1 Molecular Dynamics Simulation of Cross-linked Graphene–Epoxy anocomposites R.Rahman 1 , A. Haque 2 ABSTRACT: This paper focuses on molecular dynamics (MD) modeling of graphene reinforced cross-linked epoxy (Gr-Ep) nanocomposite. The goal is to study the influence of geometry, and concentration of reinforcing nanographene sheet (NGS) on interfacial properties and elastic constants such as bulk Young’s modulus, and shear modulus of Gr-Ep nanocomposites. The most typical cross-linked configuration was obtained in order to use in further simulations. The mechanical properties of this cross-linked structure were determined using MD simulations and the results were verified with those available in literatures. Graphene with different aspect ratios and concentrations (1%, 3% and 5%) were considered in order to construct amorphous unit cells of Gr-Ep nanocomposites. The Gr-Ep nanocomposites system undergoes NVT (constant number of atoms, volume and temperature) and NPT (constant number of atoms, pressure and temperature) ensemble with applied uniform strain field during MD simulation to obtain bulk Young’s modulus and shear modulus. The stress-strain response was also evaluated for both amorphous and crystalline unit cells of Gr-Ep system under uni-axial deformation. The cohesive and pullout force vs. displacement response were determined for graphenes with different size. Hence as primary goal of this work, a parametric study using MD simulation was conducted for characterizing interfacial properties and elastic constants with different NGS aspect rations and volume fractions. The MD simulation results show reasonable agreement with available published data in the literature. KEY WORDS: Molecular dynamics, graphene-epoxy nanocomposites, elastic properties. ITRODUCTIO Epoxy resins are a big class of compounds containing two or more epoxy groups, which can react with many compounds (called curing agents) with chemical groups such as amines and anhydrides. The resultants exhibit a series of excellent performance, i.e. high modulus and fracture strength, low creep and high-temperature performance, and thus widely serve as coatings, adhesives, composites, etc. in electronics and aerospace industries. It is considered to be an important structural resin material particularly used in aerospace industry due to its low molecular weight and good mechanical property. Because of its wide range potential in the field of structural, automobile and aerospace engineering, researchers focused on determining bulk mechanical property of cross-linked epoxy resin. 1,2 Department of aerospace engineering, The University of Alabama, Tuscaloosa, AL 35487,USA Email: [email protected]
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1
Molecular Dynamics Simulation of Cross-linked Graphene–Epoxy
anocomposites
R.Rahman1, A. Haque
2
ABSTRACT: This paper focuses on molecular dynamics (MD) modeling of graphene reinforced
cross-linked epoxy (Gr-Ep) nanocomposite. The goal is to study the influence of geometry, and
concentration of reinforcing nanographene sheet (NGS) on interfacial properties and elastic
constants such as bulk Young’s modulus, and shear modulus of Gr-Ep nanocomposites. The
most typical cross-linked configuration was obtained in order to use in further simulations. The
mechanical properties of this cross-linked structure were determined using MD simulations and
the results were verified with those available in literatures. Graphene with different aspect ratios
and concentrations (1%, 3% and 5%) were considered in order to construct amorphous unit cells
of Gr-Ep nanocomposites. The Gr-Ep nanocomposites system undergoes NVT (constant number
of atoms, volume and temperature) and NPT (constant number of atoms, pressure and
temperature) ensemble with applied uniform strain field during MD simulation to obtain bulk
Young’s modulus and shear modulus. The stress-strain response was also evaluated for both
amorphous and crystalline unit cells of Gr-Ep system under uni-axial deformation. The cohesive
and pullout force vs. displacement response were determined for graphenes with different size.
Hence as primary goal of this work, a parametric study using MD simulation was conducted for
characterizing interfacial properties and elastic constants with different NGS aspect rations and
volume fractions. The MD simulation results show reasonable agreement with available
Figure 14. Stress-strain response of amorphous system with type-(a) graphene
Figure 15. Stress-strain response of amorphous system with type-(b) graphene
Table V. Young’s modulus calculated from stress-strain response
The bulk Young’s modulus is predicted
reasonable agreement with the prediction from
proposed by Ji [10]. The micromechanics model is based on homogenized po
Hence the prediction shows a monoto
increasing volume fraction of nanofiller. But in real
in this manner. There are some factors such as percentage of void, dispersion
etc cause decreasing in Yong’s modulus.
decrease in the Young’s modulus of graphene
increases. They considered graphene
dimension in nanometer scale. The unit cells in the current work may be represented according to
their case by scaling down to angstroms. Thus weight fraction of graphene is scaled up ten times
relative to the one considered in the paper by
times. The graphene is closely comparable
on this hypothetical comparison
graphene has good agreement with th
Atom density in the unit cell also plays an important role in this
(Figures 10 and 11) comparatively larger gap between graphene
weight fraction for both types of graphenes: G
in all the amorphous cells are represented in Figures 16 and 17
of G-Ep-Nc-I and G-Ep-Nc-II compared to
system.
0.02
0.04
0.06
Ato
m d
en
sity
(ato
ms/
vo
lum
e)
Figure 16. Atom density in amorphous system with type
23
bulk Young’s modulus is predicted from stress-strain response is observed to have a
reasonable agreement with the prediction from graphene-polymer micromechanics model
he micromechanics model is based on homogenized po
prediction shows a monotonically increasing nature in bulk Young’s modulus with the
of nanofiller. But in real, Young’s modulus may not
There are some factors such as percentage of void, dispersion quality of graphene
cause decreasing in Yong’s modulus. The work by Rafiee [9] shows first increase and then
decrease in the Young’s modulus of graphene-epoxy nanocomposites as the volume fraction
They considered graphene sheet with aspect ratio of 19 (approximately)
The unit cells in the current work may be represented according to
their case by scaling down to angstroms. Thus weight fraction of graphene is scaled up ten times
o the one considered in the paper by Rafiee. This also leads to scale up the stress by ten
The graphene is closely comparable to the one with AR=13 (type-(b)) in this paper. Based
on this hypothetical comparison, the Young’s modulus at 1%, 3% and 5% cases for type
graphene has good agreement with the experimentally calculated [9].
Atom density in the unit cell also plays an important role in this regard.
) comparatively larger gap between graphene and epoxy in the case of 5%
weight fraction for both types of graphenes: G-Ep-Nc-V and G-Ep-Nc-V. Average a
represented in Figures 16 and 17 explains higher Young’s modulus
II compared to other cases due to distinguishably denser atoms in the
G-Ep-Nc-I G-Ep-Nc-III G-Ep-Nc-V
0
0.02
0.04
0.06
Figure 16. Atom density in amorphous system with type-(a) graphene
strain response is observed to have a
micromechanics model
he micromechanics model is based on homogenized polymer matrix.
bulk Young’s modulus with the
t always increase
quality of graphene
first increase and then
epoxy nanocomposites as the volume fraction
sheet with aspect ratio of 19 (approximately) with
The unit cells in the current work may be represented according to
their case by scaling down to angstroms. Thus weight fraction of graphene is scaled up ten times
e up the stress by ten
in this paper. Based
cases for type–(b)
. The RDFs show
and epoxy in the case of 5%
Average atom density
explains higher Young’s modulus
other cases due to distinguishably denser atoms in the
During deformation process it is important to observe the
of energy. The applied strain causes change in atom positions, velocities and overall molecular
structure. An equilibrated system responds to deformation by increasin
However it is expected to increase in the potential energy of the system as the deformation
process is quasi-static. Potential
mol Bond Angle Dihedral ImproperE E E E E= + + +
comparatively larger contribution from the molecular energy than van der Waals energy.
Molecular energy is expected to be increasing
molecular energy clearly explains the elongation in t
0.02
0.04
0.06
Ato
m d
en
sity
(ato
ms/
vo
lum
e)
0.00E+00
5.00E+03
1.00E+04
1.50E+04
2.00E+04
2.50E+04
3.00E+04
E_
mo
l (
kca
l/m
ole
)
Figure 17. Atom density in amorphous system with type
Figure 18. Molecular energy in amorphous system with type
24
During deformation process it is important to observe the response of the system
. The applied strain causes change in atom positions, velocities and overall molecular
structure. An equilibrated system responds to deformation by increasing its
it is expected to increase in the potential energy of the system as the deformation
Potential energy consists of molecular energy
mol Bond Angle Dihedral ImproperE E E E E ) and van der Waals energy [20]. Potential energy has
comparatively larger contribution from the molecular energy than van der Waals energy.
Molecular energy is expected to be increasing (Figure 18 and 19). The increase in slope of this
molecular energy clearly explains the elongation in the molecular topology with
G-Ep-Nc-II G-Ep-Nc-IV G-Ep-Nc-IV
0
0.02
0.04
0.06
0 0.05 0.1 0.15Strain (A 0/A 0)
G-Ep-Nc-I
G-Ep-Nc-III
G-Ep-Nc-V
Figure 17. Atom density in amorphous system with type-(b) graphene
Figure 18. Molecular energy in amorphous system with type-(a) graphene
the system in terms
. The applied strain causes change in atom positions, velocities and overall molecular
g its overall energy.
it is expected to increase in the potential energy of the system as the deformation
consists of molecular energy (
otential energy has
comparatively larger contribution from the molecular energy than van der Waals energy.
he increase in slope of this
he molecular topology with applied strain.
0.2
(b) graphene
(a) graphene
25
Kinetic energy in all the cases has least effect on the total energy during deformation
period. As the MD during was under NVT condition at low temperature (0.1 K) it is obvious to
have rescaling of atom velocities in order to be consistent with the temperature. Thus kinetic
energy was scaled down and eventually became very small in order to sustain the stability of the
system. This is interestingly important for quasi-static deformation process because the change in
potential energy of the atoms has a significant correlation with the deforming molecular
topology.
Besides the energy we can analyze the “Mean square displacement” (MSD) of the
graphene-epoxy system during deformation process. MSD in uniaxial direction during quasi-
static deformation process should represent the diffusion of atoms into the newly elongated unit
cell. So clearly the slope of this MSD is expected to be non-zero throughout this time (Figures 20
and 21).
0.00E+00
2.00E+04
4.00E+04
6.00E+04
8.00E+04
1.00E+05
1.20E+05
0 0.05 0.1 0.15 0.2
E_
mo
l (k
cal/
mo
le)
Strain (A0/A0)
G-Ep-Nc-II
G-Ep-Nc-IV
G-Ep-Nc-VI
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
3.00E+00
3.50E+00
4.00E+00
4.50E+00
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Me
an
sq
ua
re d
isp
lace
me
nt
(A 0
)
Strain (A 0/A 0)
G-Ep-Nc-I
G-Ep-Nc-III
G-Ep-Nc-V
Figure 19. Molecular energy in amorphous system with type-(b) graphene
Figure 20. MSD of amorphous system with type-(a) graphene
26
Crystalline systems: Amorphous systems are quite useful in calculating the bulk elastic
properties of the graphene-epoxy polymer nanocomposites. Graphene also has a tendency to
restack and form graphite due to van der Waals interaction between layers. Hence the effect of
graphite formation from graphene on elastic properties needs to be addressed in the MD
simulation. For all three different cases mentioned in Table 2 the stress-strain response in xx, yy,
zz directions are shown separately.
Configuration umber of
graphene plates
E11 (GPa) E22 (GPa) E33 (GPa)
CRYS-GnEp-I 1 1.89 1.94 0.9
CRYS-GnEp-II 3 (separated) 4.81 8.76 0.32
CRYS-GnEp-III 3 (stacked) 3.99 5.67 3.80
0.00E+00
1.00E+00
2.00E+00
3.00E+00
4.00E+00
5.00E+00
6.00E+00
7.00E+00
8.00E+00
9.00E+00
1.00E+01
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Me
an
sq
ua
re d
isp
lace
me
nt
(A0)
Strain (A0/A0)
G-Ep-Nc-II
G-Ep-Nc-IV
G-Ep-Nc-VI
0.00
0.01
0.01
0.02
0.02
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Str
ess
(G
Pa
)
Strain (A0/A0)
sig_zStress along Z- direction
Figure 21. MSD of amorphous system with type-(b) graphene
Table 6. Young’s modulus calculated from stress-strain response for crystalline model
27
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Str
ess
(G
Pa
)
Strain (A0/A0)
sig_x
sig_y
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.00 0.20 0.40 0.60 0.80 1.00
Str
ess
(G
Pa
)
Strain (A0/A0)
sigma_z
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0.00 0.20 0.40 0.60 0.80 1.00
Str
ess
(G
Pa
)
Strain (A0/A0)
sigma_x
sigma_y
Stress along X-direction
Stress along Y-direction
Stress along Z-direction
Stress along X-direction
Stress along Y-direction
Figure 22. Stress-strain response in xx, yy and zz directions for CRYS-GnEp-I
Figure 23. Stress-strain response in xx, yy and zz directions for CRYS-GnEp-II
28
The scales were different for different cases due to varying strain rates in order to sustain
stability during deformation process. Hence the stress-strain plots are shown separately in
Figures 22, 23 and 24. The Young’s modulus is calculated from the linear region of the stress-
strain curve and tabulated in Table 6. In the crystalline model graphene sustains its stiffness
along x and y direction. This is a primary difference between the amorphous model and the
crystalline model. Weight percentage of epoxy remains 3% in all these three crystalline
structures and the volume fraction of graphene increases as graphene forms graphite. The
objective is to emphasize on effect of graphene restacking on the elastic properties.
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.00 0.00 0.00 0.01 0.01 0.01 0.01
Str
ess
(G
Pa
)
Strain (A0/A0)
sigma_z
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Str
ess
(G
Pa
)
Strain (A0/A0)
sig_x
sig_y
Stress along Z-direction
Stress along X-direction
Stress along Y-direction
Figure 24. Stress-strain response in xx, yy and zz directions for CRYS-GnEp-III
29
The in plane Young’s modulus ,xx yyE E are highly dependent on the effect of graphene
volume fraction because graphene’s in plane property (Young’s modulus is approximately 1 TPa
0.00E+00
5.00E+03
1.00E+04
1.50E+04
2.00E+04
2.50E+04
0 0.02 0.04 0.06 0.08 0.1
E_
mo
l (k
cal/
mo
le)
Strain (A0/A0)
Molecular energy due to Z-deformation
Molecular energy due to Y-deformation
Molecular energy due to X-deformation
0.00E+00
5.00E+04
1.00E+05
1.50E+05
2.00E+05
2.50E+05
3.00E+05
3.50E+05
4.00E+05
0.00 0.20 0.40 0.60 0.80 1.00
E_
mo
l (k
cal/
mo
le)
Strain (A0/A0)
Molecular energy due to Z-deformation
Molecular energy due to Y-deformation
Molecular energy due to X-deformation
0.00E+00
1.00E+05
2.00E+05
3.00E+05
4.00E+05
5.00E+05
0.00 0.20 0.40 0.60 0.80 1.00
E_
mo
l (k
cal/
mo
le)
Strain (A0/A0)
Molecular energy due to Z-deformation
Molecular energy due to Y-deformation
Molecular energy due to X-deformation
Figure 25. Molecular energy for CRYS-GnEp-I
Figure 26. Molecular energy for CRYS-GnEp-II
Figure 27. Molecular energy for CRYS-GnEp-III
30
[17]). However, the off-plane Young’s modulus of the graphene-epoxy nanocomposites zzE is
mostly controlled by the van der Waals interaction between graphene-epoxy or graphene-
graphene. The increase in xxE and yyE from CRYS-GnEp-I to CRYS-GnEp-II in Table 6 indicates the
effect of increase in graphene reinforcement. As graphenes are restacked and form graphite (CRYS-
GnEp-II to CRYS-GnEp-III), the in plane Young’s modulus ( ,xx yyE E ) drops whereas zzE increases
because graphene-graphene van der Waals interaction starts playing significant role. The molecular
energy is increased as the system was deformed under strains in x and y directions (Figures 25, 26 and
27). However, lower in-plane modulus for CRYS-GnEp-I can be explained by very small change in the
slope of molecular energy curve (Figure 25) with respect to applied strain. The change in molecular
energy due to deformation in z-direction seems to be significantly less responsive to the applied strain. In
all these cases molecular energy has trivial role on zzE . This is because the major contribution of van der
Waals interaction in the total potential energy. The average van der waals energy for these three cases are
-2474.83 kcal/mole, -5405.64 kcal/mole and -5789.92 kcal/mole. Van der Waals energy decreases
significantly from CRYS-GnEp-I to CRYS-GnEp-II due to epoxy molecules between two graphenes.
Effect of restacking is observed as non-bonding energy is increased by -384.28 kcal/mole from CRYS-
GnEp-II to CRYS-GnEp-III.
Interfacial property calculation: Interface between graphene and epoxy plays a significant role in
load transfer mechanism from graphene to epoxy or vice versa. It is possible to determine the
normal and shear force-displacement response this interface. As model was controlled by
displacement, certain reaction force was observed in the graphene sheet. Normal displacement of
graphene leads us to obtain cohesive law between graphene and epoxy whereas shear
displacement helps us to study the pullout mechanism (Figures 8 and 9).
Configuration Graphene sheet
dimension
(length x
widths) (A0)
2
umber of
carbon
atoms in
graphene
Interaction
force type
Ultimate
strength
(MPa)
Displacement
at separation
or critical
length (nm)
Mode-I-small 39.36 x 19.02 248 Normal 0.03 0.00075
Mode-I-big 118.08 x 19.02 766 Normal 9.93x10-3
0.023
Mode-II-small 39.36 x 19.02 248 Shear 0.12 0.025
Mode-II-big 118.08 x 19.02 766 Shear 0.91 0.165
Table 7. Unit cell configuration for interface model
31
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
0 0.05 0.1 0.15 0.2 0.25
Fo
rce
(p
ico
Ne
wto
ns)
Displacement (nm)
Mode-I-big
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
0 0.0005 0.001 0.0015 0.002 0.0025 0.003
Fo
rce
(p
ico
Ne
wto
ns)
Displacement (nm)
Mode-I-small
0.00E+00
5.00E-03
1.00E-02
1.50E-02
2.00E-02
2.50E-02
3.00E-02
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Fo
rce
(p
ico
Ne
wto
ns)
Displacement (nm)
Mode-II-big
Mode-II-small
Critical lengths
Figure 28. Force vs displacement curve for Mode-I-big graphene-epoxy system
Figure 29. Force vs displacement curve for Mode-I-small graphene-epoxy system
Figure 30. Force vs displacement curve for Mode-II-big and Mode-II-small graphene-epoxy systems
Displacement at failure=0.023 nm
(approximately)
Displacement at failure =0.00075 nm
(approximately)
32
The cohesive or normal force-displacement curve is obtained in Figures 28 and 29 for
graphenes with large and small surface areas respectively. Ultimate cohesive strength is
comparatively higher in the Mode-I-small because of smaller surface area of graphene. In both of
the cases, maximum force at separation is approximately 2.3x10-1 pN. But the displacement at
separation is expectedly higher for Mode-I-big than Mode-I-small. Hence the fracture energy or
work of separation is higher for bigger graphene sheets. This causes higher interfacial stiffness
for larger graphenes.
Unlike mode-I failure, the mode-II or pullout strength is higher for longer graphene
(Mode-II-big). From Figure 30 the interfacial stiffness in pullout direction seems to be similar
for both small and large graphenes. For Mode-II-small the early drop in the pullout force
indicates failure. However, the pullout force was not observed to be monotonically decreasing
like Mode-II-big. It clearly indicates the effect of atoms. For Mode-II-big the number of atoms is
three times larger than that of Mode-I-small. Hence the effect of thermal fluctuation is higher for
smaller graphene. As a result the pullout force vs. displacement curve is smoother for larger
graphene.
COCLUSIO
In this paper mechanical properties of graphene reinforced epoxy composite are predicted
using MD simulation. The predicted results showed reasonable agreement with available
experimental data and theoretical prediction in the literature. Besides mechanical properties, the
MD simulation also provided some meaningful information on epoxy-graphene interaction
energy. This work successfully applies MD based frame work to graphene based polymer
nanocomposites which can be further extended.
REFERECE
1. Wu, Chaofu and Xu, Weijian. (2006), Atomistic molecular modeling of crosslinked epoxy resin,
Polymer. 47: 6004-6009.
2. Fan, Bo, Hai and Yuen, M.F. Matthew. (2007), Material properties of the cross-linked epoxy resin
compound predicted by molecular dynamics simulation, Polymer. 48: 2174-2178.
3. Bandyopadhay, Ananyo., Jensen, D.,Valavala K. Pavan and Odegard M. Georgory. (2010), Atomistic
modeling of cross-linked epoxy polymer, presented at 51st AIAA/ASME/ASCE/ASC Structures,
Structural Dynamics and Materials conference, 12-15th April, 2010.
4. Yu, Suyoung., Yang, Seunghwa., and Cho, Maenghyo. (2009), Multi-scale modeling of cross-linked
epoxy nanocomposites, Polymer. 50: 945-952.
33
5. Zhu, R., Pan, E. and Roy, A.K. (2007), Molecular dynamics study of the stress-strain behavior of
carbon-nanotube Epon 862 composites, Materials science and engineering A. 447: 51-57.
6. Franklans S.J.V, Harik V.M., Odegard G.M., Brenner D.W., and Gates T.S. (2003), The stress–strain
behavior of polymer–nanotube composites from molecular dynamics simulation, Composites Science
and Technology, 63: 1655-1661.
7. Yasmin, Asma., Daniel, M. Issac. (2004), Mechanical and thermal properties of graphite/epoxy
composites, Polymer. 45: 8211-8219.
8. Cho, J., Luo, J. J., and Daniel, I.M. (2007), Mechanical characterization of graphite/epoxy
nanocomposites by multi-scale analysis,” Composites science and technology. 67: 2399-2407.
9. Rafiee MA, Rafiee J, Wang Z, Song H, Yu ZZ, and Koratkar N.(2009), Enhanced mechanical
properties of nanocomposites at low graphene content, ACS 7anoletters, 3(12):3884-90.
10. Ji. Xiang-Ying; Cao. Yan-Ping; Feng, and Xi-Qiao.(2010), Micromechanics prediction of the
effective elastic moduli of graphene sheet-reinforced polymer nanocomposites , Modelling and
Simulation in Materials Science and Engineering, 16:45005-45020. 11. Lv. Cheng, Xue. Qingzhong, and MingMa .DanXia. (2011), Effect of chemisorption structure on the
interfacial bonding characteristics of graphene–polymer composites, Applied Surface Science,
to be published.
12. Liao, Kin; Li, Sean. (2001), Interfacial characteristics of a carbon nanotube–polystyrene composite
system, Applied Physics Letters, 79: 4225 – 4227.
13. Amnaya P. Awasthi, Dimitris C. Lagoudas, Daniel C. Hammerand. (2009), Modeling of graphene–
polymer interfacial mechanical behavior using molecular dynamics, Modelling and
Simulation in Materials Science and Engineering, 17: 015002.
14. Sun, H. (1998), Compass: An ab initio force field optimized for condensed phase applications –
Overview with details on Alken and Benzene compounds, Journal of Physical chemistry B. 102 (38):
7338-7364.
34
15. Leach. Andrew, R. Molecular Modelling: Principles and Applications (1997), Addison Wesley
Publishing Company,
16. Fan, Feng, Cun., and Hsu, Ling, Shaw. (1992), Application of the molecular Simulation technique to
characterize the structure and properties of an aromatic polysulfone system. Mechanical and Thermal
Properties, Macromolecules. 25: 266-270.
17. Pour-Sakhaee, A. (2009). Elastic properties of single layered graphene sheet, Solid state
communications. 149: 91-95.
18. Schinepp C. Hannes., Li, Je-Luen., Michael J. McAllister., Hiroaki, Sai., Margarita Herrera-Alonso.,
Douglas H. Adamson., Robert K. Prud’homme., Roberto, Car., Dudley A. Saville, Ilhan A. Aksay.
(2006), Functionalized single graphene sheet derived from splitting graphite oxide, Journal of
physical chemistry B Letters. 110: 8535-8539.
19. S.M.-M. Dubois, Z. Zanolli, X. Declerck, and J.-C. Charlier. (2009), Electronic properties and
quantum transport in Graphene-based nanostructures, Europian Physical Journal B. 71(1): 1-24.
20. http://lammps.sandia.gov/
21. Tack, Lee Jermey. (2006), THERMODYNAMIC AND MECHANICAL PROPERTIES OF
EPON 862 WITH CURING AGENT DETDA BY MOLECULAR SIMULATION, Thesis, Texas
A&M University.
22. Komuves, Francis., Ajit D. Kelkar., and Vinaya A. Kelkar. (2010)., Prediction of mechanical
properties of EPON 862 (DGEBF) W (DETDA) using MD simulations” presented at 51st
AIAA/ASME/ASCE/ASC Structures, Structural Dynamics and Materials conference, 12-15th April,