Molecular Dynamics Simulations of Graphite-Vinylester

Vol. 11, No. 4 December 2010 pp. 316-324

Molecular Dynamics Simulations of Graphite-Vinylester

Nanocomposites and Their Constituents

H. Alkhateb, A. Al-Ostaz♠ and A. H.-D. Cheng

Nano Infrastructure Group, The University of Mississippi, University, MS 38677, U.S.A.♠e-mail: [email protected]

(Received August 20, 2010; Accepted December 14, 2010)

Abstract

The effects of geometrical parameters on mechanical properties of graphite-vinylester nanocomposites and their constituents

(matrix, reinforcement and interface) are studied using molecular dynamics (MD) simulations. Young’s modulii of 1.3 TPa and

1.16 TPa are obtained for graphene layer and for graphite layers respectively. Interfacial shear strength resulting from the

molecular dynamic (MD) simulations for graphene-vinylester is found to be 256 MPa compared to 126 MPa for graphite-

vinylester. MD simulations prove that exfoliation improves mechanical properties of graphite nanoplatelet vinylester

nanocomposites. Also, the effects of bromination on the mechanical properties of vinylester and interfacial strength of the

graphene–brominated vinylester nanocomposites are investigated. MD simulation revealed that, although there is minimal effect

of bromination on mechanical properties of pure vinylester, bromination tends to enhance interfacial shear strength between

graphite–brominated vinylester/graphene-brominated vinylester in a considerable magnitude.

Keywords : Molecular dynamics simulation, Exfoliated graphene nano-platelets, Graphite-vinylester nanocomposites

1. Introduction

A critical issue for the development of nanotechnology isthe ability to understand, to model, and to simulate thebehavior of these nano structures and to make the connectionbetween nano structure properties and their macroscopicfunctions. Material modeling and simulation aid inunderstanding this process, help in setting objectives thatguide laboratory investigation, and assist in setting controlson material structures, properties, and processes for physicalimplementation. These capabilities are vital to engineeringdesign at the component and systems levels [1-6].

Nanolayer reinforcement of composite materials cangreatly improve the materials structural and physicalperformance, such as stiffness, heat deflection temperature,and tensile strength. It also tends to lower thermal expansioncoefficient and permeation rate without adding significantweight, thereby allowing nanolayer polymers to achievegreater thermal stability (to become less flammable) and toreduce permeability (improve barrier performance) [7-10].Nanolayer-enhanced polymers distribute internal stressesmore uniformly by allowing greater dimensional latitudeduring the forming and shaping processes, as compared toconventional macroscale reinforcements. For example, theunparalleled ability of clay nanolayers to boost mechanicalproperties of an engineering polymer (nylon-6) was firstdemonstrated by Toyota researchers. An increase of only4.2 wt% of clay nanolayers doubled the modulus, increased

heat distortion temperatures by 80oC (compared to pristinepolymer), reduced permeability for water, and increasedflame retardant properties.

Carbon-based nanomaterials have been attracting muchattention during the last decade, because of their superiormechanical, electrical and thermal properties. Since the late1990’s, research has been reported that intercalated,expanded, and/or exfoliated graphite nano-platelets couldalso be used as nano-reinforcements in polymer systems.The key point of utilizing graphite as a nano-reinforcementis in its ability to be exfoliated into platelets of nanometerdimensions using Graphite Intercalated Compounds (GICs).Natural graphite is abundant and its cost is low compared tothe other nano size carbon materials. The graphite nanoplateletsare expected to be marketed at approximately $10-20/lb oncehigh demand and full production is achieved. This issignificantly less expensive than single wall nanotubes (SWNT)(>$45,000/lb) or vapor grown carbon fiber (VGCF) ($40-50/lb), yet the mechanical, electrical, and thermal properties ofcrystalline graphite flakes are comparable to those of SWNTand VGCF.

Graphene is a single layer sp2-bonded carbon sheetforming a honeycomb crystal lattice [11], first introduced byMouras, et al. (1987) as the two dimensional (2D) form ofgraphite. Novoselov et al. [12,13] reported that these 2Dcarbon materials formed gigantic flat fullerene moleculesand first described their electronic properties. Lee et al.reported a Young’s modulus of 1.0 TPa, and an intrinsic

Carbon

Letters

Molecular Dynamics Simulations of Graphite-Vinylester Nanocomposites and Their Constituents 317

strength of 130 GPa measured by nanoindentation atomicforce microscope for the monolayer graphene sheet [14]. By,those measurements, Lee categorized the graphene monolayersheet as the strongest material ever measured. Consequently,Graphene nanocomposites are expected to perform extremelyenhanced mechanical properties. Exfoliated graphite nano–platelets are new types of nanoparticles consisting of graphenestacks that are 1~15 nm thick and with diameters rangingfrom sub-micrometer to 100 µm. Exfoliated graphene nano-platelets share chemical structures with carbon nanotubes(CNT). In fact, their edges could be easily modifiedchemically for dispersion enhancement in polymericcomposites [15]. Fig. 1 shows the morphology of exfoliatedgraphene nano-platelets. These nano-platelets are typicallyless than 5 nm thick and can be synthesized with lateraldimensions ranging from less than 1 µm to up to 100 µm.

Vinylester is a copolymer thermoset resin produced by theesterification of an epoxy resin with unsaturated monocarboxylicacid. The reaction product is then dissolved in a reactivesolvent, such as styrene, to (35-45) percent content byweight. Vinylester can be used as an alternative to polyesterand epoxy materials in matrix or composite material becauseits distinctive characteristics, strength, and bulk cost lieintermediately between polyester and epoxy. Vinylester haslow resin viscosity, less than polyester and epoxy [16,17].However, the epoxy-based vinylester resins have remarkablecorrosion resistance, desirable physical properties, andimproved adherent properties compared to polyester due totheir chemical composition, and due to the presence of polarhydroxyl and ether groups in their chemical chain. Simulatedvinylester chains are 65% epoxy and 35% styrene; Fig. 2shows a schematic of an ideal vinylester chemical chainassuming that all the epoxy had reacted.

Vinylester-resin systems have other challenge: poorresistance to crack propagation, brittleness, and large shrinkagethat occurs during polymerization. Methods of incorporatingnanoparticles into polymer matrices could be ex-situ, likedispersion of the synthesized nanoparticles into resinsolution, or in-situ, like monomer polymerization process inthe presence of the nanoparticles.

One of the key interactions between the nanoparticles andthe matrix, for the ex-situ fabricated composites, is van derWaals force. However, the in-situ synthesis methods maycreate stronger chemical bonding within the composite.Introducing good interfacial bonding between nanofillers andthe resin is often used to alleviate volume shrinkage, voidformation and improve surface dispersion along withtoughness. Control of interfacial adhesion appears to becrucial since a major cause of impact-related problems isbelieved to be associated with the level of adhesion at theinterface between fiber and matrix. A variety of fiber surfacetreatment and modification techniques are used to control theinterfacial bonding. The strong interface favors a brittlefracture mode with relatively low energy absorption;whereas, a weak interface favors a multiple shear mode withhigh energy absorption. Therefore, optimization of theinterfacial adhesion is required to obtain excellent interfacialstrength along with enhanced impact properties [16].According to Gou, et al. [18], molecular dynamic simulationscan provide detailed information on interface structure andinteraction. The vinylester bromination effect is simulated tostudy the effect of bromination on the interfacial strength ofvinylester-graphene and vinylester-graphite nanocomposites.High interfacial strength will result high stiffness, strength,and toughness in the composite [18,19]. Fig. 3 shows aschematic chemical chain for a brominated vinylester.

In general nano-platelet composites are classified into fourtypes: conventional composite, intercalated composite, longrange ordering composite (LRO), and disordered composite(Fig. 4). In a conventional composite (Fig. 4a), clay orgraphite exists as a layered material with layers held togetherby van der Waals forces without any intercalation orexfoliation. In an intercalated composite (Fig. 4b), polymerchains are introduced into the graphite galleries, but thegraphite still retains its layered structure. The distancebetween layers is in the range of 10~30 Å. The size of thelayered graphite extends from several hundred nanometers(nm) to several microns. Exfoliated composites have bothexfoliated and dispersed graphite platelets with 1 nmthicknesses and several hundred-nm widths. This type can bedivided into two groups, long-range ordered (LRO) (Fig. 4c)

Fig. 1. Images of exfoliated graphene nano-platelets: (a) lateralview using SEM, (b) edge view using TEM micrograph (Cour-tesy of L. T. Drzal).

Fig. 2. Molecular structure of a single vinylester chain: 35%styrene, 65% epoxy.

318 H. Alkhateb et al. / Carbon Letters Vol. 11, No. 4 (2010) 316-324

and disordered composites (Fig. 4d). LRO composites haveintercalated separated graphite platelets within (30~105 Å)so that the adjacent platelets do not interact with each other.This configuration allows a comparable reinforcing effect fordisordered composites. The key reasoning behind makingplatelet nanocomposites are intercalation of polymers insidethe galleries and exfoliation of platelets in the matrix.Exfoliation leads to the improvement of bulk reinforcementby increasing its mechanical properties and aspect ratio

In order to understand nanocomposites; atomic structures;interfacial interaction between different matrices; andnanoreinforcements; atomic level interactions should be studiedin details. Mechanical properties of nanocomposites could bepredicted by realistic computational techniques that vary intime and length scales [20-22]. Molecular dynamics (MD)simulations can provide the structure, and the dynamicintercalated molecule details. MD is used to model nano layeredgraphite polymeric nanocomposites and their constituents elasticproperties. After performing MD simulation, the resultingdeformed molecular structure is analyzed to determine theelastic constants. Following the initial stage, three tensile andthree pure shear strains with magnitudes of ±0.0005 are appliedto the energy minimized system, with the system re-minimizedfollowing each deformation [23].

In the work presented in this paper, molecular interactionsare described by Condensed–phase Optimized MolecularPotentials for Atomistic Simulation Studies (COMPASS)

forcefield. COMPASS force field accounts for two functioncategories, valence terms including the diagonal and off-diagonal cross coupling terms, and nonbond interactionterms. The valence terms represent internal coordinates ofbond, angle, torsion angle, and out-of-plane angle. The crosscoupling terms include two or three internal coordinatespotentials. The nonbond interaction terms include van derWaals for the Lennard-Jones function, and a Coulombicfunction for electrostatic interactions [23,24]. The MDsimulations are performed using commercial software,Material Studio 4.1 [23].

2. Simulation of Graphene Platelet CompositesUsing Molecular Dynamics

2.1. Simulations of graphene/graphite

Graphite atomic hexagonal crystal group 186 P63MC isconstructed with dimensions shown in Fig. 5. Moleculardynamic geometry parameters, such as periodic cell size andnumber of layers, are simulated to study their effect ongraphene mechanical properties. NVT, which stands forconstant number of atoms, constant volume, and constanttemperature, associated with Anderson thermostat is thethermodynamic ensemble applied through the entiresimulated configurations.

A structure energy minimization followed by a dynamicsystem equilibration under NVT ensemble is applied for pre-determined dynamic time. Dynamic time for simulatedatomic structures is proportional to the number of atomsincluded in each supercell. A dynamic step of 0.1 fs, and a100 kcal/mol energy deviation are kept constant for allgraphene conducted simulations.

2.2. Simulations of polymeric matrices (vinylester, brominated

vinylester)

An amorphous cell molecular dynamics module isrecommended for amorphous polymers to optimize their

Fig. 3. Molecular structure of a single chain brominatedvinylester.

Fig. 4. Schematic diagram of nanocomposites: (a) conventional,(b) intercalated, (c) long range, and (d) disordered.

Fig. 5. Molecular graphite structure: (a) crystal dimensions and(b) atomic crystal structure.


mechanical behavior, surface characteristics, and interfaceinteractions. An Amorphous module is a suite of computationaltools that allow assembly of representative models ofcomplex amorphous system that anticipate the keyproperties. Simulation parameters which are required tosetup the simulation include: system composition chemicalchain, temperature, and density. Representative volumeelement (RVE) models are established from equilibratedvinylester/brominated vinylester atomic structures governedby COMPASS forcefield. The RVE is constructed of tenatomic vinylester/brominated vinylester chains each of230 atoms. Vinylester simulation parameters are bulk periodiccell density 1.04 g/cm3 at room temperature 298 K, and Tg =400 K, Fig. 6. Brominated vinylester simulation parametersare bulk periodic cell density 1.53 gm/cm3 at room temperature298 K, and Tg = 400 K, Fig. 7. Bromination of vinyl esterwill increase the density due to the replacement of some ofthe hydrogen atoms. There are four bromine (Br) atomsreplacing four hydrogen (H) atoms. Br has a large atomweight (79.904 g/mol) compared to H (1 g/mol). Consideringchemical chain structure shown in Fig. 2 and 3, thecalculated molecular weight of the regular vinyl ester is1190, while that of the brominated vinyl ester is 1822.Assuming that the unit cell volume is about the same, thedensity will increase by about 53%.

RVE molecular systems are condensed with NPT (constantnumber of atoms, pressure, and temperature, MD simulationsat 300 K and 1 atm for 50 ps. This process is followed byNVT (constant number of atoms, volume, and temperaturefor 100 ps raising the molecular system temperature from300 K to 400 K in stepwise dynamic simulation. For eachpolymeric system temperature, this is followed by an NPTdynamic step-wise temperature reduction back to roomtemperature 300 K. Static mechanical properties arecalculated for each equilibrated cell.

2.3. Simulations of graphene-vinylester and graphene-

brominated vinylester interfacial properties

The pullout energy, Epull-out, is defined as the energydifference between the fully embedded graphene plate andthe complete pull-out configuration. It can be related to theinterfacial shear stress, τi, by the following:

Epul- out (1)

(2)

where, W, L and t are the width, length, and thickness of the

2 W t+( ) . L x–( ) xd

0

L

∫= W t+( )L2=

τi

Epull out–

W t+( )L2

-----------------------=

Fig. 6. (a) Atomic vinylester single vinylester chain (230) atomsand (b) 10 chain vinylester unit cell (2300) atoms.

Fig. 7. (a) Atomic single brominated vinylester chain (230)atoms and (b) 10 chain brominated vinylester unit cell (2300)atoms.

Fig. 8. Atomic model for graphene-vinylester reinforcementinterfacial pull-out.

Fig. 9. Atomic model for graphite-vinylester reinforcementinterfacial pull-out.


graphene plate, respectively, and x is the displacement of thegraphene sheet. Molecular dynamics simulations are carried outfor the following fiber–polymer pull-out energies: 1. graphene–vinylester interface (Fig. 8), 2. graphite–vinylester interface(Fig. 9), 3. graphene–brominated vinylester interface (Fig. 10),and 4. graphite–brominated vinylester interface (Fig. 11).

2.4. Simulations of graphene composites

Simulations are carried out for 10 and 20% of graphite–vinylester (Fig. 12a and b), and for exfoliated graphene–vinylester composites (Fig. 13a and b). The simulationconditions and cell sizes that have been constructed arementioned later in Table VIII. The NVT and NPT stepsimulations described earlier in matrix molecular modeling are

applied to the composite simulations. Hence, the temperatureof the system is maintained at 298 K throughout the simulation.

3. Results

3.1. Mechanical properties of graphene

Graphene supercells of different sizes are shown in Fig.14. Elastic constants of the numerous super cells are shownin Table 1. Where E, G, K are the Young’s, shear, bulkmoduli respectively, and ν is the Poisson’s ratio. The periodiccell size for the graphene is a 2×2 supercell crystal.

3.2. Mechanical properties of graphite

3.2.1. Effect of unit cell sizeFig. 15 shows a double layered graphite molecular

Fig. 10. Atomic model for graphene-brominated vinylesterreinforcement interfacial pull-out.

Fig. 11. Atomic model for graphite-brominated vinylesterreinforcement interfacial pull-out.

Fig. 12. (a) 10% Graphene-vinylester composite and (b) 20%graphene-vinylester composite.

Fig. 13. (a) 10% Exfoliated graphene-vinylester composite and(b) 20% exfoliated graphene-vinylester composite.

Table 1. Graphene engineering constants versus number ofsupercells

Graphene Unit cell (NVT)

Single Layer Number of Supercells

Eng.Constants

2×2(8 atoms)

4×4(32 atoms)

6×6(70 atoms)

8×8(128 atoms)

E11 (GPa) 1373.3 1373.7 1373.9 1373.7

E22 (GPa) 830.3 831.8 832.1 832.3

ν12 0.30 0.31 .31 .31

G (GPa) 340.5 340.5 340.5 340.5

K (GPa) 621.1 625.4 626.3 626.6

Fig. 14. Graphene atomic supercell (a) graphene two supercells,(b) graphene four supercells and (c) graphene eight supercells.


supercell, side and top views. Several graphite supercells aresimulated to study the effect of the supercell size on graphitemechanical properties and to obtain the periodic celldimensions for the graphite atomic structure.

Table 2 and 3 show the engineering constants for thegraphite molecular structure of different supercell sizes.From Table 2 and 3 it can be seen that the engineeringconstants tend to remain steady for both supercell structuresat 4×4 size for the double layer, and at 8×8 for the fourlayered graphite. Increasing the number of layers simulatedrequires a larger supercell to represent the periodic simulatedgraphite cell.

3.2.2. Effect of Number of LayersSeveral layers are simulated to study their geometrical

effect on graphite mechanical properties. Fig. 16 shows a

molecular crystal structure for a four-layered and a ten-layeredgraphite supercell. Table 4 demonstrates the engineeringconstants for double, four, and ten layered graphite periodiccells. The results recorded in Table 4, affirm that thevariation of the engineering constants for the multi layeredgraphite periodic cells is less than 5%.

3.3. Mechanical properties of vinylester

Table 5 shows the engineering constants of a vinylesteramorphous cell for 6, 10, and 12 chains. From results shown,an amorphous cell of 10 chains of vinylester and 3200 totalatoms is the periodic cell of such a polymeric structure.Hence, increasing the amorphous cell atomic size andsimulated number of atoms will not induce any mechanicalproperty variation or improvement beyond the 2300 atomperiodic cell.

Fig. 15. Double layered graphite super cell (a) side view and (b)top view.

Table 2. Double layer graphite engineering constants versus numberof supercells

Double Layer

Graphite (NVT) Number of Supercells

Eng.Constant

4×4(64 atoms)

6×6(144 atoms)

8×8(256 atoms)

10×10(400 atoms)

12×12(576 atoms)

E11 (GPa) 26.9 27.5 27.5 27.6 27.7

E22 (GPa) 1159.6 1160.3 1160.3 1160.2 1160.2

ν13 0.0 0.0 0.0 0.0 0.0

G23 (GPa) 406 406.2 406.2 406.2 406.1

K23 (GPa) 1014 1014.8 1014.8 1015 1015

Table 3. Four layer graphite engineering constants versus numberof supercells

Graphene Unit cell (NVT)

Four Layer Number of Supercells

Eng. Constants 8×8 (512 atoms) 12×12 (1152 atoms)

E11 (GPa) 29.2 29.1

E22 (GPa) 1161.3 1160.6

ν12 0.0 0.0

G23 (GPa) 406.6 406.4

K23 (GPa) 1015.4 1014.7

Fig. 16. Multi layered graphite super cell: (a) four layers and (b)ten layers.

Table 4. Periodic graphite cells engineering constants versusnumber of layers

Graphite Unit cell (NVT)

Number of Layers

Eng.Constants

2 Layers(64 atoms)

4 Layers(512 atoms)

10 Layers(9640 atoms)

E11 (GPa) 26.9 29.2 27.8

E22 (GPa) 1159.6 1161.3 1160.1

ν12 0.0 0.0 0.0

G23 (GPa) 406 406.6 406.05

K23 (GPa) 1014 1015.4 1015

Table 5. Vinylester engineering constants versus number of chains

Eng. Constants 6 Chains 10 Chains 12 Chains

E11 (GPa) 2.83 3.7 3.7

ν12 0.30 0.31 0.31

Table 6. Brominated vinylester engineering constants

Eng. Constants 10 Chains

E11 (GPa) 3.5

ν12 0.32


3.4. Mechanical properties of brominated vinylester

Table 6 demonstrates the engineering constants forbrominated vinylester amorphous cell, of 10 chains. Theresults indicate as expected that the bromination ofvinylester did not vastly affect the mechanical properties.

Comparing the MD results shown in Table 5 and 6, thecalculated elastic modulus of vinylester is higher than that ofbrominated vinylester. This result does not match observedexperimental values where bromination is expected toincrease stiffness of vinylester. However, in thesesimulations an ideal vinylester chain, that does not includeunreacted epoxy, was used. The presence of unsaturatedvinylester reduces the mechanical properties. Differentamount of unreacted epoxy molecules may exist for cases ofbrominated and unbrominated vinylester. This paper,indirectly, suggests that bromination could reduce theamount unreacted epoxy molecules in vinylester.

3.5. Interfacial strength (graphene/graphite-vinylester/

brominated vinylester)

The Epull-out calculated from MD simulation for thevinylester-graphene is 149.61 kcal/mol. The energy plot is

shown in Fig. 17(a). The properties of the unit cell simulatedfor the pull-out energy are: density of 0.37 g/cm3, molecularweight of 10672 gm/mol, and cell dimensions of (L=29.64 Å,W=29.64 Å , t=3.4 Å) Fig. 8. According to equations (1-2),the interfacial strength is calculated to be τi= 256 MPa,which is double the calculated interfacial strength value forthe SWCNT- Polyethylene reported in [18,25].

A similar atomic cell structure is constructed for thegraphite (Fig. 9) to study the interfacial strength of a multilayered graphene nanoplatelet. Double layered graphite ischosen with a density of 0.572 g/cm3, molecular weight of13104 g/mol, and cell dimensions of (L=29.64 Å, W=29.64 Å,t=3.4 Å). Epull-out for the double layer of graphite is 69.8 kcal/mole Fig. 17(b). The interfacial strength calculated from

Fig. 17. Potential energy variation for a pull-out simulation forreinforced vinylester composite: (a) graphene and (b) graphite.

Fig. 18. Potential energy variation for a pull-out simulation forreinforced brominated vinylester composite: (a) graphene and(b) graphite.

Table 7. Interfacial strength for graphene-vinylester nanocomposites

Composite Interfacial Strength ( MPa)

SWCNT-Polyethylene 133

Graphene-Vinylester 256

Graphite-Vinylester 125

Graphene-Brominated vinylester 534.4

Graphite-Brominated vinylester 368


equations (1-2) is 125 MPa, which is less than half of thegraphene interfacial strength.

Vinylester bromination effect on interfacial strength ofvinylester bromination- graphene/graphite is simulated inthis study. Although the mechanical properties of thebrominated vinylester are comparably close to vinylester, agreat interfacial strength enhancement is shown in thesimulated pull-out energy configurations. Potential energyvariation plots for a pull-out simulation for (a) graphene-brominated vinylester and (b) graphite-brominated vinylesterare shown in Fig. 18 Interfacial strengths summary is shownin Table 7.

3.6. Molecular dynamic simulations of vinylester

nanocomposites

Stiffness matrices for 10 and 20 wt.% reinforcements areshown in Table 8. Results shown in Table 8 demonstrate thatexfoliated graphene platelets nanocomposites have higherelastic properties than the graphite nanocomposites.

4. Conclusions

This paper demonstrates the viability of using moleculardynamics simulations to estimate mechanical properties ofgraphite-vinylester composites and their constituents (matrix,reinforcement and interface). Engineering constants forvinylester matrix (brominated and unbrominated), reinforcement(graphene and graphite), and composites were theoreticallycalculated. Interfacial shear strength at vinylester-graphene/or graphite was estimated.

Acknowledgement

This work was partially supported by the funding receivedunder a subcontract from the Department of HomelandSecurity-Sponsored Southeast Region Research Initiative(SERRI) at the Department of Energy's Oak Ridge NationalLaboratory, USA.

References

[1] Varley, R. J.; Groth, A. M.; Leong, K. H. Compos. Sci.

Tech. 2007, 68, 2882.

[2] Meyer, J. C.; Geim, A. K.; Kastnelson, M. I.; Novoselov, K.

S.; Booth, T. J.; Roth, S. Nature 2007, 446, 60.

[3] Figiel, L.; Buckley, C. P. Comput. Mater. Sci. 2008, inpress.

[4] Valavala, P. K.; Odegard, G. M. IUTAM Symp. Modelling

Nanomaterials and Nanosystems: Proc. IUTAM Symp.,

Aalborg, Denmark, 2008, 19.

[5] Zeng, Q. H.; Yu, A. B.; Lu, G. Q. Progr. Polym. Sci. 2007,

Table 8. Stiffness matrices of graphene-vinylester nanocomposite

Graphene-Vinylester Composite Stiffness Matrix: 10%

Unit Cell size: (19.76×19.76×58.6) ATriclinic cell: α=β=90o, γ=120o

Thermodynamic: NVTNumber of Atoms: 2232

Temperature: 400 KElastic Properties: at 298 K

Graphene -Vinylester Composite Stiffness Matrix: 20%

Unit Cell size: (19.76×19.76×91.54) ACubic cell: α=β=90o, γ=120o

Thermodynamic: NVT Number of Atoms: 3246

Elastic Properties: at 298 K

Exfoliated Graphene-Vinylester Composite Stiffness Matrix: 10%

Unit Cell size: (19.76×19.76×58.6) ATriclinic cell: α=β=90o, γ=120o

Thermodynamic: NVTNumber of Atoms: 2232

Temperature: 400 KElastic Properties: at 298 K

Exfoliated Graphene -Vinylester Composite Stiffness Matrix: 20%

Unit Cell size: (19.76×19.76×91.54) ACubic cell: α=β=90o, γ=120o

Thermodynamic: NVT Number of Atoms: 3246

Elastic Properties: at 298 K

Cij

GPa=

Gij GPa=

Gij

GPa=

Gij

GPa=


33, 191.

[6] Harkin- Jones, E.; Figiel, L.; Spencer, P.; Abu-Zurayk, R.;

Al-Shabib, W.; Chan, V.; Rajeev, R.; Soon, K.; Buckley, P.;

Sweeney, J.; Menary, G.; Armstrong, C.; Assender, H.;

Coates, P.; Dunne, F.; McNally, T.; Martin, P. Plastics,

Rubber & Composites 2008, 37, 113.

[7] Lan, T. T.; Kaviratna, P. D.; Pinnavaia, T. J. J. Chem. Mater.

1995, 7, 2144.

[8] Lan, T. T.; Pinnavaia, T. J. Proc. Mat. Res. Soc. Symp. 1996,

435.

[9] Vaia, R. A.; Price, G.; Ruth, P. N.; Nguyen, H. T.; Lichten-

han, J. Appl. Clay Sci. 1999, 15, 67.

[10] LeBaron, P. C.; Wang, Z.; Pinnavaia, T. J. Appl. Clay Sci.

1999, 15, 11.

[11] Mouras, S.; Hamm A.; Djurado, D.; Cousseins, J. C.

Revue de Chimie Minerale 1987, 24, 572.

[12] Novoselov, A. K.; Geim, A. K.; Morsozov, S. V.; Jaing,

D.; Zhang, Y.; Dubonus, S. V.; Grigrieva, I. V.; Firsov, A.

A. Science 2004, 306, 666.

[13] Novoselov, K. S.; Jaing, D.; Booth, T. J.; Khotkevich, V.

V.; Morzov, S. V.; Geim, A. K. PNAS 2005, 102, 10451.

[14] Lee, C.; Wei, X.; Kysar, J. W.; Hone, J. Science 2008, 321,

385.

[15] http://en.wikipedia.org/wiki/Graphene.

[16] Karger-Kocsis, J., Gryshchuk, O., Schmitt, S. J. Mater.

Sci. 2003, 38, 413.

[17] Derkane Momentum ™ 640-900. Epoxy Vinyl Ester Resin,

2004.

[18] Gou, J.; Minaie, B.; Wang, B.; Liang, Z.; Zhang, C. Com-

put. Mater. Sci. 2004, 31, 225.

[19] Wagner, H. D.; Vaia, R. A. Materials Today 2004, 7, 38,

[20] Liao, K; Li, S. Appl. Phys. Lett. 2001, 79, 4225.

[21] Xiao, M.; Sun, L.; Liu, J.; Li., Y.; Gong, K. Polymer 2001,

43, 2245.

[22] Leach, R. A. “Molecular Modeling Principles and Appli-

cation”, Pearson Education, EMA, 2001, Chapter 1.

[23] MS Modeling 4.0 Online Help Manual, Accelrys Inc.,

2005.

[24] Sun, H. J. Phys. Chem. B 1998, 102, 7338.

[25] Al-Ostaz, A.; Pal, G. J. Mater. Sci. 2008, 43, 164.

Documents

Molecular Dynamics Simulations of Graphite-Vinylester