Multiscale Modeling of Epoxies and Epoxy-Based Composites
271
2.2 Coarse-Grained Molecular Dynamics Methods
One of the most commonly used length/time scale bridging methods for epoxy
simulations is coarse-grained molecular dynamics simulations (CG-MD). Generally, there are two steps in developing a CG-MD model for epoxies. The first
step is to map groups of atoms into coarser particles, commonly known as superatoms, and the second step is to define the interactions between these coarse
particles [62]. It should be noted that the individual atoms grouped into superatoms typically have much less significant motion with respect to each other as
compared to the whole molecule. In addition, the interactions between super-atoms
are modeled by spring-like bonds, as well as angular and torsional potentials
that properly average the high-frequency internal degrees of freedom of the
molecules.
The CG-MD simulations are roughly two orders of magnitude faster than allatom MD simulations [63]. Thus, CG-MD simulations can model time scales of
up to microseconds depending on the degree of coarse-graining implemented [62].
Additionally, a CG-MD model can include thousands of prepolymers and curing
agents.
The highest level of coarsening reduces a single polymer chain into one “CG”
bead. However, this is not popular for epoxy modeling due to the loss of major
details of the epoxy structures (e.g., the lengths of monomers), which can strongly
influence the epoxy response. The lowest level of coarsening usually involves
grouping hydrogen with other atoms to create united-atom force fields. One such
low-level CG method that has been used in literature to simulate epoxy behavior is
the OPLS united-atom force field method [49, 55]. In this method, CH 3 , CH 2 , CH,
and alkyl groups were grouped into single united atoms [49].
In mid-level epoxy CG methods, a few non-hydrogen atoms are also grouped
into a single super-atom. An example of coarsening a DGEBA monomer based
on its full atomic structure is shown in Fig. 1. This mid-level CG model was used
by Aramoon et al. to study the curing structure evolution and thermal properties
of a DGEBA epoxy [27, 64]. Other examples for the utilization of mid-level CG
models include creating high degree of cross-linked epoxy systems using a dynamic
curing process with very long bonds [65]; studying the failure mechanism of general
thermoset and thermoplastic materials [30]; coarse-graining EPN-3mer, EPN-4mer,
and BPA molecules and predicting various thermomechanical properties including
their tensile failure [66, 67]; studying the cross-linking process of an epoxy under
Couette and Poiseuille flow conditions [68]; studying the interfacial failure and
microstructural evolution at interphase in epoxy/Cu [69] and epoxy/rigid walls
[62, 70] systems; as well as studying the glass transition temperature [52, 64].
271
2.2 Coarse-Grained Molecular Dynamics Methods
One of the most commonly used length/time scale bridging methods for epoxy
simulations is coarse-grained molecular dynamics simulations (CG-MD). Generally, there are two steps in developing a CG-MD model for epoxies. The first
step is to map groups of atoms into coarser particles, commonly known as superatoms, and the second step is to define the interactions between these coarse
particles [62]. It should be noted that the individual atoms grouped into superatoms typically have much less significant motion with respect to each other as
compared to the whole molecule. In addition, the interactions between super-atoms
are modeled by spring-like bonds, as well as angular and torsional potentials
that properly average the high-frequency internal degrees of freedom of the
molecules.
The CG-MD simulations are roughly two orders of magnitude faster than allatom MD simulations [63]. Thus, CG-MD simulations can model time scales of
up to microseconds depending on the degree of coarse-graining implemented [62].
Additionally, a CG-MD model can include thousands of prepolymers and curing
agents.
The highest level of coarsening reduces a single polymer chain into one “CG”
bead. However, this is not popular for epoxy modeling due to the loss of major
details of the epoxy structures (e.g., the lengths of monomers), which can strongly
influence the epoxy response. The lowest level of coarsening usually involves
grouping hydrogen with other atoms to create united-atom force fields. One such
low-level CG method that has been used in literature to simulate epoxy behavior is
the OPLS united-atom force field method [49, 55]. In this method, CH 3 , CH 2 , CH,
and alkyl groups were grouped into single united atoms [49].
In mid-level epoxy CG methods, a few non-hydrogen atoms are also grouped
into a single super-atom. An example of coarsening a DGEBA monomer based
on its full atomic structure is shown in Fig. 1. This mid-level CG model was used
by Aramoon et al. to study the curing structure evolution and thermal properties
of a DGEBA epoxy [27, 64]. Other examples for the utilization of mid-level CG
models include creating high degree of cross-linked epoxy systems using a dynamic
curing process with very long bonds [65]; studying the failure mechanism of general
thermoset and thermoplastic materials [30]; coarse-graining EPN-3mer, EPN-4mer,
and BPA molecules and predicting various thermomechanical properties including
their tensile failure [66, 67]; studying the cross-linking process of an epoxy under
Couette and Poiseuille flow conditions [68]; studying the interfacial failure and
microstructural evolution at interphase in epoxy/Cu [69] and epoxy/rigid walls
[62, 70] systems; as well as studying the glass transition temperature [52, 64].