Antoine Tardy

Noémie Gil

Christopher M Plummer

Chen Zhu

Simon Harrisson

Didier Siri

Julien Nicolas

Didier Gigmes

Yohann Guillaneuf

Catherine Lefay
email: catherine.lefay@univ-amu.fr

Noemie Gil

DFT-calculation-assisted prediction of the copolymerization between cyclic ketene acetals and traditional vinyl monomers

Introduction

Radical polymerization remains one of the primary polymerization techniques due to several advantages such as its compatibility with a broad range of monomers, experimental conditions that only require the removal of oxygen, etc. In addition to these advantages, radical polymerization has also witnessed the advent of controlled/living radical polymerization (CLRP) techniques that allow for the preparation of polymer chains with well-defined length, composition and end-groups. 1 Recently the extension of CLRP to include a photochemical process has led also to both temporal and spatial control of the polymerization giving the possibility to finely tune the polymer chains. 2 To date, the main disadvantage of the radical polymerization process is the non-degradability of the resulting polymer backbone since only C-C bonds are produced. Several strategies have been developed to address this problem. 3 Among them, the use of cyclic ketene acetals (CKAs) is one of the most promising routes. After radical addition to the exo-methylene moiety, these cyclic monomers are able to fragment into an ester group and a new alkyl radical that can propagate the chain (Figure 1a). 4, 5 In particular, five-and seven-membered ring CKA monomers (Figure 1b) such as 2-methylene-4-phenyl-1,3dioxolane (MPDL), 2-methylene-1,3-dioxepane (MDO) and 5,6benzo-2-methylene-1,3-dioxepane (BMDO) are widely used owing to their good stability and high tendency for ringopening. When a copolymerization is performed with a vinyl monomer, the consumption of CKA monomers creates an ester moiety in the polymer backbone that will confer (bio)degradability to the resulting polymer (Figure 1c). The copolymerization of CKA with common vinyl monomers has been extensively studied. 4, 5 The radical copolymerization of CKA monomers under various experimental conditions and with many common vinyl monomers such as styrenic, (meth)acrylate derivatives and vinyl acetate (VAc) enables the preparation of polymeric materials with enhanced (bio)degradable properties compared to the standard materials. Nevertheless, whatever the system studied, a primary limitation of their copolymerization with vinyl monomers is the weak reactivity of the cyclic monomer resulting in their low incorporation into the final copolymer and a high discrepancy between the initial monomer feed ratio and the final copolymer composition (Table 1). The particular reactivity of CKAs can be attributed to the strong nucleophilic character of the double bond. Nevertheless, the radical addition of electrophilic radicals (such as those derived from acrylates and methacrylates) onto nucleophilic CKA-derivative radicals does not promote a high incorporation of the cleavable ester units into the copolymer backbone. Surprisingly VAc has been identified as one of the most interesting monomers to be copolymerized with CKA. 6,[9][10][11][12] In the case of MDO as the CKA monomer, the reactivity ratios were indeed both close to 1, enabling the synthesis of a nearly statistical copolymer (r MDO = 0.47 and r VAc = 1.53).

9

Recently we investigated 13 the copolymerization of CKA monomers with vinyl monomers (methyl acrylate and VAc), and concluded, with the assistance of quantum chemistry and frontier molecular orbital analyses, that the differences in reactivity observed between vinyl monomers was attributed to the rate of addition of the vinyl-based radicals onto the vinyl monomers and not to the rate of cross-addition between the vinyl radical and the CKA monomer. Such findings helped to discover a new copolymerization pair: CKA/vinyl ethers.

13 Indeed, such systems afford random copolymers with MDO thereby giving functional polyesters that could be used in a broad range of applications.

13, 14

To expand our understanding of radical CKA copolymerization with vinyl monomers, and to find other relevant CKA/vinyl monomer pairs to copolymerize, the reactivity of model CKAs (MDO or BMDO) with a large range of vinyl monomers was investigated. In particular, after determining the enthalpy of addition for nucleophilic, electrophilic and ambiphilic-electrophilic primary, secondary and tertiary radicals onto BMDO using quantum calculations, the reactivity ratios of several monomer couples were then theoretically evaluated. Indeed, the kinetics of a copolymerization can be described simply by using the terminal model. This approach is based on the assumptions that the growth of the chains depends on the reactivity of the radicals at the end of the chain, and that the propagation reactions are irreversible. The copolymerization of 2 monomers M 1 and M 2 is then summarized by 4 possible propagation reactions, two homopropagation reactions (k 11 and k 22 ) and two cross-propagation reactions (k 12 and k 21 ). The reactivity ratio defined as follow r 1 =k 11 /k 12 and r 2 =k 22 /k 21 ) allow to evaluate the microstructure of the copolymer chains.

Based on these results, 1-(trifluoromethyl)vinyl acetate (CF 3 VAc, Figure 2) appeared as a promising new candidate to copolymerize with MDO to give an alternating copolymer. These theoretical results were then confirmed by experimental copolymer synthesis and detailed NMR characterization. This Please do not adjust margins Please do not adjust margins system is therefore a novel way to prepare degradable fluorinated polymers that could have many different interesting applications, such as biomedical imaging.

Experimental Section

Materials 2-methylene-1,3-dioxepane (MDO) was prepared following a previously described protocol. C). The 1 H chemical shifts were referenced to the solvent peak for acetone-d6. All integrations of the 1 H NMR spectra were normalized to a peak at 7.5 ppm relating to bromobenzene which was used as an internal reference. SEC analyses were performed using an EcoSEC system from TOSOH equipped with a differential refractometer detector. THF was used as an eluent with 0.25 vol% toluene as a flow marker at a flow rate of 0.3 mL min -1 after filtration using Alltech PTFE membranes with a porosity of 0.2 µm. The column oven was kept at 40 °C, and the injection volume was 20 µL. One ResiPore Pre-column (50 mm, 4.6 mm) and two ResiPore columns (250 mm, 4.9 mm) from Polymer Laboratories were used in series. The system was calibrated using polystyrene standards from Agilent in the range 580-400,000 g.mol -1

.

CF 3 VAc and MDO radical copolymerization

In a typical polymerization reaction, 0.2 mmol of thermal initiator (DEAB), 2-4 droplets of bromobenzene (used as an internal reference for NMR) and 8 mmol of monomer were placed in a flask previously rinsed with triethylamine. The homogenized mixture was then syringed into a Wheaton prescored ampule of 2 mL which was also previously rinsed with triethylamine. After, the mixture was degassed by three cycles of freeze-pump-thaw and the ampule then sealed. The ampule was then placed in a preheated oil bath at a specific temperature. After a prescribed time, the ampule was removed and placed in ice-cold water, and then opened. The reaction mixture was dissolved in CDCl 3 to obtain the 1 H and 13 C NMR spectra of the crude polymers and then dried and redissolved in THF to obtain the GPC distributions. Finally, the solution was precipitated in pentane.

Results and Discussion

Determination of the activation enthalpy of the reaction of addition of radicals onto BMDO

In a previous study, 13 it was demonstrated that the difference in reactivity observed with VAc and methyl acrylate (MA) copolymerizations in the presence of MDO arises from the rate of addition of the vinyl-based macroradicals onto the vinyl monomers (k vinyl-vinyl ), as opposed to the rate of crossaddition of the vinyl-based macroradicals onto the CKA monomers (k vinyl-CKA ). Such findings led us to propose vinyl ether derivatives as good comonomers for CKA polymerization. To obtain a deeper understanding of the copolymerization mechanism, we extended our previous study to a large quantity of alkyl radicals. Although more expensive in calculation time, the use of BMDO in the calculations seemed simpler because the monomer has a greater rigidity and therefore fewer possible conformations after addition. To perform the calculation of polar radical addition activation energies on various alkenes, the UB3-LYP/6-31G(d) method was used. 15, 16 This commonly used method was previously validated by Fisher and Radom, 17 indicating that it allows for a good estimation of the energy barriers at a moderate calculation cost. The effectiveness of this DFT method for free radical addition reactions with polar effects has been confirmed more recently, even with the lowest level of theory (6-31G(d)). 18 We therefore modelled the addition reactions of various primary, secondary and tertiary carbon-based radicals from various families, i.e. nucleophilic (alkyl, methoxyalkyl, hydroxyalkyl, acetylalkyl, chloroalkyl); apolar-nucleophilic (aromatic, methyl) ; electrophilic-ambiphilic (cyanoalkyl, phophonoalkyl, methoxycarbonylalkyl, methylcarbonylalkyl) and electrophilic (trifluoromethylalkyl, trifluoroacetonyl -FAc • , cyclic malonyl -cMal • ). The structures and calculation results for UB3-LYP/6-31G(d) are presented in Table S1 and the activation enthalpies are compared in Figure 3.

In this work, it was considered that the enthalpies of activation ΔH ‡ and the activation energies E a are similar and that the ΔH ‡ values consequently give consistent information on the energetical barrier. Considering apolar radicals (Me-, alkyl, aromatic) there is a linear correlation between the activation energy and the enthalpy of reaction comparable to the Evans-Polanyi-Semenov equation (see Figure S1) as already observed by Fischer and Radom. 17 For all other radicals, a deviation of the values below this line is observed, demonstrating the presence of polar interactions during the addition of these radicals to the CKA monomer. 17 Thus, we concluded that the DFT calculation with the UB3-LYP/6-31G(d) method should be sufficient to identify behavioral trends since similar trends were observed compared to common radical addition onto alkenes. 17 On the other hand, it was also with the aim of "averaging" potential non-systematic errors that the study was undertaken on a large number of radicals. The analysis of Figure 3 also gives many insights. First, the additions of all nucleophilic radicals were performed with a low activation barrier (ΔH ‡ <35 kJ.mol -1

). Besides, nucleophilic radicals present different energy barriers depending on the type of primary, secondary or tertiary radicals. In fact, apart from the addition of the hydroxymethyl (MOH • ) radical, which seems to be an outlier, the enthalpies of activation of the primary radicals are of the order of 22 to 29 kJ.mol -1

, whereas they are slightly ). On the other hand, there is a clear difference in enthalpy of activation concerning the additions of electrophilic-ambiphilic radicals. In particular, primary radicals show a high reactivity towards the CKA double bond (ΔH ‡ = 10-20 kJ.mol -1

) whereas their tertiary analogs present much more difficulty (ΔH ‡ = 35-44 kJ.mol -1 ). This large difference can be explained by steric hindrance which increases and reduces the reactivity of the tertiary radical, but there should be the same effect for nucleophilic radicals, which is not the case. From another point of view, the electrophilic behavior of primary radicals is modified into a more ambiphilic behavior by the addition of two electrondonating methyl substituents. Finally, a major difference with nucleophilic radicals is that electrophilic-ambiphilic radicals exhibit forms of resonance, so tertiary radicals are particularly stabilized and therefore less reactive. Indeed, when we look at the enthalpies of addition (Table S1) we observe that the addition of the tertiary radicals 2-methoxycarbonyl-2-propyl (PEst ). For all other radical additions, the enthalpies are higher and indicate more thermodynamically favorable reactions. The addition of truly electrophilic radicals such as FAc

• or radicals with a mesomeric donor but inductively electro-withdrawing trifluoromethyl (CF 3 ) groups are extremely fast, which is to be expected since the philicity of these radicals is completely opposite to that of the CKA double bond. This reactivity seems to be confirmed with the addition of the cMal • radical, which even seems to present no energy barrier (Table S1). Nevertheless, the geometry of the corresponding transition state is not comparable with the others because it is not possible to avoid the presence of hydrogen bonds with one of the carbonyls of the cMal • radical.

The most important point to note is that for secondary radicals, whether nucleophilic or electrophilic-ambiphilic, the calculations carried out give identical enthalpies of activation; of the order of 25-30 kJ.mol -1

. Since the propagation of the monomers such as MA and VAc takes place via secondary radicals, these singular results could perhaps explain the particular reactivity of CKAs in copolymerization. It has been shown that the most inaccurate UB3-LYP calculations concern species with an oxygen atom directly linked to the reactive center (hydroxymethyl (MOH • ), 2-hydroxy-2-propyl (POH • ) and 2-methoxy propylene monomer radicals). 18 Since CKAs possess two oxygen atoms linked to the double bond, the calculations made here may not be sufficiently reliable. In addition, the level of theory UB3-LYP/6-31G(d) is known to overestimate the stabilization of radical species 19 • )), the UBMK method hardly differentiates between secondary and tertiary radicals but separates them from the addition of a primary radical. Even more surprisingly, it seems from the G3(MP2)RAD method that all methoxycarbonylalkyl radical additions are performed with the same ease (ΔH ‡ = 13±1 kJ.mol -1

) without steric hindrance being important. Furthermore, in contradiction to the results obtained with UB3-LYP/6-31G(d), the addition of the tertiary radical 2-acetyl-2-propyl radical (PAc

Evaluation of the reactivity ratios

This theoretical study aiming at determining the ΔH ‡ values for addition of different vinyl-based radicals to CKA monomers was then completed by the study of the reactions of crossadditions and self-addition to get all the rate constants of addition involved in the copolymerization scheme (Table S2).

The theoretical reactivity ratios at 70 °C by the ratio of the rate constants of self-addition compared to cross-addition were then determined. The reactivity ratios obtained for the different systems are gathered in Table 3. For such evaluation the UB3-LYP method was used, considering that the errors among the various alkyl radicals are similar and will be compensated. The reactivity ratios calculated in this work have values with similar orders of magnitude as those reported within the literature; in the case of styrene (r CKA = 10 The values of the rate constants are relatively well approximated even if the absolute values of the activation energies are not correct. In addition, and as previously observed, vinyl ether monomer (VE) appears to be a monomer of choice for copolymerization with CKA to obtain a random copolymer (r 1 and r 2 are both close to 1). This approach has been previously validated on the MDO/vinyl ether pair.

The aim of this work was to obtain a better understanding of the reactivity of different couples of vinyl/CKA monomers, and also to try to identify any other systems of interest for producing degradable vinyl-based copolymers with a high rate of CKA incorporation.

Isoprene is an interesting vinyl monomer since it is a major component of elastomers 26, 27 and has been recently shown to be a promising carrier for drug delivery [28][29][30] via a prodrug approach. The theoretical calculations of the reactivity ratios between isoprene and MDO did not let us envision that an efficient random degradable polyisoprene could be prepared via its radical copolymerization with CKA monomers. Nevertheless, a low incorporation of cleavable ester groups seemed possible. We then performed the polymerization of isoprene at 115°C in dioxane for 30 hours in the presence of 0-75 mol% of MDO as the CKA and initiated by dicumyl peroxide to favor CKA incorporation. Polyisoprenes with an M n close to 10,000 g.mol -1 were obtained showing between 5 and 7 mol% of ester units in the polymer backbone (see ESI for details).

Such polymers were then degraded in accelerated conditions and showed a close to 50% decrease in the M n (Figure 4). The nature of the CKA monomer was also investigated. A similar isoprene polymerization was also performed using BMDO as a CKA monomer. In order to favor CKA incorporation, only an initial feed ratio of 75 mol% CKA was used. Even with this large excess of CKA, the conversion was less than 2% of CKA, thus showing almost no incorporation of degradable bonds into the polyisoprene chains. The theoretical reactivity ratios (Table S3) between BMDO and isoprene were then computed using the same methodology used in Table 3, providing r BMDO = 6.5 × 10 -3 , r isoprene = 150. This result confirms the very difficult incorporation of CKA, in agreement with the experimental data. Unlike isoprene, and based on this theoretical study, a potentially interesting copolymerization system was noticed since the CF 3 VAc/MDO pair presents theoretical reactivity ratios both close to 0, thus being expected to produce alternating copolymers. Such kind of alternating copolymers were already obtained using maleic anhydride 31 and maleimides monomers. [32][33][34] Another interesting aspect of the CF 3 VAc is the presence of a mesomeric electron-donating acetate function as well as an inductively electron-withdrawing CF 3 group. Thus, the formation of charge transfer complexes (possible with a mesomeric electron-withdrawing group) that could lead to low cycle opening, 35 should be avoided.

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Copolymerization of MDO with CF 3 VAc

To confirm these theoretical results, we first studied the homopolymerization of the two monomers. Homopolymerization of CF 3 VAc is known to be difficult.

36, 37

The best results observed by Haas 38 are oligomers with 30% conversion in the presence of benzoyl peroxide at 70 °C for 8 days. We thus performed such homopolymerizations at 70 °C for 12-15 hours with 3 mol% of diethyl azobisisobutyrate (DEAB) as the initiator. The results showed a maximum conversion of 40% (Figure S2). On the other hand, the molar masses obtained are about 20,000 g.mol -1

, which is surprisingly high even though we used conventional PS calibration. Using the same experimental conditions, the MDO reaches a conversion plateau of ca. 80% after about 6 hours (Figure S2).

We thus performed various copolymerizations with different initial molar ratios of MDO and CF 3 VAc ([MDO] 0 :[CF 3 Vac] 0 = 18:82, 45:55 and 82:12) and stopped them after 6 hours of reaction time at 70°C with 3 mol% of DEAB as the initiator. The 1 H NMR analyses of the crude products (Figure 5a) show markedly different behavior when the composition of the initial medium is varied. Indeed, for initial compositions with 18 and 82% of MDO, a significant amount of the excess monomer remains unreacted after 6 hours, as can be observed in Figure 5a (peaks α, β, γ, δ and ε), whereas for an initial molar composition of 45%, the two monomers almost completely reacted within 6 hours. This difference is even more striking when we look at the consumption of the monomers. Indeed, it can be seen in Figure 5b that monomer consumption is extremely rapid and the conversion plateau (90%) is almost reached after only 2 hours. Moreover, the conversion of the two monomers followed the same trend. The system is therefore strongly accelerated when both monomers are present in an equimolar fashion.

This is confirmed by the other two polymerization kinetics (Figure 5b) where total conversions only reached 40-60% conversion. When MDO is introduced in excess, copolymerization is rapid until the CF 3 VAc monomer is consumed, and then stops at ca. 20% conversion of MDO, the characteristic peak of which can be observed in the 1 H NMR spectrum (Figure 5a). Conversely, when CF 3 VAc is introduced in excess, the polymerization stopped at 40% molar monomer conversion. It is important to note that the initiator system used for these copolymerizations is the same as that used for the homopolymerization of each of the monomers. Using this kinetic study, we determined the reactivity ratios by fitting the evolution of the feed ratio versus the overall molar conversion (Figure 6), using the Skeist equation and a non-linear least square method (NLLS). 13, 39 This method provides reactivity ratios of r CF3VAc = 0.11 and r MDO = 0.07, in good agreement with the calculated values. Concerning the molar masses of the polymers, they were determined by SEC calibrations using an apparent PS calibration and are gathered in Table S4. This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins The chemical structure of the obtained polymers are truly dissimilar to the standards, and thus the molar masses are not necessarily comparable. Nevertheless, for copolymers containing a majority of CKA, masses around 10,000 g.mol -1 are well within the expected range for a radical polymerization of MDO. The masses obtained during a copolymerization initiated with the molar ratio of the monomers being 45:55 are much higher which again confirms the better reactivity of this system. The dispersity begins to increase when the amount of introduced MDO monomer is higher owing to transfer reactions which are known to occur during MDO polymerization. 40, 41 It should also be noted that the molar masses obtained at the beginning of the polymerization are higher than at the end when the initial feed ratio is not equimolar. This can perhaps be explained by the preparation of polymer chains of a different nature (i.e. homopolymers) with different reactivities when all the alternating copolymer has been formed.

Characterization of the copolymer

To confirm the theoretical results and the synthesis of an alternating copolymer, we analyzed the copolymer obtained from an equimolar ratio of MDO and CF 3 VAc at 70 °C with 3 mol% of DEAB as initiator. A homopolymer of the CF 3 VAc monomer was prepared under similar conditions before the NMR peak assignment of the copolymer (Figure S3). The absence of the acetal peaks generally observed at ca. 100 ppm and the presence of ester functionalities at 170 ppm within the 13 C NMR (Figure 7, top) both provide proof of the ring-opening of the MDO monomer. This was confirmed by 2D HMBC NMR analysis which attributed the peak at 169 ppm to the polycaprolactone ester function (coupling between proton 3 and carbon 2, Figure 5a). The peak at 170.2 ppm was attributed to the acetyl group of CF 3 VAc based on the coupling between carbon 10 and proton 11. These results prove that the copolymerization of MDO with CF 3 VAc takes place with quantitative ring-opening of the CKA monomer. The full ringopening of the MDO monomer is essential for introducing cleavable ester functions into the copolymer backbone thereby enabling the production of degradable materials. The alternating structure of the copolymer was confirmed by 2D NMR HSQC-ED (Figure 8b) by the presence of specific couplings between carbon signals at 34.4 and 37.3 ppm with a doubled triplet at 2.1-2.3 ppm and a doubled doublet at 3.0-3.3 ppm, respectively, with the absence of a strong correlation characteristic of the homopolymers of MDO and CF 3 VAc. Significant coupling observed between proton 1 and carbon 2 provides additional evidence of the presence of an alternating structure (Figure 8a).

This detailed NMR study thus confirmed that the copolymerization of MDO with CF 3 VAc with an equimolar initial molar ratio of monomers ([MDO] 0 :[CF 3 VAc] 0 = 0.45 : 0.55) gives alternating copolymers with 100% ring-opening of the MDO monomer. It should be noted that Maynard and Sawamoto recently showed that degradable methacrylatebased copolymers with pendant fluorinated group could also be prepared by the copolymerization of BMDO and fluorinated methacrylate. 42 Our system is thus another straightforward methodology to prepare degradable fluorinated copolymers with the fluorinated group directly linked to the backbone and not only present as a pendant group.

Degradation and formulation studies

The prepared alternating copolymers were subsequently subjected to degradation tests. Hydrolysis in solution was first investigated under accelerated conditions using 5% potassium hydroxide in THF. The degradation was monitored by SEC and the result of such degradation tests are depicted in Figure 9.

The results showed a total degradation in less than 15 minutes for a pristine polymer of (M n = 26,000 g.mol -1

, Ɖ = 3.4). This kinetics is similar to the ones of other degradable CKAcontaining copolymers. 33, 43 The degradation led to oligomers with an M n below 400 g.mol -1

, in agreement with an alternating copolymer structure. The hydrophobic poly(MDO-alt-CF 3 VAc) copolymer was then formulated into nanoparticles in the presence of surfactants using the nanoprecipitation technique as previously performed for poly(MDO-co-CEVE) copolymers. 14 Briefly, nanoparticles were formulated at 1 mg•mL -1 in the presence of 1 wt% of F127 Pluronic as surfactant. We thus obtained a stable nanoparticle suspension with an intensity-averaged hydrodynamic diameter (Dz) of 242 nm and particle size distribution of 0.181 (Figure 10). This result showed that highly fluorinated nanoparticles prepared using a degradable polymer could be prepared and let us envision their use in biomedical imaging.

Conclusion

One of the primary advantages of the radical ring-opening polymerization of CKA monomers consists of their copolymerization with common vinyl monomers, thereby allowing the introduction of ester units into vinyl-based polymer backbones and thus conferring (bio)degradability. This study therefore aimed to rationalize the copolymerization behavior of CKA monomers with common vinyl monomers via DFT calculations. For example; the theoretical determination of the reactivity ratios allowed us envision a low but possible introduction of ester units into a polyisoprene backbone which was later confirmed by experimental studies.

Efficient copolymerization of CKA monomers was found to only be achievable with non-activated comonomers such as vinyl ether or vinyl acetate, or as an alternating copolymerization with maleimides through charge transfer complexes. In this work, we first confirmed this behavior and then extend the alternating copolymerization to trifluoromethyl vinyl acetate (CF 3 VAc). The later system was therefore studied experimentally, and the alternating structure of the copolymer confirmed by NMR. Degradation studies were performed under accelerated conditions and showed the total degradation of the polymer chains. Finally, nanoparticles of this highly fluorinated degradable copolymer were then obtained by a nanoprecipitation technique. This novel material could potentially find applications within biomedical imaging.

Figure 1 .

 1 Figure 1. a) Radical Ring-Opening Polymerization (rROP) of Cyclic Ketene Acetals (CKAs) b) Structures of the most used CKA monomers. c) Preparation of degradable vinylbased polymers by the radical copolymerization of CKAs and common vinyl monomers.

Figure 2 .

 2 Figure 2. Theoretical reactivity ratios determined by DFT calculations and the new CKA/vinyl monomer pair: MDO and trifluoromethyl vinyl acetate (CF3VAc).

Figure 3 .

 3 Figure 3. Calculated activation enthalpies ΔH ‡ for the addition of various radicals onto the BMDO monomers using the UB3-LYP/6-31G(d) level of theory.

1 ,

 1 • ), 2-cyano-2-propyl (PCN • ) and 2-methylcarbonyl-2-propyl (PCO • ) are not very stabilizing (ΔH r = -23, -27 and -10 kJ.mol respectively) in the same way as that of the styryl radical (ΔH r = -26 kJ.mol -1) and cumyl radical ΔH r = -6 kJ.mol -1

1 ,

 1 r vinyl =1), methyl acrylate (MA) and methyl methacrylate (r 1 pertinence of the UB3LYP/6-31G(d) method.

Figure 4 .

 4 Figure 4. SEC chromatograms of the polyisoprene (red) and poly(isoprene-co-MDO) (blue) before (solid) and after (dash and dot) accelerated degradation experiments (24h THF, KOH, 5 wt% in MeOH)

Figure 5 .

 5 Figure 5. a) Crude 1 H NMR analysis of the bulk copolymerization of MDO and CF3VAc. b) Molar conversion of () CF3VAc, MDO () and overall () for the the bulk copolymerization of MDO and CF3VAc.]

Figure 6 .

 6 Figure 6. Experimental and theoretical MDO monomer composition versus overall molar conversion with rCF3VAc = 0.11 and rMDO = 0.07 during the bulk copolymerization of CF3VAc and MDO at 70°C initiated with 3 mol% of DEAB.

13 CFigure 8 .

 138 Figure 7. 13 C NMR (top) and 1 H NMR (bottom) spectra of the copolymer obtained from the initial molar ratio [MDO]0:[CF3VAc]0 = 0.45 : 0.55.

e

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Figure 9 .

 9 Figure 9. SEC chromatograms of the poly(MDO-alt-CF3VAc) before (dark) and after (red) accelerated degradation experiments

Figure 10 .

 10 Figure 10. Volume size distribution of the poly(MDO-alt-CF3VAc) nanoparticles measured by DLS.

Table 1 .

 1 Initial

				4, 5
	CKA	Vinyl monomer	f CKA,0	F CKA	Ref
		Styrene	50	23
		4-vinylanisole	50	19
		MMA MMA	50 50	33 25	6
		VAc	50	49
		VAc	50	34
		Styrene	50	32
		4-vinylpyridine MMA	50 50	34 40	7
		VAc	50	40
		Styrene	50	27
		MMA	50	24
		Styrene	50	31	8
		4-vinylanisole	50	33
		MMA	50	13

CKA feed ratio (fCKA,0) and overall CKA molar composition of the polymer (FCKA) during the copolymerization of CKAs with various vinyl monomers.

  and this may be the reason for the low reactivity of electrophilic-ambiphilic tertiary radicals. are presented in Table2. It can first be observed that the UBMK/6-31G(d) method indicates values of the same order of magnitude as UB3-LYP while at the level of UBMK/6-311++G(2dp3df) theory, the energy estimates are on average 10 kJ.mol -1 above the previous values. On the contrary, the G3(MP2)RAD method gives rather low values. The results of the calculations that are theoretically more accurate are much more nuanced than the first estimate for the various radicals I, II and III. Indeed, whereas with the UB3-LYP method, the ΔH ‡

	of methoxycarbonylalkyl radicals increases from primary to
	tertiary radicals (methoxycarbonylmethyl radical (MEst	• )< 2-
	methoxycarbonylethyl radical (EEst	• )< 2-methoxycarbonyl-2-
	propyl radical (PEst
			Recently Mardirossian and Head-Gordon	20 reported that root
			mean square deviation for barrier heights could reach ~6
			kcal.mol	-1 , and that absolute values have to be taken with care.
			To confirm these results, we thus used other DFT methods,
			namely BMK	21	with various levels of theory and
			G3(MP2)RAD	19, 22 which are both known to describe well the

reactivity of radicals. In that case we also initially focused on MDO as it has less atoms thus saving computational time, and alkyl radicals that mimic the propagating macroradicals. The Please do not adjust margins Please do not adjust margins results

Table 2 .

 2 Activation Enthalpies ΔH ‡ for the addition of various secondary alkyl radicals onto the MDO monomer using various level of theory.

	secondary counterpart 2-acetyl-ethyl radical (EAc	• ) according

• ) to the CKA is easier than to its

6 | J. Name., 2012, 00, 1-3

This journal is © The Royal Society of Chemistry 20xx

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Table 3 .

 3 Theoretical reactivity ratios at 70°C between MDO and various vinyl monomers, and comparison with experimental data

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 7

Acknowledgements

We thank the French Ministry of Research for the financial support of the PhD thesis of A.T and the CNRS and the French National Research Agency (ANR-15-CE08-0019 and ANR-18-CE08-0019). This work was also supported by the 'Centre Régional de Compétences en Modélisation Moléculaire de Marseille'. Arkema is acknowledged for providing DEAB.

Conflicts of interest

The authors declare no competing financial interest.


Antoine Tardy

Noémie Gil

Christopher M Plummer

Dr Didier Siri

Didier Gigmes

Catherine Lefay

Yohann Guillaneuf
email: yohann.guillaneuf@univ-amu.fr

Dr N A Tardy

Dr C M Gil

Pr D Plummer

Dr C Gigmes

Dr Y Lefay

Guillaneuf

Polyesters by a Radical Pathway: Rationalization of the Cyclic Ketene Acetal Efficiency

Keywords: DFT Calculations, Polyester, Radical polymerization, Cyclic Ketene Acetals, Kinetic modelling

Radical Ring-Opening polymerization (rROP) of Cyclic Ketene Acetals (CKAs) combines the advantages of both ringopening polymerization and radical polymerization thereby allowing the robust production of polyesters coupled with the mild polymerization conditions of a radical process. rROP was recently rejuvenated by the possibility to copolymerize CKAs with classic vinyl monomers leading to the insertion of cleavable functionality into a vinyl-based copolymer backbone and thus imparting (bio)degradability. Such materials are suitable for a large scope of applications, particularly within the biomedical field. The competition between the ring-opening and ring-retaining propagation routes is a major complication in the development of efficient CKA monomers, ultimately leading to the use of only four monomers that are known to completely ring-open under all experimental conditions. In this article we investigate in detail the radical ring-opening polymerization of model CKA monomers and demonstrate by the combination of DFT calculations and kinetic modeling using PREDICI software that we are now able to predict in silico the ring-opening ability of CKA monomers.

Introduction

Recently, the final outcome of synthetic polymers has become a major issue due to the accumulation of wastes that are damaging the environment. [1][2][3] To overcome this problem the use of biodegradable polymers such as polyesters, in particular polylactides, has been widely investigated. [4][5][6] These polymers are commonly prepared by polycondensation or Ring-Opening Polymerization (ROP). [7] Nevertheless, a large part of commodity and specialty polymers are produced by radical polymerization techniques that impede the introduction of ester linkages into the backbone of the polymer chains. [8] Relatively few studies, [9][10] initiated by the pioneering work of Bailey et al. [11] , have demonstrated that various cyclic monomers bearing vinyl or exomethylene groups could be polymerized radically through a ring-opening process (Scheme 1a). Radical Ring-Opening Polymerization (rROP) presents the advantages of both ring-opening polymerization and radical polymerization, specifically the production of (co)polymers with the possibility to insert heteroatoms and/or functional groups into the main chain by facile polymerization procedures (Scheme 1a). [10] The ring-opening polymerization of Cyclic Ketene Acetals (CKAs) by free radical or controlled radical mechanisms has attracted considerable interest since it presents an alternative route for the synthesis of functionalized aliphatic polyesters [12][13][14][15] and is a powerful tool for imparting degradability to vinyl polymers [16][17][18][19][20] by introducing ester linkages into their backbone (Scheme 1b). [9][10] Scheme 1. a) Mechanism of Radical Ring-Opening Polymerization (rROP). b) rROP of Cyclic Ketene Acetals (CKAs) and their use in the preparation of functionalized polyester or segmentable vinyl-based polymers.

Indeed, the copolymerization of vinyl-based monomers and CKAs has been used to prepare (bio)degradable polyethylene, [21] fluoropolymers, [22] polymethyl methacrylate materials, [18] marine anti-biofouling coatings, [23][24] etc., offering a promising route to reduce plastic pollution. This approach has also been used to confer (bio)degradability to many vinyl-based biomaterials such as polymer prodrugs, [25] nanoparticles, [26][27] thermo-responsive materials, [20,[28][29] ice-recrystallization inhibitors, [30] etc. To confer efficient (bio)degradability, the incorporation of ester bonds into the polymer backbone has to be performed randomly, as demonstrated theoretically by Lefay et al. [31] using kinetic modelling. Even though the rROP has been known since the eighties, very few mechanistic studies have been performed and no clear structure-reactivity relationships have been established for those monomers. [10,[32][33] Indeed, the major drawback of this family of monomer is related to the competition between the ring-opening process and the undesired direct vinyl propagation that leads to polyacetal (Scheme 2). Thus, for the majority of CKA monomers, the resultant polymer is a random copolymer of ester and acetal units. This situation leads to the predominant use of two cyclic monomers in all of the literature; 2-methylene-1,3-dioxepane (MDO, C7, Scheme 3) and the 5,6-benzo-2-methylene-1,3dioxepane (BMDO, C7B, Scheme 3), both known to undergo complete ring-opening polymerization independent of the conditions. [10] Promising results have been obtained for biomedical applications with these two monomers (gene transfection, etc.). [10] The development of new CKA monomers that can extend the properties of the corresponding polyester by tuning the mechanical properties, degradation rate, etc. is paramount. To design a monomer for radical ring-opening polymerization, originally two factors were taken into account in order to improve the selectivity of the ring-opening process: (i) the ring strain and (ii) the stabilization of the ring-opened radical. For example, 6-membered ring monomers are recognized to be difficult to polymerize via a ring-opening process. This is usually explained by the low ring-strain of monomers analogous to cyclohexane (whose ring-strain is set to zero). The addition of an aromatic ring close to one oxygen (2 methylene-4-phenyl-1,3dioxane, C6P, Scheme 3) was also expected to increase the ring-opening ability via the stabilization of the released alkyl radical, but the radical polymerization of such monomers, under both UV at 25-50 °C and thermal initiation at 80 and 120 °C, gave polyacetals of high molar mass (> 30,000 g.mol -1 ). [34] On the contrary, an analogous chemical modification of the 5membered monomer (2-methylene-4-phenyl-1,3-dioxolane or MPDL, C5P, Scheme 3) increases the ring-opening ability. [35][36] There are many similar examples showing that the aforementioned factors were not key parameters for rationalizing the reactivity of such monomers. [10] These results demonstrate why only a few known monomers are used within the literature and why the versatility of the rROP technique to prepare a wide range of functionalized polyesters has not been extensively investigated. In order to efficiently design new monomers, it would be useful to be able to predict the efficiency of a given monomer in rROP before its synthesis and polymerization. Herein, we propose a theoretical approach that combines quantum calculations and kinetic modeling based on the competitive process described above (Scheme 2) to achieve this goal. More precisely, our strategy is to use Density Functional Theory (DFT) to calculate the various rate coefficients that will be later implemented into a kinetic model to obtain the theoretical composition of ester and acetal units in a polymer backbone. These theoretical results were then experimentally confirmed by studying the radical polymerization of C5, C5H, C6 and C7 CKA monomers (Scheme 3). Such an approach allows the in silico prediction of the behavior of new CKA monomers.

Results and Discussion

Experimental Study

O O O O O O C5P C5 C5H O O O O R7B R7 O O O O O O R5P R5 R5H O O O O C7B C7 O O O O R6P R6 O O O R8O O O O O C6P C6 O O O C8O
A significant problem when rationalizing the reactivity of CKA monomers arises from the many experimental conditions that have been reported within the literature (initiator nature and concentration, temperature, etc.). Additionally, since many of the published studies were performed in the 80-90s, some nonreliable characterization methods have been used to assess the ratio between acetal and ester repeating units. To ensure the validity of the experimental data before implementing the modeling, we performed the polymerization of monomers C5, C5H, C6 and C7 coupled with careful microstructure analysis to obtain an accurate ratio between the acetal and ester units for these model CKA polymers. As was previously stated by Bailey et al. [11] in their pioneering studies, CKA monomers with 5-and 6-membered rings are prone to cationic polymerization initiated by contact with glass making purification steps particularly problematic. This is a crucial issue when attempting to quantify the ester percentage obtained by radical polymerization as cationic polymerization typically results in a high quantity of acetal units, or even pure polyacetal (see ESI Fig. S1). Thus, spontaneous cationic polymerization contamination during monomer purification, storage, radical polymerization and subsequent analysis was avoided through strict experimental conditions. The bulk polymerizations were performed using 3 mol% of the various radical initiators depending on the polymerization temperature (see ESI for details). After the polymerization of monomers C5, C5H, C6 and C7 and purification by precipitation, the four polymers were analyzed by 1 H and 13 C NMR. All 1 H and 13 C NMR signals can be assigned and are consistent with the data reported within the literature. 2D NMR techniques also confirmed these assignments (see ESI for details, Figure S2 and S3 for PC5 for example). The analysis of the 13 C NMR spectra (Fig. 1 for the polymerization of monomer C5, other NMR spectra are provided in ESI) confirmed the presence of two repeating units within the copolymers. These spectra display peaks in the characteristic zones of both acetal and ester units, at 100 and 170 ppm, respectively. We also noted a change in the number (i.e. the presence of diads, see Figure 1) and intensity of these peaks corresponding with the temperature of polymerization. The acetal peaks were more intense at low temperatures, while there was an inversion in the intensity of the two main ester peaks with temperature. It is clear that an increase in temperature promotes the presence of ester units, which are highly prevalent at 150 °C. After full assignment of the 1 H NMR spectrum, quantification of the percentage of ester units in PC5 can be performed using multiple different calculation procedures. The results are extremely close regardless of the applied method (see ESI for details, Table S2). It should be noted that the difference between the values is almost negligible at 120 and 150 ° C, while it is less than ± 5% at low temperatures. Accordingly, there is a perfectly linear trend of ring-opening percentage and temperature, allowing a change in ester unit percentage from ca. 50% to 80% by increasing the temperature from 50 to 100 °C. Extrapolating these conditions, the polymerization of monomer C5 should be performed beyond 200 °C to obtain pure polyester, which is not relevant. These results are in good agreement with those previously reported in the literature concerning the trend, but also with ring-opening percentage values. In the case of the C5H polymerization, only acetal units were observed in the polymer chains by both 1 H and 13 C NMR (see Figure S4 and S5), as was previously reported within the literature. [37] Moreover, unlike the other CKA monomers, molar masses were found to be very high (>30,000 g.mol -1 ). The sixmembered ring monomer (C6) was then polymerized at the same temperatures. The quantity of precipitated polymer was lower than previous reactions and therefore the uncertainty was higher, and thus a sample polymerized at 100 °C was added to compensate. The obtained molar masses were also relatively small when compared to PC5. We noted that the 13 C NMR spectra had the same basic characteristics as those presented in Figure 1 (the presence of peaks corresponding to both ester and acetal units at all temperatures; an increase in the temperature leading to better ring-opening ability). However, whereas previously the ester peak intensity significantly exceeded the intensity of acetal peaks at temperatures above 120 °C, the intensities are much closer in this case. Moreover, the peak b is almost absent at low temperatures (Figure S6 50-60% ester units, which is significantly below the value of 85% reported within the literature [11] (Figure 2).

As expected from the literature data, the 7-membered ring monomer (MDO, C7) provided only polyester regardless of the temperature used (see ESI Figure S9-S10 for details). All of the obtained experimental data is in good agreement with the literature data. Indeed, the order for obtaining polyesters follows the trend: C5H << C6 < C5 << C7. Nevertheless, we are now able to examine these results in detail. The 5-and 6membered monomers both have the ability to form aliphatic polyester, their ring-opening ability increasing also linearly with temperature, with an almost identical slope, whatever the monomer. It was also demonstrated that there is a clear difference in the ring-opening ability of the 5-and 6-membered ring CKA monomers, with the 6-membered CKA being less prone to ring-opening. These obtained data were subsequently used as a reference set for the following theoretical modeling.

Computational study

The different structures of the monomer and adduct radicals have been optimized by the DFT method B3LYP / 6-31G (d), commonly used for its excellent quality of results and calculation times. [14,[38][39] Moreover, this method has already been efficiently used in conformational studies of various heterocyclic rings. [40][41] The acetalyl propagating macroradicals has been optimized by simulating the polymer chain using a methyl group (Scheme 3, R5-R7 radicals) to mimic steric hindrance without requiring significant calculation costs, while simultaneously reducing energy errors due to free rotation of the chains. In each case, the two C-O bonds susceptible to β-scission were broken to find the transition state of lowest energy. Here we only show the values for the selected transition state. Concerning the various cyclic radicals having an aromatic substituent (R5P, R6P and R7P) the homolysis is always located on the same side as the substitution, as expected. There is only scarce experimental data for the β-scission of CKA monomers on which we can base a theoretical approach. The only values originate in a 1982 study where Ingold [42] studied I1 and I2 (Figure 3) intermediates by EPR and measured their β-scission rate coefficient. To determine the activation energies we used different quantum methods (i.e., UB3LYP, MO6-2X and G3(MP2)RAD) since it was shown that the particular method applied could lead to drastic differences when compared with experimental data. The results of the calculations are displayed in Figure 3. Importantly, it was observed that calculations performed using the UB3LYP method led to a lower Ea than the experiment, while calculations made with G3(MP2)RAD and MO6-2X are slightly and exceedingly higher than the experimental data, respectively. This result is not surprising as the UB3LYP method is known to generally underestimate the energy of structures. [43] It is additionally important to note that a difference of 5-8 kJ.mol -1 between the energies of activation for the two species I1 and I2 is correctly assessed by all techniques (difference between 3 and 6.5 kJ.mol -1 ). The values obtained with the method UB3LYP/6-31G(d) are very close but lower than the experimental values with a 3 kJ.mol -1 deviation. On the other hand, the use of a larger base (i. e. 6-311++G(3df, 2p)) is not interesting as it further underestimates the energies with a deviation of 5-6 kJ.mol -1 . The G3(MP2)RAD method, [43][44] known for the quality of its absolute values, is less close to the experimental data than UB3LYP (10-11 kJ.mol -1 higher deviation). As the G3(MP2)RAD calculations require much longer and are limited to a few atoms, the UB3LYP/6-31G(d) method appeared to present the best compromise in speed/performance. We already utilized the same DFT method for other quantum calculations of CKA monomers. [14,[45][46] The activation energy values of β-scission all range between 35 and 70 kJ mol -1 (Figure 4a). All of the 7-membered CKA monomers known to polymerize exclusively by the ring-opening mechanism have an activation enthalpy lower than 40 kJ mol -1 , in agreement with the previous calculations of Endo. [32] This study also confirmed that the stabilization of the released radical is not a key parameter since there is no direct link between the percentage of ring-opening and the presence of an aromatic ring in the β position to the cyclic acetal functionality. Moreover, these calculations also do not allow a discrimination between a partial and the absence of ring-opening. Thus far, only β-scission reactions have been studied; here and within the literature. This is only a part of the complete mechanism since radical ring-opening polymerization is characterized by the competition between the β-scission and the direct addition. The reactions involved are not of the same order (unimolecular and bimolecular), and thus they are not comparable in terms of thermodynamics or activation energy, such comparisons usually being performed to identify the most-favorable reaction mechanism.

The correct method to understand the role of the different reactions is to achieve a kinetic model using not only the energy of activation but also the rate coefficients kβ and kadd,closed (Scheme 4). Indeed, to describe the macroscopic result (the ratio between the acetal and ester units in the polymer backbone) we need to compute the number of the two propagation events that occurred during the polymerization process, and thus the addition reaction after opening kadd,open is also mandatory. Since our interest is focused on the propagation steps, we used classic initiation and termination steps and disregarded all side reactions such as chain transfer reactions that are known to occur during the polymerization of MDO, as an example. [47] To make an accurate estimate of the addition rate coefficient of macroradicals onto monomers it is recommended to model dimers or trimers instead of unimers. [48] However, as this work involves relatively large molecules (15-60 atoms) we thus chose to directly use the rate coefficient of simple addition reactions to limit computing time. Moreover, in the case of the addition of radicals after ring-opening, the penultimate effect was not envisioned since the previous unit is at minimum 5 atoms away. In the case of the radical addition of acetalyl-based radicals, it is assumed that the effects of steric hindrance and the specificity of such radicals are well above any potential penultimate effect. In the calculations we also did not take into account any solvent effect. Indeed, this study aimed at comparing ring-retaining and ring-opening reactions and in this case, absolute rate constants that require more complex calculations are not necessary. Moreover, since the polymerizations are performed in bulk, the solvent's parameters are related to the monomers themselves and are thus unknown. It is therefore beyond the scope of the manuscript to take them into account.

Concerning the addition of ring-opened radicals, the growing number of possible rotations along the length of the aliphatic chains gives access to a very large amount of possible geometries. In this way, there is too great an uncertainty in the values of calculated energies. To avoid this limitation, simple representative radicals mimicking the macroradical were modelled i.e. the ethyl radical for monomers C5-C7 and the styryl-or methyl-benzyl-type radical for the C5P-C7B monomers (Figure 4b). The work of Fisher and Radom [38] which was dedicated to modeling additions of radical reactions by DFT indicates that in the case of relatively large systems the B3LYP method is appropriate and has a good compromise between time and result, also later confirmed by Moscatelli. [39] Thus, and also to be consistent in the various calculations (addition and βscission), this method was chosen to be applied.

The results for the addition of ring-opened radicals onto the CKA monomers are described in Figure 3b. Since in all cases the polarity of both adding radicals and CKA are similar, thus the rate of addition is dependent only on the stabilization of the alkyl radical (primary, secondary or tertiary alkyl radicals or the presence of a stabilizing aromatic ring). For example, the activation enthalpies of primary alkyl radicals are centered around 28 ± 5 kJ.mol -1 , while are higher in the case of secondary radicals (35,5 kJ.mol -1 for C5H). For aromatic-based monomers, the benzylic type radical has a lower activation enthalpy (43 kJ.mol -1 for C7B) than styryl-based radicals (48±1 kJ.mol -1 for C5P -C6P). These obtained values can be compared to the values described by Fischer and Radom [38] dealing with the addition of methyl and benzyl radicals onto vinyl ethers. In this case, activation energies of 25 and 40 kJ.mol -1 were given, respectively, that are both 3 kJ.mol -1 lower than the values that we obtained for CKA, which are vinyl ethers in which an additional oxygen atom is located in the α position to the vinyl functionality. Moreover, for the C5 monomer, Coote et al. [49] proposed a value of 30 ± 5 kJ.mol -1 via high level ab initio calculations for the propagation rate coefficient that is coherent with our value. From these results we could conclude that the ring-size does not greatly affect the activation enthalpies for similar structures (C5-C6-C7 and C5P-C6P).

To our knowledge, there is no data within the literature reporting the radical addition of acetalyl-type radicals, especially onto cyclic ketene acetals. The obtained results are summarized in Figure 4c. The data shows that the calculated energy values do not differ significantly, i.e. all the activation enthalpies being centered around 27 ± 5 kJ.mol -1 and the reaction enthalpies around -66 ± 8 kJ.mol -1 . It can be observed that only the ring size seems to influence such values since C5, C5H and C5P are similar, and such behavior holds true for 6-and 7-membered ring CKA monomers. It should be noted that these values are of the same order of magnitude as the addition of primary alkyl radicals on the CKA while the acetalyl radicals here are tertiary, showing the specific reactivity of such radicals. The activation energies calculated for different reactions are not directly comparable to know whether a monomer is more likely to propagate directly or undergo β-scission. Indeed, there are different order reactions; i.e. monomolecular and bi-molecular. Therefore, kinetic modeling is required. Kinetic modeling is performed from the rate coefficients of the various reactions. These coefficients can be obtained by knowing the free energy of activation ∆G ‡ or from the Eyring equation through the various components of enthalpy and entropy of activation (∆H ‡ and ∆S ‡ , respectively). However, DFT methods are known to give erroneous evaluations of entropy. [50][51] Indeed, the Gaussian software treats all vibrations like harmonic oscillators. This is correct for certain vibrations, but the entropy associated with certain hindered rotations is not properly taken into account. In the cyclic ketal intermediate, such hindered rotations are important and thus ∆S ‡ leads to erroneous results. The use of the Arrhenius equation simplifies the problem. Indeed, the pre-exponential factor A contains the component of entropy and its value is rather similar for the same type of reaction in a narrow range of temperatures. [38] For the addition of open radicals, the values of log A that are recommended are 7.5, 8, and 8.5 depending on whether the groups are tertiary, secondary or primary, respectively. [38] However, no value for the addition of tertiary acetalyl-based radicals exist in the literature, the presence of more oxygen atoms appears to increase the value of log A in different cases. [38] Therefore, we chose to use the average value of 8 for such acetalyl radicals. In the case of the ring-opening reaction, it is recommended to take a log A value of 13. [42,[START_REF] Benson | Thermochemical Kinetics[END_REF] Kinetic modeling was then performed using PREDICI software. This software is based on the deterministic Galerkin h-p-method has been widely used for describing molecular weight distributions and polymer reaction kinetics for a large range of polymer processes. [45][46][START_REF] Wulkow | [END_REF] The kinetic scheme is depicted in Scheme 5 while the coefficients, hypotheses and applied approximations are detailed within the ESI (Table S7 and S8). The propagating species are simply either closed or open type. We assumed that the rate coefficients are independent to the chain length. This assumption is more relevant for the propagation step than for the termination step, since diffusional limitations are more important in the latter case. [54] Scheme 5. Kinetic model used in the PREDICI software. which would complexify the system and thus would require many additional calculations that are not necessarily useful in this particular case. Counters have been inserted into the model to quantify the amount of ester and acetal functions introduced in the copolymer. The acetal counter was increased when there is an addition of a closed-type radical. The ester counter increased when ring-opening occurred. In that way, it does not include counting when there is an addition of an open-type radical since the resulting chain end is then of a closed type and can therefore react in both ways. At the end of the modelling, the number of acetal and ester counters were recorded and compared to determine the percentage of ester units in the final polymer backbone. The result of the modeling is depicted in Figure 5. A good agreement between the experimental values and those obtained from the model can be observed in the case of simple monomers C5, C6 and C7. Indeed, Figure 5 shows relatively identical behavior between the simulation and the experimental observations for these monomers; C7 monomer gives only ester units at 50 °C while C5 and C6 form copolymers. Moreover, the difference in ability between C5 and C6 to form polyesters is also in good agreement with the experimental results, with 75% and 45% polyester at 100 ° C, respectively, (on average 20% more for C5 than C6) and an increase in percentage of polyester with an increase in temperature. In contrast, the slope defining the increase in ester percentage depending on the temperature is slightly steeper for the simulation results in comparison to the experimental data. This discrepancy could originate from the assumptions made regarding chain length independency of the various kinetic rate coefficients. Nevertheless, this modeling approach provides an interesting and relatively accurate tool to describe the reactivity of CKA monomers. We additionally performed such modeling on more complex monomers. With C5P, C7B and C8O the model gives complete ring-opening, in accordance to the literature data. [10] In contrast to experimental data, the model predicts that C5H should contain some ester units even if such a monomer has a lower tendency to ringopen. [37] The results obtained for C6P (Figure 6) is not in agreement with the literature data [34] since the modeling showed an enhancement in the ring-opening ability in comparison to the C6 CKA monomer (75% instead of 25% at 70 °C).

The discrepancy between the theoretical results and the literature data can be explained by cationic polymerization that was not inhibited. [34] This explanation is further supported by a study on C6 CKA derivatives bearing methyl groups on the carbon in the α position relative to the cyclic acetal functionality.

In that case, using base to prevent cationic polymerization, they obtained 89% ester units at 120°C. [55] Another parameter that could be used to increase the ring-opening ability of CKA monomers is to decrease the monomer concentration in order to favor the unimolecular reaction compared to the undesired bimolecular acetal propagation. To simulate the monomer dilution, the ring-opening percentage of the C6 monomer at different initial monomer concentrations and temperatures was modeled (Figure 6). As expected, an evolution towards the production of more polyester at high dilution was observed. Using such an approach, only the β-scission of the intermediate acetalyl-radical has to be calculated. Secondly, we performed the modeling using the parameters used for C6 and C8O monomers (i.e. the monomers that have the highest and lowest activation energies for ring-opening) and determined the percentage of ester units in the polymer backbone versus a constant K that is determined by the ratio kβ/kadd, closed (Figure 7). Interestingly all the data followed a master curve. A threshold value of 1 × 10 3 seems mandatory to obtain pure polyester. Using this threshold and the values of the pre-exponential factors, we can estimate that a CKA monomer should have a difference between the activation energies of ring-opening and addition of the ring-retaining acetalyl lower than 13-15 kJ.mol -1 to efficiently obtain polyester. If we assume that the radical addition of the acetalyl intermediate is only determined by the ring size, this approach gives an upper limit for the β-scission reaction depending of the ring size (Table 1).

Conclusion

The competitive process of ring-retaining propagation is a major obstacle in the development of efficient CKA monomers. In this study we investigated this key parameter by a combination of experimental and theoretical approaches. First, it was demonstrated that the ratio between ester and acetal units in the polymer backbone is linearly correlated to the polymerization temperature, with the ease of ring-opening following the order C7 > C5 > C6. DFT calculations of the ring-opening reaction showed that complete ring-opening behavior could be obtained with a ΔH ‡ < 40 kJ.mol -1 but it was not possible to discriminate or quantify the behavior for other monomers. By further utilizing the kinetic modeling software PREDICI the behavior of CKA monomers was able to be rationalized by considering the impact of the addition of acetalyl and open-type radicals onto the CKA monomer.

Although relatively simple, the developed kinetic model is based on relevant values and seems robust enough to allow for an approximation of the behavior of a CKA monomer after completing the necessary energy calculations. Furthermore, this model allows an attempt at the rationalization of behavioral differences between the monomers through structure-reactivity relationships. The analysis of molecular orbitals is also predicted to be an excellent method for this because it can separate the contributions due to hyper-conjugation and those due to other energy contributions such as steric and electrostatic interactions. This will be the subject of a subsequent study.

Scheme 2 .

 2 Scheme 2. Competition between ring-opening and direct vinylic propagation leading to either ester units or acetal units.

Scheme 3 .

 3 Scheme 3. Structures of CKA monomers and their corresponding intermediate acetalyl radicals.

Figure 1 . 1 H and 13 C

 1113 Figure 1.1 H and 13 C NMR spectra and structure of PC5 obtained at different temperatures.

  -S8), demonstrating a lower ringopening ability of such 6-membered CKA monomer when compared to their 5-membered analogues. Nevertheless, the results still demonstrated a linear evolution in the ring-opening percentage in relation to temperature. At 130 °C we calculate 189-190_13C P1S.1r.esp 189-190_13C P1S.1r.P1S BW.1r.esp 189-190_1H P1S BW.1r.esp 1D

Figure 2 .

 2 Figure 2. Ring-opening percentage as a function of temperature for the bulk polymerization of monomers C5-C7.

Figure 3 .

 3 Figure 3. Influence of the quantum method on the activation energies of the βscission reaction of acetalyl-based radicals and their comparison with experimental data.[42]

Figure 4 .

 4 Figure 4. Enthalpies of activation ΔH ‡ and reaction ΔHr for the ring-opening reaction (left) and the different radical addition (open-type radical, middle) and acetalyl-based radical (right).

  It has been already stated that the chain length was not taken into account because the larger molecular size requires too much computation time. Moreover, by modeling propagating radicals in the form of dimers or trimers, the penultimate unit would be different according to the previous addition (e.g. closed-closed, open-closed, closed-open or open-open dimers),

Figure 5 .

 5 Figure 5. a) Theoretical (plain symbol and straight line) and experimental (empty symbol and dashed-dotted line) ring opening percentage as a function of the temperature for the bulk polymerization of C5 (), C6 (▲) and C7 (✭) monomers; b) Theoretical ring opening percentage as a function of the temperature for the bulk polymerization of C5H (•) and C6P () monomers.

Figure 6 .

 6 Figure 6. Theoretical ring-opening percentage as a function of temperature and initial monomer concentration [M]0 for the C6 monomer.

Figure 7 .

 7 Figure 7. Theoretical ring-opening percentage as a function of the parameter K=kβ/kadd,closed see Scheme 4 for the definition of the rate coefficients; () C6 monomer at 70 °C; (•) C6 monomer at 120 °C; (▲) C8O monomer at 70 °C.

Table 1 .

 1 Upper values for the enthalpy of activation for the ring-opening reaction to obtain pure polyester according to CKA ring size

	CKA Monomer	Average	ΔH ‡ β max
	Size	ΔH	‡ add, closed	(kJ.mol	-1 )
		(kJ.mol	-1 )
	5		27		40
	6		24		37
	7		31		44

Scheme 4. Complex mechanism to theoretically determine the ester/acetal ratio in a polymer backbone.

Acknowledgements

We thank the French Ministry of Research for the financial support of the PhD thesis of A.T and the CNRS and the French National Research Agency (ANR-15-CE08-0019 and ANR-11-JS08-0005). This work was also supported by the 'Centre Régional de Compétences en Modélisation Moléculaire de Marseille'. Arkema is acknowledged for providing DEAB.

Entry for the Table of Contents

Draw me a CKA: the radical ring-opening polymerization of model CKA monomers was investigated using quantum calculations and kinetic modeling. The results were supported by a detailed experimental study. The new methodology we propose allows to predict in silico the efficiency of CKA monomers to prepare polyester via a radical pathway.


Nicholas S Hill

Melinda J Fule

Jason Morris

Jean-Louis Clément

Yohann Guillaneuf

Didier Gigmes

Michelle L Coote

Mesolytic versus Homolytic Cleavage in Photochemical Nitroxide Mediated Polymerization

Time-dependent density functional theory calculations have been performed to study the photocleavage reactions of chromophore-functionalized alkoxyamines in nitroxide-mediated photopolymerization. Two case studies were considered: azaphenalene derivatives and benzophenone-based alkoxyamines. For the azaphenalenes, we show that the expected homolysis pathway is actually inaccessible. Instead, these alkoxyamines exhibit low-lying excited states that exhibit an electronic structure about the nitroxide moiety similar to that of the formally oxidized radical cation. As a result, the cleavage of these alkoxyamines can be described as mesolytic-like, rather than homolytic. As with formally oxidized species, mesolytic cleavage can result in the production of either carbon-centered radicals or carbocations, with only the former resulting in radical polymerization. Here, the cleavage products are found to be dependent on the respective radical/cation stabilities of the monomer units of choice (styrene, ethyl propanoate, and ethyl isobutyrate). In contrast to the azaphenalenes, in the benzophenone-based alkoxyamines, conjugation between the nitroxide and chromophore moieties appears to facilitate homolysis, due to the ideal alignment of singlet and triplet states of different symmetries.

INTRODUCTION

Methods for controlling the molecular weight and architecture in free-radical polymerization have broad applications in the synthesis of smart materials for use in applications ranging from drug delivery to lithography. [START_REF] Matyjaszewski | Controlled/Living Radical Polymerization[END_REF][START_REF] Matyjaszewski | Architecturally Complex Polymers with Controlled Heterogeneity[END_REF] One such technique is nitroxide mediated polymerization (NMP). [START_REF] Hawker | New Polymer Synthesis by Nitroxide Mediated Living Radical Polymerizations[END_REF][START_REF] Grubbs | Nitroxide-Mediated Radical Polymerization: Limitations and Versatility[END_REF][START_REF] Bertin | Kinetic Subtleties of Nitroxide Mediated Polymerization[END_REF] In this process, control is achieved through a dynamic equilibrium between the dormant alkoxyamine and active propagating radical (Scheme 1). By minimizing the concentration of activate propagating radicals with respect to the population of dormant alkoxyamines, bimolecular termination is minimized with respect to chain growth while imparting a synthetically useful nitroxide functionality on the chain end. However, a key drawback of NMP is the requirement for elevated temperatures, which can lead to side reactions that deactivate the dynamic equilibrium upon NMP depends. [START_REF] Gryn'ova | Which Side-Reactions Compromise Nitroxide Mediated Polymerization?[END_REF] Scheme 1. Controlling equilibrium for NMP where an alkoxyamine is thermally cleaved into the active transient carbon centered radical and persistent nitroxide radical.

To address this problem the use of light, rather than heat, to activate the alkoxyamine has been explored. [START_REF] Chen | Light-Controlled Radical Polymerization: Mechanisms, Methods, and Applications[END_REF][START_REF] Guillaneuf | Toward Nitroxide-Mediated Photopolymerization[END_REF][START_REF] Morris | Novel Polymer Synthesis Methodologies Using Combinations of Thermally-and Photochemically-Induced Nitroxide Mediated Polymerization[END_REF] However, while socalled photo-nitroxide-mediated polymerization (PNMP) has shown extremely promising results in certain systems, overall the results have been mixed, with some systems displaying control, others displaying non-controlled polymerization and some displaying no reaction at all. For example, while azaphenylenes are effective PNMP agents for styrene polymerization, alkoxyamines containing chromophores such as 9,10-diphenylanthracene and 9,10-bis(phenylethynyl) anthracene undergo fluorescence instead. [START_REF] Bottle | Light-Active Azaphenalene Alkoxyamines: Fast and Efficient Mediators of a Photo-Induced Persistent Radical Effect[END_REF] A better understanding of the photochemical processes involved and their dependence on chemical structure is essential to the design of more effective PNMP agents. To date it has been assumed that PNMP occurs via energy transfer from the chromophore to the breaking NO-R bond on the triplet surface, so as to cause homolysis in the same manner as standard NMP. [START_REF] Chen | Light-Controlled Radical Polymerization: Mechanisms, Methods, and Applications[END_REF][START_REF] Huix-Rotllant | Theoretical Study of the Photochemical Initiation in Nitroxide-Mediated Photopolymerization[END_REF] This reactive process is in competition with various nonreactive processes, as represented in Figure 1. However, mesolytic cleavage (Scheme 2) is a conceivable alternative which could help to explain some of the unexpected failures of PNMP agents. The excited state capable of leading to mesolytic cleavage is the state, on either the singlet or triplet surface. This excited state results in the transfer of a non-bonding electron from the nitrogen atom into the -system of the chromophore, resulting in a biradical charge-separated state. The radical cation centered on the nitrogen therefore possesses the valency necessary for mesolysis. As shown in Scheme 2 mesolytic cleavage results in the formation of a radical and a cation, with the ultimate location of these species dependent on their respective stabilities, i.e. nitroxide radical and carbocation versus oxoammonium cation and carbon-centered radical. In these situations, it is unclear if the propagating species and nitroxide can recouple to reform the dormant species. However, it is likely that if a carbon centered radical is formed, the zwitterionic nitroxide fragment could relax back to a nitroxide allowing controlled radical polymerization to proceed. If, however, a carbocation is formed, cationic polymerization may occur with fate of the nitroxide radical anion dependent on protic impurities.

Scheme 2. Alternative homolysis (black) and mesolysis (blue) pathways demonstrated for an azaphenlane. Mesolytic cleavage can result in either a carbocation or a carbon-centered radical depending on their relative stabilities and those of the nitroxide and oxoammonium.

Interestingly, the local [NO-R] •+ environment in the state directly resembles that of formally oxidized alkoxyamines, which have recently been shown to undergo mesolytic cleavage. Experiments have shown that the exact specific cleavage behavior depends on the leaving group and the presence or absence of nucleophiles including coordinating solvents such as acetonitrile (see Scheme 3). [START_REF] Hammill | Effect of Chemical Structure on the Electrochemical Cleavage of Alkoxyamines[END_REF][START_REF] Noble | Mechanism of Oxidative Alkoxyamine Cleavage: The Surprising Role of the Solvent and Supporting Electrolyte[END_REF][START_REF] Norcott | An Electrochemically Activated Methylating Agent[END_REF][START_REF] Zhang | Electrochemical and Electrostatic Cleavage of Alkoxyamines[END_REF] As seen in Scheme 3, in the oxidized species at least, cleavage to a carbon-centered radical is expected for acrylate and methacrylate polymerizations, but not for styrene which will produce carbocations. [START_REF] Hammill | Effect of Chemical Structure on the Electrochemical Cleavage of Alkoxyamines[END_REF] Summing up, while it has been assumed until now that PNMP proceeds via energy transfer and standard homolytic cleavage, the possibility of mesolytic cleavage and its implications has not been explored. If it occurs, this has significant implications for the success or failure of PNMP as it can lead to species other than carbon-centered propagating radicals being produced. In this work we use computational chemistry to study the cleavage pathways in two key PNMP families, azaphenalenes (1) and benzophenone-based nitroxides (2), with a view to better informing reagent design.

+ R + R 3 1 or 3 N O R + R MESOLYSIS HOMOLYSIS hv n N π* ππ* N O R N O N O N O N O R N O R N O R oxidation N O + R N O + R N +

Scheme 1. Test set considered

COMPUTATIONAL METHODOLOGY

All electronic structure calculations were performed with density functional theory (DFT) or its excited state extension, timedependent DFT (TD-DFT), using the Gaussian 16.C01 software package. [START_REF] Frisch | Gaussian 16 Revision C[END_REF] The M06-2X functional [START_REF] Zhao | The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Function[END_REF] was used for both types of calculation, as it has been shown to perform well when describing free-radical processes, and the excited states of organic chromophores. The 6-31+G(d,p) basis set was employed for all calculations, and the SMD universal solvent model [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] was used for solvent-phase electronic energies. The solvent used was ethyl ethanoate, as it is a solvent that will exhibit similar properties to that of bulk acrylate monomer. TD-DFT was chosen for investigating the excited states of the alkoxyamines as multireference calculations, requiring a large active space that includes , and , and orbitals for a proper description of the dissociation pathways, are too expensive for these systems. M06-2X has, however, been shown to give good agreement with respect to predicting the ordering of states of differing symmetries, as well as at predicting singlet-triplet gaps. [START_REF] Jacquemin | Assessment of Functionals for TD-DFT Calculations of Singlet-Triplet Transitions[END_REF] Whilst accurate excited state free energies are not possible with TD-DFT, enough information about the character and therefore reactivity of the excited states is possible.

RESULTS AND DISCUSSION

Azaphenalenes (1). To explore the likelihood of homolytic versus mesolytic cleavage, TD-DFT calculations were first used to construct Jablonski diagrams for a family of 6azaphenalenes (Figure 1). 6-Azaphenalenes have been shown to be effective PNMP agents for styrene polymerization, but not for (meth)acrylates, though this latter result was attributed to side reactions rather than problems in the photodissociation. In the present work styrene, methyl acrylate and methyl methacrylate were modelled using unimeric R-groups of styrene (STY), ethyl propanoate (EP) and ethyl isobutyrate (EIB), respectively. Qualitative results for each of the three leaving groups are shown in Figure 2; the low-lying states are localized to the chromophore and the character of these states are found to be independent of the R-group, and the vertical excitation energies change only minimally. In the azaphenalenes, the first singlet excited state is a transition centered on the chromophore. However, the accompanying triplet state nearest in energy (average ES-T( ) = -0.07 eV between R-groups) is also, of character rather than character. Intersystem crossing between the singlet and triplet states of the same symmetry does not occur, [START_REF] Mcnaught | Compendium of Chemical Terminology[END_REF] and so the reactive 3 ππ* state is inaccessible. Thus, populating the bright 1 ππ* would not result in any reaction, as the valency around the nitroxide moiety will remain unchanged. Instead, for dissociation to occur, only mesolytic cleavage from S3 (average ES-T( ) = -0.05 eV) is available. In the azaphenalene derivatives, population of the dark state is likely possible by first populating the bright S4( ) state which lies relatively close in energy to the S3( ) state (average E = +0.3 eV). As a result, mesolysis, if it occurs, is the only possible reactive outcome in this family of reagents. While TD-DFT is sufficiently reliable to draw this qualitative conclusion, it is not sufficiently accurate for predicting quantitative reaction energies. As described above, accurate alternatives such as multireference methods are cost prohibitive for these large systems. To qualitatively assess the likely mesolytic cleavage behavior we can instead examine the ground state formally oxidized species. Figure 3 shows the computed bond dissociation Gibbs free energies for mesolytic cleavage to a nitroxide radical and a carbocation, and cleavage to an oxoammonium and a carboncentered radical. From Figure 3, it is seen that the styrenederivative of oxidized 6-azaphenalene prefers to undergo cleavage to a carbocation, while the (meth)acrylates prefer to cleave to a radical. Moreover, the energetic cost of cleavage is least for the styrene leaving group and most for the acrylate leaving group, as one might expect based both radical and carbocation stability considerations. This is consistent with experimental observations for the oxidative cleavage of the corresponding TEMPO-based analogues. [START_REF] Hammill | Effect of Chemical Structure on the Electrochemical Cleavage of Alkoxyamines[END_REF][START_REF] Noble | Mechanism of Oxidative Alkoxyamine Cleavage: The Surprising Role of the Solvent and Supporting Electrolyte[END_REF][START_REF] Norcott | An Electrochemically Activated Methylating Agent[END_REF][START_REF] Zhang | Electrochemical and Electrostatic Cleavage of Alkoxyamines[END_REF] If the results above were to apply also to corresponding the excited state mesolytic cleavage, it would suggest styrene actually undergoes photoinitiated cationic polymerization with this PNMP agent (which would still be consistent with the observed control), and the acrylates in particular struggle to undergo cleavage at all, which could help to explain the failed experiments with this monomer. While most of the trends in the calculations of Figure 3 would be mirrored in the excited state mesolysis energies, there are two important differences: (1) the excited states are higher in energy and this additional energy can help to overcome the otherwise unfavorable Gibbs free energies requirements;

(2) the chromophore bears a remote negative charge which is able to electrostatically interact with the nitroxide functionality. This latter effect would preferentially stabilize the oxoammonium over the nitroxide and systematically reduce the mesolytic cleavage energies for carbon-centered radical production.

In order to assess the potential impact of the negative charge that will be present in the charge-separated, biradical excited state, a negatively charged BF4 ion was introduced to the azaphenalene-styrene radical cation system. The difference in reaction free energies for styrene/azaphenalene radical/cation formation with and without the BF4 salt is shown in Table 1. Table 1 clearly shows how the electrostatic interaction between the negative BF4 salt and positive radical cation stabilizes the formation of the oxoammonium and styrene radical. One could consider the formally oxidized species, and the zwitterionic BF4 salt as limiting cases, with the true behavior somewhere in between the two. While quantitative results are not possible without prohibitive multireference calculations, one can conclude that mesolysis is the only available pathway for these systems. For (meth)acrylates carbon-centered radicals are preferred over carbocations, while for styrene the two pathways are in reasonably close competition and cations should not be ruled out. Indeed, examining the excited states from TD-DFT highlights some clear differences between the benzophenone and azaphenalene derivatives. In Figure 2, TD-DFT predicts singlet and triplet states of the same symmetry close in energy, suggesting that ISC to the triplet manifold would be uncompetitive, relative to reactivity from the singlet states. In Figure 4, however, this is not the case, with singlet and triplet states of different symmetries predicted to be near degenerate in energy. In contrast to azaphenalene derivatives, this would allow for efficient population of low-lying triplet states, resulting in triplet photoreactivity like that of acetophenone. As well as this, population of the [START_REF] Matyjaszewski | Controlled/Living Radical Polymerization[END_REF] state, which would possess the correct valency for mesolysis, is:

1. Difficult to populate, due to the transition being symmetry-forbidden and no other singlet states being close in energy (slow internal conversion) 2. Likely unreactive; Figure 5 shows the BDFEs for mesolysis of the formally oxidized benzophenone derivatives suggests that even upon oxidation, cleavage to either a nitroxide or oxoammonium is unfavourable (except for with styrene as an R group).

Summing

up, in contrast to the azaphenalenes, for the benzophenone derivatives the triplet ππ* state can be populated, while the nNπ* state is difficult to populate and likely to be in any case unreactive. Hence triplet reactivity and bond homolysis, rather than mesolysis, is the preferred pathway for these systems.

CONCLUSION

Theoretical calculations have been performed which highlight the potential role of mesolytic cleavage in describing the cleavage pathways of photoactive NMP agents. Mesolytic cleavage can be used to explain the monomerdependent performance of PNMP. The radical rearrangement upon mesolytic-like cleavage can regenerate the nitroxide radical (when mesolysis produces R • ) or the hydroxyamine (when mesolysis produces R + ). However, analogous to Type II photoinitiators such as anthraquinones, electron transfer reactions with additives (or impurities) such as amines, halides and so forth can compete, and negatively impact the radical-radical recombination required for "living" polymerization reactions.

The consequences of this study are as follows:

1. Conjugation between the nitroxide and chromophore moieties appears to facilitate homolysis, due to the ideal alignment of singlet and triplet states of different symmetries. However, it must be noted that such conjugation can also promote side reactions such as N-O homolysis or beta-fragmentation (on the second alkyl group bearing by the nitroxide).

2. When there is no conjugation between the nitroxide and the chromophore, a lowlying, charge-separated excited state is accessible, which possesses the valency around the nitroxide to undergo mesolytic, rather than homolytic cleavage.

The choice of monomer remains

important when designing PNMP agents: as with thermally-initiated NMP, acrylate derivatives still suffer with side-reactions and poor "living" behavior.

4. The mesolytic pathway may lend itself to other synthetically useful photoreactions, outside that of NMP applications, analogous to our recent use of formally oxidized alkoxyamines as in situ methylation agents. [START_REF] Norcott | An Electrochemically Activated Methylating Agent[END_REF] ASSOCIATED CONTENT

Figure 1 .

 1 Figure 1. A simplified Jablonski diagram showing the photochemical processes leading to homolytic cleavage and the competing non-reactive relaxation processes.

Scheme 3 .

 3 Scheme 3. Effect of R on the oxidation behavior of TEMPO-based alkoxyamines. Included among the R groups are models of the propagating species in polymerizations of vinyl acetate (VA,

Figure 2 .

 2 Figure 2. Simplified Jablonski diagram for azaphenalenes functionalized with R groups shown in Scheme 1. The characters of the lowlying states are found to be independent of the R group, as they are localized on the azaphenalene moiety. Radiative processes are

Figure 3 .

 3 Figure 3. Bond dissociation Gibbs free energies for the (ground state) oxidized 6-azaphenalenes, showing results as a function of leaving group for mesolytic cleavage to a nitroxide radical and a carbocation, and cleavage to an oxoammonium and a carbon-centered radical.

Figure 4 .

 4 Figure 4. Simplified Jablonski diagram for Rfunctionalized benzophenone derivatives.

Figure 5 .

 5 Figure 5. Bond dissociation Gibbs free energies for cleavage of oxidized benzophenone nitroxide and oxoammonium species.

  CH 2 OCOCH 3 ), styrene (STY, CH(CH 3 )Ph), methyl acrylate (MA, C(CH 3 )COOCH 3 ), methyl methacrylate (MMA, C(CH 3 ) 2 COOCH 3 ), and acrylonitrile (AN, CH(CH 3 )CN).

		Nu:	N O
			+ NuR
	reduction
			coordinating solvent,
			electrolyte or added
	R+, R• unstable
			nucleophiles
	e.g. n-alkyl, VA
			OR
	stable R+	R+ unstable / R• stable	R+, R• unstable / OR+
			stable

SN2 e.g. t-Bu, STY e.g. MA, MMA, AN e.g. Ph

Table 1 .

 1 Reaction free energies (kJ mol -1 ) for azaphenalene-styrene mesolysis with and without BF 4 present

	Product	STY radical	STY cation	G 0 rad-cat
	No BF 4	+35.0	-12.5	+47.4
	With BF 4	+55.7	+70.5	-14.8
	Benzophenone	Derivatives	(2).	The
	benzophenone-based alkoxyamines have been
	shown to initiate photopolymerization of n-
	butyl acrylate with partial living character. In
	contrast	to	the	azaphenalenes,	the
	chromophore is directly bonded to the
	nitroxide moiety making them a better
	candidate for direct homolysis via energy
	transfer.

Funding Sources

Australian Research Council (CE140100012, FL170100041)