Competing Effects of Cohesive Energy and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

To develop structure–property relationships for cross-linked thermosetting polymers, it is crucial to better understand key factors that control their segmental dynamics and macroscopic properties. Here, we employ a coarse-grained (CG) polymer model to systematically explore the combined effect of varying the cohesive energy (ε) and cross-link density (c) on the segmental relaxation time and mechanical properties for a model cross-linked glass-forming thermoset material. We find that increasing c increases both the glass transition temperature Tg and fragility of glass formation, while the fragility decreases with an increase in ε. These competing effects of ε and c on fragility are practically important since fragility determines the overall temperature width of the glass formation over which the non-Arrhenius temperature dependence is observed. Our simulation results show that the basic mechanical properties (i.e., bulk and shear moduli) of cross-linked thermosets are mainly influenced by ε. More interestingly, the macroscopic mechanical properties are found to be strongly correlated with the Debye–Waller parameter ⟨u2⟩, a measure of material "stiffness" at a molecular level. In particular, the distribution of local molecular stiffness, 1/⟨u2⟩, exhibits a nearly universal Gaussian distribution at a fixed reduced temperature T/Tg. Our work reveals the key and competitive roles of cohesive energy and cross-link density in controlling the segmental dynamics, large scale, and local mechanical properties of cross-linked thermosets, providing an understanding that should be useful in the molecular design of these materials.