K Henni

I Stenger

J-S Merot

F Fossard

Jean-Charles Arnault

H Girard

High quality

and research institutions in France or abroad, or from public or private research centers.

High quality crystalline boron doped diamond growth on spherical monodisperse silica particles and impact of seeding density on the microstructure K.Henni 1 , I. Stenger 2 , J-S. Merot 3 , F. Fossard 3 , J. C. Arnault 1 and H. A. Girard CO2 conversion to chemical fuels such as alcohol and hydrocarbons has been found to be one of the most promising renewable energy source. It has urged the scientific community to develop efficient material in favor of CO2 reduction. Boron-doped diamond (BDD) electrodes have aroused an interest among scientists for its outstanding electrochemical properties in particular its wide potential window, making it a good candidate for the electrochemical reduction of CO2 [1].Moreover, hydrogenated BDD films, under UV illumination, could generate solvated electrons in aqueous solutions, making it highly relevant for photo(electro)catalytic CO2 reduction [2].

In this study, we report an innovative approach that aims to grow a BDD coating onto monodisperse silica cores to obtain SiO2@BDD core-shell particles by microwave plasma chemical vapor deposition (MPCVD). After removal of the core, hollow BDD could be used in the development of new electrode architectures which allows a significant gain in electro/photo-active surface. Currently, BDD particles are obtained by grinding massive BDD films, expensive process that produces in small amounts highly polydisperse particles.

Several investigations have correlated the electrochemical behavior of BDD with its crystallinity [3].

We therefore dedicated our work on the influence of several parameters on the crystalline quality, the morphology and the sp 2 /sp 3 carbon ratio of diamond coating. These parameters are (i) the methane concentration in the gas phase, (ii) the nature of seeds (milled or detonation nanodiamonds), (iii) their density and (iv) the oxygen species removed from seeded silica cores during MPCVD process. The morphology of diamond coatings was characterized by scanning electron microscopy (SEM). Results showed that the lower initial seeds density and methane concentration, the larger grain size we obtain with faceted structure. Raman measurements on diamond coatings allowed to compare diamond crystalline quality and sp 2 /sp 3 carbon ratio for the different growth conditions. Transmission electron microscopy (TEM), coupled with EELS, EDS spectroscopies were performed in order to access the diamond microstructure. The associated growth mode and the nature of the SiO2 / diamond interface were studied in cross-sections obtained by Focused ion beam (FIB).


Lorris Saoudi

Hugues Girard

Jean-Charles Arnault

Colloidal stability of synthetic hydrogenated nanodiamonds in water

Colloidal stability of synthetic hydrogenated nanodiamonds in water

L. Saoudi 1 , H. A. Girard 1 , J. C. Arnault 1 1 Université Paris-Saclay, CEA, CNRS, NIMBE, CEDEX, 91 191 Gif sur Yvette, France Two main processes are used to synthesize nanodiamonds (NDs): (i) by detonation (DND) giving rise to 5 nm mono-dispersed but highly defective nanoparticles, or (ii) by milling of bulk diamond (natural or synthetic) into polydispersed nanoparticles (MND). The latter preserves the crystallinity of bulk diamond and similar semi-conductor properties suitable for energy related applications. Able to host NV or SiV color centers, these MND are also currently under study for nanomedecine or quantum applications [START_REF] Nunn | Brilliant blue, green, yellow, and red fluorescent diamond particles: synthesis, characterization, and multiplex imaging demonstrations[END_REF]. These applications imply a fine control of colloidal properties, especially for a hydrogenated surface chemistry. Hydrogenated DND colloidal stability is well understood but its hydrogenated MND counterpart still needs further comprehension for a stability over time.

State of the art research has demonstrated that sp 2 carbon content, generated by a prior vacuum annealing, is essential to confer the colloidal stability to MND hydrogenated under pure H2 in mild conditions [START_REF] Ginés | Positive zeta potential of nanodiamonds[END_REF]. The present study reports on another route towards colloidal hydrogenated MND, which relies on the direct treatment of untreated MND at high annealing temperature (750°C) and under hydrogen pressures ranging from 10 mbar to atmospheric pressure. Our results show the possibility to obtain stable suspensions of hydrogenated MND over several months. Colloidal properties were investigated through DLS, zetametry and SAXS measurements. A thorough analysis of surface chemistry and morphology (FTIR, XPS, Raman, SEM, XRD) enables us to correlate stability of H-MND to their surface chemistry. Finally, the origin of the colloidal stability of hydrogenated DND and MND will be discussed.


Emilie Bérard
email: e.berard75@laposte.net

Philippe Dillmann

Alexandre Disser

Enrique Vega

Catherine Verna

Valérie Toureille

The medieval bombards of Meaux: Manufacturing processes and supply of the metal

Keywords:

Well-dated and preserved medieval bombards are rare and, most of the time, only exist in single exemplar. They are nevertheless exceptional testimonies of the medieval metallurgical skills. The musée de l'Armée (Paris), owns six impressive powder chambers, found in the same place (Meaux, France) and dated from the same period (15th c.). For the first time, this unique set has been studied by classical metallographic investigation, and recent approaches on slag inclusions using SEM-EDS and LA-ICP-MS analyses. The analyses permit to discuss the nature of the metal as well as the process used to obtain the metal (bloomery or finery) but also to consider the diversity of provenances for the metal that was used. These results suggest that five bombards may have been forged in the same area and possibly even in the same workshop, but anyway using metal produced through the bloomery process.

Introduction

The bombards are medieval large bore guns, that could weigh several tons (i.g. Mons Meg exposed in Edinburg Castle or Dulle Griet exposed in Gent) (de [START_REF] De Crouy-Chanel | Le canon jusqu'au milieu du XVIe siècle. France, Bretagne et Pays-Bas bourguignons[END_REF]. They were designed to throw stone round shots and appeared with the artillery development at the end of the 14th and the beginning of the 15th century for the cities attack or defence. They were produced either in iron alloys or bronze, however this study focuses only on iron forge-welded bombards. Bombards fabrication was a technical challenge in medieval times, both because of the large quantities of involved metal and the required performances of resistance. Therefore, several authors have highlighted the artisans know-how [START_REF] Benoît | Artisans ou combattants? Les canonniers dans le royaume de France à la fin du Moyen Age[END_REF][START_REF] Gaier | L'industrie et le commerce des armes dans les anciennes principautés belges du XIIIeme à la fin du XVeme siècle[END_REF], in making these impressive pieces. Several studies [START_REF] Balasubramaniam | A marvel of medieval Indian metallurgy: Thanjavur's forge-welded iron cannon[END_REF][START_REF] Benoit | Iron, cast iron and bronze, New approaches of the artillery history[END_REF][START_REF] Smith | Bombards Mons Meg and hers sisters[END_REF][START_REF] Walker | Investigation of a 16th-century gun powder chamber from the Tudor warship Mary Rose[END_REF] have been carried out to decipher the way bombards were assembled. Results have showed that they were made of two distinct parts: the barrel and the powder chamber. The barrel was constituted by long staves running on its whole length and bound together with multiple hoops. Regarding the powder chamber, several hypotheses were formulated, from the use of cast iron to the direct forging of crude iron products. Other approaches, based on both experimental and calculated data, have also been carried out to estimate the effectiveness of these weapons according to their assemblage [START_REF] Hansen | Rekonstruktion og skydeforsog med Loshultkanonen[END_REF][START_REF] Lefebvre | Le secret de Jehan Cambier, maître de forge de la Mons Meg[END_REF][START_REF] Lefebvre | La puissance de feu de la Mons Meg, maître de forge de la Mons Meg[END_REF].

Beyond the assembling techniques of these imposing guns, the nature of the metal and the possible heat treatments applied by the craftsmen are also crucial to consider. Indeed, they determine the resistance of these objects subjected to violent shocks. Previous studies [START_REF] Balasubramaniam | A marvel of medieval Indian metallurgy: Thanjavur's forge-welded iron cannon[END_REF][START_REF] Benoit | Iron, cast iron and bronze, New approaches of the artillery history[END_REF][START_REF] Smith | Bombards Mons Meg and hers sisters[END_REF][START_REF] Walker | Investigation of a 16th-century gun powder chamber from the Tudor warship Mary Rose[END_REF] have revealed that the guns examined were made of low or medium-carbon steel (%C < 0.8) with significant heterogeneities in the metal (carbon amount, grain size, slag inclusions and phosphorus content). Widmanstätten structures were also frequently observed, suggesting a high-temperature forging and welding followed by a fast cooling. On the staves, Starley has noticed higher carbon structures, lower phosphorus content and finer grains than from the powder chambers and hoops [START_REF] Smith | Bombards Mons Meg and hers sisters[END_REF]. For the author, it could be explained by differences within the manufacturing process. Contrary to the staves, the powder chambers were shaped at high temperature, which would lead to a more important decarburization, at least on the surface. Equiaxed ferrite grains were observed most of the time on the powder chambers by Benoit et al., showing also evidence of hammering and holding the metal at high temperatures for a long time [START_REF] Benoit | Iron, cast iron and bronze, New approaches of the artillery history[END_REF]. However, as the authors point out, the small number and size of the examined samples examined did not allow to draw definitive conclusions. Indeed, archaeological bombards are scarce. To the authors' knowledge, archaeometallurgical investigation have been carried out on only a dozen of forge-welded and they all are single finds.

Another interesting aspect relies on the nature of the ironmaking process used to produce the bombards. At the end of the Middle Ages important changes occurred in the iron and ferrous alloy production chain. The new indirect process, made up of blast furnace and finery, appears in the north of Europe between the 12th and 15th centuries [START_REF] Awty | The development and dissemination of the walloon method of ironworking[END_REF][START_REF] Belhoste | Mutations techniques et filières marchandes dans la sidérurgie alpine entre le XIIIe et le XVIe siècles[END_REF]Dillmann andL'Héritier, 2017, 2007). The chaîne opératoire related to this process differs from the bloomery one as two main steps are involved. In the first one cast iron is produced, which gives the possibility to create objects by moulding. This step is followed by a refining of the cast in order to produce iron or steel alloys. If most of a bombard should be made of this latter, some parts of the bombard, like the powder chamber, could have been made from cast iron. The archaeological bombard of Nancy (France) was, for instance, made entirely with this material [START_REF] Benoit | Iron, cast iron and bronze, New approaches of the artillery history[END_REF]. Some texts dating from the 15th century also mention small pieces made of cast iron [START_REF] Belhoste | fer et fonte dans l'artillerie française et bourguignonne au XVe siècle, in: Nouveaux Regards Sur l'artillerie Primitive XIVe s.-XVe S[END_REF]. Thus, several authors have assumed that the large parts of bombards, such as powder chambers, were made of cast iron and moulded parts [START_REF] Belhoste | La métallurgie normande XIIe-XVIIe siècles. La révolution du haut fourneau[END_REF]. However, the archaeological bombard of Nancy is the only reported example of the use of cast iron to make bombards. Eventually deciphering bombards metal (and its manufacturing process) is therefore part of an extensive approach to study the use and diffusion of the indirect process and its impact on medieval technical and economic systems. Determining the ironmaking process of ferrous alloys is possible by studying the chemical composition of entrapped slag inclusions ("SI") [START_REF] Dillmann | Slag inclusion analyses for studying ferrous alloys employed in French medieval buildings: supply of materials and diffusion of smelting processes[END_REF][START_REF] Disser | Iron reinforcements in Beauvais and Metz Cathedrals: from bloomery or finery? the use of logistic regression for differentiating smelting processes[END_REF]. Furthermore, the chemical analyses of the SI also give the opportunity to determine the origin of the metal produced by the bloomery process, as they carry the chemical signature of the metallurgical production area. Then, by determining this signature with both major and trace elements [START_REF] Blakelock | Slag inclusions in iron objects and the quest for provenance: an experiment and a case study[END_REF][START_REF] Buchwald | Slag analysis as a method for the characterization and provenancing of ancient iron objects[END_REF][START_REF] Charlton | The last frontier in 'sourcing': the hopes, constraints and future for iron provenance research[END_REF][START_REF] Coustures | The use of trace element analysis of entrapped slag inclusions to establish ore -Bar iron links: examples from two Gallo-Roman iron-making sites in France (Les Martys, Montagne noire, and les Ferrys, Loiret)[END_REF][START_REF] Desaulty | Does it come from the Pays de Bray? Examination of an origin hypothesis for the ferrous reinforcements used in French medieval churches using major and trace element analyses[END_REF]Dillmann et al., 2017;[START_REF] Disser | Iron supply for the building of Metz cathedral: new methodological development for provenance studies and historical considerations[END_REF][START_REF] L'héritier | Characterization of slag inclusions in iron objects[END_REF][START_REF] Leroy | First examination of slag inclusions in medieval armours by confocal SR-µ-XRF and LA-ICP-MS[END_REF], Leroy et al., 2017[START_REF] Leroy | The medieval iron market in Ariège (France). Multidisciplinary analytical approach and multivariate analyses[END_REF], and comparing them with geochemical database references, it is possible to test hypotheses on the origin of the employed materials. While large quantities of metal were obviously needed to make medieval bombards, the origin of the metal remains unknown. In addition to providing valuable information on the medieval European iron market, studying the provenance of the bombards materials could also give some insights into the location of the workshops. Excepting Mons Meg, for which historical sources identified its manufacturer, Jehan Cambier [START_REF] Smith | Bombards Mons Meg and hers sisters[END_REF], little is known about the location or the organization of the gunsmiths workshops.

Therefore, the present paper aims to a better knowledge of the bombards metallurgy by examining with all the aforementioned approaches the exceptional set of 6 well-dated (15th c.) bombards related to a single archaeological context (Meaux, France).

Set of artefacts

The bombards of Meaux seem to be the last evidences of the cannons used by the English and left on site after the siege of Meaux in 1422. They were dismantled in the 18th century. Only the powder chambers (N21, N22, N23, N24, N26 and N27) remained. The barrels, probably easier to dismantle are likely to have been recycled in 1726 [START_REF] Carro | Histoire de Meaux et du pays meldois[END_REF][START_REF] Leduc | La collection des pièces de Meaux. Un exemple de réemploi[END_REF]. These were used as bollards in Meaux city until 1843, when they became part of the collection of the Artillery Museum [START_REF] Leduc | La collection des pièces de Meaux. Un exemple de réemploi[END_REF]. Their weights have been estimated around 1000 kg (see Table 1 and reached 1440 for the bombard N21. The bombard N27 is the smaller one, with a powder chamber diameter around 13 cm (see Fig. 1. They are made of several layers of staves and hoops, but their advanced state of corrosion makes their original assemblage shaping difficult to identify. Detailed descriptions of the pieces are available in the publication "Nouveaux regards sur l'artillerie primitive XIVe s.-XVe s." [START_REF] Collectif | Nouveaux regards sur l'artillerie primitive XIVe s.-XVe s[END_REF].

Samples of several tens of mm 3 were collected at different locations on the bombards (Table 2. Due to the advanced degree of corrosion in some places, the position of the sample (powder chamber, hoop, stave) could sometimes not be clearly identified.

Materials and methods

All analysed samples were mounted in epoxy resin, then grinded using SiC abrasive paper (grade 80 to 1200). Final polishing was performed using Struers diamond polishing medium 3 and 1 µm. Metallographic etchings were done on the samples using 3% Nital. Then, optical observations were performed using an OLYMPUS microscope (model BX51) in order to estimate carbon content, distinguish the different kinds of inclusions and possible welding lines. An average carbon content and a weighted standard deviation were estimated for each sample and plotted into a graph of bell-shape, following the methodology of [START_REF] Leroy | The ties that bind: archaeometallurgical typology of architectural crampons as a method for reconstructing the iron economy of Angkor, Cambodia (tenth to thirteenth c.)[END_REF][START_REF] Pagès | A study of the Roman iron bars of Saintes-Maries-de-la-Mer (Bouches-du-Rhône, France). A proposal for a comprehensive metallographic approach[END_REF].

Major elements were quantified using Energy Dispersive Spectrometry (EDS) coupled to Scanning Electron Microscope (SEM) with a 15 kV accelerating voltage. Each spectrum corresponding to a single inclusion is treated following the ZAF semi quantification method using IDFix and Maxview softwares (SAMX company). The weight content of detected elements is then calculated and normalized to 100%. Results are expressed as oxides. For minor elements (between 0.5 and 1 wt%) it was assumed that the relative quantification error is about 10%. For the other elements (>1 wt%) the error is over-evaluated by assuming a relative error of 2%. A minimum of 30 inclusions were analysed for each sample. Full details on the procedure can be find on Disser et al., [START_REF] Disser | Iron reinforcements in Beauvais and Metz Cathedrals: from bloomery or finery? the use of logistic regression for differentiating smelting processes[END_REF].

The discrimination between the two smelting processes was done by following the procedure proposed by Dillmann and L'Héritier [START_REF] Dillmann | Slag inclusion analyses for studying ferrous alloys employed in French medieval buildings: supply of materials and diffusion of smelting processes[END_REF] and Disser et al. [START_REF] Disser | Iron reinforcements in Beauvais and Metz Cathedrals: from bloomery or finery? the use of logistic regression for differentiating smelting processes[END_REF]. It implies to identify SI families with constant Non Reduced Compounds (NRC) ratios (%Al 2 O 3 /%SiO 2 , %K 2 O/%CaO, %MgO/%Al 2 O 3 ). Then, a weighted content of each considered element called (%E * i , see Eq.1) and a subcompositional ratio (%E ** i , see Eq.2) were calculated according to the following formula:

%E * i = ∑ n i=1 (%E i × Si St ) (1)
%E ** i = %E * i × 100 100 -%E * FeO (2)
%E * i : average weighted content for all the inclusions of an artefact coming from the smelting stage %E i : composition of a given inclusion Si : surface of the inclusion analysed St : sum of all the inclusion surfaces Finally, the determination of smelting process was made by comparing the amount of NRC compounds (%E ** ) with a reference database. The comparison has been made by using both the abacus proposed by Dillmann and L'Héritier [START_REF] Dillmann | Slag inclusion analyses for studying ferrous alloys employed in French medieval buildings: supply of materials and diffusion of smelting processes[END_REF] and the logistic regression to model the data, both useful for solving unspecified cases. Then, a probability that the sample is associated with the finery process is calculated according to the model [START_REF] Disser | Iron reinforcements in Beauvais and Metz Cathedrals: from bloomery or finery? the use of logistic regression for differentiating smelting processes[END_REF]. However, as pointed out by the authors, an area, for which the process cannot be identified, remains, due to an overlap of the chemical features of the two processes in the reference dataset (it was already observed with the abacus proposed by Dillmann and L'Héritier built with the same dataset). To avoid the risk of making wrong predictions Disser et al., recommended for the logistic regression approach to define the reduction process as "undetermined" according to the following threshold: 0.3 < p f inery < 0.7. Therefore, the process will be considered as "bloomery" when p f inery < 0.3 and indirect when p f inery > 0.7.

Only the metal made by the bloomery process can lead to a provenance analysis, as the chemical signature of the iron ore is lost from the very first step (through cast iron production) of the finery process. Trace elements were quantified using Laser Ablation Inductively Coupled Plasma Mass Spectrometer (LA-ICP-MS) at the Ernest Babelon Centre (UMR-5060 IRAMAT CNRS, Orléans, France) on a dozen of SI per sample. The laser repetition rate was set to 7 Hz, the ablation time to 50 s, and the ablation crater between 50 and 80 µm in diameter depending of the SI size analysed. The quantification procedure fixed by Gratuze et al. was used [START_REF] Gratuze | Mass spectrometry with laser sampling: a new tool to characterize archaeological materials[END_REF]) using both internal standardization and external calibration. As the amount of removed material is not the same for each ablation, the signal obtained for each trace element was compared to the internal standard: the isotope 28 Si. Then, silicon values determined previously by SEM-EDS on SI were used to recalculate trace element concentrations instead of normalizing all contents to 100%. The calculation process also implies using an external standard, the certified glass NIST610. With this method, a significant number of trace element (up to 39) were quantified in the SI.

Among the measured trace elements, only a restricted set could be quantified with an acceptable accuracy of measurement at the concentrations observed in the samples: Y, Nb, La, Ce, Pr, Nd, Sm, Eu, Yb, Hf, Th, U. This set of elements was selected to compare the chemical signatures between the samples through multivariate analyses. To ensure scale-invariant representations, a log-ratio data transformation (see Eq.3) was applied for the selected traces elements as recommended by several authors [START_REF] Aitchison | The statistical analysis of compositional data[END_REF][START_REF] Disser | Iron supply for the building of Metz cathedral: new methodological development for provenance studies and historical considerations[END_REF][START_REF] Leroy | The medieval iron market in Ariège (France). Multidisciplinary analytical approach and multivariate analyses[END_REF].

X ij E = Log([E]) - 1 N ∑ N k=1 Log([E k ]) (3)
Where:

X ij E is the transformed value for each element [E] is the measured element concentration We have chosen to lead a non-supervised multivariate statistical approach, PCA (Principal Component Analysis) as its implementation in ancient iron provenance investigation has already provided good results on highlighting provenance groups [START_REF] Charlton | Investigating the production provenance of iron artifacts with multivariate methods[END_REF]Dillmann et al., 2017;[START_REF] Disser | Iron supply for the building of Metz cathedral: new methodological development for provenance studies and historical considerations[END_REF].

Results and discussion

Nature of the metal

All the samples are constituted of heterogeneous ferritic or/and hypoeutectoid steels. An important heterogeneity of the distribution of the carbon content was noticed, within each sample (see Fig. 2. In addition, weighted mean rate of carbon contents is variable even for samples coming from the same bombard (see for instance samples N24 A and D in Fig. 3. Most of the samples show relatively low weighted mean rate of carbon contents (<0.2) but some more carburized samples are also observed in medium carbon steel (N21B, N21C, N22C, N24C, N26C, N26D, N27B), and high carbon steel areas (N24A). Four of them (N21C, N22C, N24C, N26C) were taken from the rear of the powder chamber of the bombards. Nevertheless, two samples also taken from the powder chamber (N27C, N23D) were made of low carburized iron. No ghost structure indicating a significant amount of phosphorus in the metal was observed.

Furthermore, no evidence of casting was visible. Hence, this does not help to prove that the production of cast iron have had a major influence on the fabrication of the bombard. Although the use of cast iron seems the easiest way to produce imposing artefacts such as bombards, this result could be explained by the mechanical behaviour of the cast, more brittle compared to steel [START_REF] Benoit | Iron, cast iron and bronze, New approaches of the artillery history[END_REF]. While the mechanical behaviour of cast iron may have impeded its use for late medieval artillery, the technical limitations due to the casting of pieces as large as barrels or powder chambers may also have played a role in this choice. The pieces have to be cast in one go and in a very short time to avoid structural weaknesses. This implies the availability of a large quantity of cast iron either in the blast furnace crucible or in a casting crucible. As the amount needed would have ranged from 0.71 to 1.44 tons, meeting such requirements may have been proved challenging for late medieval gunsmiths and may only have been used for pieces of smaller size than the Meaux bombards, as the bombard of Nancy [START_REF] Benoit | Iron, cast iron and bronze, New approaches of the artillery history[END_REF].

The analyses also suggest that steel alloys were not specifically selected. In addition, the amount of carburization does not seem to be related to a given part of the bombard (stave, hoops, power chamber…) in order to improve its resistance during shooting. Our results does not confirm the observations made by Starley, namely higher carbon structures on the staves compared to the powder chamber, that would suggest a deliberate choice of metal or a different manufacturing process, the powder chamber being built up at higher temperature which could have led to a decarburisation [START_REF] Smith | Bombards Mons Meg and hers sisters[END_REF]. No evidence of heat-chemical treatment as quenching or carburizing, part of the armour fabrication [START_REF] Bérard | L'armure du XIIIe au XVIIe siècle en Europe : une approche matérielle. production, nature et circulation du métal[END_REF][START_REF] Williams | The knight and the blast furnace: a history of the metallurgy of armour in Middle Ages and the Early Modern period[END_REF] for instance at the same period, were found either. Eventually, the manufacture of the bombards is based on an unspecific and mostly heterogeneous metal as already highlighted by previous studies [START_REF] Benoit | Iron, cast iron and bronze, New approaches of the artillery history[END_REF][START_REF] Smith | Bombards Mons Meg and hers sisters[END_REF]. This feature could be compared to the pattern of metallic structures found in the metal used for cathedral and monuments during the Middle-Age, showing no specific material choice or heat treatments [START_REF] Dillmann | Use of iron for the building of medieval monuments. The Palais des Papes in Avignon and other french buildings[END_REF][START_REF] L'héritier | Iron? Which iron? Methodologies for metallographic and slag inclusion studies applied to ferrous reinforcements from Auxerre Cathedral[END_REF][START_REF] L'héritier | L'approvisionnement en fer des chantiers de construction médiévaux : coût, quantités et qualité[END_REF][START_REF] Timbert | L'homme et la matière: l'emploi du plomb et du fer dans l'architecture gothique[END_REF]. Most of the time, these reinforcements are also constituted of bars with sections and dimensions roughly comparable to the ones used for the staves. These products directly reflect the heterogeneity of the bloom originating from the furnace of reduction or refining, where the thermodynamic kinetic conditions are heterogeneous. At least, the metal used for the manufacture of bombards looks quite common, telling us that the technical prowess would lie rather in the techniques of shaping and assembly at the forge.

Smelting process

All the samples are located in the bloomery process area on the abacus (see Fig. 4 and have a high probability to have been made by the bloomery process (p finery < 0.08) according to the logistic regression (see Table 3.

In the 15th century, the indirect process is attested in several areas in Europe, in Sweden [START_REF] Magnusson | Lapphyttan. An example of medieval iron production[END_REF], the North of Germany and West of Switzerland [START_REF] Tauber | Eisenverhüttung im Dürsteltal[END_REF] since the 13th-14th c. [START_REF] Jockenhövel | Mittelalterliche Eisengewinnung im Märkischen Sauerland[END_REF], in Namur since the second half of the 14th c. [START_REF] Awty | The development and dissemination of the walloon method of ironworking[END_REF], in the kingdom of France since the 14th c. [START_REF] Rouillard | L'homme et la rivière : histoire du bassin de la Vienne au Moyen Âge (XIIe-XVIe siècles)[END_REF], in Champagne [START_REF] Verna | Les mines et les forges des Cisterciens en Champagne méridionale et en Bourgogne du Nord[END_REF] and in Normandy [START_REF] Belhoste | La métallurgie normande XIIe-XVIIe siècles. La révolution du haut fourneau[END_REF]. Notably, the first evidences in England are dated from the 16th century [START_REF] Cleere | The iron industry of the Weald[END_REF].

It is important to notify that the development of the indirect process in a region does not necessarily imply the disappearance of the direct process at the same time. Both historic, archaeometric and archaeological data have demonstrated that the two processes have coexisted during several decades or centuries in numerous areas [START_REF] Dillmann | Archéométrie et histoire des techniques : les procédés direct et indirect en sidérurgie (XIVe -XVIIe siècles)[END_REF]. Consequently, the process used to obtain the metal is not a reliable marker to identify the provenance of the metal or the location of a workshop. Thus, should the bombards of Meaux be made in England, we can only confirm that our results are compatible with the historical data regarding the diffusion of the indirect process in the North of Europe. However, this hypothesis is not asserted, as in the military framework this kind of artefact was often employed successively by several groups, above all during war background [START_REF] Collectif | Nouveaux regards sur l'artillerie primitive XIVe s.-XVe s[END_REF].

Metal provenance

PCA results are presented in Fig. 5. Only the four first components which express 90% of the variance are presented. All the SI belonging to the same bombard are plotted in the same colour.. On Fig. 5 C three samples are isolated: N22B, N23B, N26A while Fig. 5 A isolates sample N27A. Lastly, on Fig. 5 B three groups can be defined:

• Group 1: N21A, N27B, N22A, N26C, N23C

• Group 2: N24A, N24B, N24C, N24D, N21C, N21B, N23A, N23D, N26D, N22C • Group 3: N27C.

Then, in order to determine possible subsets within these clusters, new PCA were performed on each group. Only the projections on the plans defined by the principal components which contain pertinent information to differentiate groups are presented (PC1-PC2) (Fig. 6). It was checked that the remaining components do not contain relevant information to distinguish provenance groups (see Supplementary Materials).

Samples N22A and N26C belonging to Group 1 stay mixed contrary to samples N21A, N27B and N23C, whereas for Group 2 sample N23A have a different chemical signature from the others, forming one cluster. A summary of all the results is presented on Fig. 7.

A first observation is that, except for N24, all the bombards were made with metal of several origins. It strongly suggests that, faced with the large quantity of metal required to manufacture these objects, gunsmiths probably had to call on different suppliers. This hypothesis is supported by historical sources such as a purchase dated from 1375 to make a cannon in which three different metal supplies are mentioned (de Crouy-Chanel, 2014).

Furthermore on Fig. 7 only bombard N27, which differs most from the others by its size and shape, is isolated from a chemical point of view.

All the other bombards appear to have been made at least with one common supply of metal (Group gathering N24A, N24B, N24C, N24D, N21C, N21B, N23D, N26D, N22C). Further research is needed to determine to which geographical area it may correspond. However, this result could suggest that all the powder chambers were made at the same time, in the same geographical area or even by the same workshop, which used several metal supplies to produce them. The latter implies that the work was performed by an important workshop, able to set up equipment and people to forge at least five massive powder chambers.

Conclusion

This study presents archaeometric results on an unique assemblage of six bombard parts found at the same place (Meaux, France) and dated from the same period (15th c.). Our results confirm previous observations made on other pieces dated from this period: no deliberate choice was made regarding the nature of the ferrous alloys. Metal used to produce bombards was an ordinary material, showing heterogeneities in carbon content along with no heat-chemical treatment. The specific use of steel material, more resistant than other ferrous alloys, has not been evidenced on any of the studied parts of the bombards. Our results, based on a limited number of pieces, do not allow us to affirm that cast iron, whose use by moulding was attested in Northern Europe at this period, played a major role in the manufacture of these objects. Nevertheless, the assembly of these impressive artefacts certainly required a technical craftsmanship. For the first time, major and trace elements of SI embedded in the metal were measured. The results showed that bombards of Meaux were made by using a metal produced through the bloomery process. This observation is compatible with the actual data known for the diffusion of the indirect process in Europe confirming the concomitance of the two processes at this period. The analysis of trace element in the SI revealed a supply heterogeneity for each bombard, except for bombard N24. This result could be explained by the need of important quantities of metal to make these massive pieces. Nevertheless, except for bombard N27, metal from a same origin can be found in each of the bombard, which may suggest a synchronous manufacturing of the bombards, at the same place or even by the same workshop. This key observation, reinforced by the morphological similarities of the bombards, brings new insights to the fabrication of these massive pieces that were supposed to be realized in an isolated way.

Seine Graduate School Humanities, Creation, Heritage, Investissement d'Avenir ANR-17-EURE-0021 -Foundation for Cultural Heritage Sciences.

Fig. 1 .

 1 Fig. 1. "A" Photograph of bombard N24, "B" photograph of bombard N27

Fig. 2 .

 2 Fig. 2. Metallographic study for sample N24C showing the distribution of the carbon content, inclusions, and pores.

Fig. 3 .

 3 Fig. 3. Compositional domains of the bombards alloy structure according to the bell shape diagram proposed by[START_REF] Leroy | The ties that bind: archaeometallurgical typology of architectural crampons as a method for reconstructing the iron economy of Angkor, Cambodia (tenth to thirteenth c.)[END_REF].

Fig. 4 .

 4 Fig. 4. Abacus.

Fig. 5 .

 5 Fig. 5. "A": PCA carried out on transformed compositional data of SI projected onto PC1-PC2, "B": PCA carried out on transformed compositional data of SI projected onto PC1-PC3, "C": PCA carried out on transformed compositional data of SI projected onto PC1-PC4.

Fig. 6 .

 6 Fig. 6. PCA carried out on the transformed data of SI projected onto PC1 and PC2 for Group1 and Group2.

Table 1

 1 Bombards dimensions.

	Name	Total	Internal	External	Weight
		length(cm)	diameter (cm)	diameter (cm)	estimation (kg)
	N21	93	21	55	1440
	N22	104	18	50	1413
	N23	121	17	39	910
	N24	122	22	45	1122
	N26	100	19	37	709
	N27	89	13	42	832

Table 2

 2 Samples localisations.

	Bombard	N • Sample	Localisation
	N23	N23A	Hoop (Powder chamber and barrel joint)
		N23B	Hoop or stave
		N23C	Hoop or stave
		N23D	Rear end of the powder chamber
	N24	N24A	Hoop (Powder chamber and barrel joint)
		N24B	Hoop (Powder chamber and barrel joint)
		N24C	Rear end of the powder chamber
		N24D	Internal hoop of the powder chamber
	N21	N21 A	Stave?
		N21 B	External hoop
		N21 C	Rear end of the powder chamber
	N22	N22 A	Stave?
		N22 B	External hoop
		N22 C	Rear end of the powder chamber
	N26	N26 A	Stave?
		N26 B	External hoop
		N26 C	Rear end of the powder chamber
		N26 D	Internal hoop
	N27	N27 A	Externa hoop
		N27 B	External hoop
		N27 C	Rear end of the powder chamber

Pages

et al., and Leroy et al.,

Table 3

 3 Results of the process prediction for the samples.

		Process	p finery
	N21A	bloomery	<0,01
	N21B	Bloomery	<0,01
	N21C	Bloomery	<0,01
	N22A	Bloomery	<0,01
	N22B	Bloomery	0,04
	N22C	Bloomery	<0,01
	N23A	Bloomery	<0,01
	N23B	Bloomery	<0,01
	N23C	Bloomery	<0,01
	N23D	Bloomery	<0,01
	N24A	Bloomery	<0,01
	N24B	Bloomery	<0,01
	N24C	Bloomery	<0,01
	N24D	Bloomery	<0,01
	N26A	Bloomery	<0,01
	N26B	Bloomery	<0,01
	N26C	Bloomery	<0,01
	N26D	Bloomery	<0,01
	N27A	Bloomery	<0,01
	N27B	Bloomery	<0,01
	N27C	Bloomery	0,07

Acknowledgements

We would like especially to thank Sylvie Leluc (musée de l'Armée) for allowing us to study the bombards and her support, Antoine Leduc (musée de l'Armée) and Diana da Silva for their contributions to this work during the sampling campaign and reviewers for their feedback and comments. This work was supported by the LabEx PATRIMA ANR-10-LABX-0094-01 and the Fondation des Sciences du Patrimoine, Paris Fig. 7. Origin of the metal: summary of the results for each bombard.

Funding

This work was supported by the LabEx PATRIMA ANR-10-LABX-0094-01 and the Fondation des Sciences du Patrimoine, Paris Seine Graduate School Humanities, Creation, Heritage, Investissement d'Avenir ANR-17-EURE-0021 -Foundation for Cultural Heritage Sciences.

Declaration of Competing Interest

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

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.jasrep.2021.103307.


Alice Vilotte

Clément De Loubens
email: clement.de-loubens@univ-grenoble-alpes.fr

Deniz Z Gunes

Christophe Schmitt

Hugues Bodiguel

Hydrodynamic spinning of protein fractal aggregates into core-shell fibers

Keywords: cold gelation, calcium, whey protein isolate, osmotic flow, microfluidics, food

Using fractal protein aggregates as building blocks, porous fibers were produced. The suspension of aggregates was co-injected with a solution of calcium chloride. Sol-gel transition of the suspension was induced by diffusion of calcium ions in the jet. The production of these fibers required a precise control of both hydrodynamic and physicochemical conditions as hydrodynamic instabilities competed with the gelation kinetics. By increasing the calcium concentration, several regimes were observed: swollen, dispersed and shrunk fibers. In the first regime, homogeneous fibers were obtained. In the last one, osmotic phenomena led to a spontaneous core-shell structure with a dense shell.

Hydrogel microfibers have attracted interest in a wide range of fields: bio-engineering, 1 food science 2 or microelectronics. [START_REF] Guo | Conductive polymer hydrogel microfibers from multiflow microfluidics[END_REF] The high surface-to-volume ratio of fibers makes them an asset for tailoring the rheological properties of suspensions [START_REF] Zirnsak | Normal stresses in fibre suspensions[END_REF] and for the controlled release of molecules. [START_REF] Singh | Nanofibers: An effective tool for controlled and sustained drug delivery[END_REF] Nature also offers examples of protein-based fibers with unique mechanical strength. [START_REF] Rammensee | Assembly mechanism of recombinant spider silk proteins[END_REF] The control of fiber morphology also opens up new perspectives in term of applications. [START_REF] Wu | Review of microfluidic approaches for fabricating intelligent fiber devices: importance of shape characteristics[END_REF] For example, alginate core-shell fibers were used as scaffold for cells [START_REF] Andrique | A model of guided cell self-organization for rapid and spontaneous formation of functional vessels[END_REF] or for the design of flexible electronic systems. [START_REF] Guo | Conductive polymer hydrogel microfibers from multiflow microfluidics[END_REF] Lipid digestion was also controlled by encapsulation of lipid in biopolymers fibers. [START_REF] Sordo | Microstructured fibers for the production of food[END_REF] By taking advantage of the control of multilaminar flows, microfluidics is becoming the method of choice for producing fibers with controlled shapes. [START_REF] Wu | Review of microfluidic approaches for fabricating intelligent fiber devices: importance of shape characteristics[END_REF] For example, the production of hollow fibers is generally achieved by the coinjection of at least three different phases. [START_REF] Naeimirad | Recent advances in core/shell bicomponent fibers and nanofibers: A review[END_REF] The inner phase contains the compound to be encapsulated in the core; the middle phase contains the biopolymer and the external phase contains the cross-linker which diffuses to form the shell. [START_REF] Shin | On the fly" continuous generation of alginate fibers using a microfluidic device[END_REF] However, these multi-phase reactive flows of complex fluids are prone to hydrodynamic instabilities,, [START_REF] Williams | Modeling gel fiber formation in an emerging coaxial flow from a nozzle[END_REF][START_REF] Bonhomme | Elastic instability in stratified core annular flow[END_REF][START_REF] Cubaud | Regimes of miscible fluid thread formation in microfluidic focusing sections[END_REF] which makes them difficult to scale-up.

To control not only the shape but also the structure of the fibers, protein-based colloidal objects were also used as a building block. [START_REF] Wu | Review of microfluidic approaches for fabricating intelligent fiber devices: importance of shape characteristics[END_REF] Indeed, proteins can form colloidal objects with various structures depending on the physicochemical conditions of aggregation. Nanofibrils of proteins were oriented inside the fibers using microfluidic technologies. [START_REF] Wu | Review of microfluidic approaches for fabricating intelligent fiber devices: importance of shape characteristics[END_REF][START_REF] Kamada | Flow-assisted assembly of nanostructured protein microfibers[END_REF][START_REF] Lu | Strong silk fibers containing cellulose nanofibers generated by a bioinspired microfluidic chip[END_REF] Their ori-entation and entanglement enabled modulation of the mechanical strength of the fiber. [START_REF] Kamada | Modulating the Mechanical Performance of Macroscale Fibers through Shear-Induced Alignment and Assembly of Protein Nanofibrils[END_REF] Here, we went a step further in the formation of protein-based fibers with a hierarchical structure by using sub-micrometric fractal aggregates as the building block. The interest of using fractal aggregates instead of homogeneous particles lies in the fact that their density ρ decreases as their size R increases, as ρ ∝ R d f -3 where d f is the fractal dimension. Since, size, fractal dimension and density of aggregates are controllable, [START_REF] Nicolai | β-Lactoglobulin and WPI aggregates: Formation, structure and applications[END_REF][START_REF] Vilotte | Kinetic and structural characterization of whey protein aggregation in a millifluidic continuous process[END_REF] it should be possible to tune the physical properties of such fibers (density, elasticity), if these sub-micrometric aggregates can be assemble into micrometric fibers.

In this Letter, we focused on the spinning of edible whey protein isolate (WPI) derived from cow's milk which is mainly composed of two globular proteins, β-lactoglobulin and αlactabulmin. At temperatures higher than 65-70 • C, proteins lose their native structure and form aggregates. Depending on the balance between repulsive and attractive forces, nanofibrils, microgels or fractal aggregates are obtained by changing the pH from 2.0 to 7.0 and adjusting the ionic strength. [START_REF] Nicolai | β-Lactoglobulin and WPI aggregates: Formation, structure and applications[END_REF][START_REF] Zuniga | Kinetics of formation and physicochemical characterization of thermally-induced β-lactoglobulin aggregates[END_REF] Using fractal aggregates as building blocks, we produced porous fibers. Gelation was triggered by the addition of calcium chloride [START_REF] Alting | Number of thiol groups rather than the size of the aggregates determines the hardness of cold set whey protein gels[END_REF] in a core-annular flow. Although this process was simple, obtaining porous fibers required a precise control of both hydrodynamic and physicochemical conditions. Surprisingly, these fibers spontaneously exhibited a core-shell structure, triggered by osmotic phenomena.

The suspension of fractal aggregates was obtained by heat-induced denaturation and aggregation at 92 • C for 30 min of a solution of WPI (17.5 × 10 3 g/mol) at pH 7.0. The initial dispersion used to produce fibers just below the sol-gel transition, i.e. 8 wt% WPI at 10 mM NaCl (Fig. 1-a). These conditions led to the formation of aggregates 17 with a fractal dimension of about 2 and a hydrodynamic radius R h of 70 nm, as measured by dynamic light scattering (Vasco Cordouan Technologies, λ=658 nm). The concentration of the aggregates, C agg , was then varied from 6.6 to 10.1 wt%, either by dilution or by gentle evaporation at 30 • C for several hours. The viscosity of these suspensions was measured using standard rheometry and increased exponentially from 6.9 to 38 mPa.s when the concentration of the aggregates was increased from 6.6 to 10.1 wt%, in agreement with Ref. [START_REF] Inthavong | Structure and flow of dense suspensions of protein fractal aggregates in comparison with microgels[END_REF] By adding calcium chloride at room temperature, the suspensions of aggregates gelled for calcium concentrations higher than 5 mM. It resulted from both screening of electrostatic interactions and specific binding of calcium ions to the aggregates. Above 30 mM, syneresis was observed. [START_REF] Kharlamova | Calcium-induced gelation of whey protein aggregates: Kinetics, structure and rheological properties[END_REF] As depicted in Fig. 1-b, the shaping of continuous gelled fibers requires two key steps: hydrodynamic spinning with a core-annular flow between the suspension of aggregates (inner phase) and a solution of calcium chloride (outer phase); maturation of the fibers in a bath of a calcium chloride solution at the same concentration as that used for the outer flow. This concentration ranged from 35 mM to 5.9 M and is expressed as a molar ratio, R m , between calcium ions and WPI (R m = 7.8 -1560).

The core-annular flow was established by a coaxial needle (Ramé-Hart Instruments), with inner and outer radii r i = 178 µm and r o = 356 µm, respectively. A syringe pump (Nemesys, Cetoni) was used to control the core and annular flow rates, Q agg and Q Ca 2+ . The needle was embedded into a fluorinated ethylene-propylene flexible tube (Fluigent) immersed in a water-bath (27 • C). The tube length L was adjusted from 11 to 225 cm in order to keep the residence time τ r = L/v unchanged when flow rates were varied, where

v = (Q agg + Q Ca 2+ )/πr 2
o is the mean velocity. To avoid long tube length, τ r was set to 6 s, which was almost two orders of magnitude lower than the characteristic time of calcium ions diffusion in the core of the flow τ d r 2 i /D 300-500 s. However this short first step was sufficient to stabilize the fiber by ionic cross-linking of the aggregates at the periphery of the inner jet, of its initial length before break-up. Images of the gelled fibers were systematically taken by bright field microscopy (Olympus IX-72) with a ×4 objective just after the production, and all along the maturation step.

We will first consider results on the role concerning the role of the hydrodynamic parameters. Depending on the flow rates, either long fibers or some pieces of gel were observed at the outlet of the tube (see examples displayed in Fig. 2-b). The state diagram of fiber formation (Fig. 2-a) shows that fibers were only obtained in a narrow range of mean velocity, v 1 < v < v 2 , for a given flow rate ratio q = Q Ca 2+ /Q agg . When q was increased, the fiber diameter decreased but the range of existence was reduced further as v 1 increased and v 2 decreased simultaneously.

In core-annular laminar flows of Newtonian fluids, and after an entrance region of the order of a few tube diameters, the diameter D of the inner phase is predicted by solving momentum balance and mass conservation equations. [START_REF] Bonhomme | Elastic instability in stratified core annular flow[END_REF] It reads

D = 2r o [(α -1) / (α -1 + m)] 1/2
, where m is the viscosity ratio m = η Ca 2+ /η agg and α = 1 + m/q. Since we focused on regimes where q > 1 and m 1, α ≈ 1, and the diameter could be more simply expressed as D = 2r 0 / √ 1 + 2q. In Fig. 2-c, this prediction is plotted together with the experimental data as a function of q, and for several molar ratio R m . A good quantitative agreement was found. This was expected since the diffusion of the protein aggregates was negligible. Note that a small but significant decrease of the diameter was observed when the calcium concentration was increased. This point will be discussed, further in this paper.

The two critical velocities v 1 (q) and v 2 (q) likely have two different physical origins.

For v < v 1 , direct observation at the inlet of the tube revealed the formation of a clog on the needle that was regularly evacuated. By introducing a characteristic gelation time τ g , we can tentatively write that a plug is formed when the distance travelled by the aggregates during τ g is smaller than the entrance region ( r o ), i.e. when τ g < r [START_REF] Guo | Conductive polymer hydrogel microfibers from multiflow microfluidics[END_REF] o /Q agg . This condition is equivalent For each calcium chloride concentration, the thinnest fiber produced is highlighted using a full symbol. At higher q, the fibers were cut into small pieces. The solid line is the model prediction, D = 2r o (1 + 2q) -1/2 . d: Examples of fiber images obtained using bright field microscopy.

to v < v 1 , where v 1 = r o (q + 1) /τ g . It provides a good description of the low-velocity limit of the diagram with τ g = 0.4 s (Fig. 2-a, plain line). This characteristic time is consistent with the fact that a droplet of WPI dropped in 1.5 M CaCl 2 solution gelled almost instantaneously. Conversely, the high velocity limit, v 2 , is likely to arise from flow instabilities, which are common in core-annular flows of miscible fluids. [START_REF] Govindarajan | Instabilities in viscosity-stratified flow[END_REF] Thread destabilization is triggered by diffusion or inertia depending on the Péclet (Pe) and Reynolds numbers (Re). [START_REF] Cubaud | Regimes of miscible fluid thread formation in microfluidic focusing sections[END_REF] Our experiments were carried out in flow conditions which were stable with respect to diffusive instabilities, since Pe = vr o /D Ca 2+ ranged from 0.5 to 10 ×10 4 , whereas diffusive instabilities are triggered for Pe smaller than 0.5×10 4 . 12 Inertiadriven instabilities were observed for miscible (and non-reactive) fluids above a critical value of Reynolds number Re c = 900/q for a viscosity ratio of 10 12 (Fig. 2-a, dashed-dotted line). The order of magnitude of Re c matches the high velocity limit v 2 , especially for q > 10. A discrepancy is found at lower q, and the scaling is not consistent, since we found v 2 ∼ q -0.5 . This apparent disagreement might originate from the fact that in the work of Cubaud and Notaro, 12 the investigated range of q was typically 10-1000. Other experimental or theoretical work have also been reported on miscible core-annular flow instabilities, [START_REF] Olce | Pearl and mushroom instability patterns in two miscible fluids' core annular flows[END_REF][START_REF] Martin | Convective/absolute instability in miscible core-annular flow. Part 1: Experiments[END_REF][START_REF] Salin | Revisiting the linear stability analysis and absolute-convective transition of two fluid core annular flow[END_REF] but only scarce data as a function of q are available, in particular for the viscosity ratio range considered in this Letter. Therefore, it seems difficult to draw conclusions concerning the low-q regime (q<10), but the qualitative agreement found at higher q with the work of Cubaud and Notaro supports the idea that the v 2 limit of fiber formation was due to inertial hydrodynamic instabilities.

Since cold-set gelation of WPI is a slow and complex process (the shear modulus of the gel increases slowly over several decades in time [START_REF] Kharlamova | Calcium-induced gelation of whey protein aggregates: Kinetics, structure and rheological properties[END_REF] ) and the residence time is short compared to the time of Ca 2+ diffusion, a maturation step was required to consolidate the fibers. We observed rather complex phenomena during this maturation step, summarized in Fig. 3-a.

At low calcium chloride concentration (e.g. R m = 28), the fibers tended to swell (Fig. 3-c). In contrast, the diameter of the fibers produced at very high calcium concentration remained steady. In these two regimes, as cross-linking by calcium ions is irreversible, fibers could be stored during several days without any significant change in size or strength. More surprisingly, in between these two regimes (e.g. R m = 53), we observed that the fibers eventually broke up and dispersed after being swollen (Fig. 3-c,d). We were not able to produce fibers at protein concentrations below 6 wt%, Fig. 3-A. At 8 wt% and above, the three regimes were systematically observed. Final diameters of the fibers were roughly independent of protein concentration (Fig. 3-b). In the swelling regime, the final diameter increased from 180 µm up to 260 µm when the calcium concentration was increased. In the stable regime, a rather strong decrease of the diameter was observed when the calcium concentration was further increased, suggesting a shrinkage occurring during the production step.

These observations are puzzling since the increase of the calcium concentration led successively to a swelling, then to a dispersion, and finally to a shrinkage of the fibers. Such a non-monotonic behavior was reported for calcium-induced gelation of whey proteins: [START_REF] Hongsprabhas | The structure of coldset whey protein isolate gels prepared with Ca++[END_REF] both the gelation rate and the Young's modulus of the gel exhibited a maximum when the calcium concentration was increased. [START_REF] Hongsprabhas | The structure of coldset whey protein isolate gels prepared with Ca++[END_REF][START_REF] Roefs | Aggregation and gelation of whey proteins: specific effect of divalent cations. Food colloids: Fundamentals of formulation[END_REF] Concomitantly, the fractal dimension of the aggregates was seen to increase. This phenomenon might result from a balance between inter-and intra-aggregate bridging by the calcium ions, the latter being dominant at high concentration. This led to a micro-phase separation, as the density of the aggregates increased due to intra-aggregate bridging of carboxylate groups. Similar behavior was reported in globular protein/polyelectrolyte mixtures as a function of the charge neutralisation ratio. [START_REF] Gummel | Finite size and inner structure controlled by electrostatic screening in globular complexes of proteins and polyelectrolytes[END_REF] One macroscopic consequence of this phe-nomenon is syneresis, which is observed in gels at high calcium concentration. [START_REF] Kharlamova | Calcium-induced gelation of whey protein aggregates: Kinetics, structure and rheological properties[END_REF] It can explain both the swelling and the dispersion of the fibers observed during the maturation step. Indeed, swelling or dispersion of the fibers were rather slow, typically 10 3 s, an order of magnitude which coincides with the diffusion time of the aggregates over the fiber radius, τ d ∼ r 2 /D agg ∼ 8 × 10 2 s with r ∼ 50 µm and D agg ∼ 3 × 10 -12 m 2 /s. The range in calcium concentration where fiber dispersion occurred (typically 100 mM) was also compatible with the onset of macroscopic syneresis 21 (30 mM) for similar initial protein aggregates. The shrinkage regime observed at even higher calcium concentration remains to be elucidated as it does not match this physical picture. Indeed, shrinkage occurred during the 6 s of the production step.

An additional physical phenomenon must therefore be considered. In a forthcoming communication, we proved that gelled biopolymers such as WPI or alginate very partially act as a semi-permeable membrane.we proved that gelled biopolymers such as WPI or alginate very partially act as a semi-permeable membrane. The consequence of this behaviour is the spontaneous generation of an osmotic flux from the solution of biopolymer towards the solution of calcium through the gel at high osmotic pressure difference. This osmotic flux tends to concentrate the aggregates in the gel under formation. Transposing this osmotic flow in the case of fibers, one can expect, as observed, a shrinkage of the fibers, together with an increase of the protein concentration at its periphery, as shown in Figure 1-g.

To check this assumption, electronic (SEM) and confocal fluorescence microscopy (Leica TCS SP8) were used. The apparent porosity seen on SEM images was due to freeze-drying (Fig. 4-a,b, see Supp. Mat.). Fibers produced in the low calcium concentration regime exhibited a uniform inner structure (Fig. 4-a). In contrast, those obtained in the high concentration regime showed a dense shell surrounding a core (Fig. 4-b). This core-shell structure of the shrunk fibers was further confirmed more quantitatively using confocal microscopy by imaging the fibers mid-plane Fig. 4-c,d. As WPI were labelled with a fluorescent dye, 29 the fluorescent intensity is approximately proportional to the protein concentration. The shrunk fibers exhibited an intensity gradient along the radial direction, whereas the fluorescent intensity was constant for the fibers produced at low calcium concentration (Fig. 4-d). The excess protein concentration in the shell was about 20% for the shrunk fibers. This order of magnitude might appear moderate, but it represents a significant increase in terms of mechanical properties [START_REF] Kharlamova | Calcium-induced gelation of whey protein aggregates: Kinetics, structure and rheological properties[END_REF] . These observations are consistent with the scenario proposed above: an osmotic flow occurred from the inside to the periphery of the fiber, leading to an increase of the aggregate concentration in the shell, and a decrease of its radius.

In conclusion, fibers made of whey protein aggregates were shaped by hydrodynamic spinning. Fiber diameter was simply tuned by the hydrodynamic conditions. The velocity range where long and uniform fibers could be produced, was relatively narrow because the velocity needed to be sufficiently high to delay gelation near the inlet, and sufficiently low to prevent hydrodynamic instabilities. The concentration of calcium ions had important consequences. At low concentrations, fibers with uniform inner structure were produced. Then, fibers were not stable. At very high calcium concentrations, fibers shrunk and exhibited a dense shell. Although the intermediate regime is probably specific to the particular interaction between the whey proteins and the calcium ions, the concentration gradient observed in the high concentration regime is likely to be generic to other systems. It was interpreted as a consequence of an osmotic flow taking place from the inside to the outside of the fiber. The possibility of obtaining a composition gradient or a core-shell structure spontaneously paves the way to controlling the structure of fibers or microparticles made of colloidal particles.

Figure 1 :

 1 Figure 1: a: Sol-gel diagram of suspensions of fractal WPI aggregates obtained by heating at 92 • C and for 30 min a solution of WPI at pH 7.0. b: Solutions of fractal aggregates were spun in a core-annular flow with a solution of CaCl 2 to initiate the sol-gel transition at the periphery of the fiber. During the maturation step, fibers were kept for 20 min in a solution of CaCl 2 to completely gel the fibers. c: Photograph of WPI aggregate fibers. d: Snapshots of a fiber being manually stretched up to break-up. Scale-bar 1 mm. e-g: Fibers were gelled by diffusion and ionic crosslinking of Ca 2+ . f: At low ionic strength, the gelation was uniform in the fibers. g: At high ionic strength, an osmotic water flux from the fiber to the CaCl 2 solution concentrated the aggregates at the periphery of the fiber and spontaneously generated a core-shell structure.

Figure 2 :

 2 Figure2: a: State diagram of fiber production in the v -q plane, for C agg = 8%, t = 6 s and Ca 2+ = 1.5M. The dashed line is a guide-for the eye corresponding to the high velocity limit v 2 . Solid line is the v 1 criterion given by r 0 (1 + q)/τ g with τ g = 0.4 s (see text). The dash-dotted line is the inertial instability threshold determined in Cubaud and Notaro 12 . b: Image examples of the three regimes. Experimental conditions are (from left to right): v = 0.018, 0.0739, and 0.3359 m/s; q = 40, 10 and 5. c: Fiber diameter measured just after the production, for v = 7.5 × 10 -2 m/s, C agg = 8% and t = 6 s. For each calcium chloride concentration, the thinnest fiber produced is highlighted using a full symbol. At higher q, the fibers were cut into small pieces. The solid line is the model prediction, D = 2r o (1 + 2q) -1/2 . d: Examples of fiber images obtained using bright field microscopy.

Figure 3 :

 3 Figure 3: a: State diagram of fiber formation and maturation for various calcium concentrations (converted in molar ratio R m ) and injected protein aggregate concentration C agg . Flow conditions were v = 7.4 × 10 -2 m/s and q = 10. Circles stand for stable fibers within 20 min of maturation step. Crossed circles for cases where a fiber was initially formed but then was dispersed during the maturation step. Crosses are for cases where no fibers were formed. b: Final fiber diameters (after 20 min maturation). c: Examples of fiber diameter measured during the maturation step and plotted as a function of time (C agg = 9.2%). d: image sequence during the maturation step in the dispersed fibers regime (R m = 53, C agg = 9.2%).

Figure 4 :

 4 Figure 4: Imaging of freeze-dried fibers by scanning electron microscopy at low (a, R m = 17) and high (b, R m = 145) calcium concentrations. The apparent porosity was due to freeze-drying. Confocal scanning microscopy of the mid-plane of fibers made of WPI labelled with a fluorescent in distilled water at low (c, R m = 17) and high (d, R m = 145) molar ratios. e: Fluorescent intensity profile along the radial direction r of the fiber (red lines) at high and low molar ratios and for fibers of different diameters. For each sample, the fluorescent intensity is an averaged over 4-5 cross-sections and was rescaled by the mean intensity.

Acknowledgement LRP is part of the LabEx Tec21 (ANR-11-LABX-0030) and of the PolyNat Carnot Institute (ANR-11-CARN-007-01). The authors thank Christine Lancelon-Pin (CERMAV-CNRS, Grenoble, France) for her assistance with scanning-electron microscopy. The authors acknowledge the NanoBio-ICMG chemistry platform (UAR 2607, Grenoble) for granting access to the electron microscopy facilities.

Supporting Information Available

A table of the notations and a description of the experimental procedure for scanning-electron microscopy are given in supplementary material.

TOC Graphic

Calcium Aggregates

Fiber of aggregates

Core-shell structure Hydrodynamic spinning


Juliette Karpiel
email: juliette.karpiel@cea.fr

Pierre Lonchambon

Frédéric Dappozze

Nathalie Herlin

Chantal Guillard

Chantal Guillard Fab

Fabrication of photocatalysts by laser pyrolysis for alkenes production

received her engineering master degree in materials sciences in 2019. She now is a PhD student affiliated to the French Alternative Energies and Atomic Energy Commission (CEA) in the fundamental research department based in Paris-Saclay. She also works with the Research Institute on Catalysis of Lyon