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Carbon 153 (2019) 745e756

Contents lists avai

Carbon

journal homepage: www.elsevier .com/locate/carbon

Creep performance of CNT-based nanocomposites: A parametric study

Wei Jian a, Denvid Lau a, b, *

a Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, Chinab Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

a r t i c l e i n f o

Article history:Received 6 May 2019Received in revised form1 July 2019Accepted 19 July 2019Available online 22 July 2019

* Corresponding author. Department of Civil andMassachusetts Institute of Technology, Cambridge, M

E-mail address: denvid@mit.edu (D. Lau).

https://doi.org/10.1016/j.carbon.2019.07.0690008-6223/© 2019 Elsevier Ltd. All rights reserved.

a b s t r a c t

Epoxy materials have been widely applied in various applications ranging from nanoscale structures,such as microelectronic devices, to macroscale components in aerospace and building constructions. Thestructural stability under constant loadings is a major concern for polymeric materials during long-termservice. The incorporation of carbon nanotubes (CNTs) into epoxy matrix has been considered to enhancecreep resistance in recent decades. Substantial improvement of CNT-based nanocomposites largely relieson optimized design of material microstructures, and such manipulation requires comprehensive un-derstanding of creep behavior in CNT-epoxy nanocomposites. In addition, effective arrangement of CNTsin epoxy matrix for enhancement in creep resistance needs a systematic study of related parametriceffects. In this work, the effects of CNT length, CNT weight fraction and CNT dispersion state on the creepresponse of nanocomposites are investigated using molecular dynamics simulations. The creep defor-mation of nanocomposites including creep strain and system dynamics are found to decrease with theincreasing length, weight fraction and good dispersion state, showing the contribution of the additionalCNTs towards the resistance in time-dependent deformation. These results suggest that the CNT-epoxynanocomposites with superior creep resistance can be achieved in the design by optimizing the CNT-associated parameters.

© 2019 Elsevier Ltd. All rights reserved.

1. Introduction

Due to its excellent functions of gap filling and surface protec-tion, epoxy has been widely used as coatings or adhesives forvarious engineering applications. Triggered by the increasing needfor better mechanical performance, the incorporation of nano-fillers into polymer matrices has been reported as an advancedapproach to develop strengthened composite materials over thepast few decades. Among these additives, carbon nanotubes (CNTs)become an attractive candidate because of their high aspect ratio,low density, and exceptional physical properties such as highYoung's modulus, heat conductivity, and electrical conductivity.CNT-reinforced epoxy nanocomposites present many advantagesover neat epoxy, and are considered promising compositematerialsfor the new generation, having been employed as bonding adhe-sives, electronics encapsulation in nano-devices, and structuralparts in automobiles and airplanes [1e3]. While the mechanicalproperties of CNT-reinforced epoxy nanocomposites, including

Environmental Engineering,A, 02139, USA.

high strength, stiffness and toughness, have been extensivelyinvestigated [4e8], the research on creep behaviors showing thelong-term performance of these material systems is still limitedand not adequately thorough. Due to its inherent viscoelastic na-ture, the epoxy matrix usually undergoes time-dependent defor-mation when subjected to continuous stress. The irreversibledisentanglement of polymer chains including slippage andstretching, takes place over time. Progressive plastic deformationcan lead to failure in epoxy nanocomposites, causing unexpectedmalfunction or even life threatening hazard in structural compo-nents. Therefore, a good description of creep response in thesepolymeric systems and an optimal addition of CNTs for improvedcreep resistance are important aspects to be considered for prac-tical engineering applications that require long-term stability anddurability.

In the existing literature [9e13], creep experiments on CNT-reinforced epoxy nanocomposites yield inconsistent conclusionson whether the addition of CNTs can greatly improve the creepresistance of nanocomposites. The creep deformation of epoxynanocomposites in long-term creep tests is found to be reducedwith low CNT weight fractions (wt%) in the range from 0.1% to0.25%, but the creep deformation accelerates when the CNT weight

W. Jian, D. Lau / Carbon 153 (2019) 745e756746

fraction reaches 1wt%, which is attributed to the aggregation ofCNTs [9]. The incorporation of CNTs with up to 1wt% is reported tohave a negligible influence on the creep behavior of the epoxymatrix [10]. The reinforcing ability of CNTs in nanocomposites isweaker with higher weight fraction and creep loads as theagglomeration occurs and the adhesion between CNT and epoxymatrix deteriorates [14]. In contrast, increasing CNTweight fractionwith good dispersion results in a noticeable decrease of creepdisplacements [11]. The pronounced improvement in creep resis-tance of nanocomposites remains even under high temperatureand creep loads due to high aspect ratio and interfacial area be-tween CNT and epoxy matrix [12,13,15]. Such a discrepancy inexperimental findings is caused by various fabrication factors,indicating the dependency of the creep resistance on CNT size, CNTweight fraction and state of dispersion. Polymer nanocompositesshould be designed with emphasis on the CNT-associated param-eters in order to obtain optimal creep resistance, which requires theknowledge of the effects of CNT geometry, amounts, and dispersionstates on the creep responses. The creep responses of polymernanocomposites with various volume fractions, diameters and ar-rangements of CNTs, applied loading levels and conditions havebeen analyzed using micromechanical modeling, which are foundto be in good agreement with experiments [16e18]. In addition tothese theoretical results, the understanding of the creep deforma-tion and the reinforcing mechanism of creep resistance in nano-composites at the atomistic level is still needed as creep response isfundamentally related to the change of molecular mobility inpolymeric systems. The stress-induced segmental dynamics inpolymer matrix has been quantitatively measured using an opticalphotobleaching technique [19], and a quantitative connection be-tween molecular mobility and macroscopic deformation has beenestablished. It is speculated that the addition of CNTs has a hin-drance effect on polymer chain mobility of epoxy matrix, as well asthe chain slippage and disentanglement [9,12,15]. However, it isinsufficient to investigate the effect of individual parameter on thesegmental dynamics in epoxy matrix solely by experiments asthere are limitations in the precise control of changing variablesand the visualization of microstructures. Therefore, the investiga-tion from nanoscale perspective can help to uncover the micro-structural interactions and dynamics in the CNT-epoxynanocomposites, enabling the analysis of the effects from differentCNT-associated parameters.

Molecular dynamics (MD) simulations are considered to be aneffective tool to elucidate various effects on mechanical perfor-mance and connect mechanical response and structural deforma-tion to molecular interactions and motions in nanocompositesystems. MD simulations have been applied to explore the materialproperties, uncover the mechanical phenomena at the molecularlevel, and capture the atomic movements in different materials andbonded systems [20e24]. The structures and physical properties ofepoxy materials have been predicted using MD simulations[25e28]. The nanoparticles are found to alter the topological con-straints and enhance the entanglement under deformation inpolymer nanocomposites [29]. In addition, MD simulations hasbeen applied to investigate the effect of interactions between CNTand polymer matrix in the interfacial region on the structural anddynamical properties of nanocomposites [30]. It is reported that theoptimization on the mechanical behavior of the CNT-reinforcedepoxy nanocomposites highly depends on the interactions be-tween CNTs and epoxymatrix [31e33]. The dispersion state of CNTshas a significant effect on the interfacial interactions between CNTsand epoxy matrix, which changes the interphase, thermal andmechanical properties in nanocomposites [34]. Although MD sim-ulations are employed in measuring and analyzing the mechanicalproperties of material systems, it is noted that MD approach is

inherently limited by the accessible time scales down to the orderof nanoseconds. Creep of materials spreads a wide range of timescales, from seconds of microscopic process to years of macroscopicdeformation. However, MD simulations can still reproduce trendssimilar to the experimental observations, even though there arediscrepancies in the timescale, as the macroscopic deformation islinked to themicroscopic displacement in a consistentmanner [35].The simulation results using extreme settings for surroundingconditions (such as high temperature or external stress) candescribe the creep response in different material systems andelucidate the underlying mechanism of creep deformation [36e38]from a relatively short time duration as suitable interactions be-tween molecules in the systems are correctly provided. Moreover,MD simulations are capable of capturing the features of individualsegmental movement in material systems corresponding to thecreep response observed in the experimental timescales, uncover-ing the details in molecular interactions that cannot be obtainedfrom bulk measurement.

The objective of this study is to investigate the effects of CNT-associated parameters on the creep responses of CNT-epoxynanocomposites, and to understand the role of CNT in creepresistance of nanocomposite during the deformation process. Inorder to characterize the creep response, the time-dependentstrains and the microstructural evolutions in different materialsystems are captured and compared using MD simulations. Inaddition, the segmental dynamics of the nanocomposite systemsare quantified to reveal how CNTs affect the movements of epoxychains during the creep process. Mechanical insights into thecreep-resistant mechanism with the addition of nano-fillers topolymer matrix, as well as guidance for the optimal design of CNT-reinforced polymer nanocomposites with enhanced creep resis-tance for applications through modulating the CNT-associated pa-rameters, are provided.

2. Simulation methods

2.1. Molecular models

In this study, the cross-linked epoxy matrix of nanocompositesconsists of two widely used constituents, diglycidyl ether ofbisphenal A (DGEBA) as the epoxy monomer and triethylenetr-amine (TETA) as the cross-linker. The chemical and atomisticstructures of these molecules are shown in Fig. 1(a). To make faircomparison in different cases, the numbers of epoxy monomersand cross-linkers are kept constant, which are 270 and 90 respec-tively. The pristine single-walled carbon nanotube (SWCNT) ofarmchair (5,5), one of the well-recognized and typical structures ofnanotubes, is prepared as the nano-filler. The end effect of the CNTsincluding the cap and the hydrogenation is not considered in thisstudy. In order to understand how the addition of CNTs affects thecreep performance of nanocomposites, the effects of three pa-rameters associated with the nano-filler, including CNT length, CNTweight fraction, and CNT dispersion (i.e. dispersed and aggregatedstates) are investigated. The set-up of atomistic models involvestwo main steps: (1) the strategic placement of the CNTs with var-iable parameters into the unreacted mixture of epoxy moleculesand (2) the cross-linked reaction of epoxy molecules around theCNTs. In step one, different arrangements of CNTs in the systems arecarried out by varying one chosen parameter while keeping theremaining parameters fixed to separate the effect from these pa-rameters. To elucidate the effect of the CNT length, the lengths areset in the range of 4e50 Å, corresponding to the aspect ratios of0.73, 2.18, 3.63 and 7.26 respectively. The selected range containsvarious CNT shapes from the particle shape to the rod shape.Although the CNT length is several orders of magnitude shorter

(a)

DGEBA

TETA (b)

NH2 NH2R

NH NH2R

(c)

C1C2

u

O O

OO

NH

HN NH2

H2N

Fig. 1. (a) Chemical and atomistic structures of DGEBA (epoxy monomer) and TETA(cross-linker); (b) Cross-linking reaction; (c) The definition of the unit vector con-necting C1 and C2 carbon atoms on the epoxy monomer for the calculation of bondautocorrelation function. (A colour version of this figure can be viewed online.)

W. Jian, D. Lau / Carbon 153 (2019) 745e756 747

than the bulk materials, the mechanical properties and the trendsfromMD simulations are in good agreement with the experimentalresults [39] as the models still can represent the interfacial struc-tures between CNT and polymer matrix from atomistic scale. To

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elucidate the effect of CNT weight fraction, the weight fractions arevaried from 2wt% to 12wt%, covering the low and high amountcases. This range is selected because the loading of nanofiller innanocomposite is commonly set around 10wt% in the experiments[40]. The major issue in adding CNTs with high weight fraction (i.e.over 10wt%) into epoxy matrix is the aggregation of CNTs. Severalprocessing techniques have been applied to overcome this obstacleduring fabrication, such as ultrasonic bath, shear mixing, extrusionand chemical purification of CNTs, which are common approachesin lab or for large-scale production [41]. The incorporation of highCNT content has been realized in previous studies [42e44]. Toelucidate the effect of dispersion state, the CNTs are placed uni-formly in the simulation box for the dispersed case, while they formbundles for the aggregated case because of the strong van derWallsforces between sidewalls and the tendency to orient parallel toeach other [45]. The initial distance between the adjacent CNTs in

aggregation is taken as 3.4 Å, which is the interlayer separationdistance in multi-walled CNTs. The classification of these two CNTdispersion states has been stated in the previous study [46]. Thedispersion of individual CNTs represents the nanodispersion,whereas the dispersion of CNT bundle represents the macro-dispersion. The initial uncross-linked structures of nanocompositesare prepared with epoxymolecules and the designed arrangementsof CNTs using the Monte Carlo packing algorithm according to therotational isomeric states model [47]. In step two, the cross-linkedepoxy matrix is built using the computational algorithm developedin the previous study [25]. Before the cross-linking reactions, theenergy minimization and equilibration run of the structure arecarried out. The procedure in the cross-linking algorithm isdescribed as follows: (1) the reactive atoms of monomers andcross-linkers located within the reaction radius are recognized; (2)the C-O and N-H bonds comprising the recognized reactive atomsare broken; (3) the recognized reactive atoms are bonded to formcross-links as shown in Fig. 1(b); (4) the unreacted atoms at theopen epoxide groups are saturated with hydrogen atoms; (5) thecross-linked structure is relaxed every time before entering thenext reaction process. The reaction radius is selected as 3 Å to 10 Åwith an increment of 0.5 Å, as the geometric distortions in thesystem are usually generated during the cross-linking process witha reaction radius over 10 Å without a long equilibrium process [25].All the material systems are constructed using Materials Studiosoftware [48].

The intra- and intermolecular interactions in the nanocompositesystems are described by the polymer consistent forcefield (PCFF)[49], which is parametrized from quantum mechanics calculationsand works well with polymers and organic materials. The func-tional form of PCFF is expressed as [49]:

Here, the energy terms consist of the bonded energy terms, thecross-terms and the non-bonded energy terms. The first four termsare bonded interactions, including the covalent bond stretchingenergy, the bond angle bending energy, the torsion angle rotationenergy and the improper energy. The next several cross-couplingterms are for cross interactions, including bond-bond, bond-angle, angle-angle, bond-torsion, angle-torsion, and angle-angle-torsion coupling terms, respectively. The last two terms representthe van der Waals force and the Coulombic force. The predictedphysical mechanical and thermal properties of epoxy materialshave been found in good agreement with experimental data[25,50], showing the reliability of PCFF. In addition, the propertiesof CNT [51] and the interfacial interactions between CNT and epoxy[26,52] can be characterized with PCFF, which is well correlated toexperimental findings. Therefore, PCFF is chosen in this study. Thepartial charges on different types of atoms are calculated using the

W. Jian, D. Lau / Carbon 153 (2019) 745e756748

QEqmethod, as the prediction of charges in polymeric systems is ingood agreement with experiments and ab initio calculations [53].The non-bonded interactions, including both Coulombic in-teractions and van der Waals interactions are calculated with acutoff distance of 10 Å, which is commonly selected in the study ofCNT-epoxy systems [25,34]. The particle-particle particle-mesh(PPPM) algorithm [54] is used to account for the long-rangeCoulombic interactions. All the simulations are performed underperiodic boundary conditions.

2.2. Simulation details and theoretical analysis

The initial configurations are first equilibrated using NVTensemble (constant number of particles and constant temperature)at the temperature of 300 K for 100 ps. Then, the internal stressesare removed by a further relaxation at the pressure of 1 atm usingNPT ensemble (constant number of particles, constant temperatureand constant pressure) for another 10 ns. The root mean squaredisplacement (RMSD) of the atoms reaches a constant level beforethe competition of equilibration, which indicates that the systemshave been equilibrated properly. The whole process is repeatedthree times for different equilibrium configurations in each case tominimize random errors in the simulation results. The corre-sponding density of equilibrated structures and the system pa-rameters for nanocomposite systems are summarized in Table 1.The densities are found to be higher than the obtained value of neatepoxy in the previous study [55]. The increase of density in epoxynanocomposites with the addition of CNTs has been found in thevarious experimental and simulation work, which is attributed tomore closely packed polymer structure at the CNT-epoxy interface[34]. All the simulations are conducted with the Large-scaleAtomic/Molecular Massively Parallel Simulator (LAMMPS) pack-age [56] using a time step of 1 fs. For the creep simulations, aconstant tensile stress of 100MPa is applied along the z directionwhile keeping the other two directions at the stress of 1 atm. Thisgives a large load on the nanocomposites to obtain an obvious creepdeformation during the simulation time. The resulting evolution of

the strain is calculated as εðtÞ ¼ LðtÞ�L0L0

� 100%, where L denotes theinstant length of the simulation box parallel to the direction of theapplied stress and L0 the initial equilibrium value of this lengthbefore creep simulation. In addition, the changes of configurationsin the nanocomposite systems during the deformation process aretracked for comparison to analyze the creep responsewith differentCNT-associated parameters.

During creep deformation, the chain reorientation in the poly-mer matrix is induced by the external stress, and the molecularmotion is altered over time. There is a strong correlation betweenthe molecular mobility and the strain rate [19,57e59]. To quantifythe local segmental dynamics of polymer chains in the epoxy

Table 1Summary of CNT-epoxy nanocomposite structures.

System CNT length

Nanocomposites containing dispersed CNTs with different lengths 4.9214.7624.6049.19

Nanocomposites containing dispersed CNTs with different weight fractions 24.60

Nanocomposites containing aggregated CNTs with different weight fractions 24.60

matrix under constant stress, the bond autocorrelation function iscommonly employed [60,61], which is defined as:

Cb ¼ hP2½uð0Þ,uðtÞ�i (2)

Here, P2 is the second Legendre polynomial. uð0Þ and uðtÞ representthe unit vectors aligned along the bonds connecting the end carbonatom to the central carbon atom in DGEBA at the initial state andthe running time t respectively, as shown in Fig. 1(c). The angularbrackets denote an average over all the bonds in the systems. Thisfunction can help to characterize the changed mobility of polymerchains in nanocomposites during creep deformation. The change ofdynamics can be further quantified by fitting the bond autocorre-lation function to the Kohlrausch-Williams-Watts (KWW) function,which is expressed as [62,63]:

CbðtÞ ¼ C0e�ðt=teff Þb (3)

where C0, teff and b are fitting parameters, representing the pre-exponential factor that accounts for the relaxation process in veryshort time scales, the characteristic relaxation time, and thestretching exponent. The polymeric systems experience a range ofrelaxation times under stress. The different ranges, including theshort-time regime that corresponds to the bond and angle vibra-tions known as b relaxation, and the long-time regime that corre-sponds to the conformational transitions known as a relaxation, areconsidered in the fitting of the bond autocorrelation function by theKWW function [64,65]. Here, the characteristic relaxation time teffis taken as the measure of the change in dynamics in different timeregions instead of the measure of structural relaxation time, whichassumes a single relaxation process is dominant over the probedtime scales [57]. Moreover, the characteristic relaxation time re-flects the relaxation time to the equilibrium state of polymerchains, therefore the larger value of the characteristic relaxationtime indicates that a longer time is required to generate the samecreep deformation of material systems.

3. Results and discussion

3.1. Effect of CNT length

We first examine the effect of CNT length on the creep responseof CNT-epoxy nanocomposites. Fig. 2(a) plots the time evolution ofcreep strain for the CNT-epoxy nanocomposites containing CNTswith lengths of 4.92 Å, 14.76 Å, 24.60 Å and 49.19 Å. The creep re-sponses of these nanocomposites present two creep stages duringthe simulation time, including the primary creep and the secondarycreep, which are consistent with the trend observed from experi-ments [66,67]. After applying the stress, the system deforms at ahigh strain rate at the primary creep stage with an instantaneous

(Å) CNT weight fraction (wt%) No. of CNT Total no. of atoms Density (g/cm3)

4.4 10 16230 1.156± 0.0024 16170 1.157± 0.0012 16150 1.159± 0.0021 16150 1.176± 0.003

2.2 1 15950 1.158± 0.0034.4 2 16150 1.159± 0.0028.4 4 16550 1.173± 0.00312.1 6 16950 1.188± 0.0014.4 2 16150 1.158± 0.0028.4 4 16550 1.181± 0.00312.1 6 16950 1.202± 0.001

(a) (b)

0 500 1000 1500 20000

2

4

6

8

10

12

Str

ain

(%)

Time (ps)

CNT(L4.92)-epoxyCNT(L14.76)-epoxyCNT(L24.60)-epoxyCNT(L49.19)-epoxy

0 10 20 30 40 500.5

1.0

1.5

2.0

2.5

3.0

Str

ain

rate

(109

s-1)

Length (Å)

Fig. 2. (a) Creep strain as a function of time during creep deformation of nanocomposites with the CNT lengths of 4.92Å, 14.76 Å, 24.60 Å and 49.19 Å. (b) The correspondingconstant strain rate at the secondary creep stage. It is found that the creep strain and the creep strain rate decrease with increasing length. (A colour version of this figure can beviewed online.)

W. Jian, D. Lau / Carbon 153 (2019) 745e756 749

response at the beginning, followed by a slow decrease of strainrate from the initial value. The strain rate then remains constantduring the secondary creep stage. The secondary creep stage, as thesteady-state creep evolution, generally takes up a relatively largefraction of creep time, and the constant strain rate plays animportant role in determining the dimensional stability of materialsystems. The simulation results show that the longer length leadsto less instantaneous strain and creep strain during the deforma-tion process, indicating stronger creep resistance in nano-composite. This is confirmed with experimental results that longerCNTs induced smaller creep rate than shorter CNTs, which can beattributed to better load transfer efficiency from longer CNTs [68]. Asimilar trend with the effect of CNT length has also been found inthe mechanical modulus under tensile deformation [39,69]. Tobetter quantify the steady-state creep, the constant creep strainrates at the steady stage as a function of different lengths arecalculated in Fig. 2(b). The creep strain rate is effectively reducedwith the increasing CNT length, showing a high dependence ofcreep response on the CNT length. Specifically, the creep strain rateat the system with long CNT length (49.19 Å) is about 61.7% lowerthan the corresponding creep strain rate with short CNT length(4.92Å).

The energy change during creep deformation is also explored toexplain different creep responses during deformation. The changesin potential energy, bonded and non-bonded energies of thenanocomposites with short CNT (4.92 Å) and long CNT (49.19 Å) areshown in Fig. 3(a) and (b), which suggest different deformationmechanisms for different CNT lengths. During the primary creepstage, the bond, bond angle and improper energies change slightlyfor the short CNT case in Fig. 3(a). The increase in the potentialenergy is associated with increases in the dihedral angle and thenon-bonded interaction energies, which are caused by chain rota-tion and chain slippage in the epoxy matrix under stress. For thelong CNT case in Fig. 3(b), the increase of the potential energy ismainly associated with the non-bonded interaction, while thebond, bond angle, dihedral angle, and improper energies changeslightly. During the steady-state creep stage, the dihedral angle andthe non-bonded energies contribute to the increase of the potentialenergy in both systems. The chain rotation starts in the secondarycreep for the long CNT case. A close look at microstructural evolu-tion in the nanocomposites with short and long CNT is presented inFig. 3(c) and (d). For the epoxy chains near the CNTs, the aromatic

ring on the DGEBA monomer tends to align parallel to the sidewallof CNT due to the p-p stacking type attraction [31,70]. This orien-tation of epoxy chain appears less in the short CNTcase, while moreepoxy chains lie flat on the sidewall of CNT in the long CNT case.This is because the epoxy monomers in the crosslinked networkstructure are not allowed to interact easily with the CNT to achievea large amount of aligned aromatic rings, and the long lengthprovides more probability for the reorientation. This also indicatesmore attraction between CNT and epoxy matrix in the long CNTcase. Before applying the external stress, the molecular sizes ofCNT-epoxy nanocomposites in the four cases are similar to eachother after equilibrium (see Table 2), and the average of simulationbox dimensions is 53.2 Å� 53.9 Å� 54.6 Å with the volume of156,564.4Å3. However, the increase in density is evident for thelong CNT (49.19 Å) as can be seen from Table 1, as the increase inattraction results in a more packed structure at the interface. Theinterfacial interaction between CNT and epoxy matrix hinders andslows down the stretching and sliding of epoxy chains towards thedirection of the applied load, which leads to smaller creep strainand creep strain rate during the deformation process. Additionally,the short CNT is easily driven by the surrounding epoxy chains andtends to rotate andmove during the deformation process, while thelong CNT remains almost in its the original position. The MSDcharacterizing the movement of CNT for these two cases are eval-uated in Fig. 3(e), which suggests the short CNT provides lessenhancement of creep resistance than the long CNT. The change inthe creep strain rates in different systems is associated with thepolymer chain movement in the epoxy matrix. The local segmentaldynamics and the corresponding relaxation time are measured inorder to explore quantitatively the chain mobility in nano-composites during creep deformation as shown in Fig. 4(a). Themobility is significantly lowered with longer CNT length as evi-denced by the slower decay of Cb(t) immediately after the stress isapplied. The trends of the bond autocorrelation decays also corre-spond to different creep stages during the deformation process. Thefast decay apparently appears in the primary creep stage where thestrain rate is high. To further explore the change in creep strain ratein different nanocomposites during steady stage creep, the localpolymer relaxations are measured by fitting the KWW function.The normalized characteristic relaxation time and the stretchingexponent as a function of the CNT length from the KWW fittings areshown in Fig. 4(b) and (c). The epoxy chains exhibit longer

(a) (b)

0 500 1000 1500 20000

5

10

15

20

25

30

35

40

MS

D(Å

2 )

Time (ps)

CNT(L4.92)-epoxyCNT(L49.19)-epoxy

(e)

0 500 1000 1500 2000-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Enon-bonded

Ebond

Eangle

Edihedral

Eimproper

Epot

E-E

0(1

03K

cal/m

ol)

Time (ps)

Primary Secondary

0 500 1000 1500 2000-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Eimproper

Edihedral

Enon-bonded

E-E

0(1

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Time (ps)

Epot

Ebond

Eangle

Primary Secondary

(c) t = 0 ps t = 200 ps t = 2000 ps

(d) t = 0 ps t = 200 ps t = 2000 ps

sliding sliding

sliding

rotation

sliding

rotation

Fig. 3. The energy changes during creep deformation in the nanocomposites with the CNT lengths of (a) 4.92Å and (b) 49.19 Å. The snapshots capture the structural evolutionduring creep deformation in the nanocomposites with the CNT lengths of (c) 4.92Å and (d) 49.19 Å. The CNTs are colored in black. The epoxy segments aligned parallel to thesidewall of CNT are colored in red, and the stretched and sliding epoxy chains are colored in blue. The single-headed arrow indicates the slippage, and the double-headed arrowindicates the stretching. (e) The mean-squared displacement of the CNTs during deformation in the two cases. (A colour version of this figure can be viewed online.)

W. Jian, D. Lau / Carbon 153 (2019) 745e756750

relaxation time with longer CNT length, resulting in slower chaindynamics in the corresponding nanocomposite during creepdeformation. Enhanced mobility and faster relaxation time relatedto strain rate under stress have been found in previous studies[57e59,65]. The stretching exponents increase slightly with

increasing CNT length, indicating a narrowing of the relaxationspectrum in the nanocomposite system. These results implicitlyreveal that the creep deformation is affected significantly by thechange from the short length to the long length.

Table 2Dimension of equilibrated systems with different CNT lengths.

CNT length (Å) x (Å) y (Å) z (Å) Volume (Å3)

4.92 53.8 54.3 54.5 159213.014.76 53.2 54.1 54.9 158008.824.60 53.2 53.3 54.3 153970.949.19 52.7 53.7 54.8 155083.5

W. Jian, D. Lau / Carbon 153 (2019) 745e756 751

3.2. Effect of CNT weight fraction

We next investigate the effect of CNT weight fraction on thecreep response of CNT-epoxy nanocomposites. The time-dependent creep strain of different nanocomposites containingCNTs with weight fractions of 2.2%, 4.4%, 8.4%, and 12.1% are plottedin Fig. 5(a). The results show that the creep response becomes lesspronounced with the increasing amount of CNTs when CNTs arewell dispersed. The enhancement of creep resistance in nano-composites is more obvious at high CNT weight fraction, i.e., 12.1wt%. This trend is also found in previous experimental results, whichshow that the increasing content of CNTs with good dispersion canlead to improved creep resistance [12,14]. The strain rates ofdifferent systems at the secondary creep stage are calculated inFig. 5(b). The strain rate presents a linear descending trend withincreasing weight fraction. While the strain rate is altered by alarger range under the effect of CNT length, the reduction in thevalue of creep strain rate is more pronounced when the CNTweightfraction is increased.

To further investigate the difference in the creep response, the

(a) (b)

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b(t)

Time (ps)

Fig. 4. (a) The bond autocorrelation decay for nanocomposites with the CNT lengths of 4.92Å(b) The fitted characteristic relaxation time in different nanocomposites as a function of thsystems. (c) The corresponding stretching exponent as a function of aspect ratio. The trendsthis figure can be viewed online.)

(a)

0 500 1000 1500 20000

2

4

6

8

10

Str

ain

(%)

Time (ps)

CNT(2.2%)-epoxyCNT(4.4%)-epoxyCNT(8.4%)-epoxyCNT(12.1%)-epoxy

Fig. 5. (a) Creep strain as a function of time during creep deformation of nanocompositeconstant strain rate at the secondary creep stage. The increasing creep response is found w

microstructural evolution of the nanocomposites with low (2.2wt%) and high (12.1wt%) CNTweight fractions during the deformationare shown in Fig. 6(a) and (b). In the low CNT weight fraction case,fewer epoxy chains are aligned to the CNT sidewall, and themovement of these epoxy chains are restricted. More epoxy chainsaway from the CNT surface are stretched by the external stress andslide against each other during the deformation process. In theheight weight fraction case, more surface area of CNTs with thesame aspect ratio is allowed to interact with the epoxy matrix,which induces more confinement in the movement of epoxychains. The CNTs are surrounded by more epoxy chains, and thestretching in the epoxy matrix is restricted. The epoxy chainsslippage mainly appears in the area without CNTs, resulting in thecreep deformation smaller than that in the low weight fractioncase. However, it should also be noted that the higher CNT weightfraction can cause the aggregation of CNTs due to the van derWaalsattractions between them during the dispersion process. Similarly,the tendency for CNTs to move close to their neighbors can beobserved in the simulation of the nanocomposite with high CNTweight fraction as shown in Fig. 6(c). The bundle formation of nano-fillers in the polymer matrix has been observed in the previoussimulationwork [71]. Theway the dispersion state affects the creepresponse will be investigated in the next section.

The dynamics and polymer relaxation in the creep process aremeasured by the bond autocorrelation function and the charac-teristic relaxation time from KWW fitting as shown in Fig. 7(a) and(b). The slower decay of the bond autocorrelation function underconstant stress appears in the nanocomposite systems with higherCNT weight fraction. In the low weight fraction case, the external

(c)

30 40 50

gth (Å)

0 10 20 30 40 500.90

0.92

0.94

0.96

0.98

1.00S

tret

chin

gE

xpon

ent(

)

Length (Å)

, 14.76 Å, 24.60 Å and 49.19 Å during the creep deformation within the simulation time.e CNT length, the values are normalized by the relaxation time from the undeformedindicate the increasing chain mobility with decreasing CNT length. (A colour version of

(b)

2 4 6 8 10 120.0

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ain

rate

(109

s-1)

Weight fraction (wt%)

s with the CNT weight fractions of 2.2%, 4.4%, 8.4% and 12.1%. (b) The correspondingith decreasing weight fraction. (A colour version of this figure can be viewed online.)

(a) t = 0 ps t = 200 ps t = 2000 ps

(b) t = 0 ps t = 200 ps t = 2000 ps

(c)

Fig. 6. The snapshots capture the structural evolution during creep deformation in the nanocomposites with the CNT weight fractions of (a) 2.2% and (b) 12.1%. The CNTs are coloredin black. The epoxy segments aligned parallel to the sidewall of CNT are colored in red, and the stretched epoxy chains are colored in blue. The double-headed arrow indicates thestretching. (c) The tendency of aggregation of CNTs in the high CNT weight fraction case. (A colour version of this figure can be viewed online.)

(a)1 10 100 1000

0.88

0.90

0.92

0.94

0.96

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CNT(2.2%)-epoxyCNT(4.4%)-epoxyCNT(8.4%)-epoxyCNT(12.1%)-epoxy

Bon

dA

utoc

orre

latio

nC

b(t)

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0.92

0.94

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etch

ing

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onen

t()

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0 2 4 6 8 10 12 14

10-1

100

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axat

ion

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e(

eff/

eff,0

)

Weight fraction (wt%)

Fig. 7. (a) The bond autocorrelation decay for nanocomposites with the CNT weight fractions of 2.2%, 4.4%, 8.4% and 12.1% during the creep deformation within the simulation time.(b) The fitted characteristic relaxation time during secondary creep stages in different systems as a function of weight fraction, the values are normalized by the relaxation time fromthe undeformed systems. (c) The corresponding stretching exponent as a function of weight fraction. The trends indicate the increasing chain mobility with decreasing CNT weightfraction. (A colour version of this figure can be viewed online.)

W. Jian, D. Lau / Carbon 153 (2019) 745e756752

W. Jian, D. Lau / Carbon 153 (2019) 745e756 753

constant stress raises the global orientation of the individual chainsin the direction of the deformation, accompanied by a fast increasein local segmental mobility. The results of the characteristic relax-ation time calculated from the curve fitting of KWW functionindicate that, stronger attraction between the CNTs and the epoxymatrix with increasing weight fraction of CNTs causes a significantslowdown in the relaxation time of the polymer chains, resulting ina deceleration in the decay of CbðtÞ to zero and the reinforced creepresistance of the nanocomposites. Thus, higher CNT weight fractionconstraints the movement of the epoxy chains, leading to slowerdynamics in the material systems. The calculated stretching expo-nents are shown in Fig. 7(c). Similarly to the earlier results, theheterogeneity exhibits with the increase in the CNTweight fraction.The simulation results suggest that the addition of CNTs with highweight fraction results in better creep resistance due to interfacialinteraction between CNTs and epoxy and the slow relaxation dy-namics in epoxy matrix.

3.3. Effect of CNT dispersion

The previous experimental studies found that the aggregation ofnano-fillers in polymer matrix leads to poor mechanical perfor-mance, which reduces the efficiency of reinforcement for nano-composites [72e74]. For the creep responses, the simulation resultsof time-dependent creep strain in the CNT-epoxy nanocompositeswith two different dispersion states, including well dispersion andaggregation are shown in Fig. 8(a). Consistent with the experi-mental observations [9,74], all sets of results show a considerabledecrease in creep strainwith dispersed CNTs compared to that withaggregated CNTs. The creep deformation becomes severe with highCNT weight fraction, especially in the case of 8.4 wt% CNTs. Thecorresponding creep strain rate at the steady stage shown inFig. 8(b) exhibits opposite trends in these two cases. The strain ratedecreases with good dispersion of CNTs, and increases with theaggregation of CNTs. Although there is little difference in the initialcreep for the two dispersion states with the same weight fractions,the deviation in the creep strain rate leads to different deformationduring creep process. These results suggest that the function ofcreep resistance is severely impaired in the aggregation state,especially at high CNT weight fraction.

The creep responses of the nanocomposites with 8.4 wt% CNTsin two dispersion states are shown in Fig. 9(a) and (b). In contrast tothe well-dispersed state, fewer epoxy chains are aligned parallel tothe direction of the CNT sidewall in the aggregated state. The sliding

0 500 1000 1500 20000

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12

Str

ain

(%)

Time (ps)

CNT(4.4%, dispersed)-epoxyCNT(4.4%, aggregated)-epoxyCNT(8.4%, dispersed)-epoxyCNT(8.4%, aggregated)-epoxyCNT(12.1%, dispersed)-epoxyCNT(12.1%, aggregated)-epoxy

(a)

Fig. 8. (a) Creep strain as a function of time during creep deformation of nanocomposites wstates. (b) The corresponding constant strain rate at the secondary creep stage. The increascolour version of this figure can be viewed online.)

and rotation in the direction of the external stress in the epoxymatrix are more obvious in the aggregated state. This is mainlyattributed to the difference in the interfacial area between CNT andepoxy. The well-dispersed state provides more available interfacialarea under the same volume fraction condition, maximizing theinterfacial attraction between CNT and epoxy and the confinementof epoxy movement.

Accordingly, the local segmental dynamics are measured asshown in Fig. 10(a). The enhancement of dynamics is more signif-icant in the aggregated state with higher CNT weight fraction. Thenanocomposites with dispersed CNTs has a better structuralnetwork that can provide better creep resistance, as the movementof epoxy chains is uniformly trapped during creep deformation. Incontrast, the aggregation of CNTs apparently causes local confine-ment of chain movement. The dynamics in the nanocompositespresents heterogeneous, and the epoxy chains far from the CNTcluster have higher mobility. Therefore, the addition of aggregatedCNTs leads to reduction in the performance of creep resistance. Thecharacteristic relaxation time and the stretching exponent arecalculated in Fig. 10(b) and (c). Compared with the dispersed state,the relaxation time is reduced in the aggregation state, resulting infast chain dynamics and increasing creep response. For thedispersed state, the increases in both the relaxation time and thestretching exponent indicate that more epoxy chains are effectivelyrestricted with high weight fraction. The decreasing stretchingexponent in the aggregated state shows that the distribution ofbond relaxation time becomes more heterogeneous as the localconfinement becomes more apparent high weight fraction. Theresults indicate that the achievement of better creep resistance innanocomposites from experiments relies on the state of nano-dispersion, where each CNT is individually dispersed in epoxymatrix.

The above simulation results demonstrate that the improve-ment of creep resistance in epoxy-CNT nanocomposites can beobtained by modulating different CNT-associated parametersincluding the length, the weight fraction and the dispersion state.The increasing CNT length provides more probability for theinterfacial binding, and the increasing CNT weight fraction in thewell-dispersed state enlarges the interfacial area for the in-teractions between CNT and epoxy matrix. Therefore, long CNTlength and high CNT weight fraction with a good dispersion statecan effectively reduce creep deformation and slow the dynamics ofthe system, leading to an enhancement in creep resistance. Whilethis work focuses on the three important factors that are commonly

2 4 6 8 10 12 140.0

0.5

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rate

(109

s-1)

Weight fraction (wt%)(b)

ith the CNT weight fractions of 4.4%, 8.4% and 12.1% at the dispersed and aggregateding creep response is found in the aggregated state with the same weight fraction. (A

(a) t = 0 ps t = 200 ps t = 2000 ps

(b) t = 0 ps t = 200 ps t = 2000 ps

Fig. 9. The snapshots capture the structural evolution during creep deformation in the nanocomposites with the CNT weight fraction of 8.4% at the (a) dispersed and (b) aggregatedstates. The CNTs are colored in black. The epoxy segments aligned parallel to the sidewall of CNT are colored in red, and the stretched and rotated epoxy chains are colored in blue.The single-headed arrow indicates the rotation, and the double-headed arrow indicates the stretching. (A colour version of this figure can be viewed online.)

1 10 100 10000.80

0.82

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CNT(4.4%, dispersed)-epoxyCNT(4.4%, aggregated)-epoxyCNT(8.4%, dispersed)-epoxyCNT(8.4%, aggregated)-epoxyCNT(12.1%, dispersed)-epoxyCNT(12.1%, aggregated)-epoxy

Bon

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eff, 0

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Fig. 10. (a) The bond autocorrelation decay for nanocomposites with the CNT weight fractions of 4.4%, 8.4% and 12.1% at the dispersed and aggregated states during the creepdeformation within the simulation time. (b) The fitted characteristic relaxation time during secondary creep stages in different nanocomposites as a function of weight fraction atthe dispersed and aggregated states, the values are normalized by the relaxation time from the undeformed systems. (c) The corresponding stretching exponent as a function ofweight fraction the dispersed and aggregated. The trends indicate that the chain mobility increases with aggregated CNTs, and the effect becomes more significant with higher CNTweight fraction. (A colour version of this figure can be viewed online.)

W. Jian, D. Lau / Carbon 153 (2019) 745e756754

encountered in applications, there are still some other designconstraints. The roles of other control parameters such as CNTradius, CNT orientation and CNT/epoxy interactions will be inves-tigated in a future study.

4. Conclusions

In this study, the effects of CNT-associated parameters on thecreep responses of nanocomposites are investigated using MD

simulations. The simulation results reveal that both the creep strainand the creep strain rate decrease with increasing CNT length andCNT weight fraction. Such enhancement in creep resistance mustbe achieved alongside a well-dispersed state of CNT in the epoxymatrix. In addition, the dynamics of materials systems are alteredwith changes in the relaxation time during the creep deformation,which is in line with the changes in the creep strain rate. Themolecular simulations provide direct insight into the role played byCNTs in the conformational changes and the interfacial interactions

W. Jian, D. Lau / Carbon 153 (2019) 745e756 755

between CNT and epoxy that governs the creep response of CNT-epoxy nanocomposites. The sliding and stretching of epoxychains are effectively confined in the nanocomposites with longCNT length, high CNT weight fraction and good CNT dispersion. Theunderstanding of the effect of different CNT-associated parameterson the creep deformation and the strengthening mechanism inCNT-epoxy nanocomposite is useful for the design of targetedcreep-resistant nanocomposites in applications.

Acknowledgment

The authors are grateful to the support from the Research GrantsCouncil (RGC) of the Hong Kong Administrative Region, China[Project No. CityU11255616].

References

[1] R.H. Baughman, A.A. Zakhidov, W.A. de Heer, Carbon nanotubes–the routetoward applications, Science 297 (5582) (2002) 787e792.

[2] J.N. Coleman, U. Khan, Y.K. Gun'ko, Mechanical reinforcement of polymersusing carbon nanotubes, Adv. Mater. 18 (6) (2006) 689e706.

[3] A.K. Naskar, J.K. Keum, R.G. Boeman, Polymer matrix nanocomposites forautomotive structural components, Nat. Nanotechnol. 11 (2016) 1026.

[4] J.N. Coleman, U. Khan, W.J. Blau, Y.K. Gun’ko, Small but strong: a review of themechanical properties of carbon nanotubeepolymer composites, Carbon 44(9) (2006) 1624e1652.

[5] L. Guadagno, L. Vertuccio, A. Sorrentino, M. Raimondo, C. Naddeo, V. Vittoria,G. Iannuzzo, E. Calvi, S. Russo, Mechanical and barrier properties of epoxyresin filled with multi-walled carbon nanotubes, Carbon 47 (10) (2009)2419e2430.

[6] C. Kingston, R. Zepp, A. Andrady, D. Boverhof, R. Fehir, D. Hawkins, J. Roberts,P. Sayre, B. Shelton, Y. Sultan, V. Vejins, W. Wohlleben, Release characteristicsof selected carbon nanotube polymer composites, Carbon 68 (2014) 33e57.

[7] W. Zhai, N. Srikanth, L.B. Kong, K. Zhou, Carbon nanomaterials in tribology,Carbon 119 (2017) 150e171.

[8] R. Nadiv, G. Shachar, S. Peretz-Damari, M. Varenik, I. Levy, M. Buzaglo, E. Ruse,O. Regev, Performance of nano-carbon loaded polymer composites: dimen-sionality matters, Carbon 126 (2018) 410e418.

[9] W. Zhang, A. Joshi, Z. Wang, R.S. Kane, N. Koratkar, Creep mitigation incomposites using carbon nanotube additives, Nanotechnology 18 (18) (2007)185703.

[10] O. Starkova, S. Buschhorn, E. Mannov, K. Schulte, A. Aniskevich, Creep andrecovery of epoxy/MWCNT nanocomposites, Compos. Part A Appl Sci Manuf43 (8) (2012) 1212e1218.

[11] A.K. Dutta, D. Penumadu, B. Files, Nanoindentation testing for evaluatingmodulus and hardness of single-walled carbon nanotubeereinforced epoxycomposites, J. Mater. Res. 19 (1) (2011) 158e164.

[12] M. Tehrani, M. Safdari, M.S. Al-Haik, Nanocharacterization of creep behavior ofmultiwall carbon nanotubes/epoxy nanocomposite, Int. J. Plast. 27 (6) (2011)887e901.

[13] T. Glaskova-Kuzmina, A. Aniskevich, M. Zarrelli, A. Martone, M. Giordano,Effect of filler on the creep characteristics of epoxy and epoxy-based CFRPscontaining multi-walled carbon nanotubes, Compos. Sci. Technol. 100 (2014)198e203.

[14] G.C. Papanicolaou, A.G. Xepapadaki, E.D. Drakopoulos, K.P. Papaefthymiou,D.V. Portan, Interphasial viscoelastic behavior of CNT reinforced nano-composites studied by means of the concept of the hybrid viscoelasticinterphase, J. Appl. Polym. Sci. 124 (2) (2012) 1578e1588.

[15] T. Glaskova, K. Aniskevich, A. Borisova, Modeling of creep for multiwall carbonnanotube/epoxy nanocomposite, J. Appl. Polym. Sci. 129 (6) (2013)3314e3324.

[16] R. Ansari, M.K. Hassanzadeh-Aghdam, Micromechanical investigation ofcreep-recovery behavior of carbon nanotube-reinforced polymer nano-composites, Int. J. Mech. Sci. 115e116 (2016) 45e55.

[17] R. Ansari, M.K. Hassanzadeh-Aghdam, Micromechanical characterizing elastic,thermoelastic and viscoelastic properties of functionally graded carbonnanotube reinforced polymer nanocomposites, Meccanica 52 (7) (2017)1625e1640.

[18] Q. Sun, Z. Meng, G. Zhou, S.-P. Lin, H. Kang, S. Keten, H. Guo, X. Su, Multi-scalecomputational analysis of unidirectional carbon fiber reinforced polymercomposites under various loading conditions, Compos. Struct. 196 (2018)30e43.

[19] H.-N. Lee, K. Paeng, S.F. Swallen, M.D. Ediger, Direct measurement of molec-ular mobility in actively deformed polymer glasses, Science 323 (5911) (2009)231e234.

[20] Z. Yu, D. Lau, Flexibility of backbone fibrils in a-chitin crystals with differentdegree of acetylation, Carbohydr. Polym. 174 (2017) 941e947.

[21] L-h Tam, A. Zhou, Z. Yu, Q. Qiu, D. Lau, Understanding the effect of temper-ature on the interfacial behavior of CFRP-wood composite via molecular dy-namics simulations, Compos. B Eng. 109 (2017) 227e237.

[22] H. Hao, L-h Tam, Y. Lu, D. Lau, An atomistic study on the mechanical behaviorof bamboo cell wall constituents, Compos. B Eng. 151 (2018) 222e231.

[23] W. Xia, X. Qin, Y. Zhang, R. Sinko, S. Keten, Achieving enhanced interfacialadhesion and dispersion in cellulose nanocomposites via amorphous in-terfaces, Macromolecules 51 (24) (2018) 10304e10311.

[24] S. Wang, E. Gao, Z. Xu, Interfacial failure boosts mechanical energy dissipationin carbon nanotube films under ballistic impact, Carbon 146 (2019) 139e146.

[25] L-h Tam, D. Lau, A molecular dynamics investigation on the cross-linking andphysical properties of epoxy-based materials, RSC Adv. 4 (62) (2014)33074e33081.

[26] Q.L. Xiong, S.A. Meguid, Y. Wang, G.J. Weng, Molecular dynamics and atom-istic based continuum studies of the interfacial behavior of nanoreinforcedepoxy, Mech. Mater. 85 (2015) 38e46.

[27] Y. Li, Q. Wang, S. Wang, A review on enhancement of mechanical and tribo-logical properties of polymer composites reinforced by carbon nanotubes andgraphene sheet: molecular dynamics simulations, Compos. B Eng. 160 (2019)348e361.

[28] Y. Li, S. Wang, Q. Wang, M. Xing, Enhancement of fracture properties ofpolymer composites reinforced by carbon nanotubes: a molecular dynamicsstudy, Carbon 129 (2018) 504e509.

[29] R.A. Riggleman, G. Toepperwein, G.J. Papakonstantopoulos, J.-L. Barrat, dePablo, JJ. Entanglement network in nanoparticle reinforced polymers, J. Phys.Chem. 130 (24) (2009) 244903.

[30] Z. Wang, Q. Lv, S. Chen, C. Li, S. Sun, S. Hu, Effect of interfacial bonding oninterphase properties in SiO2/epoxy nanocomposite: a molecular dynamicssimulation study, ACS Appl. Mater. Interfaces 8 (11) (2016) 7499e7508.

[31] X. Chen, L. Zhang, M. Zheng, C. Park, X. Wang, C. Ke, Quantitative nano-mechanical characterization of the van der Waals interfaces between carbonnanotubes and epoxy, Carbon 82 (2015) 214e228.

[32] S. Haghighi, R. Ansari, S. Ajori, Influence of polyethylene cross-linked func-tionalization on the interfacial properties of carbon nanotube-reinforcedpolymer nanocomposites: a molecular dynamics study, J. Mol. Model. 25 (4)(2019) 105.

[33] M. Rahmat, P. Hubert, Carbon nanotubeepolymer interactions in nano-composites: a review, Compos. Sci. Technol. 72 (1) (2011) 72e84.

[34] K.S. Khare, R. Khare, Effect of Carbon Nanotube Dispersion on glass transitionin cross-linked epoxyecarbon nanotube nanocomposites: role of interfacialinteractions, J. Phys. Chem. B 117 (24) (2013) 7444e7454.

[35] T. Sentjabrskaja, P. Chaudhuri, M. Hermes, W.C.K. Poon, J. Horbach,S.U. Egelhaaf, M. Laurati, Creep and flow of glasses: strain response linked tothe spatial distribution of dynamical heterogeneities, Sci. Rep. 5 (2015) 11884.

[36] I.H. Sahputra, A.T. Echtermeyer, Creep-fatigue relationship in polymer: mo-lecular dynamics simulations approach, Macromol. Theory Simul. 24 (1)(2015) 65e73.

[37] K. Darling, M. Rajagopalan, M. Komarasamy, M. Bhatia, B. Hornbuckle,R. Mishra, K.N. Solanki, Extreme creep resistance in a microstructurally stablenanocrystalline alloy, Nature 537 (7620) (2016) 378e381.

[38] A.L. Bowman, S. Mun, S. Nouranian, B.D. Huddleston, S.R. Gwaltney,M.I. Baskes, M.F. Horstemeyer, Free volume and internal structural evolutionduring creep in model amorphous polyethylene by molecular yynamicssimulations, Polymer 170 (2019) 85e100.

[39] B. Arash, Q. Wang, V.K. Varadan, Mechanical properties of carbon nanotube/polymer composites, Sci. Rep. 4 (2014) 6479.

[40] M. Ionita, Multiscale molecular modeling of SWCNTs/epoxy resin compositesmechanical behaviour, Compos. B Eng. 43 (8) (2012) 3491e3496.

[41] J. Chen, B. Liu, X. Gao, D. Xu, A review of the interfacial characteristics ofpolymer nanocomposites containing carbon nanotubes, RSC Adv. 8 (49)(2018) 28048e28085.

[42] N. Li, Y. Huang, F. Du, X. He, X. Lin, H. Gao, Y. Ma, F. Li, Y. Chen, P.C. Eklund,Electromagnetic interference (EMI) shielding of single-walled carbon nano-tube epoxy composites, Nano Lett. 6 (6) (2006) 1141e1145.

[43] Y. Huang, N. Li, Y. Ma, F. Du, F. Li, X. He, X. Lin, H. Gao, Y. Chen, The influence ofsingle-walled carbon nanotube structure on the electromagnetic interferenceshielding efficiency of its epoxy composites, Carbon 45 (8) (2007) 1614e1621.

[44] Z. Spitalsky, G. Tsoukleri, D. Tasis, C. Krontiras, S.N. Georga, C. Galiotis, Highvolume fraction carbon nanotubeeepoxy composites, Nanotechnology 20(40) (2009) 405702.

[45] S.W. Kim, T. Kim, Y.S. Kim, H.S. Choi, H.J. Lim, S.J. Yang, C.R. Park, Surfacemodifications for the effective dispersion of carbon nanotubes in solvents andpolymers, Carbon 50 (1) (2012) 3e33.

[46] M.J. Green, Analysis and measurement of carbon nanotube dispersions:nanodispersion versus macrodispersion, Polym. Int. 59 (10) (2010)1319e1322.

[47] D.N. Theodorou, U.W. Suter, Detailed molecular structure of a vinyl polymerglass, Macromolecules 18 (7) (1985) 1467e1478.

[48] Materials Studio, Accelrys Software Inc., 2017.[49] H. Sun, S.J. Mumby, J.R. Maple, A.T. Hagler, An ab initio CFF93 all-atom force

field for polycarbonates, J. Am. Chem. Soc. 116 (7) (1994) 2978e2987.[50] M. Li, H. Zhou, Y. Zhang, Y. Liao, H. Zhou, Effect of defects on thermal con-

ductivity of graphene/epoxy nanocomposites, Carbon 130 (2018) 295e303.[51] J. Lee, V. Varshney, A.K. Roy, B.L. Farmer, Single mode phonon energy trans-

mission in functionalized carbon nanotubes, J. Chem. Phys. 135 (10) (2011)104109.

[52] Q.L. Xiong, S.A. Meguid, Atomistic investigation of the interfacial mechanicalcharacteristics of carbon nanotube reinforced epoxy composite, Eur. Polym. J.

W. Jian, D. Lau / Carbon 153 (2019) 745e756756

69 (2015) 1e15.[53] A.K. Rappe, W.A. Goddard III, Charge equillbratlon for molecular dynamics

slmulations, J. Phys. Chem. 95 (8) (1991) 3358e3363.[54] R.W. Hockney, J.W. Eastwood, Computer Simulation Using Particles, CRC

Press, 1988.[55] F. Jeyranpour, G. Alahyarizadeh, B. Arab, Comparative investigation of thermal

and mechanical properties of cross-linked epoxy polymers with differentcuring agents by molecular dynamics simulation, J. Mol. Graph. Model. 62(2015) 157e164.

[56] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics,J. Comput. Phys. 117 (1) (1995) 1e19.

[57] R.A. Riggleman, K.S. Schweizer, Pablo JJd, Nonlinear creep in a polymer glass,Macromolecules 41 (13) (2008) 4969e4977.

[58] H.-N. Lee, R.A. Riggleman, J.J. de Pablo, M.D. Ediger, Deformation-inducedmobility in polymer glasses during multistep creep experiments and simu-lations, Macromolecules 42 (12) (2009) 4328e4336.

[59] R.A. Riggleman, G.N. Toepperwein, G.J. Papakonstantopoulos, J.J. de Pablo,Dynamics of a glassy polymer nanocomposite during active deformation,Macromolecules 42 (10) (2009) 3632e3640.

[60] R.A. Riggleman, H.-N. Lee, M.D. Ediger, J.J. de Pablo, Free volume and finite-size effects in a polymer glass under stress, Phys. Rev. Lett. 99 (21) (2007)215501.

[61] A.V. Lyulin, N.K. Balabaev, M.A.J. Michels, Correlated segmental dynamics inamorphous atactic polystyrene: A molecular dynamics simulation study,Macromolecules 35 (25) (2002) 9595e9604.

[62] R.G. Palmer, D.L. Stein, E. Abrahams, P.W. Anderson, Models of hierarchicallyconstrained dynamics for glassy relaxation, Phys. Rev. Lett. 53 (10) (1984)958e961.

[63] J.C. Phillips, Stretched exponential relaxation in molecular and electronicglasses, Rep. Prog. Phys. 59 (9) (1996) 1133e1207.

[64] G.E. Logotheti, D.N. Theodorou, Segmental and chain dynamics of isotactic

polypropylene melts, Macromolecules 40 (6) (2007) 2235e2245.[65] G.N. Toepperwein, K.S. Schweizer, R.A. Riggleman, J.J. de Pablo, Heterogeneous

segmental dynamics during creep and constant strain rate deformations ofrod-containing polymer nanocomposites, Macromolecules 45 (20) (2012)8467e8481.

[66] P. Majda, J. Skrodzewicz, A modified creep model of epoxy adhesive atambient temperature, Int. J. Adhesion Adhes. 29 (4) (2009) 396e404.

[67] I. Costa, J. Barros, Tensile creep of a structural epoxy adhesive: experimentaland analytical characterization, Int. J. Adhesion Adhes. 59 (2015) 115e124.

[68] J. Yang, Z. Zhang, K. Friedrich, A.K. Schlarb, Creep resistant polymer nano-composites reinforced with multiwalled carbon nanotubes, Macromol. RapidCommun. 28 (8) (2007) 955e961.

[69] A. Martone, G. Faiella, V. Antonucci, M. Giordano, M. Zarrelli, The effect of theaspect ratio of carbon nanotubes on their effective reinforcement modulus inan epoxy matrix, Compos. Sci. Technol. 71 (8) (2011) 1117e1123.

[70] C. Wu, Competitive absorption of epoxy monomers on carbon nanotube: amolecular simulation study, J. Polym. Sci., Polym. Phys. Ed. 49 (15) (2011)1123e1130.

[71] G.N. Toepperwein, R.A. Riggleman, J.J. de Pablo, Dynamics and deformationresponse of rod-containing nanocomposites, Macromolecules 45 (1) (2012)543e554.

[72] Y.S. Song, J.R. Youn, Influence of dispersion states of carbon nanotubes onphysical properties of epoxy nanocomposites, Carbon 43 (7) (2005)1378e1385.

[73] M.K. Hassanzadeh-Aghdam, R. Ansari, M.J. Mahmoodi, A. Darvizeh, Effect ofnanoparticle aggregation on the creep behavior of polymer nanocomposites,Compos. Sci. Technol. 162 (2018) 93e100.

[74] M.K. Hassanzadeh-Aghdam, M.J. Mahmoodi, R. Ansari, Creep performance ofCNT polymer nanocomposites-An emphasis on viscoelastic interphase andCNT agglomeration, Compos. B Eng. 168 (2019) 274e281.