Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures ( Tg). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with Tg, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τα becomes almost a universal function of reduced temperature, ( T − Tg)/ Tg, a phenomenon that underlies the applicability of the “universal” Williams–Landel–Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed ( T − Tg)/ Tg. Evidently, Tg dominates both τα and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

No abstract

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 T g 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 ⟨u 2⟩, a measure of material “stiffness” at a molecular level. In particular, the distribution of local molecular stiffness, 1/⟨u 2⟩, exhibits a nearly universal Gaussian distribution at a fixed reduced temperature T/T g. 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.

No abstract

a Covalent adaptable networks are polymers that can alter the arrangement of network connections by bond exchange reactions where an active unit attaches to an existing bond then kicks off its pre-existing peer to form a new bond. When the polymer is stretched, bond exchange reactions lead to stress relaxation and plastic deformation, or the so-called reforming. In addition, two pieces of polymers can be rejoined together without introducing additional monomers or chemicals on the interface, enabling welding and reprocessing. Although covalent adaptable networks have been researched extensively in the past, knowledge about the macromolecular level network alternations is limited. In this study, molecular dynamics simulations are used to investigate the macromolecular details of bond exchange reactions in a recently reported epoxy system. An algorithm for bond exchange reactions is first developed and applied to study a crosslinking network formed by epoxy resin DGEBA with the crosslinking agent tricarballylic acid. The trace of the active units is tracked to show the migration of these units within the network. Network properties, such as the distance between two neighboring crosslink sites, the chain angle, and the initial modulus, are examined after each iteration of the bond exchange reactions to provide detailed information about how material behaviors and macromolecular structure evolve. Stress relaxation simulations are also conducted. It is found that even though bond exchange reactions change the macroscopic shape of the network, microscopic network characteristic features, such as the distance between two neighboring crosslink sites and the chain angle, relax back to the unstretched isotropic state. Comparison with a recent scaling theory also shows good agreement.