A Kinetic Model for Off-Stoichiometric Crosslinking Reactions of End-Linked Polymer Gels and Networks

The formation of end-linked polymer networks and dilute gels is commonly modeled as idealized chemical reactions resulting in defect-free networks. However, many widely used industrial processes including platinum-catalyzed vinyl-silane crosslinking 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 crosslinking events. Elastic effectiveness of the resulting network is calculated with the nonlinear Miller-Macosko theory (MMT), updated to account for side reactions and side crosslinking. Combined, the updated KGT and MMT provide elasticity estimates which capture the experimental peak in elastic modulus observed at an off-stoichiometric silane:alkene ratio in PDMS gels. This model is useful in systems where the crosslinking 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.