Characterizing thermal and mechanical properties of graphene/epoxy nanocomposites

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Characterizing thermal and mechanical properties of graphene/epoxy

nanocomposites

Sung-Chiun Shiu, Jia-Lin Tsai

⇑

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 6 September 2012

Received in revised form 4 September 2013 Accepted 7 September 2013

Available online 17 September 2013 Keywords:

A. Nano-structures B. Mechanical properties B. Thermal properties Molecular dynamics simulation

a b s t r a c t

This study aims to investigate the thermal and mechanical properties of graphene/epoxy nanocomposites using molecular dynamics (MD) simulation. Three different formats of graphene: graphene ﬂakes, inter-calated graphene and interinter-calated graphene oxide, were incorporated respectively in an epoxy matrix to form the graphene/epoxy nanocomposites. The mechanical properties of the graphene/epoxy nanocom-posites, including Young’s modulus (E), glass transition temperature (Tg) and coefﬁcient of thermal

expansion (CTE), in terms of three different formats of graphene, were characterized in this study. In addition to the mechanical properties, the influences of graphene on the density distribution of epoxy polymers in the nanocomposites were also examined. The results showed that the local density in the vicinity of the graphene is relatively high, and then progressively decreases to the bulk value in regions further away from the interface. On the other hand, for the mechanical and thermal properties, the nano-composites with intercalated graphene exhibit a higher Young’s modulus, a higher glass transition tem-perature and a lower thermal expansion coefficient than do those with graphene flakes. This is because the intercalated graphene can lead to a high amount of high density polymer in the nanocomposites, and thus enhance the overall properties of the nanocomposites. In addition, the interacted graphene oxide provides the best reinforcement of the three systems of nanocomposites. Based on the calculation of interaction energy, it appears that the oxide modification of the graphene surface can effectively lead to the high interaction energy, such that the graphene oxide can demonstrate a relatively high reinforcing efficiency.

1. Introduction

Graphene is a monolayer structure in which the carbon atoms are arranged in a hexagonal pattern. The interatomistic distance between the adjacent carbon atoms is 1.42 Å, and the associated atomistic interaction is covalently bonded by sp2_hybridized

elec-trons. With the employment of micromechanical cleavage, Novose-lov et al.[1] successfully isolated the individual graphene from graphite bulk materials. Experiments indicated that the graphene exhibits a high modulus of 1 TPa and a high strength of 130 GPa

[2]. In addition to the superior mechanical properties, the high spe-ciﬁc surface of the 2D layer structure makes the graphene a poten-tial reinforcement in nanocomposites. Several researches have incorporated graphene sheets into epoxy resin to form the nano-composites, indicating that the modulus and glass transition tem-perature of the nanocomposites can be effectively increased[3–8]. In addition, a decreasing tendency of the coefﬁcients of thermal expansion associated with the improved thermal stability was also observed in the epoxy-based nanocomposites reinforced with

graphene sheets[4,5]. Shen et al.[3]introduced graphene sheets into epoxy resin and investigated the mechanical properties of the nanocomposites at room temperature and at a cryogenic tem-perature of 77 K, respectively. It was discovered that with 0.5 wt% of graphene sheets, the modulus of the epoxy was increased from 2 GPa to 3.1 GPa at room temperature, and from 5.9 GPa to 7.4 GPa at cryogenic temperature. An increasing tendency in modulus was also noted by Lee et al. [4], who examined the mechanical and thermal properties of epoxy in conjunction with graphene sheets at various temperatures. They showed that the glass transition temperature of graphene nanocomposites was raised, and the cor-responding coefﬁcient of thermal expansion was reduced. Wang et al.[5]investigated the thermal properties of graphene nanocom-posites, revealing that graphene can effective improve the thermal stability of epoxy polymer. A higher glass transition temperature in epoxy nanocomposites caused by the addition of graphene sheet was also observed by Martin-Gallego et al.[6,7], who fabricated and tested UV cured nanocomposites. Tang et al.[8]explored the effect of graphene dispersion on the mechanical properties of graphene/epoxy nanocomposites. It was shown that the nanocom-posites with highly dispersed graphene exhibit higher strength and fracture toughness than those with poorly dispersed graphene. 1359-8368/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.compositesb.2013.09.007

⇑ Corresponding author. Tel.: +886 3 5731608; fax: +886 3 5720634. E-mail address:[email protected](J.-L. Tsai).

Contents lists available atScienceDirect

Composites: Part B

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Raﬁee et al.[9]compared the mechanical performances of epoxy resin reinforced by graphene platelets, single walled carbon nano-tubes and multiwall carbon nanonano-tubes. It was shown that in terms of the same amount of reinforcement, the nanocomposites in con-junction with graphene platelets exhibit higher modulus and strength than the other two nanocomposites.

In addition to the epoxy polymer, the improved thermal and mechanical properties in other polymer systems have also been reported[10–21], and it appears that the graphene sheet can effi-ciently modify the mechanical performances and thermal stabil-ity of the polymeric nanocomposites. However, the influence of the dispersion of the graphene sheet, as well as the morphology of the epoxy resin on the behavior of the nanocomposites has rarely been explored in the available literature. Furthermore, the effect of the functional groups adhered onto the graphene associated with the mechanical properties of nanocomposites has also seldom been investigated. In this study, three different formats of graphene sheets: intercalated graphene, intercalated graphene oxide and graphene flakes, were incorporated respec-tively in an epoxy matrix to form graphene nanocomposites. The mechanical properties of the nanocomposites, including Young’s modulus, glass transition temperature and thermal expansion coefficient, in terms of different formats of graphene, were characterized. Moreover, the influences of graphene on the morphology and density of nearby polymers were examined, and the underlying mechanism resulting in the improvement of the mechanical properties of nanocomposites was discussed. The influence of surface modification, in terms of the interfacial bonding energy on the mechanical properties of graphene nano-composites, was also investigated.

2. Graphene/epoxy nanocomposites

In order to explore the mechanical properties and morphologies of graphene/epoxy nanocomposites using MD simulation, atomis-tic models of nanocomposites were first constructed. Three differ-ent formats of graphene: intercalated graphene, intercalated graphene oxide and graphene flakes, were incorporated, respec-tively, in epoxy matrix to form the graphene nanocomposites. For the nanocomposites with graphene flakes, the molecular model consists of an eight-layer graphite (stacked along the z direction in A-B sequence) and 96 epoxy units exposed randomly on each side of the graphite. It must be noted that the epoxy is a cross-linked polymer, and the consideration of the cross-linking behavior in MD simulation based on probability is too time consuming to be applied to a larger model. In order to save on computing cost, a representative cross-linked unit proposed by Yu et al.[22]was em-ployed to denote the cross-linked epoxy where three molecular chains of EPON862Ò_{resin were incorporated with one molecular}

chain of TETAÒ_{curing agent, as shown in}_{Fig. 1}_{. On the other hand,}

for the nanocomposites with intercalated graphene, three graph-ene sheets deployed homoggraph-eneously within the molecular model, in which 36 epoxy units were intercalated randomly between the graphene sheets. In addition to the intercalated graphene, the graphene modiﬁed with the hydroxyl group and epoxy group

which were commonly observed in the experiments[23]was also

considered in the atomistic model. The graphene with surface modification is shown inFig. 2(a). Basically, the ratio of hydroxyl group (shown inFig. 2(b)) to epoxy group (shown inFig. 2(c)) is as-sumed to be 1:1.5[24], and the modification ratio[25], defined as the number of surfactant atoms divided by the atom number of graphene, is 10%. Note that in the above atomistic model, the graphene with dimensions of 26.47 Å and 26.81 Å is embedded in the epoxy polymer, and the weight fraction of the graphene with respect to the nanocomposites considered in this study is around

18%. In the MD simulations, the atomistic interactions between the atoms are described using a potential function. In general, there are two kinds of potential functions considered in the atom-istic system: one is the bonded potential, such as the covalent bond, and the other is the non-bonded potential, such as the van der Waals force. For the graphene/epoxy nanocomposites, the covalent bonding, as well as the non-bonding interaction among the molecular chains was described by the COMPASS force ﬁeld

[26].

The equilibrated molecular structure of epoxy/graphene nanocomposites with minimized energy was accomplished by sequentially performing the NVT and NPT ensembles in the MD

Fig. 1. Representative unit of epoxy polymer[22].

(a)

Oxygen Hydrogen Carbon

(b)

(c)

Fig. 2. (a) Atomistic structures of graphene oxide, (b) hydroxyl group and (c) epoxy group.

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simulation, with a time increment of 1 fs. The NVT ensemble was conducted at 1100 K for 200 ps, the purpose of which was to sup-ply enough kinetic energy to the epoxy molecules so that homoge-neous molecular structure within the simulation box could be achieved. After this, the temperature was designated to 600 K for another 200 ps in the NVT ensemble. In the NVT ensemble, the car-bon atoms on the graphene were fixed at their original position throughout the simulation. Subsequently, the NPT ensemble was performed at 0 atm in order to achieve a stress-free state, and at the same time the corresponding temperature was gradually re-duced from 600 K to 1 K. In fact, there were two sub-steps intro-duced during the cooling process. In the first sub-step, the temperature was designated at 300 K, and the simulation time was 200 ps. In the beginning of the first sub-step, the frozen atoms of graphite were released so that the entire nanocomposites sys-tem could be equilibrated under a stress-free condition. In the sec-ond sub-step, the target temperature was 1 K, and the simulation time was also set to 200 ps. During the simulation, the total poten-tial energy variation was examined, and when the quantity fluctu-ated around a certain mean value for a while, the system was considered to be in a state of energy minimization. Note that NVT ensemble stands for the number of atoms (N), volume (V) and temperature (T) being fixed during the simulation, and NPT ensemble indicates that the number of atoms (N), pressure (P) and temperature (T) remain constant during the simulation. The MD simulations for graphite/epoxy nanocomposites were carried out using a commercial code, Materials Studio, developed by Accel-rys Inc.[27]. The dimensions of the simulation cell under energy minimization condition for the stacked and intercalated graphene nanocomposites are shown inFig. 3. Subsequently, the morphol-ogy, as well as the mechanical properties of the nanocomposites

was then characterized from the simulation cell of the

nanocomposites.

3. Observation of molecular conﬁguration

The inﬂuence of graphite on the molecular conﬁguration of epoxy was investigated by observing the density variations of epoxy molecular chains. This can be done by partitioning the epoxy along the z axis into several small regions, as shown inFig. 4. It must be noted that the position z = 0 denotes the central section of the simulation cell, and the partition sizeDz = zi+1 ziindicating

the thickness of each small region is around 1 Å. In each small re-gion, the total atomic mass and the corresponding volume were calculated, and then the density was calculated as the mass divided by the associated volume. The density distributions of epoxy poly-mer with the nanocomposites along the z axis are shown inFig. 5. It can be seen that for the nanocomposites with graphene ﬂakes, the density near the graphite/epoxy interface is higher, and then rapidly decreases to the bulk value of 1.23 g/cc[28](indicated by the horizontal dash line), as the location is a small distance from the interface. In addition, the density distributions of epoxy in the nanocomposites with intercalated graphene are shown in

Fig. 5, where the vertical dash lines denote the interface between

the intercalated graphene and the epoxy. It appears that on both sides of the graphene, the polymer density is relatively high. As compared to the graphene ﬂakes, the dispersed graphene may lead to a greater amount of epoxy with high density because more interfacial areas were generated in the interacted nanocomposites. Moreover, the increased amount of high density polymer may have more appreciable inﬂuence in the mechanical properties of nano-composites, which will be discussed in the next section.

4. Determination of thermal and mechanical properties of graphene/epoxy nanocomposites

4.1. Young’s modulus

In addition to the density distribution of epoxy polymer, the mechanical properties of the molecular structures of nanocompos-ites were characterized using MD simulation. By applying a small amount of strain component to the simulation cell in one direction, while the other strain components remained ﬁxed, the deformed state of the simulation cell, as shown inFig. 6, was generated. After conducting the NVT ensemble for 400 ps, the energy minimization condition of the deformed state was attained, and the stress com-ponents of the simulation cell associated with the deformed con-ﬁguration were then calculated using the virial theorem[29]:

r

¼ 1 V0 X i<j rijfij ! ð1Þ

where rijand fijdenote the atomic distance and the corresponding

interaction force between any two atoms, respectively. Vo

repre-sents the total volume of the simulation cell. In Eq.(1), because the model was simulated at 1 K, the temperature effect was ne-glected in the stress computation. By following the concept of con-tinuum mechanics, the constitutive relation of nanocomposites in terms of the stiffness matrix [C] can be calculated as the derivative of the stress associated with the corresponding strain component. The explicit form for the normal stress and normal strain relation can be expressed as:

r

xx

r

yy

r

zz 2 6 4 3 7 5 ¼ Cxx Cxy Cxz Cyx Cyy Cyz Czx Czy Czz 2 6 4 3 7 5

e

xx

e

yy

e

zz 2 6 4 3 7 5

where [C] is the stiffness matrix. In this study, the small amounts of extension were employed respectively in the x, y and z directions, and the corresponding stress components were calculated from

(a)

32.8Å 32.8Å 137.4Å

(b)

(c)

34.4Å 34.4Å 51.9Å 34.6Å 34.6Å 52.0Å

Fig. 3. Atomistic structures of epoxy nanocomposites ((a) graphene ﬂakes, (b) intercalated graphene and (c) intercalated graphene oxide).

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Eq.(1). By taking the inverse of the stiffness matrix, the compliance matrix [S], in terms of engineering constants, is derived as:

½S ¼ ½C1 ¼ 1 Ex myx Ey mzx Ez mxy Ex 1 Ey mzy Ez mxz Ex myz Ey 1 Ez 2 6 6 4 3 7 7 5 ð3Þ

from which the elastic properties of the materials were obtained. In Eq.(3), E denotes Young’s modulus, and

m

designates Poisson’s ratio. With the microstructures of the simulation cell shown inFig. 3, the nanocomposites were assumed to be orthotropic and, in theory, the mechanical properties in the x and y directions should coincide. However, because there is variation in the atomistic simulation, the properties in the two directions may not be the same. Thus,

(a)

(b)

(c)

Density (g/cc) Density (g/cc) Density (g/cc) -60 -40 -20 0 20 40 60 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 -20 -10 0 10 20 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Z position (Å) Z position (Å) Z position (Å) -20 -10 0 10 20 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Fig. 5. Density distribution of epoxy in graphene nanocomposites ((a) graphene ﬂakes, (b) intercalated graphene and (c) intercalated graphene oxide).

(a)

(b)

(c)

Fig. 4. Partitioning the epoxy from z = z0along z axis into several small regions in

nanocomposites ((a) graphene ﬂakes, (b) intercalated graphene and (c) intercalated graphene oxide).

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the averaged value of Exand Eywas regarded as the in-plane

mod-ulus of the nanocomposites. The moduli of the nanocomposites in terms of the three different formats of graphene are listed inTable 1. For comparison, the modulus of pristine epoxy is also included in the same table. Basically, the epoxy was assumed to be isotropic, and thus the properties obtained in x, y and z directions were taken in average, and then presented in the table. It can be seen that the addition of the graphene can effectively improve the moduli of the epoxy, and the extent of the increase is dependent on the formats of the graphene. The intercalated graphene is generally superior to the graphene flakes, and the intercalated graphene oxide provides the best reinforcement among the cases. In fact, from the density distri-bution of the epoxy, it can be seen that more interfaces are gener-ated by the intercalgener-ated graphene, and a greater amount of high density polymer is created in the intercalated nanocomposites. Thus, the moduli of the intercalated nanocomposites are higher than those of the nanocomposites with graphene flakes. The degree of dispersion resulting in the change of morphology of epoxy is an essential factor influencing the properties of nanocomposites. In addition to the dispersion, the oxide functional group on the graph-ene is the other important factor which may influence the mechan-ical properties of the graphene nanocomposites. The effect of surface modification will be elaborated from the computation of the interaction energy between the graphene and surrounding epoxy polymers in the next section.

4.2. Glass transition temperature

Glass transition temperature (Tg) is a physical property at

which a material changes from a glassy state to a rubbery state. The effect of the graphene on the Tgof nanocomposites was

ex-plored in MD simulation, in which the temperature was varied from 600 K to 200 K step by step with a temperature difference of 20 K. In each step, the NPT ensemble was adopted for 100 ps, so that the conﬁguration with energy minimization could be accomplished. When the volume of the simulation cell was deter-mined from MD simulation, the corresponding density was then

computed. The density variation of the nanocomposites associ-ated with temperature variation is shown in Fig. 7. By taking the bi-linear curve-ﬁtting of the data, the intersection of the two linear curves was recognized as the Tgof the sample. From

Fig. 7(a), it seems that the Tg value of pristine epoxy is 380 K,

which is quite compatible with the experimental data of 377 K

[30]. For the nanocomposites, the density variations associated with the temperature change are shown inFig. 7(b)–(d). The cor-responding values of the Tgfor the nanocomposites are

summa-rized inTable 1. It can be seen that Tgincreases as the graphene

is incorporated in the nanocomposites, and the intercalated

nano-composites exhibit higher Tgthan do the nanocomposites with

graphene flakes. It is interesting to note that the oxide modifica-tion of graphene has no significant influence on the value of Tg.

The reason for this could be that Tgis sensitive to the morphology

of the epoxy polymer in the vicinity of graphene, but not to the surface modiﬁcation of graphene.

4.3. Coefﬁcient of thermal expansion

In addition to the Tg, the coefﬁcient of thermal expansion is

an-other thermal property related to the thermal stability of epoxy polymer. The CTE of epoxy nanocomposites containing different formats of graphene were also computed from MD simulation. The simulation procedure is basically the same as that in the calcu-lation of Tg. When the volume variation corresponding to the

tem-perature change was determined from the MD simulation, the CTE was then calculated as follows:

a

¼ 1 V0

D

V

D

T ð4Þ

whereDV denotes the volume change associated with the temper-ature variation ofDT, and the Vois the volume of the simulation cell

prior to the temperature variation. Note that the range of tempera-ture variation in the calculation of CTE was designated from Tgto

room temperature. The CTE values for the nanocomposites in terms of different formats of graphene are also shown inTable 1. It can be seen that the CTE drops as the graphene is incorporated in the epoxy polymer. Moreover, the introduction of graphene oxide leads to a lower CTE value than in the other cases, and can thus provide great thermal stability in the polymer system. The mechanical prop-erties of epoxy listed inTable 1were calculated based on the COM-PASS force ﬁeld. From the comparison of the simulation results with the experimental data[28,30,31], it is found that both results coin-cide quite well. This is the reason we selected the COMPASS force ﬁeld to characterize the nanocomposites associated with epoxy polymer.

4.4. Calculation of interaction energy

In light of the forgoing properties of graphene nanocomposites, it appears that the graphene oxide can produce better moduli and lower CTE than pristine graphene in the nanocomposites. In order to understand the effect of oxide surface modiﬁcation, the interac-tion energy between the graphene and epoxy were calculated as[25]:

Table 1

Thermal and mechanical properties of epoxy and epoxy nanocomposites in terms of three different formats of graphene. Epoxy (Exp.) Epoxy (Simulation) Nanocomposites

Graphene ﬂakes Intercalated graphene Intercalated graphene oxide

Young’s modulus (GPa) 3.24[28] 3.16 5.48 5.63 6.36

Tg(K) 377[30] 380 390 400 400

CTE (106_/K) _366[31] ₃₆₂ ₃₁₂ ₂₉₀ ₂₈₄

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EInteraction¼ Etotal Egraphene Eepoxy ð5Þ

where Etotal indicates the total energy of the nanocomposites, as

shown inFig. 8(a). However, Egrapheneand Eepoxydenote the

poten-tial energy of graphene and epoxy, respectively. Egraphenecan be

cal-culated independently from the simulation cell where the polymer was eradicated, as shown inFig. 8(b). A similar approach was em-ployed to calculate the potential energy of epoxy, as shown in

Fig. 8(c). The difference between the total energy of

nanocompos-ites and the potential energy of graphene and epoxy is regarded as the interaction energy between the two constituents. The inter-action energy for the graphene with and without surface modiﬁca-tion is compared inTable 2. It can be seen the interaction energy in the graphene nanocomposites with surface modiﬁcation is higher than that of pristine graphene. This higher interaction energy may be responsible for the improved mechanical and thermal properties in graphene oxide nanocomposites.

5. Conclusions

The mechanical properties of nanocomposites in terms of the three different formats of graphene: intercalated graphene, inter-calated graphene oxide and graphene flakes, were explored using MD simulation. Basically, the graphene nanocomposites demon-strate higher moduli, higher glass transition temperature and low-er values of CTE than does the pristine polymlow-er without any reinforcements. Moreover, the influences of graphene are more considerable in the nanocomposites with intercalated graphene than are those in the nanocomposites with graphene flakes. By

Fig. 8. Calculation of interaction energy between graphene and matrix. Table 2

Comparison of interaction energy of epoxy associated with graphene and graphene oxide.

Epoxy/graphene Epoxy/graphene oxide Interaction energy (kcal/mol) 340.25 460.47

(a)

(b)

(c)

(d)

Temperature (K) 200 300 400 500 600 0.9 0.95 1 1.05 1.1 1.15 1.2 Tg=380K Temperature (K) Density (g/cc) Density (g/cc) Density (g/cc) Density (g/cc) 200 300 400 500 600 1.1 1.15 1.2 1.25 1.3 Tg=390K Temperature (K) 200 300 400 500 600 1.1 1.15 1.2 1.25 1.3 Tg=400K Temperature (K) 200 300 400 500 600 1.1 1.15 1.2 1.25 1.3 Tg=400K

Fig. 7. Estimation of glass transition temperature for epoxy and graphene/epoxy nanocomposites ((a)epoxy polymer (b) graphene ﬂakes nanocomposites, (b) intercalated graphene nanocomposites and (c) intercalated graphene oxide nanocomposites).

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observing the morphology of polymer chains, it was found that the local density close to the graphene is relatively high, and there are greater amounts of high density polymers in the intercalated graphene nanocomposites. These high amounts of high density polymer are responsible for the enhanced thermal and mechanical properties in the intercalated nanocomposites. In addition, the graphene oxide can provide a superior reinforcement effect than can the pristine graphene associated with the Young’s modulus and CTE of the nanocomposites. The enhanced mechanism was elaborated by the higher interaction energy between the graphene and surrounding matrix in the graphene oxide nanocomposites. In summary, with the combined advantage of the high interaction en-ergy and the high extent of high density polymer, the incorporation of intercalated graphene oxide can lead to the superior thermal and mechanical properties of nanocomposites.

Acknowledgment

This research was supported by the National Science Council, Taiwan, under the contract no. NSC 99-2212-E-009-023 to National Chiao Tung University.

References

[1]Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, et al. Electric ﬁeld effect in atomically thin carbon ﬁlms. Science 2004;306(5696):666–9.

[2]Lee C, Wei X, Kysar JW, Hone J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 2008;321(5887):385–8. [3]Shen XJ, Liu Y, Xiao HM, Feng QP, Yu ZZ, Fu SY. The reinforcing effect of

graphene nanosheets on the cryogenic mechanical properties of epoxy resins. Compos Sci Technol 2012;72(13):1561–7.

[4]Lee JK, Song S, Kim B. Functionalized graphene sheets-epoxy based nanocomposite for cryotank composite application. Polym Compos 2012;33(8):1263–73.

[5]Wang S, Tambraparni M, Qiu J, Tipton J, Dean D. Thermal expansion of graphene composites. Macromolecules 2009;42(14):5251–5.

[6]Martin-Gallego M, Verdejo R, Lopez-Manchado MA, Sangermano M. Epoxy– graphene UV-cured nanocomposites. Polymer 2011;52(21):4664–9. [7]Martin-Gallego M, Hernandez M, Lorenzo V, Verdejo R, Lopez-Manchado MA,

Sangermano M. Cationic photocured epoxy nanocomposites ﬁlled with different carbon ﬁllers. Polymer 2012;53(9):1831–8.

[8]Tang LC, Wan YJ, Yan D, Pei YB, Zhao L, Li YB, et al. The effect of graphene dispersion on the mechanical properties of graphene/epoxy composites. Carbon 2013;60:16–27.

[9]Raﬁee MA, Raﬁee J, Wang Z, Song H, Yu ZZ, Koratkar N. Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 2009;3(12):3884–90.

[10]Steurer P, Wissert R, Thomann R, Mülhaupt R. Functionalized graphenes and thermoplastic nanocomposites based upon expanded graphite oxide. Macromol Rapid Commun 2009;30(4–5):316–27.

[11]Fang M, Wang K, Lu H, Yang Y, Nutt S. Covalent polymer functionalization of graphene nanosheets and mechanical properties of composites. J Mater Chem 2009;19(38):7098–105.

[12]Ansari S, Giannelis EP. Functionalized graphene sheet-poly(vinylidene ﬂuoride) conductive nanocomposites. J Polym Sci Pol Phys 2009;47(9):888–97. [13]Ramanathan T, Abdala AA, Stankovich S, Dikin DA, Herrera-Alonso M, Piner RD, et al. Functionalized graphene sheets for polymer nanocomposites. Nat Nanotechnol 2008;3(6):327–31.

[14]Liang J, Huang Y, Zhang L, Wang Y, Ma Y, Guo T, et al. Molecular level dispersion of graphene into poly(vinyl alcohol) and effective reinforcement of their nanocomposites. Adv Funct Mater 2009;19(14):2297–302.

[15]Kim H, Macosko CW. Morphology and properties of polyester/exfoliated graphite nanocomposites. Macromolecules 2008;41(9):3317–27.

[16]Kim H, Macosko CW. Processing-property relationships of polycarbonate/ graphene composites. Polymer 2009;50(15):3797–809.

[17]Yadav SK, Cho JW. Functionalized graphene nanoplatelets for enhanced mechanical and thermal properties of polyurethane nanocomposites. Appl Surf Sci 2013;266:360–7.

[18]Zhang LB, Wang JQ, Wang HG, Xu Y, Wang ZF, Li ZP, et al. Preparation, mechanical and thermal properties of functionalized graphene/polyimide nanocomposites. Composites Part A 2012;43(9):1537–45.

[19]An JE, Jeon GW, Jeong YG. Preparation and properties of polypropylene nanocomposites reinforced with exfoliated graphene. Fibers Polym 2012;13(4):507–14.

[20] Bora C, Gogoi P, Baglari S, Dolui SK. Preparation of polyester resin/graphene oxide nanocomposite with improved mechanical strength. J Appl Polym Sci 2013;129(6):3432–8.

[21]Kuila T, Khanra P, Mishra AK, Kim NH, Lee JH. Functionalized-graphene/ ethylene vinyl acetate co-polymer composites for improved mechanical and thermal properties. Polym Test 2012;31(2):282–9.

[22]Yu S, Yang S, Cho M. Multi-scale modeling of cross-linked epoxy nanocomposites. Polymer 2009;50(3):945–52.

[23]Schniepp HC, Li JL, McAllister MJ, Sai H, Herrera-Alonso M, Adamson DH, et al. Functionalized single graphene sheets derived from splitting graphite oxide. J Phys Chem B 2006;110(17):8535–9.

[24]Szabó T, Berkesi O, Forgó P, Josepovits K, Sanakis Y, Petridis D, et al. Evolution of surface functional groups in a series of progressively oxidized graphite oxides. Chem Mater 2006;18(11):2740–9.

[25]Lv C, Xue Q, Xia D, Ma M, Xie J, Chen H. Effect of chemisorption on the interfacial bonding characteristics of graphene–polymer composites. J Phys Chem C 2010;114(14):6588–94.

[26]Sun H, Ren P, Fried JR. The COMPASS force ﬁeld: parameterization and validation for phosphazenes. Comput Theor Polym S 1998;8(1–2):229–46. [27] Materials Studio. User’s Manual, Version 1.2. Accelrys, Inc. (San Diego, CA);

2001.

[28]Zunjarrao SC, Singh RP. Characterization of the fracture behavior of epoxy reinforced with nanometer and micrometer sized aluminum particles. Compos Sci Technol 2006;66(13):2296–305.

[29]Theodorou DN, Suter UW. Atomistic modeling of mechanical properties of polymeric glasses. Macromolecules 1986;19(1):139–54.

[30] Mukherjee N, Wavhal D, Timmons RB. Composites of plasma surface functionalized barium titanate nanoparticles covalently attached to epoxide matrices: synthesis and evaluation. ACS Appl Mater Int 2010;2(2):397–407. [31]He Y, Li Q, Kuila T, Kim NH, Jiang TW, Lau K, et al. Micro crack behavior of

carbon ﬁber reinforced thermoplastic modiﬁed epoxy composites for cryogenic applications. Composites Part B 2012;44(1):533–9.