Dual-Function Enhancer for Near-Infrared Photopolymerization: Kinetic Modeling for Improved Efficacy by Suppressed Oxygen Inhibition

There are many strategies for improved conversion efficacy such as the reduction of oxygen inhibition effects (OIH). Three-component system using the phosphine to reduce the OIH effects during the free radical polymerization of (meth)acrylate monomers has been reported. Addition, near-infrared (NIR) photopolymerization offers advantages of safer, less light diffusion and scattering, and deeper penetration into the materials. This study presents the detailed kinetics, and modeling the conversion efficacy associated with the experimental results of Bonardi et al. (Macromolecules, 2018, 51, 1314–1324). The dual function of the enhancer additive includes: (i) regenerating the photoinitiator, and (ii) producing extra reactive radical. The temporal profiles of the concentration of each of the 3-component system and the associate conversion efficacy are numerically produced. In this study, several new findings showing unique features of various factors influencing the conversion will be demonstrated. For examples, reverse trends (roles) are found in: (i) the light intensity and enhancer concentration, and (ii) the coupling rate constants of radical-oxygen and radical-monomer. The monomer conversion is an increasing function of enhancer, oxygen concentration, and the light intensity. However, they have significantly different steady state features. The steady-state conversion increases from 10% without the enhancer (with enhancer concentration [B]0 = 0) to (30%, 50%, 80%) for [B]0 = (0.5, 1.0, 2.0)%. High conversion also requires a long lifetime of the free radical. Finally, the measured conversion profiles at various conditions reported by Bonardi et al. (Macromolecules, 2018, 51, 1314–1324) are compared and analyzed by our modeling.


I. INTRODUCTION
Free radical photopolymerization consists of two types of photoinitiation (PI), in which type-I is related to the direct coupling of the UV-light initiated radical and the monomers; whereas type-II is related to oxygen-mediated crosslink, or visible-light initiated radicals which coupled to the co-initiator [1], [2]. UV lights (360-400 nm) have been commonly used in most type-I photopolymerization of (meth)acrylate monomers [1]- [3]. However, the UV The associate editor coordinating the review of this manuscript and approving it for publication was Navanietha Krishnaraj Krishnaraj Rathinam.
wavelength suffers the disadvantages of being unsafe to skin and eyes, small penetration depth and larger light scattering in tissues [1]. Camphorquinone (CQ), due to its good visible absorption properties, is the most common type-II PI of (meth)acrylates under visible light [4]- [8]. The first threecomponent system of (CQ)/amine/ (aryliodonium ylides) was reported by Kirschner et al. [8].
In comparison, near-infrared (NIR) light offers advantages of safer, less light diffusion and scattering, and deeper penetration into the materials [1], [2]. Thus, the curing of a thick and filled material can be potentially enhanced compared to curing with UV or visible light. However, the use of NIR VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ photoinitiation systems such as cyanine is often associated with a low reactivity and requires a high light intensity [1]. Phthalocyanines and conjugated macrocycles have been used as commercial pigments and dyes having a high molar absorptivity coefficient in the red and NIR wavelength of 650-810 nm [9], [10]. Efficient polymerization conversions using NIR photoinitiation by cyanine/iodonium salt couples are reported by Strehmel et al [9]. Three-component system with a dye as a photosensitizer absorbing in the NIR range, an iodonium salt (as an initiator), and a phosphine (as a co-initiator) was reported, in which the phosphine is used to reduce oxygen inhibition (OIH) during the free radical polymerization of (meth)acrylate monomers [10], [11].
There are many other strategies to reduce (OIH) including: working in an inert or closed environment, increasing the photoinitiator concentration, increasing the light dose, or light intensity, use of multiple photoinitiators with different rate of initiation, or addition of oxygen scavengers [12], [13]. Furthermore, functionalized monomers which are insensitive to oxygen, such as the thiol-ene and thiol-acrylate-Michael additive systems were also reported [14], [15]. Additive enhancer-monomer were also proposed to improve the curing (crosslink) efficacy by either reducing the oxygen inhibition effect by stable-monomer, or increase the lifetime of radicals in clinical applications [16], [17]. In addition, dual-wavelength (red and UV) photopolymerization was reported, in which pre-irradiation of red-light was used to prereduce the OIH [18].
Recently, Bonardi et al [19] reported the first threecomponent system for high performance NIR (785 nm) photopolymerization of thick methacrylates, which used (i) a borate dye used as a NIR photosensitizer (PS), (ii) an iodonium salt as a photoinitiator (PI) for the free radical polymerization of the (meth)acrylates, and (iii) a dual-function enhancer (phosphine) to prevent oxygen inhibition, and to regenerate the PS upon irradiation, in which a stable radical is coupled with the enhancer.
This study presents the detailed kinetics, and modeling the conversion efficacy associated with the experimental results of Bonardi et al [19]. The dual function of the enhancer additive includes (i) prevention of OIH, and (ii) regeneration of the PS, which will be explored numerically and analytically in a 3-initiator system. The temporal profiles of the concentration of each of the 3-component and the associate conversion efficacy are numerically produced. In this study, several new findings showing unique features of various factors influencing the conversion will be demonstrated. For examples, the reverse trends (roles) are found in: (i) the light intensity and enhancer concentration on the PS concentration; and (ii) the coupling rate constants of radical-oxygen and radical-monomer coupling. Finally, the measured conversion profiles at various conditions reported by Bonardi et al [19] are compared and analyzed by our modeling.
We note that due to the complexity of the kinetics, this article is highly theoretical. Therefore, for those readers without a strong theoretical background may skip the In addition, readers may read the measured data reported by Bonardi et al [19] which also explained the important features as predicted by our analytic formulas. The kinetic equations for our previous single-initiator systems are revised for the 3-initiator system as follows [9]- [12] ∂

II. MATERIALS AND METHODS
where b=83.6a'wq, with w being the NIR light wavelength (in cm) and q is the excited state C * quantum yield, a' is the mole absorption constant, in (1/mM/%) and light intensity, I (z, t) in mW/cm2. We will use the so-called quasi-steady state assumption [5] described as follows. The life time of radical C * and [RO] are very short (ns to µs time scale) since they either decay or react with the substrate monomer after they are created. However, [ROO] is a rather stable radical and could not be assumed at a steady-state. The steady-state solutions of Eq. (4) to (6)   The dynamic light intensity is given by [9], [10] ∂I(z,t) ∂z where a' and b' are the extinction coefficients of Initiator-C and the photolysis product, respectively; Q' is the absorption coefficient of the monomer at NIR wavelength. Greater detail may be found in Ref. [9], [10]. We note that the dynamic feature of Eq. (17) due to the depletion of C(z,t) and the spatial dependence of both I(z,t) and C(z,t) are critical in optically-thick polymers [10]. The steady-state radical of Eq. (13) is given by where For the radical [R] dominant case with 8k T bIC G 2 , we obtain an approximate radical given by which is a decreasing function of the oxygen inhibition term G. We note that the conversion is a decreasing function of the oxygen initial concentration, whereas conversion is improved by enhancer Solutions of Eq. (10) to (18) are available by the approximated analytic formulas for I j (z,t) as follow [2], [4] where A 1 = 2.3(a'-b')C0I0bz. We note that the -A 1 t term represents the decrease of A', or increase of light intensity due to PS depletion, which is important for optically-thick polymers. Using Eq.
For analytic solution of Eq. (23), we could solve for the approximated solution of Eq. (11) and (12) Therefore, by the definition of efficacy C EFF = 1-M/M 0 , we obtain where radical [R] is proportional to bICg, but is a decreasing function of oxygen, as shown by Eq. (20). We note that g= k 7 /(k 5  . We note the coupling constant bI, a product of b and light intensity (I), will be considered as one parameter which also represents the light intensity for a given absorption constant (b).    Figure 3 could be further interpreted as follows. As shown by Figure 1 and Eq. (5) and (6) ] are, respectively, an increasing and decreasing function of time. Therefore, the combined effect leads to the optimal (or peak) of the temporal profile of [RO]. Furthermore, a larger co-initiator concentration ([B] 0 leads to a larger radical [RO] as shown in Figure 3 (A). In contrast, a higher light intensity leads to a faster oxygen depletion and thus a faster drop of [RO] profile as shown in Figure 3 (B). Figure 4 and 5 show the concentration profiles of initiator C(t), and oxygen [O 2 ] associate to Figure 2(A) and 2(B), respectively. We note that C(t) has a higher value in the presence of enhancer ([B]) due to the regeneration of C, shown by Figure 4 having various [B] 0 . In contrast, a reversed trend is shown by Figure 5 having various coupling constant of b'= bI0, in which a larger b' leads to a stronger depletion and lower value of C(t).   , which is an increasing function of oxygen. In the absence of oxygen, radical [RO]=0, the efficacy is given by gbIC and k'R, as shown by curve-1 of Figure 6(B). In contrast, for the k'R dominant case, conversion is reduced by OIH, as shown by Eq. (20), in which bimolecular termination leads to a reverse-trend of light intensity, i.e., a lower intensity leads to a higher steady state conversion.    [19] could be compared to our modeled results as follows. Figure 8 shows that higher coupling constant b'= bI0 leads to higher efficacy, which is also an increasing function of light intensity, as shown by Figures 4, 6 and 8 of Bonardi et al [19]. Furthermore, the photolysis (% decomposition of the peak at 800 nm) upon laser diode at 785 nm, shown by Figure 10 of Bonardi et al [19] could be compared with our Figure 4(A) for the initiator concentration C(t), in which a higher enhancer concentration [B] leads to a higher C(t), or less depletion due to the regeneration of C(t) by the enhancer [B]. We note that the photolysis or the  relative peak spectrum height at 800 nm, D(t) reported by Bonardi et al [19], is related to C(t) by D We suggest that readers should read the measured data reported by Bonardi et al [19], which also explained the important features as predicted by our analytic formulas and our numerical results. For a more comprehensive modeling, readers may refer to Ref. [20]. This article explores the kinetics of a single-wavelength system. We also suggest readers to read our other articles which further explored 2-wavelength and 3-wavelength polymerizations [23], [24] for the applications in 3D bioprinting.

IV. CONCLUSION
We have demonstrated that efficacy of NIR photopoly-

CONFLICTS OF INTEREST
Jui-Teng Lin is the CEO of Photon Vision Corp., Taipei, Taiwan. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.