Prof R Hoogenboom

Nikola Toshikj

Jean-Jacques Robin

Sebastien Blanquer

biodegradable triblock copolymers by organocatalytic ROP from poly(lactide) macroinitiators

Keywords: Biodegradable block copolymers, organocatalysis, poly(caprolactone), poly Biodegradable block copolymers, organocatalysis, poly route

A simple and general approach for the synthesis of biodegradable triblock copolymers by organocatalytic ROP from poly(lactide) macroinitiators

Biodegradable polyesters and polycarbonates are the most renowned biodegradable polymer and are synthesized by ring opening polymerization. However, reproducible and efficient catalytic approaches to synthesize biodegradable triblock copolymers with PLA first route is considering as a high challenge. To date, no study succeeded to synthesize biodegradable triblock copolymers with PLA macroinitiators using an organocatalytic pathway.

In this study we describe different catalytic approaches to achieve the most appropriate mechanism for yielding well-defined biodegradable triblock copolymers starting from PDLLA macroinitiator: PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL. Complete monomer conversion has been reached for both investigated triblock structures without observing transesterification.

We explain that an activated monomer mechanism using cationic activation was the most effective approach for leading to a controlled block copolymerization using PDLLA blocks as macroinitiators. The block copolymerization by cationic ring opening polymerization has been demonstrated via step and sequential copolymerizations.

We believe this work is an important contribution to the field of biodegradable polymer synthesis and will be of great interest to the readers of your journal: European Polymer Journal.

All authors have been listed on the manuscript and have agreed to the content of the paper.  General approach for biodegradable triblock copolymer synthesis with PDLLA first route with no side reactions.

 Study of the catalytic influence on the block copolymerization when PDLLA is employed as macroinitiator.

 Effective triblock copolymerization is obtained using cationic activated monomer mechanism.

 One pot sequential copolymerization is achieved via traceless switch organocatalysis approach.

Biodegradable polymers are knowing growing interest, especially due to the eco-friendly concerns but also for the huge potential in biomedical applications. Consequently, in the past couple of years, degradable aliphatic polyesters and polycarbonates have gained noticeable attention and are becoming the gold standard of biodegradable synthetic materials. More particularly, poly(lactide)s (PLA) have received the highest interest due to their tuneable degradability, high mechanical strength and rigidity.

Poly(caprolactone)s (PCL) polyesters have also been used for their elastic properties and likewise show remarkable drug permeability. Finally, amorphous poly(trimethylene carbonate) (PTMC) presents high flexibility and controlled bioresorption through surface erosion and is largely used for biomedical applications such as soft tissue engineering. All these polymers can be synthesized by ring opening polymerization of the corresponding cyclic monomers: lactide (LA), epsilon-caprolactone (ε-CL) and trimethylene carbonate (TMC) respectively. Block copolymerizations of their respective monomers have also been widely investigated in the goal to easily adjust the properties of the resulting copolymers.

Those can generate microphase separation, essentially by controlling the composition and microstructure of the copolymers. In that context, copolymers based on PLA (with different D and Llactide enantiomers rates), PCL and PTMC generating A-B diblocks and A-B-A triblocks are the most current block copolymers encountered in the literature [START_REF] Cui | Ring-opening polymerization and block copolymerization of L-lactide with divalent samarocene complex[END_REF][START_REF] Pospiech | Multiblock copolymers of L-lactide and trimethylene carbonate[END_REF][START_REF] Zhang | Triblock copolymers based on 1,3-trimethylene carbonate and lactide as biodegradable thermoplastic elastomers[END_REF]. The development of such block copolymers has resulted in new biomaterials with combination of soft and hard blocks and has therefore significantly influenced their degradability kinetics, the elasticity and the physico-chemical behaviour. The most current polymerization routes in ROP are cationic, anionic and coordination-insertion where the control of the molecular weight and dispersity greatly depends on the monomer/catalyst couple. However, it has to be noticed that the reactivity of the various monomers over specific catalytic systems are generally different making sometimes difficult to synthesize the copolymers in one pot. The choice of the catalyst, the type of macroinitiator depending on the first synthesized block and the feeding order of monomers for sequential block copolymerization are crucial parameters to claim for a controlled and effective copolymerization.

A wide variety of organometallic catalysts have been used for the synthesis of biodegradable copolymers [START_REF] Kricheldorf | Biodegradable multiblock copolyesters prepared from epsiloncaprolactone, L-lactide, and trimethylene carbonate by means of bismuth hexanoate[END_REF][START_REF] Guillaume | Recent advances in ring-opening polymerization strategies toward alpha,omegahydroxy telechelic polyesters and resulting copolymers[END_REF][START_REF] Albertsson | Recent developments in ring opening polymerization of lactones for biomedical applications[END_REF]. However, elevated temperature is usually necessary for the polymerization, which considerably increases the risk of transesterification [START_REF] Kricheldorf | Polylactones 48. SnOct(2)-initiated polymerizations of lactide: A mechanistic study[END_REF]. Furthermore, the presence of metal in the final polymer is nowadays more and more banned, principally for environmental and biomedical applications. Hence, organocatalysis gained a growing interest in ring opening copolymerization. Curiously, the synthesis of biodegradable block copolymer while using an organocatalyst is poorly reported [START_REF] Guerin | Macromolecular engineering via ring-opening polymerization (1): L-lactide/trimethylene carbonate block copolymers as thermoplastic elastomers[END_REF][START_REF] Brannigan | Block Copolymer Materials from the Organocatalytic Ring-Opening Polymerization of a Pentaerythritol-Derived Cyclic Carbonate[END_REF]. One of the reasons of this lack can be explained by the divergent reactivity of monomers according to the catalytic mechanism employed, notably in the case of electrophilic or nucleophilic activations [START_REF] Wang | Traceless switch organocatalysis enables multiblock ring-opening copolymerizations of lactones, carbonates, and lactides: by a one plus one approach in one pot[END_REF][START_REF] Couffin | Selective O-acyl ring-opening of betabutyrolactone catalyzed by trifluoromethane sulfonic acid: application to the preparation of well-defined block copolymers[END_REF]. To overcome this orthogonal activation, Wang et al. have recently developed the "traceless switching organocatalysis" [START_REF] Wang | Traceless switch organocatalysis enables multiblock ring-opening copolymerizations of lactones, carbonates, and lactides: by a one plus one approach in one pot[END_REF], which was the first efficient approach to generate biodegradable multiblock copolymers with organocatalysis. The principle is based on the use of two orthogonal catalytic systems by switching the initial electrophilic activation of the first block synthesis by using nucleophilic catalyst to initiate the second one. Block copolymerization without transesterification [START_REF] Dakshinamoorthy | Block and Random Copolymerization of epsilon-Caprolactone, L-, and rac-Lactide Using Titanium Complex Derived from Aminodiol Ligand[END_REF] Biodegradable block copolymerization through PLA macroinitiator faces serious limitations that have often been highlighted in the literature. Indeed, biodegradable copolymers with PLA first route are barely reported in opposition to PLA last route [START_REF] Deng | Synthesis and characterization of biodegradable block copolymers of epsilon-caprolactone and D,L-lactide initiated by potassium poly(ethylene glycol)ate[END_REF][START_REF] Dubois | Macromolecular Engineering of Polylactones and Polylactides .4. Mechanism and Kinetics of Lactide Homopolymerization by Aluminum Isopropoxide[END_REF]. Table 1 reports various attempts of block copolymerization using PLA first route and subsequently used as macroinitiator for copolymerization of the second monomer. From the Table 1, it is apparent that most of the attempts using traditional organometallic catalyst routes showed remarkably low reactivity or else generated significant transesterification. Till now, the only successful way of copolymerizing with PLA macroinitiator has been achieved by either using specific additives or modifying the metal complex by bulky ligands, which then act as initiator and therefore present a serious limitation for the generation of triblock copolymers [START_REF] Han | Click chemistry synthesis, stereocomplex formation, and enhanced thermal properties of well-defined poly(L-lactic acid)-bpoly(D-lactic acid) stereo diblock copolymers[END_REF]. Therefore, universal and controlled catalytic route to synthesize biodegradable block copolymer B-A-B from PLA macroinitiator as central block remains a considerable challenge, especially by using an organocatalytic strategy. Although, block copolymerization with PLA macroinitiator would allow to generate new type of biodegradable multiblocks that might be interesting to create new materials with rigid blocks surrounded by soft blocks which would display specific phase separation behaviour and interesting properties.

Consequently, in this article, we propose to investigate different catalytic systems from coordinationinsertion, anionic and cationic mechanisms to synthesize biodegradable block copolymer B-A-B from PDLLA macroinitiator. Hence, bishydroxy terminated PDLLA are first prepared and then used as macroinitiator for the copolymerization of PCL and PTMC via step and sequential copolymerization to lead to PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL copolymers (Figure 1). The three classical mechanisms of ring opening polymerization have been investigated to generate these block copolymers: i/ coordination insertion has been tested using stannous octanoate, ii/ nucleophilic activation with guanidine molecules such as TBD, iii/ electrophilic activation with methyl sulfonic acid catalyst.

2.Materials and Methods

Materials

The monomers, DL-LA was purchased from Corbion (The Netherlands), ε-CL (99 %) was obtained from Santa Cruz Biotechnologies (Germany), while TMC was obtained from Foryou Medical (China).

The initiator (1,6 hexane diol, 99 %) and the catalysts (MSA, TBD, Sn(Oct) 2 ) were purchased from Sigma-Aldrich (France) and used as received. Anhydrous dichloromethane was retrieved from solvent purificator Inert PureSolv™ (USA) and anhydrous toluene (99.8 %) was purchased from Sigma Aldrich (France) were used as polymerization solvents.

Synthetic procedures

All the syntheses were performed in two-necked round bottom flasks (100 ml), previously dried in an oven at 130°C, and equipped with a magnetic stirrer and a thermometer.

General procedure of homopolymerization of DL-LA.

DL-lactide (DL-LA) (1,05 g, 14,5 mmol, 100 eq) was solubilized in dichloromethane (DCM) (10,5 ml, [DL-LA] 0 = 0.7 mol/L). The initiator 1,6 hexane-diol (8,61 mg, 0,073 mmol, 1 eq) and the catalyst, 1,5,7-triazabicyclo [4.4.0] dec-5-ene (TBD) (1,42 mg, 0,051 mmol, 1.4 eq) were then added into the solution. The reaction mixture was stirred for 2 minutes at room temperature until the complete conversion of DL-LA, determined by 1 H-NMR. Afterwards the catalyst was neutralized by an excess of acetic acid and the reaction mixture was concentrated under vacuum. The polymer was then precipitated in cold methanol and dried in vacuum oven for 24 hours. Conversion rate was >98 % and yield reaction around 95 %.

General procedure for PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL triblock copolymers

syntheses by step copolymerization using PDLLA macroinitiator.

Previously synthesized PDLLA macroinitiator (1,05 g, 0,138 mmol, 1 eq) was introduced in a flask; with TMC monomer (1,43 g, 13,8 mmol, 100 eq) or ε-CL (1,57 g, 13,8 mmol, 100 eq). The quantity of monomer and macroinitiator used were based on the desired proportions between the blocks and was fixed for this study at 50-100-50. Some cycles of vacuum and dry argon were performed before injecting the anhydrous solvent ([TMC/ε-CL] 0 =1 mol/L). The reactions with MSA (0,026 g, 0,276 mmol, 2 eq) or TBD (0,0162 g, 0,1932 mmol, 1,4 eq) as catalyst were performed in anhydrous dichloromethane at room temperature while for stannous octoate (Sn(Oct) 2 ) (0,1 wt. % to initiator) as catalyst the used solvent was anhydrous toluene with reaction temperature of 100°C. After full reaction, an excess amount of triethylamine (3 eq in respect to catalyst) was added when using MSA, in order to neutralize this one.

Likewise, when using TBD as catalyst, an excess amount of acetic acid (3 eq to TBD) was used in order to neutralize it. Finally, the polymers were slowly poured in cold methanol, the precipitated polymers were filtered and washed several times in the same solvent and dried in vacuum oven for 24 hours.

General procedure of sequential one-pot synthesis of PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL triblock copolymers.

Following the procedure for the synthesis of PDLLA homopolymer reported above, once the conversion of the previous reaches >99 % after 2 min of reaction, MSA (2.5 eq to TBD) was firstly added in the reaction mixture in order to quench the TBD catalyst and then TMC or ε-CL monomer was added to carry on the second polymerization step. The reactions were performed at room temperature for 17 h for the synthesis of PTMC-b-PDLLA-b-PTMC triblock copolymer and 6h for the synthesis of PCL-b-PDLLA-b-PCL triblock copolymer. After complete conversion of the monomers, the MSA was quenched with an excess of trimethylamine (3 eq to MSA). Finally, the polymers were slowly poured in cold methanol, filtered and then washed several times in the same solvent and at last, dried in an oven in vacuum for 24 hours.

Instruments

Size exclusion chromatograms were recorded using a triple detection (GPC Varian 390-LC viscometer detector, Varian 390-LC refractive index detector and UV detector (at 254 nm)) from Agilent Technologies. The analyses were performed in tetrahydrofuran (THF) at a flow rate of 1.0 mL/min at 30 °C. An Agilent PLgel 5 µm guard column and two columns 5 µm PLgel Mixed D were used. Data acquisition and calculations were performed using Cirrus Multi GPC/SEC software. Universal calibration was performed with PS standards from Agilent Technologies (EasiVial) using the intrinsic viscosities given by the supplier.

Nuclear Magnetic Resonance Spectrometry -1 H and 13 C NMR spectra were recorded on a 400MHz Bruker Aspect Spectrometer while DOSY spectra were recorded on a 600MHz Bruker Aspect Spectrometer. CDCl 3 was used as deuterated solvent. Chemical shifts were given in parts per million (ppm): for 1 H and DOSY NMR the reference peak was residual CDCl 3 at 7.26 ppm and for 13 C NMR at 77 ppm.

Results and Discussion

Synthesis of triblock copolymers with PLA as a central block remains as a challenge due to the absence of simple and universal catalytic approach for their preparation (Table 1). In addition, despite the significant rising of studies devoted to ring opening polymerization by organocatalysis, block copolymerization has been very poorly studied with this type of catalysts. Therefore, we investigated the synthesis of biodegradable triblock copolymer B-A-B via PDLLA first route using coordinationinsertion mechanisms with an organometallic catalyst, cationic and anionic mechanism with an organocatalyst.

To start, DL-LA, -CL and TMC have been firstly homopolymerized in order to control the reactivity of each monomer using the selected catalysts. Theoretical degree of polymerization was initially fixed to 100 for all the homopolymers synthesized using hexanediol as a bifunctional initiator. Monomer conversion and degree of polymerization were determined by 1 H-NMR (details in SI). Table 2 shows the conversion rate of each monomer as a function of the polymerization mechanism.

Monomer conversion has been determined by 1 H-NMR spectra by comparing the integrated areas of characteristic peaks of the monomers with those of protons from the growing polymer chains. Degree of polymerization was determined from the ratio of the peak integrals of the characteristics protons from the polymer chain with the peak integrals of the characteristic protons from the last unit of the polymer chain or with the characteristic integral peak from the hexanediol initiator. Homopolymerization of each monomer resulted in bishydroxy-terminated homopolymers but the reactivity was not identical since total conversion were note reached in similar times. Indeed, the polymerization of PDLLA via cationic mechanism using MSA catalyst was relatively low with 10 % of conversion after 17 h (Figure S1).

Nucleophilic activation with TBD at room temperature was faster for homopolymerization of DL-LA than for TMC (Figure S2). In the case of -CL, homopolymerization reached a plateau at 17 % of conversion after 6 h of reaction (Figure S3). In contrast, Sn(Oct) 2 successfully resulted in bishydroxyterminated homopolymer, with a conversion rate similar for all the monomers. It has to be noted that according our experimental conditions, no transesterification has been detected for all the studied catalysts.

In order to explore the possibility to generate block copolymers with various activation mechanisms, step copolymerization was performed. This approach consisted in polymerization and purification of the first block by precipitation and elimination of residual reactive species such as initial catalyst. As previously presented, nucleophilic activation was the most efficient way to homopolymerize DL-LA and was consequently used to synthesize the first PDLLA block with terminal OH groups. This initial bis-hydroxyl PDLLA block was used to start the copolymerization of the second blocks. The synthesis of triblock PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL copolymers was therefore obtained in solution by using the three studied catalysts. Conversion rate of the second blocks was measured by 1 H-NMR (Figure 2A). In addition, molar fraction of each block was evaluated by 1 H-NMR from the ratio of characteristic proton peak integrals for each polymer chain (Figure S4). For all the copolymers PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL, the targeted ratio was fixed at 50-100-50.

Sn(Oct) 2 catalyst has been already investigated for diblock copolymer PLLA-b-PCL with PLLA first route and lead to transesterification (Table 1). Bero and Kaspercky demonstrated the strong analytical potential of 13 C-NMR spectroscopy to determine chain microstructure irregularities that can be due to random transesterification on the same diblock copolymer [START_REF] Kasperczyk | Coordination Polymerization of Lactides .4. The Role of Transesterification in the Copolymerization of L,L-Lactide and Epsilon-Caprolactone[END_REF][START_REF] Kasperczyk | Coordination Polymerization of Lactides .2. Microstructure Determination of Poly[(L,L-Lactide)-Co-(Epsilon-Caprolactone)] with C-13 Nuclear-Magnetic-Resonance Spectroscopy[END_REF]. Later, this study has been widely used as reference to demonstrate the presence of transesterification for any type of block copolymers based on poly(lactide) [START_REF] Florczak | L,L-lactide and -caprolactone block copolymers by a poly(L,L-lactide) block first route[END_REF][START_REF] Lipik | Synthesis of Block Copolymers of Varying Architecture Through Suppression of Transesterification during Coordinated Anionic Ring Opening Polymerization[END_REF][START_REF] Dakshinamoorthy | Block and Random Copolymerization of epsilon-Caprolactone, L-, and rac-Lactide Using Titanium Complex Derived from Aminodiol Ligand[END_REF]. In full awareness of such risk, we investigated the coordination/insertion approach to synthesize the triblock copolymers with PDLLA first route. A full conversion after 24 h have been found for the triblock PCL-b-PDLLA-b-PCL and monomer sequencing in the triblock was characterized by 13 C-NMR. Figure 2C shows the carbon spectra of the triblock, and the expanded carbonyl carbon region from 169-174 ppm. Carbonyl peaks from PDLLA is characterized by a sharp multiplet at 169.5 ppm due to the stereochemistry from the sequential units of L and D lactide.

However, the presence of various peaks in between the carbonyl peaks of PDLLA block at 169.5 ppm and the carbonyl peaks of PCL block at 173.5 ppm are also clearly visible and confirm the random monomer sequencing (triads assigned in figure 2C), and therefore demonstrate the presence of significant transesterification. In addition, 1 H NMR spectrum also allows to determine the presence of transesterification by the apparition of characteristic peaks at 2.4 ppm and 4.15 ppm (represented by the blue arrows in the Figure 2A). Consequently, -CL monomers was incorporated within the PDLLA chain by transesterification during the reaction of copolymerization. Such transesterification influenced also the chromatogram where the detected copolymer showed a wide signal with dispersity of 2.3 (Figure 2B). In parallel, synthesis of triblock PTMC-b-PDLLA-b-PTMC by Sn(Oct) 2 showed extremely low reactivity compared to the homopolymerization of TMC, with conversion rate that reached only 33 % after 72 h of reaction (Figure 3A). By contrast, TMC was nicely homopolymerized by anionic mechanism with TBD and the attempt to synthesize PTMC-b-PDLLA-b-PTMC showed also the same reactivity with a total conversion after 1 h of reaction. However, DOSY NMR analyses showed different diffusion coefficients between the PTMC homopolymer and the synthesized copolymer which thus means a mixture of PDLLA and PTMC homopolymers (Figure 3B). Furthermore, diffusion coefficient of the initial PDLLA was exactly similar to that of PDLLA block after copolymerization which therefore confirms that PDLLA did not act as initiator. To corroborate this result, SEC analysis of the synthesized block copolymer PTMC-b-PDLLA-b-PTMC was performed (Figure 3C and Table 3). From the SEC, it was expected to detect chain extension approximately double that of initial PDLLA block size. However, the chromatogram from the copolymer shows a wide Gaussian curve leading to huge dispersity calculated around 11.9 while the initial PDLLA was around 1.24 (Table 3). In addition, calculated Mp was around 44000 g.mol -1 instead of 17400 g.mol -1 for the expected copolymer which probably means homopolymerization of PTMC. In summary, it was not possible to synthesize PTMC-b-PDLLA-b-PTMC triblock copolymer via anionic mechanism.

As previously mentioned for the homopolymerization of -CL with anionic organocatalysis using TBD, the copolymerization of -CL using PDLLA macroinitiator shows a total absence of reaction after 72 h where the monomer -CL is still present as observed by 1 H-NMR where no characteristic peaks from PCL appeared. As a result, no PCL-b-PDLLA-b-PCL triblock could be obtained from anionic catalysis (Figure S5).

Finally, step copolymerization was also studied using cationic catalysis with MSA. For both synthesized PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL triblocks, complete conversion was reached after 17 h and 6 h, respectively. 13 C-NMR spectroscopy was used to determine the sequential distribution of copolymers. Surprisingly, carbon spectrum of PCL-b-PDLLA-b-PCL in the carbonyl region did not show the presence of triad peaks that would have come from the transesterification (Figure 4). Table 3. Molecular weights and dispersities of the synthesized copolymers measured by SEC.

Catalysis approach

Block copolymer * Mn th (g.mol -1 ) Mn SEC (g.mol ppm (Figure 4). Carbon NMR indicated that the transesterification processes did not occur when MSA was used as catalyst. DOSY-NMR spectra for both copolymers (Figure 5A and 5C) clearly identifies an uniform diffusion coefficient which confirms the formation of block copolymerization for both investigated copolymers. For SEC chromatograms for both triblock copolymer, the curves noticeably shifted toward lower retention times compared to those of corresponding PDLLA macroinitiators (Figure 5B and 5D et Table 3). Clearly, the reactivity of secondary alcohols is known to be lower compared to that of primary alcohols.

Such reactivity issue for different protic compounds has also been found for the initiation of ring opening polymerization [START_REF] Alamri | Phosphazene-catalyzed ring-opening polymerization of epsilon-caprolactone: influence of solvents and initiators[END_REF][START_REF] Zhu | Influences of a Dizinc Catalyst and Bifunctional Chain Transfer Agents on the Polymer Architecture in the Ring-Opening Polymerization of epsilon-Caprolactone[END_REF]. Consequently, the presence of bis-hydroxy terminal groups on PDLLA influences the reactivity of the block copolymerization. Steric hindrance from methyl group of lactic acid unit might significantly impair the ring opening polymerization. In addition, it has been suggested from the literature that the activation of the hydroxyl end groups of poly(lactide) is lowered by the welldispersing negative charges which reduces the nucleophilicity of the protic group and consequently weaken the ROP initiation from that site [START_REF] Deng | Synthesis and characterization of biodegradable block copolymers of epsilon-caprolactone and D,L-lactide initiated by potassium poly(ethylene glycol)ate[END_REF][START_REF] In't Veld | Melt block copolymerization of epsilon-caprolactone and L-lactide[END_REF]. In this study, we demonstrated that B-A-B block copolymers with PDLLA central block can only be efficiently activated without any transesterification via an activated monomer mechanism (AMM) (Figure 6). Hence, electrophilic activation with MSA catalyst generated proper B-A-B triblock without transesterification while activated chain-end mechanism (ACEM) caused by Sn(Oct) 2 and nucleophilic TBD (Figure 6) lead to transesterification or no copolymerization and is therefore not appropriate for copolymerization with PLA first route.

Lastly, the study on step copolymerization allowed to determine that MSA activation was the only solution to generate block copolymers based on PLA macroinitiator. This catalytic approach would take a remarkable advantage if sequential one-pot copolymerization could also lead to controlled block copolymer with PDLLA first route and without transesterification. Traditionally, sequential copolymerization is the classic approach for obtaining highly defined and well-controlled block copolymerization with low molecular weight dispersity. Typically, sequential copolymerization consists on feeding the reaction by addition of a second monomer once the initial block polymer has been achieved. Hence, we tried to generate triblock copolymers PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL in one pot by sequential copolymerization, with a particular interest in the conversion rate and absence of transesterification (Figure S6, S7). As we mentioned in the introduction, block copolymerization by sequential polymerization using organocatalysis is not frequent in the literature especially due to the divergent reactivity between the monomers/catalysts couples [START_REF] Wang | Traceless switch organocatalysis enables multiblock ring-opening copolymerizations of lactones, carbonates, and lactides: by a one plus one approach in one pot[END_REF]. In the traceless switching approach from Wang et al., sequential one pot block copolymerization has been obtained by switching the catalysis from a Bronsted cationic acid to a nucleophilic base one. A similar approach was thus used in our block copolymerization, where the first PDLLA block was synthesized by nucleophilic activation and then switched to an electrophilic one for the synthesis of the second block. Hence, a traceless switch organocatalysis strategy from Bronsted guanidine base to cationic sulfonic acid was employed for one pot PDLLA first-route block copolymerization. The conversion of the second block was similar to those obtained by step copolymerization, and no trace of transesterification was detected by NMR and SEC.

Conclusions

Owing to the deep investigation of the different ring opening polymerization mechanisms, we succeeded in the determination of the most appropriate catalytic pathway for the preparation of well-defined triblock copolymers starting from PDDLA as macroinitiator. In particular, cationic catalysis using electrophilic MSA was the single approach to synthesize PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL triblock copolymers without any secondary reactions such transesterification. Activated monomer mechanism was the most convenient approach leading to a controlled block copolymerization.

In such a way, sequential copolymerization was achieved via traceless switching organocatalysis using sequentially TBD and MSA catalysts to successfully generate triblock copolymer according to the PDLLA first route.

Homopolymerization of TMC.

In the case of TMC homopolymerization, the polymer peak area at 4.18 ppm and the monomer peak area at 4.35 ppm are taken into consideration for the calculation of monomer conversion percentage. On the spectrum represented in Figure S2A we note a conversion of 99% (by MSA catalysis) and therefore absence of all monomer peaks. The 1 H-NMR spectra of TMC homopolymer obtained by stannous octanoate and TBD catalysis are similar to Figure S2B and is not represented. The degree of polymerization equals to the initially desired 100 units is calculated by comparing the ratio of the peak area at 3.67 ppm (belonging to 4 equivalent H of the hexane diol initiator) with the peak area at 4.18 ppm (belonging to the 2-CH 2 -in the PTMC repeating unit).

Homopolymerization of ε-CL.

In the case of ε-CL homopolymerization, the polymer peak area at 4.06 ppm and the monomer peak area at 4.15 ppm are taken into consideration for the calculation of monomer conversion percentage. On the spectra represented in Figure S3A, we observe no presence of any monomer peaks after 24 hours of reaction (catalyzed by stannous octanoate) and therefore we conclude that the reaction is complete (> 99 % conversion). On the opposite, on the spectra in Figure S3B, we note weak DL-LA conversion of around 17 % after 24 hours of reaction, catalyzed by TBD, with catalyst residues present between 3.

  Blanquer Institut Charles Gerhardt de Montpellier (ICGM) University of Montpellier, Place Eugène Bataillon Batiment 17 34095 Montpellier, France Tel: + 33467144970 Email: sebastien.blanquer@umontpellier.frHighlights  Synthesis of biodegradable PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL triblock copolymers by ring opening polymerization.

Figure 1 .

 1 Figure 1. Synthesis of triblock PTMC-b-PDLLA-b-PTMC and PCL-b-PDLLA-b-PCL via PDLLA first route.

Figure 2 .

 2 Figure 2. NMR analyses of the copolymer PCL-PDLLA-PCL formed upon Sn(Oct) 2 catalysis. A/ 1 H-NMR spectrum in CDCl 3 of the copolymer with the assigned signals. The arrows represent the characteristic peaks of random sequence of copolymer coming from the transesterification, B/ SEC chromatograms of the initial homopolymer PDLLA (dots) and the PCL-PDLLA-PCL copolymer (solid

Figure 3 .

 3 Figure 3. Spectroscopy analyses after copolymerization of TMC using PDLLA macroinitiator through anionic activation with TBD. A/ 1 H NMR spectrum in CDCl 3 of the copolymer with the assigned signals, B/ 2D DOSY 1 H-NMR spectrum shows the different diffusion coefficient after reaction, the peaks of

  block was synthesized by TBD activation and led to M nth = 7200 g.mol -1 ; Mn SEC = 9881 g.mol -1 ; Mp SEC = 11370 g.mol -1 .

Figure 4 .

 4 Figure 4. 13 C-NMR spectra in CDCl 3 for each triblock PTMC-b-PDLLA-b-PTMC (A) and PCL-b-PDLLA-b-PCL (B) obtained by cationic activation using MSA catalyst, with expanded carbonyl region. Specific assignment signals are specified.

Figure 5 .

 5 Figure 5. A/ 2D DOSY 1 H-NMR spectrum of PTMC-b-PDLLA-b-PTMC, diffusion coefficients (black for block copolymer and red for the initial PDLLA homopolymer, B/ SEC chromatograms of initial homopolymer PDLLA (dots) and PTMC-b-PDLLA-b-PTMC (solid line), C/ 2D DOSY 1 H-NMR spectrum of PCL-b-PDLLA-b-PCL, diffusion coefficients (black for block copolymer and red for initial PDLLA homopolymer), D/ SEC chromatograms of initial homopolymer PDLLA (dots) and of PCL-b-PDLLA-b-PCL (solid line).

Figure 6 .

 6 Figure 6. Activation mechanisms of the different employed catalysts through ACEM or AMM approaches.

Figure S1. 1 H

 1 Figure S1. 1 H-NMR spectra of DL-LA homopolymerization. A/ Full conversion of DL-LA after 2 minutes of reaction, catalyzed by TBD (in red -DL-LA monomer, in black -PDLLA after full conversion, before precipitation: absence of all monomer peaks); B/ 10% of DL-LA conversion after 17 hours of reaction, catalyzed by MSA (in red -DL-LA monomer, in black -

Figure S2. 1 H

 1 Figure S2. 1 H-NMR spectra of TMC homopolymerization. A/ Full conversion of TMC after 17h of reaction, catalyzed by MSA (in red -TMC monomer, in black -PTMC after full conversion, before precipitation: absence of all monomer peaks) B/ Final spectrum of PTMC homopolymer after precipitation with end-chain functionalities present at 3.67 ppm.

  2 and 3.3 ppm. The 1 H-NMR spectrum of DL-LA homopolymer obtained by MSA catalysis is not represented because it is similar to the spectrum of FigureS3C. The degree of polymerization equals to the initially desired 100 units and is calculated by comparing the ratio of the peak area at 3.67 ppm (belonging to 4 equivalent H of the hexane diol initiator) with the peak area at 4.06 ppm (belonging to the -CH 2 -in the PCL repeating unit).

Figure S3. 1 H

 1 Figure S3. 1 H-NMR spectra of ε-CL homopolymerization. A/ Full conversion of ε-CL after 24 hours of reaction, catalyzed by stannous octanoate (in red -ε-CL monomer, in black -PCL homopolymer after full conversion, before precipitation); B/ 17% of ε-CL conversion after 24 hours of reaction, catalyzed by TBD (in red -ε-CL monomer, in black -the reaction mixture); C/ Final spectrum of PCL homopolymer after precipitation with end-chain functionalities present at 3.67 ppm.

Figure S5. 1 H

 1 Figure S5. 1 H-NMR spectra of PCL-b-PDLLA-b-PCL triblock copolymer formation catalyzed by TBD after 72 hours of reaction (in black -the reaction medium; in red -ε-CL monomer).

Figure S6 .

 S6 Figure S6. Characterization of PTMC-b-PDLLA-b-PTMC by sequential one-pot copolymerization A/ 1 H-NMR; B/ 13 C-NMR spectra; C/ SEC chromatogram.

Figure S7 .

 S7 Figure S7. Characterization of PTMC-b-PDLLA-b-PTMC by sequential one-pot copolymerization A/ 1 H-NMR; B/ 13 C-NMR spectra; C/ SEC chromatogram.

Table 1 .

 1 List of the reported attempts to synthesize block copolymer with PLA macroinitiator.

	Block

copolymer type Activation process Active reagents (catalyst or initiator) Effect on block copolymerization References

			Dimethyl(salicylaldi	Block copolymerization
	PLLA/PCL	Initiation	minato)	without	[21]
			aluminum	transesterification
	PLLA/PCL PDLLA/PCL	Initiation	Ti(OiPr) 2 supported by aminodiol ligand
	PLLA-PDTC	Initiation	Al(O-sec-Bu) 3 Zn(Et) 2 Bu 2 Sn(OMe) 2	Presence of transesterification	[12]
			Potassium
	PDLLA/PCL	Initiation	poly(ethylene glycol)ate	No reaction	[13]
			macroinitiator
	PLLA/PCL PDLLA/PCL	Catalysis	Al(OiPr) 3	Presence of transesterification	[14]
	PLLA/PCL	Catalysis	Al(OiPr) 3	Presence of transesterification	[15]
	PLLA/PCL	Catalysis	K[(N(SiMe) 3 ] 3	No reaction	[16]
	PLLA/PCL	Catalysis	SnOct 2	Presence of transesterification	[17]
	PDLA/PTMC PLLA/PTMC	Initiation	Al(OiPr) 3 + Schiff base ligand	Block copolymerization transesterification without	[18]
	PLLA/PCL	Initiation	Al(OiPr) 3 + Schiff base ligand	Block copolymerization transesterification without	[19]
	PLLA/PTMC PLLA/PCL	Catalysis + protective additive	SnOct2 + α-Methyl styrene	Block copolymerization transesterification without	[20]

Table 2 .

 2 Comparison of the conversion rate for the homopolymerization of the studied monomers using 1,6 hexanediol as initiator.

	Catalysts Mechanism	T (°C)	Conversion of TMC	Conversion of DL-LA	Conversion of ε-CL
	MSA	Cationic	30 °C	100 % after 17 h 10 % after 17 h	100 % after 6 h
	TBD	Anionic	25 °C	100 % after 1 h	100 % after 2 min	17 % after 24 h
	Sn(Oct) 2	Coordination-insertion	100 °C 100 % after 24 h 100 % after 24h 100 % after 24 h

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Supplementary Information

A simple and general approach for the synthesis of biodegradable triblock copolymers by organocatalytic ROP from poly(lactide) macroinitiators Monomer conversion is followed by the disappearance of the characteristic monomer peaks and by appearance of new, shifted ones, polymer peaks. The monomer conversion is calculated by the following formula: % monomer conversion =

x 100

Homopolymerization of DL-LA.

In the case of DL-LA homopolymerization, the polymer peak area at 5.17 ppm and the monomer peak area at 5.02 ppm are taken into consideration for the calculation of monomer conversion percentage. In Figure S1A, we observe no presence of any monomer peaks after 2 minutes of reaction (catalyzed by TBD) and therefore we conclude that the reaction is complete (> 97 % conversion). TBD catalyst residues are present between 3.2 and 3.3 ppm, observable in the reaction mixture and later eliminated through precipitation. On the opposite, on the spectra in Figure S1B, we note weak DL-LA conversion of around 10 % after 17 hours of reaction (catalyzed by MSA). Figure S1C represents PDLLA homopolymer after precipitation in methanol. 1 H-NMR spectrum of PDLLA homopolymer obtained by stannous octanoate catalysis is similar to the spectra of Figure S1C and is therefore not represented. The degree of polymerization equals to the initially desired 100 units is calculated by comparing the ratio of the peak area at 4.14 ppm (belonging to 4 equivalent H of the hexane diol initiator) with the peak area at 5.17 ppm (belonging to the -CH-in the PDLLA repeating unit). The molar ratios of (50/50) were determined by comparing the characteristic peak areas of the -CH-repeating unit of PDLLA situated at 5.17 ppm with the peak area of the 2-CH 2 -repeating units of PTMC at 4.18 ppm for the PTMC 50 -PDLLA 100 -PTMC 50 triblock copolymer represented in Figure S4A.


Yuki Orikasa

Kisu Kazuaki

Naohisa Ohara

Kentaro Rozier

Kazuaki Kisu

Etsuro Iwama

Wako Naoi

Yusuke Yamaguchi

Yoshitomo Yamaguchi

Naohisa Okita

Koji Ohara

Toshiyuki Munesada

Masashi Hattori

Kentaro Yamamoto

Patrick Rozier

Patrice Simon

Katsuhiko Naoi

researchers and makes it freely available over the web where possible Noncrystalline Nanocomposites as a Remedy for the Low Diffusivity of Multivalent Ions in Battery Cathodes

Rechargeable batteries using multivalent metals are among the most promising next-generation battery systems due to their high capacity, high safety, and low cost compared with lithium-ion batteries. However, strong cation-anion interaction degrades diffusion in solid cathodes, an effect that must be mitigated to yield practical multivalent metal batteries. We show that a highly defective iron phosphate-carbon composite prepared by ultracentrifugation serves as a reversible insertion/deinsertion for magnesium ions with, and operates beyond, a 2-V cell voltage at room temperature. A composite of noncrystalline particles that embeds the surrounding carbon structure enhances the magnesium-ion diffusion in the solid phase with stability for cycle life. X-ray absorption spectroscopy, transmission electron microscopy with energy-dispersive X-ray spectroscopy, and high-energy X-ray scattering measurements demonstrate magnesium-ion insertion and extraction in the defective iron phosphate without conversion reactions. This work suggests promising applications for highly defective structures as intercalation hosts for multivalent ions.

■ INTRODUCTION

The need for high-energy-density, abundant, inexpensive, and nontoxic metals for battery anodes has recently led to a renewal in interest from the scientific community for the use of multivalent metal anodes, such as Mg, Ca, or Al. 1 The advantages of multivalent metals include safety, 2 high energy density (e.g., increase in charge carrier density and decrease in the occupation of host structure sites by charge carrier cations), and a relatively large negative standard electrode potential, 3 although recent research on the magnesium anode has reported dendrite formation of magnesium in a specific condition. 4 Multivalent metals are also advantageous from the perspective of natural-resource conservation, a problematic aspect of lithium-ion batteries. 5 However, despite these advantages and several years of research, applications for devices based on multivalent metals remain limited. 6,7 A key issue lies in the dramatic reduction in conductivity compared to monovalent cation systems due to strong electrostatic interactions between multivalent cations and anions. This challenge results in devices based on multivalent cations continuing to require high operating temperatures to achieve realistic operating rates, despite many years of effort (see Table S1 in the Supporting Information). The kinetics of ion insertion and deinsertion, the topochemical reactions crucial for active materials of rechargeable batteries, is particularly slow for multivalent cation systems, and designing practical devices will require novel strategies for addressing this problem.

The main challenge of multivalent cation systems is to design cathode materials as host structures for intercalation of multivalent ions that can match the performance of lithium-ion battery cathodes. 8 Although the radius of the magnesium ion (72 pm) is nearly identical to that of the lithium ion (76 pm in a hexacoordinated environment), 9 the divalent character of the magnesium ion doubles the charge density over that of the monovalent lithium ion. This reduces the solid-state (chemical) diffusivity of magnesium ion in active materials, resulting in the slow kinetics of electrochemical insertion and deinsertion. For example, Levi et al. considered the diffusion of magnesium ions in the active materials of the transition-metallayered oxide A x CoO 2 (A = Li, Mg) 10 and showed that when the mobile ion is located at a stable AO 6 site, the defect formation energy is larger for magnesium ions due to larger Coulomb interactions. Rong et al. performed first-principles calculations using the structure of typical lithium-ion active battery materials to estimate the diffusion barriers for lithium ions and various multivalent ions, including magnesium, zinc, calcium, and aluminum. 11 They found that the ion charge density and the anion coordination number of the insertion site within the crystal structure greatly influence the ion diffusion barrier, which is drastically increased for a multivalent ion. Based on simple one-dimensional (1D) diffusion calculations using the diffusion length Dt (where D and t are the diffusion constant and the diffusion time, respectively) and the relation ν ≈

- ( ) D a exp E kT 2 act
between the diffusion constant and the activation energy (with a, ν, E act , and kT representing the hopping length, atomic transition frequency, activation energy, and temperature in energy units, respectively), Canepa et al. showed that for activation energies >0.8 eV, particles of size ≤10 nm are required to achieve magnesium-ion insertion/deinsertion at a rate of 0.1C at room temperature (Figure S1). 8 As a result, cathode materials that usually present particle sizes >10 nm are generally operated at slow rates or elevated temperatures to improve ion diffusion for solid electrodes.

Following these theoretical advantages and disadvantages of multivalent cation batteries, we next survey previous studies of host structures used for multivalent cation insertion and extraction (see Table S1). One successful system leverages chalcogenides with Chevrel-structured Mo 6 S 8 7 and spinelstructured titanium sulfide or selenide. 12,13 However, all chalcogenide-based systems studied suffer from low operating potentials and poor rate characteristics. As an alternative to chalcogenides, oxide-based host structures, such as V 2 O 5 and α-MnO 2 , have been considered to increase the operating potential. V 2 O 5 has been used as a model system in many studies attempting to realize multivalent cation insertion/ deinsertion reactions at acceptable rates, which revealed the critical role of water in the electrolytes. [14][START_REF] Nam | The High Performance of Crystal Water Containing Manganese Birnessite Cathodes for Magnesium Batteries[END_REF][START_REF] Gershinsky | Electrochemical and Spectroscopic Analysis of Mg 2+ Intercalation into Thin Film Electrodes of Layered Oxides: V 2 O 5 and MoO 3[END_REF][START_REF] Hayashi | Electrochemical Insertion/Extraction of Calcium Ions Using Crystalline Vanadium Oxide[END_REF][START_REF] Amatucci | Investigation of Yttrium and Polyvalent Ion Intercalation into Nanocrystalline Vanadium Oxide[END_REF][START_REF] Novaḱ | Magnesium insertion electrodes for rechargeable nonaqueous batteriesa competitive alternative to lithium? Electrochim[END_REF][START_REF] Novaḱ | Electrochemical Insertion of Magnesium in Metal Oxides and Sulfides from Aprotic Electrolytes[END_REF][START_REF] Parija | Evaluation of Multivalent Cation Insertion in Single-and Double-Layered Polymorphs of V 2 O 5[END_REF][START_REF] Verrelli | On the strange case of divalent ions intercalation in V 2 O 5[END_REF] Another example of a host structure is α-MnO 2 , which exhibits promising properties but suffers from poor cycle performance. [START_REF] Zhang | α-MnO 2 as a cathode material for rechargeable Mg batteries[END_REF] Despite numerous advances, oxide-based cathode materials, like the chalcogenide compounds, appear incapable of meeting the performance requirements for practical multivalent cation batteries.

The difficulties encountered in constructing practical multivalent cation batteries from chalcogenides and oxides spurred researchers to consider a third family of candidate materials, polyanion compounds, which are known, from experience with lithium-ion batteries, to exhibit good performance in several key areas. For example, olivine-structured polyanion compounds exhibit high operating potential, high charge and discharge rates, and good cycle performance. [START_REF] Kang | Battery materials for ultrafast charging and discharging[END_REF][START_REF] Padhi | Phospho-olivines as positive-electrode materials for rechargeable lithium batteries[END_REF] Ling et al. conducted first-principles calculations of redox potentials and lattice volumes for olivine-type compounds with and without intercalation of magnesium ions. They showed that, among the various compounds, FePO 4 is particularly promising because it allows magnesium-ion insertion and extraction within the electrolyte stability potential window, as well as exhibits relatively small changes in lattice volume. [START_REF] Ling | Firstprinciples study of the magnesiation of olivines: redox reaction mechanism, electrochemical and thermodynamic properties[END_REF] Le Poul et al. demonstrated experimentally that up to 0.38 magnesium ions can be inserted and extracted in FePO 4 . [START_REF] Poul | Development of potentiometric ion sensors based on insertion materials as sensitive element[END_REF] However, these experiments were conducted at extremely slow charge/discharge rates. Subsequent work showed that, at moderate or higher rates, magnesium intercalation into FePO 4 fails to proceed due to instabilities in the olivine crystal structure. [START_REF] Zhang | Unveil the Chemistry of Olivine FePO 4 as Magnesium Battery Cathode[END_REF] Thus, the promising theoretical capabilities of FePO 4 remain unrealized in practice.

In this study, we propose and experimentally validate a strategy that uses a noncrystalline host, specifically, a FePO 4carbon composite, prepared by the ultracentrifugation (UC) method we previously pioneered for fabricating electrodes for nanohybrid capacitors. [START_REF] Naoi | Ultrafast Nanocrystalline-TiO 2 (B)/Carbon Nanotube Hyperdispersion Prepared via Combined Ultracentrifugation and Hydrothermal Treatments for Hybrid Supercapacitors[END_REF][START_REF] Naoi | Ultrafast charge-discharge characteristics of a nanosized core-shell structured LiFePO 4 material for hybrid supercapacitor applications[END_REF][START_REF] Iwama | Enhanced Electrochemical Performance of Ultracentrifugation-Derived nc-Li 3 VO 4 /MWCNT Composites for Hybrid Supercapacitors[END_REF][START_REF] Naoi | (PO 4 ) 3 /Carbon Nanofiber Composites[END_REF][START_REF] Yonekura | Progress of the conversion reaction of Mn 3 O 4 particles as a function of the depth of discharge[END_REF][START_REF] Naoi | Second generation 'nanohybrid supercapacitor': Evolution of capacitive energy storage devices[END_REF] We demonstrate that UCprepared composite electrodes allow for ultrafast insertion and deinsertion of lithium ions, [START_REF] Naoi | Ultrafast Nanocrystalline-TiO 2 (B)/Carbon Nanotube Hyperdispersion Prepared via Combined Ultracentrifugation and Hydrothermal Treatments for Hybrid Supercapacitors[END_REF][START_REF] Naoi | Ultrafast charge-discharge characteristics of a nanosized core-shell structured LiFePO 4 material for hybrid supercapacitor applications[END_REF] and also show that this yields high-performance electrode materials for multivalent cation rechargeable batteries. Here FePO 4 is selected as the electrode material due to its stable structure, reinforced by the P-O bonds, and relatively high operating potential for insertion and extraction of multivalent cations. Because the insertion and deinsertion of magnesium ions in olivinestructured FePO 4 crystals have been reported to be irreversible, [START_REF] Zhang | Unveil the Chemistry of Olivine FePO 4 as Magnesium Battery Cathode[END_REF] we consider the preparation of noncrystalline, highly defective FePO 4 to be highly dispersed throughout the carbon structure. We demonstrate that the crystallinity of the obtained active material is related to the crystallinity of the carbon used during the UC process, and triggers the efficiency and reversibility of the faradic insertion and deinsertion of multivalent cations, even at room temperature.

Furthermore, we use transmission electron microscopy, Xray absorption spectroscopy, and the pair distribution function from X-ray total scattering to analyze the reaction mechanisms of the charge and discharge processes. Our findings show that the enhancement of multivalent cation intercalation and extraction reactions is due to (a) a reduced diffusion length with reversible ion insertion and deinsertion using nanoactive materials embedded into the carbon and (b) enhanced ionic diffusion due to the highly defective active material. We anticipate that our work will offer opportunities toward the practical realization of multivalent cation batteries.

■ MATERIALS AND METHODS

Synthesis of UC-Derived Materials (UC-FePO 4 ). UC-FePO 4 was prepared via the "ultracentrifugation (UC)" method described previously. [START_REF] Naoi | Ultrafast charge-discharge characteristics of a nanosized core-shell structured LiFePO 4 material for hybrid supercapacitor applications[END_REF] Fe(CH 3 COO) 2 , LiCH 3 COO, and H 3 PO 4 were used as the Fe, Li, and PO 4 sources, respectively, while citric acid (C 6 H 8 O 7 ) was used as the chelating agent. Hollow-structured Ketjen black (KB; EC600JD, Ketjen Black International) with 50-nm-diameter primary particles with a specific surface area (SSA) of 1270 m 2 g -1 was selected as the precursor carbon matrix for bedding the nanoscale FePO 4 due to its high electronic conductivity and specific surface area. Ultrapure water (17 Ω cm) was used as the medium for the entire preparation scheme.

Two solutions, A and B, were prepared. For solution A, LiCH 3 COO, Fe(CH 3 COO) 2 , and C 6 H 8 O 7 were dissolved in H 2 O and mixed at a molar ratio of 1:1:1. For solution B, H 3 PO 4 solution and KB were mixed for 30 min using ultrasonication and then treated by a first UC process for 5 min to form a blackish gel. After the addition of solution A into B, a second UC treatment was performed for 5 min. Following a drying process using a spray dryer, further annealing for 8 min (3 min heating, 5 min holding) at 700 °C under a nitrogen flow yielded the UC-FePO 4 /KB composite powder with a carbon content of 50 wt %. As discussed in Results and Discussion, the lithium source is not distributed into the FePO 4 particles even though it remains in the composite powder. Electrodes were prepared from the composite powder and poly(tetrafluoroethylene) (PTFE) with a weight ratio of 90:10. As a result, the weight ratio of the active material, carbon, in PTFE was 45:45:10.

Crystalline FePO 4 . Crystalline FePO 4 was prepared following a two-step procedure consisting of first preparing crystalline carboncoated LiFePO 4 and then further chemically oxidizing it to remove lithium. Carbon-coated LiFePO 4 was prepared by a solid-state reaction. Li 2 CO 3 , FeC 2 O 4 •2H 2 O, and (NH 4 ) 2 HPO 4 were mixed at stoichiometric ratios in ethanol using a planetary ball mill with a zirconia pot and balls for 12 h at 400 rpm. After milling and drying, the precursor was mixed with 10 wt % carbon black in the ball mill for 24 h at a rotation speed of 400 rpm. The mixture was pelletized and annealed at 600 °C under a 97% argon-3% hydrogen atmosphere for 6 h. FePO 4 was prepared by chemical oxidation from the obtained LiFePO 4 using nitronium tetrafluoroborate (NO 2 BF 4 ) as an oxidizing agent. NO 2 BF 4 was dissolved in acetonitrile, and then the LiFePO 4 powder was stirred in the solution for 48 h. The mixture was filtered and washed with acetonitrile. The results of the crystal structure analyses for the latter are shown in Figure S2 and Table S2. Electrodes were prepared from the FePO 4 active material, carbon black, and PTFE with a weight ratio of 45:45:10.

Electrochemical Measurements. For electrochemical lithium insertion and deinsertion, two-or three-electrode cells were prepared using metallic lithium as the reference and counter electrodes. 1 M LiPF 6 in a 3:7 volume ratio of ethylene carbonate (EC) and diethyl carbonate (EMC) was used as the electrolyte solution. For electrochemical magnesium insertion and deinsertion reactions, charged cells using the lithium electrolyte were dismantled in an Ar-filled glovebox. The working electrode was rinsed several times with dimethyl carbonate and dried in vacuum. Electrochemical measurements were carried out using a three-electrode cell with an Ag + /Ag double-junction reference electrode. The counter electrode used was active carbon, and the electrolyte was 0.5 M magnesium bis(trifluoromethanesulfonyl)amide in acetonitrile [Mg(TFSA) 2 / AN]. A titanium mesh was employed as the current collector. Galvanostatic discharge and charge measurements were performed.

X-ray Absorption Spectroscopy. For Fe K-edge X-ray absorption spectroscopy (XAS) measurements, charged and discharged electrodes were finely intermixed with boron nitride powder and pressed into pellets. These pellets were sealed in laminated packets in an Ar-filled glovebox. XAS spectra were measured near the Fe K-edge energy at room temperature in transmission mode at the beamline of the SPring-8 synchrotron radiation facility (BL01B1 and BL14B2) in Hyogo, Japan, and data were collected at room temperature. Extended X-ray absorption fine structure (EXAFS) analysis was performed using REX2000 data analysis software with the theoretical backscattering phases and amplitudes calculated using the FEFF8 code.

X-ray Total Scattering Measurement. The high-energy X-ray total scattering measurement was conducted at room temperature at the SPring-8 high-energy X-ray diffraction (XRD) beamline BL04B2 using a two-axis diffractometer. The incident X-ray energy obtained from a Si(220) crystal monochromator was 61.4 keV. The diffraction patterns of the samples were measured at angles from 0.3 to 48°. The intensity of the incident X-ray was monitored in an ionization chamber filled with Ar gas, and the scattered X-rays were observed by CdTe detectors. The collected datasets were corrected for absorption, background, and polarization effects.

Transmission Electron Microscopy. The UC-FePO 4 composite nanostructure and particle size distribution were characterized using high-resolution transmission electron microscopy (TEM) (Hitachi models H9500 and HD2700). Only the UC-FePO 4 composite and KB were subjected to electrical measurements using the nanoprobing system Hitachi N-6000SS. 1a) exhibits an absorption edge energy nearly identical to that of crystalline FePO 4 , which shows that iron has solely the trivalent state, in agreement with the chemical formulae of FePO 4 . However, inductively coupled plasma (ICP) analysis of the sample shows that Fe and P, as well as Li, are present in equal quantities (atomic composition ratio Li/ Fe/P = 1.0:1.0:1.0). Together with the XANES results, this observation supports the presence of lithium in the graphitic KB carbon phase, not in FP. The composite corresponds then to a mixture of pure FePO 4 and Li-doped KB.

Figure 1b,c shows bright-and dark-field TEM images of the pristine UC-FePO 4 /KB, and observations at several magnifications are shown in Figure S3. The images show particles with sizes around 10 nm embedded in KB (random graphitic carbon), as designated by the schematic representation in Figure 1d, which confirms the benefit of the UC treatment for preventing grain growth and agglomeration. In addition, the strong interaction between the FePO 4 particles and carbon is confirmed by the comparison of the conductivity measured for the pristine UC-FePO 4 /KB, which is higher than that of KB alone (Figure S4).

Crystal Structure Analysis. The XRD pattern seen in Figure 1e exhibits broad peaks at 10°and near 18°, attributed to the glass capillaries and the carbon, respectively, with no evidence of FePO 4 Bragg peaks. Also, a clear lattice image cannot be confirmed by the TEM observation of our UC-FePO 4 /KB composite. On the other hand, the existence of short-and medium-range ordering is demonstrated by the radial distribution functions obtained from the EXAFS measurements (see Figures 1f andS5), which indicate atomic correlations persisting to large distances associated with second-and third-nearest-neighbor atoms. This coexistence of short-and medium-range orders with long-range disorder demonstrates that the state of the pristine UC-FePO 4 /KB is not fully amorphous but highly defective. This feature also demonstrates that pristine UC-FePO 4 /KB prepared using random graphitic carbon, the KB, includes a highly defective structure without long-range order. To confirm the importance of the crystallinity of the carbon matrix used as a UC precursor, we synthesized another composite using well-crystallized and multiwalled carbon nanotubes as the carbon matrix. XRD and TEM characterization techniques (Figure S6) unambiguously show the formation of the well-crystallized (long-rangeordered) LiFePO 4 with an epitaxial olivine crystal growth along the crystal face of the carbon nanotube, indicating that the lithium source is maintained in the LiFePO 4 particles, and a very strong interaction exists with the carbon in which they are embedded.

In contrast, with samples prepared with KB, carbon regions are highly disordered following the UC treatment, preventing the emergence of long-range ordering during crystal growth. The nature of carbon impacts (1) the location of Li that changes the valence state of Fe and (2) the crystallinity of the active material sample. The former effect has not been analyzed, and further investigations are required. In our previous study, the core-shell nanocomposite composed of crystalline LiFePO 4 and the highly defective amorphous phase containing Fe 3+ encapsulated by a graphitic carbon was prepared using the UC process. [START_REF] Naoi | Ultrafast charge-discharge characteristics of a nanosized core-shell structured LiFePO 4 material for hybrid supercapacitor applications[END_REF] While this study used the slow drying process with a vacuum oven, our current synthesis utilized the spray drying method. This rapid drying process could prevent the particle growth of the thermodynamically stable LiFePO 4 crystal.

Figure 1g shows the pair distribution functions (PDFs) of the crystalline FePO 4 and the UC-FePO 4 /KB. The total structure factors, S(Q), are provided in Figure S7. The experimental PDF profile of the crystalline FePO 4 agrees well with the simulation profile based on the crystal structure of the crystalline FePO 4 (Figure S8a). The first peak at 1.5 Å is related to the P-O correlation associated with PO 4 polyanions, and the second and third peaks at 2.1 and 2.4 Å correspond to the Fe-O correlation in FeO 6 octahedra and the O-O correlation in PO 4 tetrahedra, respectively. Both peaks at 2.8 and 3.2 Å are related to the Fe-P correlation, which may overlap with the O-O correlations in the FeO 6 octahedra, while all peaks observed above 3.5 Å involve various types of bonds that cannot be easily deconvoluted.

For the UC-FePO 4 /KB, the correlations are visible up to only 5 Å, which is in perfect agreement with the loss of the long-range ordering previously observed using XRD. Characteristic points in the profile of UC-FePO 4 /KB include the highintensity peak located at 1.4 Å and a new peak observed at 2.4 Å, which can be attributed to the contribution of the C-C bonds derived from KB (where the first-and second-neighbor C-C bonds in the layer structure of graphite are 1.42 and 2.46 Å). [START_REF] Trucano | Structure of graphite by neutron diffraction[END_REF] Comparing the trivalent crystalline FePO 4 with UC-FePO 4 /KB, the shift toward lower values of the peak located at 2 Å shows a lowering of the Fe-O interatomic distance, Electrochemical Behavior. We first use Li half-cells to compare the electrochemical behavior of pristine UC-FePO 4 / KB and crystalline FePO 4 samples. Figure 2a shows the charge/discharge curves for the pristine UC-FePO 4 /KB using a lithium-ion battery electrolyte. As discussed above, the Fe Kedge XANES results confirm that Fe in pristine UC-FePO 4 /KB exists nearly exclusively at the valence state of +3, and, thus, the Fe 3+ /Fe 2+ redox couple makes almost no contribution to the initial charge cycle, at which point the cell might be expected to exhibit near-zero capacity on first charging. As a result, the capacity of about 50 mAh g -1 measured during the first charge (the black curve in Figure 2a) is due to nonfaradic reactions involving KB. During subsequent discharging and charging reactions, the Fe 3+ /Fe 2+ redox couple is active and delivers a capacity of 110 mAh g -1 , yielding, taking into account the extra capacity due to Li-KB reaction, a total capacity of 160 mAh g -1 .

As noted above, the results of the XANES measurements demonstrate that lithium, although present in equal abundance with iron, is only present in the KB part of the composite and should have no effect on the overall electrochemical behavior of FePO 4 . To confirm that, an extra UC-FePO 4 /KB composite synthesized following the chemical process described above but without the lithium reactant has been prepared. The electrochemical tests show that this Li-free composite, besides exhibiting the same nonfaradic capacity at the first charge, delivers a lower charge/discharge capacity compared to samples prepared with the lithium reactant (Figure S9). This result shows that lithium, despite not contributing to the charge/discharge capacity, plays an indirect role. This, though currently under investigation, can be speculated to be related to the enhancement of the composite's conductivity, allowing reaching a capacity close to the theoretical one of FePO 4 .

To investigate the structural evolution of our synthesized materials in response to the lithium intercalation during cycling, we conduct intermittent charge and discharge tests on the pristine UC-FePO 4 /KB electrodes using a three-electrode cell setup. The resulting curves from the open-circuit potential vs charge/discharge state are plotted in Figure 2b and show a slopping potential profile different from the well-known broad plateaus typically obtained for crystalline FePO 4 (Figure S10). While the plateaus are a typical indicator of a two-phase coexistence, the continuous potential variation observed for UC-FePO 4 /KB corresponds to a continuous variation of the lithium chemical potential through the electrode, indicating the absence of phase separation. Therefore, the pristine UC-FePO 4 /KB remains in a single phase throughout the process of the lithium-ion insertion and deinsertion. This finding agrees with previously reported results for amorphous FePO 4 . [START_REF] Zhang | Construction of a cathode using amorphous FePO 4 nanoparticles for a high-power/energy-density lithium-ion battery with long-term stability[END_REF][START_REF] Fang | Mesoporous Amorphous FePO 4 Nanospheres as High-Performance Cathode Material for Sodium-Ion Batteries[END_REF][START_REF] Yin | Enhanced cathode performances of amorphous FePO 4 hollow nanospheres with tunable shell thickness in lithium ion batteries[END_REF][START_REF] Yin | A grapheneamorphous FePO 4 hollow nanosphere hybrid as a cathode material for lithium ion batteries[END_REF] The formation of Fe 2 O 3 /Li 3 PO 4 nanocomposite can be ruled out as the voltage range used in this experiment excludes the possibility of activating the corresponding redox couple with a voltage reported to be <2.0 V. [START_REF] Larcher | Effect of Particle Size on Lithium Intercalation into α-Fe 2 O 3[END_REF] Charge/Discharge Properties of Pristine UC-FePO 4 as a Cathode Material for Magnesium-Rechargeable Batteries. The electrochemical magnesium-ion insertion and deinsertion in the UC-composite were investigated next. Although lithium's contribution to the electrochemical reaction is not significant (see the XANES experiments), pristine UC-FePO 4 /KB samples were first electrochemically Then, the fully oxidized sample was rinsed several times with a dimethyl carbonate solvent and dried in vacuum. These samples, noted as "treated UC-FePO 4 /KB", were then characterized in a three-electrode cell using Ag + /Ag as a reference electrode and 0.5 M magnesium bis-(trifluoromethanesulfonyl)amide in an acetonitrile electrolyte. We also conducted the charge/discharge measurement in the Mg-containing electrolyte using the pristine UC-FePO 4 /KB samples (Figure S11).

Figure 3a shows the charge/discharge profiles of the treated UC-FePO 4 /KB in the magnesium electrolyte beginning in the discharge mode and operating at room temperature at a C/20 rate. All experiments were achieved in anhydrous conditions (electrolyte water content <300 ppm), so the water-assisted cointercalation reactions reported previously for V 2 O 5 cannot be observed. [START_REF] Novaḱ | Magnesium insertion electrodes for rechargeable nonaqueous batteriesa competitive alternative to lithium? Electrochim[END_REF] A reversible capacity of 150 mAh g -1 at an average potential of 2 V vs Mg 2+ /Mg, converted according to the literature, [START_REF] Lu | On the electrochemical behavior of magnesium electrodes in polar aprotic electrolyte solutions[END_REF] was observed and remained stable over several cycles (Figure 3b). The discharged sample was analyzed ex situ by electron energy loss spectroscopy (EELS). From the measured spectrum shown in Figure S12, an atomic weight ratio for Fe/Mg of 75:25, corresponding to a composition Mg 0.33 FePO 4 , was found for the particles.

The results demonstrate that, in contrast to the conventional belief that the use of magnesium requires high temperatures and very low cycling rates, 12,23,42-44 the samples prepared using the UC treatment and the control it offers over the morphology and the crystalline state of FePO 4 exhibit significant activation of the reversible insertion of Mg 2+ ions even at room temperature and moderate cycling rates.

Figure 3c compares the second-cycle charge/discharge behavior of the crystalline FePO 4 active material to that of the treated UC-FePO 4 /KB. To ensure we assessed the charge/ discharge properties of the two materials under comparable conditions, we used a modified synthesis procedure for the crystalline FePO 4 electrodes to raise their carbon content to 45 wt %, equal to that of the treated UC-FePO 4 /KB electrodes, although these carbon structures between the two electrodes are not similar to each other. Whereas crystalline FePO 4 exhibits low capacity at room temperature, the treated UC-FePO 4 /KB exhibits a significantly improved charge/discharge capacity of about 150 mAh g -1 . This observation demonstrates that the use of highly defective UC-FePO 4 /KB, whose crystal structure differs significantly from that of crystalline materials, enables reversible magnesium-ion insertion and deinsertion in cathode materials. Figure 3d compares the rate capabilities of these two materials. For crystalline FePO 4 , the capacity is low and remains constant through cycling at rates ranging from C/ 20 to 10C, corresponding to the contribution of nonfaradic reactions due to the added carbon content. In contrast, the observed capacity for the treated UC-FePO 4 /KB composite depends strongly on the C rate, which decreases drastically from 150 mAh g -1 at C/20 to 50 mAh g -1 at 10C. This result indicates the occurrence of faradic reactions that correspond to the insertion of magnesium ion into FePO 4 along with the nonfaradic reaction due to carbon.

The capacity measured at a high rate (50 mAh g -1 ) is assumed to correspond to the nonfaradic surface contribution of the carbon from the composite, which should remain constant at any cycling rate. For reference, the chargedischarge tests using only KB with no active materials exhibited a capacity of approximately 50 mAh g -1 of KB (Figure S13), which is in good agreement with the capacity observed for UC-FePO 4 /KB at high rates. As a result, at the low C/20 rate, a capacity of 100 mAh g -1 for the magnesium insertion can be estimated and compared to the capacity of 177 mAh g -1 calculated for the full reduction of Fe 3+ down to Fe 2+ (Mg 0.5 FePO 4 ). Assuming the faradic reaction corresponds only to the insertion process of the magnesium ion into FePO 4 , the composition after discharge corresponds to Mg 0.28 FePO 4 .

However, because of the phase separation between the transition-metal oxide and MgO being reported to be more thermodynamically stable than that for the magnesiuminserted crystal structure, [START_REF] Hannah | On the Balance of Intercalation and Conversion Reactions in Battery Cathodes[END_REF] the possibility of such a phase separation in the case of a polyanionic compound should be considered. Zhang et al. reported, based on thermodynamic calculations, that under reducing condition [START_REF] Zhang | Unveil the Chemistry of Olivine FePO 4 as Magnesium Battery Cathode[END_REF] and for the oxidizing condition Fe 3 (PO 4 ) 2 will form Fe 2 O 3 , FePO 4 , and Fe 7 (PO 4 ) 6 . The kinetic effects, well known to prevent the formation of thermodynamically stable phases, are not considered here. To investigate if the phases resulting from such a thermodynamically driven separation are formed, a XANES analysis was performed ex situ on samples electrochemically charged and discharged at 55 °C to minimize the kinetic effects and reach thermodynamically stable states. Fe K-edge XANES spectra of charged and discharged UC-FePO 4 /KB with the magnesium electrolyte were compared with those of different iron-based compounds used as standards (Figure S14). The XANES of Fe 2 O 3 and FeO exhibit the characteristic peaks at 7131 and 7142 eV, respectively, which are not observed in the charged and discharged UC-FePO 4 /KB. This XANES result rules out the formation of iron oxide, but cannot confirm the absence of Fe 3 (PO 4 ) 2 due to similar Fe 2+ oxygenated surroundings (as in the XANES spectra) with discharged Mg x FePO 4 . In Figure 4a, the absorption edge at the Fe K-edge shifts downward in energy, reflecting the reduction of iron ions to maintain electrical neutrality upon the magnesium-ion insertion in the discharge reaction. This shift being observable at the early stage of the discharge process suggests that the reduction of Fe 3+ to Fe 2+ occurs before the nonfaradic process at the end of discharge.

XANES measurements are achieved for the various charged and discharged states to obtain further insights into the reaction mechanism. During discharge (intercalation), the Fe XANES signals shift to lower energy, evidencing a decrease in the oxidation state of Fe without reaching the value characteristic of a full iron reduction, as observed in LiFePO 4 . Moreover, the shape of the XANES curve near the intensity peak at 7124 eV is quite different from that of LiFePO 4 , which confirms again that some iron ions remain at the (+III) valence state. During charge (Figure 4b), the oxidation of Fe ions proceeds and the XANES curve overlaps with that of the treated UC-FePO 4 /KB, showing that the change in the valence of iron ions due to the insertion and deinsertion of magnesium ions is reversible. In a two-phase coexistence reaction between LiFePO 4 and FePO 4 , Fe K-edge XANES provides isosbestic points, [START_REF] Orikasa | Transient Phase Change in Two Phase Reaction between LiFePO 4 and FePO 4 under Battery Operation[END_REF] which cannot be observed, considering the enlarged view around 7128 eV (Figure S15). Although this indeterminate crystal structure precludes the definition of precise phases, these results confirm that the insertion and deinsertion of magnesium ions in UC-FePO 4 are not twophase reactions. The deconvolution of the XANES spectra in terms of Fe 2+ and Fe 3+ contributions was performed (Figure S16) to estimate the composition of the fully discharged sample. A composition of Mg 0.22 FePO 4 was found, which is close to the rough estimation that corresponds with the discharge faradic capacity responsible for Mg intercalation and EELS analysis.

To further investigate the possibility of the existence of a phase separation mechanism between Fe 3 (PO 4 ) 2 and Mg 3 (PO 4 ) 2 , we performed TEM-EDS measurements. As seen in the transmission image of the electrodes after discharge (Figure 5a), the structure of the FePO 4 particles embedded in carbon is preserved. The element mapping images (Figure 5bf) show that Fe, P, and O are located in the same region that does not overlap with regions in which C is observed, confirming that the composite is made of FePO 4 particles embedded in carbon. In addition, the intensity of Mg is observed only in regions where FePO 4 particles exist, which confirms that no phase segregation of Fe 3 (PO 4 ) 2 and Mg 3 (PO 4 ) 2 occurs.

The low-crystalline nature of UC-FePO 4 /KB complicates XRD analysis, so we used the total X-ray scattering and EXAFS analysis to evaluate the local structural changes. Figure 6a,b shows the reduced pair distribution functions (PDF) of the treated UC-FePO 4 /KB (before Mg discharge) and the discharged UC-FePO 4 /KB (after Mg discharge). The PDF profile of UC-FePO 4 /KB and the discharged sample appear quite similar with primilary peak shifts observed. The most apparent shift corresponds to the one toward higher values of the peak located close to 2 Å, attributed to Fe-O interatomic distances, which is in perfect agreement with the reduction of the Fe valence state and related increase of the Fe ion radius. Two other shifts are observed during Mg insertion toward higher and lower values for the peaks located at 2.5 and 3.2 Å, respectively. Without any structure data for the discharged sample, and knowing the similarity in the crystalline chemistry of Mg and Li, we simulated the PDF profile for a virtual Mg 0.5 FePO 4 that was considered isostructural with LiFePO 4 and compared it with those calculated for crystalline FePO 4 and LiFePO 4 (Figure S8). Based on this comparison, we consider that, besides the reduction of iron ions, the insertion of Mg in the FePO 4 structure induces the appearance of a peak close to 2.5 Å attributed to Mg-P interatomic distances and another close to 3.2 Å corresponding to the overlap of several contributions, including those from Mg-Mg correlations. Despite being based on a hypothetical structure, this information allows explanation of the evolution of the PDF profiles during Mg insertion. These shifts of the peaks located around 2.5 and 3.2 Å can effectively be interpreted as a result of the overlap of the peaks already present in the treated UC-FePO 4 /KB (with a C-C interatomic distance of 2.4 Å and Fe-P interatomic distance of 3.4 Å) with the Mg-based interatomic distances. Although the structural analysis of UC-FePO 4 /KB is complicated, and an accurate simulation cannot be achieved, this experimental PDF result captures the magnesium-ion insertion behavior.

The evolution of the local surrounding during Mg insertion and deinsertion also follows using EXAFS analysis, which provides a probe of the local distortion simulated by the use of the Debye-Waller factor (Figures S17 andS18) in addition to the interatomic distances. The evolution of the Fe-O interatomic distance and degree of distortion of the FeO 6 octahedra versus the depth of discharge estimated from the calculation of the average Fe valence state are represented in Figure 6c,d, respectively. They confirm that the Fe-O interatomic distance increases linearly during the discharge process, which agrees with a solid solution mechanism. In addition, the slope of the evolution of the interatomic Fe-O distance as a function of the Fe valence state in UC-FePO 4 is nearly similar to the one calculated considering the LiFePO 4 and FePO 4 crystal structures, which indicates that the local structure change of the neighbor FeO 6 shell is influenced solely by the ionic radii of the iron ion. These two results are in good agreement with the observed PDF analysis in Figure 6a. The provided PDF and EXAFS data also exclude the formation of Fe domain and confirm the absence of conversion reaction.

We have provided four evidences of the electrochemical magnesium insertion/deinsertion of UC-FePO 4 /KB: (1) existence of Mg species in FePO 4 matrix by TEM-EELS (Figure S12), (2) faradic reaction of iron ion in UC-FePO 4 by Fe K-edge XANES (Figure 4), (3) excluding of phase separation during charge/discharge in magnesium electrolytes by EDS (Figure 5), and (4) correlation between magnesium and FePO 4 matrix by X-ray PDF analysis (Figure 6). Therefore, the primary reaction discussed in this study is focused on electrochemical magnesium insertion/deinsertion in the FePO 4 matrix.

■ DISCUSSION

Conventional approaches to the design of optimal intercalation hosts typically focus on the crystal structures of the materials. For example, LiCoO 2 , LiMn 2 O 4 , and LiFePO 4 , which are lithium-ion battery cathode materials, [START_REF] Padhi | Phospho-olivines as positive-electrode materials for rechargeable lithium batteries[END_REF][START_REF] Thackeray | Electrochemical extraction of lithium from LiMn 2 O 4[END_REF][START_REF] Mizushima | 2 (0<x<1): A new cathode material for batteries of high energy density[END_REF] have stable lithium-ion sites and stable host structures accompanying reversible insertion and extraction for a wide range of lithium. The insertion and deinsertion of magnesium ions in these types of structures are associated with large activation energy for Mg 2+ hopping between adjacent sites, 11 which hinders the development of suitable cathode materials. For example, in the olivine crystal structure, motion between magnesium sites must proceed through an extremely narrow bottleneck, which is the main factor slowing diffusion in this rigid crystal structure (Figure 7). 11 In contrast, an amorphous structure, such as V 2 O 5 -P 2 O 5 glasses, has a diffusion barrier that is partly relieved but the cycle performance is not reversible. [START_REF] Arthur | Amorphous V 2 O 5 -P 2 O 5 as high-voltage cathodes for magnesium batteries[END_REF] With UC-FePO 4 /KB, as prepared in this study and unlike the other extreme cases, the XRD and scattering experiments show that while the long-range ordering is suppressed the short-range ordering (i.e., in the local structure of Fe-O-P) is preserved, and middle-range ordering (i.e., the connection between the different oxygenated polyhedra) is weakened, as observed through the broadening of the high correlation at high r values. This result evidences some flexibility of the structure, which then accommodates free spaces such as the free volume observed in glass. Therefore, smooth diffusion pathways through the solid are created, allowing even strongly interacting divalent magnesium ions to move through the solid phase. Our previous report demonstrated that the redox reaction in noncrystalline components exhibits no diffusion limitation within a large potential scan rate range. [START_REF] Kisu | Electrochemical kinetics of nanostructure LiFePO 4 /graphitic carbon electrodes[END_REF] Here, the UC process results in nano-FePO 4 particles with a noncrystalline structure embedded in graphitic carbon, which provides an efficient environment for reversible electrochemical insertion and deinsertion of magnesium ions. However, as shown in Figure 3a, the large hysteresis is still observed for magnesium charge-discharge, where the potential change at the beginning of the charging (magnesium deinsertion process) is obvious. This confirms the strong interaction between Mg 2+ and the anion, which, while facilitating the insertion process, prevents easy extraction of stabilized Mg ions.

The particle size of the noncrystalline (middle-rangeordered) FePO 4 is particularly small (10 nm) compared to the one used for the battery application. The experimental control of particle size while maintaining the noncrystallinity of FePO 4 may further provide crucial evidence showing the advantage of using defective structured active material. However, small particle size and noncrystallinity of FePO 4 are inseparable factors, as metastable noncrystalline FePO 4 particles can be stabilized only within the carbon framework of KB. In our previous study, we demonstrated that the nanoparticles are required to be encapsulated within the KB to maintain noncrystallinity. Naturally, the FePO 4 particles embedded/encapsulated in KB become smaller than the inner space of KB (few 10 nm).

■ CONCLUSIONS

We demonstrated that a hybridized structure of nano-UC-FePO 4 /KB particles embedded in carbon could operate as a host structure for multivalent cation insertion and extraction at moderate rate conditions at room temperature. Magnesium ions were reversibly inserted into UC-FePO 4 , leading to a capacity of 160 mAh g -1 with an operating voltage of 2 V vs Mg 2+ /Mg, which makes our UC-FePO 4 /KB composite interesting as the cathode for a magnesium-ion rechargeable battery cathode. Fast reversible ion intercalation reactions were favored by the medium-and long-range structural disorders, as well as the unique morphology resulting from carbon embedding, achieved during the UC synthesis process. These findings, showing that the charge and discharge reaction characteristics of magnesium ions are improved by the careful control of the crystallinity and the structure, offer significant utility for future material designs and represent an important advance toward the realization of multivalent-ion batteries.

■ ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.9b03665.

Representative multivalent-ion battery cathodes, additional XRD, SEM, TEM, XANES, EXAFS, PDF, nanoprobe, and electrochemical data; relationship between the diffusion length in active materials and the activation energy under various rates and temperature conditions; and refined crystal parameters and reliability factors (PDF)

Figure 1 .

 1 Figure 1. (a) Fe K-edge XANES spectra of the UC-FePO 4 /KB composite, crystalline FePO 4 (Fe 3+ ) and crystalline LiFePO 4 (Fe 2+ ). (b) Bright-field and (c) dark-field TEM images of the UC-FePO 4 composite. (d) Schematic illustration of the UC-FePO 4 composite. (e) Synchrotron X-ray diffraction pattern of UC-FePO 4 , crystalline FePO 4 , and the glass capillary. (f) Fourier transform magnitudes from EXAFS oscillation at the Fe Kedge of UC-FePO 4 and crystalline FePO 4 . (g) Reduced pair distribution functions G(r) obtained from the Fourier transformation of S(Q), shown in Figure S7, for crystalline FePO 4 and UC-FePO 4 /KB.

Figure 2 .

 2 Figure 2. (a) Charge/discharge profile of UC-FePO 4 /KB at 1C rate with 1 M LiPF 6 /EC-EMC. (b) Galvanostatic intermittent titration technique profile of UC-FePO 4 /KB with 1 M LiPF 6 /EC-EMC.

Figure 3 .

 3 Figure 3. (a) Charge/discharge profile of the treated UC-FePO 4 /KB composite electrode at 1/20C rate and 25 °C with 0.5 M Mg(TFSA) 2 /AN. (b) Discharge capacity from the cycle test of the treated UC-FePO 4 /KB composite electrode at 1/20C rate and 25 °C with 0.5 M Mg(TFSA) 2 / AN. (c) Comparison of the charge/discharge property for a Mg rechargeable battery cathode between UC-FePO 4 /KB and crystalline FePO 4 . (d) Rate capability of UC-FePO 4 /KB and crystalline FePO 4 in the discharge mode in 0.5 M Mg(TFSA) 2 /AN at 25 °C.

Figure 4 .

 4 Figure 4. Normalized Fe K-edge XANES spectra of a UC-FePO 4 /KB electrode (a) during Mg discharge and (b) during Mg-charge processes at 55 °C with 0.5 M Mg(TFSA) 2 /AN. The dashed lines represent the standard sample data.

Figure 5 .

 5 Figure 5. (a-f) Results from the TEM-EDS observation of the UC-FePO 4 /KB composite after the first discharge using 0.5 M Mg(TFSA) 2 /AN.

Figure 6 .

 6 Figure 6. (a) Reduced pair distribution functions G(r) obtained from the Fourier transformation of S(Q) for UC-FePO 4 /KB and discharged UC-FePO 4 /KB in Mg electrolyte and (b) the enlarged figure. Fitting results of EXAFS analysis of UC-FePO 4 /KB and crystalline FePO 4 : (c) Fe-O interatomic distance and (d) Debye-Waller factor as a function of Fe mean valence calculated from the XANES two-component analysis.

Figure 7 .

 7 Figure 7. Reaction model for Mg diffusion in the UC-FePO 4 composite electrode.

https://dx.doi.org/10.1021/acs.chemmater.9b03665

Author Contributions

Y.O. conceived and designed the project and analyzed the experimental data. K.K., E.I., and N.O. prepared highly dispersed defective FePO 4 . W.N. measured the transmission electron microscopy. T.M., Yu.Y., and Yo.Y. measured the electrochemical property of highly dispersed defective FePO 4 . M.H. and K.Y. performed the charge-discharge test and XAS of olivine-type FePO 4 . K.O. performed the X-ray scattering analysis. P.R. and P.S. analyzed the electrochemical measure-