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.

The synergetic features of a three-component photoinitiating systems (A/B/C) based on the measured data and proposed mechanism of Liu et al (Polymers, 2020, 12(6), 1394) are analyzed. The co-initiators/additives B and C have dual functions of : (i) regeneration of photoinitiator A and (ii) generation of extra radicals. The synergic effects lead to higher conversion of free radical polymerization (FRP) and cationic polymerization (CP). The key factors and rate constants influencing the conversion efficacy are explored by analytic formulas. Enhancing strategies for various photopolymerization systems are summarized including one component (or monomer) and one-wavelength, two-component and one, two and three-wavelength, and three-component, one-wavelength system. The synergetic effects for higher monomer conversion can be achieved by co-initiators for extra radicals and multiple wavelengths for reduced oxygen-inhibition. Co-initiator B, however, might also reduces the CP radical produced by initiator C. The conversion rate of FRP is proportional to the square root of the light intensity (I), absorption (b) and the initiator initial concentratios (A0, B0, C0), whereas CP is proportional to the linear power of a parameter defined as P=bIA0C0, a stronger dependence than FRP. The CP conversion is governed by a steady-state value proportional to P, and a rate fucntion defining the depletion rate of [A][C], or the increasing rate of the conversion profile. The measured results of Liu et al (Polymers, 2020, 12(6), 1394) are well analyzed and matching the predicted features of our modeling. The specific systems analyzed are: benzophenone derivatives (A) ethyl 4-(dimethylamino)benzoate (B), and (4-tert-butylphenyl)iodonium hexafluorophosphate (C) under a UV (365 nm) LED irradiation; and monomers of trimethylolpropane triacrylate (TMPTA, for FRP) and (3,4- epoxycyclohexane)methyl 3,4-epoxycyclohexylcarboxylate (EPOX, for CP).

This article presents, for the first time, the kinetics and the general conversion features of free radical polymerization (FRP) in a 3-component system (A/B/N), with [A] being the initiator, and [B] and [N] are additives, based on the proposed mechanism of Rahal et al. Higher FRP can be achieved by additives [B] and [N], via the dual function of (i) regeneration [A], and (ii) generation of extra radicals (R) via the radicals (S' and S) produced by N.The initiator (coumarin) shows a dual photo-oxidation and photo-reduction character for high efficacy. The FRP conversion efficacy (CE) depends not only on the property of the initiator [A], the additives [B] and [N}, but also the types of monomers. For example, when [A]=CoumC, [A]/NPG is more efficient than [A]/Iod, but revserse trend occurs in some monomers. However, 2-component systems (with CE=0% to 80%) are always less efficient than that of 3-component systems (with CE=70% to 86%, in TMPTA). Specific systems with [A]=coumarins, [B]=Iodonium salt, and N=NPG are analyzed. Analytical formulas for the role of each component concentration, light intensity and coupling rates on the conversion efficacy are derived.

This article presents, for the first time, the kinetics and the general conversion features of a 3-initiator system (A/B/N), based on proposed mechanism of Mokbel et al, for both free radical polymerization (FRP) of acrylates and the free radical promoted cationic polymerization (CP) of epoxides using copper complex as the initiator. Higher FRP and CP conversion can be achieved by co-initiators concentration [B] and [N], via the dual function of (i) regeneration [A], and (ii) generation of extra radicals S' and S. The FRP and CP conversion is proportional to, respectively, the nonlinear and linear power of bI[A][B], where b and I are the absorption coefficient and the light intensity, respectively. System in air has lower conversion than in laminate due to the oxygen inhibition effects. For thick samples (with thickness z), there is an optimal concentration [A*] which is inverse proportional (bzI), in contrast with very thin sample, in which the conversion is an increasing function of [A] and [B]. The unique feature of dark polymerization in CP conversion enables the polymerization to continue in living mode, in contrasts with that of the radical-mediated pathway in most conventional FRP. The measured results of Mokbel et al are well analyzed and matching the predicted features of our modeling.

. This article presents, for the first time, the kinetics and the general features of a photopolymerization system (under visible light) G1/ Iodonium/ TEA/gold chloride (or A/B/N/G), having initial concentrations of A0, B0, N0 and G0, based on the proposed mechanism of Tar et al. Analytic formulas are developed to explore the new features including: (i) both FRP efficacy and the production of nanogold (NG) are proportional to the relative concentration ratios of (A0+B0+N0)/G0, which may be optimized for maximum efficacy; (ii) the two competing procedure of NG production and efficacy of free radical photopolymerization (FRP) can be tailored for optimal system with nanogold in the polymer matrix;(ii) the FRP efficacy is contributed by 3 components: the coupling of the excited state of copper complex (T) with the radicals (R and S) produced by the iodonium and the amine; (iii) the production of NG is contributed by 2 components: the coupling of T and radical (S) with gold ion; (iv) NG production has a transient state value which is an increasing function of light intensity and the combined concentration ratio [(A0/G0)+(N0/(K'M0). whereas it has a steady-state independent to the light intensity.