A comparison study on mechanical properties of polymer composites reinforced by carbon nanotubes and graphene sheet

Accepted Manuscript A comparison study on mechanical properties of polymer composites reinforced by carbon nanotubes and graphene sheet Yunlong Li, Shijie Wang, Quan Wang, Malcolm Xing PII:

S1359-8368(17)32208-4

DOI:

10.1016/j.compositesb.2017.09.024

Reference:

JCOMB 5270

To appear in:

Composites Part B

Received Date: 30 June 2017 Revised Date:

5 September 2017

Accepted Date: 9 September 2017

Please cite this article as: Li Y, Wang S, Wang Q, Xing M, A comparison study on mechanical properties of polymer composites reinforced by carbon nanotubes and graphene sheet, Composites Part B (2017), doi: 10.1016/j.compositesb.2017.09.024. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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A comparison study on mechanical properties of polymer composites reinforced by carbon nanotubes and graphene sheet Yunlong Lia,b, Shijie Wanga∗, Quan Wangb∗∗, Malcolm Xingc School of Mechanical Engineering, Shenyang University of Technology,

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a

Shenliao West Road No. 111, Shenyang 110870, P.R. China b

Department of Mechanics and Aerospace Engineering, Southern University of Science and

c

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Technology, Shenzhen, Guangdong 518055, P.R. China

Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB,

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R3T 5V6, Canada Abstract

To compare enhancements of mechanical properties of polymer composites reinforced by

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carbon nanotubes and graphene sheet, molecular models of polymer matrix reinforced by the same weight percentage of carbon nanotubes and graphene sheet are developed. Pull-out process and strain constant method are applied to find mechanical properties of the

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nano-composites by examining the interfacial interactions between nano-reinforcements and

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polymer matrices. The results show that about 18% higher in Young’s modulus, 8.7% higher in tensile strength, and 5% higher in surface crack energy are obtained for the composites by incorporation of graphene sheet than those by incorporation of carbon nanotubes. Graphene sheet is found to play a better role in delaying the propagations of cracks. To explore the mechanisms on the enhanced tensile and fracture properties, the interfacial interaction energy and shear forces between the nano-reinforcements and polymer matrices, and total van der

∗

Corresponding author. E-mail address: [email protected] (S.J. Wang) Corresponding author. E-mail address: [email protected] (Q. Wang). 1

∗∗

ACCEPTED MANUSCRIPT Waals energy of the polymer composites are examined and interpreted accordingly. Keywords: A. Polymer-matrix composites (PMCs)

B. Interface/interphase

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B. Mechanical properties

B. Fracture

1. Introduction

Carbon nanotubes (CNTs) and graphene sheet (GNS) with their remarkable thermal,

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mechanical, specific surface area and light weight properties [1-11] have attracted

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considerable applications as reinforcements in polymer composite industry. In order to facilitate the development of the polymer nano-composites, studies have been dedicated to investigate the mechanical properties of CNTs or GNS reinforced polymer composites. Deplancke et al [12] conducted an experimental study on the impact of CNT prelocalization

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on mechanical properties of ultra high molecular weight polyethylene (UHMWPE) nano-composites. The results showed that the yield stress and strain-hardening of CNT/UHMWPE composites can be improved at higher CNT concentrations in their solid

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state. Wang et al [13] reported the enhancements of mechanical properties of graphene

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reinforced polyvinyl chloride (PVC) composites. The results indicated that the tensile strength, impact toughness of PVC/graphene composites can be enhanced significantly by uniform dispersions at an extremely low graphene loading (0.3 wt.%). A study on the effective elastic modulus of CNT/epoxy composites based on shear-lag models and global force equilibrium was carried out [14]. Based on their theoretical results, increases in CNTs length, layer number and volume percentage lead to an increase in the effective Young’s modulus. Multi-walled CNTs were found as well to be able to enhance mechanical properties 2

ACCEPTED MANUSCRIPT of polymer composites. Although experimental and theoretical researches have been conducted on mechanical properties of CNTs and GNS/polymer composites, the inherent mechanisms on revealing the

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enhanced mechanical properties have not yet been elaborated at an atomic level because of the small length and time scales associated with atomic level dynamics. Molecular dynamics (MD) simulations have emerged as an effective computational simulation tool to investigate

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the physical behaviors of materials at an atomic scale and generate microscopic data and

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details of molecular interactions in addition to experimental and theoretical studies. MD simulations have become applicable to study polymer nano-composites and proven to be qualified in providing microscope insights into the enhanced properties of nano-materials [15-24].

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Alien et al [25] conducted an MD simulation study to investigate the effects on nano-indentation properties of multilayered graphene reinforced polymer composites. Different types of molecular models of GNS/polymer composites were developed and

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investigated. The simulation results revealed that by coating graphene layers on the surface of

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a polymer matrix, the indentation resistance can be enhanced about fourteen times. Arash et al [26] provided a method of calculating the mechanical properties of CNT/polymer composites by examining the total potential energy of the nano-composites using molecular dynamics simulations. The simulation results demonstrated that the Young’s modulus of PMMA matrix reinforced by an infinite long CNT is significantly increased about 16 times higher than that of a pure PMMA matrix. Li et al [27] conducted MD simulations on studying enhancement of mechanical properties of GNS/polymer composites. The results reported that 3

ACCEPTED MANUSCRIPT by incorporation of GNS reinforcement into pure polymer matrix, increases of about 150% in Young’s modulus, 27.6% in shear modulus, and 35% in hardness can be achieved. It is noted that MD simulations have become indispensable in studying mechanical properties

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of CNT/polymer and GNS/polymer composites. However, still very few MD works have been conducted to describe and reveal the mechanisms of GNS, CNT/polymer composites from an atomic view. In addition, scattered data have been dedicated to provide a

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polymer composites to the authors’ knowledge.

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comprehensive comparison study on mechanical properties of both CNT and GNS reinforced

Hence, in this work, a comparison study is conducted on enhancements of mechanical properties of polymer composites reinforced by CNTs and graphene sheet. Pull-out processes are used to study the interfacial interactions between the nano-reinforcements and polymer

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matrices using MD simulations. The strain constant method is then applied to study the tensile properties of both the CNT and GNS polymer composites. By monitoring the total van der Waals (vdW) energy of nano-composites and interfacial interaction energy between the

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nano-reinforcements and polymer matrices, the mechanisms of the enhancements on

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mechanical properties of the two nano-composites are discussed and analyzed.

2. Method

2.1 Pull-out simulations

A (5, 5) CNT with a length and radius of 29.51 and 6.78 Å is first developed and displayed in Figure1 (a). A graphene sheet shown in Figure 1 (b) can be obtained by unfolding this (5, 5) CNT. The two reinforcements are then located respectively in the middle positions of two

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ACCEPTED MANUSCRIPT simulation boxes in a same size of 40 × 40 × 40 Å 3. A number of the PMMA (CH2=C[CH3]CO2CH3) chains are packed into the two simulation boxes with a predefined density of 1.1 g/cm3. Each PMMA chain is built by 10 monomer repeat units. By this way, a

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same weight percentage of 3.8% of the nano-reinforcements embed in the PMMA matrix can be achieved. The geometry optimization (conjugate-gradient method [28] with a convergence criteria of 0.0001 kcal/mol) and isothermal-isobaric ensemble (NPT) simulations (300 K, 101

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KPa for 2ns with time step of 1fs) are then followed to obtain a structure of globally

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minimum energy while removing the internal stresses in the two polymer composites. Finally, the CNT and GNS reinforcements are assigned by a same initial speed of 1.5 nm/ps in the axial direction. In addition, vacuum layers with a thickness of 50 Å is added in the pull-out direction to provide a space to fulfill a relative sliding between the nano-reinforcements and

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polymer matrices. During the pull-out MD simulations, A NVE ensemble has been adopted.

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The pull-out models of the CNT, GNS/PMMA composites are shown in Figure 1 (c) and (d).

Figure 1. Molecular models of the : (a) (5, 5) CNTs, (b) GNS, (c) pull-out structure of the 5

ACCEPTED MANUSCRIPT CNT/PMMA composites, (d) pull-out Structure of the GNS/PMMA composites. In the snapshots of (c) and (d), CNT and GNS reinforcements are presented by green color. The PMMA matrices are presented by the color of white, red and gray. Colors in all figures

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throughout this paper could be used for any print.

2.2 Tensile property of nano-composites

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A (6, 6) CNT with a length and radius of 71.33 and 8.14 Å, and a GNS unfolding by the (6, 6) CNT are developed and provided in Figure 2 (a) and (b) respectively. The (6, 6) CNT and

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GNS reinforcements are then placed into the middle positions of two empty unit cells in a same size of 100 × 60 × 30 Å 3. The two unit cells are filled with a number of PMMA chains with a predefined density of 1.1 g/cm3 respectively. An equilibration process

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containing geometry optimizations and NPT MD simulations have been conducted to obtain the globally and locally minimum energy configurations. The detailed information of the geometry optimizations and NPT simulations is the same with that in the section 2.1. To

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obtain strain-stress curves of the two nano-composites, the constant-strain method [27] is

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then adopted. A series of expansions of 0.01% are applied to the two unit cells in the x direction. The stresses in the x direction of the simulation box can be calculated by the virial stress method.

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Figure 2. Molecular models of the: (a) CNT/PMMA composites, (b) GNS/PMMA composites,

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(c) and (d) cross section views of the interfacial interactions between the nano-reinforcements and PMMA matrices. The PMMA matrices and nano-reinforcements are presented by the colors of orange and green respectively.

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2.3 MD simulation method

The Modulus of Forcite and Amorphous Cell Package in MATERIALS STUDIO are adopted

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to conduct all the MD simulations and molecular models. COMPASS force-field [29], which is the first ab initial force-field which enables precise prediction of a wide range of polymer

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materials, has been applied. This comprehensive potential is proven to be applicable to examine physical properties of CNT and GNS/polymer materials [30-32]. In the COMPASS force field, the total potential energy, E, is summered as follows: ∅ ∅

E= ∅

∅

(1)

∅

where b and b' are the lengths of two adjacent bonds respectively; θ and θ' are the adjacent 7

ACCEPTED MANUSCRIPT two-bond angles; φ is the dihedral torsion angle; and ϒ is the out of plane angle. The total potential energy may be divided into two categories, namely, (i) contributions from each of ,

∑

,

∑

cross-coupling terms between internal coordinates (i.e., ∑ ∑

′

, ∑

,

∑

∅

, and ∑

′

, ′

∑E

, ∑

); and (ii) , ∑

∅

,

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the internal valence coordinates (i.e., ∑

). Lennar-Jones terms [33] are used to represent

the vdW interactions among atoms. Andersen feedback thermostat [34] and Berendsen

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barostat [35] algorithms are adopted to calculate the temperature and pressure conversions.

3. Results and discussions 3.1 Pull-out process

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Periodic boundary conditions and a cutoff radius of 12.5 Å are applied in simulations.

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It is noted that nano-reinforcements such as CNTs and GNS play an important role in enhancing the capability of arresting crack propagation of polymer matrices due to the evenly interactions between inserted reinforcements and matrices [36, 37]. Pull-out behavior has

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been confirmed to be an effective way to identify the main mechanisms for the improvements

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on resistance to crack growth [38]. To investigate difference effects on improvements of mechanical properties of the polymer matrix by introductions of CNT and GNS reinforcements, pull-out processes are used. The details of the pull-out simulations have been mentioned in the section 2.1. To study the interactions between the embedded reinforcements and polymer matrices, the interfacial friction forces between the CNT, GNS reinforcements and PMMA matrices are essential. During the pull-out processes, it can be noted that the loss of the global kinetic energy of the CNT and GNS reinforcements is due to the energy

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ACCEPTED MANUSCRIPT conservations in the NVE ensemble. Therefore, the interfacial frictional forces can be obtained based on the following expression: ∆

=

#

!"

(2)

∆

$%& '%

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where s is the relative movement distances of the CNT and GNS reinforcements; and is the difference of the kinetic energy of the CNT and GNS reinforcements

between the initial and final states of the pull-out processes.

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The final speeds and the loss of the kinetic energy of CNTs and GNS can be obtained to be

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9.447 and 6.443 Å/ps, and 8.18, 12.44×10-18 J respectively. The interaction frictional forces are calculated to be 16 and 35.54 nN accordingly. It is indicated that the interfacial frictional force between the GNS reinforcements and PMMA matrix is 1.2 times greater than that between the CNT reinforcements and PMMA matrix. To look into the nature of the

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improvement on the interfacial frictional force of the GNS/PMMA composites, the interaction potential energy between the two nano-reinforcements and PMMA matrices during the pull-out processes are calculated based on the equation shown below:

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*

(3)

is the interaction potential energy between the PMMA matrices and

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where 5)&'

U)&' * = UTotal - UPMMA - Unano

nano-reinforcements; 567'8 is the total potential energy of the nano-composites; 59::; is the potential energy of the PMMA matrices; and 5nano is the potential energy of the nano-reinforcements. By measuring the parameters mentioned above, the variations of the interaction potential energy of both the CNT, GNS/PMMA composites versus the pull-out simulations times are obtained and shown in Figure 3.

9

250

Graphene reinforcement 200

CNT reinforcement

100

50

0 0.5

1

1.5

2

Time （ ps）

2.5

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150

3

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Interaction potential energy （ Kcal/mol）

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3.5

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Figure 3. The variations of the interfacial potential energy between the CNT, GNS and PMMA matrices during the pull-out MD simulations.

From figure 3, it can be seen that the interfacial interaction energy in the CNT/PMMA and

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GNS/PMMA composites decrease from about 176.84 and 243.61 to 6.55 and 12.45 kcal/mol respectively. The decrease of the interfacial energy can be interpreted that in the pull-out

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simulations, less interaction area between the nano-reinforcements and PMMA matrices are formed gradually due to the relative movements. The average interaction potential energy in

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the GNS/PMMA and CNT/PMMA composites are obtained to be 102.98 and 68.32 kcal/mol respectively. 50.7% higher in the average interaction potential energy during the pull-out simulations are obtained by the introduction of GNS than by that of CNTs as reinforcements. The higher interfacial interaction energy can be understood by the fact that during the pull-out process, more interactions occur between the GNS reinforcement and PMMA matrix than those in the CNTs/PMMA composites. It is hence concluded that because of the distinctive 2D plate structure of the GNS reinforcement, more PMMA chains can be absorbed 10

ACCEPTED MANUSCRIPT by both sides of the GNS reinforcement leading to higher interfacial non-bond interaction energy. The snapshots for the MD simulation process for the process by the two reinforcements at t=2ps and t=3.5ps are shown in Figure 4 (a), (b), (c) and (d). From figure 4,

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it shows that both the CNT and GNS reinforcements are gradually pulled out from the PMMA matrices in the axil directions. It can be clearly seen that when the CNT reinforcements are completely pulled out of the PMMA matrix at t=3.5ps, the GNS

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reinforcement are still in the debonding stage due to its enhanced properties of surface

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adsorption [39].

Figure 4. (a) and (b) the pull-out process of the CNT/PMMA composites at the MD simulation times of 2 and 3.5 ps respectively; (c) and (d) the GNS/PMMA composites at the MD simulation times of 2 and 3.5 ps respectively.

3.2 Young’s modulus and tensile strength To further study mechanical properties of the CNT, GNS/polymer composites, the tensile 11

ACCEPTED MANUSCRIPT processes are investigated in this section. The molecular models of the CNT, GNS/PMMA composites are developed and shown in Figure 2. The strain constant method is applied to obtain the tensile processes. The strain-stress curves of both the CNT, GNS/PMMA

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composites are acquired and provided in Figure 5. The Young’s modulus can be determined by examining the slope ratios of the fitting lines in the ranges of elastic stage of strains from 0 to 0.01. The Young’s modulus of the CNT/PMMA and GNS/PMMA composites are predicted

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respectively to be 3.7 and 4.4 GPa. It is indicated that an increment of 18% in the Young’s

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modulus of the PMMA composites are obtained by introduction of the GNS as reinforcement than by introduction of CNT. In addition, the tensile strength of the CNT, GNS/PMMA composites are obtained to be 103 and 112MPa respectively. An increase of 8.7% in the tensile strength are achieved by incorporation of the GNS than by incorporation of CNTs.

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Both the Young’s modulus and tensile strength of the CNT, GNS/PMMA composites obtained

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by the MD simulations are in a reasonable range compared to previous studies [40-43].

Figure 5. The strain-stress curves of the CNT, GNS/PMMA composites.

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ACCEPTED MANUSCRIPT To explore the mechanisms on the increments of the Young’s modulus and tensile strength, the interaction potential energy between CNT, GNS reinforcements and PMMA matrices are calculated based on Eq. (3) and shown in Figure 6. From Figure 6, it shows that the average

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absolute value in the linear variations of the interaction potential energy of the GNS/PMMA composites for the strain from 0 to 0.05 are obtained to be 759 kcal/mol, which is 13% higher than that of the CNT/PMMA composites which is 667 kcal/mol. It can be thus understood

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that more interactions between the GNS and PMMA matrix are observed during the tensile

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process than those in the CNT/PMMA composites because of the 2D structure of GNS.

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Figure 6. The variations of the interaction potential energy of the interfacial region between CNT, GNS reinforcements and PMMA matrices during the tensile processes.

The radius distribution functions (RDF) values between GNS, CNT reinforcements and PMMA matrices are calculated and plotted in Figure 7. From Figure 7, the average RDF values of both the GNS, CNT/PMMA composites are calculated to be 0.74 and 0.67 respectively. It is indicated RDF is higher in GNS/PMMA materials as well. Furthermore, it 13

ACCEPTED MANUSCRIPT has to be noted that the PMMA matrices have been stretched continuously during the tensile process leading to a relative movements and interactions between the nano-reinforcements and PMMA matrices. The internal shear stresses between the nano-reinforcements and

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PMMA matrices can thus be formed to prevent the tensile deformations. It can hence be concluded that with its unique 2D structure, greater surface adsorption forces can be provided by the GNS reinforcement to resist the external loadings leading to the whole polymer

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composites a better resistibility than CNT reinforcements.

Figure 7. RDF values between the GNS, CNT reinforcements and PMMA matrices during the

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tensile processes.

In addition, to achieve a deeper understanding on the interfacial interactions between CNT, GNS reinforcements and PMMA matrices during the tensile processes, shear-lag models in predicting the interfacial shear stress between the nano-reinforcements and polymer matrices are intriduced and used below [44, 45]:

< =

=

>?@A

BC

D%&E FG

H7#E F I/ > 14

K

;L ;A A ;L L M;A A

NO

(4)

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R;

=

=

;A A

L L

D%&E & I/'


X Y

& I/' / >

=/>

SK

(5)

Z

(6)

>QL ' \

6

(7)

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λ= B

where < and
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Gm is the shear modulus of the PMMA matrix; E1, Em and Ef are the Young’s modulus of the

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CNTs, PMMA matrix and GNS; Am and A1 are the cross-section area of the PMMA matrix and CNT reinforcement. L is the length of the polymer composites, which is set to be 10nm; NO is the tensile strength of CNT/PMMA composites. Z is the distance from the boundary side to the middle positon of the polymer composites. T and t are the thickness of the polymer

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matrix and GNS (30 and 0.35 nm). em is the strain corresponding to the tensile strength in the GNS/PMMA composites. The rest parameters for the calculations on the interfacial shear

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stress are shown in Table 1.

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Table 1. Parameters for the calculations on the interfacial shear stress R1

R2

(Å)

4.07

Gm

E1

Em

(Å) (Gpa)

(TPa)

(GPa)

15

1.65[18] 2.86[18]

1

Ef

Am

A1

T

em

(TPa) (nm2) (Å2) (Å) 1[37]

18

66.2

30

NO (MPa)

0.085

112

The interfacial shear stresses in the CNT, GNS/PMMA composites during the tensile processes are calculated to be 35.6 and 40 MPa respectively based on the above model. The 15

ACCEPTED MANUSCRIPT results indicate that the interfacial shear stress in the GNS/PMMA composites is about 12.3% greater than that in the CNT/PMMA composites. The result also validates our finding via the interaction potential energy predicted by our MD results. It can be proven that the effects on

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the interfacial shear stress are mainly derived from the non-bond interactions between the reinforcements and polymer matrices. The GNS reinforcement is further proven to be able to

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enhance better mechanical properties of the polymer matrix than CNT reinforcement.

3.3 Fracture processes

The fracture processes of the CNT, GNS/PMMA composites are explored. From figure 5, it can be observed that the stress values of the CNT, GNS/PMMA composites tend to fluctuate

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around the average values of 98 and 106 MPa at the strains from about 0.05 to 0.085 and 0.095. It is indicated from our MD simulations that stress relaxations lead to a period of initial generations of local cracks. Then, the stresses in the CNT/PMMA and GNS/PMMA

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composites decrease from 112 MPa and 98 MPa to 90 MPa and 80 MPa gradually from the

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strains around 0.085 and 0.095 to 0.17. It is noted that stress relaxations in the nano-composites tend to be further aggravated leading to the propagation of the cracks in the matrices. Notable observations in Figure 5 can be found that the strain, 0.095 corresponding to the final state of the initial crack generation period, of the GNS/PMMA composites, is 11.7% greater than that of the CNT/PMMA composites, which is 0.085. It can thus be concluded that the GNS reinforcement plays a better role in delaying the propagation of cracks. From figure 6, it can be obtained that the absolute average values of the interaction potential energy 16

ACCEPTED MANUSCRIPT between the GNS reinforcement and PMMA matrix is around 746.9 kcal/mol which is about 14% greater than in the CNT/PMMA composites, i.e. 654.8 kcal/mol, in the initial crack generation stage. It is thus noted that greater interaction energy of the reinforced interactions

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are formed between the GNS reinforcement and PMMA matrix during the crack initiation and propagation process. It can be known that by the greater interaction energy, more PMMA chains tend to be absorbed around the GNS reinforcement to resist crack generation and

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promote the composites to be sustained by longer tensile strain. Meantime, the variations of

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the total vdW energy of the two nano-composites are calculated and shown in Figure 8. From figure 8, it can be seen that the absolute values of the total vdW energy of the CNT, GNS/PMMA composites continuously perform linear variations from around 798 and 977 kcal/mol to 26 and 270 kcal/mol between the strains from 0 to 0.085 and 0.095 respectively.

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It is clearly indicated that the PMMA matrix keeps a longer elastic stage by introduction of the two reinforcements with 11.7% longer by the GNS reinforcement than by CNTs. Therefore, it can be concluded that due to its specific 2D structure, greater interfacial

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adsorption forces can be provided by the GNS reinforcement lead to longer elastic period and

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a better delay of the crack growth than by the CNT reinforcement.

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Figure 8. Total vdW energy of the CNTs, GNS/PMMA composites during the tensile

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processes.

Finally, the snapshots of the CNT, GNS/PMMA composites at strains of 0.1 (a) and (d), 0.012 (b) and (e), and 0.014 (c) and (f) have seen shown in Figure 9 respectively. It can be clearly

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seen that the cracks in the CNT/PMMA composites are bigger and propagates faster than

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those in the GNS/PMMA composites at each same strain.

Figure 9. The snapshots of the CNT/PMMA and GNS/PMMA composites at strains of 0.1 (a) and (d), 0.012 (b) and (e), and 0.014 (c) and (f).

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ACCEPTED MANUSCRIPT For deeper understanding of the fracture processes of the two nano-composites, the surface energy of both the CNT, GNS/PMMA composites in generating a same crack length are used [46]. _ ` ?8 >

(8)

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γ=

where γ is the surface energy; a is the crack length, which is set to be 2 nm; E presents the Young’s modulus of the two nano-composites. N presents the stresses of the CNT,

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GNS/PMMA composites corresponding to the crack length a, which is obtained be to 94 and

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105 MPa based on the MD simulation results respectively. The surface crack energy of the CNT, GNS/PMMA composites are then calculated to be 74.9 and 78.6 mJ/m2 respectively. It is indicated that the surface crack energy of the GNS/PMMA composites is 5% greater than that of the CNT/PMMA composites. The higher surface crack energy of the GNS/PMMA

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composites can also be interpreted by the fact that due to the difference of the 2D and 3D structures, more polymer materials can be absorbed by the GNS reinforcement leading the

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reinforcement.

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whole composites to be more stable and better resistant properties than that by the CNT

Conclusion

A comprehensive comparison study has been conducted to investigate mechanical properties of the GNS/polymer and CNT/PMMA composites using MD simulations. Molecular models of PMMA matrix reinforced by same weight percentage of CNTs and graphene sheet as reinforcement are built. Pull-out processes and strain-stress behaviors of the two composites are mainly studied. The results show that about 18% higher in Young’s modulus, 8.7% higher 19

ACCEPTED MANUSCRIPT in tensile strength and 5% higher in surface crack energy are obtained by incorporation of graphene sheet as reinforcement than by incorporation of CNT reinforcement. By examining the interfacial interaction energy and total vdW energy of the two polymer composites, the

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mechanisms of the enhanced mechanical properties of the GNS/PMMA composites are explored and discussed accordingly.

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Acknowledgement

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This research is supported by the Program for Liaoning Innovative Research Team in

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University-LNIRT (LT2014003) and Liaoning Climbing Scholar (10142) Program.

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