S M Wahidur Rahaman

Krzysztof Matyjaszewski

Rinaldo Poli

S M Wahidur

Cobalt(III) and copper(II) hydrides at the crossroad of catalysed chain transfer and catalysed radical termination: a DFT study

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Cobalt(III) and copper(II) hydrides at the crossroad of catalysed chain transfer and catalysed radical termination: a DFT study

Introduction

Reversible deactivation radical polymerization (RDRP), 1 in which metal mediated methods occupy a prominent place, is now dominating macromolecular engineering. [START_REF] Matyjaszewski | Macromolecular Engineering: Precise Synthesis, Materials Properties, Applications[END_REF] In ATRP, which is the dominant method within this area, [START_REF] Matyjaszewski | [END_REF][4][5][6][7] the active radical (Pn • ) concentration is controlled by a dynamic equilibrium (Scheme 1) where an atom (typically a halogen, Y) is transferred to the radical from a suitable metal complex Y-Mt x+1 /L, generating a halogen-capped dormant chain Pn-Y and a reduced metal complex Mt x /L.

Although mechanistically simple, this process may however be accompanied by a number of side reactions 5,8 that could negatively affect the polymerization control, in some cases even driving the system toward complete failure. [9][START_REF] Poli | Polymer Science: A Comprehensive Reference[END_REF][START_REF] Poli | [END_REF] Most of these side reactions involve the direct interaction of the active radicals with the reduced metal complex. There are three important ways in which a metal complex can react with radicals, as shown in Scheme 2. The first one is to form a direct metal carbon bond, i.e. an organometallic dormant species Pn-Mt x+1 /L. If this process is reversible and not contaminated by other phenomena, it constitutes an alternative mechanism to control the polymerization (organometallic-mediated radical polymerization, OMRP). [9][START_REF] Poli | Polymer Science: A Comprehensive Reference[END_REF][START_REF] Poli | [END_REF][12][13][14] The second possibility involves an electron transfer and reduction ((or oxidation) of a radical to carbanion (or carbocation) and associated side reactions. [15][16][17] Another way in which the same two partners can interact is by transfer of a β-H atom to yield the hydride complex H-Mt x+1 /L and a dead chain with an unsaturated chain end, Pn (-H) . When this occurs, the hydride complex may be able to subsequently transfer the H atom back to a monomer, completing a catalysed chain transfer (CCT) cycle. Cobalt(II) complexes are currently the most efficient catalysts for CCT. 18 An alternative way to obtain the same hydride intermediate is by β-H elimination from the Scheme 1. ATRP controlling mechanism. Please do not adjust margins Please do not adjust margins organometallic dormant chain, a well-known process for certain metals able to catalyse coordination polymerization. [START_REF] Collman | Principles and Applications of Organotransition Metal Chemistry[END_REF] The hydride intermediate H-Mt x+1 /L and the organometallic dormant chain Pn-Mt x+1 /L, however, may also interact with a new radical chain (Pm • ). The former leads, through either an H atom transfer process (Pm (H) , regenerating the reduced complex. The latter leads, by a similar process, to a coupled dead chain Pn-Pm. In addition, associative radical exchange processes involving the organometallic dormant species are responsible for controlled radical polymerization by degenerative transfer. [START_REF] Lu | [END_REF][21][22] The two processes leading from H-Mt x+1 /L or Pn-Mt x+1 /L to dead chains (Pm (H) +Pn (-H) or Pn-Pm) and regenerating Mt x /L constitute catalysed radical terminations (CRT). The CRT phenomenon has recently been discovered as a side reaction in Cu-catalysed ATRP and takes place extensively also when radicals are generated from a conventional initiator (OMRP conditions) rather than from an organic halide (ATRP conditions). 23,24 It has also been later shown to play a role in Fe-catalysed ATRP. 25 The current evidence is in favour of the hydride complex, rather than the organometallic dormant species, being the key intermediate for CRT. This is shown by the dominant formation of Pn (-H) + Pm (H) dead chains (resembling disproportionation) in Cu-CRT for methyl acrylate, 24 whereas polyacrylates have a natural preference to terminate by coupling in free radical polymerization. [START_REF] Moad | The Chemistry of free Radical Polymerization[END_REF] The above described results show that the hydride complex H-Mt x+1 /L lies at the crossroad of the CCT and CRT catalytic cycles. While the operating conditions (monomer and metal concentrations, radical flux) are similar, the hydride intermediate H-Co III /L generated by an initiator/Co II system prefers to react with monomer, leading to CCT, whereas the hydride intermediate H-Cu II /L generated by an initiator/Cu I system (or the H-Fe III /L intermediate generated by an initiator/Fe II system) prefers to react with radicals, leading to CRT. To the best of our knowledge, no Cu-CCT process has ever been reported whereas the CRT process has so far not been evidenced in the presence of cobalt complexes. This surprising dichotomy has stimulated us to carry out DFT calculations in an attempt to rationalize the different behaviour of the two metal systems. The goal of the present study is to better understand what factors promote CRT and whether it is possible to engineer system where this phenomenon is suppressed or eliminated, thus improving the ATRP performance. Suppression of CRT may also allow to improve the performance of OMRP systems.

Results

(a) Systems and methods selected for the investigation

Comparative calculations of OMRP equilibrium, CCT and CRT energy profiles were carried out for two systems, one based on cobalt(II) and the other one based on copper(I). The three processes are intertwined as illustrated in Scheme 3, which is a simplified version of Scheme 2. On the left, the reversible radical trapping by Mt x /L leads to the organometallic dormant species. The competitive β-H atom transfer process involving the same two partners (middle) generates the key hydride intermediate H-Mt x+1 /L and olefin. The reverse H atom transfer from the hydride complex to the olefin completes the CCT process. On the right, the hydride complex transfers the H atom to a radical to complete the CRT process. The generation of the hydride complex by β-H elimination from the OMRP dormant species has not been considered because this typically occurs for organometallic complexes that can offer a cis open coordination site and that are able to bind the produced olefin. [START_REF] Collman | Principles and Applications of Organotransition Metal Chemistry[END_REF] This is not the case for the systems of interest here. It is also pertinent to mention that a β-H elimination from an OMRP dormant species was proposed to be responsible for CCT in a Fe II -catalysed ATRP or styrene, [START_REF] Shaver | [END_REF]28 but subsequent computational work has indicated that the preferred pathway to CCT is in fact the direct β-H atom transfer from the radical chain to the Fe II catalyst. 29 Finally, on the basis of the evidence discussed in the introduction, the possible CRT via the OMRP dormant species has not been considered in the present investigation. For this process to occur, it would be necessary that the dialkyl intermediate Mt x+2 (Pn)(Pm)/L has the two chains placed in cis positions and this is certainly not possible, at least for the cobalt porphyrin systems which undergoes rapid degenerative exchange when Pn-Mt x+1 /L finds itself in the presence of excess radicals.

Methyl acrylate was initially chosen as the common monomer, with the dormant chain modelled by the CH3(COOCH3)CH • radical, namely replacing the polymer chain beyond the radical carrying chain-end unit with a hydrogen atom. This monomer choice does not appear the most appropriate one to probe the CCT activity of cobalt systems, Scheme 2. Possible interactions between an active radical and a reduced metal complex.

Scheme 3. Investigated reaction coordinate.

Please do not adjust margins

Please do not adjust margins because acrylates are not the monomers leading most easily to CCT (relative to e.g. methacrylates and styrene). 18 This phenomenon is attributed to the stronger bond established between the acrylate radical and cobalt (OMRP dormant species), thus leaving a lower equilibrium amount of the Co II /L catalyst to operate the CCT process. Indeed, a living chain growth controlled by the OMRP equilibrium is often observed for these monomers using cobalt complexes. 30,31 On the other hand, acrylates are the monomers most readily involved in CRT with copper catalysts. It is important to compare the energy profile of the CCT and CRT for two representative metal complexes using the same radical species. Selected studies, however, were also carried out for the porphyrin system with the (CH3)2(COOCH3)C • radical as a model of the methyl methacrylate polymer chain, even though the reactivity of the isobutyrate radical is quite different from the PMMA radical, due to a strong penultimate effect. 32 The two metal complexes were selected in order to be both representative and manageable in terms of computational time. The chosen cobalt system is [Co(porphyrin)] (A in Scheme 4), since porphyrinato derivatives of cobalt(II) are commonly used in radical polymerization. 30,31,33,34 The most successful complexes, leading to OMRP with acrylate monomers and CCT for methacrylate monomers, contain substituents on the pyrrole C3 and C4 positions or on the methine bridges, such as for instance tetramesitylporphyrin (TMP). However, removing the ring substituents is not considered to introduce a strong electronic perturbation while greatly reducing the computational effort. The same simplification was adopted in previous computational studies of the [Co(porphyrin)] system. 35,36 It should also be underlined that these previous studies have addressed the OMRP equilibrium 35 and the β-H atom transfer (CCT) equilibrium 36 for a different radical species (CH3(OAc)CH • , modelling the PVAc growing radical chain), but did not investigate the CRT process. Selected calculations have also been carried out on the full (TMP)Co system using the QM/MM methodology, treating the four mesityl groups at the molecular mechanics level.

The selected copper system is [Cu(TPMA)] + (B in Scheme 4, TPMA = tris(2-pyridylmethyl)amine), since this complex gives CRT for methyl acrylate. 24 Thus, this calculation presents no simplifications of the real system. In addition, B is also a simplified model of the [Cu(TPMA*)] + complex (TPMA* = tris((4methoxy-3,5-dimethylpyridin-2-yl)methyl)amine), which also has CRT activity for methyl acrylate. 23 All calculations were carried out using the BP86 functional, which was also employed in the already mentioned previous [Co(porphyrin)] computational study 35,36 and found much more adapted than the more popular B3LYP functional. However, rather than adopting the same strategy of the previous study, which employed a low-quality basis set for optimizations followed by single point calculations with an improved basis set, we carried out optimizations directly with a high quality basis set constituted by 6-311G(d,p) functions for the light atoms (O,N,C,H) and LANL2DZ(f) for the metal atoms (Co, Cu). The electronic energy values were corrected for ZPVE, thermal (PV, TS), solvent and dispersion effects. Views and Cartesian coordinates for all optimized structures are available in the SI (Table S1).

(b) Optimized minima

The optimized geometries of the two Mt x /L complexes are shown in Figure 1. The cobalt complex was optimized in the experimentally well-established doublet state, 37 whereas the copper complex is diamagnetic.

Addition of the CH3(COOCH3)CH • (R • ) radical leads to the formation of the OMRP dormant species, represented in Figure 2. The R-Co III complex is diamagnetic, as well established for a number of 5-coordinate organocobalt(III) species, for instance Co(TMP)(CH2tBu). 38 The geometry of the spin doublet R-Cu II product is pseudo-trigonal bipyramidal, as observed for the related [Cu(TPMA)X] + complexes (X = Cl, Br; 39 no alkyl derivatives of this type have been isolated).

The calculated ΔG 0 298 for the Co-R bond breaking process, with all corrections included, is 21.6 kcal/mol, whereas the value related to the Cu-R bond is much weaker, 14.5 kcal/mol, see Figure 3 Please do not adjust margins Please do not adjust margins the MA polymerization but without a sufficient level of control. 23,40 From the computational point of view, it should be underlined that while the solvation correction makes a relatively small and weakening contribution to the homolytic bond strengths (-4.1 and -2.1 kcal/mol for the Co and Cu system, respectively), the dispersion interaction correction makes a very large strengthening contribution (+19.4 and +14.2 kcal/mol, respectively). The value calculated here for [(porphyrin)Co-CH(CH3)(COOCH3)] may be compared with 22.8 kcal/mol calculated using the same functional for the homolytic dissociation of [(porphyrin)Co-CH(CH3)(OCOCH3)], though without solvent or dispersion correction and for the gas phase standard state. 35 Given that these corrections have the overall effect of increasing the dissociation energy, the comparison is consistent with the notion that the more stabilized methyl acrylate-related • CH(CH3)(COOCH3) radical forms weaker bonds than the vinyl acetate-related • CH(CH3)(OCOCH3) radical. 41 The Co-C BDE was also calculated, at the same level of theory, for the • C(CH3)2(COOCH3) (methyl methacrylate-related) radical, yielding 14.8 kcal/mol when all corrections are included (dispersion and solvent PCM in MMA). This is much weaker than the bond to the methyl acrylate-related radical (21.6 kcal/mol), as expected.

The reaction coordinate that ultimately transfers the radical β-H atom to the metal atom starts with the establishment of a van der Waals [L/Mt x •••H-CH2-CH • (COOMe)] adduct. The optimized geometry of this adduct gives a slightly higher Gibbs energy for the Co(porphyrin) system (1.1 kcal/mol relative to the two separate components). For the above mentioned related Co(porphyrin) + • CH(CH3(OAc) system, 36 a similar energy minimum was also optimized and found (ΔG = -2.66 kcal/mol relative to the separate species in the gas phase). Like for that system, this adduct gave a closed-shell singlet solution, even though the geometry was optimized as a broken symmetry open-shell singlet. This shows that complete quenching of the two radicals spin density has already taken place at the level of this adduct. The C-H and H-Co distances, highlighted in the detailed image of Figure 4 (left), illustrate that extensive C-H bond stretching has taken place and that the H-Co separation is already rather close to that of the final hydride product (vide infra). The corresponding optimized van der Waals adduct for the Cu system, on the other hand, exhibits a rather loose interaction between the C-H bond, which is only slightly elongated relative to the other C-H bonds (see excerpt in Figure 4, right), and the copper atom. The energy is essentially unchanged relative to the sum of the two separate species (-0.5 kcal/mol), even less so than for the Co(porphyrin system). The spin density in this adduct is almost entirely localized on the organic fragment (0.809 on the C atom and 0.163 on the carbonyl O atom) with only 0.04 being transferred to the Cu atom.

The product of the β-H atom transfer to Mt x /L, namely the hydride complex H-Mt x+1 /L, has the same basic geometry of the OMRP dormant species, see Figure 5. The optimized Mt x+1 -H distances are 1.412 Å for the Co III system and 1.551 Å for the Cu system. Relative to the Mt x /L precursor, the hydride systems are less stabilized than OMRP species. This is because whereas the OMRP species is generated by a simple Mt-C bond formation process, formation of the Mt-H bond in the examined process is accompanied by the bond breaking of a strong C-H bond, which is partially compensated only by the formation of a weaker C-C π bond. Like for the generation of the OMRP species, the process is less energetically favourable for the [Cu(TPMA)] + system than for the [Co(porphyrin)] system, see Figure 3. There is a greater difference in favour of the cobalt system for the CCT process (14.8 kcal/mol) than for the OMRP trapping process (7.1 kcal/mol). The most relevant consequence of this phenomenon is that the H atom transfer process is close Please do not adjust margins Please do not adjust margins to thermoneutral for the [Co(porphyrin)] system while it is significantly endothermic for the copper system. In the previous study of the β-H atom transfer process to [Co(porphyrin)] the reaction was also calculated as exothermic (-5.1 kcal/mol from the • C(CH3)2(CN) radical and -13.6 kcal/mol from the • CH(CH3)(OCOCH3) radical). 36 In this case, both solvation (-1.7 kcal/mol) and dispersion (+0.2 kcal/mol) effects are very small since the process involves two molecules on each side.

(c) CCT transition state

The optimized transition state of the β-H atom transfer process is represented in Figure 6. The H-atom transfer for the [Co(porphyrin)] system occurs smoothly, with an activation barrier of only 2.2 kcal/mol on the G scale for the forward process (generation of the hydride intermediate) and 2.9 kcal/mol for the backward process. As also previously found for the corresponding calculation on the Co(porphyrin)/ • CH-(CH3)(OAc) system 36 and by analogy to the van der Waals minimum described above, the broken symmetry open-shell minimum optimization led to a closed-shell singlet solution, with a spin density of essentially zero on every atom. Compared to the optimized geometry of the van der Waals adduct, the C-H bond is further stretched and the Co-H bond is almost fully formed (see the close-up image of Figure 6, left) but the changes are minimal. The β-H atom transfer transition state leading to the (porphyrin)Co-H intermediate was also optimized when involving the methacrylate related radical • C(CH3)2(COOCH3), yielding an even lower barrier (0.3 kcal/mol). This agrees with the great propensity of methyl methacrylate to undergo CCT.

On the other hand, the barrier is much greater for the [Cu(TPMA)] + system, in the forward direction (19. 6, right). The Mt-H bond lengthening on going from the hydride complex to the transition state is actually greater for the cobalt system (Δd = 0.069 Å) than for the copper system (Δd = 0.038 Å). However, this bond lengthening is compensated by a much greater degree of C-H bond forming in the cobalt case (C•••H = 1.596 Å) than for the copper case (C•••H = 1.959 Å, vs. a C-H bond distance of 1.107 Å in the radical product). The spin density related to the single unpaired electron in the copper system is delocalized essentially on the Cu centre (0.383), on the transferring H atom (0.283) and on the α-C atom that eventually carries the spin density in the radical product (0.223).

(d) Hydride quenching along the CRT pathway

One possible hypothesis to rationalize the preference of the cobalt system for H atom transfer to olefin (monomer) rather than to radical is to imagine that the latter process involves a greater barrier, while the opposite preference (greater barrier to transfer to monomer than to radical) would occur for the copper hydride intermediate. However, a partial optimization scan for the two systems indicates that the H atom transfer to radical is electronically barrierless in both cases (Figure 7). It is interesting to note that the hydride-radical interaction develops at an earlier stage along the transfer coordinate for the copper system, a significant energy gain being already evident at a C•••H distance > 2 Å (e.g. 7.8 kcal/mol at 2.44 Å and 23.7 kcal/mol at 1.94 Å). For the cobalt system, on the other hand, the energy is lowered by < 4 kcal/mol at a distance of 2 Å.

For the cobalt system, the global spin state along this specific reaction coordinate is ½, with the unpaired spin being transferred from the free radical, which becomes the diamagnetic alkane product, to the diamagnetic hydride complex, which regenerates the spin doublet [Co(porphyrin)] catalyst. A Mulliken analysis shows the gradual transfer of the spin density from the C atom (for the hydride + radical combination at long C•••H distances) to the cobalt atom (for the catalyst + alkane combination at short C•••H distances).

For the copper system, the spin state is also invariable from beginning to end: spin zero for the antiferromagnetic

Please do not adjust margins

Please do not adjust margins combination the spin doublet hydride and organic radical on one side and for the copper(I) catalyst and alkane products on the other side. However, the antiferromagnetic combination of the two radicals required the entire scan to be explored in broken symmetry. Indeed, the restricted spin zero calculations for long C•••H distances only yielded charge transfer excited states. At infinite distance, the hydride complex has the majority of the spin density on the Cu atom (-0.691) and on the hydridic H atom (-0.291) whereas the radical has the majority of the spin density on the C atom (+0.858), the rest being delocalized on the carboxylic function. When the two species are still quite separated from each other (C•••H = 3.04 Å), the spin density is already significantly decreased (Cu, -0.393; H, -0.283; C, +0.717). At a C•••H distance of 2.44 Å, all the spin density is already completely quenched with < 0.001 remaining on the Cu and the C atoms.

Figure 8 shows the geometries of the two systems at approximately the same C•••H distance. The Mt-H bond lengthening relative to the optimized hydride complex is quite comparable for the two metal systems (Co: 1.470 Å, Δ = +0.058 Å; Cu: 1.612 Å, Δ = +0.061 Å), although the energetic stabilization is quite different has shown in Figure 7. This is likely related to the spin density quenching process.

The hydride quenching for the Co(porphyrin) model was also explored with the • C(CH3)2(COOCH3) radical, a model of the methyl methacrylate growing chain for which the highest CCT activity is experimentally observed for this catalyst family. No CRT has so far been reported for Co(porphyrin)-type CCT catalysts. It is therefore of interest to probe whether the introduction of a second methyl group on the radical carrying C atom would introduce a sterically related barrier, hampering the H atom transfer to radical. However, as shown in Figure 7, the energy profile for the Co(porphyrin)/ • C(CH3)2(COOCH3) system is essentially identical to that of the Co(porphyrin)/ • CH(CH3)(COOCH3) system. At a C-H distance of 2.0 Å (see view in Figure 9), the Co-H bond lengthening is identical to that observed for the acrylate-related radical (1.470 Å, Δ = +0.058 Å).

Finally, wondering whether the lack of CRT could be related to the steric impediment of the porphyrin ring substituents, we have carried out calculations of the CRT hydride quenching step for the full (TMP)Co-H molecule. Given the considerable size of the molecule, the four mesityl substituents were handled at the molecular mechanics level in a QM/MM approach. This methodology is nevertheless able to capture any existing steric effect. The results of the calculations, also shown in Figure 7, indicate however that the energy curve follows exactly the same trends of the • CH(CH3)(COOCH3) and • C(CH3)2(COOCH3) radical approaches to the simplified Co(porphyrin) model. For the fixed C-H distance of 2.0 Å (Figure 9), the Co-H bond lengthening is only marginally smaller (1.467 Å, Δ = +0.055 Å) than those of the acrylate and methacrylate related radicals at the same C-H distance. This indicates that four mesityl groups do not introduce a significant steric effect on the putative hydride quenching pathway. The introduction of the mesityl groups imposes a slight corrugation of the porphyrin ring, which is found also in the fully optimized (TMP)Co III (H) molecule and is essentially independent on the C-H distance along the CRT hydride quenching pathway.

Discussion

Comparison of the OMRP/CCT/CRT energy profiles involving either the [Co(porphyrin)] or the [Cu(TPMA)] + systems (Figure 3) is not sufficient to fully rationalize their different behaviour under OMRP conditions. In particular, it is well known that [Co(porphyrin)]-type systems are efficient chain transfer catalysts under conditions where the hydride intermediate is in the simultaneous presence of monomer and radicals and a CRT phenomenon has not yet been reported for this metal. The profile in Figure 7, however, suggests that once the hydride complex is generated, its quenching by an additional radical should occur very favourably to yield a CRT process, even though the H transfer to monomer to complete the CCT cycle is also facile. The analysis of the same quenching pathway upon introduction of steric bulk in the radical (e.g. going from the acrylate to the methacrylate related radical) or in the porphyrin ring (going to the real TMP ligand) do not significantly alter the CRT hydride quenching pathway and notably do not introduce a sterically related electronic barrier. The only expected free energy barrier is entropic, mostly related to the loss of translational and rotational degrees of freedom upon association of the two separate partners and is therefore expected to be substantially similar for all investigated systems (Figure 7).

However, there is a kinetic factor to be kept in mind. The two competitive processes that lead to consumption of the hydride intermediate should follow the rate laws: transfer to olefin (CCT): kCCT[H-Mt x+1 /L][R (-H) ]; (1) Although the activation barriers may be in favour of the CRT process (kCRT > kCCT), at least for the copper system, the concentrations are very much in favour of CCT ([R (-H) ] >> [R • ]). Considering that the CCT barrier is quite small for the cobalt system and should be even less effected by steric encumbrance in the porphyrin ring and in the radical relative to the CRT barrier (the H atom transfer involves a more accessible sp 2 C atom in the monomer), the efficiency of the cobalt system as a chain transfer catalyst appears qualitatively rationalized.

We also have to take into consideration that a minor contamination of the CCT activity with a catalysed termination would remain undetected, because the Pn (-H) chains (unsaturated chain ends) generated by disproportionation are common to the CCT process and the Pn (H) chains (saturated chain ends) may also be generated by the spontaneous (noncatalysed) radical terminations. Hence, it is quite possible that the CRT process indeed occurs also for cobalt systems, but only to a small extent not allowing its clear identification.

Moving now to the more challenging copper system, the energetic profile in Figure 3 shows that generation of the hydride intermediate is slower. More importantly, there is a greater barrier for H atom transfer to olefin, hence this process should also be slower. On the other hand, Figure 7 indicates that H atom transfer to the radical, like for the cobalt system, does not have any barrier and the stabilizing effect develops at greater C•••H distances. Therefore, in the comparative rate expressions for the consumption of the hydride intermediate (equations 1 and 2), the kCRT/kCCT ratio is expected to be much greater in the copper system. In addition, because of the ligand structure and coordination geometry, steric effects in the ligand system are less likely to perturb the CRT pathway and therefore to disfavour it relative to CCT. This is because the H atom is relatively accessible in the trigonal bipyramidal geometry of the [H-Cu II (TPMA)] + complex (see Figure 8) and substitution on the pyridine rings at the 3, 4 and 5 positions in the TPMA* system does not affect the open space around the hydride ligand.

On the basis of these considerations, we may argue on what kind of ligand engineering might allow reducing the impact of CRT in either an ATRP or OMRP process. In ATRP, the dominant metal species is generally the copper(I) complex, unless the redox properties and reactivity of the complex and/or the nature of the polymerized monomer favour the establishment of a strong Cu II -R bond. For instance, in the [Cu(TPMA)] + /MA system, analysed in this contribution, the formation of the OMRP dormant species appears favourable (Figure 3), but the halogen atom transfer also becomes more favoured for very active ATRP catalysts and the dominant species in the system may in fact become a Br-Cu II species. 42,43 Thus, the concentration of CRT catalyst is generally high. One solution to this problem has already been highlighted: 24 while the CRT activity depends on the [Cu I ] concentration (to which the [H-Cu II ] concentration in equation 2 is proportional), the overall rate of ATRP depends on the [Cu I /L]/[X-Cu II /L] ratio, thus lowering the overall catalyst concentration while maintaining the same ratio of reduced and oxidized forms, as in the ARGET-ATRP protocol, 24,[44][START_REF] Matyjaszewski | Proc. Nat. Acad. Sci[END_REF][START_REF] Konkolewicz | [END_REF] allows maintaining a high polymerization rate while decreasing the impact of CRT. In order to further diminish the CRT process, it is necessary to disfavour the formation of the hydride intermediate and especially of the transition state leading to it. Once the hydride intermediate is formed, it may be difficult or impossible to manipulate the ligand coordination sphere in order to force the system to transfer the H atom to monomer (CCT activity) rather than to radical.

Concerning OMRP, copper has so far not shown any useful applications, contrary to cobalt. This also contrasts with the ubiquitous role of copper in ATRP. Early studies have shown that a copper complex, [Cu(R-bipy)2] + (R-bipy = substituted bipyridine), slows down the polymerization of acrylates but does not insure any reasonable level of control. 40 The same occurs for [Cu(TPMA)] + and [Cu(TPMA*)] + . 23,24 Hence, the Cu I catalyst concentration remains relatively high and extensive CRT can take place under these conditions. The reasonable question to ask is whether OMRP with Cu complexes has a potential under any circumstances. The attempts to use copper complexes under OMRP conditions have so far been limited to reactive monomers (such as acrylates, styrene). Less reactive monomers (e.g. vinyl acetate) should lead to stronger Cu II -C bonds in the OMRP dormant species, [START_REF] Poli | [END_REF] thus the OMRP equilibrium should contribute to lowering the CRT catalyst concentration. Under these conditions, if the activation barrier for the β-H atom transfer leading to the formation of the hydride intermediate remains high, the impact of CRT should decrease and developing a Cu-based OMRP with reasonable control should become possible.

Conclusions

The present DFT study has provided a framework of understanding for the contrasting behaviour of cobalt(II) and copper(I) systems in terms of their catalytic activity, under essentially identical experimental conditions, in competing chain transfer and radical termination processes. For both systems, the two catalytic processes occur via the same hydride species, Co III -H or Cu II -H respectively. In terms of electronic energy, the hydride quenching by radical leading to CRT is barrierless for both systems, although the associative nature of the reaction introduces an entropy related barrier. A significant interaction starts to develop at longer H•••C distances for the copper system because of the spin density quenching between the two radical species. On the other hand, the H transfer to monomer has a relatively high electronic barrier for the Cu system and thus CRT prevails, although the much greater monomer concentration should favour CCT. Conversely, the cobalt system features a low energy hydride intermediate and a very low electronic barrier for H atom transfer to monomer. This is related to the spin quenching process along the conversion of the (porphyrin)Co II /organic radical pair to the combination of hydride and olefin. In combination with the dominant monomer concentration, the resulting energy profile favour CCT activity. The acquired understanding illustrates the necessary conditions for limiting the CRT phenomenon in the Please do not adjust margins Please do not adjust margins application of copper complexes in ATRP and also in the OMRP of less reactive monomers.

  Scheme 4. Molecules used in this study.

Figure 1 .

 1 Figure 1. Optimized geometries of the [Co II (porphyrin)] (left) and [Cu I (TPMA)] + (right) complexes.

Figure 2 .

 2 Figure 2. Optimized geometries of the OMRP dormant species [R-Co III (porphyrin)] (left) and [R-Cu II (TPMA)] + (right), R = CHCH3(COOCH3).

Figure 3 .

 3 Figure 3. Gibbs energy profile (corrected for dispersion and solvation effects) for the investigated reactions. The relative G values are given in kcal/mol.

Figure 4 .

 4 Figure 4. Optimized geometries of the van der Waals [L/Mt x •••H-CH2-CH • (COOMe)] adduct [L/Mt x = Co II (porphyrin), left; Cu II (TPMA) + , right].

Figure 5 .

 5 Figure 5. Optimized geometries of the CCT/CRT hydride intermediate complex, [H-Co III (porphyrin)] (left) and [H-Cu II (TPMA)] + (right).

  3 kcal/mol, in part because of the endothermic transformation) but also in the backward direction (5.2 kcal/mol). This means that the [H-Cu(TPMA)] + intermediate is slower in transferring back the H atom to a new monomer relative to the [H-Co(porphyrin)] intermediate. The bonding details of the C•••H•••Mt moiety in the transition state indicate a slightly longer Cu•••H separation (see the close-up image of Figure

Figure 6 .

 6 Figure 6. Optimized geometries of the β-H atom transfer transition state and close-up of the C•••H•••Mt moiety for the [Co(porphyrin)] (left) and [Cu(TPMA)] + (right) systems.

Figure 7 .

 7 Figure 7. Energy profile for the H atom transfer from the different H-Mt x+1 /L systems to the • CH(CH3)(COOCH3) radical (red, blue and green lines) or to the • C(CH3)2(COOCH3) radical (purple line).

Figure 8 .

 8 Figure 8. Partially optimized geometries (fixed C•••H distance) along the H atom transfer from the H-Mt x+1 /L intermediate to the • CH(CH3(COOCH3) radical. Left: [Co(porphyrin)] system (C•••H = 2 Å); right: [Cu(TPMA)] + system (C•••H = 1.94 Å).

Figure 9 .

 9 Figure 9. Partially optimized geometries (fixed C•••H distance of 2.0 Å) along the H atom transfer from the H-Co(porphyrin) intermediate to the • C(CH3)2(COOCH3) radical at the full QM level (left) and from the H-Co(TMP) intermediate to the • CH(CH3)(COOCH3) radical at the QM/MM level (right).

  adjust margins Please do not adjust margins transfer to radical (CRT): kCRT[H-Mt x+1 /L][R • ]. (2)

  Electronic Supplementary Information (ESI) available: computational details, full table of Cartesian coordinates, energies and views of all optimized geometries. See DOI: 10.1039/x0xx00000x

	a. CNRS, LCC (Laboratoire de Chimie de Coordination), Université de Toulouse, UPS,
	INPT, 205 Route de Narbonne, BP 44099, F-31077, Toulouse Cedex 4, France.
	b. Department of Chemistry, Carnegie Mellon University, 4400 Fifth Avenue,
	Pittsburgh, Pennsylvania 15213, USA.

c. Institut Universitaire de France, 103, bd Saint-Michel, 75005, Paris, France.

J. Name., 2013, 00, 1-3 | 3

J. Name., 2013, 00, 1-3 | 5

J. Name., 2013, 00, 1-3 | 7

Acknowledgements

We thank the CNRS (Centre National de la Recherche Scientifique) for support of this work through the PICS 06782 grant. RP also acknowledges additional support from ANR (Agence National de la Recherche) through the project FLUPOL (grant ANR-14-CE07-0012) and KM acknowledges additional support from the NSF (DMR 1400052). This work was granted access to the HPC resources of CINES and IDRIS under the allocation (2006 through 2015)-086343 made by GENCI (Grand Equipement National de Calcul Intensif) and to the resources of the CICT (Centre Interuniversitaire de Calcul de Toulouse, project CALMIP).


Baptiste Quienne

Rinaldo Poli

Julien Pinaud

Sylvain Caillol

Enhanced aminolysis of cyclic carbonates by β-hydroxyamines for fully biobased polyhydroxyurethanes

Keywords: DFT, reactivity, β-hydroxyamines, cyclic carbonate, polyhydroxyurethanes, biobased polymers

The aminolysis of five-membered cyclic carbonates which results in polyhydroxyurethanes (PHUs) is one of the most promising synthetic pathway to achieve isocyanate-free polyurethanes (NIPUs), one of the main industrial challenges over the coming years. This study highlighted the higher reactivity of β-hydroxyamines toward cyclic carbonate in comparison to classical alkylamines through the determination of their reaction rate constants. The key role of the β-OH substituent in the aminolysis was enlighten by a DFT investigation. Polyfunctional alkylamine and β-hydroxyamine were then used for the synthesis of fully biobased PHU thermosets. The higher reactivity of β-hydroxyamines was confirmed by the gelation time gap between the two formulations studied. After curing, the thermal and thermo-mechanical properties of the thermosets were compared.

Introduction

Polyurethanes (PUs), ranking 6 th among all polymers based on annual worldwide production, are commonplace in everyday life as foams, coatings, adhesives, elastomers, insulation, composites, and so forth. [START_REF] Randall | The Polyurethanes Book[END_REF][START_REF] Tenorio-Alfonso | [END_REF][3] They are present in a wide range of applications due to the numerous industrially available polyols, which allow to cover a large panel of properties. 4,5 However, their synthesis requires the use of isocyanates, known to be harmful for human health and for the environment. 6,7 In order to limit the use of isocyanates, the development of isocyanate-free PUs has emerged over the last decade and has gained increasing attention in both the academic and industrial communities. [8][9][10] Hence, the aminolysis of 5-membered cyclic carbonates, which yields polyhydroxyurethanes (PHUs), is nowadays the most promising and described route to non-isocyanate polyurethanes (NIPUs). [11][12][13][14] This route has the advantage that these carbonates are easily obtained by the carbonation of commercial epoxides. Moreover, this route valorizes CO 2 as a cheap, renewable and non-toxic resource, which makes this pathway the least toxic and most eco-friendly route to NIPU and PHUs. 15- chloroformates for their synthesis. 18,19 However, five-membered cyclic carbonates suffer from lower reactivity compared to isocyanates or larger cyclic carbonates. 20,21 Therefore, the aminolysis of cyclic carbonates has been thoroughly investigated in order to understand and optimize the ring opening reaction. For this reason, the influence of many parameters such as solvent, temperature, catalyst, cyclic carbonate substituents or amine structure has been studied. [22][23][24] However, depending of the final application, the use of solvent or catalyst is not always possible. Therefore, the choice of both cyclic carbonate and amine structures remains a crucial step. Five-membered cyclic carbonates are more reactive when they are substituted by electron withdrawing groups, because of increased electrophilicity of the carbon from the carbonyl group. 25,26 On the other hand, primary amines with NH 2 attached to a primary carbon atom with α or β electron withdrawing substituents are the most reactive amines, while primary aromatic amines and aliphatic ones with NH 2 attached to a secondary carbon atom are the less reactive ones. 27 Furthermore, secondary amines can also react with cyclic carbonates but only at higher temperatures, around 90 °C for the most reactive amines and up to 200 °C for sterically hindered ones. 28 Recently, our team demonstrated the higher reactivity of primary β-hydroxyamines toward epoxy monomers compared to alkylamines. 29 Indeed, 1,2-epoxy-3-phenoxypropane was fully converted with 1-amino-2-butanol after only 20 min at 60 °C in bulk, whereas only 31% was consumed with butylamine under the same conditions and full conversion took 2 hours. In addition to high reactivity, the use of β-hydroxyamines also presents strong advantages. Indeed, biobased β-hydroxyamines can be easily synthesized by reacting biobased epoxides with aqueous ammonia. 30,31 This one-step process is inexpensive, does not require complex purifications and can be easily implemented. While the carbonation of a polyfunctional epoxide affords a polyfunctional cyclic carbonate, the ring opening with aqueous ammonia leads to the equivalent polyfunctional β-hydroxyamines. 31 Di-, triand tetra-β-hydroxyamines were already reacted with polyfunctional cyclic carbonates by Blattmann et al. for the synthesis of 100% biobased PHU thermosets. 32 However, the reactivity of the βhydroxyamines were only assessed by comparing the gelation time of different formulations. The authors reported longer gelation times for the formulations containing higher amounts of βhydroxyamines and concluded that they are less reactive, which is quite surprising in regards to their reactivity with epoxides.

We thus thoroughly investigated, for the first time, the aminolysis of a cyclic carbonate by comparing a β-hydroxyamine to non-functionalized alkylamine. Along with the kinetic study of the ethylene carbonate aminolysis with 1-amino-2-butanol and butylamine by 1 H NMR, quantum chemical calculations of the mechanism were carried out by the DFT method. The higher reactivity of βhydroxyamines toward cyclic carbonates was then confirmed by rheological experiments and 100% biobased thermosets were synthesized and characterized by structural and thermo-mechanical analyses (IR, DSC, TGA, DMA). The higher reactivity of β-hydroxyamines was confirmed by the gelation time gap between the two formulations studied.

Experimental Materials

Ethylene carbonate (purity 99%) was purchased from Alfa Aesar (Kandel, Germany). Butylamine (purity 99.5%), tetrabutylammonium bromide (purity 99%) and trimethylolpropane triglycidyl ether were purchased from Sigma-Aldrich Merck (Darmstadt, Germany). 1-Amino-2-butanol (purity 98.5%) was purchased from TCI EUROPE N.V (Zwijndrecht, Belgium). N,N'-Carbodiimidazole (purity 98%) and glycerol carbonate (purity 90%) were purchased from abcr GmbH (Karlsruhe, Germany). Aqueous ammonia (25% NH 3 ) and ethyl acetate were purchased from VWR International S.A.S (Fontenay-sous-Bois, France). Pripol TM 1012 was purchased from Croda (East Cowick, United Kingdom). All materials were used as received. The NMR solvent CDCl 3 was purchased from Eurisotop (Saint-Aubin, France).

Characterizations Nuclear Magnetic Resonance

Proton Nuclear Magnetic Resonance ( 1 H NMR) analyses were carried out in deuterated chloroform (CDCl 3 , 99.50% isotopic purity) using Bruker Avance III 400 MHz NMR spectrometer at a temperature of 25 °C.

Fourier Transform Infrared Spectroscopy

Infrared (IR) spectra were recorded on a Nicolet 210 Fourier transform infrared (FTIR) spectrometer.

The characteristic IR absorptions mentioned in the text are reported in cm -1 . Materials analyses were recorded using an ATR accessory.

Thermogravimetric Analyses

Thermogravimetric Analyses (TGA) were carried out using TG 209F1 apparatus (Netzch).

Approximately 10 mg of sample were placed in an aluminum crucible and heated from room temperature to 580 °C at a heating rate of 20 °C/min under nitrogen atmosphere (60 mL/min).

Differential Scanning Calorimetry

Differential Scanning Calorimetry (DSC) analyses were carried out using a NETZSCH DSC200F3 calorimeter, which was calibrated using indium, n-octadecane and n-octane standards. Nitrogen was used as purge gas. Approximately 10 mg of sample were placed in a perforated aluminum pan and the thermal properties were recorded between -150 °C and 190 °C at 20 °C/min to observe the glass transition temperature. The T g values were measured on the second heating ramp to erase the thermal history of the polymer. All the reported temperatures are average values.

Dynamic mechanical analyses

Dynamic mechanical analyses (DMA) were carried out on Metravib DMA 25 with Dynatest 6.8 software. Samples were tested according to uniaxial tension mode while heating at a rate of 3 °C/min from -100 °C to 100 °C at a frequency of 1 Hz with a fixed strain of 10 -5 m. All the thermosets were analyzed at least two times for repeatability.

Rheology experiments

Gelation times were measured using a Thermo Fisher HAAKE MARS rheometer with a plate-plate geometry with a diameter of 25 mm. Gelation times were analyzed by the crossover of the storage modulus (G') and loss modulus (G") during an oscillatory experiment at 1 Hz at 80 °C and 10 Pa of stress, according to the previously determined linear domain.

Titration of the amine equivalent weight of Priamine™1071 by 1 H NMR

The Amine Equivalent Weight (AEW) is the amount of product needed for one equivalent of reactive amine function. It was determined by [START_REF] Randall | The Polyurethanes Book[END_REF] H NMR using an internal standard (benzophenone). A known mass of product and benzophenone were poured into an NMR tube and 500 µL of CDCl 3 were added.

The AEW was determined using Equation 1 by comparing the integration value of the signals assigned to the benzophenone protons (7.5-7.8 ppm) with the integration of the signals arising from amine moiety protons (2.67 ppm). Determination of the secondary amine content of TMPT-β-HA by 13 C NMR TMPT-β-HA was dissolved in CD 3 OD at a concentration of 200 mg/mL and 13 C NMR spectra were carried out on a Bruker spectrometer Avance I at 25 °C using the following parameters: 30 kHz for spectral width, 10 kHz for transmitter frequency offset, 2 s for acquisition time, 2864 scans.

Quantitative conditions could be approached (as best without T1 measurement) with a 30° pulse (3.3 µs) and a relaxation delay of 30 s (D1). [START_REF] Randall | The Polyurethanes Book[END_REF] H decoupling was applied during acquisition (waltz16 method with a pulse of 90 µs). Pulse program was zgig30 from the Bruker library. The spectrum was calibrated with the CH 3 peak at 8.00 ppm.

Titration of the amine equivalent weight of TMPT-β-HA by 13 C NMR

The AEW of TMPT-β-Ha could not be measured by [START_REF] Randall | The Polyurethanes Book[END_REF] H NMR because of the overlap of the primary and secondary amines α proton peaks. Therefore, it was determined by 13 C NMR using the approached quantitative conditions, presented in the previous section, with an additional internal standard (phenol). A known weight of product and phenol were poured into an NMR tube and 500 µL of CDCl

Cross-linking density

From rubber elasticity theory, the uniaxial stretching was studied on the rubbery plateau at T > T α +50, and at very small deformations. Under these hypotheses, the cross-linking density (ν'), can be obtained from Equation 4, where E' is the storage modulus (Pa), R is gas constant (8.314 J.K -1 .mol -1 ) and T α is the temperature, in K, of transition from vitreous to rubber domain, determined at the maximum of the tan δ curve. Calculated values are only qualitative and not absolute.

Equation 4

Swelling index

Three samples from the same material, of around 20 mg each, were separately immersed in THF for 24 h. The swelling index (SI) was calculated using Equation 5, where m 2 is the mass of the swollen material and m 1 is the initial mass. Reported swelling index are average values of the three sample.

Equation 5

Gel Content

After the SI measurements, the three samples were dried in a ventilated oven at 70 °C for 24 h. The gel content (GC) was calculated using Equation 6, where m 3 is the mass of the dried material and m 1 is the initial mass. Reported gel content are average values of the three sample.

Equation 6

General procedure of 1 H NMR kinetic monitoring Typically, 8.8 mg of ethylene carbonate (0.1 mmol, 1 eq.) were placed in 1.490 g of CDCl 3 (1 mL) in a hemolysis tube, followed by stirring using a vortex. Once the carbonate was fully dissolved, the desired amount of amine was carefully added and the mixture was homogenized with 30 s of vortex stirring. Then, 450 µL of the solution were transferred to a NMR tube and the reaction was monitored at fixed time intervals by 1 H NMR analyses using a Bruker Avance III 400 MHz NMR spectrometer.

Computational details

All calculations were carried out using the Gaussian09 suite of programs. 33 Gas-phase geometry optimizations were performed without any symmetry constraint using the BP86 functional and the 6-311G (d,p) basis functions for all atoms. A correction for dispersion was also included during the geometry optimizations using Grimme's D3 empirical method (BP86-D3). 34 All final geometries were characterized as local minima (or first-order saddle points for the transitions states) by verifying that all second derivatives of the energy were positive (or that only one was negative). Thermochemical corrections were obtained on the basis of frequency calculations, using the standard approximations (ideal gas, rigid rotor and harmonic oscillator). The final free energy values also included a solvation correction in chloroform, estimated by the polarizable continuum model using the SMD model with standard parameters. 35 A further correction of 1.95 kcal/mol was applied to bring the G values from the gas phase (1 atm) to the solution (1 mol/L) standard state. 36 The Cartesian coordinates and energies of all optimized structures are deposited as Supporting Information.

Synthesis Synthesis of trimethylolpropane tricarbonate (TMPTC)

Trimethylolpropane triglycidyl ether (TMPTGE; 20 g, 0.139 mol) and tetrabutylammonium bromide (TBAB; 0.6 g, 1.86 mmol) were solubilized in 50 mL of AcOEt and added to a 100 mL sealed reactor.

The reaction was carried out at 80 °C under 20 bars of CO 2 for 72 h. The crude mixture was then washed with water and brine to remove TBAB. The organic layer was then dried with magnesium sulfate and under vacuum. The pure product was obtained as a yellowish viscous liquid (yield = 88%).

Synthesis of Pripol-C 5

Pripol™ 1012 (30 g, 0.12 mol, 1 eq.) was solubilized in 60 mL of AcOEt in a round-bottomed flask.

N,N'-carbodiimidazole (22.45 g, 0.14 mol, 1.2 eq.) was dissolved in 60 mL of AcOEt and the resulting solution was then added dropwise to the Pripol™ 1012 solution at 25 °C. The reaction was monitored by [START_REF] Randall | The Polyurethanes Book[END_REF] H NMR until full conversion of the acid to the imidazolide intermediate. Then, glycerol carbonate (16.35 g, 0.14 mol, 1.2 eq.) was added to the reaction. The reaction was carried out at 25 °C for 3 days until full conversion of imidazolide to ester functions. The crude mixture was first washed with a 5% HCl aqueous solution and then with a saturated NaHCO 3 aqueous solution. Finally, the mixture was washed with brine and dried with magnesium sulfate and under vacuum. The pure product was obtained as a yellow oil (yield = 85%).

Synthesis of trimethylolpropane tri-β-hydroxyamine (TMPT-β-HA)

TMPTGE (10 g, 0.099 mol, 1 eq.) was dissolved in 139 mL of a 25% NH 3 aqueous solution (0.99 mol, then evaporated with a rotatory evaporator and then freeze-dried to remove water traces. The pure product was obtained as a yellow viscous liquid (yield = 99%).

General procedure of PHU thermoset synthesis

Materials were synthetized with a cyclic carbonate/amine molar ratio of 1/1. The amine and carbonate masses were calculated with the Equation 7and Equation 8, respectively, where n carbonate and n amine are the number of moles of cyclic carbonate and amine, respectively, and AEW is the amine equivalent weight and CEW is the carbonate equivalent weight. Equation 7Equation 8

The cyclic carbonate and the amine were stirred using a SpeedMixer TM under vacuum for 5 minutes at 2 500 rpm. Then, the resulting homogeneous mixture was poured in a silicon mold and cured at 80 °C for 10 h, then 6 h at 120 °C and finally 1 h at 150 °C.

Results & Discussion

Kinetic and DFT studies

The aminolysis was first studied by 1 H NMR using ethylene carbonate (EC) as a model five-membered cyclic carbonate, comparing the reactivity of butylamine (BuNH 2 ) and 1-amino-2-butanol (BuNH 2 -βOH). The conversion was monitored by measuring the intensity of the EC signal in 1 H NMR (δ = 4.41 ppm) over time (Figure S1 and Figure S2). The resulting conversion plots are presented in Figure 1. The 1-amino-2-butanol is much more reactive compared to butylamine. Indeed, after one hour, the reaction with the β-hydroxyamine reached a 50% conversion against only 7% for the alkylamine.

However, even after 14 hours of reaction with β-hydroxyamine, the conversion was stalling around 85%. This phenomenon is well-known for the aminolysis reaction, indeed, the formation of the new hydroxyl group during the reaction creates a dense network of hydrogen bonds, increasing the viscosity and decreasing the reagents' mobility, which prevents quantitative conversion. Even though the 1-amino-2-butanol contains a pendant hydroxyl group, which further increases the density of hydrogen bonds, the EC conversion could still reach 85%, which is comparable to the literature values (around 80%). 25 On the other hand, the reaction with butylamine only reached a 57% conversion after 14 h. Therefore, the 1-amino-2-butanol hydroxyl group allows to strongly increase the amine reactivity. To understand this effect, detailed experimental (kinetic) and theoretical (DFT calculations) mechanistic investigations were carried out.

Kinetic studies gave us access to the rate law and rate constants for the reaction with each amine. To this end, observed rate constants were first obtained using a significant excess (from 10 to 50 eq.) of 1-amino-2-butanol and butylamine compared to the EC concentration (0.1 mol/L). The EC decay followed a first order rate law in each case, see Figure 2. The pseudo-first order rate constants, k obs , were determined with Equation 9and are given in Table 1. The dependence of k obs on the amine concentration is shown in Figure 3. The trends are clearly non-linear with an upward curvature (positive second derivative), indicating that the reaction order in amine is greater than one. The data were analyzed on the basis of Equation 10, as already described by Zabalov et al. 37 for the reaction of EC with butylamine in n-butanol and dioxane:

Equation 10 k obs = k 1 [Amine] + k 2 [Amine] 2
The meaning of this rate law is that the reaction may occur by two parallel channels with the participation of one (k 1 ) and two (k 2 ) amine molecules. The k 1 and k 2 values were determined by fitting Equation 2to the data in Table 1, with a correlation coefficient R² > 0.99 in each case, and the results are given in Table 2. These results are interesting for a few reasons. First of all, the rate law for the reaction with the butylamine exhibits a pure second order for the amine reagent, without significant contribution of the pathway involving only one amine molecule. This result is in contrast with those reported by Zabalov et al. for the same reaction in other solvents, where both pathways contributed to the reaction with [k 1 (L mol -1 s -1 ); k 2 (L 2 mol -2 s -1 )] = (0.75•10 -5 ; 1.88•10 -5 ) in n-butanol at 28 °C37 and (0.24•10 -5 ; 2.5•10 -5 ) in DMSO at 55 °C. 38 However, the k 1 pathway was also found insignificant in dioxane (k 1 = 8.4•10 -8 L mol -1 s -1 , vs. k 2 = 2.98•10 -5 L 2 mol -2 s -1 at 28 °C). 37 Secondly, the reaction in chloroform is much faster, since k 2 = (179 ± 2)•10 -5 L 2 mol -2 s -1 at 25 °C. The rate law for the reaction with 1-amino-2-butanol, on the other hand, in addition to having a greater k 2 value, also shows a relevant contribution of the pathway involving a single amine molecule. The involvement of a single amine molecule is not surprising when the reaction is conducted in a solvent that can participate in the proton transfer chain (e.g. n-butanol), but is less obvious in a solvent that cannot ensure this role such as chloroform.

A rationalization of these differences requires a detailed analysis of the reaction mechanism. The EC aminolysis has previously been analyzed by computational methods by Zabalov et al. [37][38][39] Two main reactant and n-BuOH solvent). 37 A subsequent thorough analysis of the effect of several MeOH molecules (up to six) for both concerted and stepwise mechanisms revealed the presence of several distinct pathways with similar activation barrier and a complex role of the H-bonding solvent, including the possible stabilization of zwitterionic intermediates (e.g. EC-NHR -•••H 2 X + ). 39 Finally, a recent contribution detailed the catalytic action of guanidine as H-X for the EC aminolysis by MeNH 2 in DMSO. 38 The latter study underlines the assistance of the DMSO solvent for the stabilization of cyclic intermediates and transition states, even though it cannot be directly involved in proton transfer chains. This mechanistic scheme allows us to formulate the following hypotheses. The rate law for the reaction with butylamine in chloroform has only a second order term in amine because the chloroform solvent (like the previously investigated 37 dioxane solvent) cannot play any assistance in the proton transfer chain. The k 2 value in chloroform is much higher than in n-butanol, dioxane or DMSO, because unlike all other solvents, chloroform cannot operate as a proton acceptor in Hbonding. Therefore, the only proton acceptor in the reaction mixture is the EC substrate and consequently the amine can display enhanced reactivity as a proton donor. Conversely, chloroform is a weak proton donor in H-bonding because of the inductive effect of the CCl 3 group. 40 Therefore, it can assist the reaction at the transition state level through a screening of the developed negative charge, similarly (but better) to what was shown for the CH 3 protons of DMSO. 38 Concerning the reaction with 1-amino-2-butanol, we must rationalize two different effects: i) the greater k 2 value relative to butylamine; ii) the contribution of a first-order term in amine (k 1 ). The first effect can be easily rationalized, on the basis of the published computational analysis, by a transition state stabilization linked to the H-bonding ability of the OH substituents. The second effect, given that the solvent cannot participate in the proton chain, suggests that the 1-amino-2-butanol must somehow allow a proton chain with the involvement of a single amine molecule.

The last proposition is the most relevant result of the present kinetic study and was therefore further analyzed by the DFT approach. We wish to underline that the purpose of this DFT investigation was not to quantitatively reproduce the relative rates and activation barriers, because the previously published work has demonstrated that this requires the explicit inclusion of several solvent molecules and a lengthy investigation of a large number of pathways. [37][38][39] We only wished to highlight the key role of the β-OH substituent in opening a single amine molecule pathway for the reaction. Therefore, no solvent molecules (CHCl 3 ) were explicitly included in the calculations and the effect of the solvent was only accounted for by the inclusion of a polarizable continuum. To capture the β-OH substituent effect, the chosen computational models for the reagents are CH 3 CH 2 NH 2 (for the alkylamine) and HOCH 2 CH 2 NH 2 (for 1_amino-2-butanol). In addition, our study was limited to the analysis of the stepwise process. Other computation details are given in the Experimental section.

We have comparatively analyzed three reaction pathways: i) the two-molecule (k 2 ) pathway for the alkylamine; ii) the two-molecule pathway for the alkoxylamine; iii) the one-molecule pathway (k 1 ) for the alkoxylamine. The first one only serves as a reference since they do not present unprecedented features relative to the work of Zabalov et al. [37][38][39] The starting reactant complex features two H bonds, one between a first EtNH 2 molecule as a donor and the EC carbonyl O atom as an acceptor, the second one between the second EtNH 2 as a donor and the first EtNH The barrier difference between the one-molecule pathway (Figure 5, 24.8 kcal mol -1 ) and the twomolecule pathway (Figure 4, 11.4 kcal mol -1 ) appears too large when considering that both pathways are competitive. In the real system, this difference may be attenuated by specific stabilizing effects by solvent molecules. In conclusion, the DFT analysis of the single-hydroxyamine pathway, though only qualitative and limited to the stepwise mechanism, indicates that the reaction channel with the first-order dependence on the amine concentration, in a solvent that cannot participate directly as a proton shuttle in the proton transfer chain, is made possible by the ability of the β-OH group to fulfil this role intramolecularly.

Synthesis of monomers

The PHU synthesis suffers from the low reactivity of five membered cyclic carbonates. Therefore, many studies described the use of catalysts or the optimization of the reaction parameters. 23,24 For certain applications, where solvents and catalysts must be avoided, the monomer structure is the only available parameter to tune the aminolysis reactivity. The kinetic study has highlighted the difference of aminolysis reactivity between alkylamines and β-hydroxyamines. Moreover, βhydroxyamines can easily be synthesized from biobased epoxy compounds. Therefore, we focused on the synthesis of polyfunctional β-hydroxyamine and polyfunctional cyclic carbonate monomers in order to synthesize 100% biobased PHU thermosets. To this end, two polyfunctional cyclic carbonates and a trifunctional β-hydroxyamine monomer were synthesized (Figure 6).

Trimethylolpropane tricarbonate (TMPTC) was accessed by condensation of trimethylolpropane triglycidyl ether (TMPTGE) and CO 2 (20 bar) in ethyl acetate in the presence of tetrabutylammonium bromide (TBAB) as catalyst. Full conversion after 72 h of reaction was confirmed by [START_REF] Randall | The Polyurethanes Book[END_REF] H NMR (Figure S4). On the other hand, aminolysis of TMPTGE with 25% aqueous ammonia solution at 100 °C for 4 h yielded the trimethylolpropane tri-β-hydroxyamine (TMPT-β-HA) equivalent. The epoxides were fully converted with a high β-hydroxyamine content (85%) and around 15% of secondary amines according to approached quantitative 13 C NMR (Figure S7). Moreover, Pripol™ 1012 from Croda, a biobased diacid derived from fatty acids, was reacted with glycerol carbonate in the presence of N,N'-carbonyldiimidazole (CDI) in ethyl acetate at 25 °C for 3 days, producing Pripol™ 1012 dicarbonate (Pripol-C 5 ). The reaction was monitored by [START_REF] Randall | The Polyurethanes Book[END_REF] H NMR and stopped once the full conversion of the acid functions was achieved (Figure S5). To compare two similar thermoset networks, Priamine™ 1071 (Figure S8), a biobased diamine derived from fatty acids, was selected for its similar structure with the Pripol™ 1012.

PHU thermosets

Rheological experiments

Since the higher reactivity of β-hydroxyamines compared to alkyl amines for the aminolysis of cyclic carbonates was demonstrated by the model reactions on EC, the next step was to highlight this reactivity difference in the synthesis of 100% biobased PHU thermosets. In order to compare two structurally similar networks, two simple formulations were defined with the four monomers presented in the previous section. The first one consisted of a TMPTC and Priamine™ 1071 formulation (PHU1), while the second one was composed of TMPT-β-HA and Pripol-C 5 (PHU2). In both formulations, the cyclic carbonate/amine ratio was 1:1. Therefore, both thermoset networks will contain similar aliphatic backbone from Priamine™ 1071 and Pripol™ 1012 and trimethylolpropane backbones. However, TMPT-β-HA/Pripol-C 5 material would present supplementary ester functions and hydroxyl groups coming from the β-hydroxyamines. Those two functions may increase the hydrogen bond density in the material and could improve its mechanical properties.

The pot life and gelation time of the two formulations were measured by oscillatory rheology.

Indeed, the pot life corresponds to the time during which the mixture viscosity remains low enough to allow its processing by casting. Typically, the pot life is determined as the time needed for the mixture to reach a viscosity of 10 Pa.s. On the other hand, the gelation time is the time required for the gelation of the polymer system, resulting from the aminolysis crosslinking. Since the gelation time is representative of the network formation rate, it depends on the monomer functionality.

Indeed, the more the monomer functionality increases, the more the gelation time decreases, as the polymer network is achieved at a lower function conversion. Therefore, thanks to the similar structure and functionality of our monomers and formulations, the gelation times of both PHU1 and PHU2 are representative of their reactivity. Typically, the gelation time is determined as the time at which the storage modulus (G') and loss modulus (G") crossover takes place. The oscillatory rheological experiments were performed with plate-plate geometry at 80 °C at 1 Hz and an applied stress of 10 Pa (Figure 7), according to the determined linear domain. Pot life and gelation times of both PHU1 and PHU2 are given in Table 3.

PHU1 achieved the gelation point after 5 h 22 with a pot life of 3 h 05, whereas PHU2 crosslinking was quicker with a gelation time of 1 h 04 and a pot life of 50 min. Conversely, in 2016 Blattmann et al. 32 reported prolonged gelation times with the increase of β-hydroxyamine ratio in their formulations, probably because they were using very viscous, highly functional β-hydroxyamines, which entailed a lack of reactive function mobility. Therefore, the crosslinking rate was most likely governed by the mixture physical parameters than the chemical kinetic itself. Hence, gelation times measured was not necessarily representative of the function reactivity. In our case, the use of βhydroxyamine (TMPT-β-HA) strongly increased the crosslinking aminolysis in comparison to alkylamine (Priamine™ 1071) in agreements with our previous kinetic study.

Indeed the thermoset synthesis was performed solventless, therefore, the capacity of the βhydroxyamine groups in PHU2 to lower the activation energy through H-bonds and to participate to the proton transfer chain in both inter-and intramolercular strongly favor the aminolysis reaction in comparison to PHU1. Priamine™ 1071 can only participate to the proton transfer chain via intermolecular conformations, it results to a longer gel time.

Thermoset synthesis

To obtain PHU thermosets, both formulations PHU1 and PHU2 were prepared and cured at 80 °C for 10 h, and 6 h at 120 °C, then post-cured 1 h at 150 °C. The conversion of cyclic carbonates into polyhydroxyurethanes was confirmed by IR spectroscopy with the appearance of the urethane bands at 1787 cm -1 and 1797 cm -1 , for PHU1 and PHU2 respectively (Figure S9). Moreover, PHU2 exhibited the supplementary ester band at 1726 cm -1 from Pripol-C 5 (Figure S10). Furthermore, both thermosets had a high gel content of 94 % and 96 % for PHU1 and PHU2 respectively, which confirmed an efficient crosslinking.

Thermo-mechanical properties

Both PHU1 and PHU2 were first analyzed by DSC to determine their T g (Figure S11), yielding the results summarized in Table 4. As expected, very close T g values were obtained, -5 °C and -7 °C for

Thermal properties

The thermal stability of the PHUs was explored by TGA from room temperature to 600 °C under a N 2 atmosphere (Figure S12). PHU2 degraded at lower temperature (T d5% = 246 °C) compared to PHU1

(T d5% = 300 °C). Indeed, ester functions are less resistant to temperature than hydroxyurethane linkages. Hence, the thermal stability of PHU2 was strongly reduced. However, the two thermosets had close char values, 8 % and 10 % for PHU1 and PHU2 respectively.

Conclusion

β-hydroxyamines are readily available from biobased epoxides by aminolysis with ammonia. Indeed, polyfunctional β-hydroxyamines are obtained through a one-step process without involving complex purifications. In addition to their eco-friendly synthesis, we have highlighted their higher reactivity toward cyclic carbonates compared to conventional alkylamines. Kinetic studies have revealed that butylamine exhibits a pure second order rate law for the EC aminolysis in CDCl 3 , whereas both first and second order pathways contribute to the aminolysis with 1-amino-2-butanol. Moreover, 1amino-2-butanol had a greater k 2 value of 5.6•10 -3 L² mol -2 s -1 against 1.79•10 -3 L² mol -2 s -1 for butylamine, which also justifies its higher reactivity. A DFT investigation highlighted the key role of the β-OH substituent in lowering the activation barrier through H-bonding assistance relative to the alkylamine. The β-OH substituent is able to participate in the proton transfer chain both inter-and intramolecularly. Nevertheless, the single molecule pathway still represents a minor contribution relative to the two-hydroxyamine pathway.

Furthermore, the higher β-hydroxyamine reactivity toward cyclic carbonates was confirmed for PHU thermoset synthesis by rheology. Indeed, the gelation time was reduced by a factor of five compared to alkylamine-based PHUs. Moreover, the two fully biobased PHU thermosets synthesized had very similar physico-chemical properties as expected from their complementary formulations. However, PHU2 presented a heterogeneous network with two T α probably due to the ester linkages from Pripol-C 5 . These ester linkages also reduced the thermal stability of PHU2 compared to PHU1. βhydroxyamines are very promising curing agents combining a green synthesis pathway and a higher reactivity toward epoxides and cyclic carbonates.

  integration of the signal from benzophenone protons; ∫ amine : integration of the signals from protons in α of the amine function; H amine : number of protons in α of the amine function; H PhCOPh : number of benzophenone protons; m amine : product mass; m PhCOPh : benzophenone mass; M PhCOPh : benzophenone molecular weight.

Figure 1 : 1 H

 11 Figure 1 : Comparative kinetic monitoring of the ethylene carbonate (1 mol/L) ring opening with butylamine (1 mol/L) and 1-amino-2-butanol (1 mol/L) by 1 H NMR in CDCl 3 at 25 °C.

Equation 9 :Figure 2 :

 92 Figure 2 : Kinetic of the aminolysis of ethylene carbonate (0.1 mol/L) with (a) butylamine and (b) 1amino-2-butanol at different concentrations by 1 H NMR in CDCl 3 at 25 °C.

Figure 3 :

 3 Figure 3 : Dependence of k obs of ethylene carbonate reaction with butylamine and 1-amino-2-butanol in CDCl 3 on amine concentration at 25 °C.

  and stepwise, have been highlighted as shown in Scheme 1. In the concerted pathway, the proton from the nucleophile is directly transferred to the leaving group in one step, whereas the stepwise mechanism involves proton transit through the carbonyl O atom with generation of a tetrahedral intermediate. However, a simple two-molecule collision (i.e. carbonyl substrate and nucleophile) leads to high barriers in both cases because of the strained 4-membered cycles in the transition state, Scheme 1(a). The reaction has a much lower barrier when assisted by at least one additional proton shuttle molecule (H-X), which must have amphiphilic H-bonding properties, namely both proton and acceptor. Scheme 1(b) shows the example with only one H-X molecule. In a first computational study of the EC aminolysis by MeNH 2 , Zabalov et al. considered only the concerted pathway with one H-X molecule (MeNH 2 or MeOH, models of the n-BuNH 2

Scheme 1 :

 1 Scheme 1: Accepted mechanism for EC aminolysis.

  2 as an acceptor, EC•••H 2 N(Et)•••H 2 NEt. In the optimized structure, the NH 2 group of the second EtNH 2 molecule is suitably positioned for the nucleophilic attack at the carbonyl C atom. The transition state of each step, the tetrahedral intermediate and the product were optimized, yielding the reaction profiles shown in the SI (FigureS3). The highest free energy TS is that of the second step, leading from the tetrahedral intermediate to the opened product, at 16.3 kcal/mol from the reactant complex. The additional EtNH 2 molecule remains H-bonded as proton acceptor to the OH group in both intermediate and product, and also acts as proton donor to the carbonyl group in the product.The alkoxylamine two-molecule pathway is shown inFigure 4. The starting reactant complex shows strong O-H•••O interactions between the β-OH groups and the EC O atoms (a ring O atom for one alkoxylamine molecule and the C=O atom for the second one) and an additional N-H•••N bond between the two amine functions. One NH 2 function is once again correctly positioned in front of the EC carbonyl group (N•••C = 2.69 Å), even closer than for the EtNH 2 system (3.06 Å). The NH 2 addition to the carbonyl group is accompanied by transfer of a proton to the second amine NH 2 function. The shuttle for this system occurs in two separate steps, via a charge-separated intermediate, [(EC)NHCH 2 CH 2 OH] -[NH 3 CH 2 CH 2 OH] + , which sits in a shallow minimum at 7.4 kcal mol -1 from the reactant complex between two transition states (TS1 and TS1') at only slightly higher free energy. This intermediate has the formally negative O atom stabilized by two H-bonds, one from the β-OH of the attacking hydroxyamine and the second one from the cationic NH 3 group of the hydroxyamine shuttle. The tetrahedral intermediate obtained from the charge-separated species via TS1' (at 4.4kcal mol -1 ) must rearrange to prepare the proton transfer chain for the second step, leading to a second tetrahedral intermediate at 6.0 kcal mol -1 , differing from the previous one only in the Hbonding scheme. The second proton transfer occurs in one step via TS2. This corresponds to the highest point along the free energy profile and the overall barrier from the reactant complex (at 11.4 kcal mol -1 ) is significantly reduced relative to that of the EtNH 2 system (16.3 kcal mol -1 ). The fundamental steps of the two pathways are the same, but the two additional O-H•••O interactions that remain present throughout the reaction profile have a greater stabilizing effect on the intermediates, transition states and product than on the reactant complex.

Figure 4 :

 4 Figure 4 : Free-energy profile for the two-amine-molecule pathway of the ethylene carbonate aminolysis with HOCH 2 CH 2 NH 2 . The pathway involving only one hydroxyamine molecule is illustrated in Figure 5. The most stable reactant configuration features an H-bond between the amine β-OH substituent as proton donor and the EC carbonyl O atom as proton acceptor. Once again, the NH 2 group is properly positioned for the nucleophilic attack at the carbonyl C atom. The transition state of the first step (TS1) leading to the tetrahedral intermediate features the assistance by the β-OH group in an intramolecular proton shuttle with a 6-membered ring. It has a higher energy, relative to the reactant complex (24.8 kcal mol -1 ), than those of the two-amine pathways with EtNH 2 or HOCH 2 CH 2 NH 2 , because the involvement of the OH group in the proton shuttle requires the adoption of a strained 5-membered ring for the hydroxyamine. The intermediate generated from TS1 (at 12.8 kcal mol -1 ) maintains the O-H•••O interaction between the generated OH group as a proton donor and the hydroxyamine β-OH group as a proton acceptor (1.85 Å), but the β-OH group cannot form a strong H-bond as a proton donor with the residual NH function because of the 5-membered ring strain (H•••N = 2.40 Å). In order to prepare for the second step, the β-OH group must move from the N atom toward the ring O atom.The resulting configuration is optimized with a minimum at nearly the same energy (13.6 kcal mol -1 ) and features two H-bonds (1.94 Å between the ring OH group and the hydroxyamine β-O atom; 1.95 Å between the β-OH group and the ring O atom). The next transition state (TS2) involves, like TS1, the participation of the β-OH group as an intramolecular proton shuttle in a 6-member cycle and its

Figure 5 :

 5 Figure 5: Free-energy profile for the single-amine-molecule pathway of the ethylene carbonate aminolysis with HOCH 2 CH 2 NH 2 .

Figure 6 :

 6 Figure 6: Monomer structures with their synthetic pathways. Pripol™ 1012 and Priamine™ 1071 representations are ideal structures.

Figure 7 :

 7 Figure 7: Rheological experiments for determination of gelation and pot life time at 80 °C for PHU1 and PHU2 at 1 Hz and 10 Pa of stress.

  Figure .Once again, the properties of the two materials are comparable, with E' glassy of 1.28 GPa and 1.44 GPa for PHU1 and PHU2, respectively, and E' rubbery of 0.6 MPa for both. Moreover, the alphatransition temperature (T α ) was measured by the maximum of tan δ of each material. Interestingly, PHU2 presented two T α at 2 °C and 22 °C, while PHU1 had a single one at 10 °C. Nevertheless, the

Figure 8 :

 8 Figure 8: DMA measurements of PHU thermosets (right: storage modulus (E'); left: tan δ).

Table 1 :

 1

Pseudo-first order rate constants for the ethylene carbonate (0.1 mol/L) aminolysis in CDCl 3 at 25 °C. [BuNH 2 -βOH] (mol/L)

k obs x10 3 (s -1 ) [BuNH 2 ] (mol/L) k obs x10 3 (s -1 )

	0.96	20.4 ± 0.2	1.04	1.795 ± 0.006
	2.01	65.6 ± 0.5	2.19	7.54 ± 0.03
	2.96	122 ± 2	2.99	16.8 ± 0.1
	4.02	190 ± 3	4.08	29.5 ± 0.2
	4.93	247 ± 2	5.07	46.0 ± 0.4

Table 2 :

 2 Rate constant for the ethylene carbonate aminolysis in CDCl 3 at 25 °C.

Table 3 :

 3 Formulation, pot life and gelation time of PHU1 and PHU2.

		Cyclic carbonate		Amine
		TMPTC	Pripol-C 5	TMPT-β-HA	Priamine™ 1071 Pot life	Gelation time
	PHU1	100	-	-	100	3 h 05	5 h 22
	PHU2	-	100	100	-	50 min	1 h 04

Table 4 :

 4 Physico-chemical properties of PHU thermosets.

PHU T d5% (°C) Char (%) T g (°C) T α (°C) E' glassy (Gpa) E' rubbery (MPa) ν' (mol/m 3 ) Swelling index (%)

										Gel content
										(%)
	1	300	8	-5	10	1.28	0.6	76	251	94
	2	246 10	-7	2 / 22	1.44	0.6	72	213	96

Author information

Co-corresponding authors * E-mail address: rinaldo.poli@lcc-toulouse.fr (R. Poli); sylvain.caillol@enscm.fr (S. Caillol)

Notes

The authors declare no competing financial interest