Journal of Materials Science and Chemical Engineering, 2014, 2, 26-30
Published Online January 2014 (
Molecular Dynamic Simulation Study on Glass Transition
Temperature of DGEBA-THPA/SWCNTs Composites
Cai Jiang, Jianwei Zhang, Shaofeng Lin, Dazhi Jiang
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, China
Received October 2013
Molecular dynamic (MD) simulations were carried out to predict the thermo-mechanical properties of the cured
epoxy network composed of diglycidyl ether bisphenol A (DGEBA) epoxy resin and tetrahydrophthalic anhy-
dride (THPA) curing agent and their single-walled carbon nanotubes (SWCNT) reinforced the epoxy matrix
composites. Different characters such as the density of the materials and mean square displacements (MSDs)
were calculated to estimate the glass transition temperatures (Tgs) of of the materials. 365 K and 423 K of the
Tgs were obtained respectively, whereas the latter is much higher than the former. The simulation results indi-
cated that the incorporation of SWCNTs in the epoxy matrix can significantly improve the Tg of the cured epoxy.
The approach presented in this study is ready to be applied more widely to a large group of candidate polymers
and nanofillers.
Molecular Dynamics Simulation; Glass Transition Temperature; Carbon Nanotubes Composites
1. Introduction
Glass transition temperature (Tg) is a key descriptor to
evaluate the thermal properties of the heat-resistant ma-
terials, while the useability determined by the mechanical
properties at high temperature. The ability to predict the
Tg and mechanical properties is of great value in the se-
lection and design of new materials. Conducting experi-
ments to measure the Tg and mechanical properties is a
reliable, however, time-consuming and expensive ap-
proach. Recently, molecular dynamics (MD) simulation
has provided great insight into the Tg and elastic re-
sponse of polymer and its composite materials.
Abu-Sharkh [1] conducted the rigid unit model and the
explicit atom model to generate volume-temperature (V-
T) data of poly (vinylchloride) respectively, which con-
firmed the validity of MD simulation in predicting the Tg
of amorphous polar polymers. Wu et al. [2,3] calculated
the density and elastic constants of diglycidyl ether bis-
phenol A (DGEBA) cured with isophorone diamine (IPD)
using atomistic molecular simulation. The results indi-
cated that both the use of COMPASS force-field and
DREIDING force-field resulted in unrealistically high
elastic constants whereas the former compared more fa-
vorably with the corresponding experimental values than
the later. Fan et al. [4] used PCFF force-field to predict
the Tg, linear thermal expansion coefficients (LCTEs)
and Young’s modulus of cross-linked EPON862-TETA
(triethylenetetramine) systems from MD simulations.
Their results were in good agreement with the experimen-
tal values in the literature. Li et al. [5,6] and Bandyop-
adhyay et al. [7,8] studied the EPON862-DETDA (die-
thylene toluene diamine) systems. The simulation results
indicated a significant increase in Tg, Young’s modulus
and yield stress with degree of polymerization, while the
thermal expansion coefficient (CTE) decreased with the
overall crosslink density, and the yield strain was less
sensitive to it, however, there was no discernible influ-
ence of cross-link distribution on the elastic modulus and
the LCTE. Shenogina et al. [9,10] employed a new
method-dynamic deformation approach to simulate the
thermo-mechanical constants and the elastic constants of
DGEBA-DETDA systems. Results were in very good
agreement with experimental data of actual cured poly-
mers. The approach showed excellent improvement
compared to constants calculated using the static defor-
mation approach.
Epoxy resin matrix composites are of special interest
in the aerospace industry for the current andfuture air-
craft and spacecraft due to their good heat-resistance and
outstanding mechanicalproperties, comparing to other
lightweight structural materials. It has been observed that
the incorporation ofCNTs[11] in the epoxy resin can sig-
nificantly enhance its mechanical, thermal, and electri-
calproperties, and thus, CNTs can be used as a potential
reinforcement for epoxy. Gou et al. [12] investigated the
interfacial bonding of single-walled carbon nanotube
(SWCNT) reinforced epoxy resin composites in terms of
stress transfer. A 250% ~ 300% increase in storage
modulus with the addition of 20 ~ 30 wt% nanotubes was
resulted. Liang et al. [13] found that both the EPON862
resin and DETDA molecules have attractive intercala-
tions with (10, 10) SWCNT, and the aromatic ring struc-
tures of the molecules try to align the aromatic ring
planes toward the SWCNT surface and wrap around it.
Mittal et al. [14] found that the reinforcement of
SWCNTs with different diameters, whereas the (8, 8)
SWCNTs reinforced EPON862 resin composites exhib-
ited the highest enhancement of the Young's modulus.
Chakraborty et al. [15] investigated the properties of the
composites of pure monomer and trimer polycarbonate
and their mixtures with different weight percentages of
embedded SWCNTs at different temperatures. It was
seen that the diffusivity of solvent molecules decreased
with increasing percentage of CNTs at a specific tem-
perature; and the polymerization played a role in en-
hancement of binding energy.
In this study, molecular dynamic (MD) simulations
werecarried out to predict the thermo-mechanical proper-
ties of the curedepoxy network composed of diglycidyl
ether bisphenol A(DGEBA) epoxy resin and tetrahy-
drophthalic anhydride (THPA) curing agent and sin-
gle-walled carbon nanotubes (SWCNT) reinforced the
epoxy matrix composites, respectively. Density of the
materials and mean square displacements (MSDs) were
calculatedto estimate the glass transition temperatures
(Tgs) of the materials.
2. Molecular Dynamic Simulation
MD simulations were conducted using the Materials Stu-
dio 5.5 (Accelrys Inc.) software. COMPASS force-field
was used in the simulation, which has been shown to
provide accurate predictions of thermo-mechanical prop-
erties of thermosetting polymers [3,4,10]. The non-bond
interactions with a cutoff distance of 9.5Å, including van
der Waals and electronic static forces, were applied. The
atom approach was used for the dispersion interactions.
The cured epoxy network is composed of DGEBA
resin and THPA curing agent. Chemical structures of the
resin and hardener segments are shown in Figure 1.
During the curing reaction, the acid anhydride groups of
the curing agent molecules reacted with the epoxide
groups of the epoxy resin. Initially, one THPA molecule
reacted with one epoxide group. As the reaction contin-
ued, more cross-links were generated between the epoxy
resin and the curing agent. The cross-linking activity
expanded in all directions and formed a network of mac-
romolecules. Schematic of the curing reactions are
shown in Figure 2.
In this study, the polymer model was dynamically built
by assumptions. Firstly, 8 epoxy segments and 16 hard-
ener segments containing reactive sites with a density
equal to 1.2 g/cm3 were packed into a 3D periodic cell
box using the Amorphous Cell tool. This formulation
was then mixed using the ensembles of the constant
number of particles, constant volume and constant tem-
perature (NVT) MD simulation for 100 ps performed at
298 K after initial molecular minimization (MM) based
Figure 1. Chemical structures of the resin, hardener. (a)
Figure 2. Schematic of the curing reactions.
on COMPASS force-field. Under close proximity, cova-
lent bonds were formed between the nearest reactive
pairs within the reaction cutoff distance of 9.5 Å consid-
ering the removal of ring catenation or spearing. Repeat-
ing these steps to form bonds for several times, a 19.33 Å
× 19.33 Å × 19.33 Å cross-linked polymer network with
a conversion of 80% was finally obtained. For the CNT
composites, a zigzag SWCNT (4,0) with the diameter of
3.13 Å and length of 34.08 Å consisting of 196 atoms is
embedded into the above amorphous DGEBA-THPA
systems with a density equal to 1.0 g/cm3, followed by
the cross-linking activities. The resulting model system
has a cell dimension of 21.52 Å × 21.52 Å × 21.52 Å
with a conversion of 60%. Periodic boundary conditions
are applied in all three directions for both models.
After the initial microstructure was generated, the
minimization of the potential energy of the model was
carried out, where COMPASS force-field was used. Then
simulated annealing was performed by raising the tem-
perature from 500 K to 900 K and cooling down to 500
K with steps of 20 K and an annealing time of 50 ps.
After that, geometric optimization of 10000 steps and
NVT MD simulation of 200ps were performed at a tem-
perature above the Tg, such as 523 K in Forcite modules,
and repeated for several times to relax the polymer
In order to imitate the thermal performance in a kinetic
process, simulation of cooling process was performed.
The system was cooled stepwise from 523 K to 283 K
with the rate of 10 K/200 ps. At each temperature, 10000
steps geometric optimization simulation was performed
to relax the polymer chains, followed by the ensembles
of the constant number of particles, constant pressure and
constant temperature (NPT) MD simulation under a
pressure of 0.1 MPa for 200 ps to obtain the optimized
density. In terms of non-bonding interaction treatments,
atom-based direct cutoff of 9.5 Å and a buffer of 0.5 Å
were used depending on the accuracy and efficiency of
the computation. Velocity Verl et al. gorithm with a time
step of 1fs was used for the integration of the atom mo-
tion equations throughout all simulations. Nose thermo-
stat and Anderson barostat with cell time constant of 1.0
ps have been adopted. Each subsequent simulation was
started from the final configuration obtained at the pre-
ceding temperature. The simulation in each case was
performed with an interval of 1 femtosecond (fs) in each
simulation step.
3. Results and Discussion
Various energies can be calculated from the MD simula-
tions, which are used to analyze the roles of them in glass
transition. The simulated results of total energy, potential
energy and kinetic energy of the system against the tem-
perature are plotted in Figure 3. It can be seen that the
plots of these energy increases almost linearly with in-
creasing temperature in the whole temperature range,
indicating that the total energy, potential energy and ki-
netic energy play no distinctive roles in the glass transi-
tion process of the epoxy resin and its CNT composites.
Densities of the epoxy resin and the composites at
room temperature were calculated to be 1.228 g/cm3 and
1.012 g/cm3, respectively, which are in good agreement
with the appointed values. The evolution of density as a
function of temperature of the DGEBA-THPA/SWCNT
composites is plotted in Figure 4. A steady increase of
the density with decreasing temperature and a clear chan-
ge in the slope of the density curve were observed. The
kink in the density vs temperature slope is defined as the
Figure 3. Energy variations as a function of tem- perature.
(a) DGEBA-THPA polymer; (b) DGEBA-THPA/ SWCNTs
values of Tg, which occurs at approximately 423 K,
where the epoxy resin passes from the glassy state to the
rubbery state.
The cross-reactions in the epoxy resin make significant
differences in structure and properties from other linear
polymers. It is instructive to analyze the motion of these
cross-links in the model systems as a function of tem-
perature. Because of incomplete reaction, segments on
the polymer chains can be classified as cross-linked and
free ones. Generally, the cross-linked segments exhibit
much lower mobility than the free ones due to topologi-
cal constraints. The value of Tg is correlated well with
the polymer rigidity, namely the segmental mobility in
polymer chain. The mean square displacements (MSDs)
of the epoxy resin chains at 30 ps were calculated, which
is plotted in Figure 5. The turning point of MSDs indi-
cated Tg of the DGEBA-THPA polymer, which occurs
around 365 K.
Figure 4. Density of DGEBA-THPA/SWCNT composites
variation as a function of tem- perature.
Figure 5. MSDs of the epoxy resin chainsvariation as a
function of temperature.
From the MD simulations, Tg of the DGEBA-THPA/
SWCNT composites is much higher than the DGEBA-
THPA polymer, which is consistently with the fact.
It is very inspiring to see that the MD simulation
method can be successfully applied to investigate the
thermomechanical properties of the CNT/polymer com-
posites. Once established, this approach can be applied
more widely to a large group of candidate polymers and
nanocomposites, proving a much more cost-effective
way to narrow the fabrication and testing efforts to the
selectedbest performers predicted by the MD simula-
4. Conclusion
In the current study, two models of DGEBA-THPA
cross-linked resin and its CNT composites were investi-
gated by MD simulations. Different characters were cal-
culated for the two models. The calculated results
showed that the Tg of the two systems are 365 K and 423
K, respectively, whereas the value of latter is much
higher than the former, which is consistent with the fact.
It can be expected that the method would be employed in
further molecular simulation of structure and properties
for cross-linked epoxy resin or other cured polymer net-
work and their CNTs composites.
The present work is supported by the Key Projects of
National High-tech R&D Program of China (863 Pro-
gram) under Grant No. 2012AA03A205, Hunan Province
Technology Major Project of China under Grant No.
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