Wuhib Tamrat

Zewde

Jérôme Rose

Olivier Grauby

Emmanuel Doelsch

Clément Levard

Perrine Chaurand

Isabelle Basile-Doelsch

Composition and molecular scale structure of nanophases formed by precipitation of biotite weathering products

Because of their large surface area and reactivity, nanometric-size soil mineral phases have a high potential for soil organic matter stabilization, contaminant sorption or soil aggregation. In the literature, Fe and Al phases have been the main targets of batchsynthesized nanomineral studies while nano-aluminosilicates (Al and Si phases) have been mainly studied in Andic soils. In the present work, we synthesized secondary nanophases of Fe, Al and Si. To simulate a system as close as possible to soil conditions, we conducted laboratory simulations of the processes of (1) biotite alteration in acidic conditions producing a Al Si Fe Mg K leachate solution and (2) the following neoformation of secondary nanophases by titrating the leachate solution to pH 4.2, 5 and 7. The morphology of the nanophases, their size, crystallinity and chemistry were characterized by TEM-EDX on single particles and their local atomic structure by EXAFS (Extended X-ray Absorption Fine Structure) at the Fe absorption K-edge. The main nanophases formed were amorphous particles 10 to 60 nm in size whose composition (dominated by Fe and Si) was strongly controlled by the pH conditions at the end of the titration. At pH 4.2 and pH 7, the structure of the nanophases was dominated by the polymerization of Fe, which was hindered by Al, Si, Mg and K. Conversely, at pH 5, the polymerization of Fe was counteracted by precipitation of high amounts of Si. The synthetized nanophases were estimated to be rather analogous to nanophases formed in natural biotite-bearing soils. Because of their small size and potential high surface

reactivity, the adsorption capacities of these nanophases with respect to the OM should be revisited in the framework of soil C storage.

Introduction

Because of their large surface area, large percentage of surface atoms with unbalanced charge and large number of surface functional groups per unit of mass, nanometric-size mineral phases have a high potential for soil organic matter stabilization [START_REF] Levard | Structure and distribution of allophanes, imogolite and proto-imogolite in volcanic soils[END_REF][START_REF] Qafoku | Terrestrial Nanoparticles and Their Controls on Soil-/Geo-Processes and Reactions[END_REF], contaminant adsorption, [START_REF] Levard | Role of natural nanoparticles on the speciation of Ni in andosols of la Reunion[END_REF] or soil aggregation [START_REF] Asano | Evidence of aggregate hierarchy at micro-to submicron scales in an allophanic Andisol[END_REF] . These natural nanoparticles (NPs) may occur either as « mineral NPs » (defined as minerals that can also exist in larger sizes) or as « nanominerals » (defined as minerals that only exist at the nanometric scale) [START_REF] Hochella | Nanominerals, Mineral Nanoparticles, and Earth Systems[END_REF].

In surface environments, Fe and Al systems have been the main subjects of previous studies due to soil observations [START_REF] Kaiser | The role of DOM sorption to mineral surfaces in the preservation of organic matter in soils[END_REF] as well as due to the poor solubility of Fe and Al species in most soil pH and redox conditions (pH above ≈2 for Fe in oxidative conditions and pH above ≈5 for Al). However nanominerals other than Al and Fe oxy-hydroxides are known to form in surface systems, one of the best known examples being the Al and Si imogolite/allophane phases (Basile- [START_REF] Basile-Doelsch | Mineral control of carbon pools in a volcanic soil horizon[END_REF][START_REF] Basile-Doelsch | Mineralogical control of organic carbon dynamics in a volcanic ash soil on La Réunion[END_REF][START_REF] Basile-Doelsch | Are Interactions between Organic Compounds and Nanoscale Weathering Minerals the Key Drivers of Carbon Storage in Soils?[END_REF][START_REF] De Junet | Characterisation of organic matter from organo-mineral complexes in an Andosol from Reunion Island[END_REF][START_REF] Torn | Mineral control of soil organic carbon storage and turnover[END_REF].

Released by the continuous alteration of the primary minerals, Al, Si, Fe, etc. can form nanominerals at the surface of the primary mineral or at a distance from the initial altered surfaces. Direct formation of nanophases by the weathering of rock material has been described in oxic waters [START_REF] Faimon | Formation of Colloidal Silica and Alumina During Experimental Granodiorite Weathering[END_REF][START_REF] Zänker | Formation of iron-containing colloids by the weatheringof phyllite[END_REF]. In presence of organic matter, these newly formed nanophases can complex the organic compounds and stabilize them for extended periods of time. The conceptual model proposed by [START_REF] Basile-Doelsch | Are Interactions between Organic Compounds and Nanoscale Weathering Minerals the Key Drivers of Carbon Storage in Soils?[END_REF] represents this mechanism. To validate the model, it is necessary to show that (1) the products of the alteration of primary minerals are likely to form nanophases and (2) these nanophases complex the OM. In this paper, we focus on step (1). We characterized the chemical nature and the structure of the nanophases formed from the elements resulting from the alteration of a primary mineral in the absence of OM. For this purpose, we considered biotite as a common soil primary mineral able to provide a complex combination of elements (Fe, Al, Si, Mg and K) via weathering.

The formation of nanophases from a solution requires a polymerizing step by hydrolysis of metallic cations like Fe or Al [START_REF] Doelsch | Speciation and Crystal Chemistry of Iron(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 1. An Fe K-Edge EXAFS Study[END_REF][START_REF] Manceau | Local structure of ferrihydrite and feroxyhite by EXAFS spectroscopy[END_REF][START_REF] Rose | Structure and Mechanisms of Formation of FeOOH(NO3) Oligomers in the Early Stages of Hydrolysis[END_REF]. In oxic conditions and at pH higher than 3-4, Fe 3+ for instance, is known to be insoluble and reactive. [START_REF] Buffle | Iron hydrolysis and solubility revisited: observations and comments on iron hydrolysis characterizations[END_REF][START_REF] Dousma | Hydrolysis-Precipitation Studies of Iron Solutions .1. Model for Hydrolysis and Precipitation from Fe(iii) Nitrate Solutions[END_REF][START_REF] Rose | Kinetics of Hydrolysis and Precipitation of Ferric Iron in Seawater[END_REF]. Polymerization steps start from elementary monomeric building blocks such as [Fe(H2O)6] 3+ octahedron and are accomplished via intramolecular condensation that initially involves deprotonation [START_REF] Combes | Formation of ferric oxides from aqueous solutions: A polyhedral approach by X-ray absorption spectroscopy: I. Hydrolysis and formation of ferric gels[END_REF][START_REF] Rose | Structure and Mechanisms of Formation of FeOOH(NO3) Oligomers in the Early Stages of Hydrolysis[END_REF]. Formation of small clusters via edge and double corner sharing between Fe octahedra is all included in the initial stage of "nucleation" which is followed by later stages of growth and aggregation [START_REF] Rose | Structure and Mechanisms of Formation of FeOOH(NO3) Oligomers in the Early Stages of Hydrolysis[END_REF][START_REF] Wells | Structural Inorganic Chemistry[END_REF]. Polymerization routes have also been found for Al, with the formation of a transient Al13 polymer (Bottero et al., 1980). It has been shown that Si can strongly impair the polymerization stages in both elements [START_REF] Doelsch | Speciation and Crystal Chemistry of Iron(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 1. An Fe K-Edge EXAFS Study[END_REF][START_REF] Lartiges | Flocculation of colloidal silica with hydrolyzed aluminum: An Al-27 solid state NMR investigation[END_REF].

Our experimental protocol combined a weathering step that provided a complex solution of Fe, Si, Al, K and Mg cations, followed by the polymerization of nanophases in a range of pH corresponding to soil conditions (pH 4.2, 5 and 7). The atomic structures of the nanophases were determined by Fe k-edge EXAFS (Extended X-ray Absorption Fine Structure) spectroscopy and size, shape, crystallinity and chemical composition by TEM-EDX. Three main questions are raised in this paper: (1) Does the proposed experimental protocol make it possible to obtain nanophases? (2) Are the polymerized nanophases homogeneous or of variable chemical composition? (3) Are the nanophases obtained representative of phases that can form in soils?

Materials and Methods

Experimental protocol

The biotite studied comes from Bancroft, Ontario Canada (Ward Science) [START_REF] Turpault | The dissolution of biotite single crystals in dilute HNO3 at 24°C: Evidence of an anisotropic corrosion process of micas in acidic solutions[END_REF]):

Eq. ( 1) Biotite was mechanically ground (< 50 μm) in a zirconium oxide 'ball mill' setup, washed, sieved with ultra pure water and dried at 40⁰C. Dissolution step: 33 g of < 50 μm biotite particles were placed in 1L of pH=2 HNO3 solution (solid:liquid ratio of 1:30). After 29 days, the dissolved species were separated from non-weathered biotite particles using Tangential Filtration flow (TFF) (Spectrum Labs) at a cut-off size of 10 kD (pore size of ~2 nm). The filtered solution is hereafter referred to as 'leachate solution'. Concentrations of dissolved species in the leachate solution were monitored with an inductively coupled plasma atomic emission spectrophotometer (ICP-AES, Horiba Jobin-Yvon "Ultima C", Longjumeau, France). The measurement uncertainty was < 10%. The preliminary experimental setup that contributed to the design of the above dissolution protocol is detailed in supplementary information (Figure A1 and Table A1).

Polymerization step: Nanophases were precipitated by increasing the pH of the leachate solution. The initial pH (2) was raised by adding 0.2N NaOH (Sigma Aldrich) at a constant rate of 70 μL/min (785 DMP Titrino). Pyrex beakers and stir bars were used.

Three final pH values were targeted: 4.2, 5 and 7. To determine the target pH values, a preliminary titration curve of the leachate solution was performed (Figure A2). The slope of this curve changed at pH 4.2 and 5. The variations in slope pointed to changes in the nature of the hydrolyzing system, inferring correlative changes in the nature and/or structure of the polymerized phases. At pH 7, the addition of NaOH no longer had an effect on polymerisation. The durations of titration were 1.4, 1.5 and 1.67 hours at pH 4.2, 5 and 7 respectively. When the target pH was reached, a 1 ml aliquot of sample was collected for TEM-EDX analyses and the remaining solution was ultra-centrifuged at 80 000 rpm for 2 h to separate precipitated nanophases from the dissolved species. The settled particles were freeze-dried for EXAFS analyses. The whole experimental protocol is summarized in Figure A3.

TEM images and analyses

Images were obtained and chemical analyses of nanophases were performed using a transmission electron microscope coupled with an EDX analyzer (JEOL JEM 2011 TEM).

For each sample, EDX analyses were performed on a set of around 40 nanophases of different sizes. The parameters were 50 000X magnification, an angular tilt of 20⁰ toward the detector, energy range of 40 keV, and corrected counting time of 30 s. A constant beam density was set at ~63.5 pA.cm -2 . Fe, Si, Al, K, and Mg were quantified using the Bruker AXS MET line mark data quantification procedure [START_REF] Berthonneau | Impact of swelling clays on the spalling decay of building limestones: insights from X-ray diffraction profile modeling[END_REF]. The size of each EDX-analyzed nanoparticle was subsequently measured on the corresponding micrograph.

EXAFS at the Fe K edge

Extended X-ray absorption fine structure (EXAFS) spectroscopy at the Fe K-edge data was performed at the ESRF synchrotron source on the FAME beam line (Grenoble, France) and on beam line 11.1 at the ELETTRA synchrotron (Trieste, Italy). Spectra were acquired using Si(220) and Si(111) double crystal monochromators at the ESRF and ELETTRA for the samples and the references respectively. Spectra were acquired at ambient conditions in both transmission and fluorescence modes (30-element solidstate Ge detector (Canberra, France)). All the samples were pressed into 5 mm diameter pellets mixed with boron nitride as a dilution agent. Each spectrum comprised an average of 3 to 5 individual spectra taken 107 eV below and 849 eV (14.75 Å -1 ) above the absorption edge of Fe (7112 eV) at a counting rate of 2-9 seconds until 14.75 Å -1 . To get representative spectra and minimize the risk of beam damage, each spectrum was collected at a different pellet location. Data were treated using Athena software [START_REF] Ravel | HEPHAESTUS: data analysis for Xray absorption spectroscopy using IFEFFIT[END_REF]. All radial distances in the RDF (Radial Distribution Function) were not corrected for phase shift (Figure 3b). According to the relation ΔR= π/2k, the minimum distance resolution of 0.11 Å was achieved.

A two-stage approach was used for the quantitative analysis of EXAFS data. The first stage consisted of using linear combination fitting (LCF) based on EXAFS spectral library of reference compounds. The second stage consisted of shell by shell fitting (SSF) to investigate the atomic environment of Fe. The two quantitative methods were performed at all three pH. The results of the two methods were in agreement. Only the SSF method is described in the paper because this method provided additional information on the local structure. Details of the LCF are presented in supplementary information.

Goethite, Ferrihydrite, Fe short range order (Fe-SRO) phase and Fe dimers were used as references. Goethite provides the highest Fe polymerization level of all reference compounds with 4 Fe-Fe octahedra edge-sharing and 4 double corner-sharing interactions. Ferrihydrite is characterized by fewer edge interactions (2 to 2.5) and double corner interactions (~3-5) than goethite [START_REF] Maillot | New insight into the structure of nanocrystalline ferrihydrite: EXAFS evidence for tetrahedrally coordinated iron(III)[END_REF][START_REF] Michel | The Structure of Ferrihydrite, a Nanocrystalline Material[END_REF].

Fe-SRO is composed of Fe polymers formed in Si rich solutions. Fe polymers are characterized by 2 edge-sharing but only a 0.6 double corner interaction. Fe polymers were synthesized at pH 5 in presence of Si (Si/Fe=4), conditions in which there are no Si-O-Fe interactions [START_REF] Doelsch | Speciation and Crystal Chemistry of Iron(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 1. An Fe K-Edge EXAFS Study[END_REF][START_REF] Doelsch | Speciation and Crystal Chemistry of Fe(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 2. Characterization of Si-Fe Aggregates by FTIR and 29Si Solid-State NMR[END_REF]. For Fe dimers only 1 edge-sharing coordination has been described [START_REF] Rose | Nucleation and Growth Mechanisms of Fe Oxyhydroxide in the Presence of PO4 Ions. 1. Fe K-Edge EXAFS Study[END_REF]). (See Supplementary Information for details on reference samples).

Shell by shell fitting (SSF) was used to extract structural information such as the coordination number (Nj) and interatomic distances (Rj) relative to the absorber atom using the software code Artemis [START_REF] Ravel | HEPHAESTUS: data analysis for Xray absorption spectroscopy using IFEFFIT[END_REF]. The contributions of the different atomic shells were assessed using back-Fourier transform of the pseudo-radial distribution function. These partial EXAFS functions were then least-squares fitted by a theoretical function (in the single-scattering approximation) in order to determine the structural and chemical parameters of the atomic neighbors in the atomic shells around Fe. Uncertainties for radial distances remained within a conservative ±0.02 Å range typical in the determination of this parameter [START_REF] Pokrovski | An X-ray absorption fine structure and nuclear magnetic resonance spectroscopy study of gallium-silica complexes in aqueous solution[END_REF]. Varying the k weight magnified or eliminated different sections of the EXAFS signal. A k weight of 3 was used for SSF techniques. To determine an appropriate value for E0 and amplitude reduction factor (So2), the lepidocrocite spectrum with pre-confirmed structural information was used to set those values to 2eV (±2eV) and 0.75 respectively. It is worth noting that in complex media, various fits of similar quality can be obtained. It is therefore important to recall that structural results are not necessarily univocal.

Results

Chemical composition of the leachate solution and conditions for the formation of nanophases

The chemical composition of the leachate solution is presented in Table 1. Fe, Mg and Si were the main contributors to the leachate solution, while Al and K contributed to a lesser extent. Mn and Ti concentrations were negligible (Figure A1) and were not included in the atomic proportions.

The preliminary titration experiment of the leachate solution (Figure A2) showed that pH 4.2, pH 5 and pH 7 were the values at which changes in the polymerization regime could be expected. Theoretically, nanophases formed at these three different pH should thus reveal differences in chemical composition and/or atomic structure.

TEM-EDX characterization of nanophases

Polymerization experiments resulted in nanophases obtained at three final pH 4.2, 5 and 7. Collected masses of nanophases ranged between 11 to 15 mg. Regardless of the pH, particles were aggregated, forming distinct clusters of small and large particles (Figure 1). The size distribution showed a bimodal Gaussian fit with maxima at 6 (±3.7) nm and 30 (±15) nm. ~15 nm was the cut-off size between smaller and larger particles.

Volume estimates showed that the volume of larger particles was 50 times larger than the volume of smaller particles. Electron diffraction analyses revealed a diffuse pattern across all pH and particle sizes (Figure 1).

Fe and Si mainly composed the nanophases regardless of the pH and size range (Figure 2 A and B). The proportions of Fe and Si were higher than in the leachate solution, indicating preferential polymerization of Fe and Si compared with the other elements. The proportions of Al in the nanophases were close to those in the leachate solution. The contribution of Al was limited, even at pH ≥ 5 when polymerization of Al was theoretically expected. The proportions of K and Mg in the nanophases were in the same range as that of Al. However, they were significantly depleted in the nanophases compared to in the leachate solution. Finally, in terms of general trends as a function of pH, pH 5 represented a singular case in which the large particles were extremely Si enriched and Fe and Al depleted.

EXAFS at the Fe K-edge: iron atomic range structure

Comparison of raw data

The structural interactions between Fe octahedra are represented as signals at ~5.2 Å -1 and ~7.5 Å -1 on the EXAFS spectra (Figure 3a and Figure B1) [START_REF] Mikutta | X-ray absorption spectroscopy study on the effect of hydroxybenzoic acids on the formation and structure of ferrihydrite[END_REF][START_REF] Mikutta | Effect of citrate on the local Fe coordination in ferrihydrite, arsenate binding, and ternary arsenate complex formation[END_REF][START_REF] Pokrovski | Iron (III)-silica interactions in aqueous solution: insights from X-ray absorption fine structure spectroscopy[END_REF]. These interactions were also observed as peaks in Rspace at radial distances of ~2.7 Å and ~3.2 Å corresponding to edge and double corner sharing interactions respectively (Figure 3b) [START_REF] Rose | Structure and Mechanisms of Formation of FeOOH(NO3) Oligomers in the Early Stages of Hydrolysis[END_REF]. In transiting from the 'goethite and 2L ferrihydrite' to 'Fe-SRO and Fe dimers' references, i.e. with decreasing Fe octahedra polymerization, the weak intensity in k-space at ~5.2 Å -1 converted into a faint shoulder and the intensity of the ~7.5 Å -1 feature decreased. The above change in crystalline order was also seen in R-space with the double corner peak at ~3.2 Å disappearing and peak at ~2.7 Å decreasing in intensity. In the reference standards, the locations of these Fe-Fe markers changes from a shoulder to a fully formed peak as the Fe polymerization increases from Fe dimers to Goethite. This increase in Fe polymerization is accompanied by shift in location of the signals from lower to higher wavenumber values.

Features at ~5.2 Å -1 and ~7.5 Å -1 on the experimental EXAFS spectra showed that iron polymers larger than dimers were formed during the precipitation steps at each pH (Figure 3). Phases formed at the pH 4.2 produced a spectrum for the above-mentioned Fe-Fe markers whose intensity was between that for goethite and 2L ferrihydrite. These phases produced distinct structural signals with the highest intensity of all the samples (Figure 3). For pH 5 and 7 phases, collective comparison of k and R-space spectra gave an average between 2L ferrihydrite and Fe-SRO references. The intensities of these two samples were weaker than that of the pH 4.2 sample.

Quantitative analysis of EXAFS data using shell by shell fitting

In all samples, the first coordination sphere around iron was composed of oxygen atoms at a distance of 1.96±0.02 Å (Table 2). The coordination number varied from 6.3-6.5±1.3 for pH 4.2 and pH 7. This result showed the formation of iron octahedra as the main iron species. However, at pH 5, the coordination number was significantly lower (4.9±1.0). This number was either related to iron octahedra considering the 15-25% range error (2000;[START_REF] O'day | Extended X-ray Absorption Fine Structure (EXAFS) Analysis of Disorder and Multiple-Scattering in Complex Crystalline Solids[END_REF] or to the presence of a proportion of tetrahedral coordinated iron like in ferrihydrite due to a Keggin-like motif [START_REF] Maillot | New insight into the structure of nanocrystalline ferrihydrite: EXAFS evidence for tetrahedrally coordinated iron(III)[END_REF][START_REF] Michel | The Structure of Ferrihydrite, a Nanocrystalline Material[END_REF].

The SSF of the second and third coordination spheres of all samples was performed by successively testing Fe-Fe, Fe-Si and Fe-Al atomic pairs. R-factors of all three atomic shell fits were systematically better than two atomic shell fits. Only three shell fits were selected (Figure 4). Detailed steps in the SSF for all three phases are given in Figures C2. B1 andB2). For the pH 5 sample, two solutions had almost equal quality of fit (only differing in the path used for the 3 rd atomic shell). The first solution used Fe-Fe2 edge sharing interaction at R=3.01±0.02 Å with NFe2=1.1±0.2 and Fe-Si (or Al) path at R=3.18±0.02 Å with NSi=3.9±0.8. The Fe-Si (Al) distance corresponded to a single corner sharing between the Fe octahedron and the Si (or Al) tetrahedron. The second solution only used Fe-Fe octahedra edge sharing with Fe-Fe2 at R=2.99±0.02 Å with NFe2=1.2±0.2 and Fe-Fe3 path at R=3.13±0.02 Å with NFe3=0.6±0.1. However, in both cases, the Fe-Fe coordination number (1.1-1.8±20%) was much smaller than for the pH 4.2 sample. For the pH 7 sample, the best fits showed 3 solutions. The fit with the Fe-Fe2 edge sharing path at R=3.07±0.02 Å with NFe2=3.4±0.7 and the Fe-Fe3 double corner sharing path at R=3.36±0.02 Å with NFe3=0.5±0.1 could be the most reliable solution, according to the Fe dominant composition of the nanophases. Whatever the solution, at pH 7, the total Fe-Fe coordination number (2.5-3±20%) was higher than at pH 5 but lower than at pH 4.2.

Discussion

Biotite dissolution rate and physical-chemical conditions of polymerization in batches

The proportions of Fe, Si, Al, K and Mg in the leachate solution (Table 1) differed from those in stoichiometry in biotite (Figure A1b). These proportions showed, as expected, that the dissolution of biotite is incongruent [START_REF] Kalinowski | Kinetics of muscovite, phlogopite, and biotite dissolution and alteration at pH 1-4, room temperature[END_REF]; [START_REF] Turpault | The dissolution of biotite single crystals in dilute HNO3 at 24°C: Evidence of an anisotropic corrosion process of micas in acidic solutions[END_REF]; [START_REF] Bonneville | Plant-driven fungal weathering: Early stages of mineral alteration at the nanometer scale[END_REF][START_REF] Bonneville | Tree-mycorrhiza symbiosis accelerate mineral weathering: Evidences from nanometer-scale elemental fluxes at the hypha-mineral interface[END_REF]). However, the calculated dissolution rates (Table A1) were slower than the values reported in the literature (see [START_REF] Bonneville | Tree-mycorrhiza symbiosis accelerate mineral weathering: Evidences from nanometer-scale elemental fluxes at the hypha-mineral interface[END_REF] for a review). A 10 kD filtration was applied in our protocol. This ~2 nm cutoff allowed the truly dissolved components to be retreived separately from the undissolved colloidal particules [START_REF] Buffle | Iron hydrolysis and solubility revisited: observations and comments on iron hydrolysis characterizations[END_REF][START_REF] Mccarthy | Environmental Science & Technology (ACS Publications)[END_REF]. By comparison, the most frequently used filtration protocols in other studies utilized filters with a cutoff size of 200 nm [START_REF] Bonneville | Tree-mycorrhiza symbiosis accelerate mineral weathering: Evidences from nanometer-scale elemental fluxes at the hypha-mineral interface[END_REF][START_REF] Bray | The effect of pH, grain size, and organic ligands on biotite weathering rates[END_REF] to define the threshold for dissolved species. This difference may explain the observed slower dissolution rates in our experiments. We thus obtained a solution with elemental proportions that are representative of the weathering of a mineral (Table 1). This composition is therefore more representative of soil solutions than solutions produced by commercial metal salts as well as solutions that consider only Fe and Al ions in the formation of nanophases [START_REF] Kleber | Mineral-Organic Associations: Formation, Properties, and Relevance in Soil Environments[END_REF] and references therein).

As revealed by TEM, the polymerization step enabled the formation of nanophases at pH 4.2, 5 and 7. These values correspond to realistic pH values in soils [START_REF] Schwertmann | Effect of pH on the formation of goethite and hematite from ferrihydrite[END_REF][START_REF] Yong | pH influence on selectivity and retention of heavy metals in some clay soils[END_REF]. Moreover, experimental polymerization involves rapid changes in pH. Such abrupt variations have also been observed at very small spatial scales [START_REF] Bonneville | Tree-mycorrhiza symbiosis accelerate mineral weathering: Evidences from nanometer-scale elemental fluxes at the hypha-mineral interface[END_REF] on biotite surfaces.

Consequently, the batch approach used in our protocol, although greatly simplified compared to a soil system, made it possible to reproduce physical-chemical conditions that realistically mimic soil processes.

Local structure of nanophases

The presence of Al, Si, Mg and K in the system limits Fe polymerization

The coordination number (Ntot) is a direct proxy for the degree of polymerization.

The levels of polymerization of the nanophases synthesized in our experiments were less than 3.4 whatever the pH (Figure 5). This value is lower than the number of Fe-Fe bonds in polymers synthesized in pure Fe systems [START_REF] Combes | Formation of ferric oxides from aqueous solutions: a polyhedral approach by X-ray absorption spectroscopy. II. Hematite formation from ferric gels[END_REF][START_REF] Combes | Formation of ferric oxides from aqueous solutions: A polyhedral approach by X-ray absorption spectroscopy: I. Hydrolysis and formation of ferric gels[END_REF][START_REF] Doelsch | Speciation and Crystal Chemistry of Iron(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 1. An Fe K-Edge EXAFS Study[END_REF]. The same difference in values was also observed in systems in which Fe is hydrolyzed in presence of Si [START_REF] Doelsch | Chemistry and structure of colloids obtained by hydrolysis of Fe(III) in the presence of SiO4 ligands[END_REF][START_REF] Doelsch | Speciation and Crystal Chemistry of Iron(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 1. An Fe K-Edge EXAFS Study[END_REF][START_REF] Doelsch | Hydrolysis of Iron(II) Chloride under Anoxic Conditions and Influence of SiO4 Ligands[END_REF][START_REF] Doelsch | Speciation and Crystal Chemistry of Fe(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 2. Characterization of Si-Fe Aggregates by FTIR and 29Si Solid-State NMR[END_REF][START_REF] Pokrovski | Iron (III)-silica interactions in aqueous solution: insights from X-ray absorption fine structure spectroscopy[END_REF]. In our case, the presence of Al, Si, Mg and K in the solution clearly hinders the polymerization of Fe regardless of pH.

The pH controls the local structure of nanophases

At pH 4.2, the level of polymerization of the nanophases was the highest of our experiments (Figure 5) and Fe was the main element in the nanophases (Figure 2). Fe-Fe bonds with double corner interactions dominated the local structure. The number of edge interactions was lower than double corners interactions (Figure 5). These polymers are therefore structured in three dimensions, resembling the local structure of the polymers described in systems where Fe polymerizes in the presence of Si at a pH close to 3 [START_REF] Doelsch | Speciation and Crystal Chemistry of Iron(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 1. An Fe K-Edge EXAFS Study[END_REF][START_REF] Pokrovski | Iron (III)-silica interactions in aqueous solution: insights from X-ray absorption fine structure spectroscopy[END_REF]. The occurrence of Fe-O-Si bonds between Fe octahedra and Si-tetrahedra was not observed (Table 2), which is consistent with the Fourier transformed infrared (FTIR) results obtained in conditions similar to our systems (Si/Fe = 1, pH 3) [START_REF] Doelsch | Speciation and Crystal Chemistry of Fe(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 2. Characterization of Si-Fe Aggregates by FTIR and 29Si Solid-State NMR[END_REF]. At pH 7, Fe was still the main element (Figure 2) but its degree of polymerization was slightly lower than that at pH 4.2. However, unlike pH 4.2, the octahedra were mostly bounded by their edges (Figure 5), forming rather planar local structures. Again, the system we studied behaved in a quite similar way to the Fe polymerization systems in the presence of Si [START_REF] Doelsch | Speciation and Crystal Chemistry of Iron(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 1. An Fe K-Edge EXAFS Study[END_REF][START_REF] Doelsch | Speciation and Crystal Chemistry of Fe(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 2. Characterization of Si-Fe Aggregates by FTIR and 29Si Solid-State NMR[END_REF]. Moreover, these authors showed by FTIR the existence of Fe-O-Si bonds at pH 7, in agreement with the third layer of our quantification by SSF (Table 2).

At pH 5, the level of polymerization of Fe was significantly lower than that of the structures observed at pH 4.2 and 7 (Figure 5). The number of edge interactions was slightly greater than the number of double corners. This local structure is therefore quite close to a mixture of dimers and trimers. Quantification by SSF suggests the potential presence of Fe in tetrahedral form in the local structure as observed by [START_REF] Pokrovski | Iron (III)-silica interactions in aqueous solution: insights from X-ray absorption fine structure spectroscopy[END_REF], but without clearly demonstrating it. On the other hand, like at pH 7, SSF analysis (Table 2) suggests the existence of Si-O-Fe bonds that correspond to the FTIR results obtained at pH 5 for Si/Fe = 1 [START_REF] Doelsch | Speciation and Crystal Chemistry of Fe(III) Chloride Hydrolyzed in the Presence of SiO4 Ligands. 2. Characterization of Si-Fe Aggregates by FTIR and 29Si Solid-State NMR[END_REF]. Thus, unlike the nanophases formed at pH 4.2 and 7, the composition of the nanophases formed at pH 5 is largely dominated by Si (Figure 2). Fe is present only as dimers and trimers, probably isolated in an amorphous silica matrix. The polymerization of Fe at pH 5 was thus counteracted by the polymerization of high amounts of amorphous Si. Thermodynamic and/or kinetic mechanisms that control the variations in the proportions of Fe and Si in the nanophases as a function of pH remain to be explained.

Two stages of precipitation: growth and maturation

The individual nanophases had two particle size ranges (Figure 1) regardless of the pH considered. The differences in chemical composition as a function of size are better illustrated in the Fe, Si and Al ternary diagram in Figure 6. Regardless of pH, the chemical composition of the smaller particles was close to that of the initial leachate solution, with a slight enrichment in Fe. Two hypotheses can be proposed to highlight the chemical heterogeneity as function of the particle size. First, since no time series experiments were conducted the two particle types could have been formed from different precursors or second, the difference may be due to a maturation/aging mechanisms. In the case of the second hypothesis, the smallest particles could be the first nanometric phases that polymerize during titration. They could derive from the rapid growth of the initial nuclei. The chemical compositions of the larger particles differed from those of the smaller particles at the same pH. They were enriched in Fe at pH 4.2 and pH 7, and enriched in Si at pH 5. The difference in the composition of the larger and smaller particles means that simple aggregation of the smaller particles cannot explain the formation of the larger particles. Instead, we propose that these particles could be formed after the titration step, when the pH is stable, by a stage of maturation. Maturation (e.g. Ostwald ripening [START_REF] Voorhees | The Theory of Ostwald Ripening[END_REF]) is a stage of dissolution/precipitation: the most unstable small particles as a result of the large surface area can be dissolved and re-precipitation occurs on the surface of other growing particles. The composition and structure of the nanophases formed during the hypothesized stage of maturation appeared to be strongly controlled by the pH conditions.

The TEM results thus tend to indicate two polymerization steps in the formation of nanophases: we propose a first initial growth, and second maturation. It is important to note that data from EXAFS were unable to distinguish between the two stages of polymerization. EXAFS information is still an average signal over all particle size ranges within a given sample. However, the observed structural differences, in particular the contribution of Si to the structure of the particles at pH 5 (Table 2 andFigure 5) tends to show that the EXAFS signal of the polymerized phases was rather dominated by the structure of the larger particles.

Synthetized nanophases are representative of nanophases formed in surface environments

In order to test the representativeness of the products formed in our experiment as analogues to nanophases formed in surface environments, we compared the particles synthesized with two types of nanophases naturally formed: the altered layer formed at the surface of biotite and the nanophases formed at a distance from the initial altered surfaces.

The study of [START_REF] Bonneville | Tree-mycorrhiza symbiosis accelerate mineral weathering: Evidences from nanometer-scale elemental fluxes at the hypha-mineral interface[END_REF] is particularly relevant to compare our results with a layer of biotite alteration, since these authors reproduced the chemical alteration processes at mineral-mycorrhiza interface, representing the hotspot of the weathering engine at work in soils. The composition of the nanophases formed in our pH 5 experiments are reported in Figure 7 together with their results averaged over the 20 nm thick altered-biotite zone. The comparison shows very similar compositions between nanophases formed in batch at pH 5 and the products of the surface layer alterated biotite. Moreover, these authors also measured pHs at the mineral-mycorrhiza interfaces, varying from values below 4.6 up to 5.8. The nanophases formed in our pH 5 experiments can therefore be considered to be formed under rather similar conditions.

Even though the chemical compositions of nanophases pH 5 and biotite-altered layer seemed similar, comparison of local atomic structures was more complex. In an earlier study, [START_REF] Bonneville | Plant-driven fungal weathering: Early stages of mineral alteration at the nanometer scale[END_REF] identified the presence of vermiculite and ferrihydrite in the altered biotite layer. These observations were consistent with those of [START_REF] Murakami | Biotite dissolution processes and mechanisms in the laboratory and in nature: Early stage weathering environment and vermiculitization[END_REF] who, using high resolution TEM, observed these gradual mineralogical transformations in addition to the presence of chlorite. On the other hand, other studies tended to show that the alteration layer formed on the mineral surface is amorphous.

The mechanism proposed is no longer a gradual transformation associated with the preferential diffusion of selected ions, but a process of interfacial dissolutionreprecipitation [START_REF] Hellmann | Nanometre-scale evidence for interfacial dissolutionreprecipitation control of silicate glass corrosion[END_REF][START_REF] Hellmann | An EFTEM/HRTEM high-resolution study of the near surface of labradorite feldspar altered at acid pH: evidence for interfacial dissolution-reprecipitation[END_REF][START_REF] Hellmann | Unifying natural and laboratory chemical weathering with interfacial dissolution-reprecipitation: A study based on the nanometer-scale chemistry of fluid-silicate interfaces[END_REF]. The results obtained by [START_REF] Kawano | TEM-EDX study of weathered layers on the surface of volcanic glass, bytownite, and hypersthene in volcanic ash from Sakurajima volcano, Japan[END_REF] on an altered natural bytownite, which showed alteration of the amorphous layer, also support the latter process. In the case of an amorphous surface alteration layer, the nanophases synthesized by our protocol could be good analogs of the surface processes of the minerals.

Concerning the second type of nanophases (neoformed nanophases in soils at a distance from the altered mineral surface), the nanophases in our study may also be analogs of natural secondary nanomineral phases. Only a few authors have studied the composition and local atomic structure of such nanophases. [START_REF] Dai | Interaction between bentonite and Bacillus litoralis strain SWU9[END_REF] observed the formation of nanoparticle aggregates after experimental alteration of bentonite by bacteria. SEM-EDX analyses showed that the nanoparticle aggregates were composed of Si, Na, Ca, Mg, Al, Fe, K. [START_REF] Wen | Insights into complexation of dissolved organic matter and Al(III) and nanominerals formation in soils under contrasting fertilizations using two-dimensional correlation spectroscopy and high resolution-transmission electron microscopy techniques[END_REF] also extracted nanophases in a <450 nm fraction that exhibited Al, Si and Fe compositions and amorphous structures. These two studies demonstrate that not only Al and Fe, as classically described in literature, but also other elements such as Si, Na, K, Mg, and Ca may be involved in the formation secondary nanophases in surface environments. It is therefore probable that the nanophases that were synthesized in the present work are, at least in the case of the larger particles, representative of some nanophases formed in soils, sediments or other surface environments.

Conclusion

This laboratory work simulated the successive processes of biotite alteration and the following neoformation of secondary phases from ions in solution. The nanophases formed were amorphous phases that polymerized in two steps: (1) the initial growth phase formed 2 to 15 nm particles whose chemical composition closely resembled that of the alteration solution; (2) the maturation phase then resulted in 15 to 60 nm particles whose compositions are strongly controlled by the pH conditions. At pH 4.2 and pH 7, the structure of the nanophases was dominated by Fe but its polymerization was hindered by the presence of Al, Si, Mg and K. Conversely, at pH 5, the polymerization of Fe was counteracted by the polymerization of high amounts of amorphous Si. Surprisingly, Al appeared to play a minor role in polymerization, regardless of the pH.

However, thermodynamic and/or kinetic mechanisms that control the variations in the proportions of Fe and Si in the nanophases as a function of pH remain to be explained. In comparison with previous alteration studies, the laboratory-synthetized phases of our study were estimated to be analogs of the nanophases formed in natural biotite-bearing soils at varying distances from biotite surfaces.

These nanophases have a high potential for contaminant sorption, aggregation processes as well as for organic matter stabilization in soils. In the framework of the C budget issues and the 4 per 1000 initiative, it would be interesting to examine the role and the mechanisms of the interactions between these Fe, Si, Al, Mg, K nanophases and soil organic matter. Like for the Fe or Al phases reported in the literature, one could expect coprecipitation processes leading to medium to long term stabilization of C in soils.

Acknowledgements

This work was supported by Aix-Marseille University doctoral school ED251, ANR (NanoSoilC ANR-16-CE01-0012-02 project) and the Institut Universitaire de France. We would like to thank the European Synchrotron Radiation Facility (ESRF) (Grenoble,

Figure caption

For

  the pH 4.2 sample, the best solution was obtained with Fe in the 2 nd atomic shell with NFe2=1.5±0.3 at RFe-Fe2=3.01±0.02 Å and Fe in the 3 rd atomic shell with NFe3=1.9±0.4 at a distance of RFe-Fe3=3.38±0.02 Å. The interatomic distances were in agreement with Fe-Fe octahedra edge and double corners sharing. The total Fe-Fe coordination number (N=3.4±20%) indicates a low level of polymerization (Table

Figure 1 :

 1 Figure 1: TEM micrographs of nanophases. For each pH, magnification increases from left to right. On 50 nm scale images, electronic diffraction is superimposed, revealing the amorphous structure of the nanophases. SP: smaller particles; LP: larger particles.

Figure 2 :

 2 Figure 2: TEM-EDX chemical analysis of polymerized particles at three pH expressed in stoichiometric atomic %. The box-and-whisker plots represent the median value, the upper and lower quartiles, as well as the min and max of the data. The chemical composition of the leachate solution (Leachate S.) is also shown for the sake of comparison (bold dashed line, with their respective element specific error values). A: chemical composition of the smaller nanophases; B: chemical composition of the larger nanophases. n: number of particles analyzed.

Figure 3 :

 3 Figure 3: EXAFS (a) and RDF (b) plots. Arrows indicate locations of confirmed Fe-Fe signals. Spectra in black represent references. E and DC stand for edge-sharing and double corner sharing interactions respectively. Distances on the RDF are not corrected for phase shifts.

Figure 4 :

 4 Figure 4: Shell-by-Shell fitting for samples pH=4.2, pH=5 and pH=7. Fit numbers refer to Table 2.

Figure 5 :

 5 Figure 5: Changes in the coordination numbers for all Fe-Fe atomic pairs in the SSF analysis (Table 2) with the lowest R factors, leading to minimum (min) and maximum values (max) for each type of interaction and for each pH. Total represents the addition of coordination numbers by edge and double corner interactions. Total coordination numbers from pure Fe system from the literature are also shown for the sake of comparison.

Figure 6 :

 6 Figure 6: Ternary diagrams of Fe, Si and Al atomic proportions in the nanophases formed at pH 4.2, 5 and 7. The white star represents the initial composition of the leachate solution, the small black dots represent the composition of smaller nanophases and the larger grey dots the composition of larger nanophases.

Figure 7 :

 7 Figure 7: Chemical compositions expressed as K:Si, Mg:Si, Fe:Si and Al:Si ratios measured by TEM-EDX. Empty circles represent the chemical composition of the surface layer of an altered biotite (Bonneville et al., 2011) averaged over its 20 nm thickness. Black circles represent the mean composition of the larger particles formed in our pH 5 experiment. Error bars are standard deviations.

Table 2 :

 2 SSF analysis of pH 4.2, 5 and 7 phases. The R window is the radial distance range over which the fit is carried out. N, R and σ represent the coordination number, radial distance and disorder, respectively. Eo is the starting energy value for the fit and R-factor is a parameter for fit quality. Fe-Fe2 corresponds to edge sharing, Fe-Fe3 corresponds to double corner sharing. Fit numbers refer to the graph presented in Figure 4 and Figure C1.

R

Table Caption Table 1 : Chemical composition of the leachate solution provided by the dissolution experiment.

 Caption1

Table

	window Å	N ±20%	R (Å) ±0.02	σ (Å)	N ±20%	R (Å) ±0.02	σ (Å)	N ±20%	R (Å) ±0.02	σ (Å)	E o (eV)	R-factor	Fit No
		6.8	Fe-O 1.95	0.12	3.5	Fe-Si 3.25	0.05	2.2	Fe-Fe 3 3.42	0.06	0,0	0,128	2
	pH 4.2 1.00-3.63	6.6	Fe-O 1.94	0.12	3.5	Fe-Al 3.02	0.04	1.6	Fe-Fe 3 3.40	0.03	0.0	0.040	3
		6.3	Fe-O 1.97	0.12	1.5	Fe-Fe 2 3.01	0.08	1.9	Fe-Fe 3 3.38	0.08	4.0	0.023	4
		4.7	Fe-O 1.96	0.09	1.2	Fe-Fe 2 2.99	0.07	0.6	Fe-Fe 3 3.13	0.05	3.0	0.010	3
	pH 5 1.00-3.09	4.9	Fe-O 1.96	0.09	1.1	Fe-Fe 2 3.01	0.09	3.9	Fe-Si 3.18	0.09	3.0	0.006	4
		4.9	Fe-O 1.96	0.09	1.0	Fe-Fe 2 3.00	0.08	4.9	Fe-Al 3.21	0.08	3.0	0.006	5
		6.5	Fe-O 1.98	0.11	2.5	Fe-Fe 2 3.06	0.11	0.5	Fe-Fe 3 3.35	0.11	4.0	0.011	5
	pH 7 1.00-3.24	6.5	Fe-O 1.98	0.11	2.5	Fe-Fe 2 3.06	0.11	2.1	Fe-Al 3.45	0.08	4.0	0.011	6
		6.5	Fe-O 1.98	0.11	2.6	Fe-Fe 2 3.06	0.11	1.6	Fe-Si 3.42	0.08	4.0	0.011	7


Florian Bouville

Eric Maire

Sylvain Deville

Self-Assembly of Facetted Particles Triggered by a Moving Ice Front

Keywords: Ceramics, Composite Materials, Microstructures, Self-Assembly, Thermal diffusivity

The possibility to align and organize facetted particles in the bulk offers intriguing possibilities for the design and discovery of materials and architectures exhibiting novel functional properties.

The growth of ice crystals can be used to trigger the self-assembly of large, anisotropic particles and consequently to obtain three-dimensional porous materials of large dimensions in a limited amount of time. These mechanisms have not been explored so far, due to the difficulty to experimentally investigate these systems. Here we elucidate the self-assembly mechanisms of facetted particles driven by ice growth by a combination of X-ray holo-tomography and discrete element modeling, providing insights into both the dynamics of self-assembly and their final packing. The encapsulation of particles is the result of a delicate balance between the force exerted by the percolating network of concentrated particles and the force exerted by the moving interface. We illustrate the benefits of such self-assembly for thermal management composite materials.

Introduction

The controlled alignment of facetted or anisotropic particles holds the promise of a new class of crystalline materials at all length scales, exhibiting appealing structural and functional properties [START_REF] Murray | Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystals Assemblies[END_REF] . Understanding and controlling how such particles organize is required for the optimization of functional properties. Superlattices, for instance, with translational and rotational order of the building blocks, are currently investigated for their optical and electrical properties or for plasmonic applications [START_REF] Tao | Self-Organized Silver Nanoparticles for Three-Dimensional Plasmonic Crystals[END_REF] .

Most of the approaches developed so far are based on the evaporation of a solvent [START_REF] Pokroy | Self-Organization of a Mesoscale Bristle into Ordered, Hierarchical Helical Assemblies[END_REF][START_REF] Hatton | Assembly of Large-Area, Highly Ordered, Crack-Free Inverse Opal Films[END_REF] or the sedimentation of particles [START_REF] Henzie | Self-Assembly of Uniform Polyhedral Silver Nanocrystals into Densest Packings and Exotic Superlattices[END_REF] ; ordering in these phenomena is ultimately controlled by the pressure applied to a dense particles assembly, the particle interactions [START_REF] Xia | Monodispersed Colloidal Spheres: Old Materials with New Applications[END_REF] and the rate at which the particle concentration increases. Reaching an optimal packing thus requires a fine control over the particle shape, polydispersity, self-assembly driving force, and particle interactions, which restrict the applicability of the approaches to specific systems.

For larger particles (typically above one micron in diameter for ceramics), the diffusion is limited because of their weight and therefore so is their capacity to form dense structures upon concentration with conventional methods. Sequential deposition methods [START_REF] Tang | Nanostructured Artificial Nacre[END_REF][START_REF] Podsiadlo | Ultrastrong and Stiff Layered Polymer Nanocomposites[END_REF][START_REF] Walther | Large-Area, Lightweight and Thick Biomimetic Composites with Superior Material Properties via Fast, Economic, and Green Pathways[END_REF] are able to order anisotropic particles, although such methods are limited to thin samples and work only with high aspect ratio particles because the alignment results from shear forces acting on the particles. Anisotropic structural or functional properties could thus emerge from an assembly of anisotropic building blocks with an approximate alignment. Yet, very few approaches are able to provide such alignment in bulk materials (centimeter scale) and within reasonable time scale (minutes). The growth of ice crystals in a colloidal suspension can be used to drive the selfassembly of anisotropic building blocks [START_REF] Lee | The Morphology and Mechanical Properties of Layer Structured Cellulose Microfibril Foams from Ice-Templating Methods[END_REF][START_REF] Romeo | Directional Freezing of Liquid Crystalline Systems: From Silver nanowire/PVA Aqueous Dispersions to Highly Ordered and Electrically Conductive Macroporous Scaffolds[END_REF][START_REF] Hunger | Platelets Self-Assemble into Porous Nacre During Freeze Casting[END_REF] . Several benefits are associated with ice growth in this case, such as the possibility to obtain bulk materials or a reduced processing time of the order or minutes -vs. hours or days for evaporation or sedimentation processes [START_REF] Henzie | Self-Assembly of Uniform Polyhedral Silver Nanocrystals into Densest Packings and Exotic Superlattices[END_REF] . In addition, the process is in principle almost independent of the nature of the materials used [START_REF] Deville | Ice-Templating, Freeze Casting: Beyond Materials Processing[END_REF] .

Although alignment has been demonstrated experimentally, the underlying phenomena have not been deeply investigated so far. Several mechanisms have been hypothesized [START_REF] Lee | The Morphology and Mechanical Properties of Layer Structured Cellulose Microfibril Foams from Ice-Templating Methods[END_REF][START_REF] Hunger | Platelets Self-Assemble into Porous Nacre During Freeze Casting[END_REF] , and numerous important questions must be addressed. What is the driving force for the selfassembly? How do particles organize? How should the freezing conditions be adjusted to optimize the structural organization of the particles? How much do particle-particle interactions matter? The answers to these questions are essential for a proper control of the phenomenon and the resulting functional properties of the materials.

We demonstrate here how the ice growth induced self-assembly of facetted particles can be accurately described and understood by a combination of discrete element modeling and observation of the experimental spatial distribution using high resolution X-ray computed holotomography. These tools are used to explore the self-assembly behavior and predict the evolution of such colloidal system. The benefits in terms of functional properties of the resulting structures are illustrated with the thermal properties of Boron Nitride (BN)/silicon rubber composites. The methodology developed here is then extended to predict the self-assembly of cubic particles.

Materials and Methods

Materials processing

Suspensions were prepared by mixing distilled water, a cellulose ether (Tylose H4000P2, Shin Etsu, at a weight ratio Tylose on BN powder of 0.5%) an organic binder (Poly Ethylene Glycol 4M, Sigma Aldrich, 2 wt.% of dried powder mass) and the BN powder (TRES BN PUHP 3008, Saint-Gobain BN products) at different volume fractions. The powder used in the study present platelet morphology with a diameter around 8 µm and 1 µm in thickness. After a first mixing step with a propeller stirrer, ultra sonic mixing was conducted with a sonotrode (Digital Sonifier 250) with an applied energy around 150 W.h/kg.

Freezing of the slurries was done by pouring them into a silicone mold (diameter 20 mm, 21 mm height) placed on a cooled copper plate. The copper plate was cooled by silicone oil at a temperature regulated by a cryothermostat. The cooling rate were adjusted between 0.5°C/min and 2°C/min. Faster cooling rate were obtain by dipping a copper finger with the mold on top in liquid nitrogen. Measurement of ice front velocity was made by dipping a ruler at different times in the slurry and measuring the height of frozen sample. Once freezing was completed, the samples are freeze-dried for at least 48 hrs in a commercial freeze-dryer (Free Zone 2.5 Plus, Labconco, Kansas City, Missouri, USA), to ensure a complete removal of the ice crystals.

Holo-tomography experiments were carried out at European Synchrotron Facility at the beam line ID-22. More details on this technique can be found elsewhere [START_REF] Cloetens | Holotomography: Quantitative Phase Tomography with Micrometer Resolution Using Hard Synchrotron Radiation x Rays[END_REF] . To enhance phase contrast, porous sample were infiltrated by silicone rubber under vacuum prior to observation.

Segmentation and density measurements were made using the software Fiji 15 .

Thermal diffusivity measurement

A flash lamp method was used to measure the thermal diffusivity of the BN/Silicone rubber composite. Disk samples of 20 mm diameter and 5 mm thick were put in a holder, a flash produced by a lamp heated a side of the sample and the temperature profile was recorded on the other side. The thermal diffusivity was obtained by a fit of this profile by the quadripole method [START_REF] Maillet | Thermal Quadrupoles: Solving the Heat Equation through Integral Transforms[END_REF] . At least five different measurements were made on each sample.

Percolation threshold estimation

The percolation threshold of platelet particles can be estimated from an empirical formula developed for permeability clay composite [START_REF] Lu | Influence of Aspect Ratio on Barrier Properties of Polymer-Clay Nanocomposites[END_REF][START_REF] Stanley | Scaling, Universality, and Renormalization: Three Pillars of Modern Critical Phenomena[END_REF] :

ϕ p = 2 3𝑆 + 1 𝑊 𝐿 𝑝 !
With W and L the thickness and length of the platelet respectively, pc = 0.718 and S the order parameter of platelet orientation given by the following relationship:

𝑆 = 3 < 𝑐𝑜𝑠²𝜃 > -1 2
Where <cos²θ> is the mean of the platelet angles with respect to the preferred direction (equal to 54° for random orientation).

Discrete Elements Modeling

Discrete element modeling was carried out by a custom version of the LAMMPS Package. To reproduce the lamellar structure characteristic of ice crystal growth, a rectangular simulation box was created. The method used to produce platelet-like particles using spherical ones consist in the creation of a cylindrical region in the simulation box. The region was then filled with spheres with a diameter corresponding to the thickness of the particle, here 1 µm. During the simulation, the spheres were fixed together as a rigid body, the software just sums the interaction on all the spheres to calculated the resulting displacement and torque applied to the assembly. To introduce the polydispersity of particle size, a random number from a Gaussian statistical distribution was used to adjust the radius of each cylindrical region. The distribution was centered on 4 µm with standard deviation of 1 µm. To avoid any overlap of the region that could lead to truncated particles, they were created successively at different x coordinate, while the z and y coordinates was randomly selected. The simulation box dimensions were first set to 300 x 200 x 200 µm 3 , thus a dilute system was obtain. The box sizes were then shrunk to dimensions of 100 x 50 x 50 µm [START_REF] Pokroy | Self-Organization of a Mesoscale Bristle into Ordered, Hierarchical Helical Assemblies[END_REF] . The number of particles was calculated to obtain the desired volume fraction, knowing the density of BN (2.26 g/cm [START_REF] Pokroy | Self-Organization of a Mesoscale Bristle into Ordered, Hierarchical Helical Assemblies[END_REF] ) and mean particles volume.

To replicate the growth of ice crystals, two opposite walls were moved at a given speed (Figure 1a), the speed of the ice front velocity measured experimentally. The simulation box was constraint to remain small in the two directions z and y, which allows us to neglect the curvature of ice crystals tips; they were therefore fixed at 50 µm. The y direction was thus extended to 100 µm to model enough particles to have statistical information. The other walls were maintained fix during the whole simulation, at a distance corresponding to particle radius, to allow the rotation of the particle placed in the box boundaries. Software limitations do not allow a periodic condition with rigid body assemblies. Considering the low surface charge of BN particles in water [START_REF] Crimp | Suspension Properties of Hexagonal BN Powders: Effect of pH and Oxygen Content[END_REF] and the large size of the particles, only the repulsive part of the Lennard-Jones potential was used to model particle interaction:

𝑉 𝑟 = 𝜖 ! ( ! ! ) !"
where σ = 1 µm is the particle diameter, r the distance between two particles and ε 0 the Hamaker constant of the BN / water / BN interfaces. This potential, because it is only repulsive, creates an excluded volume to avoid unphysical particle overlaps, while simultaneously saving CPU time. The particle / ice front interaction is represented by a Van der Waals potential for a sphere and a plane near contact [START_REF] Dalgarno | Der Waals Forces[END_REF] :

𝑊 ℎ = - !" !"
where R = σ / 2 corresponds to the particle radius, A the Hamaker constant of particle / water / ice interaction and h the distance between the ice front and the particle. The non-retarded lifshitz theory was used to calculate the different Hamaker constants with the refractive index and dielectric constant of each material (hexagonal BN, water and ice). The input values for simulation were H = 4 x 10 -20 J and A = -3 x 10 -21 J. The negative value of the Hamaker constant for ice / particle interaction indicates repulsion, characteristic of many solidification front [START_REF] Lipp | On the Engulfment of Spherical Particles by a Moving Ice-Liquid Interface[END_REF][START_REF] Asthana | Review The Engulfment of Foreign Particles by a Freezing Interface[END_REF][START_REF] Garvin | Multiscale Modeling of Particle-Solidification Front Dynamics. Part II: Pushing-Engulfment Transition[END_REF] .

The simulations were carried out in an NVT ensemble with the temperature regulated by a Langevin thermostat. The Langevin thermostat allowed the addition of a viscous force characteristic of the solvent interaction, which is intimately linked to the repulsion / engulfment phenomenon.

The repulsive interaction between the ice front and the particle lead to a disjoining pressure thus to the appearance of a thin liquid film at the interface. If the particle comes closer to the front, there is a chance of being encapsulated in the ice. No existing model grasps the complexity of the repulsion / engulfment equilibrium in concentrated colloids and a simplified one introduced by Barr et al. [START_REF] Barr | Structural Properties of Materials Created through Freeze Casting[END_REF] has been used here. It is based on the balance between drag and repulsive forces. The repulsive forces come from the interactions with the ice front and the drag forces from solvent interaction. The maximum drag force attained at the encapsulation can be calculated via Stokes's law:

𝐹 !"# ! = 6𝜋𝜂𝑅𝑣 ! ( 3
)
where η is the viscosity of water (1.8 mPa.s at 0°C), R the particle radius and v c the critical velocity (determined experimentally at 35 µm/s for BN particle). The critical distance δ before encapsulation can be deduced by equating the force applied by the moving front (the opposite of the derivative of the interaction potential) with the maximum drag force undergoes by the particle: -

!" !! = 𝐹 !"# ! .
The construction of the anisotropic particles introduced here let us apply all the interaction and forces on each individual sphere without any assumption on the whole particle. This model comprises up to 800 particles, thus close to 42000 individual spheres.

For visualization and image analysis purpose, the center, radius and normal vector of each particle was extracted and a plugin for Fiji was developed to visually reconstruct the particles from the knowledge of their geometry. The time-lapse density measurements were made by the use of a programmed plugin and the percolation region by the existing "Find connected region" plugin with Fiji. The images presented here have been made with the software Paraview.

Results and Discussion

Ice Growth Induced Self-Assembly of Anisotropic, Facetted Particles

The self-assembly of facetted particles during ice-templating occurs at length scale of tens of microns. The resulting spatial distribution is intimately linked to dynamical interactions between the particles and the growing crystals but also to viscous interactions with the unsolidified solvent. The imaging possibility offered now by synchrotron radiation facilities [START_REF] Michiel | Fast Microtomography Using High Energy Synchrotron Radiation[END_REF] allows the visualization of the growth of large crystals in real time [START_REF] Deville | Three-Dimensional in Situ Imaging of Ice Crystal Growth in a Colloidal Silica Suspension[END_REF] but the spatial resolution is still not sufficient to image in situ the dynamic arrangement of particles. After freezing and ice removal however, the resulting samples can be imaged at a resolution good enough to distinguish the particles. In the present paper, we have used high resolution KB focused X-Ray holotomography on impregnated samples of 1x1x1 mm 3 at the ID22NI beam line at the ESRF. Microstructures of ice-templated BN platelets infiltrated by a silicon rubber are shown in Figure 1a and 1b. The 50 nm resolution of the holo-tomography is sufficient to discern the platelets packing in the wall. In Figure 1b, the slow solidification interface velocity (7 µm/s) leads to thick walls (~30 µm) and the particles that are directly in contact with the growing ice are well aligned, parallel to it. Oppositely, in the inner region of the wall the particles are less ordered. This type of structure will be referred to as the sandwich structure. When the solidification interface is moving faster, (close to 25 µm/s), the wall obtained is significantly thinner (~15 µm, Figure 1c) and the packing and alignment of particles is improved. This type of structure will be referred to as the compact structure.

The model used in this study consists in a Langevin simulation of colloidal particles with different interaction potential, one for the particles/ solidification front interaction and one for the particles/particles interaction (see details in section 2). The initial state of the modeled platelets is depicted in Figure 1d and shows the Gaussian size distribution of the particles, their random orientation, as well as the width of the model box (e.g. 50 µm). These dimensions are close to the ones of the walls obtained in the silicones/boron nitride composites. This model comprises up to 800 platelets in a volume of 100 x 50 x 50 µm 3 . The simulated volume is willingly limited to those dimensions, to reflect closely the actual experimental conditions (Figure 1) and to neglect the curvature of the ice crystals in the freezing direction. Because crystal nucleation (and therefore branching) cannot be taken into account in this type of model, the lateral dimension has been extended just enough to have a representative number of particles in a reasonable simulation time. The benefits of self-assembly of large particles in bulk materials are demonstrated here with the thermal properties of the BN/silicon rubber composite shown in Figure 1. Controlling the orientation of BN particles to take advantage of their anisotropic thermal conductivity could be highly beneficial in thermal management applications, where the heat needs to be taken away from the components in the most efficient manner. BN is a prime choice for ceramic materials that are used in thermal management systems. The crystalline anisotropy of BN can be used to obtain platelet-like particles which exhibit orthotropic thermal properties [START_REF] Levinshtein | Properties of Advanced Semiconductor Materials: GaN, A1N, InN[END_REF] that are 20 times lower in the c-axis (30 W/m/K) direction than in the perpendicular plane (600 W/m/K). Comparison of the relative improvements RI (calculated as RI = (α aligned -α random )/ α random , where α aligned and α random are respectively the thermal diffusivities' of the materials with the aligned platelets and with the randomly oriented platelets) in thermal properties due to the alignment of BN particles induced by an electric field [START_REF] Fujihara | Field-Induced Orientation of Hexagonal Boron Nitride Nanosheets Using Microscopic Mold for Thermal Interface Materials[END_REF] , a magnetic field (with [START_REF] Lin | Magnetic Alignment of Hexagonal Boron Nitride Platelets in Polymer Matrix: Toward High Performance Anisotropic Polymer Composites for Electronic Encapsulation[END_REF] or without [START_REF] Cho | Facile Orientation of Unmodified BN Nanosheets in polysiloxane/BN Composite Films Using a High Magnetic Field[END_REF] superparamagnetic nanoparticles coating), or ice templating (this study). The BN volume fractions of these composites are respectively 0.6 vol.% 31 , 10 vol.% 29 , 5 vol.% [START_REF] Cho | Facile Orientation of Unmodified BN Nanosheets in polysiloxane/BN Composite Films Using a High Magnetic Field[END_REF] , and 18 vol.%.

Here we took advantage of the ice growth induced self-assembly to obtain bulk, macroporous materials where the anisotropic particles are aligned along the freezing direction (Figure 2a). The samples were then infiltrated with a silicon rubber before their thermal properties were assessed.

For the sake of comparison, a homogeneous composite was obtained by simply mixing the same amount of particles in the silicon rubber (Figure 2a). The corresponding microstructures are shown in Figure 2, along with the results of the thermal diffusivities measurements (Figure 2b).

The material with the controlled architecture presents a thermal diffusivity almost three times greater than the homogeneous composite, illustrating the benefits of an aligned structure, even if the alignment is not completely perfect. Alternative strategies based on the application of an electric [START_REF] Fujihara | Field-Induced Orientation of Hexagonal Boron Nitride Nanosheets Using Microscopic Mold for Thermal Interface Materials[END_REF] , magnetic (with the aid of superparamagnetic nanoparticles [START_REF] Lin | Magnetic Alignment of Hexagonal Boron Nitride Platelets in Polymer Matrix: Toward High Performance Anisotropic Polymer Composites for Electronic Encapsulation[END_REF] or not [START_REF] Cho | Facile Orientation of Unmodified BN Nanosheets in polysiloxane/BN Composite Films Using a High Magnetic Field[END_REF] ) field have been proposed to align BN particles to improve the thermal properties. The relative improvement in thermal properties (Figure 2c), estimated using the difference of the thermal properties in the random and aligned structures normalized by the thermal properties of the random structure, provides a comparison of the efficiency of these strategies. Ice templating is comparatively much more efficient. On top of that, it is also able to align particles in much more concentrated suspensions (almost 20 vol.%, compared to less than 5 vol.% for the other methods).

Predictions of Particle Packing

The driving force for ice growth induced self-assembly of large (>1 µm) particles is not random thermal motion. The potential energy needed to lift a particle (of 8 µm diameter and 0.5 µm thick) from its own diameter in water can be estimated by the following relationship:

𝑈 ! = 𝑚 • 𝑔 • ∆ℎ = 𝜋𝑟 ! 𝑒 𝜌 !" -𝜌 !!"#$ • 𝑔 • 2𝑟 = 2.6×10 !!" 𝐽 (1)
where m is the weight of the particle, r its diameter, e its thickness, and ρ BN and ρ water the density of BN and water respectively. This energy is thus around three orders of magnitude superior to the energy brought by the thermal motion (of the order of 𝑘 ! 𝑇, so 3.8×10 !!" 𝐽 at 273K). This means that the behavior in water of particles of this size will not be controlled by thermal energy.

The common modeling approaches (e.g. Monte Carlo 32 ) thus cannot accurately describe the behavior of the system. In particular, the particle encapsulation by the interface [START_REF] Asthana | Review The Engulfment of Foreign Particles by a Freezing Interface[END_REF] , a key feature of the phenomenon, cannot be taken into account. Discrete element modeling (DEM) is able to take into consideration several crucial aspects of the phenomena, such as the viscosity of the suspension, the interactions between particles (modeled here by a Van der Waals and Lennard-Jones pair potential for the ice and inter particles interactions respectively), and the continuous particle size distribution. The key feature implemented is the possible engulfment of particles by the moving solidification interface. Many different analytical models have been developed to predict this complex phenomenon [START_REF] Garvin | Multiscale Modeling of Particle-Solidification Front Dynamics. Part II: Pushing-Engulfment Transition[END_REF][START_REF] Rempel | The Interaction Between a Particle and an Advancing Solidification Front[END_REF][START_REF] Casses | A General Theoretical Approach to the Behaviour of Foreign Particles at Advancing Solid-Liquid Interfaces[END_REF][START_REF] Park | The Encapsulation of Particles and Bubbles by an Advancing Solidification Front[END_REF][START_REF] Kao | Particle Capture in Binary Solidification[END_REF] , but are only valid for single, isolated particles. By using DEM, a simple force equilibrium between repulsion and drag forces can be introduced and thus take the dynamical and collective (e.g. shock between particles) of this phenomena into account. It also provides access to the dynamics (time-lapse position and orientation) of particle redistribution by the growing ice crystals, which is currently impossible to obtain experimentally.

Particular attention must be paid to the particle shape and interactions. Different pair potentials can be used for anisotropic, facetted particles. These anisotropic potentials have been developed

for clay suspension, such as the Gay-Berne [START_REF] Berardi | A Gay-Berne Potential for Dissimilar Biaxial Particles[END_REF][START_REF] Berardi | A Generalized Gay-Berne Intermolecular Potential for Biaxial Particles[END_REF] potential, based on Lennard-Jones potential and a quadripole orientation. The RE-squared [START_REF] Babadi | Analytical First Derivatives of the RE-Squared Interaction Potential[END_REF] potential, based on an assembly of small isotropic Lennard-Jones potential has also been used. Even if those potentials allow a lot of the complexity involved in anisotropic particles interaction to be taken into account, they are limited to model systems with monomodal particles and therefore, cannot accurately describe the interactions with planar interface such as the solidification front here. A different strategy has been developed here. Spheres (with an associated Lennard-Jones potential) are fixed together as cylindrical rigid bodies. The radius of those discs follows a

Gaussian distribution to represent the polydispersity of platelet size. During the simulation, the software sums the interactions on all the spheres to calculate the resulting displacement and torque applied to the assembly. The simulated engulfment phenomenon can thus take place locally, at the scale of the constitutive spheres instead of the whole platelet and thus is closer to the reality. The comparison of the modeling and experimental results in terms of structures, particle density packing and distribution of orientations are shown in Figure 3. The predicted compact structures (Figure 3b) are comparable to the experimental one (Figure 3a), with highly oriented particles in a thin wall. The same conclusion can be drawn for the sandwich structures (Figure 3e and3f), where the particles present a better alignment on the outer region of the wall than in the inner region. The use of reduced coordinates where the thickness of the wall is normalized by the periodicity λ of the structure (structural wavelength [START_REF] Deville | Ice-Templated Porous Alumina Structures[END_REF] ) allows the proper comparison between the experimental and predicted results.

The experimental and predicted particles packing (Figure 3c) are very similar: the density reaches a maximum value of 0.45 (0.41 for the experimental one) in the inner region of the wall.

The high aspect ratio and the particle size distribution lower the packing density, compared to that of random close packing of monodispersed spheres (known to be about 0.64). For the sandwich structure, the evolution of the experimental and predicted density is again similar (Figure 3g). The density appears higher in the border and reaches a value of 0.45, similar to the compact structure while the density in the inner region falls to 0.25 (0.35 and 0.29 respectively for the actual structure). Both structures present approximately the same overall density (0.32).

The dispersion of particle orientations with respect to the wall direction is plotted in Figure 3d and Figure 3h, represented by their mean orientation and the full width at half maximum (FHWM) of their cumulative distribution. In the compact structure (Figure 3d), the mean orientation corresponds to that of the wall (mean angle of 0°), for both the model and the experiment. The concentration of the particle during the freezing does not induce any tilt of the particles. The FWHM is constant in the wall, and the value is slightly smaller in the model (10°) than in the experiment (15°). The particles are slightly more aligned in the model than in the experiment and therefore the density and alignment are also slightly overestimated. In the sandwich structure (Figure 3h), the FWHM varies from 10° in the outer region to 20° in the inner region, revealing the misalignment of the particles in the inner region. We can now analyze through a parametric study the resulting structure as a function of the experimental conditions. The predicted phase diagram is shown in Figure 4. This diagram is calculated using simulation, as a function of particle size and interface velocity, the two main experimental parameters that can be adjusted to control the resulting microstructure.

Encapsulation is defined as the situation where 30% of the particles initially present have been encapsulated by the moving solidification front. The selection of this threshold of particle fraction as a criterion for encapsulation was made by looking at the fraction of engulfed particles at the critical velocities determined experimentally. To determine experimentally the critical velocity values, we froze the same suspension at different cooling rates and observed the resulting microstructure. The critical velocities values were determined when nearly all the particles did not rearrange with the front, in which case a lamellar structures pore/wall was not obtained anymore. Those structures are obtained at the same ice front velocity (above 40 µm/s)

for the entire set of initial particle fractions (which confirmed this value as an intrinsic property of the particles) except for the highest solid loading (0.22). At this point the concentration is close to the percolation threshold (estimated at 0.215, see Experimental section and references [START_REF] Lu | Influence of Aspect Ratio on Barrier Properties of Polymer-Clay Nanocomposites[END_REF][START_REF] Stanley | Scaling, Universality, and Renormalization: Three Pillars of Modern Critical Phenomena[END_REF] for more details). The transition between sandwich and compact structures occurs at a higher ice front velocity as the solid loading increases, as higher solid loadings impinge the movement of the particles. The percolating network of platelets restricts and ultimately suppresses particles rearrangement during the compaction by the solidification front.

The final densities are also represented in Figure 4 as an isodensity contour map. As described previously, the architecture of the wall reflects the particle orientation and thus the packing density. The packing density is calculated as the maximum particle density reached inside volume contained by the advancing solidification fronts. Area of high density corresponds to the compact structure. This phase diagram can be used as a predictive tool to adjust the properties of the final material, by predicting the density and structure of the particle packing as a function of the experimental conditions.

Dynamics: Self-Assembly Principles

Because the structures obtained after freezing are the result of the redistribution and concentration of particles by a solidification front, the observed differences arise from different interactions that take place in this peculiar system. In a first approximation, the process can be considered as equivalent to a simple powder compaction by two moving fronts. Nevertheless, particles can be encapsulated by the moving front, depending of the conditions (viscosity, velocity, existence of premelted films [START_REF] Garvin | Multiscale Modeling of Particle-Solidification Front Dynamics. Part II: Pushing-Engulfment Transition[END_REF][START_REF] Rempel | The Interaction Between a Particle and an Advancing Solidification Front[END_REF] ). The dynamic behavior of the system can be investigated by DEM (Figure 5). The fraction is not reaching a value of 1 as some particles are engulfed in the early stages of interface movement. (h) Time-lapse evolution of the density profile through the wall thickness, for both types of structure.

The time-lapse snapshots of the DEM results (Figure 5a to 5e) and the corresponding density profiles (Figure 5h) illustrate how the alignment is initiated in the outer region and then progressively propagates towards the inner region. Particles with the same color belong to the same percolating network. The criterion to identify the different regions is a simple pixelgrowing algorithm, available in the image analysis software used (see Methods). A different RGB color is then attributed to each percolating network of particles. The evolution of the system follows three stages (Figure 5g). Because the interface moves slowly, very few or no particle are engulfed during the first moments of growth (stage 1), they are just locally aligned and densely packed (Figure 5a and5b). Some are then engulfed (Figure 5c) as the interface keeps moving. The layer of aligned particles is still pushed and the concentration of particles in the inner region of the system starts to increase (Figure 5h). Percolating networks grow rapidly (stage 2). It starts to act against the displacement and rotation of particles. The pressure exerted by the moving interface is eventually not strong enough to overcome the counter pressure exerted by the percolating network of particles (stage 3); the system is ultimately jammed in a configuration where particles are aligned in the outer region and in the inner region (compact structure) or not (sandwich structure).

The evolution of the fraction of particles encapsulated in the ice is plotted in Figure 5f, for two initial concentrations (10 vol.% and 18 vol.%) and three different ice front velocities (15, 25 and 40 µm/s). For the 18 vol.% system, the density evolutions present similar trajectories at three different velocities (15, 25 and 40 µm/s), even if the final densities differ. The evolution is similar in a more dilute system (10 vol.%). An increase of either the volume fraction of particles or the interface velocity results in more encapsulation of particles by the moving interface.

Percolation arguments are not enough to predict the type of structure obtained. In both types of structure, complete percolation is obtained at approximately the same position of the moving interfaces (Figure 5g). Further local ordering of the particles is still possible after reaching complete percolation, as illustrated in Figure 5a to 5e (white arrows).

For large particles like the ones used here, the critical factor controlling the evolution of the system and the type of packing obtained is thus the encapsulation of the particles by the moving interface. With the same initial volume fraction of particles, an increase in interface velocity results in an increase of particle encapsulation. As a result, the concentration of the solid phase between the moving interfaces is lower. Particles have more freedom to reorient before the interface eventually encapsulates everything, leading to the compact structure. If all of them are repelled by the moving interface, the concentration is too high when the particle networks start to percolate. Particles do not have enough time to rearrange before total encapsulation, leading to the sandwich structure. The thinner the wall, the higher would be the shear stresses applied in the suspension for the same lateral growth velocity. With these conditions of solidification front velocity, particle size, and solid loading, the thickness of the wall nevertheless does not play an important role, since the shear forces in the vicinity of the solidification front induce ordering.

3.4 Self-Assembly of Cubic Facetted Particles Being able to orient platelet-like particles in porous or bulk materials is highly valuable, in particular for structural materials but also piezoelectric or thermal management materials.

However the self-assembly induced by ice-templating is not limited to this specific particle shape and might be extended to any type of facetted particle. To illustrate the fact that facetted particles can self-assemble even if they have an isotropic aspect ratio, the self-assembly of cubic particles has been explored with our simulation tool. Three different conditions (Figure 6) have been simulated, to predict the effect of the ice front velocity and the initial volume fraction. The obtained morphologies at two different ice front velocities are presented in Figure 6a and 6b.

Only one type of organization is obtained with all the simulation conditions: after solidification, all the cubes are well aligned in the wall's direction. This is confirmed by the density profile in Figure 6c, where the maximum density is at the center of the wall. However, this value changes with the applied conditions. The higher the initial density and the slower the compaction rate, the higher the final density. The packing density can reach a value as high as 0.80, slightly higher than the theoretical random packing of cubes found in the literature (0.74 for reference [START_REF] Fraige | Distinct Element Modelling of Cubic Particle Packing and Flow[END_REF] , 0.78 for reference [START_REF] Li | Maximum Packing Densities of Basic 3D Objects[END_REF] , both using different model type). The nearly perfect stacking in one direction (the direction of the wall thickness) can explain this slight discrepancy. The alignment of cubes is similar in all the conditions tested and the image analysis revealed nearly only the edges of the cube at 0° and 90° (Figure 6d). The cubes are then nearly all perfectly stacked in the thickness of the wall. Those three conditions reveal the potential of this model to easily determine the best conditions to obtain dense packing of cubic particles or any others shaped particles of interest.

Conclusions and Perspectives

Using the growth of ice crystals as a driving force for the self-assembly of large, facetted particles is an appealing alternative to the current evaporation or sedimentation strategies. A key conclusion of this work is that a high aspect ratio is not required for ice growth induced selfassembly, in contrast to the sequential deposition methods [START_REF] Tang | Nanostructured Artificial Nacre[END_REF][START_REF] Walther | Large-Area, Lightweight and Thick Biomimetic Composites with Superior Material Properties via Fast, Economic, and Green Pathways[END_REF] . The steric interaction between the moving interface and the particle is highly localized; working with facetted particles is therefore the only morphological requirement to obtain alignment. The methodology developed here can easily be generalized to other systems, in particular by taking into account different models of interaction potentials for smaller particles where gravity is not the controlling parameter.

Although the particle alignment is not perfect, in comparison to superlattices obtained by sedimentation for instance, the benefits on the functional properties have been demonstrated here for thermal properties. The possibility to align particles in the bulk (centimeter sized samples)

and in short times (minutes), holding the promise of novel crystalline materials with appealing functional properties, make it worth further research efforts.

Figure 1 .

 1 Figure 1. Comparison between the modeling initial state with 700 platelets and the holo-

Figure 2 .

 2 Figure 2. Improvement in thermal properties resulting from the control of the orientation of

Figure 3 .

 3 Figure 3. Comparison and characteristics of particle packing of the two types of architectures in

Figure 4 .

 4 Figure 4. Phase diagram of the possible anisotropic particle assemblies. sandwich structure,

Figure 5 .

 5 Figure 5. Dynamic evolution of particle organization and packing density. (a-e) Snapshots of the

Figure 6 .

 6 Figure 6. Ice growth induced self-assembly of cubic particles. (a) and (b) Final architectures

We thank Loic Courtois and Michel Perez for introducing us to the LAMMPS package. We thank Peter Cloetens from the European Synchrotron Radiation Facility for helping us to carry out the holo-tomography experiment.

AUTHOR INFORMATION

Corresponding Author

*E-mail: sylvain.deville@saint-gobain.com

Funding Sources

We acknowledge the financial support of the ANRT (Association Nationale Recherche Technologie) and Saint-Gobain through a CIFRE fellowship, convention #808/2010. ACKNOWLEDGMENTS