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X. Wu and J. A. El-Awady
contributes to the stability of the cured structure [27]. Figure 2b shows the epoxy
structure created using the new curing algorithm (right column) has a more uniform
degree of cross-linking than the ones created using the traditional method (left
column).
The degree of cross-linking is a well-controlled parameter in a simulated curing
process. Theoretically this value can be quantitatively compared to experiments.
However, the lack of experimental evaluation of the molecular structure of epoxies
has led to uncertainties in how well a constructed atomistic model represents the
true material structure. Accordingly, the molecular structure produced from curing
simulations is indirectly validated by computing other properties as discussed in the
following subsections.
3.2 Epoxy Density and Volume Shrinkage
Table 2 shows a summary of three common structural properties used to validate the
molecular structures predicted from MD and CG-MD simulations. As an example,
the predicted density of DGEBF systems is commonly in the range of 1.12–
1.21 g/cm 3 , while that for DGEBA systems is in the range of 1.1–1.169 g/cm 3 .
The variation in the predicted density is a result of the different curing agents and
force fields used (see Table 1), as well as the degrees of cross-linking reached (see
Table 2). These predicted values are qualitatively in agreement with experimental
measurements, which are in the range of 1.111–1.142 g/cm 3 for the DGEBA
systems with different curing agents [86]. Generally speaking, the error in the
molecular-based simulation-predicted densities versus the experimental measured
ones for various DGEBA based-epoxies is in the range of 1.0–5.3%.
An exact agreement between experiments and simulation is hard to achieve due
to the following: (1) the force fields used in most simulation are generic polymer
potentials without specific tailoring to the simulated system and, thus, may introduce
systematic errors in describing the atomic interactions in the material; (2) the
simulated volume is small, and the curing process in the simulations is significantly
simplified as compared to experiments; and (3) the epoxy density is a function of
the degree of cross-linking, and the difference between the conversion degree of a
simulation system (72–95% conversion) and real materials (usually considered to
be close to 100% conversion) can also contribute to the differences between the
predicted and measured densities.
In addition to the static density of the cured epoxy at room temperature, the
dynamic change of density, i.e., volume shrinkage, during the curing process is
also commonly used to validate the accuracy of the predicted molecular structure.
Figure 3a shows a linear relationship between volume and the degree of conversion
from a CG-MD simulation of DGEBA/DAB epoxy [27]. The predicted volume
shrinkage from some MD and CG-MD simulations is also summarized in Table 2. A
volume shrinkage of 5–12% is typically predicted for different epoxy systems [39].
It should be noted that the slope of the volume shrinkage is a function of the
curing temperature [83]. Additionally, the volume shrinkage often causes internal
X. Wu and J. A. El-Awady
contributes to the stability of the cured structure [27]. Figure 2b shows the epoxy
structure created using the new curing algorithm (right column) has a more uniform
degree of cross-linking than the ones created using the traditional method (left
column).
The degree of cross-linking is a well-controlled parameter in a simulated curing
process. Theoretically this value can be quantitatively compared to experiments.
However, the lack of experimental evaluation of the molecular structure of epoxies
has led to uncertainties in how well a constructed atomistic model represents the
true material structure. Accordingly, the molecular structure produced from curing
simulations is indirectly validated by computing other properties as discussed in the
following subsections.
3.2 Epoxy Density and Volume Shrinkage
Table 2 shows a summary of three common structural properties used to validate the
molecular structures predicted from MD and CG-MD simulations. As an example,
the predicted density of DGEBF systems is commonly in the range of 1.12–
1.21 g/cm 3 , while that for DGEBA systems is in the range of 1.1–1.169 g/cm 3 .
The variation in the predicted density is a result of the different curing agents and
force fields used (see Table 1), as well as the degrees of cross-linking reached (see
Table 2). These predicted values are qualitatively in agreement with experimental
measurements, which are in the range of 1.111–1.142 g/cm 3 for the DGEBA
systems with different curing agents [86]. Generally speaking, the error in the
molecular-based simulation-predicted densities versus the experimental measured
ones for various DGEBA based-epoxies is in the range of 1.0–5.3%.
An exact agreement between experiments and simulation is hard to achieve due
to the following: (1) the force fields used in most simulation are generic polymer
potentials without specific tailoring to the simulated system and, thus, may introduce
systematic errors in describing the atomic interactions in the material; (2) the
simulated volume is small, and the curing process in the simulations is significantly
simplified as compared to experiments; and (3) the epoxy density is a function of
the degree of cross-linking, and the difference between the conversion degree of a
simulation system (72–95% conversion) and real materials (usually considered to
be close to 100% conversion) can also contribute to the differences between the
predicted and measured densities.
In addition to the static density of the cured epoxy at room temperature, the
dynamic change of density, i.e., volume shrinkage, during the curing process is
also commonly used to validate the accuracy of the predicted molecular structure.
Figure 3a shows a linear relationship between volume and the degree of conversion
from a CG-MD simulation of DGEBA/DAB epoxy [27]. The predicted volume
shrinkage from some MD and CG-MD simulations is also summarized in Table 2. A
volume shrinkage of 5–12% is typically predicted for different epoxy systems [39].
It should be noted that the slope of the volume shrinkage is a function of the
curing temperature [83]. Additionally, the volume shrinkage often causes internal