"Enhancing Radical-Mediated Photopylomerization Efficacy and Crosslink Depth: Kinetic Modeling of a Two-Monomer System"

The kinetics and rate equations are derived to analyze the enhanced cross-linking via a two-monomer system, in which the photoinitiator (PI) triplet excited state interacts with monomers, [A] and [B], to form reactive intermediates radicals, which could interact with oxygen, [A],[B], and bimolecular termination. Quasi-steady-state conditions are employed to solve for radicals which are used to find the temporal prpfiles of the monomer efficacy and cosslink depth, as a function of light intensity, exposure time, and concentrations of PI, [A] and [B]. Higher light intensity and radical coupling rate constant lead to faster depletion of PI and oxygen concentration; and faster transient rising efficacy, but a lower steadystate efficacy. Conversion efficacy is an increasing function of the ratio [B]/[A]. In contrast, efficacy is a decreasing function of the reaction rate ratio of oxygen and triplet state, resulted by the stronger oxygen inhibition. Efficacy may be improved by additive enhancer-monomer or extended lifetime of photosensitizer triplet-state or oxygen singlet, in consistent with the measured clinical data. Oxygen inhibition effect may be reduced by the presence of D 2 O, which extends the lifetime of singlet oxygen. Our analytic formulas provide useful guidance for the scaling laws for further clinical studies.