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 (R_T) 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].

Kinetics and analytical formulas for radical-mediated thiol–ene photopolymerization were developed in this paper. The conversion efficacy of thiol–ene systems was studied for various propagation to chain transfer kinetic rate-ratio (R_K), and thiol–ene concentration molar-ratio (R_C). Numerical data were analyzed using analytical formulas and compared with the experimental data. We demonstrated that our model for a thiol–acrylate system with homopolymerization effects, and for a thiol–norbornene system with viscosity effects, fit much better with the measured data than a previous model excluding these effects. The general features for the roles of R_K and R_C on the conversion efficacy of thiol (C_T) and ene (C_V) are: (i) for R_K = 1, C_V and C_T have the same temporal profiles, but have a reversed dependence on R_C; (ii) for R_K >> 1, C_T are almost independent of R_C; (iii) for R_K << 1, C_V and C_T have the same profiles and both are decreasing functions of the homopolymerization effects defined by k_CV; (iv) viscosity does not affect the efficacy in the case of R_K >> 1, but reduces the efficacy of C_V for other values of R_K. For a fixed light dose, higher light intensity has a higher transient efficacy but a lower steady-state conversion, resulting from a bimolecular termination. In contrast, in type II unimolecular termination, the conversion is mainly governed by the light dose rather than its intensity. For optically thick polymers, the light intensity increases with time due to photoinitiator depletion, and thus the assumption of constant photoinitiator concentration (as in most previous models) suffers an error of 5% to 20% (underestimated) of the crosslink depth and the efficacy. Scaling law for the overall reaction order, defined by [A]^m[B]ⁿ and governed by the types of ene and the rate ratio is discussed herein. The dual ratio (R_K and R_C) for various binary functional groups (thiol–vinyl, thiol–acrylate, and thiol–norbornene) may be tailored to minimize side effects for maximal monomer conversion or tunable degree of crosslinking.

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, for both uniform and non-uniform cases, are presented. For optimal efficacy, a strategy via controlled PI concentration is proposed, where re-supply of PI in high light intensity may achieve a combined-efficacy similar to low light intensity, but has a much faster procedure. A new criterion of efficacy based on the polymerization (crosslink) [strength] and [depth] is introduced. Experimental data are analyzed for the role of PI concentration and light intensity on the gelation time and efficacy.

The synergistic features of a three-component, photoinitiating system (A/B/C) based on the measured data and proposed mechanism of Liu et al. are analyzed. The co-initiators/additives B and C have dual-functions of : (i) regeneration of photoinitiator A, and (ii) generation of extra radicals for enhanced conversion efficacy (CE). The synergistic effects led to higher CE for both free radical polymerization (FRP) and cationic polymerization (CP). The CE of FRP has 3 terms due to the direct (tyep-I) coupling of the triplet state of A with the monomer (M) and the coupling of the two radicals, R and R', with M. The CE of CP has a transient state proportional to the effective absorption constant (b), the light intensity (I) and initiator concentration (A0), but a steady state is independent of the light intensity (I). For the CE of FRP, the contribution from radical R had two cases: (i) linear dependence on T=bIA0, or (ii) nonlinear square root dependence T0.5. The synergistic effects led to higher conversion of FRP and CP, consistent with the measured results. The theoretically predicted new features include: (i) co-initiator [C] which always enhances both FRP and CP conversions, and (ii) co-initiator [B] which leads to more efficient FRP, but it also reduces CP.