Stefan Lessmann

Kristof Coussement

Koen W De Bock

Johannes Haupt

Targeting customers for profit: An ensemble learning

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P Girel

A Clabaut

M Tuel

A Besson

A Chaumonnot

P Cabiac

C Sautet
email: sautet@ucla.edu

Michel

R Réocreux

É Girel

P Clabaut

A Tuel

M Besson

A Cabiac

P Sautet

Thomas Young

Reactivity of shape-controlled crystals and metadynamics simulations locate the weak spots of alumina in water

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T he kinetic stability of solids in water is governed by their reactivity at the interface. Being able to understand and control their surface stability and desired properties is therefore at the heart of a variety of research fields: kinetics of drug release [START_REF] Sato | Dissolution mechanism of diclofenac sodium from wax matrix granules[END_REF] , corrosion of metals and alloys 2 , lithium batteries [START_REF] Chen | Interfacial reactions in lithium batteries[END_REF] , geochemistry [START_REF] Fischer | Variability of crystal surface reactivity: what do we know?[END_REF] with in particular the re-equilibration of solid phases in presence of a liquid [START_REF] Putnis | The mechanism of reequilibration of solids in the presence of a fluid phase[END_REF] , water treatment [START_REF] Pirkanniemi | Heterogeneous water phase catalysis as an environmental application: a review[END_REF] , heterogeneous catalysis [START_REF] Chheda | Liquid-phase catalytic processing of biomass-derived oxygenated hydrocarbons to fuels and chemicals[END_REF][START_REF] Sievers | Phenomena affecting catalytic reactions at solid-liquid interfaces[END_REF] , from the preparation [START_REF] Skorina | Aqueous alteration of potassium-bearing aluminosilicate minerals: from mechanism to processing[END_REF][START_REF] Chen | Successive interfacial reaction-directed synthesis of CeO 2 @Au@CeO 2 -MnO 2 environmental catalyst with sandwich hollow structure[END_REF] , the utilization to the degradation of the catalyst [START_REF] Zhang | On the water structure at hydrophobic interfaces and the roles of water on transition-metal catalyzed reactions: a short review[END_REF][START_REF] Ravenelle | Structural changes of γ-Al 2 O 3 -supported catalysts in hot liquid water[END_REF] , etc. Several parameters have been identified as key in all these fields: the solid phase (which polymorph) [START_REF] Hilfiker | Polymorphism: In the Pharmaceutical Industry[END_REF] , the nature of the surface exposed (kink, rugosity) [START_REF] Fischer | Variability of crystal surface reactivity: what do we know?[END_REF] , and the species in solutions (additives, ions, pH) [START_REF] Siegfried | Elucidating the effect of additives on the growth and stability of Cu 2 O surfaces via shape transformation of pre-grown crystals[END_REF][START_REF] Pedreira-Segade | Effects of salinity on the adsorption of nucleotides onto phyllosilicates[END_REF][START_REF] Abi Aad | Chemical weathering of alumina in aqueous suspension at ambient pressure: a mechanistic study[END_REF] .

For instance, alumina is an oxide that is used in catalysis as a support for metallic nanoparticles [START_REF] Busca | Structural, surface, and catalytic properties of aluminas[END_REF] . Its γ-allotrope (γ-Al 2 O 3 ) in particular has remarkable properties as a support, long proven in the development of gas phase transformations [START_REF] Trueba | γ-alumina as a support for catalysts: a review of fundamental aspects[END_REF][START_REF] Raybaud | From γ-alumina to supported platinum nanoclusters in reforming conditions: 10 years of DFT modeling and beyond[END_REF][START_REF] Busca | The surface of transitional aluminas: a critical review[END_REF][START_REF] Mager-Maury | Platinum nanoclusters stabilized on γ-alumina by chlorine used as a capping surface ligand: a density functional theory study[END_REF] . However, water has detrimental effects on γ-Al 2 O 3 , either as a liquid [START_REF] Ravenelle | Structural changes of γ-Al 2 O 3 -supported catalysts in hot liquid water[END_REF] or even as steam [START_REF] Sakwa-Novak | Steam induced structural changes of a poly(ethylenimine) impregnated γ-alumina sorbent for CO 2 extraction from ambient air[END_REF] . While its polymorph α-Al 2 O 3 is stable, γ-Al 2 O 3 indeed transforms into various sorts of bulk hydroxides (AlO x H y ) thereby seriously damaging the catalyst (decrease of surface area, sintering and encapsulation of catalytic particles) [START_REF] Lefèvre | Hydration of γalumina in water and its effects on surface reactivity[END_REF][START_REF] Carrier | Transformations of γalumina in aqueous suspensions 1. Alumine chemical weathering as a function of pH[END_REF][START_REF] Jongerius | Stability of Pt/γ-Al2O3 catalysts in lignin and lignin model compound solutions under liquid phase reforming reaction conditions[END_REF] . Albeit not fully described at the atomic scale yet, the decomposition of γ-Al 2 O 3 was shown to proceed, at the macroscopic scale, through a sequential mechanism involving first dissolution of Al atoms, and then precipitation thereof into the undesired hydroxides [START_REF] Abi Aad | Chemical weathering of alumina in aqueous suspension at ambient pressure: a mechanistic study[END_REF][START_REF] Carrier | Transformations of γalumina in aqueous suspensions 1. Alumine chemical weathering as a function of pH[END_REF] . These structural changes can be retarded by tuning the surface chemical composition: silica deposition [START_REF] Liu | Silica deposition as an approach for improving the hydrothermal stability of an alumina support during glycerol aqueous phase reforming[END_REF] , presence of metallic nanoparticles [START_REF] Ravenelle | Structural changes of γ-Al 2 O 3 -supported catalysts in hot liquid water[END_REF] , or impregnation with metal ions [START_REF] Abi Aad | Inhibition by inorganic dopants of γ-Al2O3 chemical weathering in hydrothermal conditions: identification of reactive sites and influence in Fischer-Tropsch synthesis[END_REF] . They are also impacted by the content of the solution: pH [START_REF] Carrier | Transformations of γalumina in aqueous suspensions 1. Alumine chemical weathering as a function of pH[END_REF] but also presence of polyols [START_REF] Ravenelle | Stability of Pt/γ-Al2O3 catalysts in model biomass solutions[END_REF] or polyphenols [START_REF] Jongerius | Stability of Pt/γ-Al2O3 catalysts in lignin and lignin model compound solutions under liquid phase reforming reaction conditions[END_REF] . The mechanism of action of these additives is believed to lie in their chemisorption on the surface that would make γ-Al 2 O 3 water-resistant [START_REF] Ravenelle | Stability of Pt/γ-Al2O3 catalysts in model biomass solutions[END_REF][START_REF] Copeland | Surface interactions of C2 and C3 polyols with γ-Al2O3 and the role of coadsorbed water[END_REF] . However little is known on which exposed facet(s) and what site(s) need to be particularly targeted for protection. The optimization of the structure of inhibitors is therefore a challenging task since the exact mechanism of the decomposition of γ-Al 2 O 3 in liquid water remains unknown. Whilst the sub-nanometric description of γ-Al 2 O 3 is difficult to reach experimentally, molecular simulations have allowed for the development of insightful atomistic models for amorphous [START_REF] Adiga | Atomistic simulations of amorphous alumina surfaces[END_REF] and nano-crystalline 31 γ-Al 2 O 3 . The model proposed by Digne et al. [START_REF] Krokidis | Theoretical study of the dehydration process of boehmite to γ-alumina[END_REF] , which was obtained from density functional theory (DFT) calculations, has proven to depict properly the reactivity of the surface under various realistic gas phase conditions [START_REF] Raybaud | From γ-alumina to supported platinum nanoclusters in reforming conditions: 10 years of DFT modeling and beyond[END_REF] . It is only recently that Ngouana-Wakou et al. [START_REF] Ngouana-Wakou | An atomistic description of the γ-alumina/water interface revealed by ab initio molecular dynamics[END_REF] and Réocreux et al. [START_REF] Réocreux | Structuration and dynamics of interfacial liquid water at hydrated γ-alumina determined by ab initio molecular simulations: implications for nanoparticle stability[END_REF] have explored the interaction of γ-Al 2 O 3 with liquid water, performing ab initio molecular dynamics (AIMD) simulations. Although these simulations give insights on the relative affinity of water for the different facets and the structuration and dynamics of the liquid at the interface, they cannot capture the details of the decomposition mechanism. Al-O bond formation and scissions are indeed rare events on the time scale achievable today with AIMD. To overcome this limitation and force the system to react along a chosen reaction coordinate, biased AIMD simulations are required. Ab initio metadynamics is an example of such methods [START_REF] Laio | Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science[END_REF] , and has been commonly used to model the reactivity between molecules in homogeneous media [START_REF] Michel | Free energy ab initio metadynamics: a new tool for the theoretical study of organometallic reactivity? example of the C-C and C-H reductive eliminations from platinum(IV) complexes[END_REF][START_REF] Blumberger | Formamide hydrolysis in alkaline aqueous solution: insight from ab initio metadynamics calculations[END_REF] or between isolated molecules and a solid surface [START_REF] Moors | Molecular dynamics kinetic study on the zeolite-catalyzed benzene methylation in ZSM-5[END_REF][START_REF] Muñoz-Santiburcio | Solvation-Induced changes in the mechanism of alcohol oxidation at gold/titania nanocatalysts in the aqueous phase versus gas phase[END_REF] . Although common using classical force field for crystal growth and dissolution of molecular and ionic crystals [START_REF] Stack | Accurate rates of the complex mechanisms for growth and dissolution of minerals using a combination of rare-event theories[END_REF][START_REF] Salvalaglio | Uncovering molecular details of urea crystal growth in the presence of additives[END_REF] , metadynamics has never been used to describe a reactive interface involving bonds with a partial covalent character (typically here Al-O and O-H bonds) hence requiring an ab initio description.

Here, we combine experiments and theory to provide the atomistic mechanism for the early-stage decomposition of γ-Al 2 O 3 in liquid water. We experimentally demonstrate that the decomposition is initiated at the (110) facet by exposing four samples of various shapes of nanoparticles to a hydrothermal treatment in the presence of aqueous solution of inhibitors (xylitol and sorbitol) with varying concentrations. Performing ab initio metadynamics simulations, we probe the reactivity of the (110)/water interface and identify specific aluminum tetrahedral centers that are particularly reactive with water. We show that interfacial water molecules are involved in the mechanism, both as reactants for the hydration of aluminum and as intermediates for the proton reshuffling required by the decomposition mechanism. We show that the substitution of chemisorbed water molecules on the surface with xylitol locally renders the surface more hydrophobic and pushes water molecules away from the water-sensitive Al sites.

Results

Identification of the facet whence the decomposition initiates. γ-Al 2 O 3 particles mainly expose three facets commonly referred to with their set of Miller indices: the predominant and hydrophilic (110) facet, the less hydrophilic (100) facet, and the (111) facet (see Fig. 1a). In order to identify the facet(s) involved in the decomposition of γ-Al 2 O 3 , we have prepared four samples containing particles of different shapes (see Fig. 1g-j). These four samples therefore show four distinct proportions of facet areas, which have been quantified using X-ray diffraction (XRD) (see Supplementary Note 1). We have had them undergo hydrothermal treatment (i.e., 200 °C, 2 h, 14 bar autogeneous pressure) using various aqueous solutions of sorbitol (represented in Fig. 1b), a known inhibitor, and xylitol (represented in Fig. 1c), a shorter sugar polyol. We have observed a very strong alumina stabilization in the presence of both sorbitol or xylitol, suggesting that the minimal -(CHOH) 5sequence, common to those two polyols, is essential to protect alumina from water. This is consistent with the work by Ravenelle et al. [START_REF] Ravenelle | Stability of Pt/γ-Al2O3 catalysts in model biomass solutions[END_REF] showing that sorbitol is a good inhibitor while glycerol (C3polyol) is not as efficient. To go beyond this qualitative statement, we have determined for each sample the minimum surface coverage of polyol at which the decomposition of alumina gets inhibited, that is no hydroxides can be detected by XRD after hydrothermal treatment (see Supplementary Note 2). This quantity, referred to as inhibiting coverage, is reached for concentrations of 4 g L -1 of polyols for 2 g of alumina in 50 mL of solution and varies from 0.15 to 0.30 nm -2 for xylitol, and from 0.20 to 0.35 nm -2 for sorbitol, depending on the shape of the nanoparticles (see Supplementary Table 4). This strong variation of the inhibiting coverage with the distribution of facet surface areas (up to a factor of two in the case of xylitol) indicates that each facet does not interact equally with the two polyols.

In the case of a specific adsorption on one facet only, the sodetermined inhibiting coverage increases linearly with the fractional surface area of this facet with a zero-intercept (see Supplementary Note 4). As shown in Fig. 1d-f, this is only with the fractional surface area of the hydrophilic (110) facet that the inhibiting coverage of both sorbitol and xylitol correlates with a zero-intercept function. We cannot establish such correlations with the other fractional surface areas. Following the same kind of reasoning, we show in Supplementary Note 5 that edges and kinks are unlikely to be involved as major active sites for hydrolysis. Therefore, the adsorption of sorbitol or xylitol is specific to the (110) facet and allows for the total inhibition of the decomposition of γ-Al 2 O 3 in liquid water at similar partial coverage of 0.36 and 0.44 nm -2 of (110) facet for xylitol and sorbitol, respectively (slopes on Fig. 1d). As a corollary, we can infer that the (110) facet must exhibit sites responsible for the hydrolysis of γ-Al 2 O 3 and that the reactivity of these sites with water can be limited or even suppressed upon the adsorption of sorbitol or xylitol.

Identification of the atomic sites on the (110) facet whence the decomposition initiates. To gain atomistic insight and identify the sites involved in the decomposition of γ-Al 2 O 3 on the (110) facet, we have performed ab initio simulations using our recently developed model for γ-Al 2 O 3 /water interfaces [START_REF] Réocreux | Structuration and dynamics of interfacial liquid water at hydrated γ-alumina determined by ab initio molecular simulations: implications for nanoparticle stability[END_REF] . The primitive cell of the model of the γ-Al 2 O 3 (110) surface shows four different surface Al sites: two octahedral and two tetrahedral sites, referred to as Al (1) and Al (2) for the former and Al α and Al β for the latter (see Fig. 2a,b). This surface is fully hydrated with five chemisorbed water fragments, the oxygen atoms of which are represented in blue in Fig. 2a,b. Some of these water molecules are dissociated, generating hydroxyl surface groups. Repeating the surface unit cell in the x and y directions, the resulting p(2 × 2) slab is surmounted by a 20 Å thick layer of liquid water that is not represented here for clarity. The iso-electric point of alumina being close to 8, we consider pure neutral water. [START_REF] Sprycha | Electrical double layer at alumina/electrolyte interface[END_REF][START_REF] Kosmulski | The pH-dependent surface charging and points of zero charge[END_REF] Since the decomposition of γ-Al 2 O 3 transforms tetrahedral Al sites into octahedral Al centers, we have focused on the tetrahedral sites, Al α and Al β , and their reactivity with water (see Fig. 2a). Both of them have a coordination number to alumina oxygen atoms (CN a ) of three and a coordination number to water oxygen atoms (CN w ) of one. Performing ab initio metadynamics, we have made each tetrahedral Al center specifically react along these two variables (see details in Methods). The statistical analysis of the variations of CN w and CN a allows for the construction of free energy landscapes (like the one given in Fig. 2c), the local depth of which assesses for the stability of the intermediates, transition states and products encountered along the course of the simulation (see details in Supplementary Note 6). Obtaining this mechanistic information is a key achievement in the quest of a better understanding of reactive interfaces and kinetic stability of solids in water. In the case of Al α , the free energy landscape mainly shows one deep minimum at (CN a ,CN w ) = (3,1), that is the initial structure (see Supplementary Fig. 6). Even within a span of 200 kJ mol -1 , no transition state to escape that deep well towards other minima has been identified. This suggests that Al α is very unlikely to react with liquid water. Conversely, the free energy landscape for Al β shows, over a span of 180 kJ mol -1 , a variety of minima spread over the nodes of a well-defined checkered pattern and associated with a decreased number of bonds to alumina surface oxygen atoms and increased number with water oxygens (see Fig. 2c). Al β therefore progressively detaches from the oxygen network of γ-Al 2 O 3 and is hydrated with the surrounding water molecules. A more detailed look at the free energy surface indicates that this hydration is sequential and follows an addition/elimination mechanism. It is only when Al β has reached a total coordination number of 5 that an Al β -O-Al bond cleavage occurs. Noticeably, five-coordinated species appear to be key intermediates in the decomposition of alumina as in the water-induced de-alumination of zeolites [START_REF] Silaghi | Dealumination mechanisms of zeolites and extra-framework aluminum confinement[END_REF] . This holds true until (CN a ,CN w ) = (1,4) where Al β readily guests a water molecule to achieve an octahedral structure with (CN a , CN w ) = (1,5). This last structure obtained from the simulation is represented in Fig. 2e and shows how Al β has been extracted from its initial position. Among the water molecules in the first coordination sphere, three of them were initially present on the surface as chemisorbed water molecules and the two others were physisorbed water molecules. Proton transfers are not included in the general reaction coordinates we designed. Nevertheless, the inspection of the trajectory shows that these early-stage steps of the hydration are accompanied with the deprotonation of some of the coordinated water molecules and a widespread reshuffling of surface protons over about 1 nm (compare Fig. 2a,d). The amphoteric character of the hydrated material allows γ-Al 2 O 3 to offer the proper local protonation level for the intermediates involved in its own decomposition into AlO x H y . In this respect, the trajectory reveals that physisorbed water molecules are involved, via a Grotthus mechanism, in this redistribution of surface protons. Physisorbed water molecules do therefore not only react but also help accommodating the protonation state of the surface to guest the final octahedral intermediate. This is particularly striking for the water fragments bound to the octahedral Al (1) and Al (2) , which need to be deprotonated to coordinate the fleeing tetrahedral Al β . This study highlights the key role of water as a reactant and as a solvent in the stability of an oxide and pre-figures the role of the pH in the interface transformation. Ab initio metadynamics can hence provide a complete atomistic picture of the alteration mechanism of an iono-covalent solid in contact with a reactive solvent.

Simulation with chemisorbed xylitol. We have performed the same simulation substituting the water fragments bound to the ). f Projected free energy profile with the structure of each intermediate and the corresponding (CN a ,CN w ). Yellow and white balls represent aluminum and hydrogen atoms, respectively. The color red is used for alumina oxygen atoms and the associated CN a . The color blue is used for water oxygen atoms and the associated CN w octahedral Al (1) and Al (2) , which are in close vicinity to the watersensitive tetrahedral Al β , with xylitol. The choice of the adsorption geometry (Fig. 3b and other views in Supplementary Fig. 7) is globally in agreement with earlier studies on polyol adsorption on alumina (Supplementary Note 8) [START_REF] Copeland | Surface interactions of C2 and C3 polyols with γ-Al2O3 and the role of coadsorbed water[END_REF] . The reactivity of Al β is described using again the coordination number of Al β to alumina oxygen atoms (CN a ) as a variable. Since now, oxygen atoms are also found in xylitol, we considered, as a second variable, the coordination number to all other oxygen atoms that are external to alumina (oxygen atoms of water molecules and polyol) and referred to as CN w+p . The resulting free energy landscape in the presence of xylitol (Fig. 3c) is profoundly modified compared to the uncoated case (Fig. 2c). Despite the exploration of a 200 kJ mol -1 energy span, the sampled (CN a ,CN w+p ) space is reduced, meaning that Al β is more constrained near its initial geometry at (CN a ,CN w+p ) = (3,1). A detailed look at the free energy landscape shows nevertheless that Al β is able to react with some surrounding oxygen atoms (CN w+p goes up to 4). The exact mechanism is however very different from that described above. To better understand why Al β reacts with xylitol rather than water, we have performed a 25 ps long regular ab initio molecular dynamics simulation of the interface with xylitol adsorbed and compared to our recently published study work on the γ-Al 2 O 3 (110)/water interface [START_REF] Réocreux | Structuration and dynamics of interfacial liquid water at hydrated γ-alumina determined by ab initio molecular simulations: implications for nanoparticle stability[END_REF] . The volume visited by physisorbed water molecules around Al β is greatly impacted by the presence of xylitol as shown in Fig. 3a,b. This is further confirmed by the radial distribution functions of Al β with physisorbed water molecules: the probabilities of finding physisorbed water molecules in the second coordination shell are indeed reduced and shifted to larger distances (Supplementary Fig. 8). This clearly evidences an important steric hindrance induced by xylitol, which is at the origin of the inhibition.

Once Al β sees its coordination number to alumina oxygen atoms diminished by one unit, it directly coordinates to two alcohol groups because of the constrained adsorption mode of xylitol (CN w+p increases by two units). The resulting squarebased pyramidal structure readily captures a water physisorbed molecule to gain a saturated octahedral geometry, reaching (CN a , CN w+p ) = (2,4). Two other adsorption modes of xylitol, which substitute the chemisorbed water molecules involved in the decomposition mechanism, have been tested. They both turn out to be able to inhibit the early stages of the decomposition, proving that the inhibition shown here does not depend on the orientation of the tridentate adsorbate, in spite of mechanistic differences as discussed in Supplementary Note 9.

Noticeably, the inhibitor does not directly interact with the weak spot, but with a neighboring site, thereby modifying the interfacial structure of the liquid. It substitutes the water molecules that are 110)/water interface with the iso-surface of the average occupation volume of xylitol in ochre, and the average occupation volume of water in gray. The iso-surfaces were computed from an extra regular ab initio molecular dynamics simulation. More details can be found in Supplementary Note 8. c Free energy surface obtained from the metadynamics simulation on Al β in presence of xylitol. CN a is the coordination number of Al β to alumina oxygen atoms. CN w+p is the coordination number of Al β to water and polyols oxygens. Yellow and white balls represent aluminum and hydrogen atoms, respectively. The color red is used for alumina oxygen atoms and the associated CN a . The color blue is used for water oxygen atoms and the associated CN w involved in the first hydration steps and prevents the necessary proton reshuffling to generate AlO x H y and therefore provides a strong stabilization of the surface of alumina. This is attributed to the γ-pentanetriol backbone of xylitol, a structural feature shared with sorbitol (a known good inhibitor) but not with glycerol (a known weak inhibitor) [START_REF] Ravenelle | Stability of Pt/γ-Al2O3 catalysts in model biomass solutions[END_REF] . Our study therefore opens the road to a rational design of the structure of coating agents able to prevent γ-Al 2 O 3 from decomposing in water.

In conclusion, the combined experimental and theoretical study presented here provides an atomistic mechanistic picture of the initial steps of the decomposition of γ-Al 2 O 3 in water. The weak spot is a tetrahedral surface Al of the (110) surface. It undergoes successive addition of water/scission of Al-O, yielding to AlO x H y . This process is accompanied by proton reshuffling. The chemisorption of a polyol on a neighbor site inhibits this hydrolysis by replacing the water molecules that initiate the process and by limiting the access of water to this weak spot. Noticeably, the weak spot of this oxide is not located at kink or edges but at the heart of a given facet. This understanding opens the road to further improvement of inhibitors. Since γ-Al 2 O 3 is an iono-covalent oxide and water potentially reacts during the process and may dissociate into (OH -, H + ), gaining such an atomistic understanding is a rather challenging task, especially regarding computational chemistry where the use of biased ab initio molecular dynamic is necessary. The present achievement thus constitutes an unprecedented milestone in the understanding of solid/liquid interface transformation. The approach that we propose here could be insightfully applied to various other relevant systems in electrochemistry, geochemistry or material science, where the reactivity of the solid with water and possibly other liquids plays a crucial role.

Methods

Alumina materials syntheses. Alumina C (for Commercial) was obtained by calcination of commercial boehmite (Sasol PURAL SB3) at 600 °C for 4 h. Alumina F (for Fibers) was synthesized by precipitation of aluminum nitrate (Al (NO 3 ) 3 •9H 2 O, 0.1 mol L -1 ) in an aqueous medium. The pH was adjusted to an initial value of 8 by addition of sodium hydroxide (NaOH, 1 mol L -1 ) and the resulting suspension was aged at 95 °C for 1 week. The final pH value of the suspension was 4.5. The solid was recovered by centrifugation and washed three times with water. This synthesis was adapted from the method described by Chiche et al. [START_REF] Chiche | Accurate determination of oxide nanoparticle size and shape based on X-Ray powder pattern simulation: application to boehmite AlOOH[END_REF] and Jolivet et al. [START_REF] Jolivet | Size tailoring of oxide nanoparticles by precipitation in aqueous medium. A semi-quantitative modelling[END_REF] Alumina P (for Plates) and R (for Rods) were obtained by an hydrothermal treatment of alumina C in water (alumina P) or in acidified water with acetic acid (alumina R). Typically, 15 g of alumina C were dispersed in 100 mL of water or acidified water (pH = 2). The mixture was heated at 200 °C for 10 h under mechanical stirring and autogeneous pressure in a stainless steel autoclave. During this step, alumina was dissolved and boehmite precipitation occurred. Boehmite nanoparticles properties (size, morphology, texture, etc.) are depending on the experimental conditions (pH, temperature, concentrations…) [START_REF] Jolivet | Size tailoring of oxide nanoparticles by precipitation in aqueous medium. A semi-quantitative modelling[END_REF][START_REF] He | Different nanostructures of boehmite fabricated by hydrothermal process: effects of pH and anions[END_REF] . In an acidic medium, boehmite precipitates as rod-like nanoparticles. In neutral medium, nanoparticles adopt a plate-like morphology. After cooling at room temperature (RT), the solid phase was recovered by centrifugation, dried at 100 °C overnight and calcinated at 600 °C for 4 h. Material characterization. XRD analyses were performed on powders with a Bragg'Brentano diffractometer (PANalytical X'Pert PRO MDP) using Cu Kα radiation. Diffractograms were obtained from 2θ = 4-74°with a step of 0.033°and 5 s per step. Textural properties of aluminas were determined by N 2 sorption studies at 77 K using a Micromeritics ASAP 2000 instrument. The BET method was applied to determine the specific surface area. Transmission electron microscopy (TEM) images were obtained on a JEOL 2010 LaB 6 microscope operating at 200 kV. A dispersion of the sample crushed in ethanol was deposited on standard holey carbon-covered copper TEM grids.

Adsorption experiments. Polyol adsorption isotherms were performed on three alumina materials exhibiting different morphologies in a 100 mL stainless steel autoclave equipped with a mechanical stirring rod (Top Industrie). Aqueous solutions of xylitol and sorbitol (0.5 g L -1 , 1 gL -1 , 2 g L -1 , 4 g L -1 , 6 g L -1 , and 8 g L -1 ) prepared using commercial polyols (Sigma Aldrich) and deionized water. Typically, 2 g of alumina were dispersed in 50 mL of an aqueous solution of polyol. After 2 h at 200 °C under autogeneous pressure (14 bar) and vigorous stirring, a sample of the liquid phase was taken and the solid phase was recovered by centrifugation. Final concentration was determined by high-performance liquid chromatography (HPLC) analysis using a Shimadzu Rezex RXM-Monosaccharide Ca 2+ 8% column connected to a differential refraction detector (Shimadzu RID10A). The amount of polyol adsorbed was calculated from the difference between initial and final concentrations.

Atomistic model. The model of γ-Al 2 O 3 (110)/water interface was taken from our previous study on the characterization of interfacial water in contact with γ-Al 2 O 3 . [START_REF] Réocreux | Structuration and dynamics of interfacial liquid water at hydrated γ-alumina determined by ab initio molecular simulations: implications for nanoparticle stability[END_REF] This model was built using the surface model proposed by Digne et al. [START_REF] Digne | Hydroxyl groups on γ-alumina surfaces: a DFT study[END_REF] (and further improved by Wischert et al. [START_REF] Wischert | γ-alumina: the essential and unexpected role of water for the structure, stability, and reactivity of "defect" sites[END_REF] ) and has been used for about 15 years to rationalize efficiently experimental data. [START_REF] Raybaud | From γ-alumina to supported platinum nanoclusters in reforming conditions: 10 years of DFT modeling and beyond[END_REF] The simulation cell consists of a 10 Å thick 2 × 2 unit cell of γ-Al 2 O 3 (110), which is surmounted with a 20 Å thick water layer and another 10 Å thick layer of void to avoid spurious confinement effects [START_REF] Bellarosa | Diversity at the water-metal interface: metal, water thickness, and confinement effects[END_REF] .

Molecular simulations. All ab initio molecular dynamics simulations (AIMD) reported here were performed using density functional theory (DFT) with the Gaussian and Plane Wave combined approach as implemented in CP2K/Quickstep [START_REF] Vandevondele | Quickstep: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach[END_REF][START_REF] Vandevondele | Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases[END_REF][START_REF] Lippert | A hybrid Gaussian and plane wave density functional scheme[END_REF][START_REF] Hutter | cp2k: atomistic simulations of condensed matter systems[END_REF] using the same model and set of parameters as in our previous work on the γ-Al 2 O 3 (110)/water interface [START_REF] Réocreux | Structuration and dynamics of interfacial liquid water at hydrated γ-alumina determined by ab initio molecular simulations: implications for nanoparticle stability[END_REF] . The electrons were treated using the exchange correlation PBE functional [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] with a Grimme D3 55 correction. Core electrons were described using the Goedecker-Teter-Hutter (GTH) pseudo-potentials [START_REF] Goedecker | Separable dual-space Gaussian pseudopotentails[END_REF][START_REF] Hartwigsen | Relativistic separable dual-space Gaussian pseudopotentials from H to Rn[END_REF][START_REF] Krack | Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals[END_REF] and the valence density was developed on a double-zeta DZVP basis set along with an auxiliary plane wave basis set with cutoff energy of 400 Ry.

During AIMD, nuclei were treated within the Born-Oppenheimer approximation with a time step of 0.5 fs for the integration of the equations of motion. The temperature of the simulation was maintained at 330 K using the Canonical Sampling through Velocity Rescaling (CSVR) thermostat coupled to the system with a time constant of 100 fs [START_REF] Bussi | Canonical sampling through velocity rescaling[END_REF] . All the systems presented here were thermalized for at least 5 ps before production of about 30 ps for statistical analysis.

For the well-tempered ab initio metadynamics simulations [START_REF] Barducci | Well-tempered metadynamics: a smoothly converging and tunable free-energy method[END_REF] , Gaussian hills of 0.04 width and 3.3 kJ mol -1 initial height were added in a two-dimensional set of collective variables, described by coordination numbers (CN) as defined in Plumed 2.0 61 . For each collective variable, the chosen CN gives the average number on a set of oxygen atoms coordinated to the probed Al atom. We used two different sets. In the first one (CN a ), the oxygen atoms belong to the surface structure of dry alumina. The second one includes all the other oxygen atoms of the simulations (CN w or CN w+p , with w for water oxygens and p for polyol oxygens, respectively). The error associated with this procedure is lower than 2 kJ mol -1 . Further details are given in Supplementary Notes 6-9.

Fig. 1

 1 Fig. 1 Implication of the (110) facet in the decomposition of γ-Al 2 O 3 . a General topology of a γ-Al 2 O 3 nanoparticle exhibiting three major facets: (110) in dark blue, (100) in light blue and (111) in gray. b, c Structures of two inhibitors: b, sorbitol (red) and c, xylitol (blue). d, e, f Comparisons between the inhibiting coverage (sorbitol in red, xylitol in blue) and the fraction of exposed (110) (d), (111) (e), and (100) (f) surface areas. The experimental data sets are fitted to the zero-intercept linear model derived in Supplementary Note 4. The fitted curves are represented as straight lines. A correlation could only be established in the case of the (110) surface (d) with slopes of 0.367 ± 0.009 and 0.443 ± 0.005 nm -2 for xylitol and sorbitol, respectively (R 2 > 0.99). Error bars are calculated from high-performance liquid chromatography (HPLC) analysis standard deviation (see Supplementary Note 3). g, h, i, j Transmission electronic microscopy images of the four differently shaped γ-Al 2 O 3 nanoparticles ordered in increasing (110) fractional area: plates (g), fibers (h), rods (i), and commercial γ-Al 2 O 3 (j)

Fig. 2

 2 Fig. 2 Exploration of the reactivity of tetrahedral Al β on γ-Al 2 O 3 (110) from ab initio metadynamics. a, b Structure of the initial surface with chemisorbed water molecules or fragments (the oxygen atoms of which are shown in blue) adsorbed on tetrahedral Al α and Al β and octahedral Al(1) and Al(2) . c Free energy surface obtained from the metadynamics simulation on Al β using the coordination numbers to alumina oxygen atoms (CN a ) and to water molecules and fragments (CN w ) as variables. The simulation starts from the point of coordinates (CN a ,CN w ) = (3,1). d, e Structure of the last intermediate obtained from the hydration of tetrahedral Al β with (CN a , CN w ) = (1,5). f Projected free energy profile with the structure of each intermediate and the corresponding (CN a ,CN w ). Yellow and white balls represent aluminum and hydrogen atoms, respectively. The color red is used for alumina oxygen atoms and the associated CN a . The color blue is used for water oxygen atoms and the associated CN w

Fig. 3

 3 Fig. 3 Inhibition of the decomposition of γ-Al 2 O 3 in the presence of chemisorbed xylitol. a γ-Al 2 O 3 (110)/water interface with the average occupation volume of water in gray. b Geometry of adsorbed xylitol at the γ-Al 2 O 3 (110)/water interface with the iso-surface of the average occupation volume of xylitol in ochre, and the average occupation volume of water in gray. The iso-surfaces were computed from an extra regular ab initio molecular dynamics simulation. More details can be found in Supplementary Note 8. c Free energy surface obtained from the metadynamics simulation on Al β in presence of xylitol. CN a is the coordination number of Al β to alumina oxygen atoms. CN w+p is the coordination number of Al β to water and polyols oxygens. Yellow and white balls represent aluminum and hydrogen atoms, respectively. The color red is used for alumina oxygen atoms and the associated CN a . The color blue is used for water oxygen atoms and the associated CN w

NATURE COMMUNICATIONS | (2019) 10:3139 | https://doi.org/10.1038/s41467-019-10981-9 | www.nature.com/naturecommunications

Acknowledgements

We are grateful to the Center Blaise Pascal and the Pôle Scientifique de Modélisation Numérique at the École Normale Supérieure de Lyon for HPC resources. We also thank also the SYSPROD project and AXELERA Pôle de Compétitivité for financial support (PSMN Data Center). This work was granted access to the HPC resources of IDRIS under the allocation 2017-A0010800609 made by GENCI.

Data Availability

The source data underlying Fig. 1d-f are available in SI. Raw data were generated at the PSMN and GENCI large-scale facilities. Derived data supporting the findings of this study are available as supplementary materials: a snapshot of each ab initio MD is provided as well as the grid-based data of the Free Energy Surface that are plotted in Figs. 2c and3c.

Author contributions

Additional information

Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467-019-10981-9.

Competing interests: The authors declare no competing interest.

Reprints and permission information is available online at http://npg.nature.com/ reprintsandpermissions/ Peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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F Gélébart

G Mériguet

V Peyre

E Dubois

R Perzynski

M Sarkar

J Riedl

G Demouchy

Inversion of thermodi↵usive properties of ionic colloidal dispersions in water-DMSO mixtures probed by forced Rayleigh scattering

Inversion of thermodiffusive properties of ionic colloidal dispersions in water-DMSO mixtures probed by forced

Rayleigh scattering

Introduction

When submitted to a gradient of temperature rT , ionic nanoparticles (NPs) dispersed in a polar solvent are subjected both to the Ludwig-Soret e↵ect [START_REF] Soret | Sur l'état d'équilibre que prend, au point de vue de sa concentration, une dissolution saline primitivement homogène, dont deux parties sont portées à des températures di↵érentes[END_REF], which induces a gradient of volume fraction r and a Seebeck e↵ect [START_REF] Putnam | Transport of nanoscale latex spheres in a temperature gradient[END_REF][START_REF] Goupil | Thermodynamics of thermoelectric phenomena and applications[END_REF], which induces an electric field E. This can be used for potential thermoelectric applications in terms of heat recovery [START_REF] Hu | Harvesting waste thermal energy using a carbon-nanotubebased thermo-electrochemical cell[END_REF][START_REF] Zinovyeva | Enhanced thermoelectric power in ionic liquids[END_REF][START_REF] Huang | Thermo-electric di↵usion of magnetic nanoparticles: alternative path toward future thermocell applications[END_REF][START_REF] Salez | Can charged colloidal particles increase the thermoelectric energy conversion eciency?[END_REF][START_REF] Dupont | Thermoelectrochemical cells for waste heat harvesting-progress and perspectives[END_REF][START_REF] Al-Masri | The electrochemistry and performance of cobalt-based redox couples for thermoelectrochemical cells[END_REF][START_REF] Salez | Thermoelectricity and thermod-i↵usion in magnetic nanofluids: Entropic analysis[END_REF]. In stationary conditions, both r and E are proportional to rT and the NPs migrate either towards the cold region or towards the hot region depending on the sign of their Soret coe cient S T , given (at high dilution) by r = S T rT . Their Seebeck coe cient S St e is given by E = S St e rT and it is connected to S T , through ŜNP , the Eastman entropy of transfer of the nanoparticles in the solvent 1 [START_REF] Putnam | Transport of nanoscale latex spheres in a temperature gradient[END_REF][START_REF] Würger | Transport in Charged Colloids Driven by Thermoelectricity[END_REF][START_REF] Majee | Collective thermoelectrophoresis of charged colloids[END_REF][START_REF] Majee | thermoélectrique dans les dispersions colloïdale[END_REF][15]. This single-particle contribution ŜNP characterizes the a nity of the ionic NPs with the polar solvent in which they are dispersed [START_REF] Würger | Transport in Charged Colloids Driven by Thermoelectricity[END_REF][15][START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF]. S T depends on the interparticle interaction (thus on the NP's concentration and that of counterions), but also on the nature of these counterions and on the nature of the solvent [START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF][START_REF] Filomeno | Ionic magnetic fluids in polar solvents with tuned counter-ions[END_REF][START_REF] Filomeno | Tuning the solid/liquid interface in ionic colloidal dispersions: Influence on their structure and ther-modi↵usive properties[END_REF]. 1 The entropy of transfer Ŝi of ionic species i is defined as in [START_REF] Agar | Single ion heat of transport in electrolyte solutions[END_REF] as Q ⇤ i /T with Q ⇤ i the heat of transport of ionic species i.

In the present study, we focus on two polar solvents with a very di↵erent structural organization, namely dimethyl sulfoxide (DMSO, H 3 C SO CH 3 ) and water. Water is a polar protic solvent strongly structured through a H-bond network [START_REF] Marcus | E↵ect of ions on the structure of water: Structure making and breaking[END_REF], while DMSO is a less organized, aprotic and polar organic solvent, with a lower dielectric permittivity " DMSO = 46 [START_REF] Plowas | Electrical conductivity in dimethyl sulfoxide plus potassium iodide solutions at di↵erent concentrations and temperatures[END_REF] than water at room temperature. Mixtures of water and DMSO are chosen for this study as they are miscible in any proportions in these conditions. Using perchlorate (ClO - 4 ) counterions, the same acidic magnetic nanoparticles can be dispersed in both solvents, with the same type of electrostatic stabilization giving stable magnetic ferrofluids [START_REF] Filomeno | Ionic magnetic fluids in polar solvents with tuned counter-ions[END_REF][START_REF] Filomeno | Tuning the solid/liquid interface in ionic colloidal dispersions: Influence on their structure and ther-modi↵usive properties[END_REF]. Here the strong electrostatic interparticle repulsion imparts the two kinds of colloidal dispersions with similar properties. However in the presence of a temperature gradient, the same maghemite NPs present a thermophilic behaviour in water (S T < 0) [START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Filomeno | Ionic magnetic fluids in polar solvents with tuned counter-ions[END_REF][START_REF] Filomeno | Tuning the solid/liquid interface in ionic colloidal dispersions: Influence on their structure and ther-modi↵usive properties[END_REF] while they present a thermophobic one (S T > 0) in DMSO [START_REF] Huang | Thermo-electric di↵usion of magnetic nanoparticles: alternative path toward future thermocell applications[END_REF][START_REF] Filomeno | Ionic magnetic fluids in polar solvents with tuned counter-ions[END_REF][START_REF] Filomeno | Tuning the solid/liquid interface in ionic colloidal dispersions: Influence on their structure and ther-modi↵usive properties[END_REF].

In order to follow progressively this change of ther-modi↵usive behaviour at room temperature, colloidal dispersions of maghemite NPs (9 nm in diameter) are dispersed in water and in DMSO at comparable [H + ] concentration (⇠ 102 mol L 1 ) with perchlorate counterions. Dispersions in water-DMSO mixtures are then prepared at various mole fractions of water x W , various NP vol-ume fraction and same [H + ]. The colloidal structure of the dispersions and the interparticle electrostatic repulsion are determined by Small Angle Neutron Scattering and the electrophoretic charge of the NPs is determined (at low volume fraction) by electrophoretic measurements and Dynamic Light Scattering (DLS). We present here a forced Rayleigh scattering (FRS) study of these dispersions.

The samples probed here with the di↵erent techniques (SANS, DLS, FRS) have the same ionic concentration [H + ] = 10 2 mole/L for all the x W solvent compositions studied.

After a presentation of the synthesis and charaterization of the probed dispersions and that of the FRS experiment, we show and discuss the results obtained for the mass di↵usion coe cient D m of the NPs and the Soret coe cient S T as a function of and x W . S T is then analyzed with the model presented in [START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF] in terms of thermophoretic and thermoelectric contributions.

2 Preparation and characterization of the colloidal dispersions

Solvent characteristics

Like water, DMSO is a polar molecular solvent. It is a green grade solvent with low toxicity used in pharmacological applications, recyclable and biodegradable [START_REF] Kiefer | Hydrogen bonding in mixtures of dimethyl sulfoxide and cosolvents[END_REF]. DMSO has amphiphilic properties with a strongly polar sulfoxide group and two hydrophobic methyl moities. Being aprotic and H bond acceptor, it is miscible with water in any proportion above the DMSO melting point (T > 18 C) in atmospheric conditions. Water-DMSO form an eutectic mixture 2 H 2 O:1 DMSO at x W = 66%, liquid down to T = 73 C [START_REF] Rasmussen | Phase diagram for the system water-dimethylsulphoxide[END_REF]. At room temperature the viscosity of DMSO is roughly twice that of water while their densities are very similar (see E.S.I. Table S1). The mixture viscosity, as well as its density present a non-ideal behavior with a maximum for molar-fractions of water x W ⇠ 66% corresponding to the eutectic mixture [START_REF] Cowie | Association in the binary liquid system dimethyl sulphoxide -water[END_REF][START_REF] Lebel | Density, viscosity, refractive index, and hygroscopicity of mixtures of water and dimethyl sulfoxide[END_REF][START_REF] Nieto-Draghi | Transport properties of dimethyl sulfoxide aqueous solutions[END_REF].

Other physical characteristics such as the thermal conductivity k [START_REF] Zhang | An improved hot probe for measuring thermal conductivity of liquids[END_REF][START_REF] Zhou | Thermal conductivity of DMSO + C 2 H 5 OH, DMSO + H 2 O, and DMSO + C 2 H 5 OH + H 2 O mixtures at T =[END_REF], the static relative permittivity " r [START_REF] Kaatze | Dielectric spectrum of dimethyl sulfoxide/water mixtures as a function of composition[END_REF][START_REF] Luzar | Dielectric behaviour of DMSO-water mixtures. an hydrogen-bonding model[END_REF] and the optical index n [START_REF] Cowie | Association in the binary liquid system dimethyl sulphoxide -water[END_REF][START_REF] Lebel | Density, viscosity, refractive index, and hygroscopicity of mixtures of water and dimethyl sulfoxide[END_REF] of water-DMSO mixtures do not present such a pronounced non-ideal behaviour and are monotonous functions of x W at room temperature; " r decreases (almost linearly) from 80 in water down to 46 in DMSO [START_REF] Kaatze | Dielectric spectrum of dimethyl sulfoxide/water mixtures as a function of composition[END_REF][START_REF] Luzar | Dielectric behaviour of DMSO-water mixtures. an hydrogen-bonding model[END_REF][START_REF] Doucet | La constante diélectrique du diméthylsulfoxyde pur et de ses mélanges aqueux[END_REF][START_REF] Skaf | Molecular dynamics study of dielectric properties of water-dimethyl sulfoxide mixtures[END_REF] and n increases from 1.33 in water up to 1.47 in DMSO [START_REF] Cowie | Association in the binary liquid system dimethyl sulphoxide -water[END_REF][START_REF] Lebel | Density, viscosity, refractive index, and hygroscopicity of mixtures of water and dimethyl sulfoxide[END_REF].

These macroscopic properties are connected to molecular scale interactions between water and DMSO, in particular through H-bonds and van der Waals forces. Hbond interactions are transient in nature, with ultrafast breaking and making processes and various kinds of Hbond associations are possible between water and DMSO molecules. A crossover is found in Ref. [START_REF] Kashid | Two-dimensional infrared spectroscopy reveals cosolvent-composition dependent crossover in intermolecular hydrogen-bond dynamics[END_REF] for the Hbond exchange rate at x W ⇠ 85%, which is associated to the fact that water-DMSO mixtures act as protein stabilizers and activators for x W > 85%, while for x W < 85% they act as denaturators and inhibitors. In [START_REF] Oh | Quantifying hydrogen-bond populations in dimethyl sulfoxide/water mixtures[END_REF], hydrogenbond population was numerically quantified on the whole range of x W . Several structural studies, both experimental and numerical, have shown concentration-dependent organizations of water and DMSO molecules [START_REF] Soper | A neutron-di↵raction study of dimethyl-sulfoxide water mixtures[END_REF], structural microheterogeneities [START_REF] Perera | On the nature of the molecular ordering of water in aqueous DMSO mixtures[END_REF], the formation of chains of water molecules [START_REF] Banerjee | Enhanced pair hydrophobicity in the water-dimethyl sulfoxide (DMSO) binary mixture at low DMSO concentrations[END_REF] or of network structures [START_REF] Roy | Solvation dynamics of tryptophan in water-dimethyl sulfoxide binary mixture: In search of molecular origin of composition dependent multiple anomalies[END_REF].

Chemical synthesis of the NP's dispersions

Ferrite NPs are synthesized following Massart's method [START_REF] Massart | Préparation de ferrofluides aqueux en l'absence de surfactant; comportement en fonction du pH et de la nature des ions présents en solution[END_REF][START_REF] Massart | Preparation of aqueous magnetic liquids in alkaline and acidic media, I[END_REF] by poly-condensation of ferric and ferrous salts in strongly alkaline aqueous medium followed by an hydrothermal oxidation at 100 C under atmospheric pressure with nitric acid [START_REF] Gomes | Synthesis of core-shell ferrite nanoparticles for ferrofluids : chemical and magnetic analysis[END_REF] leading to roughly spherical maghemite ( Fe 2 O 3 ) nanoparticles, coated with hydroxyl groups. A size-sorting of the NPs as the one described in Ref. [START_REF] Massart | Preparation and properties of monodisperse magnetic fluids[END_REF] is performed. All the present dispersions are based on the same initial batch of NPs.

These NPs can be easily dispersed in water at pH ⇠ 2, where they are positively charged. They have a point of zero charge (PZC) ⇠ 7 8 in water, where they flocculate. The method described in [START_REF] Filomeno | Ionic magnetic fluids in polar solvents with tuned counter-ions[END_REF][START_REF] Filomeno | Tuning the solid/liquid interface in ionic colloidal dispersions: Influence on their structure and ther-modi↵usive properties[END_REF] is used here to tune the NP-solvent interface in water and in DMSO. Starting from a flocculated aqueous dispersion at PZC, all extraions and all the water molecules (that can be removed) are then eliminated by repeated washings. Then the NPs are charged in the chosen medium following a controlled and reproducible process to obtain NP's dispersions with perchlorate counterions (added in known quantity) at [H + ]= 10 2 mol L 1 , either in water or in DMSO at a NP's volume fraction ⇠ 2.5%. A portion of the obtained dispersions is ultracentrifugated at 2 ⇥ 10 5 g. Providing that the ultracentrifugation does not perturb the local equilibria around NPs, concentrations of free co-ions H + and counterions ClO - 4 are determined in each dispersion by conductivity measurements in the supernatant. A solution similar to the supernatant is then used to obtain dilute dispersions at lower in the same solvent. Dispersions in water-DMSO mixtures are obtained by mixing in the adapted proportion a dispersion in water and a dispersion in DMSO at the same and the same ionic concentration.

Both in water and in DMSO, stable acidic dispersions with a long term stability (more than 15 years 2 ) are obtained with positively charged NPs (hydroxyl groups -acidic medium).

Characterization of NPs and of their dispersions

The magnetization of a dilute aqueous dispersion (at ⇠ 1%) up to 800 kA m 1 is determined at room temperature with a home-made Vibrating Sample Magnetometer (data not shown). The size distribution of the magnetic nanoparticles can then be deduced following the procedure of Ref. [START_REF] Berkovski | Magnetic Fluids and Applications Handbook[END_REF]. It is adjusted with a log-normal distribution of diameter, of median diameter d 0 = 7.5 nm and The dynamic electrophoretic charge number ⇠ 0 of the NPs and its derivative @⇠ 0 /@T are deduced (as in Ref. [START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF]) in water and in DMSO from D DLS and from measurements of the NP's electrophoretic mobility µ el at ⇠ 0.01% with a NanoZS from Malvern (with a dip cell) for 25  T  40 C, using:

⇠ 0 = kT µ el eD DLS at ! 0, (1)
leading to ⇠ 0 = 65±6 and @⇠ 0 /@T = 0.4±0.2 K 1 in water; and ⇠ 0 = 43±4 and @⇠ 0 /@T = 0.5±0.2 K 1 in DMSO. The values of ⇠ 0 and @⇠ 0 /@T for the various mixtures probed here are obtained by a linear interpolation of x W between the values in pure water and in pure DMSO. As in [START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF], this e↵ective charge ⇠ 0 is of the same sign but much smaller than the structural charge of the NPs, which is due the hydroxyl species H + present at the maghemite surface (⇠ 2 charges per nm 2 , leading to a structural charge number ⇠ 450). This di↵erence has to be related here to a large amount of ClO 4 species condensed on the surface. Small Angle Neutron Scattering measurements are performed at PACE -LLB -Saclay -France in the range of scattering vectors

Q ( 2.4 ⇥ 10 3 Å  Q  4.3 ⇥ 10 1 Å) on various dispersions.
The form factor of the nanoparticles is deduced in water as a function of the scattering vector Q by extrapolation at = 0 of the intensities of three dispersions at 0.3%, 1% and 2.5%. We follow the same procedure as in [START_REF] Filomeno | Tuning the solid/liquid interface in ionic colloidal dispersions: Influence on their structure and ther-modi↵usive properties[END_REF] to deduce the osmotic compressibility of the NP system from the scattered intensity at finite volume fraction. Fig. 1a presents the evolution of in water as a function of the NP volume fraction . As the interparticle repulsion is strong in these colloidal dispersions stabilized electrostatically, ( ) is here adjusted (as in [START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF][START_REF] Filomeno | Ionic magnetic fluids in polar solvents with tuned counter-ions[END_REF][START_REF] Filomeno | Tuning the solid/liquid interface in ionic colloidal dispersions: Influence on their structure and ther-modi↵usive properties[END_REF][START_REF] Wandersman | The cage elasticity and under-field structure of concentrated magnetic colloids probed by small-angle X-ray scattering[END_REF]) by the Carnahan-Starling expression for e↵ective hard spheres [START_REF] Carnahan | Thermodynamic properties of a rigid-sphere fluid[END_REF][START_REF] Barker | Perturbation theory and equation of state for fluids. II. a successful theory of liquids[END_REF] of volume fraction e↵ (and e↵ective diameter taking in account the screening length  1 ) as:

( ) = CS ( e↵ ) = (1 e↵ ) 4 1 + 4 e↵ + 4 2 e↵ 4 3 e↵ + 4 e↵ . (2)
The second virial coe cient A 2 of the osmotic pressure ⇧ in the dispersion then writes:

A 2 = A HS 2 e↵ = 4 e↵ with e↵ = ✓ 1 + 2 1 d NP ◆ 3 , (3)
with A HS 2 = 4, the hard sphere value of A 2 . We obtain A 2 = 33 ± 3 and  1 = 4.6 ± 0.4 nm for the aqueous samples. Inset of Fig. 1a shows the evolution of as a function of x W obtained for the mixtures water-DMSO at constant = 2.5%. For the analysis, the same NP's form factor as in water is kept to deduce . The formalism of Eqs. 2 and 3 then allows to obtain e↵ and A 2 as a function of x W (see Fig. 1b). It leads to A 2 = 17±2 and  1 = 2.8±0.4 nm in DMSO. These  1 values in water, DMSO and their mixtures are experimentally consistent with the values ✏ r of the relative permittivity in these media [START_REF] Skaf | Molecular dynamics study of dielectric properties of water-dimethyl sulfoxide mixtures[END_REF] and they roughly scale as  1 ⇠ 0.47 p ✏ r (in nm).

Forced Rayleigh Scattering experiment

The principle of the used Forced Rayleigh Scattering (FRS)3 setup (see Fig. 2) has been extensively described in Ref. [START_REF] Demouchy | Di↵usion and thermodi↵usion studies in ferrofluids with a new two-dimensional forced Rayleighscattering technique[END_REF]. Some improvements to the home-made device have been made. In particular, the modulation of the power lamp is decreased to a few Hz to probe more viscous systems than in Ref. [START_REF] Demouchy | Di↵usion and thermodi↵usion studies in ferrofluids with a new two-dimensional forced Rayleighscattering technique[END_REF] and the sample environment is now thermo-regulated allowing to work between T = 40 C and 200 C. However only results at T = 21 ± 0.4 C are presented here.

Using a high power lamp (6285 -500W -Hg Arc Lamp -Spectra Physics) and thanks to the strong optical absorption of the maghemite NPs, a thermal grating (of period ⇤ ranging between 88 and 145 µm) is created in the dispersion, contained in an optical cell of thickness 25 or 100 µm. The Soret e↵ect then induces a concentration grating in this dispersion. Both thermal and concentration gratings are here probed with the first order di↵raction of a non-absorbing He-Ne laser. The Soret coe cient S T is obtained in stationary conditions thanks to a few Hz modulation of the Hg lamp (the thermal response of the system being by orders of magnitude faster than the concentration one -see E.S.I. Sections S1 and S4). The relaxation of the concentration grating when the Hg lamp is o↵, allows to determine the mass di↵usion coe cient D m of the NPs.

With the heat source "on" (the Hg lamp heats the dispersion periodically at 8 Hz) the di↵racted intensity, related to both the growing concentration grating and the corresponding thermal one, is recorded as a function of time until a stationary state is reached. This di↵racted intensity is converted in (i) temporal index-variations n (t) related to the temporal evolution of the concentration grating and (ii) temporal index-variations n T related to the temporal evolution of the thermal grating (see E.S.I. Section S1 for more details). From the values of @n/@T and Tmax as a function of time for a dispersion at = 2.5% in DMSO at q = 7.14 ⇥ 104 m 1 ; (b) Relaxation time ⌧ 1 of when the heat source is o↵ as a function of q 2 and (c) st = f ( T St max ) for dispersions at = 2.5% in water and in DMSO at various q and various powers of the lamp (in the linear regime). and @n/@ (see E.S.I. Section S3), the temporal evolution 4 of associated to the concentration grating and of the enveloppe T max of T associated to the thermal grating are determined (see Fig. 3a for a sample at = 2.5% and q = 2⇡/⇤ = 7.14 ⇥ 10 4 m 1 (⇤ = 88 µm) in DMSO). When the heat source is switched o↵ (see Fig. 3a) T max = 0 and the di↵racted intensity relaxes to zero as the concentration grating relaxes exponentially to zero with a characteristic time ⌧ . Fig. 3b presents ⌧ 1 as a function of q 2 in water and DMSO, at = 2.5%, for di↵erent q values. These two quantities are proportional to each other, showing that the relaxation is a di↵usion process, the (mass) di↵usion coecient D m being the slope of these straight lines. We obtain D m = ⌧ 1 q 2 = 5.12 ⇥ 10 11 m 2 s 1 for water and D m = 1.23 ⇥ 10 11 m 2 s 1 for DMSO. Di↵erent powers of the lamp (ranging between 350 and 500 W) are used here to test that the response is linear and that the relaxation time ⌧ 1 is independent of the power of the lamp.

Fig. 3c presents the stationary value St of as a function of T St max , the value of T max in the steady state, for water and DMSO, at = 2.5%. They are obtained for di↵erent q values and di↵erent powers of the lamp (remaining in the range of linear response) to test that St and T St max remain proportional to each other, for a given sample independently of q and of the lamp-power. The slope of the straight lines in Fig. 3c is proportional to the Soret coe cient S T and as mentioned earlier they are of opposite sign in water and in DMSO. In the present experiment, the chopper, while operating, is equally open and closed. Thus the mean value of T is h T i = T max /2. The Soret coe cient is then given by:

S T = 2 St T St max . (4)
Fig. 3c shows that at = 2.5%, | St | is always smaller than 10 2 % while T St max  0.085 K for both DMSO and water. We obtain here S T = 4.5 ⇥ 10 2 K 1 for water and S T = + 0.10 K 1 for DMSO.

Experimental results

FRS measurements are performed at several molar fractions of water x W for di↵erent NP's volume fractions (0.5   2.5% ) at [H + ]= 10 2 mol L 1 .

Di↵usion coe cient

The mass di↵usion coe cient D m for several dispersions at di↵erent x W is presented in Fig. 4 as a function of the volume fraction . For all solvent mixtures compositions, it is an increasing function of , as expected for the strong interparticle repulsion inside the dispersions. In the low regime, where both FRS and DLS are performed Fig. 5 shows the good agreement between the two determinations of the di↵usion coe cient. For all values of volume fraction, D m is a non-monotonous function of x W , with a minimum for x W ⇠ 0.6, which corresponds to the maximum of the mixture viscosity given in Fig. 5. Indeed D m is related to the osmotic pressure ⇧ and the local friction ⇣ of the NPs in the colloidal dispersion through the following relations :

D m = 1 ⇣ @⇧ @n NP = 1 ⇣ kT and = kT @⇧ @n NP (5)
where n NP = /V NP is the number of NPs per unit volume (V NP being the NP's volume), ⇧ is the osmotic pressure of the NP system and is its osmotic compressibility written here in the framework of Carnahan-Starling formalism of e↵ective hard spheres used in Eqs. The initial values D m,0 at = 0 and = CS = 1 deduced from FRS experiments are presented in Fig. 5 as a function of x W , for all the probed x W . The good adjustment of D m,0 (x W ) by kT /⇣ 0 (deduced from the x Wdependence of the viscosity), shows that it is the solvent viscosity which controls the variations of friction when x W varies. This also attests the good NP's dispersion whatever the mixture as any aggregation of the NPs would lead to a significant decrease of the di↵usion coe cient with respect to Eq. 5 (shown by the full line in Fig. 5). We see that the non-ideal behavior of the viscosity as a function of x W in the water-DMSO mixtures is also observed in the experimental values of D m,0 (x W ). 5 Theoretical background

Soret coe cient

Theoretical model

If the dispersions of ionic NPs are submitted to small gradients of volume fraction r and of temperature rT , the Ludwig-Soret coe cient S T , being defined in stationary conditions by: r = S T rT, (6) can be rewritten [START_REF] Würger | Transport in Charged Colloids Driven by Thermoelectricity[END_REF][START_REF] Majee | Collective thermoelectrophoresis of charged colloids[END_REF][START_REF] Piazza | Thermophoresis in colloidal suspensions[END_REF][START_REF] Burelbach | A unified description of colloidal thermophoresis[END_REF] following a model 5 detailed in [START_REF] Huang | Thermo-electric di↵usion of magnetic nanoparticles: alternative path toward future thermocell applications[END_REF][START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF] as:

S T = h ŜNP kT e⇠ 0 S st e kT i . (7)
5 In a first approximation, we neglect here the term

1 nkT @⇧ @T
which is here always smaller than 9 ⇥ 10 3 K 1 . As well the contribution of DMSO is not taken into account here because ŜDMSO /kT evolves from 2.5 ⇥ 10 3 K 1 at xW = 0.1 up to +2.5 ⇥ 10 3 K 1 at xW = 0.9 following the results of Ref. [START_REF] Ning | Experimental investigation of the soret e↵ect in acetone/water and dimethylsulfoxide/water mixtures[END_REF].

Close to conditions where ST = 0, these neglected terms could become slightly relevant. ŜNP is the NP Eastman entropy of transfer [START_REF] Agar | Single ion heat of transport in electrolyte solutions[END_REF], defined as the ratio of the heat of transport of the NPs divided by T , which characterizes the a nity of the NPs with the solvent. The stationary Seebeck coe cient S st e [START_REF] Majee | Collective thermoelectrophoresis of charged colloids[END_REF] equals for monovalent free ions:

eS st e = n + Ŝ+ n Ŝ + Zn NP ŜNP n + + n + Zn NP ⇠ 0 . ( 8
)
n + (resp. n ) are the number of free H + (resp. ClO - 4 ) ions per volume unit and Ŝ+ (resp. Ŝ ) their Eastman entropy of transfer. The (static) NP's e↵ective charge Z is given by the electroneutrality of the dispersion (see Refs [START_REF] Huang | Thermo-electric di↵usion of magnetic nanoparticles: alternative path toward future thermocell applications[END_REF][START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF]). It is of the same order of magnitude as the (dynamic) NP's e↵ective charges ⇠ 0 , determined experimentally (see section 2.3). For sake of simplicity, we assimilate them to each other in the fits of S T ( ).

In Eqs. 7 and 8, the only unknown quantities are the three Eastman entropies of transfer, namely ŜNP , Ŝ+ and Ŝ . The quantities Ŝ+ and Ŝ are known in water, in the infinite dilution limit and at room temperature, from Refs. [START_REF] Agar | Single ion heat of transport in electrolyte solutions[END_REF][START_REF] Takeyama | Proportionality of intrinsic heat of transport to standard entropy of hydration for aqueous ions[END_REF], ŜH + /kT = +0.018K 1 and ŜClO 4 /kT = 0.000 K 1 . However they are not known in water-DMSO mixtures and in pure DMSO.

ŜH + and ŜClO 4 evaluation in water-DMSO mixtures

We propose here to evaluate Ŝ+ and Ŝ from the enthalpy of transfer t H ion of H + and ClO - 4 ions from water to water-DMSO mixtures, which are tabulated for several x W values in Refs. [START_REF] Hefter | Enthalpies and entropies of transfer of electrolytes and ions from water to mixed aqueous organic solvents[END_REF][START_REF] Marcus | Ion properties[END_REF]. Following the developments of E.S.I. Section S5, the Eastman entropy of transfer of the free ions Ŝ± (x W ) can be expressed with the following expression:

Ŝ± kT (x W ) = Ŝ± kT (x W = 1) t H ± (x W ) RT 2 , ( 9
)
where t H ± (x W ) is the enthalpy of transfer of (±) ions (H + and ClO - 4 ) from water to the water-DMSO mixture at mole fraction of water x W . Fig. S4a of E.S.I. shows the values of ŜH + /kT and ŜClO 4 /kT as a function of x W as deduced from Refs [START_REF] Hefter | Enthalpies and entropies of transfer of electrolytes and ions from water to mixed aqueous organic solvents[END_REF][START_REF] Marcus | Ion properties[END_REF] and Eq. 9, together with the interpolations used here (in particular for H + for which we did not find any value of t H ion (x W ) for 0 < x W < 0.7). Note that anyway ŜH + /kT presents a non-ideal behavior, with a pronounced maximum in the vicinity of the eutectic proportion, while the variations of ŜClO 4 /kT as a function of x W are smoother.

The x W -dependence of the NP's Eastman entropy of transfer ŜNP is then deduced from the measurements of S T . The results obtained from Eqs. 7, 8 and values of ŜH + /kT and ŜClO 4 /kT are presented in Fig. 7b. ŜNP /kT decreases from ⇠ +1 K 1 at x W = 0 down to ⇠ 0.5 K 1 at x W = 1, with a "plateau" close to 0 for 0.3 < x W < 0.85. In Fig. S4b of E.S.I., these results are compared to those obtained with a more basic evaluation of Ŝ± , obtained with the Born model which only takes into account electrostatic considerations. Both methods give very comparable results (see Section S5 of E.S.I. for more details).

Using Eq. 8 and the electroneutrality relation in the solution (Zn NP + n + + n = 0), the thermoelectric contribution e⇠ 0 S st e /kT in Eq. 7 can be written as :

e⇠ 0 S st e kT = ⇠ 0 kT Z n NP n+ ⇣ ( ) ŜNP Ŝ ⌘ + ⇣ Ŝ+ Ŝ ⌘ 2 + Z n NP n+ (1 + ( )⇠ 0 ) (10)
This thermoelectric contribution e⇠ 0 S st e kT is presented in Fig. 7a as a function of for the same x W -values as in Fig. 6.

In the very dilute limit

! 0 and = 1, the Soret coe cient reduces to :

S T ( ! 0) = ŜNP kT ⇠ 0 2 Ŝ+ kT Ŝ kT ! (11)
the first term coming from the NPs (single particle thermophoretic contribution) and the second from the free ions (thermoelelectric contribution of free ions at = 0). As an illustration of their relative importances, Fig. 7b compares these two terms to S T ( ! 0) as a function of x W . In this very dilute limit ( ! 0 and = 1), the single-particle contribution ŜNP from the NPs is dominant in S T for x W  0.15 (close to pure DMSO) and for 0.83  x W < 1 (close to pure water), while on the contrary for 0.4  x W < 0.8 it is the Seebeck contribution from the free ions, which dominates in the S T -values (both contributions are close to each other at x W = 1). Note that close to x W ⇠ 0.27, where S T ( ! 0) ⇠ 0, the contributions neglected in footnote 5 may become slightly relevant. Moreover we observe here that the single-particle thermophoretic contribution ŜNP changes its sign around x W ⇠ 0.8 (being negative above). This corresponds to the value of x W where the Soret coe cient of DMSO in water changes its sign in Ref. [START_REF] Ning | Experimental investigation of the soret e↵ect in acetone/water and dimethylsulfoxide/water mixtures[END_REF] (being positive above). This "anti-correlation" could be related to the fact that whatever the solvent in which they are dispersed, these NPs always keep a layer of structural water at their surface leading to ŜNP of the same sign as the Soret coe cient of water in DMSO.

Let us note as well that, contrary to what we observe in Fig. 4 for the dynamic quantity D m , there is here no mark of non-ideality at = 0 for the Soret coe cient S T in the neighborhood of the eutectic proportion x W ⇠ 0.66, nor for any of its two components ŜNP and S st e . This could be related to the nature of the counter-ions condensed at the NP surface, which are here ClO 4 and for which Ŝ does not present any bump at the eutectic composition (see Fig. S4a of E.S.I.).

At finite concentration, this simple description does not hold any longer since the interparticle interactions enter into play through the coe cient ( ) in Eq. 7 and the NPs contribute to the thermoelectric term e⇠ 0 S st e kT (see Eq. 8 and Fig. 7a).

Discussion

The Eastman entropy of transfer ŜNP of the ionic NPs is the single-particle thermophoretic contribution (all the interparticle interaction and Seebeck contributions being already eliminated). It has been shown in [START_REF] Cabreira-Gomes | Thermod-i↵usion of repulsive charged nanoparticles -the interplay between single-particle and thermoelectric contributions[END_REF][START_REF] Kouyaté | Thermodi↵usion of citratecoated Fe 2 O 3 nanoparticles in aqueous dispersions with tuned counter-ions -anisotropy of the soret coecient under magnetic field[END_REF][START_REF] Filomeno | Ionic magnetic fluids in polar solvents with tuned counter-ions[END_REF] that ŜNP depends on all the details of the interface between the NPs and the solvent (NP's coating, nature and concentration of free counterions, nature of the solvent).

This evolution of ŜNP correlates with the evolution of the structure and the dynamics of the pure water-DMSO mixtures [START_REF] Kashid | Two-dimensional infrared spectroscopy reveals cosolvent-composition dependent crossover in intermolecular hydrogen-bond dynamics[END_REF][START_REF] Oh | Quantifying hydrogen-bond populations in dimethyl sulfoxide/water mixtures[END_REF]. Indeed, adding a few DMSO molecules in water induces huge changes in the molecular organization observed in the mixtures due to strong H bonds interactions between DMSO and water [START_REF] Oh | Quantifying hydrogen-bond populations in dimethyl sulfoxide/water mixtures[END_REF]. In the range 0.85  x W  1 where ŜNP is negative, the exchange rate of H bonds moreover slows down while adding DMSO due to these H bonds between the two solvent molecules and are for example at the origin of the cryoprotective role of DMSO for proteins in this range of x W [START_REF] Kashid | Two-dimensional infrared spectroscopy reveals cosolvent-composition dependent crossover in intermolecular hydrogen-bond dynamics[END_REF]. When increasing the DMSO content further (x W < 0.85), the dynamics of the water/surface H bonds should change due to the increasing number of DMSO molecules, which can also solvate the NPs surfaces [START_REF] Kashid | Two-dimensional infrared spectroscopy reveals cosolvent-composition dependent crossover in intermolecular hydrogen-bond dynamics[END_REF]. As well, adding some water molecules in DMSO (0  x W  0.1) modifies its organization on the molecular scale, however this does not influence much ŜNP , which remains constant and positive. In the intermediate region (0.1 < x W  0.65) where the structure of DMSO does not evolve much [START_REF] Oh | Quantifying hydrogen-bond populations in dimethyl sulfoxide/water mixtures[END_REF], ŜNP does not change much either. We recall that no special behaviour is here detected in the region of the eutectic point close to x W = 0.66.

Moreover, it has been shown in Refs. [START_REF] Majee | Collective thermoelectrophoresis of charged colloids[END_REF][START_REF] Dhont | Single-particle thermal di↵usion of charged colloids: double-layer theory in a temperature gradient[END_REF][START_REF] Vigolo | Thermophoresis and thermoelectricity in surfactant solutions[END_REF][START_REF] Yang | Thermophoretically induced flow field around a colloidal particle[END_REF][START_REF] Eslahian | Specific salt e↵ects on thermophoresis of charged colloids[END_REF] that two main mechanisms of ionic shielding contribute to ŜNP . One is electrostatic. It is driven by the buildup of the NP's charge and of the ionic shell. It is usually described [START_REF] Duhr | Why molecules move along a temperature gradient[END_REF][START_REF] Dhont | Ther-modi↵usion of charged colloids: single-particle di↵usion[END_REF][START_REF] Ning | Thermal-di↵usive behavior of a dilute solution of charged colloids[END_REF] with the capacitor model Ŝ cm NP . The second one Ŝ solv NP corresponds to the solvation of the NPs and of their ionic shell in the solvent [START_REF] Duhr | Why molecules move along a temperature gradient[END_REF]. ŜNP then expresses as:

ŜNP = Ŝ cm NP + Ŝ solv NP . (12)
The capacitor contribution can be written as :

Ŝ cm NP = @ @T " (eZ (x W )) 2 2⇡" 0 "(T, x W )d NP (2 + (T, x W )d NP ) # (13)
where Z(x W ) is the static e↵ective charge in the solution (taken here equal to ⇠ 0 (x W )), "(T, x W ) is the relative permittivity of the aqueous dimethyl sulfoxide solution at x W and where  1 (T, x W ) is the screening length Ŝ cm NP (see inset of Fig. 8) then varies almost linearly from ⇠+2.5 K 1 in pure DMSO to⇠+3 K 1 in pure water; It strongly depends on d⇠ 0 /dT . Ŝ solv NP , as obtained from Eq. 12 is presented in Fig. 8 in the framework of the model of Section 5.2 for evaluating ŜH + /kT and ŜClO 4 /kT and compared to the values obtained with the Born model described in Section S5.1 of E.S.I.. In both cases Ŝ solv NP is negative, as expected in water in Ref. [START_REF] Duhr | Why molecules move along a temperature gradient[END_REF] and it stays negative whatever x W , even in pure DMSO at x W =0.

It expresses a strong solvophilicity of the NPs on the whole range of x W as Ŝ solv NP decreases from -1.5 K 1 in DMSO down to ⇠ 3.5 K 1 at large proportion of water (x W 0.9).

Summary-Perspectives

The Soret coe cient of acidic NPs dispersed at [H + ] =10 2 mol L 1 in water-dimethyl sulfoxide mixtures is measured at di↵erent mole fractions of water x W . It is observed that at low fractions of water the NPs are thermophobic (S T > 0) while at large fractions of water they are are thermophilic (S T < 0). This has to be ascribed both to the single-particle thermophoretic contribution (the socalled NP's entropy of transfer ŜNP which is linked to the particle/solvent interaction) and to the thermoelectric contribution (Seebeck term e⇠ 0 S st e kT in which all the charged species contribute).

It is shown here that the single-particle thermophoretic contribution of the NPs is dominant at low and large x W values ( x W  0.15 and 0.83) while it is the Seebeck term which dominates at intermediate x W . Whatever x W , the solvation contribution to ŜNP is negative, expressing a strong a nity of the ionic NPs with the mixtures of water and DMSO. However this solvation contribution is much stronger in absolute value at large water contents x W , which implies a huge role of the hydrogen-bonds of water molecules with the NPs surface in this solvation contribution. The (negative) solvation contribution then dominates the (positive) electrostatic contribution and both ŜNP and S T are negative. On the contrary at low values of x W , the (positive) electrostatic contribution to ŜNP dominates the (negative) solvation term and gives a positive sign to ŜNP , as well as to the Soret coe cient S T .

The interparticle interaction is here strongly repulsive. It imparts the systems with its colloidal stability and leads to higher NP's di↵usion coe cients for larger NP's volume fractions , whatever x W . It is due to the strong decrease of the osmotic compressibility of the NP's system as increases.

At low and large x W values, whatever the S T sign, the interparticle interaction reduces the Soret coe cient in absolute value as increases, because of the decrease of . In the intermediate range of x W , where the thermoelectric contribution becomes more important, the situation is more complicated. Such colloidal dispersions of ionic NPs in mixtures of water and DMSO can be very useful for thermocell applications, as tuning the proportion of DMSO in the system allows to tune in sign and amplitude the Soret coecient and the entropy of transfer of the NPs. However they can also be useful to understand the temperature evolution of hydrogen bonding in these mixtures. Indeed in the present work, only room temperature measurements have been performed and it would be also important to explore the temperature evolution of the Soret coe cient (and of the NPs entropy of transfer) at higher temperatures, and also at lower temperatures in the eutectic vicinity, for molar fraction of water x W ⇠ 0.66. The influence of the concentration of free ions [H + ] and [ClO 4 ] would be also important to examine, as it is a way to tune the Seebeck coe cient at finite concentration. As well it would be of paramount interest to study the influence of the nature of the counterion on the Soret coe cient. Unfortunately up to now ClO 4 is the only counterion that we know that leads to the colloidal stability of the dispersions of maghemite NPs in the whole range of x W in water-DMSO mixtures.

We propose here a method to evaluate the ionic contributions ŜH + and ŜClO 4 using the ionic enthalpy of transfer of H + and ClO 4 at room temperature. Direct experimental and/or numerical determinations of these quantities as a function of temperature, would be extremely useful in the near future to analyze the Soret coe cient in these solutions of ionic NPs as a function of T .

Aknowledgements

We deeply thank Amandine Anfry for the ⇠ 0 determinations as a function of temperature, Sawako Nakamae for useful discussions, Fabrice Cousin for his help in the SANS measurements and Laboratoire Léon Brillouin for the beamtime allocation on PACE in ORPHEE. This work has been supported by European Union's Horizon 2020 research and innovation programme under the grant n 731976 (MAGENTA).

Authors contributions

Jesse Riedl synthesized and characterized all the samples, under the supervision of Emmanuelle Dubois and Véronique Peyre. Mitradeep Sarkar realized all the FRS measurements under the supervision of Gilles Demouchy, Guillaume Mériguet and Régine Perzynski. The technical improvements of the FRS device were done by Frédéric Gélébart. The theoretical developments presented here were done in close collaboration between all the members of the team. All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

Figure 1 .

 1 Figure 1. (a) : Osmotic compressibility as a function of the NP's volume fraction in water; Open symbols: SANS results; Full line: CS adjustment with Eq. 2; Inset: Osmotic compressibility as a function of xW in mixtures at = 2.5%; Open symbols: Experimental SANS results; Full line: Linear adjustment; (b) : A2 as a function of xW in mixtures as deduced from SANS determinations and Eq. 3 (open symbols) and as interpolated with the Carnahan-starling model (full line).

Figure 2 .

 2 Figure 2. Experimental device -The beam of a high-power Hg lamp is temporally modulated thanks to a chopper. It illuminates a grid, the image of which is made in the thermoregulated (optical) sample-cell, producing a thermal and a concentration gratings in the colloidal dispersion. Both gratings are probed by the di↵raction of a non-absorbed He-Ne laser beam and a photo-multiplicator (PM) records the first order di↵raction as a function of time.

Figure 3 .

 3 Figure 3. (a)and Tmax as a function of time for a dispersion at = 2.5% in DMSO at q = 7.14⇥ 10 4 m 1 ; (b) Relaxation time ⌧ 1 ofwhen the heat source is o↵ as a function of q 2 and (c) st = f ( T St max ) for dispersions at = 2.5% in water and in DMSO at various q and various powers of the lamp (in the linear regime).

Figure 4 .

 4 Figure 4. Di↵usion coe cient Dm as a function of the NP volume fraction in mixtures of water and DMSO at di↵erent xW -from top to bottom xW = 1, 0.96, 0, 0.15 and 0.59 -as obtained from FRS measurements (circular symbols) and DLS measurements at = 0.2% (square symbols) -Full lines corresponds to Eq. 5 with ( ) = CS ( e↵ ) (see Eq. 2) obtained using SANS measurement of Fig. 1.

Figure 5 .

 5 Figure 5. Viscosity ⌘ of water-DMSO mixtures at 25 C as a function of the molar fraction of water xW from Ref. [24] (small squares/ full red line); Di↵usion coe cient Dm,0 obtained at 21 C by FRS and extrapolated at = 0 (open circles) and D DLS obtained at 22 C and = 0.2% (full circles) as a function of xW; Full green line adjustment of Dm,0 = kT /⇣0.

2 and 3 .

 3 The full lines of Fig. 4 corresponds to the adjustment D m ( ) = D m,0 / CS ( e↵ ) with e↵ = A 2 /4 and the A 2 values presented in Fig. 1. Here it is assumed that the local friction ⇣ of the NPs in the colloidal dispersion equals ⇣ 0 the friction in the solvent, neglecting any influence of the interparticle interaction on the local friction.

Fig. 6

 6 Fig. 6 presents S T as a function of for several mixtures. As previously shown in Fig. 3c the measured Soret coe cient is found positive in DMSO (at x W = 0) and negative in water (at x W = 1). As expected from literature [6, 16] the Soret coe cient is a decreasing function of the volume fraction in DMSO, while it increases with in water. These behaviors are also observed in mixtures at low and large x W 's. In mixtures rich in water (large values of x W ) S T is negative and increases with while it is positive and decreases with at low x W in mixtures rich in DMSO. At intermediate values of x W the situation is more complicated (data not shown). The measured Soret coe cient increases with and remains negative, close to the one measured at x W = 0.83 down to x W = 0.59. At x W = 0.43 and x W = 0.3, S T still increases with but it becomes positive at large 's. Let us analyze these dependences with the following modeling.

Figure 6 .

 6 Figure 6. Soret coe cient ST as a function of the NP volume fraction in mixtures of water and DMSO for several xW values -from top to bottom xW = 0; 0.15; 0.83; 0.96 and 1as obtained from FRS measurements (circular symbols). Full lines correspond to the adjustment of the results with Eqs. 7 and 8, the entropy of transfer of ions ( ŜH + /kT and ŜClO 4 /kT ) being deduced with the model of Section 5.2.

Figure 7 .

 7 Figure 7. (a) Thermoelectric contribution e⇠0 S st e kT as a function of for xW = 1, 0.96, 0.83, 0.59, 0.15 and 0 as obtained with the model of Section 5.2; (b) Comparaison between ST( ! 0) and its two contributions in Eq.11: ŜNP kT (the single-particle contribution to ST) and ⇠ 02

Figure 8 .

 8 Figure 8. Ŝsolv NP /kT (main figure) and Ŝcm NP /kT (inset) as a function of xW obtained using Eqs. 12 and 13; Symbols of main figure : (Open squares) Ŝsolv NP /kT deduced from Fig. 7b in the framework of the model of Section 5.2, (Open circles) as deduced from the Born model for Ŝ± and Fig. S4b of E.S.I...

as attested in DMSO by the DLS measurements presented in Section S6 of E.S.I..

FRS implies forced inhomogeneities with respect to the spontaneous fluctuations observed in a classical Rayleigh scattering experiment[START_REF] Nagasaka | Measurement of the thermal di↵usivity of liquids by the forced Rayleigh scattering method: Theory and experiment[END_REF].

By convention (see E.S.I. Section S1) is chosen here to be positive for ST < 0 (particles moving towards hot regions) and to be negative for ST > 0 (particles moving towards cold regions), with positive T between bright and dark fringes.