Non-steady scaling model for the kinetics of the photo-induced free radical polymerization of crosslinking networks

Recently, a semi-empirical scaling model was introduced to account for the free-radical polymerization kinetics of acrylated urethane precursors in the solid-state. By describing the radical initiation process in more detail, the kinetic model is extended herein towards general free-radical crosslinking irrespective of the initial physical state of the multifunctional precursors. Effects referred to as radical trapping and caging in the literature are clearly specified and a closed-form expression with a limited number of adjustable parameters is obtained which can be compared to experimental kinetics. In particular, the relation between polymerization rate and functional conversion can be reduced to expressions with three and four parameters in the limits of "solid-state" and "steady-state" kinetics, respectively. In the case of photo-induced free-radical polymerization and within the slow decomposition regime of the initiator, the single parameter with an explicit dependence on the incident light intensity is predicted to behave proportionally. The model is validated by comparing the relevant expressions to original calorimetric data for the free-radical photopolymerization kinetics of different acrylate urethane precursors at two temperatures, providing illustrations for solid-to-solid and liquid-to-rubber transformations. Careful monitoring of the effect of light intensity corroborates the expected scaling and additionally offers reliable estimates for the kinetic coefficients of propagation and termination. A unified model expressed in closed-form is elaborated for the kinetics of free-radical polymerization and successfully compared to experimental data.