Kinetic equations for a modeling system with type-I radical-mediated and type-II oxygen-mediated pathways are derived and numerically solved for the photopolymerization efficacy and curing depth, under the quasi-steady state assumption, and bimolecular termination. We show that photopolymerization efficacy is an increasing function of photosensitizer (PS) concentration (C0) and the light dose at transient state, but it is a decreasing function of the light intensity, scaled by [C0/I0]0.5 at steady state. The curing (or cross-link) depth is an increasing function of C0 and light dose (time × intensity), but it is a decreasing function of the oxygen concentration, viscosity effect, and oxygen external supply rate. Higher intensity results in a faster depletion of PS and oxygen. For optically thick polymers (>100 um), light intensity is an increasing function of time due to PS depletion, which cannot be neglected. With oxygen inhibition effect, the efficacy temporal profile has an induction time defined by the oxygen depletion rate. Efficacy is also an increasing function of the effective rate constant, K = k′/kT0.5, defined by the radical producing rate (k′) and the bimolecular termination rate (kT). In conclusion, the curing depth has a non-linear dependence on the PS concentration, light intensity, and dose and a decreasing function of the oxygen inhibition effect. Efficacy is scaled by [C0/I0]0.5 at steady state. Analytic formulas for the efficacy and curing depth are derived, for the first time, and utilized to analyze the measured pillar height in microfabrication. Finally, various strategies for improved efficacy and curing depth are discussed.

Optimal conditions for maximum efficacy of photoinitiated polymerization are theoretically presented. Analytic formulas are shown for the crosslink time, crosslink depth, and efficacy function. The roles of photoinitiator (PI) concentration, diffusion depth, and light intensity on the polymerization spatial and temporal profiles are presented for both uniform and non-uniform cases. For the type I mechanism, higher intensity may accelerate the polymer action process, but it suffers a lower steady-state efficacy. This may be overcome by a controlled re-supply of PI concentration during the light exposure. In challenging the conventional Beer–Lambert law (BLL), a generalized, time-dependent BLL (a Lin-law) is derived. This study, for the first time, presents analytic formulas for curing depth and crosslink time without the assumption of thin-film or spatial average. Various optimal conditions are developed for maximum efficacy based on a numerically-fit A-factor. Experimental data are analyzed for the role of PI concentration and light intensity on the gelation (crosslink) time and efficacy.

The kinetics and modeling of dual-wavelength (UV and blue) controlled photopolymerization confinement (PC) are presented and measured data are analyzed by analytic formulas and numerical data. The UV-light initiated inhibition effect is strongly monomer-dependent due to different C=C bond rate constants and conversion efficacies. Without the UV-light, for a given blue-light intensity, higher initiator concentration (C10) and rate constant (k’) lead to higher conversion, as also predicted by analytic formulas, in which the total conversion rate (RT) is an increasing function of C1 and k’R, which is proportional to k’[gB1C1]0.5. However, the coupling factor B1 plays a different role that higher B1 leads to higher conversion only in the transient regime; whereas higher B1 leads to lower steady-state conversion. For a fixed initiator concentration C10, higher inhibitor concentration (C20) leads to lower conversion due to a stronger inhibition effect. However, same conversion reduction was found for the same H-factor defined by H0 = [b1C10 − b2C20]. Conversion of blue-only are much higher than that of UV-only and UV-blue combined, in which high C20 results a strong reduction of blue-only-conversion, such that the UV-light serves as the turn-off (trigger) mechanism for the purpose of spatial confirmation within the overlap area of UV and blue light. For example, UV-light controlled methacrylate conversion of a glycidyl dimethacrylate resin is formulated with a tertiary amine co-initiator, and butyl nitrite. The system is subject to a continuous exposure of a blue light, but an on-off exposure of a UV-light. Finally, we developed a theoretical new finding for the criterion of a good material/candidate governed by a double ratio of light-intensity and concentration, [I20C20]/[I10C10].

A novel strategy for red‐light‐controlled oxygen inhibition for improved UV‐light‐initiated monomer conversion is theoretically presented for the first time. The dual‐wavelength kinetic equations are derived, numerically and analytically solved for the oxygen and photoinitiator concentration profiles. The UV‐light‐initiated Type I conversion efficacy is an increasing function of its concentration (C20) and the light dose at transient state, but it is a decreasing function of the light intensity, scaled by [C20/I20]0.5, at steady state. In contrast, the red‐light‐initiated Type II efficacy is mainly dose dependent. Longer red‐light preirradiation time (TP) leads to a shorter UV‐light TID of UV‐light conversion, which is strongly red‐light dose dependent, rather than intensity dependent. The numerical new finding is also predicted by the analytic formulas showing that oxygen and monomer conversion are strongly red‐light dose dependent in a Type II mechanism. Finally, strategies for controlled initiation–inhibition switch based on two mechanisms, (a) oxygen inhibition for improved conversion and (b) radical inhibition for spatial confirmation in 3D printing, are presented. To conclude, UV‐light conversion could be improved by a red‐light preirradiation and more importantly and could be customizely tailored by the controlled induction time. UV‐light photopolymerization conversion could be improved by a red‐light preirradiation and could be customizely tailored by the controlled induction time. The UV‐light‐initiated Type I conversion efficacy is an increasing function of its concentration and the light dose at transient state, but it is a decreasing function of the light intensity at steady state. In contrast, the red‐light‐initiated Type II efficacy is mainly dose dependent. Longer red‐light preirradiation time leads to a shorter UV light. © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020, 58, 683–691

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