Laurent Verny

Noellie Ylla

Fernande Da Cruz-Boisson

Eliane Espuche

Régis Mercier

Guillaume Sudre

Véronique Bounor-Legaré

Solvent-free reactive extrusion as an innovative and efficient process for the synthesis of polyimides

Keywords: solvent free synthesis, thermal imidization, partially aliphatic polyimide, reactive extrusion

Polyimides are commonly synthesized in a 2-step solution polymerization process. Such process requires long reaction times as well as specific care due to the use of potentially harmful solvents. In the present study, the total reaction time for producing polyimides has been lowered to less than 10 min by using a solvent-free continuous reactive extrusion process. The proof of concept was determined with the system based on 3,3',4,4'benzophenone-tetracarboxylic dianhydride (BTDA) and an aliphatic diamine, Jeffamine D-230 within a micro-extruder. Conversion degrees to polyimide, determined with 13 C NMR and DSC analysis, are over 90 mol% after 5 min of extrusion at 180 °C, 200 °C and 225 °C respectively. These syntheses were then transferred to a twin-screw extruder to form linear aliphatic-aromatic polyimides with two types of dianhydride: BTDA and pyromellitic dianhydride (PMDA). Comparison with a conventional solution polymerization process showed no significant differences in the polymers characteristics. The polyimides produced with this method presented glass transition temperatures ranging from 5 to 90 °C. The number average molar masses measured were between 11000 and 15000 g.mol -1 .

Introduction

Polyimides (PI) are a class of high-performance polymers, well-known for their outstanding chemical and thermal stabilities, as well as for their high mechanical properties. Examples of commercially available polyimides include DuPont's Kapton ® and Vespel ® , Saint Gobain's Meldin ® or UBE's Upilex ® . Because of their exceptional properties, polyimides are mainly used in high-end applications, for which the cost factor does not drive the selection of the materials [START_REF] Ma | A review on high temperature resistant polyimide films: Heterocyclic structures and nanocomposites[END_REF][START_REF] Tapaswi | Recent Trends on Transparent Colorless Polyimides with Balanced Thermal and Optical Properties: Design and Synthesis[END_REF][START_REF] Liaw | Advanced polyimide materials: Syntheses, physical properties and applications[END_REF] . One of the most famous applications is the multilayer insulation used for aerospace radiative protection (e.g. on satellites), identifiable by the "golden" aspect of the material [START_REF] Finckenor | Multilayer Insulation Material Guidelines[END_REF] . Polyimides are widely used as gas separation membranes [START_REF] Heck | Block copolyimide membranes for pure-and mixed-gas separation[END_REF][START_REF] Piroux | Gas transport mechanism in sulfonated polyimides. Consequences on gas selectivity[END_REF] and are also investigated for the manufacturing of polymer electrolyte membrane fuel cells (PEMFC) [START_REF] Genies | Soluble sulfonated naphthalenic polyimides as materials for proton exchange membranes[END_REF][START_REF] Hickner | Alternative polymer systems for proton exchange membranes (PEMs)[END_REF][START_REF] Miyatake | Proton conductive polyimide electrolytes containing fluorenyl groups: Synthesis, properties, and branching effect[END_REF][START_REF] Asano | Aliphatic/aromatic polyimide lonomers as a proton conductive membrane for fuel cell applications[END_REF] .

More common applications are related with their mechanical and electric insulation properties: for instance polyimides are often used in the wiring insulation of laptop computers [START_REF] Ma | A review on high temperature resistant polyimide films: Heterocyclic structures and nanocomposites[END_REF][START_REF] Tapaswi | Recent Trends on Transparent Colorless Polyimides with Balanced Thermal and Optical Properties: Design and Synthesis[END_REF][START_REF] Liaw | Advanced polyimide materials: Syntheses, physical properties and applications[END_REF][START_REF] Finckenor | Multilayer Insulation Material Guidelines[END_REF] .

The polyimide synthesis was first described by Bogert in 1908, where 4-aminophthalic acid is first heated and dried to form 4-aminophthalic anhydride. The thermal treatment of the anhydride leads to the formation of a "polymolecular imide", as written by the authors [START_REF] Bogert | 4)-Amino-o-phthalic acid and some of its derivatives[END_REF] . However, the most common way to synthesize polyimides consists of the polycondensation reaction of diamine and dianhydride monomers in solution.

The reaction is generally achieved in two steps. First, an intermediate poly(amic acid) (PAA) is formed, which is then cyclized into polyimide (imidization reaction) upon heating in a range of temperatures between 100 °C and 300 °C, depending on the chemical structure. For this polymerization reaction performed in solution, high-boiling-point aprotic solventssuch as N-methyl-2-pyrolidone (NMP), N,N-dimethylformamide (DMF) or N,Ndimethylacetamide (DMAC)are commonly used [START_REF] Bower | Aromatic polyimides[END_REF][START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF][START_REF] Dine-Hart | Preparation and fabrication of aromatic polyimides[END_REF] . The preparation of polyimides through solvent route is a straightforward process; however the total preparation time is long and comprises the formation of the PAA, the imidization reaction and the solvent removal (precipitation and filtering then vacuum drying, or solvent casting). The formation of the PAA lasts between 15 min (with LiCl to avoid charge transfer issues [START_REF] Nosova | Direct synthesis of aromatic polyamic acids under the action of catalytic compositions[END_REF] ) and 2 h [START_REF] Volksen | The synthesis of polyamic acids with controlled molecular weights In Polyimides[END_REF] at room temperature, but can be carried out for longer times to ensure complete conversion of the formulation. The thermal imidization reaction time ranges between few minutes (e.g. 15 min at 300 °C) [START_REF] Laius | Some characteristics of the kinetics of polyimide formation[END_REF] and several hours (4 h at 160 °C) [START_REF] Yu | Kinetic Study of Low-Temperature Imidization of Poly(amic acid)s and Preparation of Colorless, Transparent Polyimide Films[END_REF] . Besides, the chemical imidization reaction requires carboxylic dianhydrides as dehydrating agents and tertiary amines as catalysts. This second imidization route is described as allowing a better control of the reaction than thermal imidization. Furthermore, it can advantageously prevent the thermal degradation of the monomers and is subsequently carried out for thermally sensitive reagents [START_REF] Endrey | Process for preparing polyimides by treating polyamide-acids with lower fatty monocarboxylic acid anhydrides[END_REF][START_REF] Kailani | Chemical Imidization Study by Spectroscopic Techniques. 1. Model Amic Acids[END_REF] .

In order to ensure fast synthesis of polyimides, some research works have reported the imidization into an extruder of a PAA oligomer obtained from the reaction of 4,4'-bisphenol A dianhydride (BPADA) with 1,3-phenylenediamine, carried out in dichlorobenzene. The temperature of the extrusion process is between 370 and 400 °C and the average molar masses of the resulting product are 20 000 g.mol -1 and 50 000 g.mol -1 for and , respectively.

The drawbacks of this process are the solvent elimination during extrusion and the total reaction time: the solution polymerization of the PAA lasts 11 h prior to the extrusion. The residence time in the extrusion is very short (less than 2 min) and indicates that fast formation of polyimides could be achieved in specific conditions [START_REF] Silvi | Method for preparing polyimide and polyimide prepared thereby[END_REF] .

The solution polymerization of polyimides requires the use of solvents that are now considered as hazardous chemicals or suspected to be carcinogenic, such as NMP. The solvent elimination step, carried out for both chemical and thermal imidization, requires the solvent to be disposed of, which can have a non-negligible impact on the environment. In a sustainable environment approach, there is thus a real interest to develop alternative methods for preparing polyimides, and polymers in general, preventing the use of such solvents.

Early studies on the synthesis of polyimides described melt synthesis of the polymers as DuPont patent on the formation of poly(amide imide) fibers (PAI) 22 . Tri-and tetracarboxylic acids are used as reagents with primary diamines. The tetracarboxylic acid forms the imide moieties whereas the tricarboxylic acid leads to the amide part. The synthesis was carried out by melt process in a closed reactor heated at 200 °C. Similarly, Frosch's Bell patent [START_REF] Frosch | Linear polymer containing cyclic imide groups[END_REF] describes the formation of linear polyimides. However, the aliphatic structure of such polyimides cannot allow an injection molding process because of their poor thermomechanical stability, which subsequently limits their use as coatings or drawn fibers from the melt process.

Preparation of massive polyimide materials was described in Edwards' DuPont patents [START_REF] Edwards | Polyimides of pyromellitic acid US2710853 (A)[END_REF]25 where the incorporation of aromatic structures in the dianhydride moieties and the use of "long" linear amine monomers offer the possibility of injection molding at 320 °C. The diamine and dianhydride reagents are first mixed together in a water/ethanol mixture leading to the formation of a prepolymer (PAA) that is under a salt form. Such process allows the PAA salt to be slightly soluble in water and requires no harmful solvents. The aqueous media is then heated over a few hours at 140 °C to progressively remove water, and then further treated at 280 °C (0.5 to 2 h) to complete the water removal and imidization reaction. The polyimides are then processed by injection molding into tubing for instance, and their glass transition temperature is claimed to be slightly over 100 °C, preventing the use of such polymers at high temperatures.

Fully aromatic polyimides have been investigated by Bower and Frost [START_REF] Bower | Aromatic polyimides[END_REF] and meet the requirements of high temperature materials; however, because of a lower alkaline activity of the aromatic diamines, no salt of the PAA can be formed, forbidding the synthesis in water.

Melt synthesis has been tested with aromatic reagents, but the fast hardening of the reaction media with the extent of the imidization decreases strongly the mobility of the diamine and dianhydride groups, leading to low molar mass polyimides. To solve this issue, the reaction was carried out in solution, so that high temperature materials could be produced. With the development of this process, the solvent-free approach has been progressively dropped out.

One way to produce "solvent-free" high temperature polyimides was to use slightly flexible monomers such as BPADA as patented by General Electric, and to form polyetherimide (PEI) [START_REF] Takekoshi | Method for making polyetherimides US4011198A[END_REF][START_REF] Schmidt | Method for making polyetherimides US 4443592[END_REF][START_REF] Schmidt | Method for making polyetherimide[END_REF] . In this process, the dianhydride and the diamine reagents are directly introduced in the extruder in which the imidization reaction is carried out. No solvent is needed with this technique; however very high temperatures are required to achieve the polymerization and to maintain the products in a molten state (300 to 350 °C).

More recently, Polyone Corporation patented a reactive extrusion process of imide oligomers made of asymmetric monomers, limiting the formation of charge transfer complexes. The extrusion is carried out at high temperatures, ranging from 320 to 370 °C. The average molar masses indicated in this patent are 10 000 g.mol -1 and 16 000 g.mol -1 for and , respectively [START_REF] Avakian | Preparation of imide oligomers via concurrent reactive extrusion[END_REF] . The products obtained are further used as thermosetting polymers for the manufacturing of composite materials. Cao et al [START_REF] Cao | Greener dye synthesis: continuous, solvent-free synthesis of commodity perylene diimides by twin-screw extrusion[END_REF] recently reported the synthesis of naphthalic imides and perylene diimides (PDIs): the PDIs were obtained by a continuous scalable solvent-free process using a twin screw extruder.

Thus, by using the extrusion synthesis, the total reaction time (between the introduction of the monomers and the obtaining of the final material) can be decreased to a few minutes of continuous process. This time-saving feature is an additional advantage for the polymer manufacturing.

Based on our expertise in both reactive extrusion and polyimide synthesis [START_REF] Heck | Block copolyimide membranes for pure-and mixed-gas separation[END_REF][START_REF] Piroux | Gas transport mechanism in sulfonated polyimides. Consequences on gas selectivity[END_REF][START_REF] Bounor-Legaré | In situ synthesis of inorganic and/or organic phases in thermoplastic polymers by reactive extrusion" Wiley-VCH book "Reactive Extrusion[END_REF][START_REF] Cassagnau | Reactive processing of thermoplastic polymers: a review of the fundamental aspects[END_REF] and being aware that, except for the patents detailed previously, no fundamental research work dealt with the synthesis of polyimide with this specific process, we thus studied different systems based on 3,3',4,4'-benzophenone-tetracarboxylic dianhydride (BTDA) or pyromellitic dianhydride (PMDA) as dianhydride reagents and Jeffamine D-230 as aliphatic diamine reagent. The aliphatic diamine was chosen in order to bring some flexibility to the polyimide chains and thus allowing extrusion temperatures around 200 °C. The corresponding polyimides were also synthesized for the first time by solution polymerization (microwave heating) as reference. Preliminary trials and kinetics measurements were performed on the BTDA/D-230 system at the laboratory scale with the use of a micro-extruder. The scaling up of this process was carried out using a twin-screw extruder with an estimated residence time between 4 and 7 min.

The chemical structure of the polyimides was investigated by FTIR and [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR spectroscopies. The imidization reaction kinetics was determined using [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR quantification and DSC analyses. The average molar masses, the glass transition temperatures and the thermal behavior were additionally characterized to fully describe the obtained polyimides.

Experimental

Materials

1,2,4,5-benzene tetracarboxylic dianhydride or pyromellitic dianhydride (PMDA) and 3,3',4,4'-benzophenone tetracarboxylic dianhydride (BTDA) were purchased from Sigma-Aldrich and Abcr GmbH, respectively. Jeffamine D-230 was kindly provided by Huntsman.

The structure and characteristics of the monomers are reported in Table 1. All the monomers were used as received.

Two-step micro-extrusion process

The samples were prepared with an Xplore DSM vertical micro-compounder (15 cm 3 capacity) with double intermeshing counter-rotating screws. A manual floodgate, allowing either extrusion or recirculation, was used to carry out the reactive extrusion. Nitrogen inerting of the barrel was used.

a. Preparation of poly(amic acid)

Based on an equimolar ratio of BTDA and D-230, the poly(amic acid) (PAA) was obtained by blending 7 g of dianhydride (21.7 mmol) powder and 5 g of liquid diamine (21.7mmol) at ambient temperature for 5 min.

b. Imidization

The solid-like PAA was then introduced in the micro-extruder. The screws rotation speed was fixed at 50 rpm. Three processing temperatures were tested: 180 °C, 200 °C and 225 °C.

Samples of reaction medium were collected at different extrusion time for further analysis.

Single step extrusion process

The device used was a Leistritz ZSE18 (60 L/D) co-rotating twin-screw extruder (represented in Figure 1). First, the dianhydride reagent is introduced at block 0 with a Brabender twin-screw gravimetric feeder. The feeding rate of dianhydride is 500 g.h -1 (1.55 mol.h -1 of BTDA or 2.29 mol.h -1 of PMDA). The diamine monomer (liquid at ambient temperature) is injected with an HPLC pump at the block 2. The diamine feeding rate is adjusted in order to get equimolar ratio of the two monomers.

Three extrusion temperatures (180, 200 or 225 °C) of blocks 3 to 11 were tested. The residence time in the extruder was estimated between 4 to 7 minutes (slightly higher for the screw profile B). The synthesized polymers obtained at the die of the extruder are further analyzed.

Solution process

In a PTFE vessel, 3.77 g of reagents (equimolar amounts of diamine and dianhydride) were solubilized in 21 mL of dimethylacetamide. The solution was then placed under microwave irradiation at 500 W for 15 min (the medium temperature was measured at 200°C) [START_REF] Brunel | Water borne polyimides via microwave assisted polymerization[END_REF] . The polymer was precipitated by pouring the reaction mixture into water. The polymer powder was recovered by filtration. It was then washed with water and finally dried for 24 h at 50 °C under vacuum. Two different polymers BTDA/D-230 and PMDA/D-230 were synthesized.

Methods of characterization

FT-IR spectra ranging from 650 to 4000 cm -1 were recorded using a Nicolet iS10 in attenuated total reflectance (ATR) mode (16 scans). The samples were directly analyzed in the solid state. Thermal properties (glass transition temperature T g , residual reaction endotherm) were obtained from a TA Instruments DSC Q2000 under helium atmosphere. The runs were made with first a cooling step from 25 to -20 °C at 20 °C.min -1 , then a heating step to 250 °C at 10 °C.min -1 , followed by a another cooling step down to 25 °C. A second identical heating cycle was carried out to determine the T g value.

Thermal stability properties of polymers were obtained from a TA Instruments TGA Q500 under helium atmosphere. The samples were heated from 25 °C to 550 °C at 10 °C.min -1 .

Size exclusion chromatography (SEC) measurements were carried out in DMF-LiBr (0.05 M) using an Agilent PolarGel L column. A Waters 2410 refractive index detector was used.

Number average molar mass ( ) and mass average molar mass ( ) were calculated based on conventional calibration curve. The average molar masses are relative to polystyrene standards.

Results and discussion

Micro-extrusion trials

Addition of a dianhydride to a diamine at ambient temperature leads to the formation of the intermediate poly(amic acid), PAA (as checked by FT-IR and discussed in the next part), due to the nucleophilic attack of the amino group on the carbonyl carbon of the anhydride group.

This reaction, obtained by the dispersion of the solid dianhydride in the liquid diamine, is exothermic and the magnitude of the exotherm depends on the dianhydride and the diamine nature [START_REF] Harris | Synthesis of aromatic polyimides from dianhydrides and diamines. Polyimides[END_REF][START_REF] Ardashnikov | The Nature of the Equilibrium in the Reaction of Aromatic Anhydrides with Aromatics Amines and its Role in Synthesis of Polyimides[END_REF] .

Moreover, the samples obtained after the synthesis step in the micro-extruder are all amber glass-like materials with physical properties and behavior depending on the formulation and reaction time. This color classically observed as a polyimide characteristic is already an encouraging signature of the formation of a polyimide through this reactive process. The proof of concept by micro-extruder was carried out with one system based on BTDA/D-230 and was extended to another system in the extrusion part to modulate the final properties.

FT-IR characterization

FT-IR spectra and characteristic frequencies of the BTDA/D-230 based polymers prepared at 200 °C versus residence time into the micro-extruder are plotted in Figure 2. This figure also displays the spectra of the polyimide prepared in solution and the reactional medium before introduction in the micro-extruder, supposed to be mainly composed of PAA. Assignments were made according to existing literature [START_REF] Anthamatten | Solid-state amidization and imidization reactions in vapor-deposited poly(amic acid)[END_REF][START_REF] Snyder | FTIR studies of polyimides: thermal curing[END_REF][START_REF] Pyun | Kinetics and mechanisms of thermal imidization of a polyamic acid studied by ultraviolet-visible spectroscopy[END_REF][START_REF] Schab-Balcerzak | Influence of azobenzene units on imidization kinetic of novel poly(ester amic acid)s and polymers properties before and after cyclodehydration[END_REF] .

PAA shows a characteristic broad signal near 1560 cm -1 due to -C-NH-stretching of amide acid groups. The amide -C=O stretching resonance (near 1660 cm -1 ) is overlapped with the ketone stretching of the BTDA [START_REF] Cho | FT-IR studies on imidization and end-group reaction behaviors of a phenylethynyl terminated imide oligomer ICCM12 Conference Paris[END_REF] . The 1850 cm -1 , 1780 cm -1 and 1220 cm -1 signals are characteristic of the cyclic anhydride vibrations [START_REF] Anthamatten | Solid-state amidization and imidization reactions in vapor-deposited poly(amic acid)[END_REF][START_REF] Snyder | FTIR studies of polyimides: thermal curing[END_REF] , which demonstrates that the reactional mixture obtained at room temperature with BTDA and D-230 still contains unreacted anhydride. After barely 0.5 min of reaction at 200 °C, the FT-IR spectrum revealed the main polyimide characteristic absorptions such as the strong symmetric imide carbonyl stretching at 1710 cm -1 , the imide carbon-nitrogen stretching at 1370-1380 cm -1 and the imide ring bending near 730 cm -1 38 . An additional weaker band at 1770 cm -1 is due to the asymmetric imide carbonyl stretching [START_REF] Schab-Balcerzak | Influence of azobenzene units on imidization kinetic of novel poly(ester amic acid)s and polymers properties before and after cyclodehydration[END_REF] . Another strong absorption signal near 1100 cm -1 is the signature of

13 C NMR characterization

The chemical shifts for the different compounds are given in Table SI1. The assignment of the signals for the monomers and polymers was realized according to literature data [START_REF] Cho | FT-IR studies on imidization and end-group reaction behaviors of a phenylethynyl terminated imide oligomer ICCM12 Conference Paris[END_REF][START_REF] Culbertson | Advances in Polymer Synthesis[END_REF][START_REF] Seshadri | 13 C-NMR spectroscopy of polyamic acids and polyimides[END_REF][START_REF] Grubb | Highly soluble polyimides from sterically hindered diamines Polymer[END_REF][START_REF] Sun | PEG derived hydrogel: A novel synthesis route under mild condition[END_REF] .

Chemical shift predictions from Advanced Chemistry Development (ACD/Labs) software were also helpful to refine the attribution of the PAA and polyimide signals [START_REF]ACD/H+C NMR Predictor, version 2015[END_REF] . Figure 4 shows the detailed carbon labelling on the molecular structures. The [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR spectrum of the BTDA (not shown here, Table SI1) depicts a central ketone carbonyl (a, δ=193.9 ppm) that is shielded by +1.17 ppm with the formation of the PAA (see For all the samples prepared by micro-extrusion, we can confirm that the imidization reaction of PAA can be completed in short reaction times. As a matter of fact, no residual PAA signals could be spotted in the [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR spectra of the polyimides obtained after a reaction time of 5 min at 200 °C in the micro-extruder.

Imidization kinetics

The kinetics of the thermal imidization have been widely studied with various techniques [START_REF] Young | Characterisation of polyimides In Polyimides[END_REF] , such as Fourier-transform infrared spectroscopy (FT-IR) [START_REF] Koton | Investigation of the kinetics of chemical imidization[END_REF] , carbon-13 nuclear magnetic resonance ( 13 C-NMR) [START_REF] Chu | Reactivity of Poly( amic acid) Isomers in Thermal Imidization[END_REF] and ultraviolet-visible spectroscopy (UV-vis) [START_REF] Pyun | Kinetics and mechanisms of thermal imidization of a polyamic acid studied by ultraviolet-visible spectroscopy[END_REF] . The imidization of PAA is an endothermic process that can be also monitored by differential scanning calorimetry (DSC) [START_REF] Schab-Balcerzak | Influence of azobenzene units on imidization kinetic of novel poly(ester amic acid)s and polymers properties before and after cyclodehydration[END_REF] .

Polyimide conversion was calculated first from 13 C-NMR. As shown in Figure 8, the CH d4 amide/imide signal is significantly shifted as the reaction occurs. The area of this specific signal can thus provide an accurate measurement of the imidization rate. The method used here is similar to the one used by Seshadri et al. [START_REF] Seshadri | 13 C-NMR spectroscopy of polyamic acids and polyimides[END_REF] . The imidization rate α is given by the following formula (Equation 1): It has to be noticed that although the quantifications were mainly based on qualitative [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR analyses, they can be considered very accurate. Indeed, for the experiments carried out on the BTDA/D-230 system at 180 °C, we compared the spectra obtained through qualitative and quantitative conditions (detailed in experimental part). For those samples, no significant difference in relative integrals for the carbons of interest, meaning CH (d4) of PAA and polyimide, was observed for acquisitions made under those two conditions.

Note that some imide characteristic signals are already visible in the spectrum corresponding to the initial reaction medium (Figure 8). This observation is due to the fact that as soon as the dianhydride and the Jeffamine are put into contact at room temperature before their introduction in the micro-extruder, an exothermic phenomenon is observed coming from the amide-acid formation. The corresponding local increase of the temperature can lead to some parts of cyclization reaction to imide formation. With this method, we confirm that the imidization for the BTDA/D-230 is very fast in the studied range of temperatures (between 180 and 225 °C) through a continuous extrusion

process. An imidization conversion above 90 mol % after 4 min at 200 °C is specially promising for the scaling up part, where the residence time in our extruder is estimated between 4 and 7 min. Based on this result, it is expected to reach complete cyclization by using a twin-screw extrusion process. As a complementary approach, the imidization reaction was also monitored by DSC analysis.

Actually, as previously studied by Schab-Balcerzak et al. [START_REF] Schab-Balcerzak | Influence of azobenzene units on imidization kinetic of novel poly(ester amic acid)s and polymers properties before and after cyclodehydration[END_REF] , the imidization process has been observed between 100 and 220 °C through the endotherm associated to the amide-acid cyclization reaction. The enthalpy measured for the initial PAA sample is considered as a reference of a "0 %" conversion rate.

For a given formulation, the imidization enthalpy decreases versus reaction time for a given temperature (Figure 10) and versus temperature for the same reaction time. As an example, for PMDA/Benzidine (Chang [START_REF] Chang | Thermal cyclodehydration of aromatic precursor polymers to polybenzoxazole and polyimide; their thermal and mechanical properties[END_REF] ).

Subsequently, we determined the conversion rate by DSC with the following formula (Equation 2):

The results are shown in Table S 3 and plotted in Figure 11.

The DSC measurements confirm the results obtained by [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C-NMR: the imidization of our formulations in a micro-extruder is a fast process that can reach high conversion rates. The measured conversion rates are in the same range with both methods. An imidization rate over 90% can be achieved after 4 min of reaction for the temperatures investigated (180, 200 and 225 °C). The imidization reaction involves an amide and a carboxylic acid group. As these two groups belong to the same chemical species, the authors [START_REF] Pyun | Kinetics and mechanisms of thermal imidization of a polyamic acid studied by ultraviolet-visible spectroscopy[END_REF][START_REF] Chu | Reactivity of Poly( amic acid) Isomers in Thermal Imidization[END_REF] classically consider the kinetics as a first order law expressed with the following rate expression (Equation 3): where k is the rate constant, α the imidization reaction conversion and t the reaction time.

The plots of ln(1/(1-)) as a function of the reaction time t at different temperatures for the BTDA/D-230 system is reported in Figure 12a). Note that these curves have been drawn from the [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR data (similar curves not shown here were obtained from the DSC data). From the analysis of these curves and their best fitting, it is clearly shown that whatever the temperature and the system considered, the imidization reaction proceeded via a two-step process. Actually, it is characterized by an initial rapid cyclization and a second slower cyclization mechanism. These observations are consistent with the numerous studies dealing with this subject [START_REF] Seo | Kinetic Study of the Imidization of a Poly(ester amic acid) by FT-Raman Spectroscopy[END_REF][START_REF] Kim | Kinetic and Mechanistic Investigations of the Formation of Polyimides under Homogeneous Conditions[END_REF][START_REF] Yu | Kinetic Study of Low-Temperature Imidization of Poly(amic acid)s and Preparation of Colorless, Transparent Polyimide Films[END_REF] . In particular, most of the contributions dedicated to solid-state imidization reaction described these phenomena and proposed the following explanation. As the cyclization reaction proceeds in mass, the concentration of active amide-acid groups is decreasing concomitantly to a decrease of the molecular mobility in the polymer backbone.

Moreover, others authors such as Pyun et al. [START_REF] Pyun | Kinetics and mechanisms of thermal imidization of a polyamic acid studied by ultraviolet-visible spectroscopy[END_REF] argued also an initial contribution of the catalytic effect of the amide acid groups on the kinetics which also decreases with the cyclization reaction conversion. Besides, from a quantitative approach, it is possible from these curves to extract two rate constants (k 1 for the initial fast step and k 2 for the slower one BTDA/diaminonaphtalene 50.2 kJ.mol -1 according to Jen [START_REF] Jen | Characterization of the One Step Polyimide Synthesis[END_REF] ). This can be explained by the very flexible structure of our polyimides due to the non-aromatic Jeffamine monomer, promoting the cyclization of the amide acid groups.

Ln(1/(1-))

Reaction Time (min)

180°C 200°C 225°C -2 -1,5 -1 -0,5 0 0,5 1 1,5 1,9 1,95 2 2,05 2,1 2,15 2,2 2,25 2,3 ln
k 1000/T (K -1 ) a)

Reactive extrusion

Micro-extrusion results with the BDTA/D-230 system are very promising for the twin-screw extrusion transfer, especially regarding the conversion rate of PAA to polyimide, where nearly complete imidization could be achieved in a reaction time around 4-5 min. Adequate screw profiles were selected for the extrusion transfer, with a residence time comprised between 4 and 7 min.

We tested the synthesis of the BTDA/D-230 based polyimide but also enlarged our series to the PMDA/D-230 system and carried out the extrusion at 180, 200 and 225 °C. The spectra of the polyimides prepared by the three methods at 200°C are similar with the same wavenumbers and relative intensities of the absorption bands. More specifically, the characteristic absorption bands of polyimides (1780 cm -1 and 1710 cm -1 imide carbonyl stretch; 1370 cm -1 imide -C-N-stretch; 730 cm -1 imide ring bending) are present in the spectra of the samples prepared by the three methods (Figure 13). Moreover, the absence of the -C-NH-stretching of amide acid groups (near 1560 cm -1 ) confirms that all the amide acid groups were converted in imide groups during the extrusion.

Specific properties

Average molar masses

First, we monitored the evolution of the molar mass versus time of micro-extrusion at 200 °C for the system BTDA/D-230. As displayed in Figure 16, the elution peak shifts toward lower elution volumes (i.e. higher molar masses) when the imidization reaction time increases. This variation is clearly related to the conversion of the amide-acid group to imide group (from 72 to 91 and 96 mol % as determined previously by [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR for 0.5, 2 and 5 min of microextrusion, respectively). Actually, as the molar mass is fixed as soon as the PAA is formed, this shift may be plausibly due to the potential interaction of residual amide-acid groups of the polymer with the stationary phase leading to a higher elution volume. This confirmed the possibility to reach polyimide structures through a molten continuous process with molecular characteristics similar to the ones obtained in more usual solution-based chemistry, without solvent and with shorter reaction times.

Glass transition temperatures

The glass transition temperatures (T g ) of the obtained polyimides were determined by DSC analysis. The thermograms for BTDA/D-230 system are shown in Figure 17 and the values for both BTDA/D-230 and PMDA/D-230 systems are reported in Table 5. These data clearly evidenced that there are no major differences regarding the T g of the samples prepared by micro-extrusion, twin-screw extrusion or solution polymerization for both dianhydride and D-230 diamine. These analyses confirm that the synthesis of polyimides by reactive extrusion leads to materials with thermal properties similar to those obtained by a more conventional solution polymerization route but with much shorter elaboration time.

The glass transition temperature values of the polyimides based on PMDA are substantially lower by 15 to 20 °C in comparison with BTDA-based polyimides despite comparable molar masses. This is quite surprising, since PMDA-based polyimides are known for presenting a higher T g than BTDA-based polyimides for a given diamine. For instance, the T g of a PMDA/ODA polyimide is over 380 °C, whereas the T g of a BTDA/ODA polyimide is around 280 °C60 . However, this glass transition temperature can be reduced with the flexibility of the polymer chains. Eastmond et al. [START_REF] Eastmond | Polyimides with main-chain ethylene oxide units: synthesis and properties[END_REF] , who synthesized polyimides by varying the number of ethylene oxide (EO) segments, showed that the glass transition temperature can range from 270 °C to sub-ambient temperature; for example, a T g of 108 °C is found for a diamine with four EO sequence with ODA. This tendency, also observed with the D-230 diamine based structure, is thus consistent with the flexibility brought by the ethylene oxide segments 61 .

Thermal stability

All PDMA-based samples were analyzed by TGA under He atmosphere (10 °C.min -1 ). As depicted in Figure 18, the PMDA/D-230 polyimides remain stable under these dynamic conditions for temperatures up to 300 °C. Hence, the polyimides do not exhibit any significant mass drop at temperatures below 200 °C, except for the one obtained by solution polymerization. For this sample, the small weight loss (around 5wt%) observed at 200°C could be assigned to residual solvent. For the polyimides obtained by micro-extrusion or extrusion, no mass drop is evidenced at temperatures below 200°C which is consistent with a complete imidization reaction as no further water is formed. Over 350 °C, the samples then lose more than 85% of their original mass, and the residual char yield at 550 °C is around 10%. The thermal behavior is very closed whatever the synthesis protocol confirming once again the similar properties of the polyimides synthesized either by solution or melt polymerization reaction. These thermal stabilities are lower to what is generally observed for aromatic polyimides, which are stable up to a temperature of 400 °C under N 2 atmosphere.

Again, the flexibility brought by the D-230 diamine impacts the thermal stability, but this property remains interesting for a large domain of applications. It has to be noted that similar trends as those observed for PMDA/D-230 polyimides were obtained for BTDA /D-230 polyimides with a degradation temperature around 320°C in this last case. From that control, this polyimide synthesis in one-step by reactive extrusion opens a new field to reach polyimides with high glass transition temperatures and high molar masses and thus enhanced mechanical properties in particular.

Table 1 :

 1 Chemical structures and characteristics of the monomers (dianhydrides and diamine)

Figure 1 :

 1 Figure 1: Representation of the twin-screw extrusion setup with the corresponding screw profiles (A and B) Two different screw profiles were used. Screw profile B was set up to improve the mixing

13 C

 13 NMR spectra were recorded at 25 °C on a Bruker Avance II spectrometer working at 100.6 MHz for[START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C. The samples were dissolved in deuterated DMSO. Quantitative analyses were carried out with inverse gated proton decoupling (6k scans) to avoid Nuclear Overhauser Effect (NOE), a 70° rf pulse and 11.4 s recycle delay was used to allow complete relaxation of the carbons between each scan. Others samples were also qualitatively analyzed with power gated proton decoupling (3k scans), a 70° rf pulse and 4.4 s recycle delay.

Figure 3 .

 3 ether bonds from the D230 diamine. The intensity of the 1560 cm -1 amide acid -C-NHstretching broad signal decreases quickly in the early stages of the reaction (0.5 min), outlining a fast amide-acid cyclization process. The strong similarity of the FT-IR spectrum of the sample synthesized in solution with that of the sample obtained after an extrusion time equal to 4 min at 200 °C confirmed the fast imidization reaction by reactive extrusion.To go further in the analysis of the polymers synthesized by reactive extrusion, the products obtained for the same reaction time of 0.5 min but at different extrusion temperatures are compared in The spectra are very similar to each other, and the only slight difference is by the 1560 cm -1 band (amide acid -C-NH-stretching): its absorption intensity is slightly higher for an extrusion temperature of 180 °C than for 200 °C, and is no longer present for 225 °C. This observation tends to confirm the swiftness of the imidization reaction and foreshadows faster reaction kinetics for higher temperatures.

Figure 2 :

 2 Figure 2: FT-IR spectra of BTDA/D-230 polyimides obtained in a micro-extruder at 200°C for different reaction times. Comparison with the spectra of the BTDA/D-230 polyimide obtained in solution and the corresponding initial reactive medium (mainly PAA).

Figure 3 :

 3 Figure 3: FT-IR spectra of the initial reactive medium mainly PAA (BTDA/D-230) and the corresponding polyimides obtained at 180 °C, 200 °C and 225 C in a micro-extruder for 0.5 min reaction time.

Figure 4 :

 4 Figure 4: Structures and carbon identification for BTDA/D-230 poly(amic acid) and polyimide.

Figure 5 )Figure 7 .

 57 Figure 5). The anhydride carbonyl signals b at 163.0 ppm are shielded towards a multiplet

Figure 5 :Figure 6 :

 56 Figure 5: 13 C NMR Spectra (DMSO-d6, 25°C) of the initial reactive medium (mainly PAA from BTDA/D-230) (1) and BTDA/D-230 fully cyclized polyimide (micro-extrusion at 200 °C-5 min) (2)

Figure 7 :

 7 Figure 7: Structures of BTDA-based poly(amic acids) a: poly(amic acid) isomers b: partially imidized poly(amic acid) isomers

Figure 8 :

 8 Figure 8: Evolution of the 13 C-NMR d4 signal of BTDA/D-230 reaction mixture (180 °C) alongside the extrusion time. The d4 carbon atom is circled in red on the chemical structures above (left: polyimide; right: poly(amic acid). t= 0 min corresponds to the initial reactive medium (mainly PAA from BTDA/D-230) Sampling of the reaction mixture during the micro-extrusion allowed us to build the kinetics

Figure 9 :

 9 Figure 9: Imidization conversion curves over reaction time for BTDA/D-230 based polyimide systems synthesized in the micro-extruder for three different temperatures.

  the cyclization enthalpy values for BTDA/D-230 polyimide obtained at 180 °C are 37.1 kJ.mol -1 , 17.1 kJ.mol -1 and 10.2 kJ.mol -1 for 0.5, 2.5 and 4 min of reaction, respectively. As a reference, the imidization enthalpy value obtained for the initial PAA is 149 kJ.mol -1 .

Figure 10 :

 10 Figure 10: Evolution of the imidization endotherm intensity versus reaction times for the BTDA/D-

Figure 11 :

 11 Figure 11: Imidization conversion rate over time for BTDA/D-230 based polyimide systems synthesized in the micro-extruder for three different temperatures.

Figure 12 b

 12 Figure 12 b)) and finally the activation energy of both reactional steps. Actually, the values k 1 for the fast step are comprised between 1.36 min -1 at 180°C and 3.58 min -1 at 225°C; and the values of k 2 for the slow step are comprised between 0.23 min -1 at 180°C and 0.39min -1 at

Figure 12

 12 Figure 12 : a) Kinetic plots of ln(1/(1 -α)) as function of time at different temperatures: (■) 180 °C; (•) 200 °C; () 225 °C and b) the corresponding Arrhenius plot of ln k 1 (fast step upper line) and ln k 2 (slow step lower line) versus 1000/T for the BTDA/D-230 system. Lines provide the model calculations considering two first-order kinetics.

First

  , we compared by FTIR the spectrum of the BTDA/D-230 based polyimide obtained with the micro-extruder after 5 min at 200 °C with the one of polyimide extruded at 200 °C with the screw profile B. The spectra of PAA and the corresponding polyimide obtained in solution are also reported in Figure 13.

Figure 13 :

 13 Figure 13: FT-IR spectra of the initial reactive medium mainly PAA (BTDA/D-230 molar ratio = 1) with the corresponding polyimide obtained by micro-extrusion, extrusion (screw profile B) and solution polymerization at 200 °C. Similarly, the FTIR spectra of the PMDA/D-230 and BDTA/D-230 polyimides synthesized

Figure 14 :

 14 Figure 14: FT-IR spectra of PMDA/D-230 based polyimides obtained by extrusion performed at different temperatures (screw profile B) and solution polymerization carried out at 200°C.These observations are confirmed by[START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR, where the conversion rate was measured

Figure 15 :

 15 Figure 15: FT-IR spectra of PMDA/D-230 polyimides obtained by extrusion at 200°C with screw profiles A and B and the corresponding polyimide prepared by solution polymerization.This observation evidences the importance of accurately controlling the molar ratio of the

Figure 17 :

 17 Figure 17: DSC thermograms of BTDA/D-230 polyimides prepared at 200 °C by extrusion (1), micro-extrusion (2) and solution polymerization (3).

Figure 18 :

 18 Figure 18: TGA analyses of PMDA/D-230 polyimides prepared at 200 °C by respectively extrusion micro-extrusion and solution polymerization

Table 4 :

 4 SEC values of BTDA/D-230 and PMDA/D-230 polyimides synthesized at 200 °C and analyzed in DMF-LiBr (10% uncertainty)

	Polyimide	BTDA/D230		PMDA/D230
	Process	Micro-extrusion (5 minutes)	Extrusion Solution Extrusion	Solution
	(g.mol -1 )	11 000	14 750	13 500	13 350	10 900
	(g.mol -1 )	24 000	45 200	38 500	40 200	23 100
	Đ	2.2	3.1	2.8	3.0	2.1

Table 5 :

 5 T g values for polyimides obtained at 200 °C with different processes and measured by DSC analysis (uncertainty ±1°C)

		Process	BTDA/D-230	PMDA/D-230
		Micro-extrusion (5 min)	88	75
			89	71
	T g	Extrusion
	(°C)		88	73
		Solution

Acknowledgements

This research was supported by the French Ministry of Education and Research. We kindly thank Huntsman for providing some materials for this study.

hypothesis was already reported by several other authors even if the addition of LiBr should have limited/inhibited these interactions [START_REF] Krishnan | Molecular mass determination of polyamic acid ionic salt by size-exclusion chromatography[END_REF][START_REF] Konas | Molecular weight characterization of soluble high performance polyimides. 1. Polymersolvent-stationary phase interactions in size exclusion chromatography[END_REF][START_REF] Konas | Molecular weight characterization of soluble high performance polyimides. 2. Validity of universal SEC calibration and absolute molecular weight calculation[END_REF] . Besides, this observation may also be due to an evolution of the hydrodynamic volume of the polymer chains alongside the imidization reaction. 4). Some data for the PMDA/D-230 systems are also reported.

As it is clearly shown in this table, there is a good agreement between the average molar masses of the polyimides prepared at 200 °C with the different processes. For the BTDA/D-230 system, is between 11 000 and 15 000 g.mol -1 , while is between 24 000 and 45 000 g.mol -1 (Đ is between 2.1 and 3.1). The PMDA/D-230 system follows a similar trend.

The solution polymerization process seems to allow a slightly narrower polydispersity of the polyimides chains with respect to the extrusion process. Once again, this information Supporting informations consisting in three table tables (S1, S2 and S3 respectively) are dealing with Characterization of the reagents and expected products by [START_REF] Sroog | Aromatic polypyromellitimides from aromatic polyamic acids[END_REF] C NMR (Table S1) Imidization kinetics by 13C NMR (table S2) and by DSC (table S-3): . This information is available free of charge via the Internet at http://pubs.acs.org/.

A Table of Contents graphic


Esperanza Pavón
email: esperanza.pavon@gmail.com.

Francisco J Osuna

María D Alba

Laurent Delevoye

Natural Abundance 17 O MAS NMR and DFT Simulations: New Insights into the Atomic Structure of Design Micas

Keywords: 17 O NMR, DFT, natural abundance, Design mica, Lowenstein's rule, atomic structure

Combining 17 O Magic-Angle Spinning (MAS) NMR at natural abundance with DFT calculations is a promising methodology to shed light on the structure and disorder in tetrahedral sheets of designed micas with enhanced properties. Among brittle micas, synthetic mica is an important alternative to natural ones with a swelling sheet-like structure that results in many applications, by exploiting unique characteristics.

Lowenstein's rule is one of the main chemical factor that determines the atomic structure of aluminosilicates and furthermore their properties. In the present article, 17 O MAS NMR spectroscopy is used to validate (or not) the agreement of the Lowenstein's rule with the distribution of Si and Al sites in the tetrahedral sheets of synthetic micas. 17 O MAS spectra of synthetic high-charged micas exhibit two regions of signals that revealed two * *Phone: +34 954 48 9546.

Introduction

The preparation of synthetic clays, such as Na-n-Mica [START_REF] Gregorkiewitz | Characterization and properties of a new synthetic silicate with highly charged mica-type layers[END_REF][START_REF] Park | Pure Na-4-mica: Synthesis and characterization[END_REF], with 1) swelling capacity, 2) tuned high charge density and 3) charged with specific heteroatoms, has opened new possibilities in many areas of chemistry and material sciences due to their potential use as a catalyst support and novel adsorbent of hazardous and radioactive cations [START_REF] Komarneni | Environment: Superselective clay for radium uptake[END_REF]. For example, the chemical properties of the clays will be enhanced by a controlled incorporation of heteroatoms. In this context, it was demonstrated that aluminum substitution improves the chemical retention of toxic cations such as heavy metals and hydrocarbons [START_REF] Alba | Hydrothermal reactivity of Lusaturated smectites: Part I. A long-range order study[END_REF]{Alba, 2001 #2} [START_REF] Alba | Hydrothermal reactivity of Na-nmicas (n = 2, 3, 4)[END_REF].It also changes the Lewis/Brönsted acidity, modifying their catalytic properties [START_REF] Atkins | Atkins' Physical Chemistry[END_REF]. However, still today many of the structural aspects that can affect the properties of the silicates are unknown.

The Si-Al distribution in the tetrahedral sheet has been studied for decades and according to Lowensteins' rule, Al tet -O-Al tet linkages in clay mineral frameworks are forbidden. Indeed, quantum chemical studies have shown that a combination of Al tet -O-Al tet corner sharing tetrahedral linkage and Si-O-Si linkage require higher energy than two Si-O-Al tet linkages [START_REF] Hass | A non-empirical molecular orbital study on loewenstein's rule and zeolite composition[END_REF][START_REF] Navrotsky | The tetrahedral framework in glasses and meltsinferences from molecular orbital calculations and implications for structure, thermodynamics, and physical properties[END_REF], indicating the instability of Al tet -O-Al tet linkages [START_REF] Riebling | Structure of sodium aluminosilicate melts containing at least 50 mole % SiO2 at 1500°C[END_REF]. However, it has been observed that this Al tet -O-Al tet avoidance principle is not followed in several aluminosilicates, both in layered and framework silicates [START_REF] Stebbins | Al-O-Al oxygen sites in crystalline aluminates and aluminosilicate glasses: High-resolution oxygen-17 NMR results[END_REF][START_REF] Fletcher | Violations of Löwenstein's rule in zeolites[END_REF][START_REF] Klepov | Overstepping Löwenstein's Rule-A Route to Unique Aluminophosphate Frameworks with Three-Dimensional Salt-Inclusion and Ion-Exchange Properties[END_REF]. In mica-type materials, Alba et al. reported five different silicon environments in Na-4-Mica using 29 Si MAS NMR, which suggested either a violation of Lowenstein´s rule or a Al/Si ratio lower than 1 [START_REF] Alba | Hydrothermal reactivity of Na-nmicas (n = 2, 3, 4)[END_REF].

In order to remove this uncertainty, 17 O NMR could be an appropriate technique to provide a more direct evidence of a Lowenstein rule violation in Na-4-Mica. The growing interest of 17 O MAS NMR is due to the large chemical shift range for this nucleus (>1000 ppm) associated with the sensitivity of the quadrupolar coupling to the local geometry [START_REF] Gerothanassis | Oxygen-17 NMR spectroscopy: Basic principles and applications (Part I)[END_REF][START_REF] Gerothanassis | Oxygen-17 NMR spectroscopy: Basic principles and applications (part II)[END_REF]. Nevertheless, as a quadrupolar nucleus (I > 1/2), 17 O is subjected to large anisotropic broadening, even under magic-angle spinning (MAS) conditions. Moreover, due to its low natural abundance (0.037%), the acquisition of 17 O NMR spectra may become challenging and it usually requires 17 O enriched samples, high magnetic field and often long acquisition times. As a consequence, only few 17 O NMR data on layered silicates have been reported so far, even though the deduced structural information would be of high interest.

The first direct evidence of Al tet -O-Al tet sites were reported by Stebbins et al. [START_REF] Stebbins | Al-O-Al oxygen sites in crystalline aluminates and aluminosilicate glasses: High-resolution oxygen-17 NMR results[END_REF] in crystalline aluminates, showing a violation of the Lowenstein rule using 17 O MAS NMR. This work used 17 O isotopic enrichment of the samples, prior to the NMR investigations.

However, in addition to being expensive, 17 O isotopic enrichment might be challenging from the synthesis point of view as it would require, in our study, 17 O enriched SiO2 and Al(OH)3 as precursors, and further heating at high temperature (900 ºC). In a recent publication, Pavón et al. [START_REF] Pavón | Direct evidence of Lowenstein's rule violation in swelling high-charge micas[END_REF] showed that it was possible to obtain 17 O MAS NMR spectra of Na-4-Mica, at natural abundance, using high-field (18.8 T). They provided the first evidence of Lowenstein's rule violation in clay minerals by assigning the NMR signal observed between 20 and 30 ppm to apical oxygen sites Si/Al tet -O-3Mg and to Al tet -O-

Al tet .
Today, experimental NMR is often combined with density functional theory (DFT) calculations of parameters to obtain a deeper understanding of the relation between NMR data and the local structure and disorder. This is of great interest in the present context of natural abundance 17 O NMR spectra of low sensitivity. CASTEP, a planewave, pseudopotential DFT code, has been successfully applied to the calculation of the 17 O NMR parameters in crystalline and amorphous inorganic systems [START_REF] Pickard | All-electron magnetic response with pseudopotentials: NMR chemical shifts[END_REF][START_REF] Forler | New insights into oxygen environments generated during phosphate glass alteration: A combined 17O MAS and MQMAS NMR and first principles calculations study[END_REF][START_REF] Ashbrook | 17O and 29Si NMR parameters of MgSiO3 phases from high-resolution solidstate NMR spectroscopy and first-principles calculations[END_REF][START_REF] Ashbrook | Firstprinciples calculations of solid-state 17O and 29Si NMR spectra of Mg2SiO4 polymorphs[END_REF]. In the case of disorder or site substitutions, it is possible to propose models using larger unit cells in order to highlight the diversity of oxygen sites present in the structure [START_REF] Griffin | Solid-state 17O NMR spectroscopy of hydrous magnesium silicates: Evidence for proton dynamics[END_REF].

In this paper, we investigated the Si-Al distribution within the tetrahedral sheet of a new family of swelling high-charged micas by combining experimental 17 O NMR data and first-principle calculations of NMR parameters. The main objective was, for the first time, to identify and quantify the different oxygen sites, using NMR spectra collected in the challenging context of 17 O MAS NMR at natural abundance. The experimental strategy consisted in the use of three trioctahedral 2:1 phillosilicates with different tetrahedral substitution of Si by Al. One of those samples was a natural trioctahedral 2:1 phyllosilicate, saponite, in which the Lowenstein´s rule is obeyed and, it is therefore considered here as the reference. The two other samples are the swelling high-charged micas, Na-n-Mica (n=2 and 4), where n is the Al content on tetrahedral sheet based on the O20F4 unit cell, which are the target samples of the present study.

Experimental details

Sample description.

The selected aluminosilicates that are used in the present study, namely Saponite, Na-2-Mica and Na-4-Mica, belong to the trioctahedral 2:1 phyllosilicate family (Table 1).

They are all made of one sheet of octahedral coordinated cation (Mg +2 ) sandwiched between two sheets of tetrahedral cations (Si +4 /Al +3 ). Al is substituted to Si in the tetrahedral sheet, leading to a layer charge deficit. Among the three samples studied here, Saponite is the least charged silicate, followed by Na-2-Mica, and finally Na-4-Mica. This latter compound exhibits the highest layer charge with a nominal Si/Al ratio of 1.

Natural trioctahedral layered aluminosilicates, saponite, contain basal oxygens (Si-O-Si and Si-O-Al tet ), apical (Si-O-3Mg and Al tet -O-3Mg) and oxygens from the hydroxyl groups. Synthetic micas, Na-n-Mica (n=2 and 4), belong to the fluorophlogopite family, which means that instead of hydroxyl groups, the octahedral coordination of the Mg cation is balanced with fluorine ions. In Table 1 the relative ratios of the expected oxygen environments in the different samples are, as well, presented. For the saponite, it is deduced from its theoretical structure and for mica samples from the analysis of 29 Si MAS NMR spectra [START_REF] Alba | Hydrothermal reactivity of Na-nmicas (n = 2, 3, 4)[END_REF].

A procedure similar to that described by Alba et al. [START_REF] Alba | Hydrothermal reactivity of Na-nmicas (n = 2, 3, 4)[END_REF] was employed to synthesize Na-2-Mica and Na-4-Mica. Starting materials were SiO2 from Sigma (CAS no. 112945-52-5, 99.8% purity), Al(OH)3 from Riedel-de Haën (CAS no. 21645-51-2, 99% purity), MgF2 from Aldrich (CAS no. 20831-0, 98% purity), and NaCl from Panreac (CAS no. 131659, 99.5% purity). Stoichiometric amounts of the reagents were mixed and grounded vigorously before heating up to 900 °C in a Pt crucible for 15 h. After cooling, the solids were washed with deionized water and dried at room temperature. Saponite sample, supplied by the Source Clays Repository of the Clay Mineral Society, with particle diameters of less than 2 μm, was used after removal of carbonates and organic matter.

Their structural characteristics are displayed in Table 1.

In order to remove the contribution of the water signal from the 17 O NMR spectra, all the samples were dried at 300 ºC overnight and then, transferred to a sealed container in order to avoid rehydration. NMR rotors were carefully filled in an inflatable glove box to avoid contact with air humidity. 1 H MAS-NMR experiments and XRD patterns were systematically carried out to check the absence of water signal.

NMR experiments.

NMR spectra were acquired on a Bruker Avance III 18.8T spectrometer ( 17 O, 108.48 MHz) using a 4 mm HX Thalahassee probehead. 17 O excitation was achieved by applying a central-transition selective π/2 pulse of 9 μs. The spinning frequency was 10 kHz, and the recycle delay was set to 1s after optimization. A total of 149504, 89216, 56240 transients were added for Saponite, Na-2-Mica and Na-4-Mica, respectively. Pulse sequences, such as double-frequency sweep (DFS) designed for signal enhancement of quadrupolar nuclei, showing large CQ-dependency [START_REF] Grekov | 17O MAS NMR studies of oxo-based olefin metathesis catalysts: A critical assessment of signal enhancement methods[END_REF], were avoided to preserve quantitative information. 17 O chemical shift was given in ppm with respect to 17 O signal of water at 0 ppm.

Calculations methods.

First principles calculations with periodic boundary conditions were performed using the CASTEP Code [START_REF] Segall | First-principles simulation: Ideas, illustrations and the CASTEP code[END_REF][START_REF] Clark | First principles methods using CASTEP[END_REF], which relies on a plane-wave based density functional theory approach (DFT). Electron correlation effects were modeled using the PBE generalized gradient approximation (GGA) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. Geometry optimizations were performed in several steps gradually increasing the precision to achieve an optimal cutoff energy of 700 eV. The default pseudopotentials [START_REF] Vanderbilt | Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[END_REF] in CASTEP were used (Version 6.1 of Material Studio). Convergence thresholds were set to 5x10 -6 eV/Å for the total energy. The maximum ionic force and displacement were 1x10 -2 eV/ Å and 5x10 -4 Å, respectively. The Brillouin zone was sampled using a Monkhorst-Pack grid with a separation of 0.05 Å -1 giving 16 irreducible points. Dispersion corrections, important in systems with weak intermolecular interactions, were not considered because 1) no hydrogen bonds are found in Mica samples and 2) the high amount of Si/Al substitutions generates a strong electrostatic interaction, that become more important for the crystal cohesion than the dispersive forces.

The NMR calculations were performed after the geometry optimization using the Gauge Including Projector Augmented Wave approach (GIPAW) [START_REF] Yates | Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials[END_REF] and the same energy cutoff of 700 eV. Simulations of calculated spectra were achieved by SIMPSON program [START_REF] Bak | SIMPSON: A General Simulation Program for Solid-State NMR Spectroscopy[END_REF].

In order to reference the calculated chemical shifts and to compensate for the systematic errors predicted by DFT calculations, a family of silicates of known structure and known NMR parameters were used [START_REF] Ashbrook | Firstprinciples calculations of solid-state 17O and 29Si NMR spectra of Mg2SiO4 polymorphs[END_REF][START_REF] Ashbrook | Highresolution 17O MAS NMR spectroscopy of forsterite (α-Mg2SiO4), wadsleyite (β-Mg2SiO4), and ringwoodite (γ-Mg2SiO4)[END_REF] (Table S1). The corresponding plot is displayed in Fig. 1S, and the correlation function derived is obtained with the following equation: δiso ( 17 O) =-0.89•δcal ( 17 O) + 228 (in ppm).

Results and discussion

Figure 1 presents the 17 O MAS NMR spectra, recorded at natural abundance for the three samples. All possible oxygen environments overlap, making the assignment uncertain. However, the spectra for synthetic Mica samples can be separated into two regions of signals: a broad region, labelled A, between 50 and 30 ppm and a narrower contribution, region B, between 30 and 15 ppm. On the basis of previous studies [START_REF] Walter | Oxygen-17 cross-polarization nmr spectroscopy of inorganic solids[END_REF][START_REF] Lee | 17O and 27Al MAS and 3QMAS NMR study of synthetic and natural layer silicates[END_REF][START_REF] Lee | Multiple oxygen sites in synthetic phyllosilicates with expandable layers: 17O solid-state NMR study[END_REF] and on our recent communication [START_REF] Pavón | Direct evidence of Lowenstein's rule violation in swelling high-charge micas[END_REF], regions A and B can be assigned to specific 17 O environments. The group of overlapping resonances between 30 and 50 ppm are assigned to basal oxygen sites, Si-O-Si and Si-O-Al tet [START_REF] Lee | 17O and 27Al MAS and 3QMAS NMR study of synthetic and natural layer silicates[END_REF][START_REF] Lee | O atom sites in natural kaolinite and muscovite: 17O MAS and 3QMAS NMR study[END_REF]. Apical oxygens Si-O-3Mg, which link tetrahedral and octahedral sheets, are found at higher chemical shift values as stated in the literature [START_REF] Ashbrook | 17O and 29Si NMR parameters of MgSiO3 phases from high-resolution solidstate NMR spectroscopy and first-principles calculations[END_REF] and coincide with the signal at around 50 ppm.

The last oxygen environment, Al tet -O-3Mg, that is present in the structure, was previously reported considering the electronegativity only [START_REF] Pavón | Direct evidence of Lowenstein's rule violation in swelling high-charge micas[END_REF]. The Al tet -O-3Mg sites should feature smaller CQ and smaller isotropic chemical shift values than that of Si-O-3Mg environments. Therefore, the signal in region B in both the Na-4-Mica and the Na-2-Mica spectra can be empirically assigned to Al tet -O-3Mg sites (Fig. 1b andc). 27 Al MAS NMR in Na-4-Mica revealed the presence of aluminum in octahedral coordination (Fig. 3S). This environment (15% of total aluminum) might come from 1) aluminum hosted in the octahedral sheet and substituting Mg, or 2) from an impurity. If the first option is assumed, then Al tet -O-Al oct and Si-O-Al oct should be considered. Table 1 shows the percentage of those environments in this case (1.63 and 2.1 % of total, respectively) that are well below the detection limits and, hence, make those contributions impossible to be observed in the present challenging context. Note that the two regions observed in mica are shifted to higher frequency in saponite 17 O MAS NMR spectrum, probably due to the presence of OH -groups in the framework instead of F -ions in the mica structure.

Hydroxyl groups are usually associated with large quadrupole coupling constants of about 7 MHz [START_REF] Walter | Oxygen-17 cross-polarization nmr spectroscopy of inorganic solids[END_REF] that give rise to resonances, which are dominated by the second-order quadrupolar broadening [START_REF] Forler | New insights into oxygen environments generated during phosphate glass alteration: A combined 17O MAS and MQMAS NMR and first principles calculations study[END_REF]. Therefore, their detection is a challenge here in the context of 17 O NMR experiments at natural abundance. Thus, we do not expect to be able to detect the hydroxyl sites, which account for only 16.7 % of the 17 In order to clarify this latter point, DFT calculations were carried out. Two different models for Na-4-Mica were constructed, based on a natural talc structure (ICSD 100682) and modified as follows. First, the unit cell parameters a and b were changed to the values obtained experimentally by XRD [START_REF] Alba | Hydrothermal reactivity of Na-nmicas (n = 2, 3, 4)[END_REF]. The basal distance was then adjusted to 9.84 Å, i.e., the value found by XRD study in a dehydrated sample [START_REF] Pavón | Hydration properties of synthetic high-charge micas saturated with different cations: An experimental approach[END_REF]. In the talc structure, the tetrahedral layer consisted of Si atoms only, whereas in the Na-4-Mica the ratio Si/Al was equal to 1. For that reason, half of the Si atoms were replaced by Al atoms. To compensate for the layer charge, Na atoms were introduced in the hexagonal holes formed by the tetrahedral arrangement. Finally, in order to produce a fluorinate silicate, OH sites were exchanged by F ions. The resulting structure is a model for Na-4-Mica for which Si and Al are fully ordered within the tetrahedral sheet. Oxygen sites are found solely in Si-O-Al tet environments in the tetrahedral sheet, and both in Si-O-3Mg and Al tet -O-3Mg environments in the octahedral sheet. In this case, basal oxygens account for 75% of all the oxygen sites, whereas Si-O-3Mg and Al tet -O-3Mg account 12.5% respectively as the ratio Si/Al is equal to 1. This model will be referred to as Structure I in the following sections (Figure 2).

The second model is constructed to include Al tet -O-Al tet sites in the tetrahedral sheet, by replacing one Si cation by an Al cation within the tetrahedral sheet. This substitution leads to the presence of three different basal oxygen sites as depicted in Fig. 2a, b andc. This model will be called Structure II in the following sections.

Chemical shifts and quadrupolar parameters obtained by DFT GIPAW calculations for structures I and II are displayed in Table 2 and Table 3, respectively. They were used as starting values to simulate the experimental spectra (vide infra). For both structures, the calculated values can be separated into two groups: the first group corresponds to those Al tet -O-3Mg and Al tet -O-Al tet oxygen environments with low CQ (< 1.5 MHz) and low chemical shifts (<30 ppm); the second group includes the sites Si-O-3Mg, Si-O-Al tet and Si-O-Si, which experience CQ above 3 MHz and chemical shifts above 30 ppm.

For structure I, Si-O-Al tet and Si-O-3Mg calculated chemical shifts and quadrupolar parameters are in good agreement with those found in the literature [START_REF] Walter | Oxygen-17 cross-polarization nmr spectroscopy of inorganic solids[END_REF]. Chemical shifts are in the 30 to 50 ppm range and CQ values are found between 3 to 3.5 MHz (Table 2).

As far as we know, there are no studies reporting NMR parameters for Al tet -O-3Mg apical oxygens. The calculated chemical shift for this oxygen environment at around 23 ppm, and the low CQ value (0.88 MHz) are in line with the presence of a narrow resonance in region B for Na-4-Mica as well as for Na-2-Mica though at a lesser extent [START_REF] Pavón | Direct evidence of Lowenstein's rule violation in swelling high-charge micas[END_REF]. However, this environment cannot explain by itself the intensity of the resonance in region B, as the expected relative ratio in Na-4-Mica (12.5% or 9.5%, Table 1) is smaller than that observed experimentally (27%).

Structure II is characterized by a perturbation in the periodicity of the silicate network and consequently, an increase of the possible 17 O sites (Table 3). Each apical oxygen MHz) [START_REF] Stebbins | Al-O-Al oxygen sites in crystalline aluminates and aluminosilicate glasses: High-resolution oxygen-17 NMR results[END_REF]. Finally, Al tet -O-3Mg site are in the same chemical shift than that reported for Al tet -O-Al tet however their quadruplar coupling constant is smaller. Up to our knowledge, no Al tet -O-3Mg site has been reported before.

Figure 4 represents the simulated 17 O MAS NMR spectra for Na-2-Mica and Saponite, together with the experimental one. The best-fit simulation was obtained using the DFTcalculated NMR parameters of Structure II (Table 3), which includes Si-O-Si sites as expected in the structure of these two aluminosilicates. No Al tet -O-Al tet sites were considered for the modelling and relative ratios of the different oxygen sites were set at values close to those given in Table 1. The δiso, CQ and ηQ NMR parameters after fitting are summarized in Table 4. In Na-2-Mica the DFT calculated CQ and δiso values were only slightly modified within a reasonable range except for Si-O-Al tet and Si-O-Si chemical shift that was increased by about 6 ppm in the fitting. Fitting saponite spectrum generates the displacement of all the chemical shifts between 4 and 11ppm from the calculated DFT values and 6 ppm from the Na-2-Mica fitting values, probably due to the presence of OH -groups in the structure.

As expected if the Lowenstein's rule is respected, the experimental 17 A reasonable agreement is found between the experimental and calculated spectra using Structure I for region A for which two contributions, Si-O-Al tet and Si-O-3Mg are sufficient. One should note that Si-O-3Mg site largely overlap with the Si-O-Al tet sites, due to similar quadrupolar coupling constants that provoke a line broadening.

Consequently, low spectral resolution is observed. Below 30 ppm in region B, NMR parameters for Al tet -O-3Mg sites fit perfectly the experimental data. Remarkably, the narrow resonance is in line with a small CQ value (< 1 MHz), as deduced from the DFT calculations. However, as previously mentioned, the theoretical proportion of Al tet -O-3Mg sites is not sufficient by itself to explain the intensity of the resonance observed in the experimental spectrum.

Structure II was then proposed in order to add explanatory contributions from Si-O-Si and Al tet -O-Al tet sites, which would then suggest a violation of the Lowenstein's rule for the Na-4-Mica sample. Figure 5b shows the best-fit simulation of 17 O MAS NMR spectrum for Na-4-Mica using all possible oxygen environments. In region A, the NMR signal is due to the combination of the basal oxygens Si-O-Al tet and Si-O-Si, and the apical arising from Si-O-3Mg. In region B, the signal is now the result of two contributions, i.e., the apical Al tet -O-3Mg site and the basal oxygen Al tet -O-Al tet site, with relative proportions close to those expected.

Conclusion

In the present work, we demonstrated that in a synthetic swelling high charged mica, Na-4-Mica, the Lowenstein's rule is violated. Additionally, our findings reveal the viability of using 17 O MAS NMR at natural abundance on synthetic high-charged silicates. By combining the experimental work and DFT calculations, it is now possible to offer a complete description of the heteroatoms distribution within the mica sheets, distribution that depends on the total layer charge. In the Na-2-Mica (Si/Al < 1), the Si and Al atoms are randomly distributed obeying the Lowenstein's rule. However, in the Na-4-Mica (Si/Al =1), the most stable structure is produced with a completely freed Si/Al distribution, even with the formation of Al tet -O-Al tet bonds of unfavorable enthalpy cost.

Table 1

Table 1: Samples studied in this work, their structural theoretical formulae and the kind of substitution they exhibit. Relative proportion of oxygen sites for all the samples, deduced either from their theoretical structure (Saponite samples) or from the analysis of the 29 Si MAS NMR spectra (Mica samples). For the Mica systems, the amount of Al tet -O-Al tet linkages was determined using the 29 Si NMR spectra of Na-n-Mica [START_REF] Alba | Hydrothermal reactivity of Na-nmicas (n = 2, 3, 4)[END_REF] following the method described elsewhere [START_REF] Circone | Substitution of [6,4]Al in phlogopite: Mica characterization, unit-cell variation, 27 Al and 29 Si MAS-NMR spectroscopy, and Al-Si distribution in the tetrahedral sheet[END_REF]. In Na-4-Mica two different calculations for the proportion of apical oxygens is represented: a) no aluminum in the octahedral sheet is considered as ideally expected and b) the aluminum in octahedral coordination observed in the 27 Al MAS-NMR spectrum (15% of the total aluminum) [START_REF] Alba | Hydrothermal reactivity of Na-nmicas (n = 2, 3, 4)[END_REF] is considered to be in the octahedral sheet.

  O NMR signal in saponite.Stebbins et al.[START_REF] Stebbins | Al-O-Al oxygen sites in crystalline aluminates and aluminosilicate glasses: High-resolution oxygen-17 NMR results[END_REF] detected Al tet -O-Al tet environments at an isotropic chemical shift of approximately 21 ppm, with a relatively large CQ value of 3.8 MHz, in a stilbite zeolite with a ratio Si/Al=3. It was at similar chemical shifts than Al-O-Al site connecting pairs of AlO4 in crystalline NaAlO2 and in an Al-rich aluminosilicate glass[START_REF] Stebbins | Al-O-Al oxygen sites in crystalline aluminates and aluminosilicate glasses: High-resolution oxygen-17 NMR results[END_REF]. Occurring for about 11.25 % in Na-4-Mica, the17 O NMR signal at 23 ppm (region B) could also be assigned to Al tet -O-Al tet sites.

(

  Al tet -O-3Mg and Si-O-3Mg) is now spread into four different sites, slightly differing by their geometrical environment. Their chemical shifts and CQ values are in the same range than that observed in Structure I.

Figure 3

 3 Figure3shows the correlation between CQ and δiso parameters for all oxygen sites

  O MAS NMR spectra of Na-2-Mica and saponite can be fully explained considering 4 different oxygen sites: Si-O-Si, Si-O-Al tet , Si-O-3Mg and Al tet -O-3Mg.

Figure

  Figure5ashows the comparison of the experimental17 O MAS spectrum (solid black

Fig. 1 .

 1 Fig. 1. Natural abundance 17 O MAS NMR spectra recorded at 18.8 T for (a) Saponite, (b) Na-2-Mica and (c) Na-4-Mica. Regions A and B are related to NMR signals found above and below 30 ppm, respectively.

Fig. 3 .

 3 Fig.3. DFT-calculated17 O CQ and δiso of oxygen sites using Structure II. Top :17 O MAS NMR spectrum of Na-4-Mica giving a guideline for the chemical shift regions.

Figure 4 438 439 Fig. 4 .Figure 5 Fig. 5

 4439455 Figure 4

†

  Supplied by the Source Clays Repository of the Clay Minerals Society. ‡ Synthesized by Pavon et al, following Alba et al. Chemistry of Materials 2006, 18 (12), 2867-

							Oxygen sites
			Basal Oxygens		Apical Oxygens
	Silicate	Chemical formulae	Si	Si	Al tet	Si	Si	Al tet	Al tet
			-O-	-O-	-O-	-O-	-O-	-O-	-O-	OH -
			Si	Al tet	Al tet	3Mg	2Mg1Al oct	3Mg	2Mg1Al oct
	Saponite † (Na0.62K0.02Ca0.08)[Si7.2Al0. 8] [Mg5.8Fe0.14] O20 (OH)4	55.5	6.94	-	18.75	-	2.08	-	16.7
	Na-2-Mica ‡	Na2[Si6Al2]Mg6 O20F4	48.3	26	-	18.75	-	6.25	-	-
	Na-4-Mica ‡	Na4[Si4Al4]Mg6 O20F4	13.94	47.7 5	11.2 5	12.5 12.01	-2.1	12.5 9.25	-1.63	--
		2872

a b

Table 2 Table 2 .

 22 17 O NMR parameters in Na-4-Mica as deduced from DFT calculations for the different oxygen sites in Structure I with the NMR parameters obtained from modelling the spectrum.

			DFT			Modelling
	17 O sites	σiso, ppm	σiso-ref, ppm	CQ, MHz	η	δ, ppm	CQ, MHz η	%
	Al tet -O-3Mg 230.92 23.5	0.88	0.50	27.3±0.2 1.80±0.03 0.5±0.2 13.2
	Si-O-3Mg	207.50 43.4	3.13	0.11	43±2	3.6±0.4	0.4±0.2 13.3
		216.50 35.3	3.38	0.19
	Si-O-Al tet	217.86 34.1	3.43	0.49	42.0±0.3 3.0±0.1	0.6±0.05 73.5
		214.25 37.3	3.47	0.41

Table 3 364 365 Table 3 .

 33653 17 O NMR parameters in Na-4-Mica as deduced from DFT calculations for the

	366
	367	different oxygen sites present in Structure II with the NMR parameters obtained from
	368	modelling the spectrum.

Table 4 372 373 Table 4 .

 43734 17 O NMR parameters in Na-2-Mica and saponite after fitting the spectrum 374 using as starting values those obtained from DFT calculations in Structure II.

	375
	376
	377
			Na-2-Mica			Saponite
	17 O site	δ, ppm	CQ MHz	η	%	δ, ppm	CQ MHz	η	%
	Al tet -O-3Mg	27.3±0.3 1.9±0.1	0.6±0.2	5.54	34.0±0.5	1.8±0.2	0.6±0.6	2.24
	Al tet -O-Al tet	-	-	-	-	-	-	-	-
	Si-O-Mg	44. ±2	3.9±0.5	0.5±0.2	19.52 48.0±0.3 3.00±0.09	0.2±0.1	21.74
	Si-O-Al tet	42±1	3.3±0.3 0.54±0.08	29.0	48±1	3.3±0.3	0.32±0.07	7.76
	Si-O-Si	54±1	6.1±0.2	0.3±0.1	45.94 52.1±0.3 5.09±0.06 0.27±0.07 68.27
	378
	379

Acknowledgements

We would like to thank the CNRS, Université de Lille, Chevreul Institute (FR2638),

Région

Hauts de France, Ministère de l'Education Nationale de l'Enseignement Supérieure et de la Recherche and FEDER for financial support. This work was made possible through the use of the computational resources provided by the Centre de Ressources Informatiques (CRI) of the Université de Lille ST. Financial support from the TGIR-RMN-THC Fr3050 CNRS for conducting the research is also gratefully acknowledged. The authors thank the Junta de Andalucía (Spain) and FEDER (Proyecto de Excelencia de la Junta de Andalucía, project P12-FQM-567), the Spanish State Program R+D +I oriented societal challenges and FEDER (Project MAT2015-63929-R) for financial support. Dr. Pavón received support from Andalucía Talent Hub Program, co-funded by the EU in 7FP, Marie Skłodowska-Curie actions and the Junta de Andalucía. F.J. Osuna received support from the training researcher program associated with the excellence project of Junta de Andalucía (P12-FQM-567).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in the online version