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A Martini 3 coarse-grain model for the simulation of
the photopolymerizable organic phase in dental
composites
Alexander Hochwallner *and J¨
urgen Stampfl
Light-hardening dental composites can be used in a large number of applications in restorative dentistry.
They are based on photopolymerizable resins, which are highly relevant also in other industries like 3D
printing. Much effort is therefore being put into developing and optimizing photopolymers. Currently
used photopolymers still have limitations regarding mechanical properties, shrinkage and leaching of
uncured monomers. These issues are strongly linked to the network structure of the polymer and are
usually addressed using trial and error methods. Therefore, it is of interest to have a model for the
network structure of such materials and to have a tool to facilitate scientific progress and the
development of high-performance photopolymers. This work presents a coarse grain model of Bis-
GMA/TEGDMA formulations and their corresponding networks, following the Martini 3 guidelines and
using a simulated polymerization algorithm. The model proved to reproduce the densities and
volumetric shrinkage values found in the literature well. Furthermore, it was possible to estimate the final
double bond conversion of the polymer material. Martini's building block-like design makes it easy to
extend the model to other monomers in the future.
Introduction
Light-hardening composites as restorative materials in
dentistry are very popular. They are used to replace amalgam as
the default choice for dentists, and patients.
1
Dental composites
consist of an organic matrix, which solidies upon photo-
chemical initiation, and inorganic llers.
2
The organic phase
most commonly contains Bis-GMA diluted by TEGDMA.
3
Both
are bifunctional methacrylate substances. The molecular
structures are shown in Scheme 1.
For a composite to be used in restorative dentistry, it must
full several challenging requirements. The mechanical prop-
erties but also chemical stability are of high importance. Addi-
tionally, polymerization shrinkage poses a limitation to the
applicability of light-cured polymer networks.
4,5
In order to establish safe and reliable curing schemes for the
application of dental compounds, the properties of the organic
phase need to be investigated thoroughly regarding the
composition of resins and the properties in relation to the
polymerization reaction.
Photopolymer resins are not only being used in dental
applications. They are also used extensively in additive
manufacturing, which has the potential to become a key
technology in the future, provided the material properties
meet the requirements.
6
Much effort is therefore being put
into synthesizing new 3D printing materials for a variety of
applications. Polymerization shrinkage is also an issue in
additive manufacturing as it can lead to warpage and residual
stresses.
7
Both of which compromise the usability of 3D
printed parts.
Developing and optimizing photopolymer resins is a time-
consuming task, which includes mixing of the components,
photochemical curing, testing and characterization. In order to
optimize a resin composition, the outlined sequence of steps
has to be repeated with different ratios of the ingredients and
different curing schemes. This leads to a high number of
samples to be analyzed. Hence, it is of interest to establish
a method that can screen a large part of the compound space
automatically or at least semi-automatically.
Scheme 1
Institute of Materials Science and Technology, TU Wien, Getreidemarkt 9, 1060
Vienna, Austria. E-mail: alexander.hochwallner@tuwien.ac.at
Cite this: RSC Adv., 2022, 12,12053
Received 3rd February 2022
Accepted 14th April 2022
DOI: 10.1039/d2ra00732k
rsc.li/rsc-advances
© 2022 The Author(s). Published by the Royal Society of Chemistry RSC Adv., 2022, 12,12053–12059 | 12053
RSC Advances
PAPER
Another limitation to the purely experimental approach is
that no method is available to get direct information on the
network structure. It is evident that the constitution of the cured
polymer network is integral to the properties of the nal
material. Therefore, establishing structure–property relations is
of high relevance. Additional information on the network
structure may make it easier to relate material properties to the
molecular network structure obtained with different curing
conditions, giving way to optimizing dental composites and 3D
printing resins. This work aims to explore the possible usage of
molecular simulations for the investigation of photopolymer
resins. The technologically highly relevant mixture of Bis-GMA
with TEGDMA was chosen as a test system. The transferability
of the modeling approach to molecules relevant in additive
manufacturing is a key motivation for this work.
Molecular dynamics simulation is a method to investigate
a material on the molecular level with possibilities to automate
the tasks.
8
To get accurate results from molecular dynamics
simulations, the force eld must be adequate, and system sizes
and time scales must be large enough.
9
To satisfy these condi-
tions, coarse grain force elds for molecular systems are under
constant development. A coarse grain model maps groups of
individual atoms to one coarse grain bead. The underlying
chemical group then denes the inter-particle interactions as
effective interactions.
10
The reduction of the degrees of freedom
by grouping atoms to beads leads to computationally less
expensive simulations. This enables the simulations of larger
systems over a longer period of time compared to all-atom
simulations.
One widely used coarse grain potential that provides rec-
ommended mapping schemes and interparticle potentials is
Martini.
11
The strength of the Martini force eld is, on the one
hand, its easy applicability, and on the other hand, its veried
accuracy in numerous chemical problems.
12
The Martini beads
are designed to be used as building blocks and can be applied to
a variety of different molecules.
12,13
This building block
approach makes it perfectly suitable to efficiently explore the
space of photopolymer materials.
Compared to previous Martini models, Martini 3 offers more
bead types, and the mapping scheme was changed from centre
of mass mapping to centre of geometry mapping. This change
leads to better reproduction of packing densities.
14
This work presents a molecular dynamics model following
the Martini 3 mapping scheme to simulate the polymer network
of the organic phase in dental composites. Next to proper
representations of the monomers, this requires a close to reality
network structure. To achieve this, a simulated polymerization
algorithm called Polymatic
15
is applied. It is used to establish
chemical bonds between beads that represent the reactive
groups of the monomers. This is done by employing a cut-off
criterion, which means that a bond is formed if a bead
labelled as active and a bead labelled as reactive are within
a certain distance to each other. The active label is then passed
on to the reaction partner to allow for chain-growth
polymerization.
The model is veried by comparing monomer densities and
curing shrinkage to values reported in literature. A comparison
to experimental double bond conversions is also presented to
give an outlook on the predictive value of a reactive model to
study photopolymer resins. The present model should serve as
a basis for future extensions with arbitrary monomers of
interest.
Computational details
For all-atom simulations, GROMACS
16
was used. The run
parameters were obtained from the Martini web page
17
and are
in accordance with ref. 13. Only the constraints setting was
changed from all-bonds to h-bonds. All-atom OPLS force eld
les were generated using LigParGen
18–20
following ref. 17. The
simulation box was prepared to contain a single molecule of
interest, diluted in 500 molecules of TEGDMA. Energy mini-
mization, equilibration, and production run were done as
described in ref. 17. The mapping les necessary to map the
trajectories from the all-atom representation to the coarse-grain
representation were generated using CGbuilder.
17,21
The coarse
grain runs needed to obtain the coarse grain distributions were
also done with GROMACS
16
and run les taken from ref. 17. The
time step was set to 20 fs. The remaining parameters were used
as provided. All distributions were evaluated using the les
provided in ref. 17.
The simulated polymerization was done using Polymatic
15
which sequentially checks the dened bonding criterion,
updates the topology if a bond was formed, and calls LAMMPS
22
for energy minimization and molecular dynamics run. The
simulation box for the polymerization simulation was prepared
with the packing algorithm that is delivered with Polymatic.
15
First, the active monomers that acted as initiators were
randomly added to the box. Then Bis-GMA molecules were
added. The remaining TEGDMA molecules were added last.
Then energy minimization was done, and the system was
equilibrated at 298 K and hydrostatic pressure of 1 bar for
80 000 timesteps with 20 fs. Polymatic
15
was set to call
LAMMPS
22
for energy minimization, and molecular dynamics
run for 40 000 timesteps aer ten bonds were successfully
formed. A 20 000 timesteps run is performed if no bond was
formed, and the bond formation is attempted again. The cut-off
for bond formation was set to 5.5 ˚
A. The simulation was
terminated if no bond was formed aer 40 attempts. During all
runs, a temperature of 298 K and a pressure of 1 bar were
maintained. The Shake algorithm was used because LAMMPS
does not have the Lincs algorithm implemented. For that, one
angle and two bonds are constrained in every aromatic ring in
the system. The number of molecules in each formulation was
(0;559), (200;447), (300;391), (400;335), (500;279), (600;223),
(700;168), (800;112), (1000;0). The number before the semicolon
represents TEGDMA. Temperature sweeps were performed over
one million timesteps from 150 K to 500 K.
Coarse graining
Bead assignment
The mapping of the atoms into coarse grain beads was done as
indicated in Fig. 1. Care was taken to have two, three, or four
12054 |RSC Adv., 2022, 12,12053–12059 © 2022 The Author(s). Published by the Royal Society of Chemistry
RSC Advances Paper
heavy atoms grouped into tiny, small, and regular beads,
respectively. The bead type of bead number 4 was chosen to be
TN2a in accordance with methoxybenzene as proposed in ref.
23. The remaining bead types were selected to be in accordance
with the default choice of bead types as presented in ref. 14 and
24. The bead choices are summarized in Table 1.
Bonded interactions
The coefficients for the bonded interactions were set to best
match the distributions of the all-atom simulation. The values
for the harmonic bond coefficients are given in Table 2. The
harmonic bond potential has the following form:
V¼1
2kðrr0Þ2
where kis the force constant, ris the distance between bonded
beads and r
0
is the equilibrium distance. Note that the bonds
between the beads forming the aromatic structure are modelled
using constraints as the bond length distribution is narrow.
23
Two different bond lengths were used between type 5 beads. A
longer bond length was used between type 5 beads bonded to
bead type 4. Table 3 shows the coefficients for the harmonic
angles. To reproduce the shape of the all-atom simulation,
a relatively stiffangle was necessary in Bis-GMA for the angle
with a type 6 bead as the central bead. The harmonic angle
potential looks as follows:
V¼1
2kðqq0Þ2
where qis the three-body angle between bonded beads and q
0
is
the equilibrium three-body angle.
The values for the dihedral coefficients used are presented in
Table 4. Special care was taken to reproduce the angular
arrangement of the aromatic rings with respect to each other
(see Fig. 2). The all-atom simulation showed that the distribu-
tion of the dihedrals that describe the aromatic ring's rotation
are bimodal and not independent of each other. One of the
rings in a Bis-GMA molecule resides in one of two possible
Fig. 1 Mapping scheme. Choices for Martini 3 bead types are given in
Table 1.
Table 1 Choices of standard Martini 3 bead types for mapping Bis-
GMA and TEGDMA
Bead number Martini 3 bead type
1 SC4
2 N4a
3 TP1
4 TN2a
5 TC5
6 SC2
7 SN3a
Table 2 Harmonic bond coefficients
Bead–bead Distance (nm)
Force constant
(kJ mol
1
nm
2
)
1–2 0.355 35 000
2–3 0.23 5000
3–4 0.24 28 000
4–5 0.3 15 000
5–5*
constrained
0.229
5–5*
constrained
0.197
5–6 0.271 35 000
2–7 0.345 6000
7–7 0.37 9000 Fig. 2 Dihedral rotations of the aromatic rings.
Table 3 Harmonic angle coefficients
Bead–bead–bead Angle (deg)
Force constant
(kJ mol
1
rad
2
)
1–2–3 108 110
2–3–4 76 120
3–4–5 130 40
4–5–5 120 80
5–5–6 140 130
5–6–5 70 700
1–2–7 115 100
2–7–7 124 100
Table 4 Dihedral coefficients
Angle (deg)
Energy
(kJ mol
1
) Multiplicity
1–2–3–4 0 35 1
5–5–7–8 313 8.46 2
1–2–7–70 2 3
2–7–7–20 2 3
© 2022 The Author(s). Published by the Royal Society of Chemistry RSC Adv., 2022, 12,12053–12059 | 12055
Paper RSC Advances
angular arrangements, while the other one is present in both
arrangements with equal probability. This behavior could be
reproduced in the coarse grain representation using two dihe-
dral angles per aromatic ring and carefully adjusting the force
constant. A too high force constant would entrap leand right
aromatic dihedrals into one of the possible congurations. A
force constant that is too low would result in equal probability
of the congurations. Fig. 3 shows the dihedral distributions of
the central dihedrals in a Bis-GMA molecule with equal proba-
bility of both congurations. Fig. 4 shows the dihedrals at the
second aromatic ring. Here one can see that only one congu-
ration is occupied. In the case of the all-atom simulation, the
distributions are located around a single angular value. In
comparison, the coarse grain simulation also shows some
probability to be present in the other conguration. However,
the maximum is clearly located around a single angular value
which is a good approximation of the all-atom simulation.
In order to keep the aromatic rings planar, improper dihe-
drals were used. The values for the dihedral coefficients are
given in Table 5. The following functional form was used for the
dihedral potential and improper potential:
V¼k(1 + cos(nff
0
))
where k, in this case, is the energy constant, fis the dihedral or
improper angle and nis the multiplicity.
Simulated polymerization
In order to obtain a realistic network structure of the polymer-
ized material, a simulated polymerization approach was
chosen. To do this, Polymatic
15
was used. This code uses
a simple cut-offcriterion to decide whether or not a bond will be
established between two beads. All beads in a simulation rep-
resenting a reactive group are labelled as such. The beads that
currently bear the radical character are labelled as active. If two
beads labelled as active and reactive are within the cut-off
distance to each other, a bond is established between them.
The active label is then passed on to the reaction partner for the
chain polymerization to proceed. Aer a successful bond
formation, the backbone potential was updated. To evaluate the
additional interactions necessary for the polymer, a TEGDMA 4-
mer was parametrized using the same method as described
above. For the sake of numerical stability, no backbone dihe-
drals were set. The backbone angle was set to 350 kJ mol
1
rad
2
at an equilibrium angle of 125 deg. The backbone-
sidechain angle was set to 50 kJ mol
1
rad
2
at an equilib-
rium angle of 80 deg, and the backbone bond was set to
35 000 kJ mol
1
nm
2
and bond length of 0.31 nm.
Results and discussion
Simulated density
The simulated densities for the respective compounds are pre-
sented in Fig. 5. The values for the mixtures with little Bis-GMA
Fig. 3 Dihedral angles in Bis-GMA, which show two peaks in the
distribution.
Fig. 4 Dihedral angles in Bis-GMA, which show one peak in the
distribution.
Table 5 Improper dihedral coefficients
Angle (deg)
Energy (kJ
mol
1
) Multiplicity
4–5–5–5 0 65 1
5–5–5–6 180 100 1
Fig. 5 Densities as measured by Dewaele et al.
25
compared to the
presented model over the Bis-GMA content.
12056 |RSC Adv., 2022, 12,12053–12059 © 2022 The Author(s). Published by the Royal Society of Chemistry
RSC Advances Paper
content are in good agreement with the values reported by
Dewaele et al.
25
. With higher Bis-GMA content, the deviation
increases. A possible explanation for this is that Bis-GMA was
parametrized with respect to a system of a single Bis-GMA
molecule in a box of TEGDMA as a solvent. As a result, the
Bis-GMA –Bis-GMA interactions are not accurately captured,
whereas Bis-GMA –TEGDMA and TEGDMA –TEGDMA inter-
actions are properly modelled. Another possible source of
deviation is the choice of MARTINI 3 bead types. Denition of
custom bead types backed by free energy calculations could
potentially improve the overall model.
26
For the sake of simple
addition of other molecules later on, only standard beads were
used in this work. Note that for calculating the model densities,
the actual molecular weights of Bis-GMA and TEGDMA were
used, not the standard MARTINI masses. For all simulation
runs, standard MARTINI masses were used.
Shrinkage of simulated material
The shrinkage was determined as the volumetric decrease of the
simulation box aer the degree of conversion has reached the
values reported by Dewaele et al.
25
The values are presented in
Fig. 6 and are in excellent agreement with the experimental
values. The model is within the reported standard deviation
except for the compound with 20 wt% Bis-GMA and 50 wt% Bis-
GMA content. The deviation in densities of the high Bis-GMA
compounds does not seem to inuence the precision of the
shrinkage values negatively.
Double bond conversion
The simulated polymerization method offers the possibility of
learning about the investigated material's reaction kinetics
prior to material synthesis. This can be a valuable information
in resin development because the degree of polymerization
greatly inuences the material properties and possibly limits
the applicability of a photopolymer. It was investigated if the
presented simulated polymerization procedure allows for an
estimation of the nal double bond conversion of various Bis-
GMA –TEGDMA compositions. The results of the simulated
polymerization using 20 active sites are shown in Fig. 7,
together with the experimental values reported by Dewaele
et al.
25
It can be seen that the simulation yields too high values
for the case of 20 active propagation sites. Only at a Bis-GMA
content of 70 wt% is the agreement reasonable. The agree-
ment for pure Bis-GMA is not good. Generally, the simulated
double bond conversion values are expected to inherit more
uncertainties, coming from the fact that the condition for
polymerization termination was chosen more or less arbitrarily.
However, the trend of the values from the experiment is re-
ected in the simulation, showing that the model can reason-
ably accurately simulate the mobility of the reaction partners
during curing of the resin.
This series of simulations were repeated using only ten active
sites. Fewer active sites yield a lower probability of nding
a reaction partner, especially when the mobility is limited by the
onset of gelation in a later stage of the curing process. The
Fig. 6 Polymerization shrinkage as measured by Dewaele et al.
25
compared to the simulated values over the Bis-GMA content.
Fig. 7 Double bond conversion as measured by Dewaele et al.
25
compared to the double bond conversion of the model with 20 active
sites after the termination criterion was reached over the Bis-GMA
content.
Fig. 8 Double bond conversion as measured by Dewaele et al.
25
compared to the double bond conversion of the model with ten active
sites after the termination criterion was reached over the Bis-GMA
content.
© 2022 The Author(s). Published by the Royal Society of Chemistry RSC Adv., 2022, 12,12053–12059 | 12057
Paper RSC Advances
results are presented in Fig. 8. It can be seen that the double bond
conversion is generally lower than in the case of 20 active sites
and is in excellent agreement with the experimental values. Only
for 60 wt% and 70 wt% Bis-GMA content, the values are too high.
Note that the presented method does not account for any
termination reactions that might lower the degree of polymer-
ization. This model only takes propagation into account.
Termination only happens when the mobility is reduced so
much that no reaction occurs in the specied amount of time.
From the excellent agreement of the simulation with ten active
sites, it can be concluded that this is the number of ‘effective’
active sites in the system. To relate the ‘effective’number of
sites to the concentration of initiator in the real system,
a precise knowledge of the kinetics of the termination reactions
would be necessary.
To better judge the mobility change induced by the cross-
linking, temperature sweeps were performed on the 50 wt% Bis-
GMA resin and its crosslinked version to observe changes in the
density slopes. This is a common method to estimate the glass
transition temperature
27
and was also previously performed
using the Martini force eld.
28
The results are shown in Fig. 9.
For estimating the glass transition temperature, the data was
piecewise tted using linear functions. The temperature at the
intersection is 310 K for the polymer and 232 K for the resin.
This indicates that during the polymerization simulation the
resin transitions to a glassy polymer as the simulation
temperature is below the estimated glass transition for the
polymerized material.
Conclusions
The goal of this work was to explore the use of the Martini
coarse grain model for simulating photopolymerizable resins,
which are used in multiple different industries. One major eld
of application is restorative dentistry. Thus, Bis-GMA –
TEGDMA mixtures were chosen as a logical starting point. Both
molecules were parametrized as outlined on the Martini web
page.
17
The bonded interactions were parametrized to t the
distributions of the all-atom simulations best. In Bis-GMA, the
asymmetric dihedral angle conguration observed in the all-
atom simulation was also reproduced in the coarse grain
model. This was achieved while keeping the symmetry of all
bonded interaction parameters.
Atom to bead mapping was done as recommended by the
Martini authors.
14,23,24
The obtained model reproduces resin
densities reported in literature well. The use of standard
Martini building blocks makes it easy to add additional mole-
cules of interest later on and expand the set of possible resin
formulations in the future.
Critical for the use of a photopolymer is the polymerization
shrinkage and double bond conversion of the polymerized
material. This is the case in restorative dentistry as well as in
additive manufacturing. Our simulations show that the pre-
sented model can successfully predict polymerization shrinkage
of various molecular mixtures. This information is valuable for
the development of dental composites to assess the risk of
debonding of lling and tooth
4,5
or for 3D printing materials to
avoid warpage or shrinkage stresses in additively manufactured
parts.
7
The use of a simulated polymerization also allows for an
estimation of double bond conversions for different resin
mixtures and different initiator concentrations. The presented
method well reproduces double bond conversions for Bis-GMA
–TEGDMA mixtures reported by Dewaele et al.
25
Author contributions
Alexander Hochwallner: conceptualization; methodology; so-
ware; formal analysis; investigation; writing –original dra;
writing –review and editing; visualization. J¨
urgen Stamp:
conceptualization; writing –review and editing; supervision.
Conflicts of interest
There are no conicts to declare.
Acknowledgements
Funding by the Christian Doppler Research Association within
the framework of a Christian Doppler Laboratory for “Advanced
Polymers for Biomaterials and 3D Printing”and the nancial
support by the Austrian Federal Ministry for Digital and
Economic Affairs and the National foundation for Research,
Technology and Development are gratefully acknowledged.
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