Efficacy Analysis and Kinetics of 3-Component Photopolymerization by Visible-LED/Coumarin and Enhanced by Additives of Iodonium Salt and Amine

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. . .


Introduction
Photopolymerization using light sources from UV (365 nm) to near-infrared (980 nm) have been used in many industrial and medical applications such as dental curing, microlithography, stereolithography, microelectronics, holography [1,2]. Variety of photoresponsive materials such as conjugated polymers have been reported for additive manufacturing (AM) and recently for 3D and 4D bioprinting [3][4][5][6][7][8]. Both spatial and temporal controlled 3D processes were reported using single and multiple wavelength lights [6][7][8]. We have reported the kinetics and efficacy analysis for various strategies for improved conversion, such as co initiators, co additives in both single and multiple components systems [9][10][11].
Photochemical polymerization uses ultraviolet (UV) radiation has been widely known as UV curing. However, the UV light is harmful to human health (carcinogenic) and characterized by particularly low light penetration, which is a challenge for the photopolymerization of thick and filled samples [11]. Organic dyes used as visible light photosensitizers of polymerization have been extensively studied [11,12], in which high extinction coefficients and their long-living excited states, enabling the photosensitizers to react efficiently with various additives in the photocurable resins. For cost effective with long-living excited states, copper complexes have been used as a new polymerization approach enabling the formation of acetylacetonate radicals by redox reaction with a phosphine and to initiate the free radical polymerization (FRP) of acrylates or the free radical promoted cationic polymerization (CP) of epoxides [13][14][15][16]. More recently, coumarin as dual function of photoinitiators in photo-oxidation or photo-reduction in visible light were reported [17][18][19]. These dyes are characterized by very high extinction coefficients with a broad absorption extending over the near UV/visible and high quantum yields [12]. These hotoinitiators can be used in 3D printing experiments with a very high efficiency in the photocomposite synthesis (significant curing of the surface and the bottom) using a LED at 405 nm [12]. Many of the reported experiments were theoretically studied by Lin et al, including dual and three-wavelength systems [9,10,[20][21][22]. This article will present, for the first time, the kinetics and the general conversion features of the 3-component ([A]/ [B] /[N]) system based on proposed mechanism of Rahal et al [19]. The roles of coadditives [B] and [N] include their dual functions of regeneration of initiator [A] and radicals for improved conversion. The key factors influencing the conversion rates and efficacy will be explored by analytic formulas derived from a kinetic model for a 3-component system. Finally, the measured data of Rahal et al [19] will be quantitatively analyzed by our analytic formulas, rather than their qualitative discussions.

Photochemical Kinetics
As shown by Scheme 1, proposed by Rahal et al [19] for a three-component system. The photoinitiator (Coumarin) is excited by a LED light to its excited state which then couples with the Iod salt (or NPG), and dissociates and give reactive species responsible to initiate the FRP (r1-r2). A charge-transfer complex between Iod salt and NPG [Iod-NPG] is able to generate reactive species (r3-r4). Moreover, a hydrogen transfer process from NPG to Coumarins can occur (r5) which generates two types of radicals (Coum-H•) and NPG(-H)•, which can decarboxylate and lead to the radical formation (NPG(-H, -CO2)•), which reacts with Iod salt to produce reactive species (Ar• and NPG(-H, CO2)+) (r6-r7). Ar• and NPG(-H,-CO2)•) (r1-r9) radicals are assumed as the reactive species responsible to the FRP of the (meth)acrylate functions. The measured coumarins consumption is reduced in three-component system [19] can be explained by a regeneration of the photoinitiator, shown in r7, r10, r12 and r13.  [19].
The above described Scheme 1 is further expressed by our kinetic chart using the simplified notations for the concentration of each species: [A] for initiator Coumarin (ground state), which is excited to a triplet state [T}; [B] for additive Iod (or Ar2I + ); [C] for Coumarin* (in r2); [N] for NPG, and radicals R, S and S' are, respectively, for Ar o , Coumarin-H o (in r2) and NPG(-H,-CO2) o (in r7). Regeneration of initiator [A] is shown in r8 and r9. The oxygen inhibition effects are shown in r9; and coupling of Coumarin* and oxygen procing singlet oxygen is shown in r10; the monomer conversions due to T, R and singlet oxyegn are shown in r11 to r13. Above Scheme did not show the radical termination couplings of R and R, R and S, R and S', which will be included in our next kinetic chart, Fig. 1, and our rate equations.
As shown by Figure 1, a 3-components system (A/B/N) defined by the ground state of initiator-A, which is excited to its triplet excited state T, having a quantum yield (q). The triplet state T interacts with additive [B] (Iod) to produce radical R, and oxodized-A (or [C]), which could interact with the additive N (NPG) to regenerate initiator [A]. In addition, T could interact with additive N producing radical S and S', which couple with [B] to produce more radical R and regenerate initiator [A]. Both T and radical (R) could couple with the monomer for FRP. We have also shown the oxygen inhibition effects due to the coupling of R and singlet oxygen ( 1 O2), produced by the coupling of T and ground state oxygen, [ 3 O2]. The radical termination couplings (not shown in Fig.1) of R and R, R and S, R and S' will be included in our kinetic equations. Greater details about the role of oxygen was publishd by Lin et al [25]. We note that T, R and 1 O2 couple with the monomer for FRP conversion. In addition, T could interact with additive N producing radical S and S', which couples with [B] to produce more radical R. The interaction of oxygen and T produces singlet oxygen. The FRP is due to the coupling of T, R and singlet oxygen with the monomer (M). Other couplings are discussed in the text.
The kinetic equations for our previous systems [21][22][23][24][25] are revised for the above 3-component system (A/B/N) as follows, using the short hand notation X for singlet oxygen.
The regeneration of initiator [A] is given by The monomer (M) conversions for FRP is given by [21,23] = − ( + + ′ ) where the light couplig constant b=83.6a'wq, with w being the light wavelength (in cm) and q is the triplet state T quantum yield; a' is the mole absorption coefficient, in (1/mM/%) and I (z, t) is the light intensity, in mW/cm 2 , which in general is time (t) and spatial (or olymer thickness, z) dependent. All the rate constants are defined previously [22]  produced radical (R), and the oxygen induced singlet oxygen X. In most systems, type-II is dominated (for k<<K).
(v) The oxygen inhibition effects (OIE), given by k8[O2] and K'[O2], in Eq. (5) and (6), are important for system in air [22]. We note that g, g' and radical (R) are decreasing fuction of [O2] due to OIE. For laminate system or when T or R is insensitive to oxygen, the OIE may be neglected. In Eq. (6) For comprehensive modeling we will use the so-called quasi-steady state assumption [23]. The life time of the singlet and triplet states (T), and the radicals (R, S' and S), since they either decay or react with the monomer immediately after they are created. We also assume the steady state of singlet oxygen which strongly couples with theradical (R). Thus, one may set dT/dt=dR/dt=dS'/dt = dS/dt= d[C]/dt=dX/dt=0, which give the quasi-steady-state solutions [25]: . We note that g, g' and radicals (R,S, S') are are decreasing fuction of [O2] due to OIE [25]. In above solutions, we have ignored k'RR, k"RS, k"RS' term in Eq. (6) fr the case on unimolecular coupling. We note that for the bimolecular coupling case of k'R 2 , the solution of R is proportinal to the squre-root of, bI[A], a much more complext case which was published by Lin et al [23].
Under the above quasi-steady-state solutions, we obtain the simplified equations as follows. ) The regeneration of initiator [A] in Eq. (13) is reduced to The monomer (M) conversions for FRP is given by [20] = where

3.. Results and discussion
A full numerical simulation is required for the solutions of Eq. (13)- (17), which will be presenetd elasewhere. We will focus on comprehensive analysis for new features and the enhancement effects related to the measured data of Rahal et al [19], based on the analytic formulas.

Analytic results
For analytic formulas and focusing on the enhanced effects of [B] and [N], we will ignore the oxygen effects, i.e., X=0, in the following discussions. Using our previously developed approximated analytic formulas [22] for the light intensity and solving for Eq.
We will consider special cases. where, 0 is a correction factor. We note that GH has astaedy state value of G/D', which is independent to the light intensity (I0), and at high intensity and for large time, the efficacy approaches to one. The CE has a transient state of 1+ G[B]0 (t-1)(1-Gt), a nonlinear increasing function ot time (t). The CE is also proprotional to th linear power of bI0. We note that this feature is based on the case for type-II dominant, and bimolecular termination, the k'R 2 term in Eq. (6), is much weaker than the coupling terms of k"SR and KMR, such that the solution of Eq. (6) leads to that R is proportional to bI[A}. In contrast, for a strong bimolecular termination case, R is proportional to the squrae root of bI[A}, and the steady-state CE, or E" in Eq. (24) is proportional to [A]0 /(bI0) 0.5 , such that higher light intensity has a lower steady-state CE, whereas it has a faster rising time profile. [20][21][22].

General features and Analysis of measured results
As shown by Eqs. (21) to (25) Table 2 of Rahal et al [19] can be easily analyzed based on Eq. (21) to (25) as follows.
(i) Without [A], Iod/NPG alone has very weak FRP, in which its light absorption could also produce of radical for FRP. However, it is much weaker than the [A] initiated FRP. Therefore, our modeling ignores the coupling of excited state of Iod/NPG and the monomer.
(ii) As shown by Table 2  , an opposite behavior with strong photo-reduction process, in which the low rate of FRP can be also due to the strong OIE [25], which also reduces the radical (R). In some 3D systems, this OIE was pre-eliminated by a red-light [22].

Conclusion
This article presents, for the first time, the kinetics and the general conversion features of a 3component ( The monomer conversion efficacy depends on the property of the additives and also the types of monomers. In some monomers, A/NPG is more efficient than A/Iod, but revserse trend occurs in some monomers. However, 2-component systems are always less efficient than that of 3-component systems fro all types on monomers.To conclude, the measured results of Rahal et al [19] are well analyzed and matching the predicted features of our modeling. Analytical formulas for the role of each component concentration, light intnesity and coupling rates on the conversion efficacy are derived. Funding: The Agence Nationale de la Recherche (ANR agency) is acknowledged for its financial support through the NoPerox grant.