Przemyslaw Czech

Lidia Okrasa
email: lokrasa@p.lodz.pl

Francoise Méchin

Gisele Boiteux

Jacek Ulanski

Investigation of the polyurethane chain length influence on the molecular dynamics in networks crosslinked by hyperbranched polyester

Keywords: molecular dynamics, polyurethane networks, hyperbranched polymer

Several non-conventional polyurethane (PU) networks crosslinked with hyperbranched polyester (Boltorn ® H40) were synthesised with an aim to determine an influence of the PU chain length on molecular relaxations in such systems. The PU chain length was regulated by changing the macrodiol length or by changing the number of the repeating macrodiol/diisocyanate units n. Molecular dynamics were investigated by broadband dielectric spectroscopy and by dynamic mechanical analysis. It was found that the macrodiol length has a strong influence on the glass transition and the α-relaxation, and also on the crystallization. By contrast, the changes of n practically do not affect the molecular relaxations. This effect was explained by the formation of a physical network by hydrogen bonds between urethane groups, controlling the molecular mobility. The rheological measurements have shown, that at temperatures above 150 o C, when hydrogen bonds were thermally destroyed, not only macrodiol length but also n had strong influence on the flowing point.

INTRODUCTION

Polyurethanes (PUs) are unique polymeric materials with a wide range of physical and chemical properties [START_REF]Polyurethane Handbook[END_REF]. Because many different monomers are now commercially available and tailor-made properties can be obtained from well-designed combinations of precursors, PUs can be tailored to meet the highly diversified demands of modern technologies such as coatings, adhesives, fibre, foams, and thermoplastic elastomers. Several papers published on this topic show that by changing the composition and the conditions of processing one can influence the chemical and morphological structure of PUs and their properties [START_REF] Mitzner | [END_REF][3][4].

Linear segmented polyurethane elastomers can be considered as block copolymers, which consist of soft segments formed with polymer glycol and hard segments based on diisocyanate and chain extender. The properties of these PU elastomers are strongly dependent on molar mass and polydispersity of the soft segment component, as well as on the chemical structure and weight fraction of all components [5][6][7][8][9][10][11]. Especially, polyether polyurethanes have been intensively studied due to their excellent physical properties, resistance for infectiousness, and superior blood compatibility. An increase of the hard segment content in polyurethane structures gives polymers with higher elastic modulus.

Changes of molar mass and chemical structures of the soft segments and chain extenders produce polyurethanes with modified properties [12,[START_REF] Redman | Developments in Polyurethanes[END_REF].

As far as the networks are concerned, one of the important factors used for changing their properties is the type of crosslinking agent. Often enough, in PU systems two kinds of networks can be present: physical and chemical. The physical network is created by the Hbonds, which link the carbonyl groups and NH groups of adjacent chains [START_REF] Yilgör | [END_REF]. Chemical network parameters depend on the crosslinker nature. Recently some papers dealing with the use of dendritic molecules as crosslinking agents were published [15][16][17].

In this work several PU networks based on hyperbranched polyester were investigated by means of broadband dielectric spectroscopy and dynamic mechanical analysis, which give complementary information about the molecular dynamics. The comparison of these two techniques and methods of analysis and comparison of their results was discussed comprehensively by Pakula [START_REF] Pakula | Broadband Dielectric Spectroscopy[END_REF]. The synthesised polyurethane systems were different in length of the linear chain between the crosslinking points, which was regulated by using macrodiols of different molar masses or by changing the number of repeating macrodiol/diisocyanate units in the chain.

EXPERIMENTAL

Materials

Several PU networks crosslinked by the hyperbranched (HB) polyester of 4 th generation (Boltorn ® H40) were synthesized in bulk using polytetrahydrofuran (Terathane ® ) with different molar masses: 650, 1000, 2000 and 2900 g/mol, and 4,4'diisocyanatodiphenylmethane (MDI with M w =250 g/mol) as monomers. The structure of the used reagents is shown in Fig. 1. According to the producer Boltorn ® H40 has a molar mass M w = 5100 g/mol with polydispersity M w /M n = 1.8 and hydroxyl number 470-500 mg KOH/g. These data give at the average 44 primary -OH groups in the molecule. The substrates were used as supplied by the producers without additional purification.

The aim of the synthesis presented in this paper was to obtain series of networks in which polyurethane linear chains are connected by the HB crosslinker. The PU linear chains in these series have different lengths, controlled by the molar mass (i.e. length) of the macrodiol or by the number (n) of the repeating macrodiol-diisocyanate units. The constant number of primary -OH functions present in the HB polymer controls the number of PU chains connected to the hyperbranched polyester.

The synthesis of polyurethane was carried out in bulk. Amounts of ingredients for synthesis of stoichiometric systems were calculated in accordance to the numbers of the -OH groups in the HB crosslinker and to the projected length of the PU chains between the crosslinking centres [17].

The calculated amount of Terathane ® was placed in a flask equipped with magnetic stirrer and heated up to 80 o C and kept during half an hour under vacuum. Then the crosslinker was added and the mixture was stirred at about 100 o C until all was dissolved. When the solution was clear, it was placed under vacuum at 60 o C for half an hour in order to avoid bubbling during the reaction. In the next step MDI, heated up to 60 o C, was added. After quick mixing the reaction mixture was cast onto an aluminium pan and again placed under vacuum at 60 o C for half an hour. To proceed with the full conversion of reaction the pan was placed in a drying oven at 100 o C for 7 hours. The polymers were obtained as films with thickness from 0.2 to 1 mm. A schematic road of the synthesis of the PU network crosslinked with the HB centres is shown in Fig. 2. The end of reaction was determined by FTIR spectroscopy. In the final PU networks the diisocyanate -N=C=O band (2250-2275 cm -1 ) was absent in the spectra. The bands characteristic for the polyurethane formations appear at: 3320cm -1 -urethane N-H stretching; 1731 cm -1 -urethane C=O without hydrogen bonding; 1710 cm -1urethane C=O with hydrogen bonding; 1535 cm -1 -urethane N-H bonding.

Characterisation techniques.

The chemical structure of the synthesised materials was verified by FTIR absorption using a Bio-Rad FTS 175 C spectrometer in the reflection mode with the Harrick IRS attachment.

The glass transition temperatures (T g ) were determined using differential scanning calorimetry (TA Instrument DSC 2920). Two runs were performed for each sample in the range from -150°C to +200°C with a heating rate of 10 C/min under nitrogen atmosphere. The cooling scans were performed at an average rate of 25 C/min. The T g values were determined as the onset points from the second scans with an accuracy better than 1°C.

Molecular relaxations were characterised in broad temperature and frequency ranges by dynamic mechanical analysis (DMA) using TA Instrument DMA 2980 Dynamic Mechanical Analyser, and dielectric relaxation spectroscopy (DRS) using Novocontrol Broadband Dielectric Spectrometer. The DMA was performed in film tension mode in the temperature range from -130°C up to +150°C with a temperature ramp of 2 C/min using rectangular samples with the length 25 mm, width 5 mm and thickness 1 mm. Three frequencies were applied: 1, 5 and 10 Hz. The DRS was performed in the frequency range 0.01 Hz -1 MHz and in the temperature range from -150°C up to +130°C with a step 5°C with temperature stabilisation better than 0,1°C. For these measurements circular shape samples with diameter of 20 mm and thickness up to 0.5 mm were used. Dielectric results were presented in the classical representation of complex dielectric permittivity (ε* = ε' + iε"), as well as using the electric modulus (M* = M' + iM") representation defined by Macedo et al [START_REF] Macedo | [END_REF]. Τhe real M' and imaginary M" parts of the electric modulus were calculated according to the equations 3 and 4:

2 2 ε" ε' ε' M' + = (1) 2 2 ε" ε' ε" M" + = (2)
where: ε' and ε" are, respectively, real and imaginary part of the permittivity.

Although the complex permittivity representation is easier in an interpretation, the modulus representation can be very useful, where conductivity processes are involved.

The activation energy maps were prepared on the basis of both dielectric as well as mechanical spectra. The points were taken from the maxima of the ε"(f) plots using the WinFit software for the dielectric relaxations and manually from the M"(T) plots for the conductivity phenomenon. For the mechanical relaxations the points were taken from the E"(T) plots. Estimation of the position of the maxima was done with an accuracy better than 2°C. The relaxation times τ were calculated from the equation: τ = 1/(2πf), where f stands for frequency.

Viscoelastic measurements were performed using a Rheometrics Instrument RS5 apparatus in the range of temperatures from +150ºC up to +230ºC and for frequencies from 10 -2 up to 10 2 rad/s. The temperature step was 10°C. Samples for these measurements had a diameter of 25 mm and a thickness of about 0.5 mm. Additionally, the activation plots were prepared from the rheological results. As the characteristic parameter the flowing point, when tanδ = 1, was taken.

RESULTS

The glass transition temperatures of the investigated systems determined by means of DSC are collected in Table 1, where the samples nomenclature is also defined. It appears clearly that the T g of the PU networks depends mainly on the length of the macrodiol used in the reaction. For the PU with longer macrodiol segments the T g is shifted to lower temperature. For the systems with a constant high molar mass macrodiol, Terathane®2000, the increase of the number n of repeating macrodiol-diisocyanate units from 4 to 20 practically does not influence the value of the T g . Our previous investigations have shown that also for the samples with Terathane ® 650 the increase of n resulted only in a slight decrease of the glass transition temperature [17]. The DSC second run spectra recorded for the systems with different lengths of macrodiol are shown in Fig. 3. Besides the steps connected to the glass transitions, for the samples with Terathane ® 2000 and Terathane ® 2900 endothermic peaks connected with the melting of polyoxytetramethylene-rich soft domains are visible at 14ºC and 22ºC, respectively. For Terathane ® 2000 at -17ºC additionally an exothermic crystallization peak is visible. During the first heating scan, the sample is brought to an amorphous, totally disordered state. But after cooling, a partial phase separation and crystallization of the soft segments can occur [20][21][22], provided that they are long enough so that the steric hindrance is low and their chain ends do not constitute a too big amount of "impurities". This crystallization peak was not detected for the sample based on Terathane ® 2900, presumably because in this case the crystallization occurs so rapidly and effectively during the cooling that it is already completed, when the heating scan begins. Fig. 4 shows the 3D frequency and temperature dependencies of the permittivity imaginary part for the samples with macrodiols of different lengths. One can see that for the samples based on short macrodiol Terathane ® 650 (Fig. 4a), three relaxation processes in order of decreasing temperature α, β and γ are visible. Above the α-relaxation, a conductivity phenomenon occurs, that is well visible in Fig. 5 showing the dielectric modulus representation. Similar relaxations are detected for the sample based on Terathane ® 1000 (Fig. 4b). In the case of the samples with longer macrodiols Terathane ® 2000 or Terathane ® 2900, the β-relaxation is overlapped by the α-relaxation, which is shifted to lower temperatures (Fig. 4c,d). For the sample 20-T2000 at about -35ºC the frequency independent peak, labelled α', is visible. The origin of this relaxation is most probably the same as that of the exothermic peak visible in the DSC diagram. This process is also visible in DMA measurements (see Fig. 5). In this temperature range, a big increase of both parts (real and imaginary) of storage modulus is observed. Such behaviour means that the sample becomes stiffer. One can conclude that at about -35ºC cold crystallization of polyoxytetramethylene-rich domains is initialised. Fig. 5 shows the comparison of dielectric and mechanical moduli spectra for the samples with different lengths of the macrodiol and constant n = 20. One can see that the position of the α-relaxation strongly depends on the macrodiol molar mass. At 1 Hz the maximum of the α-relaxation for the sample 20-T650 is at -28ºC and shifts to -44ºC for 20-T1000, -62ºC for 20-T2000 and 20-T2900. Positions of the α-peak maxima in the DRS spectra correspond very well with those in the DMA spectra, where at 1 Hz for the sample 20-T650 the α-process has maximum at -25ºC, for 20-T1000 at -47ºC and for 20-T2000 at -67ºC. One can see that change tendencies of the α-process maximum are the same as those for T g determined by the DSC measurements (see Table 1). As was mentioned above, the β-relaxation is well pronounced only for the samples with Terathane ® 650 and Terathane ® 1000 and the maxima of these peaks at 1 Hz in DRS are at about -90ºC. In the DMA measurements the β-process occurs in the same temperature region. The γ-relaxation is well visible for all systems. The positions of the maxima are similar for all the systems, i.e. at 1 Hz about -135°C to -140ºC.

The data from dielectric and mechanical results are collected in the activation plots in Fig. 6.

In the DMA measurement for the 20-T2000 sample over -20ºC a decrease of moduli is visible. This process is connected with a partial melting of the sample, which is also detected in the DSC thermogram (Fig. 3). Unfortunately, the DMA measurements for the 20-T2900 sample were not possible because the sample was too soft for the experiments in tension mode.

The second way of changing the average PU chain length between the crosslinks was by increasing the number n of the repeating macrodiol/diisocyanate units. For this purpose, series of samples with Terathane ® 2000 and n = 4, 10 and 20 were investigated. Fig. 7 shows the dielectric and mechanical spectra of the PU systems obtained from macrodiol Terathane ® 2000. On the DRS spectra at 1 Hz for all the systems two relaxation processes are visible, α and γ, at about -60ºC and -145ºC, respectively. On the DMA spectra only the α-relaxation can be observed. Its position for 1 Hz is about -70ºC. The γ-relaxation is below the measurement temperature range. Above the α-relaxation in the DRS spectra a small peak (α') is also present. In this range in the DMA spectra for all the samples with Terathane ® 2000 an increase of the shear modulus is observed, followed by a decrease above ca -25ºC. This effect is connected with the cold crystallization and melting phenomena, as it will be discussed further on. The activation energy plots for the dielectric and mechanical measurements are shown in Fig. 8.

In Fig. 9 the results of the rheological measurements for three samples (20-T650, 20-T2000 and 4-T2000) are shown. As the characteristic parameter the flowing point (when tanδ = 1) was taken. One can see that the viscoelastic properties of the samples differ strongly. The flowing points for the samples based on the longer macrodiol appear at much lower temperatures (or at higher frequencies) than those for the networks with the shorter Terathane ® . Also an increase of the number of repeating units n results in a shift of the flowing points to lower temperatures (or to higher frequencies).

DISCUSSION

In all the investigated systems, two relaxation processes (primary α-relaxation and secondary γ-relaxation) are visible in the DRS spectra. Secondary β-relaxation is detected only for the systems prepared from Terathane ® 650 and Terathane ® 1000. In the systems with longer macrodiol, the T g is strongly shifted to lower temperatures and the β-relaxation is overlapped by the α-relaxation. The DMA measurements give similar results, however the γ-relaxation is below the measurement temperature range and only high temperature shoulder of this process is visible (cf Figs. 5 and7).

Positions of the α-relaxation, generally associated with the glass transition and observed in both the DRS and DMA measurements are in good agreement. The α-process is strongly sensitive on the length of macrodiol used in the synthesis of PU networks -with increasing the molar mass of the macrodiol the positions of the α-peak and T g shift to lower temperature. Such effect was expected because for longer chains of macrodiol the stiffness of the system decreases and glass transition should occur at lower temperature. On the other hand increasing the PU chain length by repetition of the soft-hard chain segments should also result in a decrease of the glass transition temperature, what is not observed. Such behaviour can be due to the H-bonds, which are created between the urethane groups in the PU chains and which can superimpose additional physical network to the existing chemical network. The mean distance between H-bonds in the PU chains is mainly determined by the length of the macrodiol and due to that, an increase of the macrodiol molar mass results in significant changes of T g . On the other hand an increase of n has a much weaker influence on the concentration of the H-bonds and therefore the stiffness of the systems with different numbers of repeating units is similar.

Such effect was already reported by Nabeth et al. [23], for simpler PU networks based on polycaprolactone or poly(1,4-butanediol/1,2-ethanediol)adipate macrodiols, MDI or α,α,α',α'-tetramethyl-m-xylylene diisocyanate and 2-ethyl 2-hydroxymethyl 1,3-propanediol (trimethylolpropane) as a crosslinker. The authors have found that for these homogeneous networks the empirical equations with a 2 nd order dependence of T g on the urethane weight concentration N u (T g = T g0 + AN u + BN u 2 ) can be applied [23]. We have analysed in a similar way the dependence of T g on N u for the samples listed in Table 1, as well as for those described in our previous paper [17]. The N u values were calculated from the molar masses of the precursors and their proportions, assuming that all the OH and NCO groups had reacted together. The experimental points obtained in such a way are shown in Fig. 10. One can see that these points can be also fitted by an analogous empirical 2 nd order law:

T g = -89.5 + 8.22N u + 5.20N u 2 .
This suggests that our networks, once above the possible partial melting of some polyoxytetramethylene-enriched domains, should be quite homogeneous and that their T g would be linked to the urethane concentration by a universal relationship. It is remarkable that in the cited Nabeth's work such relation was not valid for the networks with non-pointlike crosslinks obtained by free radical polymerization of acrylate chain ends, that displayed a quasi-two-phase morphology; in our case the architecture of the hyperbranched crosslinks is also complex, but nevertheless it seems to lead to a homogeneous structure of the global network. It is worthy to note that the value extrapolated for zero urethane groups, i.e. -89°C, is close to the glass transition temperature reported for high molar mass polyoxytetramethylene (-84°C) [START_REF] Peyser | Polymer Handbook, Third Edition[END_REF].

The secondary β-relaxation is most probably attributed to the local motions of the polar urethane groups [4,[START_REF] Kanapitsas | [END_REF]26]. This relaxation is well visible only for the systems with the shortest macrodiol Terathane ® 650 and Terathane ® 1000, and for these systems its position is almost identical, at about -90°C. For the networks with Terathane ® 2000 and 2900 this β-process probably is also present in similar temperature range, so its position is close to the α-relaxation, which for the networks with long macrodiols is shifted to low temperatures, and because of higher intensity overlaps the secondary β-relaxation. This overlapping is clearly visible on the activation plots for these systems (see Fig. 6).

The γ-relaxation is visible in all the investigated systems at practically the same temperatures, i.e. at ca. -140°C at 1 Hz. This relaxation is assigned to local motions of the (CH 2 ) 4 sequences of the soft segments. In the investigated systems such sequences are identical; therefore the activation energies for the γ-relaxations are also similar, around 37 kJ/mole, for all the samples.

In the dielectric measurements for the samples based on Terathane ® 2000 above their glass transition the additional relaxation peak (α') is present. Because the position of this peak corresponds to the exothermic peak present in the DSC curves as well as to the sharp increase of the storage modulus in the DMA measurements, this process is most probably connected with cold crystallization of polyoxytetramethylene-rich domains. As discussed before, all the samples obtained from longer macrodiols (Terathane ® 2000 or Terathane ® 2900) are partially crystalline. The longer the macrodiol used in the reaction, the higher melting temperature is observed. This fact is proved by the DSC measurements, which show endothermic peaks at 14ºC and 22ºC for 20-T2000 and 20-T2900 samples, respectively. The melting process is not sensitive to the changes in the repeating units number n. For the samples with Terathane ® 2000 the melting process is detected also by DMA, which shows a rapid decrease of storage modulus in this temperature range.

To verify the hypothesis that dense H-bonds can determine the behaviour and properties of the investigated systems at low temperatures, rheological measurements have been performed at high temperatures. Above ca 150ºC the H-bonds should be thermally destroyed and in this temperature range the behaviour of the chemical network should become evident.

And indeed it was found that with increasing length of the macrodiol the samples became softer, and the flowing point of the system is shifted to higher frequency (or to lower temperature) range. Also in the systems differing by the number of their repeating macrodioldiisocyanate units n one can see that for higher values of n the flowing point is present at higher frequency (or at lower temperature). These observations confirm the hypothesis that the increase of the polyurethane length by increasing the macrodiol length or by increasing the number of repeating units makes the polymer softer at high temperatures, when destruction of the H-bonds allows to reveal such behaviour.

CONCLUSION

Molecular relaxations and properties of polyurethanes crosslinked with hyperbranched polyester (Boltorn ® H40) depend on the connecting PU chain length in different ways, depending if the PU chain length was regulated by the macrodiol (Terathane ® ) length or by the number of the repeating units n. When the macrodiol length is increased and n is constant, the glass transition and the α-relaxation shift strongly to lower temperatures. The systems with the longest macrodiols additionally show ability for crystallization. By contrast, the changes of n practically do not affect the glass transition and the molecular relaxations, if the macrodiol length is fixed. This effect is explained by a formation of the physical network by hydrogen bonds between the urethane groups, which control the molecular mobility. The

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Figure captionsFig. 1. Structure of the monomers used for the PU network synthesis

Fig. 4 .Fig. 5 .

 45 Fig. 4. Frequency and temperature dependencies of the dielectric permittivity imaginary part for the PU networks based on macrodiol with different molecular weights, but constant n = 20: a) 20-T650, b) 20-T1000, c) 20-T2000 and d) 20-T2900.

Fig. 6 .

 6 Fig. 6. Activation map for relaxation process in the PU networks based on macrodiols with different molecular weight but constant n = 20: 20-T650 ( , ), 20-T1000 ( , ), 20-T2000 ( , ), 20-T2900 ( ). Open points -DRS; full points -DMA.

Fig. 7 .

 7 Fig. 7. DRS and DMA spectra for PU networks based on the same macrodiol Terathane ® 2000 but with different numbers of repeating units n: 4-T2000 ( , ), 10-T2000 ( , ) and 20-T2000 ( , ). Full points -real part, open points -imaginary part of the moduli.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Activation map for PU networks based on the same macrodiol Terathane ® 2000 but with different numbers of repeating units n: 4-T2000 ( , ), 10-T2000 ( , ) and 20-T2000 ( , ). Open points -DRS; full points -DMA.

Fig. 10 .

 10 Fig. 10. Dependence of T g (determined from the second DSC scans) versus the weight concentration of the urethane groups N u determined for the PU networks described in this work and in ref. 17 (solid line: empirical 2 nd power law T g = -89.5 + 8.22N u + 5.20N u 2 ).

Fig. 1 .

 1 Fig. 1. Structure of the monomers used for the PU network synthesis.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Diagram of the PU network synthesis

Fig. 4 .

 4 Fig. 4. Frequency and temperature dependencies of the dielectric permittivity imaginary part for the PU networks based on macrodiol with different lengths, but constant n = 20: a) 20-T650, b) 20-T1000, c) 20-T2000 and d) 20-T2900.

Fig. 5 .

 5 Fig. 5. DRS and DMA spectra for the PU networks based on macrodiols with different molecular weight but constant n = 20: 20-T650 ( , ), 20-T1000 ( , ), 20-T2000 ( , ) and 20-T2900 ( , ). Full points -real part, open points -imaginary part of the moduli.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Activation map for relaxation process in the PU networks based on macrodiols with different molecular weight but constant n = 20: 20-T650 ( , ), 20-T1000 ( , ), 20-T2000 ( , ), 20-T2900 ( ). Open points -DRS; full points -DMA.

Fig. 8 .

 8 Fig. 8. Activation map for PU networks based on the same macrodiol Terathane ® 2000 but with different numbers of repeating units n: 4-T2000 ( , ), 10-T2000 ( , ) and 20-T2000 ( , ). Open points -DRS; full points -DMA.

Fig. 9 .

 9 Fig. 9. Rheological measurements for the samples: 4-T650 ( , ), 4-T2000 ( , ) and 20-T2000 ( , ). Full points -real part, open points -imaginary part of the shear modulus G. Inset diagram shows the frequency-temperature dependence of the flowing points.

Fig. 10 .

 10 Fig. 10. Dependence of T g (determined from the second DSC scans) versus the weight concentration of the urethane groups N u determined for the PU networks described in this work and in ref. 17 (solid line: empirical 2 nd power law T g = -89.5 + 8.22N u + 5.20N u 2 ).

Table 1 .

 1 The glass transition temperatures determined from the DSC second scans for the PU based networks crosslinked with hyperbranched polyester (Boltorn ® H40).

University Lyon 1 (France) in the frame of NoE "NANOFUN-POLY" 6FP EU. We thank Professor Philippe Cassagnau for help and discussion on the rheological measurements. We would like to underline an inspiring role of late Professor Tadeusz Pakula with whom we had many fruitful discussions during realization of these investigations.


Julie Aufort
email: julie.aufort@upmc.fr

Dominique Gommery

Christel Gervais

Loïc Segalen

Nathalie Labourdette

Cristina Coelho-Diogo

Etienne Balan

Assessing bone transformation in late Miocene and Plio-Pleistocene deposits of Kenya and South Africa

Keywords: bone diagenesis, ATR-FTIR spectroscopy, secondary apatite, preservation

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

Introduction

Vertebrate bones are a major part of archaeological and paleontological records.

Although the overall shape inherited from the living animal can be preserved, significant modifications affect the chemical composition as well as the microscopic and mesoscopic structure of bone [START_REF] Trueman | The long-term survival of bone: the role of bioerosion[END_REF][START_REF] Hedges | Bone diagenesis: an overview of processes[END_REF]. The apatitic fraction of fossil bone generally exhibits an overall decrease in carbonate content, enrichment in fluorine and incorporation of trace elements as well as an increase in crystallinity parameters (e.g. [START_REF] Keenan | From bone to fossil: A review of the diagenesis of bioapatite[END_REF]). Accordingly, fossil bioapatite differs from the nanocrystalline carbonate-bearing hydroxylapatite corresponding to the main inorganic component of bone [START_REF] Pasteris | Bone and tooth mineralization: why apatite?[END_REF].

Overall, fossil bones tend to display a transformation of the original bioapatite towards a carbonated fluorapatite [START_REF] Kolodny | Dinosaur bones: fossils or pseudomorphs? The pitfalls of physiology reconstruction from apatitic fossils[END_REF]. The organic fraction of bone also experiences in most cases a rapid degradation and is rarely preserved [START_REF] Bocherens | Paleobiological implications of the isotopic signatures, 13 C, 15 N, of fossil mammal collagen in Scladina Cave (Sclayn, Belgium)[END_REF].

Despite its higher sensitivity to diagenetic transformation, the chemical and isotopic composition of fossil bones can complement the analyses performed on more resistant fossil enamel samples. When preserved in the fossil record, the stable isotope composition of biogenic apatite, and particularly the stable isotope composition (δ 13 C, δ 18 O) of structural carbonate groups, provides important information on past climates, past environments, dietary preferences and habitat of vertebrates (e.g. [START_REF] Kohn | Stable isotope compositions of biological apatite[END_REF]. On the other hand, heavily transformed fossil bones may also serve as probes of local diagenetic conditions because the uptake of trace elements depends on the physical-chemical parameters prevailing during the diagenetic recrystallization of apatite (e.g. Kohn andLaw 2006, Trueman et al. 2006).

As a matter of fact, the depositional environment plays an important role in the transformation of fossil bones. Nielsen-Marsh and [START_REF] Nielsen-Marsh | Patterns of diagenesis in bone I: The effect of site environments[END_REF] reported that site hydrology and characteristics of the burial environment strongly affect diagenetic pathways in bone.

Several studies have focused on the diagenesis of fossils from fluvial and marine settings [START_REF] Pfretzschner | Fossilization of Haversian bone in aquatic environments[END_REF][START_REF] Tütken | Early diagenesis of bone and tooth apatite in fluvial and marine settings: Constraints from combined oxygen isotope, nitrogen and REE analysis[END_REF]) and from harsh weathering environments [START_REF] Tuross | Molecular preservation and crystallographic alterations in a weathering sequence of wildebeest bones[END_REF][START_REF] Trueman | Mineralogical and compositional changes in bones exposed on soil surfaces in Amboseli National Park, Kenya: diagenetic mechanisms and the role of sediment pore fluids[END_REF]) to identify parameters controlling the early diagenesis of bones and teeth. Fossilisation in karstic environment is often considered to lead to better preservation. For example, [START_REF] Michel | Chemical and structural changes in Cervus Elaphus tooth enamels during fossilisation (Lazaret Cave): a combined IR and XRD Rietveld analysis[END_REF] reported only minor structural and chemical changes in fossil tooth enamel from the Lazaret prehistoric Cave and most fossil bones from karstic caves in Israel did not show transformation into carbonated fluorapatite [START_REF] Weiner | Three dimensional distribution of minerals in the sediments of Hayonim Cave, Israel: diagenetic processes and archaeological implications[END_REF]. Local variations in environmental conditions can also lead to different diagenetic pathways within one site (e.g. [START_REF] Stiner | Bone preservation in Hayonim Cave (Israel): a macroscopic and mineralogical study[END_REF][START_REF] Bocherens | Grotte Chauvet (Ardèche, France): A natural experiment for bone diagenesis in karstic context[END_REF].

The extent of fluoridation is usually used as a marker of diagenetic transformation of bone due to the easy formation of secondary fluorapatite. However, the availability of fluorine in the environment is variable in different fossilisation contexts (e.g. [START_REF] Parker | Fluorine in fossilized bone and tooth: distribution among skeletal tissues[END_REF], whereas the formation of secondary hydroxyapatite is less easily detected [START_REF] Aufort | Atomic scale transformation of bone in controlled aqueous alteration experiments[END_REF].

In this work, we analyse a series of Plio-Pleistocene fossil bones from karstic environments of the Bolt's Farm cave system in the Cradle of Humankind, South Africa and from late Miocene fluvio-lacustrine environments of the Tugen Hills in the Gregory Rift, Kenya. The results further document the links between atomic scale transformation of bone and fossilisation context and suggest that a primary biogenic apatite fraction is preserved even in heavily transformed samples.

Materials and Methods

Samples and fossilisation context

The fossil material consists of fragments of mammal bones from the Bolt's Farm cave system (BFCS), aka Bolt's Farm, located on the south-western edge of the UNESCO Cradle of Humankind World Heritage Site, South Africa. Bolt's Farm cave system is not a single deposit but actually corresponds to an area of more than 30 fossiliferous cave infill deposits, related to a vast ancient but interconnected karstic system [START_REF] Gommery | Preliminary results concerning the discovery of new fossiliferous sites at Bolt's farm (Cradle of Humankind, South Africa)[END_REF]. Main mammals found at Bolt's Farm include non-human primates such as Parapapio and Cercopithecoides, large felids such as Dinofelis and Panthera, as well as suids and bovids, but also a rich microfauna (mainly represented by rodents), and are described in details in [START_REF] Gommery | Bolt's Farm Cave System dans le Cradle of Humankind (Afrique du Sud) : un exemple d'approche multidisciplinaire dans l'étude des sites à primates fossils[END_REF] and [START_REF] Pickford | Fossil Suidae (Artiodactyla, Mammalia) from Aves Cave I and nearby sites in Bolt's Farm Palaeokarst System, South Africa[END_REF]. Bone fragments investigated in this study come from selected localities in Bolt's Farm: Waypoint 160 (WP), Brad Pit A and B (BPA, BPB), Aves Cave I (AC), Milo A (MA), Milo B (MB) and Bridge Cave (BC). These localities differ in age, e.g. Waypoint 160 was dated between 4.5 and 4 Ma with biochronology and corresponds to the oldest fossiliferous deposit of the Cradle of Humankind [START_REF] Sénégas | New evidence for the murine origins of the Otomyinae (Mammalia, Rodentia) and the age of Bolt's Farm (South Africa)[END_REF] while AC was dated, also with biochronology, between 3 and 2.5 Ma [START_REF] Pickford | Fossil Suidae (Artiodactyla, Mammalia) from Aves Cave I and nearby sites in Bolt's Farm Palaeokarst System, South Africa[END_REF].

Selected fossil bone samples are described in Table 1 and either come from indurated calcitic breccia (B) or decalcified breccia (DB). Note that, for this study, all fossil bones were directly sampled without chemical dissolution of the breccia.

Two fossil bone samples from the Lukeino formation (6.2-5.7 Ma, [START_REF] Sawada | The age of Orrorin tugenensis, an early hominid from the Tugen Hills, Kenya[END_REF][START_REF] Roche | Preservation assessment of Miocene-Pliocene tooth enamel from Tugen Hills (Kenyan Rift Valley) through FTIR, chemical and stable isotope analyses[END_REF]2013) located along the Tugen Hills in the Gregory Rift Valley, Kenya were added to the series.

A metapodial bone of modern ox, TH1, collected on the shores of the Bogoria Lake (Kenya) and a natural sample of carbonated fluorapatite (C-Fap) originating from the sedimentary deposit of Taiba (Senegal) were used as references [START_REF] Aufort | Atomic scale transformation of bone in controlled aqueous alteration experiments[END_REF].

Analytical techniques

A rotary drill equipped with a diamond-tipped burr was used to collect bone powders from cortical bone fragments. Powders were then finely ground with an agate mortar and pestle for 15 minutes, producing grain sizes of less than 50 µm. Prior to chemical analyses, fossil bone powders were treated with 0.1 M acetic acid for 30 minutes to remove diagenetic calcite and then rinsed 6 times with deionized water and dried at 60°C. Fluorine content and Ca/P ratios are reported in Table 1. For each analysis, 100 mg of sample was dissolved in a 30% nitric acid solution for 1h at 80°C following the protocol previously used by [START_REF] Maurer | Intra-skeletal variability in trace elemental content of Precolumbian Chupicuaro human bones: the record of post-mortem alteration and a tool for palaeodietary reconstruction[END_REF]. Fluorine content was measured using a fluoride ion selective electrode (Mettler Toledo), Ca was measured by energy dispersive X-ray fluorescence (Niton XL3t Thermo Fischer scientific) and phosphorus by spectrophotometry (Milton Roy Spectronic 301 spectrometer). The estimated analytical error based on the analysis of a certified reference material (bone ash SRM 1400) is about 5%. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectra were recorded using a Quest ATR device and a Nicolet 6700 FTIR spectrometer. Pure powder samples were packed at the surface of the ATR internal reflection element (IRE) and two different spectra were recorded for each sample, using either a diamond or a Ge ATR IRE, between 400 and 4000 cm -1 by averaging 200 scans with a resolution of 1 cm -1 . The use of a diamond ATR IRE allows the detection of relatively weak bands, such as those related to carbonate impurities. In comparison, Ge ATR is less sensitive but provides a better insight into the intrinsic properties of the sample [START_REF] Aufort | Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite[END_REF]. All ATR spectra are reported in absorbance units A=log(I0/IR) where I0 and IR are the intensities of the incident and reflected light, respectively.

Single-pulse 19 F magic angle spinning (MAS) NMR experiments were performed on an Avance 700 Bruker spectrometer (16.3T) operating at 658.93 MHz using a 4 mm rotor at a 14 kHz spinning frequency.

Results

Chemical composition of fossil bones

Compared to modern bone, all fossil bones are enriched in fluorine. The fluorine content of most Bolt's Farm fossil bones range from 0.5 to 1.4 wt.%, apart from two more fluorinated samples, AC-DB-L and MA-DB-03N, containing 1.8 and 2.4 wt.% F respectively (Table 1). In contrast, fossil bones from the Tugen Hills, TH33 and TH32, display higher fluorine content, 2.8 and 2.9 wt.% F respectively.

The Ca/P mass ratios range from 2.11 to 2.44 in all fossil samples, higher than the 2.02 value found for modern bone, as is typically observed in fossil compared to modern bioapatites (e.g. [START_REF] Reiche | A multi-analytical study of bone diagenesis: the Neolithic site of Bercy[END_REF][START_REF] Yi | Probing atomic scale transformation of fossil dental enamel using Fourier transform infrared and nuclear resonance magnetic spectroscopy: A case study from the Tugen Hills (Rift Gregory, Kenya)[END_REF]). These values are overall lower than those previously reported in Quaternary archaeological bones from Lazaret Cave (between 2.38 and 2.80; [START_REF] Michel | Assessment of archaeological bone and dentine preservation from Lazaret Cave (Middle Pleistocene) in France[END_REF]) potentially reflecting differences in sample treatments prior to chemical analysis.

Infrared spectroscopic study of fossil bone samples

ATR-FTIR spectra of fossil samples

Both diamond and Ge ATR-FTIR spectra of fossil bones (Figure 1) display the characteristic absorption bands ascribed to the internal vibrations of apatite phosphate groups, and to the structural carbonate impurities located at the A and B sites (channel and phosphate sites, respectively) (e.g. [START_REF] Legeros | Two types of carbonate substitution in the apatite structure[END_REF][START_REF] Elliott | Calcium phosphate biominerals[END_REF].

Intense bands observed between 550 and 600 cm -1 and between 1010 and 1090 cm -1 in the ATR-FTIR spectra of recent and fossil bones are related to the ν4 PO4 bending and ν3 PO4 stretching modes of the apatite phosphate groups, respectively. Amide bands related to the collagen matrix [START_REF] Lebon | Rapid quantification of bone collagen content by ATR-FTIR spectroscopy[END_REF] are not visible in the ATR-FTIR spectra of fossil bones, attesting to the degradation of the bone organic fraction. Compared to that of modern bone, diamond ATR-FTIR spectra of Bolt's Farm fossil bones containing less than 1.2 wt.% F display two additional bands at 630 and 3572 cm -1 related to the OH bending and stretching modes respectively (Figure 1, Figure S1). These bands are no longer visible in fossil bones from Bolt's Farm and the Tugen Hills with higher fluorine contents, apart from one sample, AC-DB-L (1.8 wt.% F). Most Bolt's Farm fossils collected from the indurated breccia contained calcite as attested by the presence of the v4 CO3 band at 713 cm -1 (Figure S2). Its absence in the spectrum of acetic acid treated samples confirms the removal of diagenetic calcite from these samples (Figure S2). As the ν2 CO3 and ν3 CO3 bands of calcite overlap with those of structural carbonates in apatite, the acetic acid treatment should facilitate the analysis of the environment of structural carbonates in fossil samples. Although the ATR-FTIR spectra of most fossil bones from decalcified breccia did not reveal the presence of calcite, selected samples from decalcified breccia were also treated with acetic acid to assess the effect of the treatment on the apatite structure. A systematic reduction of the relative intensity of ν 2 and ν 3 CO 3 bands is observed after acetic acid treatment on diamond ATR-FTIR spectra after normalization based on the ν4 PO4 band (Figure S3), whether the initial sample contained calcite or not. On calcitebearing samples, the calcite removal makes the characteristic signals of structural carbonate groups visible on the spectra.

Atomic-scale order and sample micro-structure probed by ATR-FTIR phosphate bands

The width of the ν4 PO4 bands is commonly used as a probe of structural order through the measurement of the Infrared Splitting Factor (IRSF; [START_REF] Weiner | States of preservation of bones from prehistoric sites in the Near East: A survey[END_REF]. IRSF values measured on Ge ATR-FTIR spectra of Bolt's Farm fossils range from 3.93 to 5.72 and are overall higher than the 3.64 value found for modern bone (Table 1). IRSF values for fossil bones from the Tugen Hills, 4.24 and 4.69, fall in the range of values found in Bolt's Farm fossils. The width of the ν4 PO4 bands is reduced after acetic acid treatment (Figure 2a), which leads to a systematic increase in IRSF in all fossil bones treated, whether the sample originally contained calcite or not (Table 1, Figure 2b).

The line shape and width of strong bands in infrared spectra are not only related to the atomic-scale structure of the samples but also depend on parameters such as porosity, grain size and shape of particles due to long-range electrostatic interactions within and between particles [START_REF] Aufort | Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite[END_REF]. In contrast the position and line shape of weaker bands, such as the band at ~960 cm -1 related to the ν1 PO4 stretching mode, are less affected by these effects. Compared with the ν4 PO4 band, the weaker ν1 PO4 band is thus expected to provide a complementary meaningful insight into the atomic-scale properties of the sample [START_REF] Balan | Line-broadening effects in the powder infrared spectrum of apatite[END_REF], Aufort et al. 2016[START_REF] Aufort | Macroscopic electrostatic effects in ATR-FTIR spectra of modern and archaeological bones[END_REF]. Its position has been shown to be well correlated to apatite crystallinity in archaeological heated bones [START_REF] Lebon | Screening in situ bone and teeth preservation by ATR-FTIR mapping[END_REF].

The ν1 PO4 Ge ATR-FTIR band is located at ~960 cm -1 in modern ox bone TH1 and at ~966 cm -1 in the carbonated fluorapatite (C-Fap) sample. It corresponds to a broad Gaussian signal in TH1 while it displays a pronounced Lorentzian shape in C-Fap. Compared to modern bone, the ν1 PO4 Ge ATR-FTIR band of fossil bones is asymmetric and systematically shifted towards higher frequencies (Table 1, Figure 1d, Figure S4), which is consistent with the incorporation of fluorine in the apatite structure. Its position correlates with the sample fluoride content (Figure 4a) and is unaffected by the acetic acid treatment. These observations are consistent with those made on artificially altered modern bones by [START_REF] Aufort | Atomic scale transformation of bone in controlled aqueous alteration experiments[END_REF] who observed the partial dissolution of biogenic apatite and precipitation of secondary apatite, in bone artificially altered in pH-buffered and fluorinated aqueous solutions. Depending on the composition of the aqueous solution, carbonated hydroxyapatite or fluorapatite was identified as the secondary phase. A quantitative analysis of ATR-FTIR bands revealed that the transformation process was incomplete with a fraction of secondary apatite limited to about 60 %. A similar approach was used in the present work. It consists in fitting the ν1 PO4 Ge ATR-FTIR band of fossil samples by using a two-component model to fit the band shape (Table S1).

The first component is a Gaussian function, whose position and width were kept fixed to that of the unaltered bone sample (TH1). Accordingly, it is expected to correspond to remnants of the biogenic material in the fossil samples. The second component, which is expected to correspond to secondary apatite, is described by a Lorentzian function whose position, relative intensity, and width are free parameters (Table S1). The fraction of secondary apatite obtained from the fits varies between 24 and 60 % in Bolt's Farm fossils, while it reaches 64 % in fossil bones from the Tugen Hills (Table S1). The position of the peak is mainly centred on 962.5-963.5 cm -1 in Bolt's Farm fossils apart from the two F-rich samples for which the position is higher and closer to that of sedimentary carbonated fluorapatite (966.1 cm -1 ). Regarding fossils from the Tugen Hills, a high proportion of secondary carbonated fluorapatite is consistent with their higher fluorine content. It is noteworthy that even in highly transformed bone samples, i.e.

TH33 and TH32, the proportion of secondary apatite is limited to about 64% (Table S1).

Environment of structural carbonate groups inferred from the ν2 CO3 band

The ν2 CO3 component of modern bone displays the usual A-and B-type components at ~880 cm -1 and ~872 cm -1 respectively, as well as an asymmetric tail on the low-frequency side, which corresponds to the broad band centred at 860-865 cm -1 attributed to "labile" carbonate groups in bone [START_REF] Rey | Non-apatitic environments in bone mineral: FT-IR detection, biological properties and changes in several disease states[END_REF]) (Figure 1c, Figure S5).

All fossil bones display an additional signal at 865 cm -1 that matches with that observed in the reference sedimentary carbonated fluorapatite. This signal is diagnostic of a clumped (CO 3 2-, F -) defect substituting for the phosphate group in the apatite structure and has been observed in fossil teeth from Rift Gregory in Kenya [START_REF] Yi | A carbonate-fluoride defect model for carbonate-rich fluorapatite[END_REF][START_REF] Yi | Probing atomic scale transformation of fossil dental enamel using Fourier transform infrared and nuclear resonance magnetic spectroscopy: A case study from the Tugen Hills (Rift Gregory, Kenya)[END_REF].

Regarding calcite-free fossils, the apparent proportions of clumped (CO3 2-, F -) defect, A-type and B-type carbonate signals are modified in the most fluorinated samples (AC-DB-L and MA-DB-03N) after acetic acid treatment (Figure S3). Together with the overall decrease in the relative intensity of the structural carbonate signals in normalized spectra, this suggests that the acetic acid treatment could have removed a fraction of carbonate-bearing secondary phases. Depending on the sample, the acid acetic acid treatment removes carbonates associated either with the clumped defect or with B-type and A-type substitutions.

19 F Nuclear Magnetic Resonance Spectroscopy

The 19 F MAS NMR spectra of fossil bones display a main signal at ~ -102 ppm ascribed to F -ions incorporated in the channel sites of the apatite structure (Figure 3). This signal is broader in Bolt's Farm fossil bone samples (FWHM of 2.12-3.69 ppm) than in the reference sedimentary carbonated fluorapatite (1.8 ppm). The less intense signal observed in sedimentary carbonated fluorapatite at -88 ppm corresponds to the clumped (CO3 2-, F -) defect substituting for the phosphate group in the structure of carbonated fluorapatite [START_REF] Yi | A carbonate-fluoride defect model for carbonate-rich fluorapatite[END_REF]). This signal is also observed in the fossil samples. 19 F MAS NMR thus confirms that fluoride is incorporated in the apatite structure, both in the channel sites and in the clumped defect to a lesser extent.

The clumped defect signal is more intense in samples with higher fluorine content, i.e. MA-DB-03N and TH33 (with an area about 3% that of the total area of the 19 F NMR spectrum), than in BPB-DB-25 (with an area about 1% that of the total area of the 19 F NMR spectrum).

The larger bandwidth (4.12 ppm) observed in TH33 compared to the other fossil samples (2.12-3.69 ppm) is consistent with the corresponding relatively broad clumped (CO3 2-, F -) defect signal observed in the infrared spectra, even though the potential occurrence of paramagnetic centres or impurities (e.g. Fe, Mn ions) in fossil bones can also affect the NMR width.

Discussion

Evidence of secondary carbonated apatite formation in fossil bones

The structural differences observed between fossil and modern bones, i.e. increase in crystallinity, formation of the clumped (CO3 2-, F -) defect, incorporation of fluoride and hydroxyl groups suggest that dissolution of the original biogenic material and formation of secondary apatite occurred. These observations support the use of a two-phase model to interpret the properties of the ν1 PO4 band, leading to a proportion of secondary apatite reaching 64 % in the most transformed samples. Variations in the position of the ν1 PO4 component related to secondary apatite also suggest that its composition may differ from one sample to the other. In F-rich fossils, i.e. TH32, TH33, MA-DB-03N, the presence of the clumped defect and the absence of structural OH signals in their ATR-FTIR spectra are in favour of secondary fluorapatite. In fossil bones with lower F content, the frequency of the second component is closer to that of hydroxyapatite (~963 cm -1 ). The presence of bending and stretching bands related to structural OH groups also supports the formation of secondary hydroxyapatite. This is consistent with the results of bone alteration experiments [START_REF] Aufort | Atomic scale transformation of bone in controlled aqueous alteration experiments[END_REF] In presence of fluorine, the formation of secondary carbonated fluorapatite is easily detected because the clumped (CO3 2-, F -) defect displays a specific spectroscopic signature, both in infrared spectroscopy and 19 F NMR. In the case of hydroxyapatite, the incorporation of carbonate in the secondary apatite also occurs during the experimental aqueous alteration of modern bone [START_REF] Aufort | Atomic scale transformation of bone in controlled aqueous alteration experiments[END_REF]). However, their spectroscopic signature does not significantly differ from that of the biogenic apatite. Accordingly, and even though their carbonate signal is close to that observed in biologic apatite, it is most likely that the secondary hydroxyapatite in fossil samples also contains a fraction of structural carbonates.

It is noteworthy that the highest fraction of secondary apatite observed is about ~60%.

This limited degree of transformation does not depend on the F enrichment of the sample and is also observed in hydroxylated samples as, e.g., sample WP-DB*, which displays about 60 % of secondary apatite. The highest fraction observed coincides with the maximum ~60% fraction of secondary apatite determined in modern bones altered under controlled conditions [START_REF] Aufort | Atomic scale transformation of bone in controlled aqueous alteration experiments[END_REF]). Accordingly, it supports the idea that the formation of secondary apatite could have a protecting role against further transformation of the original bioapatite. No correlation is observed between the extent of alteration and age and even in older (e.g. TH33, TH32, WP-DB) and F-rich (MA-DB-03N, TH33, TH32) samples, the transformation seems limited at about 60 percent of secondary apatite.

Effect of the acetic acid treatment on fossil samples

Acetic acid is the most commonly used reagent to remove exogenous carbonate from bioapatite prior to stable isotope analyses of structural carbonate and chemical analyses [START_REF] Snoeck | Comparing bioapatite carbonate pre-treatments for isotopic measurements: Part 1 -Impact on structure and chemical composition[END_REF]. It also plays a major role in fossil preparation. Indeed, extracting bones from the breccia matrix is difficult and two methods are usually used: mechanical and/or chemical preparation. The latter is more adapted to recover the microfauna and fragile fossils and, unlike mechanical preparation, does not risk leaving marks that could be misinterpreted as taphonomic or anthropic marks. For instance, the Plio-Pleistocene Palaeontology Section of the Ditsong National Museum of Natural History (Pretoria, South Africa) has developed an acid preparation lab dedicated to the extraction of fossil bones from blocks of breccia (Gommery et al. 2016). In this case, fossils are exposed to acetic acid for longer periods of time (~24h) but protected using a glue coating. Effects of acetic acid on the structure and stable isotope composition of bioapatites are thus of importance to palaeoenvironmental reconstructions and have been widely discussed along with other pre-treatments (e.g. Lee-Thorp and van der [START_REF] Lee-Thorp | Aspects of the chemistry of modern and fossil biological apatites[END_REF][START_REF] Garvie-Lok | Preparation of bone carbonate for stable isotope analysis: the effects of treatment time and acid concentration[END_REF][START_REF] Yoder | Effects of different sample preparation methods on stable carbon and oxygen isotope values of bone apatite: a comparison of two treatment protocols[END_REF][START_REF] Snoeck | Comparing bioapatite carbonate pre-treatments for isotopic measurements: Part 1 -Impact on structure and chemical composition[END_REF].

Overall these studies show that acetic acid treatment leads to an increase in crystallinity (IRSF) and a decrease in carbonate content and partially dissolves the mineral fraction of modern and archaeological bioapatites [START_REF] Snoeck | Comparing bioapatite carbonate pre-treatments for isotopic measurements: Part 1 -Impact on structure and chemical composition[END_REF]. The present results confirm that the acetic acid treatment, even at low concentration (0.1 M) and reaction time (30 min), besides removing the secondary calcite, affects the apatitic fraction of the samples. It leads to a moderate increase in the IRSF and overall decrease in the relative intensity of the signal of structural carbonates. It is noteworthy that the IRSF increase is similar for the whole set of samples and still allows a meaningful inter-comparison of crystallinity parameters (Figure 2).

The effect of the acetic acid treatment on the ν1 PO4 band is not detected, possibly due to the smaller intensity of this band. Based on these observations, it is suggested that the acetic acid treatment removes more soluble carbonate-rich apatitic domains, in addition to diagenetic calcite. A preferential use of acetate buffered acetic acid solutions has been recommended (e.g. [START_REF] Garvie-Lok | Preparation of bone carbonate for stable isotope analysis: the effects of treatment time and acid concentration[END_REF]) and leads to a smaller increase in IRSF values than unbuffered acetic acid [START_REF] Snoeck | Comparing bioapatite carbonate pre-treatments for isotopic measurements: Part 1 -Impact on structure and chemical composition[END_REF] but does not completely exclude possible dissolutionrecrystallisation of bone apatite [START_REF] Aufort | Atomic scale transformation of bone in controlled aqueous alteration experiments[END_REF].

Implications for palaeoenvironmental reconstructions

Regardless of the fossilisation conditions, dissolution-recrystallization of bone is systematically observed. Conditions prevailing in the environment, i.e. chemical composition of percolating fluids and possibly of the breccia in Bolt's Farm, are the main factor in driving the transformation of fossil bones. A certain homogeneity is observed within each site at Bolt's Farm, with similar ν2 CO3 signatures for fossil bones belonging to one locality, apart from Milo A and Aves Cave I where there might be local concentration spots of fluorine, leading to further formation of secondary fluorapatite. Overall, fossil bones from the karstic environment at Bolt's Farm are less transformed in terms of percentage of secondary apatite than fossils from the fluvio-lacustrine environment [START_REF] Pickford | Stratigraphy and paleoecology of five late Cenozoic formations in the Kenya Rift Valley[END_REF] of the Tugen Hills. In karstic environments, dissolution-recrystallization also occurs but the lower F concentration of percolating solutions leads to the preferential formation of secondary hydroxyapatite. The higher solubility of hydroxyapatite compared to fluorapatite [START_REF] Elliott | Calcium phosphate biominerals[END_REF][START_REF] Rakovan | Growth and surface properties of apatite[END_REF]) may explain why an overall smaller percentage of transformation is observed in Bolt's Farm fossils than in the more fluorinated fossils from the Tugen Hills. These observations confirm the sensitivity of bone to the nature of percolating solutions, making fossil bone a potential record of local physicalchemical conditions. Further works on older and different contexts are however required to confirm this suggestion. Another avenue to explore pertains to the development of a chemical treatment able to remove secondary apatite in fossils via selective dissolution of the secondary phase, giving access to the environmental and geochemical information preserved in the pristine biological apatite.

Table and Figure captions

Table 1 -Sample description. For Bolt's Farm fossils, the first initials correspond to the name of the locality (e.g. AC for Aves Cave I), B and DB refer to breccia and decalcified breccia respectively. The asterisk refers to preliminary ages that will be further refined in later studies. Fluorine content and Ca/P mass ratio of modern and fossil bones from Bolt's Farm and Tugen Hills. Frequency of ν1 PO4 bands and IRSF calculated from the ν4 PO4 band [START_REF] Weiner | States of preservation of bones from prehistoric sites in the Near East: A survey[END_REF]

  indicating that formation of secondary hydroxyapatite and fluorapatite always occur, only depending on the presence or absence of fluoride, respectively. In experimental alterations, two well-defined trends are thus observed in a diagram reporting the F concentration as a function of the proportion of secondary phase. In the fossil samples, intermediate situations occur (Figure 4b), suggesting the formation of both secondary fluorapatite and hydroxyapatite in a single sample. The potential formation of a solid solution with a mixed fluor-and hydroxyl-composition cannot be fully excluded. However, the observation of the OH vibrational bands at 3572 and 630 cm -1 attests to the occurrence of extended domains of hydroxyapatite (Rodriguez-Lorenzo et al. 2003). Furthermore, even in low fluoride fossil bones, formation of carbonated fluorapatite occurred as indicated by the presence of the clumped (CO3 2-, F -) defect in all fossils, even those with intense OH bending signals. Both observations are suggestive of the formation of individual domains of hydroxyapatite or fluorapatite, which is also consistent with the conclusions of the fluoridation experiments of dentin and enamel by Pasteris and Ding (2009).

Figure 1 -

 1 Figure 1 -a) Diamond and b) germanium ATR-FTIR spectra of modern bone (TH1) and selected fossil

Figure 2 -

 2 Figure 2 -a. ν4 PO4 germanium ATR-FTIR bands of a calcite-containing (WP-DB) and calcite-free

Figure 3

 3 Figure 3 19 F MAS NMR spectra of BPB-DB-25 and MA-D-03N fossil bone samples from Bolt's Farm and TH33 from the Tugen Hills compared to that of sedimentary carbonated fluorapatite. The 19 F

Figure 4 -

 4 Figure 4 -a. Evolution of the fluorine content as a function of the position of the ν1 PO4 Ge ATR-FTIR

  in Ge ATR-FTIR spectra. The prime symbol refers to the sample after acetic acid treatment.

	Sample	Description	Origin	Age	F (%)	Ca/P	ν1 PO4 (cm -1 )	ν4 PO4
						mass ratio		IRSF (IRSF')
	TH1	Modern ox bone	Bogoria Lake (Kenya)	Modern	0.20	2.02	960.6	3.64
	BPA-B	Fossil bone	Brad Pit A (BFCS, South Africa)	4-1.5 Ma*	0.5	2.36	962.7	5.35 (6.19)
	AC-DB-5	Fossil bone	Aves Cave I (BFCS, South Africa)	3-2.5 Ma	0.6	2.19	962.5	4.81 (5.49)
	AC-B-F	Fossil bone	Aves Cave I (BFCS, South Africa)	3-2.5 Ma	0.8	2.30	962.9	4.66 (5.41)
	WP-DB	Fossil bone	Waypoint 160 (BFCS, South Africa)	4.5-4 Ma	0.9	2.44	963.5	5.14 (5.82)
	BC-DB-P	Fossil bone	Bridge Cave (BFCS, South Africa)	2-0.8 Ma*	0.9	2.14	962.8	4.45 (5.01)
	BPB-DB-25	Fossil bone	Brad Pit B (BFCS, South Africa)	4-3.5 Ma*	1.0	2.21	962.4	4.48 (5.15)
	MB-DB-10	Fossil bone	Milo B (BFCS, South Africa)	2-1.5 Ma*	1.1	2.18	963.4	4.69 (5.15)
	BPA-DB-12D Fossil bone	Brad Pit A (BFCS, South Africa)	4-1.5 Ma*	1.1	2.11	962.4	5.23 (5.51)
	MA-B	Fossil bone	Milo A (BFCS, South Africa)	2-1.5 Ma*	1.2	2.21	963.5	4.44 (4.99)
	MA-B-Cal	Fossil bone	Milo A (BFCS, South Africa)	2-1.5 Ma*	1.4	2.29	964.0	4.82 (5.43)
	AC-DB-L	Fossil bone	Aves Cave I (BFCS, South Africa)	3-2.5 Ma	1.8	2.16	963.5	4.98 (5.20)
	Ma-DB-03N	Fossil bone	Milo A (BFCS, South Africa)	2-1.5 Ma*	2.4	2.15	965.3	5.72 (6.12)
	TH33	Fossil bone	Tugen Hills (Lukeino formation, Kenya)	6.2-5.7 Ma	2.8	2.26	965.7	4.24
	TH32	Fossil bone	Tugen Hills (Lukeino formation, Kenya)	6.2-5.7 Ma	2.9	2.21	965.8	4.69
	C-Fap	Sedimentary Fap	Taiba (Senegal)	n.d.	3.3	2.18	966.1	6.18

Acknowledgments

This work was supported by French state funds within the framework of the Cluster of Excellence MATISSE led by Sorbonne Universités. We We would like to thank C. Klinkert and J. Gaylord for their authorizations to conduct fieldwork on their property, R. Redelstorff and P. Hine (APM Unit, SAHRA), L. Smith (COH WHS Authority, Gauteng Provincial Government) and the French Embassy in South Africa for their continuous support. The Ditsong National Museum of Natural History, the CNRS and NRF (LIA N° 1041 HOMEN) and the French Ministry of Europe and Foreign Affairs (Sous-direction de l'Enseignement supérieur et de la Recherche -Pôle Sciences Humaines et Sociales, Archéologie et Patrimoine) (MPFSA -Mission Paléoanthropologique Franco-Sud-Africaine) funded the fieldwork. The Kenyan samples were collected on the field by the Kenya Palaeontology Expedition funded by the CNRS (GDRI 193, UMR 7207 CR2P), the Pierre-and-Marie-Curie University (UMR 7193 ISTEP), the Muséum National d'Histoire Naturelle, the Collège French Ministry of Europe and Foreign Affairs (Commission of Archaeological Excavations). Authorizations for excavation and export were provided by the Government of Kenya (Ministry of Education, Science & Technology). The French Région Ile de France-SESAME program is acknowledged for financial support (700 MHz). We thank two anonymous reviewers for their thoughtful comments.


Benjamin Moreau

Patricia Serrano-Alvarado

Matthieu Perrin

Emmanuel Desmontils

A License-Based Search Engine

) what are the available resources whose licenses are part of this set. With CaLi, we provide an answer to the first concern. CaLi is a lattice-based model that partially orders licenses in terms of compatibility and compliance. In this demonstration, we illustrate the usability of CaLi through a prototype for the second concern. That is, based on a CaLi ordering of licenses we implement a license-based search engine which can answer questions such as "find licensed resources that can be reused under a given license" or "find licensed resources that can reuse a resource that has a particular license".

Introduction and motivation

To facilitate reuse on the Web, resource producers should systematically associate licenses with resources before sharing or publishing them [START_REF] Seneviratne | Policy-Aware Content Reuse on the Web[END_REF]. Licenses specify precisely the conditions of reuse of resources, i.e., what actions are permitted, obliged and prohibited when using the resource.

For a resource producer, choosing the appropriate license for a combined resource or choosing the appropriate licensed resources for a combination involves choosing a license compliant with all the licenses of combined resources as well as analysing the reusability of the resulting resource through the compatibility of its license.

We consider simplified definitions of compliance and compatibility [START_REF] Benjamin | Modelling the Compatibility of Licenses[END_REF], a license l j is compliant with a license l i if a resource licensed under l i can be licensed under l j without violating l i . If a license l j is compliant with l i then we consider that l i is compatible with l j and that resources licensed under l i are reusable with resources licensed under l j . In general, if l i is compatible with l j then l j is more (or equally) restrictive than l i . We also consider that a license l j is more (or equally) restrictive than a license l i if l j allows at most the same permissions and has at least the same prohibitions/obligations than l i .

But producing resources whose licenses are compliant with all reused resource licenses is difficult. It is necessary to know (1) the set of licenses with which the license of the produced resource is compliant and [START_REF] Doncel | A Dataset of RDF Licenses[END_REF] what are the pertinent and available resources whose licenses are part of this set.

With CaLi [START_REF] Benjamin | Modelling the Compatibility of Licenses[END_REF], we provide an answer to the first concern. CaLi is a latticebased model to define compatibility and compliance relations among licenses. It is based on a restrictiveness relation that is refined with constraints to take into account the semantics of actions existing in licenses.

For the second concern, imagine a license-based search engine that can answer questions such as "find all resources that can be reused under the CC BY-NC license". The answer must contain resources licensed under licenses such as CC BY and CC BY-NC itself that are less or as restrictive as CC BY-NC and compatible with it.

There exist search engines in services such as GitHub 3 , APISearch 4 , CC search 5 , LODAtlas 6 , DataHub 7 , Google Dataset Search 8 or OpenDataSoft 9 that can find resources licensed under a particular license. However they can not find resources whose licenses are compatible or compliant with a particular license.

We illustrate the usability of CaLi by answering the second concern. We developed a prototype of a search engine based on a CaLi ordering of licenses, ODRL_CaLi. The goal is to be able find resources whose licenses are compatible or compliant with a particular license. Our prototype can answer questions such as: "find licensed resources that can be reused under a given license" or "find licensed resources that can reuse a resource that has a particular license".

In our search engine, resources (linked data and source code) are associated to licenses. Licenses are described in RDF with the ODRL vocabulary 10 and ordered in terms of compatibility according to the ODRL_CaLi ordering. In addition to indexing licenses, the titles, descriptions and uri of each licensed resources are also indexed to enable full-text search. We remark that we are not interested in implementing ODRL. We use the ODRL vocabulary because it is the most complete vocabulary for licenses and it is well accepted by the community.

In the following, Section 2 overviews the CaLi model and the ODRL_CaLi ordering used in our search engine, and Section 3 describes the demonstration.

Modelling the compatibility of licenses

Inspired by lattice-based access control models, we propose a CaLi model as a tuple A, LS, C L , C → that partially orders licenses, such that [1]:

1. A is a set of actions (e.g., read, modify, distribute, etc.); 2. LS is a restrictiveness lattice of status that defines (i) all possible status (e.g., permissions, obligations, prohibitions, etc.) of an action in a license and (ii) the restrictiveness relation among status denoted by S ; 3. C → is a set of compatibility constraints to identify if a restrictiveness relation between two licenses is also a compatibility relation; and 4. C L is a set of license constraints to identify non-valid licenses.

In CaLi, L A,LS defines the set of all licenses that can be expressed with A and LS. (L A,LS , R ) is the restrictiveness lattice of licenses that defines the restrictiveness relation R over the set of all licenses L A,LS . With C L non-valid licenses are identified. We consider a license l i as non-valid if a resource can not be licensed under l i . If two valid licenses have a restrictiveness relation then it is possible that they have a compatibility relation too. To identify the compatibility among licenses, CaLi refines the restrictiveness relation with compatibility constraints C → .

ODRL_CaLi, is a CaLi ordering A, LS, C L , C → such that:

-A is the set of 72 actions considered by ODRL11 ; -LS is the restrictiveness lattice of status where (i) the possible status are Permission, Duty, Prohibition12 or Undefined (for actions that do not appear in the license), and (ii) the restrictiveness relation is U ndef ined S P ermission S Duty S P rohibition; and -C L , C → are the sets of constraints, inspired from the ODRL information model, defined below. C → = {ω →1 , ω →2 } allows to identify (1) when cc:ShareAlike is required and (2) when cc:DerivativeWorks is prohibited. That is because cc:ShareAlike requires that the distribution of derivative works be under the same license only, and cc:DerivativeWorks, when prohibited, does not allow the distribution of a derivative resource, regardless of the license. Other constraints could be defined to be closer to the ODRL information model but for the purposes of this demonstration these constraints are enough.

C L = {ω L1 , ω L2 ω L3 }
The size growth of CaLi orderings is exponential |LS| |A| , so the size of ODRL_CaLi is 4 72 , which makes it impossible to build. Nevertheless, it is not necessary to explicitly build a lattice to use it. Our search engine uses a sorting algorithm that can sort any set of licenses according to the LS defined above, in approximatively n 2 /2 comparisons of restrictiveness, n being the number of licenses to sort, i.e., O(n 2 ). This algorithm is able to insert a license in a graph in linear time O(n) without sorting again the graph (see [START_REF] Benjamin | Modelling the Compatibility of Licenses[END_REF] for more details). Thus, our algorithm produces compatibility graphs of licenses conform to the ODRL_CaLi ordering of licenses. This algorithm is available on GitHub under the MIT license13 .

Demonstration

Using ODRL_CaLi and the sorting algorithm described in the previous section, we generated two compatibility graphs of licences. One for licenses that are the most used in DataHub14 and another for the most used licenses in GitHub. Licenses are in RDF. We use the dataset of licenses proposed by [START_REF] Doncel | A Dataset of RDF Licenses[END_REF].

Resources associated to licenses refer to some licensed RDF datasets from DataHub, from OpenDataSoft15 and from licensed repositories from GitHub.

The source code of the search engine is available on GitHub16 under the MIT license. Our demonstration is available online at http://cali.priloo. univ-nantes.fr.

Both compatibility graphs of licences are visually available. Figure 1a shows the compatibility graph of the CaLi ordering for some licensed RDF datasets. Blue nodes are licenses, grey arrows are compatibility relations among licenses and orange nodes are RDF datasets associated to licenses. Licenses that have the same actions in the same status are represented in the same node. In the graph, licenses that are compatible with a particular license l i are below l i and licenses that are compliant with l i are above l i . We recall that the ordering relations of compatibility and compliance that we define are reflexive, transitive and asymmetric.

During the demonstration, attendees will be able to search for resources licensed under licenses compliant or compatible with a particular license. Figure 1b shows the search bar of our search engine. It enables full-text and licensecompliant searches over each graph, for RDF datasets 17 or repositories 18 . For example, users can search for datasets about 'bikes' whose licenses are compatible with the CC BY-NC license (i.e. datasets about 'bikes' that can be reused under the CC BY-NC license). The result contains all RDF datasets indexed in the search engine where title or description contains the word 'bikes' and whose license is compatible with CC BY-NC (e.g. CC BY, MIT, CC-Ze, etc.). Both compatibility graphs of licences are available online through a documented API. Finally, these graphs are also accessible through a TPF server 1920 or can be exported in RDF (turtle, xml, n3 and json-ld).

A possible extension of our search engine is to allow the collaborative addition of licenses and licensed resources. That is, to allow users to add new licenses and resources to increase the size and therefore the interest of these two graphs.

ωL 1 (F

 1 li) = F alse if li(cc:CommercialUse) = Duty; T rue otherwise. ωL 2 (li) = F alse if li(cc:ShareAlike) = Prohibition; T rue otherwise. ωL 3 (li) = alse if ai odrl:includedIn aj AND (li(ai) = Permitted OR li(ai) = Duty) AND li(aj) = Prohibited; T rue otherwise.

ω→ 1 (

 1 li, lj) = F alse if li(cc:ShareAlike) = Duty; T rue otherwise. ω→ 2 (li, lj) = F alse if li(cc:DerivativeWorks) = Prohibition; T rue otherwise.

  (a) Compatibility graph of the ODRL_CaLi ordering for some licensed RDF datasets. (b) Search bar of the license-based search engine.

Fig. 1 :

 1 Fig. 1: Screenshoots of the license-based search engine.

https://www.w3.org/TR/odrl-vocab/#actionConcepts

https://www.w3.org/TR/odrl-model/#rule

https://github.com/benjimor/CaLi

https://old.datahub.io/

https://data.opendatasoft.com/pages/home/

https://github.com/benjimor/CaLi-Search-Engine

http://cali.priloo.univ-nantes.fr/ld/

http://cali.priloo.univ-nantes.fr/rep/

http://cali.priloo.univ-nantes.fr/api/ld/tpf

http://cali.priloo.univ-nantes.fr/api/rep/tpf