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Computational analysis of effect of modification on the interfacial characteristicsof a carbon nanotube–polyethylene composite system

Qingbin Zheng a,b, Dan Xia a, Qingzhong Xue a,*, Keyou Yan a, Xili Gao a, Qun Li a

a College of Physics Science and Technology, China University of Petroleum, Dongying, Shandong 257061, People’s Republic of Chinab Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China

1. Introduction

Since the discovery of carbon nanotubes (CNTs) by Iijima in1991 [1], CNTs have attracted great research interest due to theirunique properties such as high electrical and thermal conductivity,excellent stiffness against bending, and high tensile strength [2].Using CNTs as nanofibers to enhance the mechanical [3–10],electrical [11–14], thermal [15–17], and optical [18] properties ofcomposite materials has been pursued extensively both inexperimental and theoretical studies. Recently, experiments haveshown remarkable enhancements in elastic modulus and strengthof polymer composites with an addition of small amounts of CNTs[19–22]. Despite these first successes, some critical issues, such asthe uniform dispersion and alignment of the nanotubes within thepolymer matrix, must be overcome before the full potential ofCNTs can be realized. Another most significant challenging issue isthe interfacial bonding between the nanotubes and the polymermatrix, which determine the efficiency of load transfer from thepolymer matrix to the nanotubes [23].

It is well established, from the research on microfiber-reinforced composites over the past few decades, that the structureand properties of the fiber–matrix interface play a major role indetermining mechanical performance and structural integrity ofcomposite materials. In order to take advantage of the very highYoung’s modulus and strength of CNTs, an efficient load transferfrom the polymer matrix to the nanotubes is required. Due to highaspect ratio of the CNTs, large areas are available for load transferin CNT/polymer composites, which is unlike conventional fiber-reinforced polymer composites. However, due to their uniqueelectrical and structural properties, CNTs tend not to bond stronglywith their host matrix. As a result, the potential increases andimprovements in the mechanical properties of a nanotube-reinforced composite are limited by the degree of interfacialstress transfer that can be achieved. One possible way to improvethe interfacial bonding between CNTs and a supported matrix is bychemically functionalizing the CNTs into the matrix. Besides themodifications can also improve the CNTs’ solubility and disper-sibility in its composites.

Generally speaking, there are two main approaches for thesurface modification of CNTs. One is noncovalent attachment ofmolecules and the second is covalent attachment of functionalgroups to the walls of the nanotubes. The noncovalent

Applied Surface Science 255 (2009) 3534–3543

A R T I C L E I N F O

Article history:

Received 17 April 2008

Received in revised form 7 August 2008

Accepted 29 September 2008

Available online 14 October 2008

PACS:

81.05.Tp

Keywords:

Carbon nanotube polymer composites

Molecular mechanics

Molecular dynamics

Interfacial characteristics

A B S T R A C T

In this study, the non-covalent association of single-walled nanotube (SWNT) with polyethylene (PE)

molecule and the influence of sidewall modification on the interfacial bonding between the SWNTs and

polymer were investigated using molecular mechanics (MM) and molecular dynamics (MD) simulations.

The model of interaction between the initially separated PE and SWNT fragments, which can be either

wrapping or filling, was computed. The possible extension of polymers wrapping or filling SWNTs can be

used to structurally bridge the SWNTs and polymers to significantly improve the load transfer between

them when SWNTs are used to produce nanocomposites. The interfacial bonding characteristics between

the single-walled nanotubes, on which –COOH, –CONH2, –C6H11, or –C6H5 groups have been chemically

attached, and the polymer matrix were also investigated by performing pullout simulations. The results

show that appropriate functionalization of nanotubes at low densities of functionalized carbon atoms

drastically increase their interfacial bonding and shear stress between the nanotubes and the polymer

matrix, where chemisorption with –C6H5 groups to as little as 5.0% of the nanotube carbon atoms

increases the shear stress by about 1700%. Furthermore, this suggests the possibility to use functionalized

nanotubes to effectively reinforce other kinds of polymer-based materials as well.

� 2008 Elsevier B.V. All rights reserved.

* Corresponding author. Tel.: +86 546 8392836; fax: +86 546 8392123.

E-mail address: [email protected] (Q. Xue).

Contents lists available at ScienceDirect

Applied Surface Science

journa l homepage: www.e lsev ier .com/ locate /apsusc

0169-4332/$ – see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.apsusc.2008.09.077


attachment, which including polymer wrapping and filling, isone of the possible solutions to improve nanotube compositeinterface when CNTs with openings are used to producenanocomposites. The covalent attachment, which includes‘‘grafting to’’ and ‘‘grafting from’’ method, is the other basicapproaches to improve the strength of the interaction betweenthe CNTs and the polymer matrices [4]. However, due todifficulties in devising experiments to study the CNT–polymerinterface, molecular mechanics (MM) and molecular dynamics(MD) simulations have become increasingly popular in theinvestigations of reinforcement mechanisms in CNT–polymercomposite systems [24]. Many groups have investigated theinterfaces in CNT-reinforced polymer composites using MM andMD simulations and just cite a few.

The MM study of interfacial binding of CNT/polymercomposites was first conducted by Lordi and Yao [25]. Force-field-based MM calculations were performed to determinebinding energies and sliding frictional stresses to understandthe factors governing interfacial adhesion. The results show thatthe binding energies and frictional forces play only a minor role indetermining the strength of the interface, but that the helicalpolymer conformations are essential. It was suggested that thestrength of the interface may be due mostly to molecular-levelentanglement of the two phases and forced long-range orderingof the polymer. Liao and Li [26] have studied the interfacialcharacteristics of a CNT-reinforced polystyrene (PS) compositesystem through MM simulations and elasticity calculations. Theyfound that the fiber/matrix adhesion comes from electrostatic,van der Waals interaction, mismatch in the coefficients ofthermal expansion and radial deformation induced by atomicinteractions. Frankland et al. [27] have investigated the influenceof chemical cross-links between a single-walled nanotube(SWNT) and a polymer matrix on the matrix–nanotube shearstrength using MD simulations. The results suggest that loadtransfer and modulus of nanotube–polymer composites can beeffectively increased by deliberately adding chemical cross-linking and inadvertent chemical bonding between nanotubesand polymer matrices during processing may be in partresponsible for the enhanced stress transfer observed in somesystems of this type. Wong et al. [28] have studied local fracturemorphologies of CNT/PS rod and CNT/epoxy film composites.Transmission and scanning electron microscopy examinationsshowed that these polymers adhered well to CNT at thenanometer scale. Some of the important interfacial character-istics that critically control the performance of a compositematerial were quantified through MM simulations and elasticitycalculations. Multi-walled CNT morphology-related mechanicalinterlocking at nanometer scale, thermal residual stresses, as wellas relatively cavity free surface for polymer adsorption are alsobelieved to be contributing factors. Gou et al. [23] investigatedthe interfacial bonding of SWNT reinforced epoxy compositesusing a combination of computational and experimental meth-ods. The interfacial shear strength between the nanotube and thecured epoxy resin was calculated to be up to 75 MPa, indicatingthat there could be an effective stress transfer from the epoxyresin to the nanotube. The following experimental resultsprovided evidence of stress transfer in agreement with thesimulation results. Yang et al. [29] have studied the interactionbetween polymers and CNTs using force-field-based MD simula-tion. They found that the specific monomer structure plays a veryimportant role in determining the strength of interactionbetween nanotubes and polymers. The polymers with a backbonecontaining aromatic rings are promising candidates for thenoncovalent binding of CNTs into composite structures, whichcan be used as building blocks in amphiphilic copolymers to

promote increased interfacial binding between the CNT and thepolymeric matrix. Wei [30] has studied temperature dependentadhesion behavior and reinforcement in CNT–polymer compo-site. He found that the interfacial shear stress through van derWaals interactions increases linearly with applied tensile strainsalong the nanotube axis direction and a lower bound value for theshear strength is found up to 46 MPa at low temperatures. Directstress–strain calculations show significant reinforcements in thecomposite in a wide temperature range, with �200% increase inthe Young’s modulus when adding 6.5% volume ratio of shortCNTs.

While most of the cited literature considered MM or MDsimulations for nanotubes of different lengths with different typesof polymers, there have been few reports that investigate non-covalent association of CNT with Polyethylene (PE) molecule andthe influence of modification on the interfacial bonding character-istics. In this study, the non-covalent association of SWNT with PEmolecule and the influence of sidewall modification on theinterfacial bonding between the SWNTs and polymer wereinvestigated using MM and MD simulations.

2. Experimental

2.1. Computational method

In the CNT/polymer composite systems, the dimension of thenanotube is about the same size as a polymer chain and hence thediscrete nature of the atomic interactions between the nanotubesand surrounding polymer matrix should be taken into account. Inother words, the nature of the load transfer should be understoodusing physical-based analysis, where MM and MD simulations willbe the most important tools [31]. In this work, MM and MDsimulations were conducted to explore the interfacial character-istics between the SWNTs and the polymer, through which wecould get useful information for the development of nanotube-based polymeric composites. Here, MM and MD simulations werecarried out using a commercial software package called MaterialsStudio developed by Accelrys Inc. The condensed phase optimiza-tion molecular potentials for atomistic simulation studies (COM-PASS) module in the Materials Studio software was used to conductforce-field computations. The COMPASS was a parameterized,tested and validated first ab initio force-field [32,33], whichenables an accurate prediction of various gas-phase and con-densed-phase properties of most of the common organic andinorganic materials [34–36].

2.2. Force-field

The application of quantum mechanical techniques canaccurately simulate a system of interacting particles, but suchtechniques often cost too much time and are usually feasible onlyin systems containing up to few hundreds of interacting particles.As we know, the main goal of simulations of the systemscontaining a large number of particles is generally to obtain thesystems’ bulk properties which are primarily controlled by thelocation of atomic nuclei, so the knowledge of the electronicstructure, provided by the quantum mechanic techniques, is notcritical. Thus, we could have a good insight into the behavior of asystem if a reasonable, physically based approximation of thepotential (force-field) can be obtained, which can be used togenerate a set of system configurations which are statisticallyconsistent with a fully quantum mechanical description. As statedabove, a crucial point in the atomistic simulations of multi-particlesystems is the choice of the force-fields, a brief overview of whichis given in this section.

Q. Zheng et al. / Applied Surface Science 255 (2009) 3534–3543 3535


In general, the total potential energy of a molecular systemincludes the following terms [37]:

Etotal ¼ Evalence þ Ecross-term þ Enon-bond (1)

Evalence ¼ Ebond þ Eangle þ Etorsion þ Eoop þ EUB (2)

Ecross-term ¼ Ebond�bond þ Eangle�angle þ Ebond�angle

þ Eend-bond�torsion þ Emiddle-bond�torsion

þ Eangle�torsion þ Eangle�angle�torsion (3)

Enon-bond ¼ EvdW þ EColumb þ EH-bond (4)

The valence energy, Evalence, generally includes a bond stretchingterm, Ebond, a two-bond angle term, Eangle, a dihedral bond–torsionterm, Etorsion, an inversion (or an out-of-plane interaction) term, Eoop,and a Urey–Bradlay term (involves interactions between two atomsbonded to a common atom), EUB. The cross-term interacting energy,Ecross-term, generally includes: stretch–stretch interactions betweentwo adjacent bonds, Ebond–bond, bend–bend interactions betweentwo valence angles associated with a common vertex atom, Eangle–

angle, stretch–bend interactions between a two-bond angle and oneof its bonds, Ebond–angle, stretch–torsion interactions between adihedral angle and one of its end bonds, Eend-bond–torsion, stretch–torsion interactions between a dihedral angle and its middle bond,Emiddle-bond–torsion, bend–torsion interactions between a dihedralangle and one of its valence angles, Eangle–torsion, and bend–bend–torsion interactions between a dihedral angle and its two valenceangles, Eangle–angle–torsion. The non-bond interaction term, Enon-bond,accounts for the interactions between non-bonded atoms andincludes the van der Waals energy, EvdW, the Coulomb electrostaticenergy, ECoulomb, and the hydrogen bond energy, EH-bond.

The COMPASS force-field uses different expressions for variouscomponents of the potential energy as follows [34,35]:

Evalence ¼X

b

½K2ðb� b0Þ2 þ K3ðb� b0Þ3 þ K4ðb� b0Þ4�

þXu

½H2ðu � u0Þ2 þ H3ðu � u0Þ3 þ H4ðu � u0Þ4�

þXf

½V1½1� cosðf� f01Þ� þ V2½1� cosð2f� f0

2Þ�

þV3½1� cosð3f� f03Þ��

þX

x

Kxx2 þ EUB

(5)

Ecross-term ¼X

b

Xb0

Fbb0 ðb� b0Þðb0 � b00Þ

þXu

Xu0

Fuu0 ðu � u0Þðu0 � u00Þ

þX

b

Xu

Fbuðb� b0Þðu � u0Þ

þX

b

Xu

Fbuðb� b0Þ � ½V1 cos f

þ V2 cos 2fþ V3 cos 3f�

þX

b0

Xu

Fb0uðb0 � b00Þðb

0 � b00Þ

�½F1 cos fþ F2 cos 2fþ F3 cos 3f�

þXu

Xf

Fufðu � u0Þ � ½V1 cos f

þV2 cos 2fþ V3 cos 3f�

þXf

Xu

Xu0

Kfuu0 cos fðu � u0Þ � ðu0 � u00Þ

(6)

Enon-bond ¼Xi> j

Ai j

r9i j

�Bi j

r6i j

" #þXi> j

qiq j

eri jþ EH-bond (7)

where u, f, and x denote valence angle, dihedral angles, and Wilsonout-of-plane displacements, respectively, b and b0 are the lengthsof two adjacent bonds, and the subscript zero is used to denote thereference unperturbed values, while the remaining force-fieldparameters denoted ki. The formula (7) describes the non-bondedinteractions, while rij denotes the inter-atom distance, qi and qj

denote the atom charges, Aij and Bij denote the Lennard–Joneparameters, e denotes the dielectric constant. Hiði ¼ 2� 4Þ;f0

i ði ¼1� 3Þ;Viði ¼ 1� 3Þ; Fbb0 ; b

00; Fuu0 ; u

00; Fbu; Fbf; Fb0u; Fiði ¼ 1� 3Þ; Fuf;

Kfuu0 , are fitted from quantum mechanics calculations and areimplemented into the Discover module of Materials Studio [38], apowerful commercial atomic simulation program used in thispaper. More detailed values for the parameters are described inreferences [35–38].

2.3. Molecular model

The single chain of PE, with 10 repeating units of CH2 in eachchain, is chosen as a matrix in the study, which is due to itssimplicity and generic representation feature for polymer materi-als. The molecules are better described as oligomers than polymersand the results of our simulation describe the small part (block) of a‘‘long’’ polymer, however, because of its generic representationfeature for polymer, the simulation results is also of greatimportant in devising SWNT reinforced polymer composites. Also,it will take too much simulation time if the chain is as long as thereal polymer chain, and that is another reason for the selection ofshort chain. (10, 10) SWNTs, which have diameters of 13.56 A andlengths of 59.03 A, are selected for the simulations of the SWNT/PEcomposites. The unsaturated boundary effect was avoided byadding hydrogen atoms at the ends of the SWNTs. Each C–C bondlength was 1.42 A and C–H bond length was 1.14 A. The hydrogenatoms had charges of +0.1268e and the carbon atoms connectinghydrogen atoms had charges of �0.1268e, thus the neutrallycharged SWNTs were constructed. The computer graphics pictureof a (10, 10) SWNT model (with 960 carbon atoms and 40 hydrogenatoms) is shown in Fig. 1.

In the part of the influence of modification, MM and MDsimulations were performed on composites reinforced by pristineSWNT and the SWNTs on which 5% of the carbon atoms hadbonded groups (carboxylic group –COOH, amide group –CONH2,alkyl group –C6H11, or phenyl group –C6H5). The functional groupswere randomly end-grafted to the surface of the SWNTs. SWNTswith functional groups randomly chemisorbed to 5% of the carbonatoms are illustrated in the left panel of Fig. 2. The associatedchange in geometry of the atoms on which the phenyl groups arebonded is illustrated in the right panel of Fig. 2, where the bondednanotube atoms are ‘‘raised’’ away from the nanotube axes andhave hybridizations that change from sp2 to sp3 [39].

3. Results and discussion

3.1. Non-covalent association of SWNT with PE molecule

Generally speaking, wrapping and filling are two typicalphenomena which would take place when the interactive processof the SWNT–polymer system is simulated. Here, the MDsimulation for each case study was performed long enough toobserve several cycles of thermal vibration. The interval of eachMD simulation step was typically 1 fs (femtosecond). All calcula-tions in this section were carried out at the initial temperature of

Q. Zheng et al. / Applied Surface Science 255 (2009) 3534–35433536


300 K, using constant number of particles, constant volume andconstant temperature (NVT) ensembles. Constant NVT simulationswere carried out with undefined boundary conditions in arelatively short simulation time. The polymer would move awayeventually and very likely never interact with the CNT again if thesimulation time were long enough, which is a direct consequenceof the fact that we use infinite volume (no boundary conditions).However, this ‘‘escape’’ event is extremely rare and it does notaffect the results within our simulation time [29].

3.1.1. Wrapping

Polymer wrapping of SWNTs has received attention as apromising way for manipulating and organizing SWNTs intoordered structures and improve their dispersion into the matrixof the composites. In this section, the ‘‘wrapping phenomenon’’was investigated through putting one polymer chain at the sideof a (10, 10) SWNT. Though only one chain was investigated andthe polymer chain is short, considering the well representationof the real composite system, the simulation results can alsosupply some useful information that could not be observed bynormal experimental facilities. Fig. 3 shows the image of severalcritical moments (side view and cross-section view). Initially,the chain of PE was twisted under the minimum energy status.One end of the chain was put near the SWNT’s wall, while theother end placed away from the SWNT. The simulation showedthat all the molecular chain would stretch and move towardthe nanotube until they finally wrapped on the surface ofthe helix of the nanotube and the equilibrium was achieved. Itis worth noticing that the center of mass (COM) distancebetween the PE molecule and SWNT is continuously decreasingduring the movement, as seen in Fig. 4. This is also an indicationof the tendency of attraction between the PE molecule andSWNT [40].

Fig. 1. Molecular model of (10, 10) SWNT.

Fig. 2. Illustrating of a (10, 10) SWNT with functional groups randomly chemisorbed to 5% of the carbon atoms.



The dynamic behavior of the polymer molecules can also beillustrated by tracking the interaction energy of the SWNT–polymer molecules. Generally, the interaction energy is estimatedfrom the difference between the potential energy of thecomposites system and the potential energy for the polymermolecules and the corresponding SWNTs as follows:

DE ¼ Etotal � ðESWNT þ EpolymerÞ (8)

where Etotal is the total potential energy of the composite, ESWNT isthe energy of the nanotube without the polymer, and Epolymer is theenergy of the polymer without the nanotube. In other words, theinteraction energy can be calculated as the difference between theminimum energy and the energy at an infinite separation of thenanotube and the polymer matrix [23,24,31]. As shown in Fig. 5,the negative interaction energy indicated that the PE moleculemoved towards the surface of nanotube due to an attractive force.The interaction energy increased until the system reached theequilibrium state. An increase of about 25 Kcal/mol of interactionenergy was observed based on the MD simulation.

3.1.2. Filling

The possibility of filling polymers into nanotubes during real-world composite processing would create the desired structurebridges between nanotubes and polymers. However, the reality of

Fig. 3. Wrapping process within a simulated SWNT–PE system.

Fig. 4. COM distance between PE molecule and SWNT versus simulation time.



this filling will be mainly determined by van der Waalsinteractions between the polymers and the internal surfaces ofthe SWNTs [41]. To study the polymer molecule’s fillingphenomena, MD simulations were set up with the PE chainsinitially placed near the opening at one end of the nanotubes alongthe direction of the nanotube axis.

The configuration of PE molecule and SWNT observed atdifferent time step of the MD simulation is shown in Fig. 6.During the initial 160 ps, the PE molecule was lingering aroundthe opening, constantly changing its orientation to facilitatefilling into the SWNT opening, due to the attractive interactionbetween the molecules. Once the PE molecule achieved the rightorientation, it began entering the SWNT and gradually moved

the entire molecule body into the tube. However, the PEmolecule stayed near the opening, instead of going to the middleof the tube or the opposite opening [41]. An equilibrium state ofthe system was also achieved when the PE molecule wasentirely in the tube. Similar to the previous example, the COMdistance is also studied in this example, and the similar trend ofattraction between the PE molecule and SWNT is againobserved, as shown in Fig. 7. In addition, the approximatelyconstant value of distance after 400 ps indicated that the systemhas approached the equilibrium state [40]. The interactionenergy of the PE molecule and SWNT is given in Fig. 8, showingthat an increase of about 55 Kcal/mol interaction energy of thesystem was observed.

Fig. 6. Filling process within a simulated SWNT–PE system.

Fig. 7. COM distance between PE and SWNT versus simulation time.Fig. 5. Interaction energy of the SWNT–PE molecule.



3.2. Interfacial bonding between the SWNTs and polymer

The bonding strength between the SWNTs and the polymerscan be evaluated by interfacial energy in the composites. The totalinteraction energy, DE, is twice the interfacial bonding energy gscaled by the contact area A [25]:

g ¼ DE

2A(9)

The magnitude of interfacial shear stress from the polymer matrixto the nanotubes is known to strongly influence the mechanicalproperties of nanotube composites. The pullout simulations wereperformed to characterize the interfacial shear stress of thecomposites. The pullout energy, Epullout, is defined as the energydifference between the full embedded nanotube and the completepullout configuration [26]. The pullout energy was divided intothree terms as follows [23]:

Epullout ¼ E2 � E1 ¼ ðDE2 þESWNT2 þ Epolymer2Þ�ðDE1 þ ESWNT1 þ Epolymer1Þ ¼ ðDE2 �DE1ÞþðESWNT2 � ESWNT1Þ þ ðEpolymer2 � Epolymer1Þ

(10)

where E2, E1 is the potential energy of the composite after andbefore the pullout simulation respectively, ESWNT, Epolymer is thepotential energy of the nanotube and the polymer respectively, andDE is the interaction energy between the nanotube and thepolymer. The pullout energy can be related to the interfacial shear

stress, ti, by the following relation:

Epullout ¼Z x¼L

x¼02prðL� xÞtidx ¼ prtiL

2 (11)

ti ¼Epullout

prL2(12)

where r and L are the outer radius and length of the SWNT,respectively, and x is the coordinate along the longitudinal tubeaxis [26].

In the simulations of bonding interactions between thenanotubes and the polymer, each of the composite systems wascomposed of a fragment of SWNT totally embedded inside theamorphous polymer matrix. Each of the configurations was initiatedby randomly generating 247 PE molecular chains surrounding theSWNT using an initial density of 0.9 g/cm3. The models were put intoan NPT ensemble simulation with a pressure of 10 atm and atemperature of 300 K for 10 ps with a time step of 1 fs while holdingthe nanotube rigid. The purpose of this step was to slowly compressthe structure of the matrix polymers to generate initial amorphousmatrix with the correct density and low residual stress. The matrixpolymers were then put into an NVT ensemble simulation andequilibrated for 20 ps with a time step of 0.2 fs with rigid nanotubes.After that, the composites systems were further equilibrated for40 ps at a time step of 2 fs with non-rigid nanotubes to create a zeroinitial stress state using NVT ensembles. The energy of the compositesystems was minimized to achieve the strongest bonding betweenthe nanotubes and the polymer as shown in Fig. 9 [23,31]. Finally, theinterfacial bonding energy and interfacial shear stress werecalculated through pullout simulations.

3.2.1. Interfacial bonding for pristine SWNT

The pullout simulations of a SWNT were performed in order tocharacterize the interfacial shear strength of the composites. TheSWNT was pulled out of the PE matrix along the nanotube axisdirection. Fig. 10 shows the snapshots of the pullout simulations.The interaction energy, pullout energy and interfacial bondingenergy were plotted against the displacement of the SWNT fromthe PE matrix, as shown in Fig. 11. During the pullout, theinteraction energy changed with the displacement linearly anddecreased toward a value of zero, as shown in Fig. 11(a). This is dueto the stable interfacial binding interaction and the decrease ofcontact area during the pullout. Fig. 11(b) indicates that the pulloutenergy of the SWNT/PE composite system was increased as theSWNT was pulled out of the PE. The interfacial binding energy kept

Fig. 8. Interaction energy of the SWNT–PE molecule.

Fig. 9. Molecular model of the SWNT/PE composite system (52.7 A � 52.7 A � 62.7 A): (a) top view; (b) section view.



constant with a value of about 0.15 Kcal/mol A2 during the pullout,as shown in Fig. 11(c). After the SWNT was completely pulled outof the PE, the potential energy of the system was level off and theinteraction energy then kept zero. From the pullout simulation, theinterfacial shear strength between the pristine SWNT and the PEwas about 33 MPa.

3.2.2. Influence of modification

The SWNTs and the PE matrix were not held fixed in the pulloutsimulation. Therefore, the pullout energy has been influenced bythe deformation of the nanotubes and PE matrix during the pullout.Fig. 12 shows the interaction energy changed with the displace-ment nearly linearly during the pullout, which is due to the stableinterfacial binding interaction between the SWNTs and the PEmatrix. However, the interaction energy will keep zero after the

nanotubes were completely pulled out of the PE matrix becausethere was no interaction between the nanotubes and the PE matrix.

Fig. 13 shows the calculated interaction energy (Fig. 13(a)) andinterfacial bonding energy (Fig. 13(b)) for SWNTs as a function ofthe type of functionalization. The figure shows that although thefour types of functionalization could increase the adhesion withthe polymer matrix, the special structure of the functional groupsplays a very important role in determine adhesion to the matrix.We can observe that the SWNT functionalized with –C6H5 directlyin the surface has the most strong interaction with the matrix(about 4 times as compared with that of pristine SWNT), whereasthe SWNT with –COOH, –CONH2, or –C6H11 groups has increasedonly weakly than pristine SWNT. The interfacial bonding, whichappears to be critically dependent on the nanotube–polymerinterface surface area, will increase linearly with the total interfacesurface area4. When the SWNT is chemically functionalized, thecontact area between the nanotube and the polymer matrix will bedrastically increased, which will cause the increase of theinterfacial bonding between the nanotube and the polymer. Thearomatic ring (–C6H5) may has more contact area with the matrixthan the other three functional groups for its special ring structure,which may cause the effective increase of adhesion energy.

Fig. 13(c) shows the interfacial shear stress between SWNTs andpolymer matrix as a function of the type of functionalization. Thefigure shows that the SWNT functionalized with –C6H11 or –C6H5

has increased the shear stress effectively (–C6H11: about 3 times ascompared with that of pristine SWNT, –C6H5: about 17 times ascompared with that of pristine SWNT), whereas the SWNT with –

Fig. 10. Snapshots from the MD simulation of the pullout of the SWNT.

Fig. 12. Interaction energy plots during the pullout of the SWNTs from the matrix.Fig. 11. Energy plots during the pullout of the SWNT. (a) Interaction energy; (b)

pullout energy; (c) interfacial bonding energy.



COOH, or –CONH2 groups has almost the same value as comparedwith that of the pristine SWNT. As shown in Fig. 2, the backbones of–C6H11 and –C6H5 groups nearly parallel with the radial directionof the SWNT, while the –COOH, or –CONH2 groups nearly parallelwith the SWNT axis direction. When the functional groups ofSWNT were successfully embedded into the polymer matrix,which may possibly link SWNTs with the polymer matrix, theshear stress could be effectively increased. The successfulembedding could be happen when the functional groups parallelwith the radial direction of the SWNT, and thus the shear stresscould be effectively increased when the SWNTs are functionalizedwith –C6H11 or –C6H5 groups.

Although the covalent attachment of functional groups to thesurface of nanotubes can improve the efficiency of load transfer,these functional groups might introduce defects on the side wallsof the perfect structure of the nanotubes, which will lower thestrength of the nanotube filler. Some models predict that thechange in mechanical properties of the SWNTs with lower level(�10%) of functionalization is negligible [27]. So SWNTs withappropriate functional groups and lower level of functionalizationmay be the feasible nanotube type for reinforcement. This sectionwas about finding a viable way to get SWNT to go into the polymermatrix to act as reinforcement. The difficulties involved in doingthis arise mostly from the fact that CNTs cannot interact well withother materials. The method pursued here for making the SWNTscapable of effectively interacting with the polymer was based onthe covalent attachment of functional groups to the surface ofSWNTs. By taking advantage of these functional groups, whichcould act as an effective interfacial bridge between the SWNTs andthe polymeric matrix, an effective load transfer could be achievedbetween the SWNTs and the PE matrix. The primary objective ofthis work was to select the appropriate functional groups thatwould provide a good interaction mechanism with the composite’smatrix and act as a load transfer conduit between the SWNTs andthe composite matrix.

4. Conclusions

In this study, the non-covalent association of SWNT with PEmolecule and the influence of sidewall modification on the

interfacial bonding between the SWNTs and polymer wereinvestigated using MM and MD simulations. The model ofinteraction between the initially separated PE and SWNTfragments was computed. The results show that a PE moleculecould wrap around or fill into a (10, 10) SWNT due to theattractive van der Waals interactions. The possibility of the PEmolecule wrapping or filling tube during real-world compositeprocessing would create the desired structure bridges betweenthe nanotubes and polymer, which can be used to significantlyimprove the load transfer between them when SWNTs are usedto produce nanocomposites. The interfacial bonding character-istics between the SWNTs, on which –COOH, –CONH2, –C6H11, or–C6H5 groups have been chemically attached, and the polymermatrix were also investigated by performing pullout simula-tions. The results show that appropriate functionalization ofnanotubes at low densities of functionalized carbon atomsdrastically increase their interfacial bonding and shear stressbetween the nanotubes and the polymer matrix. This indicatesthat increasing the load transfer between SWNTs and a polymermatrix in a composite via feasible chemisorption may be aneffective way and chemical attachment of nanotubes duringprocessing may be in part responsible for the enhanced stresstransfer observed in some systems of the nanotube–polymercomposites. Furthermore, this suggests the possibility to usefunctionalized nanotubes to effectively reinforce other kinds ofpolymer-based materials as well.

Acknowledgments

This work was supported by 973 National Basic ResearchProgram (No. 2008CB617508), the Cultivation Fund of the KeyScientific and Technical Innovation Project Ministry of Education ofChina, and CNPC Innovation Fund (No. 06E1024).

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