Kinetics of primary cyclization reactions in cross-linked polymers: An analytical and numerical approach to heterogeneity in network formation

It is difficult to characterize the kinetics of cyclization reactions durin g free radical photopolymerization of multivinyl monomers because of the va rying pendant double bond reactivities and inhomogeneities in the system. P rimary cyclization, where a pendant double bond reacts intramolecularly wit h the propagating active center that formed it, leads to formation of micro gels in the network. A new analytical and numerical approach is presented t hat solves the differential kinetic equations and can be used to investigat e the factors influencing cyclization versus cross-linking reactions. Data are presented comparing two approaches, one based on numerical integration of the appropriate balances and one based on an analytical solution.