Paula Sanz Camacho

Romain Wernert

Mathieu Duttine

Alain Wattiaux

Ashish Rudola

Palani Balaya

François Fauth

Romain Berthelot

Laure Monconduit

Dany Carlier
email: dany.carlier@icmcb.cnrs.fr

Laurence Croguennec
email: laurence.croguennec@icmcb.cnrs.fr

Impact of synthesis conditions in Na-rich Prussian Blue Analogs

Keywords: Na-ion batteries, Prussian Blue Analogs, Iron hexacyanoferrates, hydrothermal synthesis, coprecipitation synthesis

Sodium rich iron hexacyanoferrates were prepared by coprecipitation, hydrothermal route, and under reflux, with or without dehydration. They were obtained with different structures described in cubic, orthorhombic or rhombohedral symmetry, with variable compositions in sodium, water and cationic vacancies, and with a variety of morphologies. This series of sodium rich Prussian Blue Analogs allowed to address the relationship between synthesis conditions, composition, structure, morphology and electrochemical properties in Na-ion batteries. A new orthorhombic phase with the Na 1.8 Fe 2 (CN) 6 •0.7H 2 O composition synthesized by an hydrothermal route at 140°C is reported for the first time, whereas a phase of Na 2 Fe 2 (CN) 6 •2H 2 O composition obtained under reflux, previously described with a monoclinic structure, shows in fact a rhombohedral structure.

Introduction

Large-scale storage of renewable energies and their integration into the grid are keys towards sustainable energy. [START_REF] Dunn | Electrical Energy Storage for the Grid: A Battery of Choices[END_REF] In this context, rechargeable batteries based on low-cost, non-toxic and abundant resources are highly desired. Na-ion batteries have been proposed due the large abundance of sodium (i.e., the 6 th most abundant element in the earth crust) and due to their similarities to the Li-ion batteries that should promote fast technology readiness level improvement. [START_REF] Palomares | Na-ion batteries, recent advances and present challenges to become low cost energy storage systems[END_REF][START_REF] Kundu | The emerging chemistry of sodium ion batteries for electrochemical energy storage[END_REF] Among the materials studied as positive electrodes for Na batteries, Prussian Blue Analogues (PBAs) have received enormous interest in the last 5 years as their open frameworks can accommodate a large panel of cations (Na + , K + , Ca 2+ , Mg 2+ , Sr 2+ , Ba 2+ ) without structure collapse. [START_REF] Wang | Highly Reversible Open Framework Nanoscale Electrodes for Divalent Ion Batteries[END_REF][START_REF] Lipson | Rechargeable Ca-Ion Batteries: A New Energy Storage System[END_REF][START_REF] Mizuno | Electrochemical Mg 2+ intercalation into a bimetallic CuFe Prussian blue analog in aqueous electrolytes[END_REF][START_REF] Qian | Prussian Blue Cathode Materials for Sodium-Ion Batteries and Other Ion Batteries[END_REF] In particular, the hexacyanoferrates (MHCFs, M = Fe, Mn) are the most interesting PBAs materials, due to their non-toxicity, low cost and attractive specific capacities (for instance 170 mAh.g -1 for Na 2 Fe 2 (CN) 6 ). [START_REF] Lee | Manganese hexacyanomanganate open framework as a high-capacity positive electrode material for sodium-ion batteries[END_REF][START_REF] Zhou | Hexacyanoferrate-Type Prussian Blue Analogs: Principles and Advances Toward High-Performance Sodium and Potasium Ion Batteries[END_REF][START_REF] Firouzi | Monovalent manganese based anodes and co-solvent electrolyte for stable low-cost high-rate sodium-ion batteries[END_REF] The structure of PBAs consists, in the absence of vacancies and water molecules, of a double perovskite-analogue framework with the CN -anions bridging high spin M A N 6 and low spin M B C 6 octahedra, while the alkali cations (here the Na + ions) are placed in the cavities as shown in Figure 1. However, depending on the synthesis conditions used, the presence of vacancies and crystalline water molecules can also be present in the structure leading to a Na x M A [M B (CN) 6 ] 1-y y •nH 2 O chemical formula, where M A and M B are different transition metal ions, y the vacancies of [M B (CN) 6 ] and n.H 2 O the number of crystalline water molecules. PBAs typically crystallise in a face-centred cubic structure, however depending on the amount of Na + ions, interstitial water molecules and vacancies, lower symmetry phases such as monoclinic or rhombohedral have been observed. This presence of crystalline water molecules and vacancies apart of having an influence on the crystal structure, does impact also their electrochemical performance. It is therefore crucial to monitor the synthesis conditions in order to control their composition and structure along with particles size. [START_REF] Zhou | Hexacyanoferrate-Type Prussian Blue Analogs: Principles and Advances Toward High-Performance Sodium and Potasium Ion Batteries[END_REF][START_REF] Song | Removal of Interstitial H 2 O in Hexacyanometallates for a Superior Cathode of a Sodium-Ion Battery[END_REF][START_REF] Wang | A Superior Low-Cost Cathode for a Na-Ion Battery[END_REF] In order to achieve high theoretical capacities, a great effort has been done to synthesize these materials as sodium rich phases, with small content of water molecules and vacancies. [START_REF] You | Sodium iron hexacyanoferrate with high Na content as a Na-rich cathode material for Na-ion batteries[END_REF][START_REF] Li | Facile Method To Synthesize Na-Enriched Na 1+x FeFe(CN) 6 Frameworks as Cathode with Superior Electrochemical Performance for Sodium-Ion Batteries[END_REF][START_REF] Wang | Prussian Blue Analogs for Rechargeable Batteries[END_REF] Figure 1 : Schematic illustration of the ideal structure of PBA, here Na 2 Fe 2 (CN) 6 . The Fe 2+ LS C 6 and Fe 2+ HS N 6 octahedra are given as blue and orange polyhedra, respectively. The Na + ions, represented by green spheres, occupy the cavities of the structure.

In literature, materials prepared with the Na 2 Fe 2 (CN) 6 target composition are reported to crystallize in three different polymorphs, with rhombohedral, cubic or monoclinic unit cell symmetry (for Na x Fe 2 (CN) 6 final composition with x ≥ 1.70). Specific capacities up to 140 mAh/g have been reported for Na x FeHCF (x ≥ 1.70). [START_REF] Wang | Rhombohedral Prussian White as cathode for Rechargeable Sodium-Ion Batteries[END_REF][START_REF] Piernas-Munoz | Higher voltage plateau cubic Prussian White for Na-ion batteries[END_REF][START_REF] Rudola | Monoclinic Sodium Iron Hexacyanoferrate Cathode and Non-Flammable Glyme-Based Electrolyte for Inexpensive Sodium-Ion Batteries[END_REF] In this work, we chose to investigate these three Na x Fe 2 (CN) 6 , where x~2 [START_REF] Wang | Rhombohedral Prussian White as cathode for Rechargeable Sodium-Ion Batteries[END_REF][START_REF] Piernas-Munoz | Higher voltage plateau cubic Prussian White for Na-ion batteries[END_REF][START_REF] Rudola | Monoclinic Sodium Iron Hexacyanoferrate Cathode and Non-Flammable Glyme-Based Electrolyte for Inexpensive Sodium-Ion Batteries[END_REF] polymorphs in order to better understand the relationship between synthesis conditions, composition, structure and electrochemical properties. In addition to X-ray powder diffraction (XRPD)

characterization technique that provides information on the long range average structure, we also analysed the local structure of the materials by 57 In our study, we selected two synthesis routes: the precipitation and hydrothermal routes with different temperature conditions. The variation of the reaction temperature has been shown to have an impact on the composition, structure and electrochemical performances of the materials. Moreover, we succeed to prepare a new Na rich Na x Fe 2 (CN) 6 polymorph with an orthorhombic cell, that was not yet reported in literature to the best of our knowledge. The structure and electrochemical properties of this phase will be discussed in comparison with the three other polymorphs.

Experimental method

Synthesis. A series of Prussian Blue Analogs Na

x M A [M B (CN) 6 ] 1-y y •nH 2 O (M A = M B = Fe)
has been prepared using different synthesis routes (coprecipitation or hydrothermal) and at different temperatures. In the following, the materials will be named accordingly, such as for instance Na-FeHCF-Cop-60°C which is obtained by a coprecipitation route at 60°C.

The synthesis of Na-FeHCF-Cop-60°C material has been inspired by the work of Piernas-Munoz et al. [START_REF] Piernas-Munoz | Higher voltage plateau cubic Prussian White for Na-ion batteries[END_REF] The initial aqueous solution, solution A, containing a mixture of Na 4 Fe(II)(CN) 6 .10H 2 O (Sigma-Aldrich; ≥ 99%) (40 mM, 100 mL), an excess of NaCl (Sigma-Aldrich; ≥ 99%) (18.9 g) and 5 mL of a solution of ascorbic acid (VWR; 100%) (45 mM, 10 mL) was heated at 60 ºC for complete dissolution. Solution A was added dropwise using a programmable syringe pump into solution B, a pale yellow-greenish solution of FeCl 2 (Sigma-Aldrich; ≥ 98%) (40 mM, 100 mL) with 5 mL of the ascorbic acid solution (45 mM, 10 mL), previously heated at 60 ºC, while stirring in Ar atmosphere. After 4h stirring and heating at 60°C in Ar flow, the mixture was aged for 2 hours (just enough time to be cooled down) before being centrifuged and filtered. The product was washed with water, then with acetone and dried at 65°C. A blue dark powder was obtained. On the contrary, to the protocol described in reference 17, ascorbic acid (1.125 equivalents) was added to both solutions to slow down the nucleation as it has been recently reported by Wang et al. [START_REF] Wang | Reversible structural evolution of sodium-rich rhombohedral Prussian blue for sodium-ion batteries[END_REF] Please note that the effect of ascorbic acid on the compound obtained was not explored here, as the purpose was to synthesize the cubic phase described by Piernas-Munoz et al. [START_REF] Piernas-Munoz | Higher voltage plateau cubic Prussian White for Na-ion batteries[END_REF] as a reference, to be compared with the other phases prepared in this work.

The material Na-FeHCF-reflux-107°C was obtained from the mixture of Na 4 Fe(CN) 6 with an excess of ascorbic acid (4.5 equivalents) heated under reflux at 107°C using an oil bath, as described in reference [START_REF] Rudola | Monoclinic Sodium Iron Hexacyanoferrate Cathode and Non-Flammable Glyme-Based Electrolyte for Inexpensive Sodium-Ion Batteries[END_REF] . The material Na-FeHCF-Vac-220°C was obtained by dehydration, heating the previous material 2h at 220°C in vacuum (2•10 -2 hPa). [START_REF] Rudola | Monoclinic Sodium Iron Hexacyanoferrate Cathode and Non-Flammable Glyme-Based Electrolyte for Inexpensive Sodium-Ion Batteries[END_REF] The Na-FeHCF-hyd-60°C, Na-FeHCF-hyd-107°C and Na-FeHCF-hyd-140°C materials were obtained through an hydrothermal route inspired by the work of Wang et al. [START_REF] Wang | Rhombohedral Prussian White as cathode for Rechargeable Sodium-Ion Batteries[END_REF] However, in contrast to their results which report a pH of 6.5, in our case a pH value of 3 was required to perform the reaction with success, therefore with an excess of ascorbic acid (4.5 equivalents).

It is worth mentioning that using a pH of 6.5, we obtained only Fe 2 O 3 . Ascorbic acid (225 mM) was rapidly added to an aqueous solution of Na 4 Fe(II)(CN) 6 10H 2 O (Sigma-Aldrich; ≥ 99%) (50 mM, 100 mL), and the mixture was left stirring until complete dissolution. The mixture was then transferred into an autoclave and heated in different conditions: 60, 107 or 140°C overnight. In each case, the resulting suspension was then washed with water and acetone and dried at 80°C in an oven. Blue-intense powders were obtained for Na-FeHCF-hyd-60°C and Na-FeHCF-hyd-107°C, while a pale-green powder was obtained for Na-FeHCF-hyd-140°C.

Structural characterization. Laboratory powder X-ray diffraction (XRD) patterns were either collected on a PANAlytical X'pert PRO MPD diffractometer in Bragg-Brentano θ-θ geometry equipped with a secondary monochromator and X'Celerator multi-strip detector, or using a PANalytical XPert 3 diffractometer in Debye-Scherrer θ-θ configuration, and both equipped with a Cu K 1,2 X-ray source. In the former case, each measurement was made within an angular range of 2θ = 8-80° or 8-120° and with a step of 0.0167°. In the latter case, the powder was packed in a 0.5 mm diameter capillary. The acquisition was performed in the 2θ range of 5° -80° with a step size of 0.0167°. High angular resolution synchrotron X-ray powder diffraction (SXRPD) was performed at the MSPD beamline of ALBA synchrotron (Barcelona, Spain). The powders were packed in a 0.5 mm diameter capillary and mounted on the goniometer in Debye-Scherrer geometry. The data were recorded by using MYTHEN detector at a wavelength of 0.8251 Å, in the 2θ angular range of 0.34 o -72 o with a 0.006 o step.

The X-ray diffraction analysis was performed with FULLPROF suite for indexing the reflection lines and with JANA2006 for the refinements and calculations of Fourier difference maps. Note that in the following, when diffraction line widths are compared, it means that it is possible to do this comparison despite the use of different diffractometers. To keep a reasonable amount of parameters refined together during Rietveld refinements and avoid major correlations, the Fe, C and N sites were considered to be fully occupied and the B iso parameters were fixed to reasonable values according to the covalency of the bonds in which these atoms are involved (B iso -Fe = 0.5 Å 2 , B iso -C = B iso -N = 0.7 Å 2 and B iso -O = 1 Å 2 .

Morphology characterization. Scanning electron microscopy (SEM) images were taken on the metallized samples (Pd-deposited) by a Hitachi Model S-4500 microscope.

Thermogravimetric analysis. Water content was determined using a TG/DTA SDT Q600 TA Instrument, the measurements were performed from room temperature to 600°C at 5°C/min in Ar atmosphere. TGA-MS analyses were performed on a SETARAM TAG 24 instrument, from room temperature until 450°C at 3°C/min in Ar atmosphere.

Mössbauer spectroscopy analyses. 57 Fe Mössbauer spectra were collected using a constant acceleration Halder-type spectrometer operating in transmission geometry with a room temperature 57 Co source (embedded in Rh matrix). The velocity scale was calibrated according to the 57 Fe Mössbauer spectrum of a pure α-Fe 0 foil recorded at room temperature.

The refinement of Mössbauer hyperfine parameters (δ isomer shift, Δ quadrupole splitting, Γ signal line width and relative areas) was performed using both homemade programs and the WinNormos software (Wissenschaftliche Elektronik GmbH). In this study, when the signal was too broad (Γ > 0.40 mm/s) a distribution of the quadrupole splitting parameters (Δ) was used following the method proposed by Hesse and Rübartsch. 20

Results and discussions

Morphological study

Scanning electron microscopy (SEM) has been used to study the morphology of the asprepared materials. The SEM images of all materials are shown in The rapid precipitation and nucleation observed for the coprecipitation route yielded to the formation of irregular aggregates containing small size particles. Although ascorbic acid, which was added into the two solutions of precursors FeCl 2 and Na 4 Fe(CN) 6 as an antioxidant, is also a chelating agent, its concentration was here not high enough to slow down nucleation versus growth. [START_REF] Wang | Reversible structural evolution of sodium-rich rhombohedral Prussian blue for sodium-ion batteries[END_REF] On the contrary, for hydrothermal syntheses, Na 4 Fe(CN) 6 is used as a single precursor in the presence of a large excess of ascorbic acid (4.5 equivalents)

that acts here as antioxidant and chelating agent boosting the growth process towards the formation of micrometric well-shaped cubic particles.

The comparison of the materials synthesized by the hydrothermal route at different temperatures (Na-FeHCF-hyd-60°C, Na-FeHCF-hyd-107°C and Na-FeHCF-hyd-140°C) is given in Figures 2b-d. It appears that the temperature does not affect the shape and size of the materials' particles, as in all cases the powder exhibits cubic-shaped particles with edges of ca. 1-3 μm.

The Na-FeHCF-reflux-107°C material was synthesized differently from those described before, despite similar precursors and concentrations to the hydrothermal synthesis. This synthesis took place in air, and the precursors, (Na 4 Fe(CN) 6 and ascorbic acid, were mixed and then heated at 107°C under reflux. Ascorbic acid as chelating agent promoted growth versus nucleation, as shown by the even bigger cubic-shaped particles obtained (ca. 5 μm) (Figure 2e) (See Figure S1 in the supporting information for a more general view of the powder). This result highlights that the difference in pressure between the reflux and hydrothermal conditions has a clear impact on the particles' size.

Figure 2f shows that the material obtained from dehydration of Na-FeHCF-reflux-107°C at 220°C in vacuum, is characterized by similar particles, in shape (cubic) and in size (ca. 5 μm) than its precursor (See Figure S1 in the supporting information for a more general view of the powder), suggesting that the dehydration process do not have any impact on the morphology.

However,

Thermogravimetric analyses

Thermogravimetric analyses coupled with mass spectrometry (TGA-MS) were performed for all materials in order to determine their content in water and their decomposition temperature.

For all of them, the decomposition starts in the 200-250°C temperature range, as highlighted by the release of HCN and CO 2 (see Figure S2 in supplementary information for more details).

TGA-MS of Na-FeHCF-Cop-60°C revealed no significant mass loss below 100°C, and about 10 wt.% at 200°C corresponding to 1.6 water molecules. However, for the material synthesized at the same temperature by the hydrothermal route (Na-FeHCF-hyd-60°C) a mass loss of only 8 wt.% is observed at 250°C, corresponding to 1.3 water molecules. This revealed changes in the water content for these two Na-FeHCF materials.

For the two other materials synthesized by the hydrothermal route at higher temperatures, the content in water varies from 3.4 to 4 wt.%, for Na-FeHCF-hyd-107°C and Na-FeHCF-hyd-140°C, respectively. It is thus worth highlighting that despite no modification of the shape and size of the particles the synthesis temperature has an effect on the water content in Na-FeHCF.

Again, despite similar synthesis temperatures for both materials, Na-FeHCF-reflux-107°C and Na-FeHCF-hyd-107°C, a mass loss of 10 wt.% was observed for the former whereas only 3.4

wt.% for the latter. This corresponds to two water molecules per formula unit for Na-FeHCFreflux-107°C and to only 0.59 for Na-FeHCF-hyd-107°C. This highlights again the impact of synthesis routes and conditions not only on the morphology but also on the composition of the NaFeHCF materials.

As expected, Na-FeHCF-Vac-220°C obtained by dehydration of Na-FeHCF-reflux-107°C

shows the smallest loss of water with only 1 wt.% at 250°C.

Structural description

The XRPD patterns of all materials are displayed in Figure 3. It can be observed that a pattern with less diffraction peaks, in good agreement with a higher symmetry of the structure, is observed for the materials synthesized at low temperatures, while for higher temperatures a deviation from a cubic-profile pattern occurs. This deviation from the cubic symmetry would be, as reported in literature [START_REF] Zhou | Hexacyanoferrate-Type Prussian Blue Analogs: Principles and Advances Toward High-Performance Sodium and Potasium Ion Batteries[END_REF] , a confirmation of the higher amount of Na in the structure. Moreover, a difference in the line width can be observed depending on the synthesis route as discussed below.

The XRPD patterns of the two samples prepared at 60°C can be indexed in the cubic Fm-3m space group, but exhibit very different diffraction line width. Note that the Na-FeHCF-Cop-60°C phase also exhibits an extra peak at Q=2.25 Å -1 attributed to an unknown impurity (Figure 3a and Figure S3). Note that we did not refine all occupancies and thermal displacement factors (B iso ) in order to not overfit the experimental data. The Fe, C and N sites were considered to be fully occupied and the B iso parameters were fixed to reasonable values according to the covalence of the bonds in which these atoms are involved (B iso -Fe = 0.5 Å 2 , B iso -C = B iso -N = 0.7 Å 2 and B iso -

O = 1 Å 2 ).
In order to understand the effect of the temperature using the hydrothermal route, the materials Na-FeHCF-hyd-107°C and Na-FeHCF-hyd-140°C were synthesized using same conditions as for Na-FeHCF-hyd-60°C but with different temperatures. [START_REF] Su | High-Capacity Aqueous Potassium-Ion Batteries for Large-Scale Energy Storage[END_REF] Note that the structural description of this potassium polymorph is not available either. The two hydrothermal samples synthetized at 107°C and 140°C can be described with the same unit cells and the corresponding lattice parameters are given in Table 1.

Table 1 : Cell parameters of Na-FeHCFs materials obtained from refinement of the X-ray powder diffraction data. This result is in agreement with the Mössbauer spectroscopy analysis discussed later in this paper. The position of the water molecules was determined using Fourier difference maps (Figure 6) and associated with an occupancy of 0.64, corresponding to ~2 water molecules per formula unit. Two oxygen sites were identified at the center of the faces of the large pseudo cubic cages, associated to significantly different electronic densities as can be seen on the cross section of the electron density isosurfaces. This suggests a different occupancy for the two H 2 O sites. However, we were not able to correctly refine the structure considering these two independent sites and their occupancy due to the limited amount of parameters that can be refined at once: only an average one could be considered to describe the two sites.

Material

Finally, the refinement of sodium site occupancy allowed to propose the chemical formula As described in reference 18, Na-FeHCF-reflux-107°C can be dehydrated thermally and under vacuum to obtain the rhombohedral phase described first by Wang et al. [START_REF] Wang | Rhombohedral Prussian White as cathode for Rechargeable Sodium-Ion Batteries[END_REF] In this work, the XRPD pattern of the corresponding material, Na-FeHCF-Vac-220°C, is displayed in crystallographic planes respectively, while much sharper linewidths (0.066, 0.077 and 0.074°(2)) were observed for Na-FeHCF-reflux-107°C before dehydration (Figure 3e).

Here, the broad diffraction peaks observed in the XRPD pattern of Na-FeHCF-Vac-220°C cannot be attributed to the nanometer size of the particles as for Na-FeHCF-Cop-60°C, since they are micrometer sized. The broadening can be tentatively attributed to a disorder leading to a reduction of the coherent domains in the particles versus the pristine hydrated precursor Na-FeHCF-reflux-107°C. Indeed, according to the coherent length calculations using the Scherrer law, the average size of diffracting domains was shown to be reduced from ~3 µm to ~150 nm for Na-FeHCF-reflux-107°C and Na-FeHCF-Vac-220°C respectively.

Mössbauer spectroscopy analyses

Room temperature Mössbauer spectra of all materials are displayed in Figure 7 and the corresponding refined hyperfine parameters of each component are reported in Table 3. They all exhibit a singlet at ~ δ = -0.12 mm/s corresponding to six-fold coordinated LS-Fe 2+ 22 and representing between 40 and 50 % of the spectrum global area: ~40 % for Na-FeHCF samples synthesized at low temperature (60°C) and ~ 50 % for all the other materials. This apparent singlet may indeed be considered as a quadrupole doublet with a very low value of the quadrupole splitting parameter (Δ ≤ 0.13 mm/s) as it is expected for LS-Fe 2+ Mössbauer signal. Note, that this splitting is slightly weaker (Δ ≤ 0.05 mm/s) for the NaFeHCF-hyd-107°C and NaFeHCF-hyd-140°C materials compared to others, reflecting slightly less local distortion on those phases.

All spectra, as shown in Figure 7, exhibit one or two additional components depending on the synthesis conditions used to prepare the Na-FeHCF materials. For Na-FeHCF-Cop-60°C, the Mössbauer spectrum can be described as the sum of an apparent singlet at δ = -0.13 mm/s, a broad and unresolved signal centered at δ ≈ 0.38 mm/s and a quadrupole doublet of very low intensity with a high isomer shift value (δ = 1.11 mm/s) and a large quadrupole splitting (Δ = 1.17 mm/s), attributed to LS-Fe 2+ (41 %), HS-Fe 3+ (57 %) and HS-Fe 2+ (2%), respectively. The detection of a trivalent iron signal implies that this Na-FeHCF material may be Na + -deficient. It has been recently proposed by Ojwang et al in ref. 23 that it could be due to reactivity with moisture. However, in our case, Mössbauer data were promptly collected after the synthesis putting special care in avoiding possible moisture. Moreover, the corresponding Fe 3+ sub-spectrum is characterized by a distribution of the quadrupole splitting hyperfine parameter (inset of figure 7a), suggesting a series of different local environments for HS-Fe 3+ with different site distortions depending on the distribution on the adjacent cationic sites (Fe/vacancy and Na/vacancy) and/or structural water molecules.

The Na-FeHCF materials prepared by the hydrothermal route (Na-FeHCF-hyd-60°C, Na-FeHCF-hyd-107°C and Na-FeHCF-hyd-140°C) exhibit Mössbauer spectra that differ significantly depending on the synthesis temperature. For Na-FeHCF-hyd-60°C, in addition to the LS-Fe 2+ sub-spectrum (38%), two quadrupole doublets assigned to HS-Fe 2+ (35%) and HS-Fe 3+ (27%) are observed at δ = 1.06 mm/s and δ = 0.37 mm/s, respectively. In contrast, the amount of HS-Fe 3+ is reduced to 5 % for Na-FeHCF-hyd-107°C and 0% for Na-FeHCFhyd-140°C, while the amount of HS-Fe 2+ increases from 46 to 50 %, respectively. Therefore, as the temperature used during the synthesis increases, the amount of HS-Fe 3+ decreases indicating larger content of Na + ions within the structure. Finally, the material synthesized at 140°C appears to be really stoichiometric with a composition in Na, Fe and CN such as Na 2 Fe 2 (CN) 6 .

The Na-FeHCF-reflux-107°C material exhibits an additional doublet, observed at δ = 1.12 mm/s corresponding to HS-Fe 2+ (50%), this signal is very similar to that observed in the Mössbauer spectrum of Na-FeHCF-hyd-140°C suggesting also that the synthesis of a perfectly stoichiometric material has been achieved. In contrast, for Na-FeHCF-Vac-220°C, the HS-Fe 2+ sub-spectrum (δ = 1.12 mm/s) is satisfactorily described by a bi-modal distribution of quadrupole doublets (inset of figure 7f) suggesting two different disordered environments for HS-Fe 2+ . A similar and broader Δ distribution was also evidenced for highspin divalent iron in the Na-FeHCF-hyd-60°C material that presents as its analogue Na-FeHCF-cop-60°C, the highest Na + deficiency (figure 7b). Thus, the Na-FeHCF compound prepared under vacuum at 220°C may also be slightly Na + -deficient, what is consistent with the detection of a low-intensity (7% in relative area) quadrupole doublet (δ = 0.41 mm/s, Δ = 0.57 mm/s) associated with HS-Fe 3+ .

In conclusion, the different synthesis methods do have a clear impact on the ratio LS-Fe 2+ / HS-Fe 2+ , presence of HS-Fe 3+ (due to Na deficiency) and local disorder around Fe species Fe 2+ / Fe 3+ . Overall, only the Na-FeHCF-hyd-140°C material appears to present the ideal LS-Fe 2+ / HS-Fe 2+ ratio (50/50) with the weakest disorder of the Fe environments. size onto the electrochemical performance in the conditions studied in this work. This is in contrast with observations made for potassium derivatives. [START_REF] He | Crystallite Size Control of Prussian White Analogues for nonaqueous Potassium-Ion Batteries[END_REF] In contrast, for the stoichiometric samples Na-FeHCF-hyd-140°C and Na-FeHCF-reflux-107°C, almost two Na + ions were extracted during the first charge confirming thus the rich Na content. A large polarization is observed during the first cycle of the battery, that is then reduced in subsequent cycles. Moreover, no extra capacity is observed in subsequent cycles and actually less Na + ions (1.37 and 1.65 Na + respectively) were re-intercalated within the structure after the first cycle. Finally, the sodium rich stoichiometry of these pristine materials is further evidenced by starting the Na half cells in discharge rather than in charge, resulting in a very limited intercalation of less to 0.2 Na + into the structure, as shown in Figure S12.

Based on all the complementary information gathered, the compositions S12. This feature is not understood yet and, although further experiments will be necessary to understand this behavior, it is interesting to point out that similar behavior was observed for iron hexacyanocobaltate materials as reported by Mullaliu et al. [START_REF] Mullaliu | Operando XAFS and XRD Study of a Prussian Blue Analogue Cathode Material: Iron Hexacyanocobaltate[END_REF] A possible explanation could be the instability of the solid electrolyte interphase formed for Na rich or close to the stoichiometry phases with low content of water, as it has been proposed recently by Fu et al. [START_REF] Fu | Improved rate performance of Prussian blue cathode materials for sodium ion batteries induced by ionconductive solid-electrolyte interphase layer[END_REF] However, in our case, Na-FeHCF-Vac-220°C was shown to be the material with the smaller amount of water, and despite of that it does not show this strange electrochemical behavior during the first charge. This behavior remains thus to be fully understood.

Conclusion

The effect of the different synthesis conditions such as synthesis routes (coprecipitation, hydrothermal, under reflux and after a dehydration), temperatures, pressure and precursors was investigated in this work. It was determined that the higher the synthesis temperature the higher is the Na content and the smaller is the amount of water in the structure, with no changes in the morphology for the hydrothermal synthesis. Furthermore, slowing down the reaction using an excess of ascorbic acid favors the formation of Na-rich phases with cubic shape morphologies. Clearly, synthesis conditions have to be carefully chosen to obtain specific compositions and morphologies. Each synthesis method presented its pros and cons: even if the coprecipitation method seems really very easy to implement since no specific equipment is required, it requires a precise control of the concentrations and feeding rates under an inert atmosphere, in order to control the particle's composition and size, as two solutions of reactants are needed. In contrast, the reflux and hydrothermal synthesis routes can be easier to implement as a single solution of precursor is used, but these synthesis routes might be less scalable for industrial production. In the latter case, the excess (4.5 equivalent) of ascorbic acid acts as antioxidant and chelating agent reducing the nucleation rate and allowing a better control of the composition and particle' size.

A variety of Na-FeHCF compounds were prepared showing different structures described in three different unit cells of cubic, orthorhombic or rhombohedral symmetry, variable compositions in sodium, water and cationic vacancies, and a variety of morphologies. Some of these Na-FeHCF were already reported in the literature, nevertheless it is worth mentioning that one polymorph is reported for the first time, an orthorhombic phase with composition Na~1 .8 Fe 2 (CN) 6 .0.7H 2 O synthesized by an hydrothermal route at 140°C; while the structure of another is also better described, the monoclinic phase obtained under reflux at 107°C, already reported by some of us [START_REF] Wang | A Superior Low-Cost Cathode for a Na-Ion Battery[END_REF] , appears finally better described in a rhombohedral symmetry.

When this material, revealed to be Na 1.86 Fe 2 (CN) 6 •2H 2 O, was dehydrated, the same symmetry is maintained despite significant change in the cell parameters due to the release of water molecules. Mössbauer spectroscopy appears as crucial to characterize these Na-FeHCF materials, as allowing to get information, on the material's composition, but also on the Fe oxidation state and on the disorder around it.

All these materials Na-FeHCF were compared in Na half-cells in similar conditions (electrolyte, electrode formulation, potential window, cycling rate, etc.), starting in charge and in discharge, in order to get complementary information on the effect of the stoichiometry on the electrochemical properties of these PBAs.

This work participates to the better understanding of the impact of the synthesis conditions on Na-FeHCF in the frame of optimizing alternative low cost and sustainable electrode materials for future battery generation.

Author information:

Corresponding Authors:

*E-mail: Dany.Carlier@icmcb.cnrs.fr

Electrochemical characterization.

  Electrochemical performance of the materials was tested in CR2032-type coin cells. The positive electrode was prepared as a slurry containing 85 wt.% active material, 10 wt.% Ketjen black (KB), and 5 wt.% polyvinylidene fluoride (PVDF, Fluka, M 534.0) dispersed in N-methyl-2-pyrrolidone (NMP, Sigma-Aldrich; ≥ 99%) casted on an Al foil with the doctor blade technique. The films as obtained were then dried at 80°C overnight in an oven to evaporate NMP. The electrodes were then cut as 14 mm diameter discs, pressed under 5 T and finally dried at 80°C in vacuum, except for the dehydrated phase which were dehydrated at 220 °C for 2h as described in reference 18. The mass loading of the as-prepared electrode was around 2 to 3 mg.cm -2 . A homemade electrolyte which contained 1M solution of NaPF 6 (Strem Chemical; 99%) in propylene carbonate (PC) (Sigma-Aldrich; ≥ 99.7%) with 2 wt.% of fluoroethylene carbonate (FEC) (Sigma-Aldrich; ≥ 99%) was used for all the electrochemical tests. The assembled cells were cycled in galvanostatic mode, at a C/20 (4.25mA/g) cycling rate between 2 and 4.25/4.3 V vs. Na + /Na.

Figure 2 .

 2 Figure 2a, the Na-FeHCF-Cop-60°C powder consists of ca. 50 nm grains aggregated into

Figure 2 :

 2 Figure 2: SEM images of the 6 different Na-FeHCF materials. Scale bar is 3 µm.

  The full width at half maximum (FWHM) of the three first diffraction peaks corresponding to the (200), (220) and (400) reflection planes are 0.233, 0.295 and 0.297°(2) for Na-FeHCF-Cop-60°C and approximately 5 times narrower for Na-FeHCF-hyd-60°C (0.0418, 0.0627 and 0.0579°) (Figure3b). This difference is mainly due to the very different crystallites' size of the two samples, as supported by the SEM analysis previously discussed. The refined cell parameter of the Na-FeHCF-Cop-60°C phase, a = 10.2585(4) Å, is different from the value a = 10.350(5) Å reported by Piernas-Munoz et al.[START_REF] Piernas-Munoz | Higher voltage plateau cubic Prussian White for Na-ion batteries[END_REF] , but we report better reliability factors here. The main diffraction peaks for the Na-FeHCFhyd-60°C phase are located at lower angles compared to the ones of Na-FeHCF-Cop-60°C, in agreement with the refined slightly larger lattice parameter value, a=10.33939(7) Å. A high quality Rietveld refinement was performed for this sample thanks to its high crystallinity and the results are described in details in FigureS4and TableS5. The occupancy of the Na and O sites, the latter corresponding to the localization of the O atom of the water molecule H 2 O, Table S6 in supplementary information).

Figure 3 :

 3 Figure 3: X-ray powder diffraction (XRPD) patterns for Na-FeHCF-Cop-60°C (red), Na-

  The XRPD and the SXRPD patterns of Na-FeHCF-hyd-107°C and Na-FeHCF-hyd-140°C are shown in Figures3c and 3d, respectively. In good agreement with the discussion on the particles size, they all exhibit sharp diffraction lines. The XRPD and SXRPD patterns of Na-FeHCF-hyd-107°C and Na-FeHCF-hyd-140°C exhibit a splitting of the main peaks in contrast to the material synthesized in the same conditions but at 60°C, suggesting an orthorhombic distortion of the unit cell. For instance, the first diffraction peak (200) Fm-3m is now shifted towards higher angles and split into two lines, corresponding to the crystallographic planes (200) and (011) in an orthorhombic unit cell, as clearly observed in the SXRPD pattern of Na-FeHCF-hyd-140°C. Similar observation is made for the second diffraction peak (220) Fm-3m , also shifted towards higher angles and split into three lines, corresponding to the crystallographic planes (020), (211) and (002) in an orthorhombic unit cell. This orthorhombic distortion is observed in both patterns as shown in FigureS7.The SXRPD pattern of Na-FeHCF-hyd-140°C was initially indexed in the Pmn2 1 orthorhombic space group to determine the unit cell parameters: a = 10.23550 (1) Å, b = 7.24140 (7) Å and c = 7.15920 (8) Å. Satisfactory reliability factors were obtained for this full pattern matching refinement (RBragg = 5.76, Rp = 1.76, Rwp = 3.35) (see Figure 4), but other orthorhombic space groups such as Pmmm gave similar results (as illustrated in Figure S8

*

  Orthorhombic space group proposed based on the information obtained on the number of Fe environments by Mössbauer spectroscopy

Figure 4 :

 4 Figure 4: Full pattern matching refinement of the SXRPD data recorded for Na-FeHCF-hyd-

Na 1 .

 1 86 Fe 2 (CN) 6 •1.92H 2 O (see Table S6 in supplementary information).

Figure 5 :

 5 Figure 5: Result of the Rietveld refinement performed in the R-3 space group of the X-ray powder diffraction data recorded for Na-FeHCF-reflux-107°C.

Figure 6 :

 6 Figure 6: Result for Na-FeHCF-reflux-107°C of the Fourier difference map calculated after the Rietveld refinement of XRD data without considering the oxygen atoms of the interstitial H 2 O. The two possible H 2 O sites are displayed in yellow and red.

Figure 3f .

 3f Figure 3f. It can be unambiguously indexed in a rhombohedral symmetry as demonstrated in

Figure 7 :

 7 Figure 7: Room temperature 57 Fe Mössbauer spectra of Na-FeHCF samples. Sub-spectra with

Figure 8 :

 8 Figure 8: The electrochemical (a) 1 st and (b) 2 nd charge/discharge cycles of Na-FeHCF vs. Na metal, at the cycling rate of C/20 per Na + , with the cut-off voltage of 4.3 V vs. Na + /Na. (c)

Na 1 . 8 Figures 8

 188 Figures 8 and S12. This feature is not understood yet and, although further experiments will

  Fe 2+ LS C 6 and Fe2+ HS N 6 octahedra as shown in Figure1(LS and HS for low spin and high spin respectively). In Na deficient compounds (Na/Fe ratio < 1), additional Fe environments are expected since Fe 3+ ions are formed due to charge compensation. This technique hence gives information on the local environments of Fe (number of sites, distortion, disorder, oxidation states), but is also very informative to establish the Na composition of the materials.

Fe Mössbauer spectroscopy. It is worth mentioning that for the ideal Na 2 Fe 2 (CN) 6 compound, only two different Fe environments are expected:

  Pmn2 1 space group. However, the structural description could not be achieved successfully as discussed in details in FigureS9in supplementary information. This orthorhombic phase is a new polymorph of Na 2 Fe 2 (CN) 6 , isostructural to the potassium

	derivative K 2 Fe 2 (CN) 6 •2H 2 O described in the space group Pmn2 1 with lattice parameters a =
	10.06 Å, b = 7.27 Å and c = 7.12 Å.

). Even though Pmmm is of higher symmetry, Pmn2 1 is probably more appropriate. Indeed, four distinct iron sites are needed to describe the PBA framework in the Pmmm space group whereas only two are needed in the Pmn2 1 space group. Provided that two Fe sites were identified by Mössbauer spectroscopy as discussed hereafter, we tried to solve the structure by ab initio in the

Table 2 :

 2 Atomic coordinates and main interatomic distances determined from the Rietveld refinement performed in the R-3 space group of the X-ray powder diffraction data recorded for Na-FeHCF-reflux-107°C.

			Na 1.86 Fe 2 (CN) 6 •1.92H 2 O
	S.G. R-3		a = b = 7.511(2) Å		R Bragg = 1.82
	Z = 3		c = 17.5086(6) Å			R p = 0.61
			V/Z = 285.15 Å 3			R wp = 0.90
	Atoms	Wyckoff positions	x/a	y/b	z/c	Occupancy	B iso
	Fe (1)	3a	0	0	0	1	0.5
	Fe (2)	3b	1/3	2/3	1/6	1	0.5
	Na	6c	0	0	0.251(2)	0.93(3)	2.4(3)
	C	18f	0.122(2)	0.868(2)	0.0582(4)	1	0.7
	N	18f	0.219(1)	0.810(1)	0.0939(4)	1	0.7
	O	9e	1/3	1/6	1/6	0.64(1)	1
			Bond		Distance (Å)
			Fe (1) -C		1.940(4)
			Fe (2) -N		2.156(2)
			C -N		1.152(6)
			Na -O		2.604(7)

Table 3 :

 3 Refined room temperature 57 Fe Mössbauer hyperfine parameters for Na-FeHCF samples (δ isomer shift in respect to α-Fe,  quadrupole splitting, Γ Lorentzian line width and A relative area). (*) mean value of the  distribution.

		 (mm/s)	(mm/s) Δ	(mm/s) Γ	(%) area	assignement
	(a) Na-FeHCF-Cop-60°C
	Site (1)	-0.13(1)	0.10(2)	0.25(3) 41(3)	LS-Fe 2+
	Site (2)	1.11(8)	1.17(9)	0.30(4) 2(2)	HS-Fe 2+
	Dist. (3)	0.38(6)	0.50*	0.30(-) 57(3)	HS-Fe 3+
	(b) NaFeHCF-hyd-60°C
	Site (1)	-0.12(1)	0.09(1)	0.25(1) 38(2)	LS-Fe 2+
	Dist. (2)	1.06(2)	0.88*	0.30(-) 35(3)	HS-Fe 2+
	Dist. (3)	0.37(5)	0.61*	0.30(-) 27(3)	HS-Fe 3+
	(c) NaFeHCF-hyd-107°C
	Site (1)	-0.12(1)	0.05(3)	0.25(1) 49(2)	LS-Fe 2+
	Site (2)	1.10(1)	1.09(1)	0.27(1) 46(2)	HS-Fe 2+
	Dist. (3)	0.47(2)	0.29(6)	0.26(4) 5(2)	HS-Fe 3+
	(d) NaFeHCF-hyd-140°C
	Site (1)	-0.12(1)	0.03(3)	0.25(1) 50(2)	LS-Fe 2+
	Site (2)	1.10(1)	1.09(2)	0.26(1) 50(2)	HS-Fe 2+
	(e) NaFeHCF-reflux-107°C
	Site (1)	-0.09(1)	0.12(1)	0.24(1) 50(2)	LS-Fe 2+
	Site (2)	1.12(2)	1.09(1)	0.28(1) 50(2)	HS-Fe 2+
	(f) NaFeHCF-Vac-220°C
	Site (1)	-0.11(1)	0.13(2)	0.28(1) 49(2)	LS-Fe 2+
	Dist. (2)	1.12(2)	0.98*	0.30(-) 44(2)	HS-Fe 2+
	Site (3)	0.41(3)	0.57(7)	0.43(5) 7(2)	HS-Fe 3+

Acknowledgements

The authors thank the RS2E Network for the funding of PSC's postdoctoral fellowship, as well as the financial support of CNRS (PEPS2017-Cellule Energie), Région Nouvelle Aquitaine, the French National Research Agency (STORE-EX Labex Project ANR-10-LABX-76-01) and the H2020 European Program (Project NAIADES). The authors also thank Eric LEBRAUD and Stan PECHEV, Philippe DAGAULT, Dominique DENUX and Catherine DENAGE (ICMCB-CNRS) for their help with XRD, TGA, TGA-MS and SEM analyses, respectively.

Electrochemical properties

The electrochemical performance of Na-FeHCFs materials were characterized in half cells in the 2.0 to 4.3 V vs Na + /Na potential window. The electrochemical profiles obtained during the 1 st and 2 nd cycles and the corresponding derivatives of the 2 nd cycles are displayed in Figure 8. Note that the Na-FeHCF-hyd-107°C was not studied due to its strong similarity with Na-FeHCF-hyd-140°C.

The two materials synthesized at 60°C, namely Na-FeHCF-Cop-60°C and Na-FeHCF-hyd-60°C, were shown to be non-stoichiometric samples combining XRPD and Mössbauer spectroscopy. This non-stoichiometry was supported (i) by the first electrochemical charge with the limited extraction of ~ 1.6 Na + ions and (ii) by the extra capacity observed during the next discharge and the subsequent charge during which ~ 2 Na + ions were intercalated first and then reversibly de-intercalated. The Na + deficiency in Na-FeHCF-Cop-60°C and Na-FeHCF-hyd-60°C was further supported by the insertion of 0.6 Na + into the structure when the Na cell is discharged first rather than being charged, as shown in Figure S12 S6 in supplementary information). However, a small discrepancy in the amount of water can be shown between PXRD and TGA-MS analysis from 1.86 to 1.3 H 2 O respectively. We believe that the right amount should be the one taken from the PXRD that allows better quantification of the oxygen associated with water molecules.

Na-FeHCF-reflux-107°C has already been tested in different conditions: at different cycling rates, with different electrolytes as well as different binders etc. [START_REF] Rudola | Monoclinic Sodium Iron Hexacyanoferrate Cathode and Non-Flammable Glyme-Based Electrolyte for Inexpensive Sodium-Ion Batteries[END_REF] Similar electrochemical performance were obtained with reversible capacities of 171 mAh.g -1 and 148 mAh.g -1 during the first charge in reference 12 and in this work, respectively.

The material Na-FeHCF-Vac-220°C is also stoichiometric as it has been shown by Mössbauer spectroscopy, with the detection of only 7% of HS-Fe 3+ . When the Na half-cell is discharged first, rather than being charged, as expected only a very limited amount of Na + ions (0.04) was incorporated into the structure. Capacities of 142 mAh.g -1 and 164 mAh.g -1 are obtained when starting the Na cells in charge and in discharge, respectively. However, in any case, similar mechanisms are observed with two plateaus observed in the overall voltage range and with capacities similar to those already reported. [START_REF] Wang | Rhombohedral Prussian White as cathode for Rechargeable Sodium-Ion Batteries[END_REF][START_REF] Rudola | Monoclinic Sodium Iron Hexacyanoferrate Cathode and Non-Flammable Glyme-Based Electrolyte for Inexpensive Sodium-Ion Batteries[END_REF] The derivative curves of the charge and discharge cycles calculated for all compounds are The evolution of the discharge capacity over the first 5 cycles is compared in Figure S13 for all Na-FeHCF materials. It can be observed that those containing less Na in their pristine state show higher reversible capacities versus those richer in Na. Nevertheless, only the latter can be used as positive electrode materials in Na-ion batteries, as the former require to be associated with a Na-containing negative electrode or Na metal.

*E-mail: Laurence.Croguennec@icmcb.cnrs.fr

Notes

The authors declare no competing financial interest.

Supporting Information

Supporting Information gives additional results on characterizations performed by scanning electron microscopy, thermogravimetric analysis coupled to mass spectrometry, X-ray diffraction, and electrochemical tests in half-cells versus Na metal.


Marie Soula
email: marie.soula.1@ulaval.ca

Fabienne Solarski

Sophie Duquesne
email: sophie.duquesne@centralelille.fr

Véronic Landry
email: veronic.landry@sbf.ulaval.ca

Fabienne Samyn
email: fabienne.samyn@univ-lille.fr

Vlatka Jirous-Rajkovic

Innovative Polyelectrolyte Treatment to Flame-Retard Wood

Keywords: fire-retardancy, polyelectrolyte complex, wood protection

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Biophilia is a concept that was introduced in the 1980s by Edward O. Wilson [START_REF] Wilson | Biophilia: The Human Bond with Other Species[END_REF] and defines humans' innate tendency to love nature. When applied to architecture, biophilia refers to a strategy that reconnects people with the natural environment by creating wide openings onto nature or by incorporating natural elements [START_REF] Ryan | Biophilic Design[END_REF]. Studies have proven the positive impact of this strategy on health, with reduced stress and increased productivity [START_REF] Joye | Architectural Lessons from Environmental Psychology: The Case of Biophilic Architecture[END_REF]. In this scope, wood interior finishing is a major tool. Wood is a widely available, durable, and easy to process material. However, it is also highly combustible, leading to major fire safety concerns (notably in terms of flame spread) [START_REF] White | Fire safety of wood construction[END_REF]. Regulations limit the use of wood interior finishing in critical areas such as emergency exits, corridors, and stairways in high-rise buildings [START_REF] Council | Fire Safety Design in Buildings: A Reference for Applying the National Building Code of Canada Fire Safety Requirements in Building Design[END_REF]. Improving wood's fire behaviour is therefore necessary to increase the presence of wood in buildings.

Much research has been carried out to understand and develop wood fire retardancy (FR). Four main strategies have been reported [START_REF] Lowden | Flammability behaviour of wood and a review of the methods for its reduction[END_REF]. Firstly, condensed phase action relies on catalysing wood degradation to increase char formation and reduce the volatilization of flammable gases. Secondly, gas-phase action aims to disturb gas-phase reactions by diluting radicals and/or flammable gases with non-flammable volatile, as water vapor, ammonia or carbon dioxide. The third strategy is based on a "thermic effect" that promotes endothermic reactions at the surface of the wood. The last strategy is to use coating. In this latter case, the key point is to create a protective layer that limits both access to oxygen in the pyrolysis zone and the release of flammable gases to the flame [START_REF] Lowden | Flammability behaviour of wood and a review of the methods for its reduction[END_REF]. Until now, this has been the most widely used technology to protect wood against fire [START_REF] Wang | Progress in Research on Fire Retardant-Treated Wood and Wood-Based Composites: A Chinese Perspective[END_REF]. Different types of thin and thick FR coatings have been described and are commercially available.

Among the different fire protective coatings available, intumescent coatings are the most effective when applied thick [START_REF] Canosa | Hybrid Intumescent Coatings for Wood Protection against Fire Action[END_REF][START_REF] Bartholmai | Influence of external heat flux and coating thickness on the thermal insulation properties of two different intumescent coatings using cone calorimeter and numerical analysis[END_REF]. However, they have several drawbacks that limit their market acceptance. First, obtaining a transparent intumescent coating is challenging, as high concentrations of mineral additives [START_REF] Bodzay | Influence of rheological additives on char formation and fire resistance of intumescent coatings[END_REF] are necessary for the coatings to be effective. Further, surface damage as well as the aging of painted wood can strongly affect the coating's effectiveness due to degradation of the main components [START_REF] Wang | Study on the effects of aging by accelerated weathering on the intumescent fire retardant coating for steel elements[END_REF] and a decrease of coating adhesion to the substrate [START_REF] Duquesne | Aging of the Flame-Retardant Properties of Polycarbonate and Polypropylene Protected by an Intumescent Coating[END_REF].

Layer-by-layer (LbL) coatings represent another type of coating that has been studied for many years and developed to protect various substrates [START_REF] Lazar | Flame-retardant surface treatments[END_REF][START_REF] Alongi | Current emerging techniques to impart flame retardancy to fabrics: An overview[END_REF], including wood [START_REF] Holder | A review of flame retardant nanocoatings prepared using layer-by-layer assembly of polyelectrolytes[END_REF]. It consists of alternating positive and negative layers made of polyelectrolytes or nanoparticles, among others [START_REF] Richardson | Technology-driven layer-by-layer assembly of nanofilms[END_REF], to form a thin protective coating on the surface of the material. Barriers of this type improve fire retardancy but their processing time related to the application and drying of each layer is prohibitive for industrial applications. For example, an LbL coating made of sodium phytate and nano-TiO 2 -ZnO maximum effectiveness of 10 bilayers has been studied [START_REF] Zhou | Flame-Retardant Wood Composites Based on Immobilizing with Chitosan/Sodium Phytate/Nano-TiO2-ZnO Coatings via Layer-by-Layer Self-Assembly[END_REF], but it requires 90 min of wood soaking and 1 h of oven drying for each layer. Different application approaches, such as spraying, have been developed to avoid this processing issue [START_REF] Zhao | On the flameproof treatment of ramie fabrics using a spray-assisted layer-by-layer technique[END_REF], but they are not industrially viable yet and improvements must be demonstrated.

Promising one-pot alternatives to LbL coatings are currently in development, notably polyelectrolyte complexes (PECs) in water-based solutions [START_REF] Kolibaba | Environmentally Benign Polyelectrolyte Complex That Renders Wood Flame Retardant and Mechanically Strengthened[END_REF]. PECs are versatile species consisting of a polyanion and a polycation [START_REF]Polyelectrolytes and Nanoparticles[END_REF]. Depending on the pH of the solution, they can be water-soluble, thereby enabling the deposition or can be in solid form [START_REF] Wang | The Polyelectrolyte Complex/Coacervate Continuum[END_REF]. Sodium phytate (SPA) is a high phosphorus compound derived from rice that has been widely used in nutrition [START_REF] Liu | Effect of dietary sodium phytate and microbial phytase on the lipase activity and lipid metabolism of broiler chickens[END_REF], antimicrobial [START_REF] Yang | Development of chitosan-sodium phytate nanoparticles as a potent antibacterial agent[END_REF] and fire protection [START_REF] Costes | Metallic phytates as efficient bio-based phosphorous flame retardant additives for poly(lactic acid)[END_REF] research. Phosphorus compounds are known to catalyze cellulose dehydration, accelerating the formation of a protective char that inhibits thermal and gas exchange at the wood surface. SPA is highly water soluble, making it an interesting polyelectrolyte for fire retardancy. Its deposition by LbL application and sol-gel processes has been studied on various substrates [START_REF] Li | Fully bio-based coating from chitosan and phytate for fire-safety and antibacterial cotton fabrics[END_REF][START_REF] Shang | Facile preparation of layered melamine-phytate flame retardant via supramolecular self-assembly technology[END_REF][START_REF] Li | Fire retardant and thermal degradation properties of cotton fabrics based on APTES and sodium phytate through layer-by-layer assembly[END_REF][START_REF] Zhou | Further improvement of flame retardancy of polyaniline-deposited paper composite through using phytic acid as dopant or co-dopant[END_REF][START_REF] Wang | Intumescent multilayer hybrid coating for flame retardant cotton fabrics based on layer-by-layer assembly and sol-gel process[END_REF][START_REF] Laufer | Intumescent Multilayer Nanocoating, Made with Renewable Polyelectrolytes, for Flame-Retardant Cotton[END_REF][START_REF] Sykam | Phytic acid: A bio-based flame retardant for cotton and wool fabrics[END_REF], including wood [START_REF] Zhou | Flame-Retardant Wood Composites Based on Immobilizing with Chitosan/Sodium Phytate/Nano-TiO2-ZnO Coatings via Layer-by-Layer Self-Assembly[END_REF][START_REF] Zhao | Preparation and Synergistic Effect of Chitosan/Sodium Phytate/MgO Nanoparticle Fire-Retardant Coatings on Wood Substrate through Layer-By-Layer Self-Assembly[END_REF]. Wood has also been impregnated with phytic acid to improve fire retardancy [START_REF] Zhang | One-step treated wood by using natural source phytic acid and uracil for enhanced mechanical properties and flame retardancy[END_REF][START_REF] Li | Combustion Behavior and Thermal Degradation Properties of Wood Impregnated with Intumescent Biomass Flame Retardants: Phytic Acid, Hydrolyzed Collagen, and Glycerol[END_REF][START_REF] Meng | Bio-based phytic acid and tannic acid chelate-mediated interfacial assembly of Mg(OH) 2 for simultaneously improved flame retardancy, smoke suppression and mechanical properties of PVC[END_REF]. In 2019, a PEC of polyethyleneimine and sodium hexametaphosphate was used to treat softwood samples [START_REF] Kolibaba | Environmentally Benign Polyelectrolyte Complex That Renders Wood Flame Retardant and Mechanically Strengthened[END_REF]. Samples were first soaked in a water-soluble PEC solution at a basic pH and then treated with an acid to make the PEC water-insoluble by protonation of polyethyleneimine's (PEI's) amine groups, leading to complexation between the two polyelectrolytes. A weight gain of only 6 wt.% was obtained after 70 min of treatment, leading to a 10% reduction in the peak heat release rate in cone calorimeter tests. This approach is very interesting, but again, the significant processing time is a limitation for process industrialization.

Regarding the processes used to impregnate wood, the vacuum-pressure process is one option to introduce FR solutions into wood lumens. With this technique, high weight gains of up to 100% can be obtained depending on the wood's anatomy, the solution's viscosity, and the molecular weight of the compounds in solution [START_REF] Wardrop | Morphological Factors Relating to the Penetration of Liquids into Wood[END_REF][START_REF] Larnøy | Uptake of chitosan based impregnation solutions with varying viscosities in four different European wood species[END_REF][START_REF] Dorvel | Probing the effect of polymer molecular weight on penetration into the wood cell wall using polyethylenimine (PEI) as a model compound[END_REF][START_REF] Triquet | Chemical surface densification of hardwood through lateral monomer impregnation and in situ electron beam polymerization, Part I: Density profile and surface hardness of three hardwood species[END_REF]. Impregnation using phosphorus-based compounds such as ammonium polyphosphate [START_REF] He | Effectiveness of impregnation of ammonium polyphosphate fire retardant in poplar wood using microwave heating[END_REF], guanyl urea phosphate [START_REF] Guo | Synergistic effect of treatment with disodium octaborate tetrahydrateand guanyl urea phosphate on flammability of pine wood[END_REF] or organo-phosphorus compounds [START_REF] Chen | Synthesis and evaluation of phosphortriamidates in wood for thermal and fungal decay protection[END_REF] provides an improvement of wood FR properties. However, it can be difficult and costly to impregnate timbers that have low permeability using this approach due to the need for non-continuous processes and drying time [START_REF] Park | Development of Physical Pretreatment Method for Wood Fire Retardant Impregnation[END_REF]. PEC deposition using a reduced pressure process, has already proven to be an interesting alternative to permit increased weight gain at shorter treatment times [START_REF] Soula | Yellow birch fire-protection using polyelectrolytes complexes[END_REF][START_REF] Frias | Parametric study of a yellow birch surface impregnation process[END_REF].

Building on the previously reported results, the flame retardancy provided by PECs formed from SPA and PEI is studied. The influence of the PEI:SPA ratio on the PECs' thermal stability and hygroscopicity of the PEC is explored. Yellow birch (Betula alleghaniensis Britt.) samples were impregnated with promising PECs using a reduced-pressure surface impregnation process. Their performance on wood was compared, which confirmed that characterizing PECs independent of the wood is of interest. Treated wood's properties have been studied by cone calorimetry, thermogravimetric analysis, and dynamic vapor sorption.

Materials and Methods

Branched PEI (Mw ~25,000 g•mol -1 ) and SPA (from rice), both of which are displayed in Figure 1, hydrochloric acid (HCl, 37%), sodium hydroxide (NaOH, 97%) and citric acid monohydrate (CA, reagent grade, 98%) were purchased from Sigma-Aldrich (St. Louis, MO, USA) and used as received. Yellow birch (YB) boards measuring 60 × 10 × 0.4 cm 3 were provided by Boa-Franc S.E.N.C. (Saint Georges, QC, Canada) and cut across the grain. All samples were free of defects and were sanded with a P-180 sandpaper grit and kept in a conditioning room (temperature = 20 • C, relative humidity (RH) = 40%) before use. For all tests, samples were selected from at least three different boards to consider wood variability.

Polyelectrolyte Solution Preparation

PEI and SPA solutions were prepared separately by dissolving PEI and SPA in deionized water. The pH of the PEI solutions was adjusted from 10.8 to 9 using 1 M HCl to keep the PEI in its unprotonated form (pKa = 8) [START_REF] Choosakoonkriang | Biophysical Characterization of PEI/DNA Complexes[END_REF]. The SPA solutions were kept at their natural pH of 3.5. Water-soluble PECs were prepared by mixing the PEI and SPA solutions at a 1:1 volume ratio. To form water-insoluble PECs, a 500 mM citric acid buffer was added. This buffer solution was prepared by dissolving citric acid in deionized water and adjusting the pH to 3.

Freeze Dried PEC Samples

To study the influence of the PEI:SPA ratio and acid treatment on the PECs' formation and properties, different solutions were prepared with acidification (noted as "AC") and without acidification. The details are summarized in Table 1. All solutions were immediately frozen for 24 h before being freeze-dried at 0.01 mbar with the collector temperature set at -80 • C using a Labconco FreeZone Plus 12 (Labconco, Kansas City, MO, USA) to analyze the PEC's properties.

Surface Impregnation of Wood Samples

The selected PEC formulations were then used to treat wood samples. As presented in Figure 2, two impregnation steps were used to obtain the insoluble PEC treatments. First, the wood was impregnated with soluble PEC solutions. The solutions were applied to the wood surface so that they covered the entire surface (approx. 10 mL for 10 × 10 cm 2 : 2.5 mL for 5 × 5 cm 2 ). Samples were placed in a reduced-pressure chamber, the pressure was reduced to 55 mbar for 40 s using a vacuum pump, and then the samples were left to absorb the solution for 5 min at atmospheric pressure. The excess solution was removed from the surface with a paper towel. The impregnation process (40 s reduced pressure + 5 min absorption time, removal of excess of solution) was then repeated with the citric acid solution (same volume as was used for the PEC). The treated samples were stored in a conditioning room for at least 10 days prior to any characterization to ensure the mass was stabilized.

Characterization

In this study, different characterizations were performed on the PEC alone and on the PEC-treated wood samples.

PEC Characterization

Turbidity: The PECs' stability in solution was evaluated using a Varian Cary 50 UV-Vis spectrophotometer (Agilent, Santa Clara, CA, USA). The wavelength selected for the analysis was 400 nm as neither PEI nor SPA absorb in solution at this wavelength [START_REF] Ouni | Spectrometric study of crystal violet in presence of polyacrylic acid and polyethylenimine and its removal by polyelectrolyte enhanced ultrafiltration[END_REF][START_REF] Marolt | Analytical Methods for Determination of Phytic Acid and Other Inositol Phosphates: A Review[END_REF]. Thus, any change in absorbance results only from the complexation of the polyelectrolyte. Solutions were prepared directly in the cell by first depositing 1 mL SPA solution and 1 mL PEI solution. Absorbance was first measured and noted as "_before". The timer was started when adding 1 mL of the citric acid solution and absorbance was measured at 0 min, 5 min, 10 min, 30 min, and 60 min, which were noted as "_0","_5","_10","_30" and "_60", respectively. Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR): Fourier transform infrared spectroscopy (FTIR) was used to characterize the PECs before and after acid treatment. FTIR spectra were recorded on the freeze-dried PECs with an INVENIO R spectrometer (Bruker Optics Inc., Billerica, MA, USA) in the range of 4000-400 cm -1 in ATR mode with 64 scans and a resolution of 4 cm -1 .

Thermogravimetric analysis (TGA): The thermal stability of the freeze-dried PEC samples was studied using a thermogravimetric analyzer from Mettler Toledo (model TGA 851e, Greifense, Switzerland). Samples weighing 5-10 mg were heated at 10 • C•min -1 from 25 • C to 800 • C under a nitrogen flow of 50 mL•s -1 .

Wood Sample Characterization

Weight gain (WG): The weight gain of the treated wood was calculated according to Equation (1) with m i as the mass before and m f as the mass after impregnation.

WG (wt. -%) = 100 × m f -m i m i (1)
Densitometry: The density of reference and treated wood samples was measured using an X-ray densitometer from QMS, Model QDP-01X, (Quintex Measurement Systems Inc, Knoxville, TN, USA). Samples measuring 5 × 5 × 0.4 cm were used. The samples' dimensions and weight were measured before scanning. Density was measured at an interval of 0.04 mm through the wood thickness.

Micro-X-ray fluorescence (micro-fluo-X): The PECs' impregnation depth was evaluated by analyzing the phosphorus presence from top to bottom of the samples using an M4 TORNADO micro-fluorescence-X spectrometer (Bruker Nano GmbH, Berlin, Germany). The incident X-ray beam voltage was 15 kV. Mapping was built with a step of 20 µm and an exposure time of 10 ms. Five wood samples were prepared by microtome (Leica model HistoCore AUTOCUT, Buffalo Grove, IL, USA) cutting to ensure a smooth defect-free surface. Analysis was conducted on 0.4 × 0.4 × 0.4 cm samples retrieved from the centre of the densitometry samples.

Inductively coupled plasma mass spectrometry (ICP-MS): The remainder wood samples from the densitometry experiments were ground using a 200 ZM grinder with a 1 mm sieve (Retsch GmbH, Haan, Germany). ICP-MS was conducted by Bureau Veritas (Québec City, QC, Canada) using an argon plasma. The dry wood powder was digested by hot nitric acid.

Dynamic vapor sorption (DVS): Sorption data were collected on a DVS Adventure water vapour sorption analyzer (Surface Measurement Systems, Allentown, PA, USA) equipped with a microbalance of 0.1 µg resolution. A 4 × 4 × 4 mm sample retrieved from the centre of the densitometry sample was placed in a stainless-steel mesh basket suspended from the balance inside a separate chamber with controlled temperature and RH. The sample's mass was continuously recorded. Samples were dried for at least 24 h at 103 • C before analysis. This first drying was followed by 2 h at 0% RH at 25 • C. Sample was then exposed to a series of RH steps from 0% to 90% RH, followed by the same series in reverse order. RH was changed when the sample's mass variation was <0.002 wt.% for 5 min or after 6 h.

Cone calorimetry: The fire reaction of materials was characterized using a dual cone calorimeter (Fire Testing Technology, East Grinstead, West Sussex, England) following the ISO5660 standard [START_REF] Iso | Taux de Dégagement de Fumée et Taux de Perte de Masse; Partie 1: Débit calorifique (méthode au calorimètre à cône) et taux de dégagement de fumée (mesurage dynamique)[END_REF]. The following characteristics parameters were obtained during testing: time to ignition (TTI), heat release rate (HRR), peak of heat release rate (pHRR), total heat release (THR), and mass loss rate (MLR) during the test. Each of the 10 × 10 × 0.4 cm horizontal wood samples previously stored in conditioning rooms (T = 20 • C and RH = 40%) were placed 2.5 cm below a conic heater and isolated at their back face by rock wool. The heating of the cone part was monitored to impose a specific irradiance of 50 kW m -2 at the top of the sample. Ignition was caused by an ignition source above the sample. The HRR was calculated from the quantity of oxygen released during the combustion and detected via a calibrated gas analyzer.

Optical microscopy: Cone calorimeter residues were observed using a VHX-7000 digital microscope (Keyence Co. Ltd., Osaka, Japan). Full ring lighting was used to enable dark field observation, which is preferred for heterogenous samples.

Results

PEC Characterization

3.1.1. Fourier Transform Infrared Spectroscopy (FTIR) PEI, SPA and CA were characterized using FTIR and the spectra are displayed in Figure 3. For PEI, the band at 1595 cm -1 corresponds to the symmetric NH 2 stretching vibration and peaks characteristic of CH 2 vibration are also visible (at 2931, 2881, 2814, 1457 and 1346 cm -1 ) [START_REF] Qi | High efficiency nanocomposite sorbents for CO2 capture based on amine-functionalized mesoporous capsules[END_REF]. SPA is characterized by the two bands of PO 4 3-at 1196 and 504 cm -1 and various C-O-P vibrations at 1048, 989, 911, 850 and 792 cm -1 [START_REF] He | Phytate extraction from coproducts of the dry-grind corn ethanol process[END_REF]. Finally, CA's major characteristic IR absorption bands are at 3492, 3448 and 3292 cm -1 for O-H stretching and 1745 and 1694 cm -1 for C=O stretching in the COOH groups [START_REF] Lin | Theophylline-citric acid co-crystals easily induced by DSC-FTIR microspectroscopy or different storage conditions[END_REF]. The spectra of the acidified PECs of different ratios are compared in Figure 5. It is interesting to note that the peak shift around 1580 cm -1 is conditioned by the PEI:SPA ratio, as described in Table 2. The shift is greater when a higher proportion of SPA is used, which suggests that the polyelectrolytes' interactions are stronger and the PECs are probably more likely to be stable in solution. In addition, a shift of the 504 cm -1 peak and the disappearance of the 1196 cm -1 one, corresponding to PO 4 3-, are also observed, which confirm greater interaction between PO 4 3-and protonated NH 2 . Finally, as is described in the literature, a band appears around 1390 cm -1 , resulting from the interaction between SPA and PEI [START_REF] Yang | Chitosan-Sodium Phytate Films with a Strong Water Barrier and Antimicrobial Properties Produced via One-Step-Consecutive-Stripping and Layer-by-Layer-Casting Technologies[END_REF].

PEI:SPA Ratio

Peak Position ≈ 1580 cm -1 Peak Position ≈ 500 cm -1

3:1 1595 cm -1 509 cm -1 2:1 1593 cm -1 509 cm -1 1:1 1580 cm -1 513 cm -1 1:2 1576 cm -1 520 cm -1 1:3 1572 cm -1 544 cm -1

Turbidity

Complex formation as a function of pH as well as stability in water was studied by evaluating the solutions' turbidity over time. Turbidity was evaluated by UV-visible absorbance, and the results are presented in Figure 6. PECs can be either water-soluble or phase-separated (including turbid, coacervated or solid dispersed) depending on their pH, stoichiometry and ionic strength [START_REF] Meka | A comprehensive review on polyelectrolyte complexes[END_REF]. For PEI:SPA_2:1, PEI:SPA_1:1, PEI:SPA_1:2, and PEI:SPA_1:3, solid formation is observed immediately after adding citric acid (t = 0 min). This solid formation is associated with an absorbance increase (PEI:SPA_2:1 = 1, PEI:SPA_1:1 = 3, PEI:SPA_1:2 = 3, PEI:SPA_1:3 = 3). After 10 min, PEI:SPA_2:1 becomes soluble (PEI:SPA_2:1_10 = 0.2), indicating weak interactions between PEI and SPA [START_REF] Sarika | Cationized gelatin/gum arabic polyelectrolyte complex: Study of electrostatic interactions[END_REF]. For PEI:SPA_1:1, PEI:SPA_1:2, and PEI:SPA_1:3, absorbance also decreases over time (PEI:SPA_1:1_60, PEI:SPA_1:2, PEI:SPA_1:3 = 2). Their absorbance is still higher than the other ratios' though indicating stronger interactions between polyelectrolytes. Also, pictures in Figure 6 indicate PEC coacervate formed, which can be described as a film more than individual particles [START_REF] Haile | Polyelectrolyte Coacervates Deposited as High Gas Barrier Thin Films[END_REF].

Thermal Stability

The thermal stability of PECs with different PEI:SPA ratios as well as PEI and SPA alone was investigated, and the results are presented in Figure 7, with the thermogravimetric analysis (TG) and the derivative thermogravimetric analysis (DTG), and Table 3. PEI thermally decomposes in one step with a maximum decomposition rate at 290 • C and no residue at 800 • C. SPA is more thermally stable, with 76% residual mass at 800 • C. Five percent decomposition happens early (138 • C) for SPA, probably due its strong water absorption properties [START_REF]Effectiveness and mechanism of sodium phytate as a green inhibitor for the dust deflagration of lysine sulfate[END_REF]. SPA decomposes in two steps around 260 • C and 320 • C. When studying PECs with different PEI:SPA ratios, it is worth noting that residual mass increases with the percentage of SPA in the complex. T 5% seems to have no clear tendency, and variation in the value may be due to residual water absorption. Early PEC decomposition might be advantageous for wood fire retardancy, as the catalysis of cellulose degradation is required to accelerate char formation. The half decomposition temperature increases with the percentage of SPA in the ratio. The remainder of the study focuses on PEI:SPA_1:2 and PEI:SPA_1:3, as they are more thermally stable and form water insoluble PECs.

Wood Samples Characterization

Weight Gain and Depth of Impregnation

Analyses were conducted to investigate the weight gain, depth of impregnation (densitometry and micro-fluo-X) and the final phosphorus content (ICP-MS) of treated wood samples. The results are summarized in Figure 8.

Weight gain is not significantly different for wood treated with PEI:SPA_1:2 versus PEI:SPA_1:3 and is around 3.5% for all samples (10 × 10 cm and 5 × 5 cm). Reducedpressure surface impregnation occurs mostly by the small intervascular pits in the birch wood surface [START_REF] Hoadley | Identifying Wood: Accurate Results with Simple Tools[END_REF]. Weight gain is low (6% reported for whitewood stud) compared to that of similar treatment reported in the literature [START_REF] Kolibaba | Environmentally Benign Polyelectrolyte Complex That Renders Wood Flame Retardant and Mechanically Strengthened[END_REF]. Weight gain variability in wood is strongly dependent on the wood species and is related to density variation, the proportion of sapwood/heartwood, and the presence of rings, among other factors [START_REF] Ding | Relationship between wood porosity, wood density and methyl methacrylate impregnation rate[END_REF][START_REF] Siau | Processes in Wood[END_REF][START_REF] Hansmann | Permeability of wood-A review[END_REF][START_REF] Tondi | Impregnation of Scots pine and beech with tannin solutions: Effect of viscosity and wood anatomy in wood infiltration[END_REF]. Also, it must be noted that surface modification is strongly affected by surface quality and great care must be taken while sanding and storing samples to avoid surface oxidation [START_REF] Petrič | Surface Modification of Wood[END_REF][START_REF] Aydin | Activation of wood surfaces for glue bonds by mechanical pre-treatment and its effects on some properties of veneer surfaces and plywood panels[END_REF]. This aspect was carefully considered in this study. The ICP-MS experiments reveal that phosphorus content is proportional to weight gain, which was expected, and that the PEI:SPA ratio has no impact on phosphorus content.

The depth of impregnation was investigated using two techniques (densitometry and micro-fluo-X); they both have drawbacks that can alter results. Cupping is a known behaviour of surface densified wood that can cause a shift of the density gradient measured by densitometer [START_REF] Belt | Cupping behaviour of surface densified Scots pine wood: The effect of process parameters and correlation with density profile characteristics[END_REF], whereas micro-fluo-X provides a mapping of phosphorus in the wood depth. On the other hand, the quality of the microtomed surface is limiting in this latter measure as some contamination can occur. Despite this, these techniques provided consistent results, which provide a good approximation of impregnation depth. When plotting impregnation depth as a function of weight gain, it is clear that they are linked (the higher the weight gain, the higher the impregnation depth) and the PEI:SPA ratio has no influence on the impregnation depth.

Cone Calorimetry

YB's fire retardancy performance with different PEI:SPA ratios was evaluated by cone calorimeter and the results are presented in Figure 9 and Table 4. For untreated wood the first peak observed, just after ignition, characterizes primary pyrolysis that leads to the formation of a natural protective char. The pyrolysis process is thus slowed by the insulating char, leading to a plateau in the HRR curve. This protection ensures the temperature inside the wood is lower than at the surface of the char, which causes strong internal thermal stresses [START_REF] Baroudi | A thermomechanical explanation for the topology of crack patterns observed on the surface of charred wood and particle fibreboard[END_REF]. When these stresses are too strong, char cracking occurs and facilitates the release of combustible volatile species leading to a second peak of higher intensity. Treatment with either of the PECs changes the aspect of the curve.

With PEI:SPA_1:2, the shoulder is considerably reduced, (Reference YB: 200 ± 10 kW•m -2 , YB treated with PEI:SPA_1: 2: 130 ± 50 kW•m -2 ), which could be interpreted as more efficient char formation. The plateau is less defined than for the reference, however, which could signify the formation of a less thermally isolating char, corresponding to a thick intermediate non-charring material [START_REF] Schartel | Development of fire-retarded materials-Interpretation of cone calorimeter data[END_REF]. As for the YB treated with PEI:SPA_1:3, the shoulder is once again reduced. Contrary to with PEI:SPA_1:2, a plateau is visible and is clearly characteristic of a thermally isolating char inducing a reduction of the second HRR peak. Based on these results, a greater impregnation depth should help with the formation a thermally isolating char. PEI:SPA_1:3 has a lower TTI compared to the reference and the other treatment. Catalysis of the cellulose degradation by the phosphorus PEC is suspected. THR is not significantly different after treatment, whereas residue increases after treatment. When looking more in depth, it is interesting to note that YB treated with PEI:SPA_1:2 exhibits great p1HRR and p2HRR variability. It is supposed that HRR is linked to weight gain and great attention should be paid to sample preparation to control weight gain variation and ensure fire retardancy performance. The cone calorimeter residues were observed using an optical microscope to better understand the charring phenomenon and images are displayed in Figure 10. The reference sample shows a carbonaceous char with the typical orthotropic pattern [START_REF] Baroudi | A thermomechanical explanation for the topology of crack patterns observed on the surface of charred wood and particle fibreboard[END_REF]. The fibrous structure of the wood is visible in the background, proving the natural protection the char provides. The treated samples display the same behaviour, as a thick char is visible above the degraded fibrous structure. However, in the YB treated with PEI:SPA_1:2 image, a glassy bubbly structure is clearly visible. The YB treated with PEI: SPA_1:3 also displays micro-bubbles, but the area observed also presents a similar pattern to the one observed in the reference sample. Similar phenomena were observed with phosphorus-based LbL systems used on cotton and have been attributed to micro-intumescence, a system acting in a condensed phase [START_REF] Jimenez | Microintumescent mechanism of flame-retardant water-based chitosan-ammonium polyphosphate multilayer nanocoating on cotton fabric[END_REF][START_REF] Carosio | Tunable thermal and flame response of phosphonated oligoallylamines layer by layer assemblies on cotton[END_REF]. Classical approaches to wood FR have been widely studied, and pHRR reductions of more than 40% are now widespread. Wood has previously been vacuum pressure impregnated with clay [START_REF] Fu | Nanostructured Wood Hybrids for Fire-Retardancy Prepared by Clay Impregnation into the Cell Wall[END_REF], silica-based compounds [START_REF] Liu | Flame Retardant Properties and Thermal Decomposition Kinetics of Wood Treated with Boric Acid Modified Silica Sol[END_REF], hydroxide-based compounds [START_REF] Lv | Flame-retardant and smoke-suppressing wood obtained by the in situ growth of a hydrotalcite-like compound on the inner surfaces of vessels[END_REF], and phosphorus-based compounds [START_REF] Lu | Flame retardancy, thermal stability, and hygroscopicity of wood materials modified with melamine and amino trimethylene phosphonic acid[END_REF]. All of those treatments involve a reduced-pressure step to remove air from the wood and a high-pressure step where fire retardant substances are forced to impregnate the wood. It can also be followed by a curing step when fire retardant substances require a polymerization. These techniques result in weight gain up to 50 wt.% [START_REF] Li | Preparation and characterization of sodium silicate impregnated Chinese fir wood with high strength, water resistance, flame retardant and smoke suppression[END_REF]. The reduced-pressure surface impregnation process described in this article does not permit such weight gain or, consequently, the same level of performance. However, this approach has to be considered as performance is satisfactory for material with only one side exposed to a fire and is more industrially viable. Comparison with LbL systems is difficult as, to the best of authors' knowledge, no cone calorimeter measurements have been taken for them [START_REF] Zhou | Flame-Retardant Wood Composites Based on Immobilizing with Chitosan/Sodium Phytate/Nano-TiO2-ZnO Coatings via Layer-by-Layer Self-Assembly[END_REF][START_REF] Zhao | Preparation and Synergistic Effect of Chitosan/Sodium Phytate/MgO Nanoparticle Fire-Retardant Coatings on Wood Substrate through Layer-By-Layer Self-Assembly[END_REF][START_REF] Rehman | Excellent Fire Retardant Properties of CNF/VMT Based LBL Coatings Deposited on Polypropylene and Wood-Ply[END_REF]. PEC deposition with PEI and sodium hexametaphosphate resulted in a 10% pHRR reduction following a one hour of treatment.

Thermogravimetric Analysis

A thermogravimetric analysis of the reference YB and YB treated with the two different PECs was conducted to understand the PECs' contribution to wood fire-retardancy, and the results are presented in Figure 11 and Table 5. Degradation of the reference YB is divided into three steps: drying, charring, and final decomposition [START_REF] Grønli | Thermogravimetric Analysis and Devolatilization Kinetics of Wood[END_REF]. First, weight loss occurs at around 100 • C and can be attributed to water removal. The charring stage, from 250 • C to 400 • C, involves decomposition of hemicellulose and cellulose into levoglucosan, the formation of char and the release of volatile species such as H 2 O, CO 2 , HCOOH and CH 3 COOH [START_REF] Beall | Thermal Degradation of Wood Components: A Review of the Literature[END_REF]. No volatile species are released anymore above 500 • C, and the residual mass corresponds to the thermally stable char [START_REF] Beall | Thermal Degradation of Wood Components: A Review of the Literature[END_REF]. Samples treated with PEI:SPA_1:2 and PEI:SPA_ 1:3 behave differently than the reference wood. According to DTG, the maximum degradation temperature is shifted down to a lower temperature with PEC treatment (Ref: 361 • C, PEI:SPA_1:2: 326 • C and PEI:SPA_1:3: 326 • C). Phosphorus compounds are widely known to catalyze cellulose degradation because of cellulose dehydration by phosphoric and polyphosphoric acids [START_REF] Kishore | Effect of diammonium phosphate on the flammability of wood and woodpolymethylmethacrylate composites[END_REF][START_REF] Stevens | The structure-activity relationship of fire retardant phosphorus compounds in wood[END_REF], which explains the shift mentioned. Treated YB with PEI:SPA_1:3 exhibits less desorption at 100 • C, which can be interpreted as a reduction in wood hygroscopicity after PEC treatment. These results show that PECs increase the wood's thermal stability at high temperatures, as was previously assumed when discussing the cone calorimeter results. The hygroscopicity of flame retardant treated wood is a major concern, as it could induce severe dimensional stability and decay issues as well as important performance losses over a product's service life [START_REF] Lu | Flame retardancy, thermal stability, and hygroscopicity of wood materials modified with melamine and amino trimethylene phosphonic acid[END_REF].

Isotherms for YB before and after treatment with the two PECs are presented in Figure 12. The reference YB presents the typical sigmoidal-shaped isotherm with hysteresis [START_REF] Hill | The water vapor sorption behavior of natural fibers[END_REF]. Water is first adsorbed as a monolayer in the internal surface of the wood's cell walls. Then, from 15% RH, an adsorption polylayer forms in cell wall microcapillaries. Finally, above 70%, RH capillary condensation is predominant [START_REF] Siau | Processes in Wood[END_REF]. Both treated samples exhibit the same behaviour as the reference YB with a moisture equilibrium content of 1% at 90% RH. Phosphorus-based fire-retardant substances are usually known to increase wood hygroscopicity [START_REF] Zhou | Effect of hygroscopicity of fire retardant on hygroscopicity of fire retardant bamboo chips[END_REF]. Treatments that result in low weight gain limit propensity of high hygroscopicity and ensure a longer service life for wood products.

Conclusions

Polyelectrolyte complexes consisting of polyethyleneimine and sodium phytate are investigated to develop fire-retardant wood. In the first part, analyses were carried out on different polyelectrolytes alone (not deposited on wood). Varying the ratio of the polyelectrolytes proved to have a strong impact on insoluble complex formation, thermal stability and hygroscopicity. The two most promising PECs (PEI:SPA_1:2 and PEI:SPA_1:3) were impregnated on the surface of yellow birch samples under reduced pressure. Weight gain and impregnation depth seem to be independent of the PEI:SPA ratio. Fire retardancy was evaluated using cone calorimetry, and PEI: SPA_1:3 displayed the best results with a reduction of the two pHRR with little weight gain. Residue observations suggested a micro-intumescence mechanism, which combines condensed and gaseous phase action. Finally, the treatments' impact on hygroscopicity was studied, and surface impregnation with PEC seems to have no negative impact on the wood.

Overall, the preliminary study of PECs makes it possible to accelerate fire-retardant material development by limiting the amount of fire testing needed. The approach is particularly interesting for variable materials, which exhibit high intrinsic standard deviation. For instance, in wood, fire behaviour can be strongly impacted by the sample's properties, such as cellulose content [START_REF] Grønli | Thermogravimetric Analysis and Devolatilization Kinetics of Wood[END_REF], crystallinity [START_REF] Poletto | Thermal decomposition of wood: Influence of wood components and cellulose crystallite size[END_REF], density and moisture content [START_REF] Tran | Burning rate of solid wood measured in a heat release rate calorimeter[END_REF]. Other important feature such as hygroscopicity were also pre-investigated, and the approach was as relevant for them as it is for fire-retardancy.

Figure 1 .

 1 Figure 1. Branched polyethyleneimine (a) and sodium phytate (b).

Figure 2 .

 2 Figure 2. Schematic representation of PEC deposition method.

Figure 3 .

 3 Figure 3. Spectra of sodium phytate (SPA), branched polyethyleneimine (PEI) andcitric acid (CA).

Figure 4

 4 Figure4compares the PEC made of PEI and SPA at a 1:1 ratio before and after acidification with CA. Before acidification, all characteristic peaks are shifted compared to the reference products. It is assumed that this shift resulted from the pH change from the original solution (PEI = 9, SPA = 3.4, PEI:SPA_1:1 = 9) and from the weak interaction between the two polyelectrolytes[START_REF] Simsek-Ege | Polyelectrolyte complex formation between alginate and chitosan as a function of pH[END_REF]. Acidification (PEI:SPA_1:1_AC = pH 5) led to further peak shifting and the appearance of new peaks around 1390 cm -1 . Comparison of the preand post-acidification spectra confirms the change in interaction depending on the pH.

4 Figure 4 .

 44 FTIR spectra of PEC_1:1 pre-and post-acidification.

Figure 5 .

 5 Figure 5. FTIR spectra of solutions of different PEI:SPA ratios after acidification.

5 6 7 Figure 6 .

 76 Figure 6. Absorbance over time for PECs after acid addition.

2 6 7 Figure 7 .

 277 TG (left) and DTG (right) curves for PEI:SPA at different ratios under N 2 .

8 9Figure 8 .

 88 Figure 8. Summary of weight gain, phosphorus content, and depth of impregnation for treated samples.

Figure 9 .

 9 Figure 9. Heat release rate curves of yellow birch depending on the PEI:SPA ratio.

3 9 10 Figure 10 .

 31010 Figure 10. Observations of cone calorimeter residues: Reference (left), YB treated PEI: SPA 1:2 (center), and YB treated PEI: SPA 1:3 (right).

Figure 11 .

 11 Figure 11. TG (left) and DTG (right) curves for reference YB and treated YB with different PEC.

12

 12

Figure 12 .

 12 Figure 12. Isotherms for reference yellow birch and treated yellow birch with two different PEC ratios.

Table 1 .

 1 Summary of tested polyelectrolyte complex solutions.

Table 2 .

 2 Peak shifting depending on the PEI:SPA ratio.

Table 3 .

 3 TG and DTG curve results for different PEI:SPA ratios under N 2 .

	PEI	187	292	290	0
	3:1_AC	184	339	330	22.4
	2:1_AC	183	357	341	31.3
	1:1_AC	193	420	329	41.4
	1:2_AC	178	584	321	46
	1:3_AC	169	-	315	50.1
	SPA	138	-	317	76.7

T 5% ( • C) T 50% ( • C) T max.decomp ( • C) Residue at 800 • C (%)

Table 4 .

 4 Cone calorimeter results of yellow birch (virgin and treated with PEC at two ratio).

	Reference

YB YB Treated PEI:SPA _ 1:2 YB Treated PEI:SPA _ 1:3

	Number of repetitions	12	12	7
	WG (wt.%)		2.7 ± 0.9	2.0 ± 0.3
	TTI (s)	31 ± 2	32 ± 6	27 ± 3
	Shoulder HRR (kW•m -2 )	200 ± 10	130 ± 50	140 ± 10
	p2HRR (kW•m -2 )	490 ± 30	440 ± 60	380 ± 20
	THR (MJ•m -2 )	44 ± 3	38 ± 4	41 ± 3
	Residue (wt.%)	7 ± 2	12 ± 2	12 ± 4

Table 5 .

 5 Results from TG and DTG curves for reference YB and YB treated with different PECs

		T 5% ( • C)	T 50% ( • C)	T max.decomp ( • C) Residue at 800 • C (%)
	Reference YB	79	353	361	11.9
	YB treated PEI:SPA_1:2	80	337	326	22.7
	YB treated PEI:SPA_1:3	91	339	326	24.8
	3.2.4. Dynamic Vapour Sorption

Acknowledgments: This work is part of the research program of Natural Sciences and Engineering Research Council of Canada (NSERC) Canlak Industrial Research Chair in Finishes for Interior wood products (CRIF). The authors are grateful to the NSERC-Canlak Industrial Research Chair in Finishes for Interior wood products (CRIF) Industrial partners for their help and support. The authors would also like to acknowledge collaborators who provided technical support: Yves Bédard, Luc Germain and Daniel Bourgault from the Renewable Materials Research Center (CRMR-Université Laval).

Funding: This work is part of the research program of Natural Sciences and Engineering Research Council of Canada (NSERC) Canlak Industrial Research Chair in Finishes for Interior wood products (CRIF) through programs CRD (RDCPJ 500157-16) and PCI (PCISA 514917-16). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable.

Data Availability Statement:

The data presented in this study are available on request from the corresponding author.

Author Contributions: Conceptualization, M.S., F.S., S.D. and V.L.; methodology, M.S., F.S., S.D., and V.L.; software, M.S.; validation, M.S.; formal analysis, M.S.; investigation, M.S.; writing-original draft preparation, M.S.; writing-review and editing, M.S., F.S., S.D., and V.L.; supervision, F.S., S.D. and V.L.; project administration, F.S., S.D and V.L.; funding acquisition, V.L. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:

The authors declare no conflicts of interest.