Multiscale Modeling of Epoxies and Epoxy-Based Composites
279
It should be noted that T g is strongly dependent on many factors, including the
degree of cross-linking, curing temperature, length of the monomers, the size of the
simulation system, cooling rate, etc. [83]. Many simulation studies report that T g
increases with increasing degree of conversion, which can be attributed to the high
degree of cross-linking in the epoxy that leads to lower mobility for the molecular
chains, leading to a stable epoxy network [31, 49, 54, 84]. Figure 4b shows the
dependence of T g on the conversion degree for two epoxy systems. As most epoxies
are cured to high conversion degrees, a slight difference in degree of cross-linking
may cause a big variation in the predicted T g .
3.4 Free Volume Distribution
Free volume (FV) holes are defined as the empty volume between polymer
chains, and the size of FV holes is related to the connectivity and mobility of
the surrounding molecules. Positron annihilation lifetime spectroscopy (PALS) is
commonly used to experimentally measure the size distribution of FV holes in a
polymer material [92, 93]. The drawback of PALS experiments is that it measures
averaged values over large volumes and lacks the resolution to characterize local
material structure (e.g., the interphase region). On the other hand, MD and CG-MD
models can capture both the average material property and local distributions.
To validate the molecular structure predicted from CG-MD simulations,
Aramoon et al. developed a computational algorithm to measure FV distribution
using spherical or ellipsoidal shapes fitted to the empty volumes between connected
epoxy molecules [64]. Figure 5 shows the predicted probability distribution
function of FV in DGEBA/DAB at different pressures as predicted from CGMD simulations [94] and those from PALS experiments [95]. These results indicate
Fig. 5 The probability
distribution function (PDF) of
FV holes as computed from
PALS experiments and
predicted from CG-MD
simulations at different
pressuress (P) [94]
279
It should be noted that T g is strongly dependent on many factors, including the
degree of cross-linking, curing temperature, length of the monomers, the size of the
simulation system, cooling rate, etc. [83]. Many simulation studies report that T g
increases with increasing degree of conversion, which can be attributed to the high
degree of cross-linking in the epoxy that leads to lower mobility for the molecular
chains, leading to a stable epoxy network [31, 49, 54, 84]. Figure 4b shows the
dependence of T g on the conversion degree for two epoxy systems. As most epoxies
are cured to high conversion degrees, a slight difference in degree of cross-linking
may cause a big variation in the predicted T g .
3.4 Free Volume Distribution
Free volume (FV) holes are defined as the empty volume between polymer
chains, and the size of FV holes is related to the connectivity and mobility of
the surrounding molecules. Positron annihilation lifetime spectroscopy (PALS) is
commonly used to experimentally measure the size distribution of FV holes in a
polymer material [92, 93]. The drawback of PALS experiments is that it measures
averaged values over large volumes and lacks the resolution to characterize local
material structure (e.g., the interphase region). On the other hand, MD and CG-MD
models can capture both the average material property and local distributions.
To validate the molecular structure predicted from CG-MD simulations,
Aramoon et al. developed a computational algorithm to measure FV distribution
using spherical or ellipsoidal shapes fitted to the empty volumes between connected
epoxy molecules [64]. Figure 5 shows the predicted probability distribution
function of FV in DGEBA/DAB at different pressures as predicted from CGMD simulations [94] and those from PALS experiments [95]. These results indicate
Fig. 5 The probability
distribution function (PDF) of
FV holes as computed from
PALS experiments and
predicted from CG-MD
simulations at different
pressuress (P) [94]