponding author. Tel.: q1-606-257-5857; Fax: q1-606-323-1929; E-mail: sinnott@engr.uky.edu

Ž .numerous different achiral, ‘‘zigzag’’ n,0 andŽ . w‘‘armchair’’ n,n configurations. Calculations 9–

x w x14 and experimental measurements 15,16 havedetermined that CNTs possess high Young’s moduli,in the range of 1–5 TPa, in the direction of thetubule axis. This has lead to their designation as the‘‘ultimate fiber’’ for use in new, ultrastrong, fiber-

w xmatrix composite materials 17 .To increase the strength of adhesion between

fibers and a polymer matrix, fibers are frequentlymodified through the chemical attachment of poly-mer groups to the walls of the fiber. The interactionof the polymer groups with the matrix ‘‘tethers’’ thefiber more securely to the matrix, thus enhancing the

w xmechanical strength of the composite 18 . When theŽcomposite is deformed quickly e.g., during a colli-

.sion , the chemical attachments are generally thoughtto break at the fiber wall. On the other hand, when

Ž .the composite is deformed slowly e.g., during creep ,the bonded chain disentangles from the surrounding

0009-2614r98r$ - see front matter q 1998 Published by Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2614 98 00969-5

( )A. Garg, S.B. SinnottrChemical Physics Letters 295 1998 273–278274

matrix. In either case, the movement of the attachedpolymer dissipates energy during deformation thusincreasing the overall resistance of the material tofailure.

Recently, researchers have worked to attachdichlorocarbene covalently to the walls of single-wall

w xCNTs 19 with the goal of using standard methodsto substitute polymer chains in place of the chlorineatoms. These functionalized tubules can then be usedto create the next generation of ultrastrong compositematerials. However, there is concern that since thecovalent chemical tethers alter the sp2-hybridizationof the tubule wall at the points of attachment, themechanical properties that made CNTs desirablefibers in the first place could be destroyed.

Therefore the goals of this letter are to investigateŽ .a the effect of covalent chemical functionalizationon the stiffness of CNTs in the direction of the

Ž .tubule axis, b the dependence of the functionaliza-tion effects on tubule helical structures and radii andŽ .c the stability of functionalized CNTs during defor-mation.

The approach is standard molecular dynamicssimulations that integrate Newton’s equations of mo-tion using a third-order Nordsieck predictor–correc-

w xtor method 20 with a time step of 0.15 fs. Theforces on the individual atoms are determined from a

Ž .reactive-empirical bond order REBO hydrocarbonpotential that realistically describes the properties ofmolecular and solid-state carbon materials, includingbond energies, bond lengths and lattice constantsw x21,22 . Because the atoms are treated as hardspheres, forces from electronic effects like orbitalresonance and symmetry are neglected. In addition,since this potential is comparatively short ranged,long-ranged forces, like H-bonding, are not included.

The potential predicts elastic constants for dia-mond of c s10.78=1011 Nrm2, c s1.31=11 12

1011 Nrm2 and c s6.8=1011 Nrm2 which com-44

pare favorably with the respective experimental val-ues of c s10.76=1011 Nrm2, c s1.25=1011

11 122 11 2 w xNrm and c s5.8=10 Nrm 23 . Further-44

more, the fitting database includes the elastic con-stants within the graphite plane so these are repro-duced exactly. Over the last few years the REBOpotential has been successfully used to simulate nu-merous processes including the deformation of car-

w xbon nanotubules 10,11,14,17 , the formation of

w xfullerenes from graphitic ribbons 24 and variousw xsurface chemical reactions 25–30 .

In this work plain and functionalized tubules withradii from 0.339 to 1.665 nm were studied. Thefunctionalized tubules had H C5C groups cova-2

lently bonded to the walls. The H C5C groups were2

chosen to chemically mimic the long chains that willultimately be attached. The number of functionalgroups varied with the helical arrangement of thetubule atoms, with about 104 segments attached to

Ž .100 unit cells of n,n armchair CNTs and 52 seg-Ž .ments attached to 60 unit cells of n,0 zig-zag

tubules. Throughout the simulations, three-five unitŽcells at each end of the tubules were held fixed i.e.,

the atoms in these unit cells were not allowed to.evolve in time . Moving towards the center of the

tubule, the next 12–15 unit cells had Langevin ther-mostats applied to maintain the temperature of the

Ž .system at 300 K. The remaining unit cells 40–60 ,including all the functional groups, evolved in timeaccording to Newton’s equations of motion with noconstraints.

To compress the tubules, the fixed atoms at oneend were displaced towards the other end in incre-ments of 0.005 nm. Following each displacement thesystem was equilibrated for 400 time steps. Theforce on the M fixed atoms that were displaced wascalculated as follows:

Ny dE rŽ .potentialF s 1Ž .i

dri

F sSMF 2Ž .total i i

Ž N .where E r is the potential energy of atom ipotential

due to the surrounding N atoms, r is the atomici

coordinate of atom i and F is the force on atom i.i

The atomic forces were calculated at each of the 400relaxation steps following each displacement andthen averaged over the last 100 steps. Additionalaveraging was performed on the resulting force dis-placement curves to filter out the noise from thermalvibrations. Most simulations ran for about 80 ps.

Snapshots from simulations of the compression ofŽ .regular and functionalized 15,15 CNTs are shown

in Figs. 1 and 2. In each case, as the tubule iscompressed, kinks or buckles develop in the body ofthe nanotube that correspond to modulations in theforce curve, shown in Fig. 3. The maximum force is

( )A. Garg, S.B. SinnottrChemical Physics Letters 295 1998 273–278 275

Ž . Ž .Fig. 1. Snapshots from the simulation where a plain, 15,15 armchair carbon nanotubule is compressed. a Initial, equilibrated structure andŽ .b compressed configuration at times34 ps.

( )A. Garg, S.B. SinnottrChemical Physics Letters 295 1998 273–278276

( )A. Garg, S.B. SinnottrChemical Physics Letters 295 1998 273–278 277

Ž .Fig. 3. Force curves for the compression of regular and functionalized 15,15 carbon nanotubules as a function of the compressiondisplacement.

the buckling force and Fig. 3 shows that chemicalcovalent functionalization decreases the buckling

Ž .force for the 15,15 tubule by about 19.4%. Thismeans that the functionalized tubule is less stiff inthe direction of the tubule axis than the regularunfunctionalized tubule and therefore is predicted todeform more readily in a composite. This degrada-tion in stiffness is caused by the formation of sp3-hy-bridized carbon ‘‘defect’’ sites on the tubule wallsfrom the attachment of the functional groups.

Table 1 summarizes the buckling forces for all theCNTs considered both with and without functional-ization. The data shows that the magnitude of thebuckling force per 100 atoms decreases as the radiusof the carbon nanotube increases. This agrees withprevious studies that find that tubules become lessstiff in the direction of the tubule axis as the radius

w xincreases 11,15–17 . In all cases, regardless of heli-cal symmetry or radius, functionalization decreasesthe stiffness of the tubule by an average value ofabout 15%.

Table 1 also shows that, on the whole, helicalstructure has little effect on the results of chemical

functionalization. However, in the case of the small-est radii CNTs, those with radii around 0.3–0.4 nm,some of the functional groups dissociate from thewalls during compression. This is due to the alreadyhigh strain associated with the smaller CNTs dis-

w xcussed by several groups 14,24 . When these smallCNTs are deformed, the strain of deformation, cou-pled with the inherent strain, causes the chemicallyattached groups to dissociate from the CNT walls.Hence, while calculations and measurements have

w xshown that smaller tubules are more stiff 11,15–17Ž .and therefore more desirable for use in composites ,they must not be so small that their residual straindestabilizes the functionalized tubule.

In conclusion, the effect of chemical covalentfunctionalization of the walls of CNTs has beenstudied using classical molecular dynamics simula-tions. The results show that the introduction of sp3-hybridized carbon defects due to chemical function-alization does degrade the mechanical strength ofCNTs by an average value of 15%. Helical symme-try has little effect on the results of chemical func-tionalization but some functional groups dissociate

Ž . Ž .Fig. 2. Snapshots from the simulation where a functionalized 15,15 armchair carbon nanotubule is compressed. a Initial, equilibratedŽ . Ž .structure, b compressed and buckled structure at times34 ps and c final configuration after straightening at times74 ps.

( )A. Garg, S.B. SinnottrChemical Physics Letters 295 1998 273–278278

Table 1Buckling force for functionalized and non-functionalized tubules as a function of tubule radius and helical structure

Nanotube Radius Buckling force of Buckling forced of Degradation of buckling Stable functionalŽ .nm plain CNTs functionalized CNT force due to state

Ž . Ž . Ž .nNr100 atoms nNr100 atoms functionalization %

Ž .5,5 0.339 130 110 14.4 NoŽ .10,10 0.678 120 105 12.5 YesŽ .15,15 1.017 108 88.6 19.4 YesŽ .25,25 1.695 86.4 76 12.0 YesŽ .10,0 0.391 82 71 13.4 NoŽ .17,0 0.665 76 63.6 17.0 Yes

A stable functional state indicates that no functional groups dissociated from the tubule walls during compression.

from CNTs with radii below about 0.4 nm duringcompression due to the high strain associated withthese systems. This improved understanding theproperties of chemically functionalized CNTs will behelpful to accurately predict their behavior as fibersin fiber-matrix composites.

Acknowledgements

The authors gratefully acknowledge the support ofŽNASA Ames Research Center Grant Number NAG

.2-1121 and many helpful discussions with RobertHaddon, Ernst Richter and Peter Eklund.

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