Modeling the Effects of Chain Length on the Termination Kinetics in Multivinyl Photopolymerizations

A model is presented that predicts photopolymerization kinetics over several orders of magnitude change in initiation rate. The model incorporates polymerization features that have long been assumed negligible when examining multivinyl photopolymerizations. The assumption that radical termination is chain‐length‐independent is relaxed by incorporating a chain‐length‐dependent termination (CLDT) parameter based on Random‐walk theory into the kinetic model. Experiments and modeling of multivinyl free‐radical photopolymerizations clearly demonstrate that CLDT is important at low conversions, where a deviation from the classical square‐root relationship between polymerization rate (R_p) and initiation rate (R_i) is observed (R_p ∝ R _i^α, α = ¹/₂, classically). At moderate conversions, when reaction diffusion dominates termination, a transition region is observed from a chain‐length‐dependent to a chain‐length‐independent region. During this transition, long chain – long chain termination is reaction diffusion controlled while the short chain – short chain termination event remains translational and segmental diffusion controlled. The scaling exponent, α, gradually increases throughout this region until achieving the classical value, where once attained, a plateau is observed. Chain‐length effects were also examined by including chain‐transfer (CT) reactions into the kinetic expressions. Upon CT agent addition, a transition region is still observed; however, at low conversion, α adheres more closely to the classical predictions. Most importantly, the model clearly demonstrates a transition from a CLDT region at low conversion to reaction diffusion controlled termination region at high conversion, where chain length is unimportant.