# Efficacy Analysis of In Situ Synthesis of Nanogold via Copper/Iodonium/Amine/Gold System under a Visible Light

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{0}, B

_{0}, N

_{0}and G

_{0}, based on the proposed mechanism of Tar et al. Analytic formulas were developed to explore the new features, including: (i) both free radical photopolymerization (FRP) efficacy and the production of nanogold (NG), which are proportional to the relative concentration ratios of (A

_{0}+ B

_{0}+ N

_{0})/G

_{0}and may be optimized for maximum efficacy; (ii) the two competing procedures of NG production and the efficacy of FRP, which can be tailored for an optimal system with nanogold in the polymer matrix; (iii) the FRP efficacy, which is contributed by three components given by the excited state of copper complex (T), and the radicals (R and S) produced by iodonium and amine, respectively; (iv) NG production, which is contributed by the coupling of T and radical (S) with gold ion; and (v) NG production, which has a transient state proportional to the light intensity and the concentration ratio A

_{0}/G

_{0}) + (N

_{0}/(K’M

_{0}), but also a steady-state independent of the light intensity.

## 1. Introduction

## 2. Methods and Modeling Systems

#### 2.1. Photochemical Kinetics

_{4}), in which 4 wt% was added in a few drops of DMF, and the PI system was dissolved in ethylene glycol diacrylate (EGDA) at 93.95 wt%.

_{4}occurs due to a transfer of electrons from the aminoalkyl radical, but also from the excited state of the copper complex (Cu*). The radical amine

^{0}produced from the coupling of Cu* and amine is able to abstract hydrogen to generate radicals, which reduces the tetrachloroaurate Au

^{+3}to form Au

^{+2}, which is then reduced to Au

^{+1}, and further to Au

^{0}, leading to the formation of nanogold (NG). The interaction of the G1, TEA, and gold chloride was very fast, (within 60 s) under a visible light at 419 nm. After 5 min under irradiation, the absorption of the complex and Au

^{+3}entirely disappeared, having an increase in the absorption at the green (532 nm), which corresponds to the surface plasmon resonance (SPR) absorption [21,22,23]. The peak absorption (at 532 nm) of NG in a spherical shape moves toward near infrared (about 810 nm), if the NG is in a rod shape, with a length and width ratio of about 4.0 [24]. We note that the decomposition of the iodonium salt through an electron transfer and the production of aryl radical could also lead to NG. However, it is a secondary reaction, which is ignored in the present modeling.

^{+*}, G = Au

^{+3,}, G’ = Au

^{+2}or Au

^{+1}. The monomer (M) is EGDA (for FRP conversion). The associated Chart for Scheme 1 is shown in Figure 1 (only the key components are shown). As shown by Figure 1, a 3-initiator system (A/B/N) defined by the ground state of initiator A, which is excited to its first-excited state, and a triplet excited state (T), having a quantum yield (q). The triplet state T interacts with initiator [B], leading to regenerating A and producing a radical R. It can also interact with N to produce another radical S. Both radicals (R and S) can interact with the monomer (M) for FRP. Furthermore, T and R can interact with the gold (G) to produce exited-gold (G’), which further couples with T and S, leading to the formation of NG in the polymer matrix. We note that Figure 1 is more general than that of Scheme 1, because it can be used in a general 3-component system, A/B/N, having a various initiator (A), or additives (B and N) and in various metal chlorid (such as gold and silver). The present article focuses on the feature of NG production and limits to FRP. The general case with both FRP and CP has been presented elsewhere [19,20].

#### 2.2. The Rate Equations

_{E}is the regeneration (REG) term of of the initiator, [A], given by R

_{E}= g(k

_{7}+ k

_{1}[B]), with g = k

_{7}+ k

_{1}[B] + k

_{2}[N] + k

_{3}G. b = 83.6a’wq, where w is 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}. All the rate constants are defined previously [25,27] and they are related by the coupling terms. For examples, k

_{j}(with j = 1,2,3) are for the couplings of T and [B], [N], and G, respectively; K is for the coupling radicals R with monomer M (for FRP). In the above kinetics, we include the bimolecular termination [25] given by k’RR coupling in Equation (5), but for analytic formulas, we will keep only the unimolecular coupling term, KM, for FRP.

_{1}bIgg’[A] [B]), S = k

_{2}bIgg”[A] [N]), G’ = (k

_{3}T + k

_{4}S)/(k

_{5}T+k

_{6}S); with g = 1/(k

_{7}+ k

_{1}[B] + k

_{2}[N] + k

_{3}G + k

_{5}G’ + kM), g’ = 1/(k”S + KM), g” = 1/(k

_{4}G + k

_{6}G’ + k”R + K’M).

## 3. Results and Discussion

#### 3.1. Analytic Results

_{4}G such that g = 1/(k

_{3}G), g’ = 1/(KM), and g” = 1/(K’M). In addition, R

_{E}is taken as a mean reduction factor (f’), such that (1–R

_{E}) = f’ = [1 − k

_{2}N

_{0}/(k

_{3}G

_{0})] is time independent, having a value of f’ = 0.5 to 1.0. The first-order solutions of Equation (11) to (15) are found: [A] = A

_{0}exp(–dt); with d = f’bI; [B] = B

_{0}exp(-H), with H(t) = DE(t), with E(t) = [1 – exp(–dt)]/d]; [N] = N

_{0}exp(–H’), H’ = D’(k

_{2}/k

_{1})D, with D = (k

_{1}/k

_{3})d(A

_{0}/G

_{0}). Also G(t) = G

_{0}– (k

_{1}/k

_{3})dt; G’ = (k

_{3}/k

_{5})[1 + k

_{4}S/T] = (k

_{3}/k

_{5})[1 + k

_{4}[N]/(KM), for k

_{5}T >> k

_{6}S. Using these approximated solutions, Equations (15) and (16) become

_{3}G).

_{0}, and G’ = (k

_{3}/k

_{5}).

_{0}exp[−P(t)] + Ho(t),

_{3})bI(A

_{0}/G

_{0}); and Ho(t) is a complex second order term proportional to bIA

_{0}(k

_{1}B

_{0}+ k

_{2}N

_{0}/B

_{0})/G

_{0.}We note that P(t) has a transient state value P = Qt, and steady-state value, P = Q/d, which is independent of the light intensity.

_{6}k

_{2}/k

_{3})(N

_{0}/(K’M

_{0}), E(t) = [1– exp(–dt)]/d]; E’(t) = [1– exp(–d’t)]/d’]; D’ = bI(A

_{0}/G

_{0}); d’ = d + (k

_{1}/k

_{3})D, D = (k

_{1}/k

_{3})d(A

_{0}/G

_{0}). We note that [NG](t) has a transient state value [NG] = D’(1 + Q’t); and steady-state value, [NG] = D’(1/d + Q’/d’), which is independent to the light intensity.

#### 3.2. General Features and New Findings

_{E}= g(k

_{7}+ k

_{1}[B]) term in Equation (11).

^{0}) which leads to FRP; and coupled with G, or Au(3+), to form Au(2+), then G’, or Au(1+), leading to Au(0) and the nanogold (NG).

_{0}+ k

_{1}B

_{0}+ k

_{2}N

_{0})/(k

_{3}G

_{0}). which is an increasing function of the absorption coefficient (b) and light intensity (I), and the concentration ratios of (A

_{0}+ B

_{0}+ N

_{0})G

_{0}.

_{5}T + k

_{6}S)G’ shown by Equation (10). In addition, as shown by Equation (20), [NG](t) has a transient state value [NG] = D’(1 + Q’)t, which is an increasing function of bI[(A

_{0}/G

_{0}) + (N

_{0}/(K’M

_{0}); and the steady-state value, [NG] = D’(1/d + Q’/d’), which is independent to the light intensity.

_{0}+ B

_{0}+ N

_{0})/G

_{0}, rather than the individual concentrations. Therefore, the photoinitiating system reported by Tar et al. [21] based on G1/TEA/Iodonium, having (0.05/1%/1% wt) and 4 wt% of gold chlorid (G

_{0}, or HAuCl

_{4}), is not optimized. Our modeling predicts that lower initial gold chlorid (G

_{0}) and/or larger (A

_{0}+ B

_{0}+ N

_{0}), leads to a higher ratio of (A

_{0}+ B

_{0}+ N

_{0})/G

_{0}, and therefore higher FRP and larger production of NG. It seems that Tar et al. [21] have used a too high concentration of gold, but too low G1 concentration. In addition, our formula of Equation (19) predicts an optimal value of the concentration ratio (A

_{0}+ B

_{0}+ N

_{0})/G

_{0,}as also predicted by our previous modeling in other systems by Lin et al. [19,28].

_{1}[B]/G − k

_{2}[N]/G)/(k

_{3}G). Furthermore, there is a reduction effect in the FRP efficacy due to the production of NG caused by the reduction of excited state (T) when it couples with gold, Au(+3). On the other hand, higher FRP (or larger K’M term) also reduces the efficacy of NG production, as shown by the factor Q’ = (k

_{6}k

_{2}/k

_{3})(N

_{0}/(K’M

_{0}) in Equation (20). Therefore, one may tailor the ratio of (A

_{0}, B

_{0}, N

_{0})/G

_{0}to achieve maximum NG production, but also the strength of polymer matrix (or higher FRP), which is a competing procedure of NG production.t

## 4. Conclusions

_{0}+ B

_{0}+ N

_{0})/G

_{0}, which has an optimal value with nanogold in the polymer matrix.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Fouassier, J.P.; Lalevée, J. Photoinitiators for Polymer Synthesis: Scope, Reactivity and Efficiency; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2012. [Google Scholar]
- Yagci, Y.; Jockusch, S.; Turro, N.J. Photoinitiated Polymerization: Advances, Challenges, and Opportunities. Macromolecules
**2010**, 43, 6245–6260. [Google Scholar] [CrossRef] - Ligon, S.C.; Liska, R.; Stampfl, J.; Gurr, M.; Mülhaupt, R. Polymers for 3D Printing and Customized Additive Manufacturing. Chem. Rev.
**2017**, 117, 10212–10290. [Google Scholar] [CrossRef] [Green Version] - Kelly, B.E.; Bhattacharya, I.; Heidari, H.; Shusteff, M.; Spadaccini, C.M.; Taylor, H.K. Volumetric additive manufacturing via tomographic reconstruction. Science
**2019**, 363, 1075–1079. [Google Scholar] [CrossRef] [PubMed] - de Beer, M.P.; van der Laan, H.L.; Cole, M.A.; Whelan, R.J.; Burns, M.A.; Scott, T.F. Rapid, continuous additive manufacturing by volumetric polymerization inhibition patterning. Sci. Adv.
**2019**, 5, eaau8723. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Van Der Laan, H.L.; Burns, M.A.; Scott, T.F. Volumetric Photopolymerization Confinement through Dual-Wavelength Photoinitiation and Photoinhibition. ACS Macro Lett.
**2019**, 8, 899–904. [Google Scholar] [CrossRef] - Lin, J.T.; Chen, K.T.; Cheng, D.C.; Liu, H.W. Dual-wavelength (UV and Blue) controlled photopolymerization confinement for 3D-printing: Modeling and analysis of measurements. Polymers
**2019**, 11, 1819. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lin, J.T.; Liu, H.W.; Chen, K.T.; Cheng, D.C. 3-wavelength (UV, blue, red) controlled photopolymerization: Improved conversion and confinement in 3D-printing. IEEE Access
**2020**, 8, 49353–49362. [Google Scholar] [CrossRef] - Chiu, Y.C.; Cheng, D.C.; Lin, J.T.; Chen, K.T.; Liu, H.W. Dual-function enhancer for near-infrared photopolymerization: Kinetic modeling for improved efficacy by suppressed oxygen inhibition. IEEE Access
**2020**, 8, 83465–83471. [Google Scholar] [CrossRef] - Lin, J.T.; Chen, K.T.; Cheng, D.C.; Liu, H.W. Enhancing blue-light-initiated photopolymerization in a three-component system: Kinetic and modeling of conversion strategies. J. Polym. Res.
**2021**, 28, 2. [Google Scholar] [CrossRef] - Lin, J.; Cheng, D.; Chen, K.; Chiu, Y.; Liu, H. Enhancing UV Photopolymerization by a Red-light Preirradiation: Kinetics and Modeling Strategies for Reduced Oxygen Inhibition. J. Appl. Polym. Sci.
**2020**, 58, 683–691. [Google Scholar] [CrossRef] - Dietlin, C.; Schweizer, S.; Xiao, P.; Zhang, J.; Morlet-Savary, F.; Graff, B.; Fouassier, J.-P.; Lalevée, J. Photopolymerization upon LEDs: New photoinitiating systems and strategies. Polym. Chem.
**2015**, 6, 3895–3912. [Google Scholar] [CrossRef] - Pigot, C.; Noirbent, G.; Brunel, D.; Dumur, F. Recent advances on push–pull organic dyes as visible light photoinitiators of polymerization. Eur. Polym. J.
**2020**, 133, 109797. [Google Scholar] [CrossRef] - Garra, P.; Dietlin, C.; Morlet-Savary, F.; Dumur, F.; Gigmes, D.; Fouassier, J.-P.; Lalevée, J. Redox two-component initiated free radical and cationic polymerizations: Concepts, reactions and applications. Prog. Polym. Sci.
**2019**, 94, 33–56. [Google Scholar] [CrossRef] - Noirbent, G.; Dumur, F. Recent Advances on Copper Complexes as Visible Light Photoinitiators and (Photo) Redox Initiators of Polymerization. Catalysts
**2020**, 10, 953. [Google Scholar] [CrossRef] - Mokbel, H.; Anderson, D.; Plenderleith, R.; Dietlin, C.; Morlet-Savary, F.; Dumur, F.; Gigmes, D.; Fouassier, J.; Lalevée, J. Simultaneous initiation of radical and cationic polymerization reactions using the “G1” copper complex as photoredox catalyst: Applications of free radical/cationic hybrid photopolymerization in the composites and 3D printing fields. Prog. Org. Coat.
**2019**, 132, 50–61. [Google Scholar] [CrossRef] - Rahal, M.; Mokbel, H.; Graff, B.; Toufaily, J.; Hamieh, T.; Dumur, F.; Lalevée, J. Mono vs. Difunctional Coumarin as Photoinitiators in Photocomposite Synthesis and 3D Printing. Catalyst
**2020**, 10, 1202. [Google Scholar] [CrossRef] - Rahal, M.; Graff, B.; Toufaily, J.; Hamieh, T.; Noirbent, G.; Gigmes, D.; Dumur, F.; Lalevée, J. 3-Carboxylic Acid and Formyl-Derived Coumarins as Photoinitiators in Photo-Oxidation or Photo-Reduction Processes for Photopolymerization upon Visible Light: Photocomposite Synthesis and 3D Printing Applications. Molecules
**2021**, 26, 1753. [Google Scholar] [CrossRef] [PubMed] - Lin, J.-T.; Lalevee, J.; Cheng, D.-C. A Critical Review for Synergic Kinetics and Strategies for Enhanced Photopolymerizations for 3D-Printing and Additive Manufacturing. Polymers
**2021**, 13, 2325. [Google Scholar] [CrossRef] [PubMed] - Abdallah, M.; Hijazi, A.; Lin, J.-T.; Graff, B.; Dumur, F.; Lalevée, J. Coumarin Derivatives as Photoinitiators in Photo-Oxidation and Photo-Reduction Processes and a Kinetic Model for Simulations of the Associated Polymerization Profiles. ACS Appl. Polym. Mater.
**2020**, 2, 2769–2780. [Google Scholar] [CrossRef] - Tar, H.; Kashar, T.I.; Kouki, N.; Aldawas, R.; Graff, B.; Lalevée, J. Novel Copper Photoredox Catalysts for Polymerization: An In Situ Synthesis of Metal Nanoparticles. Polymers
**2020**, 12, 2293. [Google Scholar] [CrossRef] - Lin, J.-T. Modeling the scaling law of surface plasmon resonance in gold spherical nanoshells. J. Nanophotonics
**2010**, 4, 049507. [Google Scholar] [CrossRef] [Green Version] - Lin, J.-T. Nonlinear optical theory and figure of merit of surface plasmon resonance of gold nanorods. J. Nanophotonics
**2011**, 5, 051506. [Google Scholar] [CrossRef] - Lin, J.T. Scaling law and figure of merit of biosensor using gold nanoshells. J. Nanophotonics
**2010**, 4, 049507. [Google Scholar] [CrossRef] [Green Version] - Lin, J.-T.; Cheng, D.-C. Modeling the efficacy profiles of UV-light activated corneal collagen crosslinking. PLoS ONE
**2017**, 12, e0175002. [Google Scholar] [CrossRef] - Lin, J.-T. Kinetics of Enhancement for Corneal Cross-linking: Proposed Model for a Two-initiator System. Ophthalmol. Res. Int. J.
**2019**, 10, 1–6. [Google Scholar] [CrossRef] [Green Version] - Lin, J.-T.; Liu, H.-W.; Chen, K.-T.; Cheng, D.-C. Modeling the Kinetics, Curing Depth, and Efficacy of Radical-Mediated Photopolymerization: The Role of Oxygen Inhibition, Viscosity, and Dynamic Light Intensity. Front. Chem.
**2019**, 7. [Google Scholar] [CrossRef] - Lin, J.-T.; Liu, H.-W.; Chen, K.-T.; Cheng, D.-C. Modeling the Optimal Conditions for Improved Efficacy and Crosslink Depth of Photo-Initiated Polymerization. Polymers
**2019**, 11, 217. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Scheme 1.**A proposed kinetics for a 3-component system of G1/Iod/amine in gold chloride (HAuCl

_{4}) solution, where G1 is the copper complex (HLCuCl), having an excited state Cu*, which couples with iodonium salt, Ar

_{2}I(+), and amine to produce radicals, (Ar

^{0}and amine

^{0}) which lead to FRP. Both Cu* and amine

^{0}can couple with Au(3+) to form Au(2+), then Au(1+), leading to Au(0) and the nanogold [21].

**Figure 1.**The schematics of a 3-component system, (A/B/N), where A is the ground state of initiator-A, having an excited triplet state T, which interacts with additives [B] and [N} to produce radicals R and S, which can interact with the monomer (for FRP), or interact with the gold (G, or Au

^{+3}) to produce exited-gold (G’, or Au

^{+2}and Au

^{+1}), which then further couples with T and S, leading to the formation of nanogold (NG, or Au

^{0}) in the polymer matrix.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lin, J.-T.; Lalevee, J.; Liu, H.-W.
Efficacy Analysis of In Situ Synthesis of Nanogold via Copper/Iodonium/Amine/Gold System under a Visible Light. *Polymers* **2021**, *13*, 4013.
https://doi.org/10.3390/polym13224013

**AMA Style**

Lin J-T, Lalevee J, Liu H-W.
Efficacy Analysis of In Situ Synthesis of Nanogold via Copper/Iodonium/Amine/Gold System under a Visible Light. *Polymers*. 2021; 13(22):4013.
https://doi.org/10.3390/polym13224013

**Chicago/Turabian Style**

Lin, Jui-Teng, Jacques Lalevee, and Hsia-Wei Liu.
2021. "Efficacy Analysis of In Situ Synthesis of Nanogold via Copper/Iodonium/Amine/Gold System under a Visible Light" *Polymers* 13, no. 22: 4013.
https://doi.org/10.3390/polym13224013