Kinetic Model for Off-Stoichiometric Cross-Linking Reactions of End-Linked Polymer Networks

The formation of end-linked polymer networks is commonly modeled as idealized chemical reactions, resulting in defect-free networks. However, many widely used industrial processes including platinum-catalyzed vinyl-silane cross-linking of poly(dimethylsiloxane) (PDMS) are mechanistically complex and involve a variety of side reactions. Here, a kinetic graph theory (KGT) model was updated to account for off-stoichiometric reactive groups and side reactions by adding two fitting parameters representing the relative rate of competing side reactions and the probability of side cross-linking events. The updated KGT outputs the population of each junction type from which the reaction fates of both starting materials are calculated. The elastic effectiveness of the resulting network is calculated with the nonlinear Miller–Macosko theory (MMT), updated to account for side reactions and side cross-linking. The MMT was validated on off-stoichiometric data and was chosen here for its ability to account for a range of effective junction functionalities. Combined, the updated KGT and MMT provide elasticity estimates that capture the experimental peak in elastic modulus observed at an off-stoichiometric silane/alkene ratio in PDMS networks. Both the Lake Thomas and micronetwork fracture theories were subsequently used to estimate the tearing energy, showing a similar peak at off-stoichiometric ratios in qualitative agreement with experimental data. This model is useful in systems where the cross-linking chemistry yields more complex reaction networks, making it relevant to many classes of polymer network chemistry where classical theories may not adequately capture network behavior.