Danwen Qin

Adel Mesbah

Nicolas Clavier

Stephanie Szenknect

Stéphanie Szenknect

Nicolas Dacheux

From Th-Rhabdophane to Monazite-Cheralite Solid Solutions: Thermal Behavior

come

Introduction

The management of radioactive waste coming from the reprocessing of nuclear spent fuel represents one of the major challenges in the nuclear power industry. [START_REF] Ewing | Nuclear waste forms for actinides[END_REF] In this frame, a tremendous number of studies have been dedicated to the conditioning and storage of high level radioactive wastes (HLW).

Particularly, glass, glass-ceramics and ceramics have been proposed as sustainable wasteforms [START_REF] Lutze | Radioactive waste forms for the future[END_REF][START_REF] Loiseau | Glass-ceramic nuclear waste forms obtained from SiO 2 -Al 2 O 3 -CaO-ZrO 2 -TiO 2 glasses containing lanthanides (Ce, Nd, Eu, Gd, Yb) and actinides (Th): study of internal crystallization[END_REF][START_REF] Deschanels | Evaluation of the technical feasibility of new conditioning matrices for longlived radionuclides[END_REF] . In this frame, France, with the "Bataille" act, adopted in 1991, set out the legislative framework of the radioactive waste management, especially underground repository to host actinides and fission products by considering different solutions as cited above. In order to meet the requirements of this law, a particular attention was paid to the specific conditioning of actinides in tailored ceramic wasteforms, such as phosphate based materials including apatites (Ca 10 (PO 4 ) 6 F 2 ), [START_REF] Bros | Occurrence of Pu and fissiogenic REE in hydrothermal apatites from the fossil nuclear reactor 16 at Oklo (Gabon)[END_REF][START_REF] Terra | Synthesis and characterization of thorium-bearing britholites[END_REF][START_REF] Terra | Synthesis and characterization of uranium-bearing britholites[END_REF] monazites (LnPO 4 ) and associated cheralites (M II M IV (PO 4 ) 2 ) [START_REF] Tabuteau | Monazite-like phase containing transuranium elements (neptunium and plutonium)[END_REF][START_REF] Meldrum | Radiation damage in zircon and monazite[END_REF][START_REF] Dacheux | Monazite as a promising long-term radioactive waste matrix: Benefits of high-structural flexibility and chemical durability[END_REF][START_REF] Kitaev | Orthophosphates of Tetravalent Ce, Th, U, Np, and Pu with the Monazite Structure[END_REF][START_REF] Terra | Immobilization of tetravalent actinides in phosphate ceramics[END_REF] or thorium phosphate-diphosphate [START_REF] Benard | Th 4 (PO 4 ) 4 P 2 O 7 , a new thorium phosphate: Synthesis, characterization, and structure determination[END_REF] . Monazite LnPO 4 with Ln = La to Gd and its related solid solutions, fulfill several requirements such as the capability to contain large amounts of actinides within its structure (up to 29 wt. % ThO 2 and 16 wt. % UO 2 in monazite ores) [START_REF] Bregiroux | Solid-state synthesis of monazite-type compounds containing tetravalent elements[END_REF][START_REF] Davis | Crystal chemistry and phase relations in the synthetic minerals of ceramic waste forms. II. Studies of uranium-containing monazites[END_REF] , good sintering capabilities [START_REF] Terra | Preparation and characterization of lanthanumgadolinium monazites as ceramics for radioactive waste storage[END_REF] , high chemical durability [START_REF] Lumpkin | Comprehensive Nuclear Materials[END_REF][START_REF] Boatner | Radioactive Waste Forms for the Future[END_REF] and good resistance to radiation damage [START_REF] Deschanels | Swelling induced by alpha decay in monazite and zirconolite ceramics: A XRD and TEM comparative study[END_REF][START_REF] Seydoux-Guillaume | Why natural monazite never becomes amorphous: Experimental evidence for alpha selfhealing[END_REF] .

The mechanism of actinides incorporation into the monazite structure depends on their oxidation state.

For trivalent actinides (e.g. Pu, Am), the direct incorporation was already reported in respect of the Ln 1-x An III x PO 4 formula [START_REF] Burakov | Self-Irradiation of Monazite Ceramics: Contrasting Behavior of PuPO 4 and (La,Pu)PO 4 Doped with Pu-238[END_REF][START_REF] Bregiroux | Plutonium and americium monazite materials: Solid state synthesis and X-ray diffraction study[END_REF] . On the contrary, a coupled substitution is always required to incorporate tetravalent actinides (An(IV) = Th, U, Np). Two substitution schemes were reported in literature: the first one consists of a simultaneous incorporation of a divalent element such as an alkaline earth metal and tetravalent actinide to form Ln 1-2x An IV x M II x PO 4 monazite-cheralite solid solution. The second one consists of the replacement of the phosphate groups by silicate entities to form Ln 1-x An x (PO 4 ) 1-x (SiO 4 ) x monazite-huttonite solid solutions [START_REF] Bregiroux | Solid-state synthesis of monazite-type compounds containing tetravalent elements[END_REF][START_REF] Hikichi | Solid solutions in the systems monazite(CePO 4 )huttonite(ThSiO 4 ), and monazite-Ca 0.5 Th 0.5 PO 4[END_REF][START_REF] Hughes | The Crystal-Structure of Cheralite-(Ce),(LREE, Ca, Th, U)(P, Si)O 4 , a Monazite-Group Mineral[END_REF] . The first mechanism is by far the most documented [START_REF] Dacheux | Monazite as a promising long-term radioactive waste matrix: Benefits of high-structural flexibility and chemical durability[END_REF] and the actinide-based monazite-cheralite solid-solutions were usually synthesized through solid-state reactions [START_REF] Hikichi | Solid solutions in the systems monazite(CePO 4 )huttonite(ThSiO 4 ), and monazite-Ca 0.5 Th 0.5 PO 4[END_REF][START_REF] Hughes | The Crystal-Structure of Cheralite-(Ce),(LREE, Ca, Th, U)(P, Si)O 4 , a Monazite-Group Mineral[END_REF][START_REF] Montel | X-ray diffraction study of brabantite-monazite solid solutions[END_REF][START_REF] Brandel | Chemistry of tetravalent actinide phosphates-Part II[END_REF][START_REF] Raison | Structural investigation of the synthetic CaAn(PO 4 ) 2 (An = Th and Np) cheralite-like phosphates[END_REF][START_REF] Clavier | Crystal chemistry of the monazite structure[END_REF][START_REF] Popa | CaTh(PO 4 ) 2 cheralite as a candidate ceramic nuclear waste form: Spark plasma sintering and physicochemical characterisation[END_REF] . However, there is a growing interest in the preparation of monazites by wet chemistry routes in order to improve the homogeneity and sintering properties of the powders [START_REF] Terra | Preparation and characterization of lanthanumgadolinium monazites as ceramics for radioactive waste storage[END_REF][START_REF] Podor | Experimental study of Th-bearing LaPO 4 (780 °C, 200 MPa): Implications for monazite and actinide orthophosphate stability[END_REF][START_REF] Fou De Kerdaniel | Actinide solubilitycontrolling phases during the dissolution of phosphate ceramics[END_REF] .

Consequently, we investigated the incorporation of tetravalent thorium into PrPO 4 through the 2 Pr 3+ ↔ Th 4+ + Ca 2+ cationic substitution [START_REF] Qin | Incorporation of thorium in the rhabdophane structure: Synthesis and characterization of Pr 1-2x Ca x Th x PO 4 •nH 2[END_REF] . A series of rhabdophane-type precursors with the general formulae Pr 1-2x Th x Ca x PO 4 •n H 2 O were firstly prepared by hydrothermal synthesis (110°C, 4 days), then associated monazite-cheralite solid solutions Pr 1-2x Th x Ca x PO 4 were obtained after heat treatment at 1100 ºC for 6 hours. As the powder crystallizing in the rhabdophane structure type is considered as the stable hydrated form for light lanthanide phosphates (Ln = La-Gd) at low temperature [START_REF] Fou De Kerdaniel | Actinide solubilitycontrolling phases during the dissolution of phosphate ceramics[END_REF] , the protocol mentioned above might be suitable for other light lanthanide monazite-cheralites having the general formulae Ln 1-2x Th x Ca x PO 4 .

Nevertheless, the dehydration process and the steps associated to the thermal conversion of Ln 1- 2x Th x Ca x PO 4 .nH 2 O compounds were never assessed while there are only few reports on the thermal behavior of rhabdophane LnPO 4 •nH 2 O. Indeed, Jonasson and Vance have investigated the transformation of rhabdophane to monazite for Ln = La -Dy using thermogravimetric analysis (TGA) and differential thermal analyses (DTA). They have reported dehydration temperatures ranging from 100 to 400°C while the temperature mentioned for the irreversible transformation into monazite was found between 500 and 900°C. Moreover, the conversion temperature increased with decreasing ionic radius [START_REF] Jonasson | DTA STUDY OF THE RHABDOPHANE TO MONAZITE TRANSFORMATION IN RARE-EARTH (LA-DY) PHOSPHATES[END_REF] . A similar study has been done by Kijkowska 34 who reported a double endothermic effect below 300°C assigned to a two-step dehydration. Furthermore, the temperature of rhabdophane to monazite transformation was found to increase with the atomic number from below 750°C (La, Ce) to above 900°C (Tb, Dy). [START_REF] Kijkowska | Thermal decomposition of lanthanide orthophosphates synthesized through crystallisation from phosphoric acid solution[END_REF] From the structural point of view, Mesbah et al. reported the dehydration process and related crystal structure changes from monoclinic LnPO 4 •0.667 H 2 O to trigonal LnPO 4 with Ln = Nd, Sm, Gd, Eu and Dy [START_REF] Mesbah | In pursuit of the rhabdophane crystal structure: from the hydrated monoclinic LnPO 4 .0.667H 2 O to the hexagonal LnPO4 (Ln = Nd, Sm, Gd, Eu and Dy)[END_REF] . The initial crystal structure (monoclinic C2, Z = 24) has six independent positions for the cations. One third of them is coordinated to 8 oxygen atoms from the phosphate groups to form an infinite chain (called ch1) while the other two thirds are coordinated by 9 oxygen atoms with the ninth represented by a water molecule to form a second different chain (Ch2) leading to a channeled structure oriented along [101] direction (Figure 1), where the water molecules fill those channels.

During the dehydration of the rhabdophane samples, which involves a two-step process, the lanthanide phosphate first turns into the hemihydrate compound (LnPO 4 •0.5 H 2 O, monoclinic C2). Within this structure, there is one kind of chains formed by half of the lanthanide atoms in 8-fold coordinated while the others are 9-fold coordinated. This leads to the disappearance of the anhydrous chains and the reconstruction of the water network. However, all the chains are oriented along the [101] direction and water molecules also stay within the structure channels (Figure 1). The full dehydration towards anhydrous rhabdophane (trigonal, P3 1 21) takes place between 190°C and 240°C. Finally, the irreversible transformation into monazite occurs for temperatures above 500°C. In this study, single phase samples of Nd 1-2x Th x Ca x PO 4 •n H 2 O (x = 0 to 0.15) were prepared by wet chemistry route then their thermal conversion into the final monazite-cheralite compounds was first followed by in situ HT-PXRD to determine the conversion temperature range and to investigate the variation of the unit cell volume. Moreover, a coupled TGA/dilatometry study was undertaken to get better understanding of the dehydration and conversion processes.

Experimental

Synthesis

Following the synthesis procedure described in our previous work [START_REF] Qin | Incorporation of thorium in the rhabdophane structure: Synthesis and characterization of Pr 1-2x Ca x Th x PO 4 •nH 2[END_REF] , the metal nitrate salts used (Sigma-Aldrich) were of analytical grade: NdCl water and once with ethanol) by going through three centrifugation cycles (at 14500 rpm for 5 minutes). Finally, the product was dried in an oven at 90°C overnight.

Powder X-Ray Diffraction (PXRD) & in situ High Temperature-PXRD (HT-PXRD)

PXRD analyses were realized on a Bruker D8 advance diffractometer, equipped with Cu Kα radiation (λ = 1.54184 Å). Data collection was performed using reflection geometry with 2θ ranging from 5 to 100° with steps of Δθ = 0.019° and a step time of t = 3.68 s. In addition, a PXRD pattern of pure silicon was collected in similar conditions to be used as an external standard to extract the instrumental function. The collected powder patterns were refined by the Rietveld method with the use of the Fullprof_Suite package [START_REF] Frontera | FULLPROF as a new tool for flipping ratio analysis[END_REF] .

Moreover, in order to identify the successive dehydration steps and phase transformation, in situ HT-PXRD experiments were performed on the same instrument for temperatures ranging from room temperature (RT) to 1100°C with a rate of 5°C.min -1 . During each experiment, the PXRD patterns were collected on a set of 30 temperature set points. For each measurement, the system was held at the target temperature for 15 minutes prior the beginning of the scan from 5 to 100° (2θ, angular step of 0.014° and time step of 1.10 s). Table S1 gathers the crystal data and the refinement parameters for the Nd 1-2x Th x Ca x PO 4 •n H 2 O series (x = 0, 0.05 and 0.1) at 30°C, 100°C, 300°C (rhabdophane) and at 30°C

(monazite-cheralite) after thermal treatment at 1100°C.

Thermo-Gravimetric Analyses (TGA) and dilatometric study

TG analyses were undertaken thanks to a Setaram Setsys Evolution apparatus equipped with a type-S thermocouple (Pt/Pt-10%Rh). After the blank was recorded using an empty alumina crucible (30 µL), about 15 mg of powder were heated in air with a rate of 5°C.min -1 from RT to 1000°C in order to follow the dehydration steps then the transition from rhabdophane to monazite.

Accordingly, the dilatometric measurements were conducted with a similar apparatus with thermomechanical analysis (TMA) configuration. Approximately 200 mg of powder were first shaped by uniaxial pressing (500 MPa) in a tungsten carbide die, resulting in a 5 mm diameter cylindrical pellet of about 1 mm in height. The linear shrinkage of the pellet was then followed as a function of temperature from RT to 1000°C with a heating rate of 1°C.min -1 . Thermal dilatation of alumina sample holder was measured under the same conditions and was subtracted from the resulting signal.

X-EDS

FEI Quanta 200 electron microscope equipped with X-EDS analyzer (BRUKER XFlash® 5010 SDD) was used for quantitative chemical analyses with an acceleration voltage of 15 kV and a chamber pressure below 2 × 10 -4 Pa. The powdered samples were first embedded in an epoxy resin, polished to mirror grade and then metalized. For each sample, 30 spots were analyzed and average values led to deduce the chemical composition of the samples.

Chemical compositions analyses with ICP-AES

In order to determine the composition of the synthesized rhabdophane samples, about 20 mg of the obtained powder was firstly dissolved completely in 2.5 mL aqua regia then diluted in 0.16 M HNO 3 solution. These solutions were analyzed through ICP-AES (Spectro Arcos EOP) after the application of SPEX standard solutions to calibrate the elementary concentrations of Ca, Th, Nd and P. The recommended emission wavelengths were taken into account in the calculation of elementary concentration leading to the evaluation of the atomic ratios.

Results

Synthesis of Nd 1-2x Th x Ca x PO 4 •n H 2 O

According to the preparation method reported recently [START_REF] Qin | Incorporation of thorium in the rhabdophane structure: Synthesis and characterization of Pr 1-2x Ca x Th x PO 4 •nH 2[END_REF] , thorium-bearing rhabdophane samples Nd 1- 2x Th x Ca x PO 4 •n H 2 O with x = 0 to 0.15 were obtained by precipitation at 110°C during 4 days. PXRD analysis was performed to examine the crystal structure and showed that the powders were single phase rhabdophane (Figure 2). The chemical composition of the powders was then determined by ICP-AES after total dissolution of the samples in aqua regia (Table 1). From these data, the prepared powders exhibited the expected stoichiometry for x = 0.05 and 0.1.

However, the precipitation of thorium and calcium appeared to be slightly different from the expected values for x = 0.15. This problem was already described during the synthesis of Pr 1-2x Th x Ca x PO 4 •nH 2 O solid solutions, the precipitation becoming non-stoichiometric for x ≥ 0.20 [START_REF] Qin | Incorporation of thorium in the rhabdophane structure: Synthesis and characterization of Pr 1-2x Ca x Th x PO 4 •nH 2[END_REF] . Consequently, the coupled substitution might exhibit a limit under these synthesis conditions. For Nd-based rhabdophane, the maximum Ca, Th incorporation might be between x = 0.10 and 0.15. Nevertheless, for x = 0.15, the charge balance seemed to be respected. Indeed, the total positive charge, i.e. In order to achieve the conversion of rhabdophane into monazite, the synthesized precursors were first directly heated at 1100°C for 6 hours in air. According to the PXRD patterns collected on the resulting powders (Figure 3), the samples obtained from x = 0 to x = 0.10 were single phase monazite-cheralite solid solutions. Conversely, the presence of the XRD lines of α-ThP 2 O 7 as secondary phase was evidenced for x = 0.15. [START_REF] Clavier | Raman and Rietveld analysis of thorium diphosphate[END_REF] In a previous work, Podor [START_REF] Podor | Synthèse et caractérisation des monazites uranifères et thorifères[END_REF] prepared the monazite under hydrothermal conditions (780°C, 200 MPa) and reported that the direct substitution of thorium in the structure of LaPO 4 (4 La 3+ ↔ 3 Th 4+ + □) was limited to only 7.45  1.12 wt.% of ThO 2 (i.e. to 6.40 ± 0.99 mol.% of thorium ). Above this value, thorium diphosphate (α-ThP 2 O 7 ) always appeared as a secondary phase. [START_REF] Podor | Synthèse et caractérisation des monazites uranifères et thorifères[END_REF] Therefore, for x = 0.15, the initial rhabdophane type structure, with a certain amount of vacancies and excess of Th, is no longer stable during its conversion into monazite-cheralite, leading to segregation of Th and thus to the formation of α-ThP 2 O 7 .

Since the monazite-cheralite solid solutions exhibited very high chemical durability, which resulted in only partial dissolution in fresh aqua regia under the application of the protocol developed for rhabdophane analysis (~ 0.020 mg sample in 2.5 mL aqua regia), the evaluation of their chemical composition was undertaken by X-EDS (Table 2). It is worth noting that the results obtained for monazite-cheralite solid solutions were not significantly different compared to that obtained for the starting rhabdophane samples, indicating the absence of phosphate elimination through decomposition during the heating treatment at high temperature. 4. This experiment underlined two phase transitions: the first one took place at 200 °C while the second began at 700 °C and ended at 850 °C.

The transition leading to the formation of the hemihydrate form reported previously by Mesbah et al. [START_REF] Mesbah | In pursuit of the rhabdophane crystal structure: from the hydrated monoclinic LnPO 4 .0.667H 2 O to the hexagonal LnPO4 (Ln = Nd, Sm, Gd, Eu and Dy)[END_REF] was not detected on the basis of the quality of the data collected using a laboratory diffractometer.

Therefore, in these experiments, the first transition observed led to the formation of anhydrous rhabdophane while the second one was assigned to the irreversible conversion into monazite-cheralite solid solution.

The in situ HT-PXRD patterns were then refined using the Rietveld method by considering the appropriate crystal structure depending on the temperature of the data collection, i.e.:

-i) at 30°C, the hydrated form Nd (P3 1 21 space group, Z = 3).

-iv) above 700°C, the monoclinic form associated to the irreversible formation of monazite Nd 1-2x Th x Ca x PO 4 (P2 1 /n space group, Z = 4).

Therefore, the unit cell volumes were systematically normalized to three formula units for each phase, underlining the variation of unit cell volume of Nd 1-2x Th x Ca x PO 4 •n H 2 O by direct comparison (Figure 5).

All the studied samples showed similar behavior. The structure change corresponding to the dehydration led to a volume swelling of about 1 % around 200°C. After a slight swelling due to the increase of temperature, the irreversible phase transition from anhydrous rhabdophane to monazitecheralite solid solution occurred between 650°C and 850°C which agrees well with the transition temperature reported by Jonasson and Vance for NdPO 4 •0.667 H 2 O (i.e. 680-790°C) [START_REF] Jonasson | DTA STUDY OF THE RHABDOPHANE TO MONAZITE TRANSFORMATION IN RARE-EARTH (LA-DY) PHOSPHATES[END_REF] . Finally, the shrinkage of the unit cell volume reached 18.5%, confirming that the monazite-cheralite solid solutions have a far more compact structure than their rhabdophane counterparts.

Thermo-Gravimetric Analysis

Even though in situ HT-PXRD experiment argued for a direct dehydration process is completed around 200 °C, it might go through several steps as in the case of lanthanide end-members [START_REF] Mesbah | In pursuit of the rhabdophane crystal structure: from the hydrated monoclinic LnPO 4 .0.667H 2 O to the hexagonal LnPO4 (Ln = Nd, Sm, Gd, Eu and Dy)[END_REF] . Also, the amount of water molecules per unit formula has not been determined yet. TGA experiments were then performed to accurately follow the dehydration process of Nd 1-2x Th x Ca x PO 4 •nH 2 O (0 ≤ x ≤ 0.10) (Figure 6). The incorporation of thorium and calcium within the structure has few impact on the temperature associated to the dehydration of the rhabdophane. Even though, the temperature of transition might increase very slightly with the incorporation rate of thorium and calcium in the structure as reported in Table 3.

Dilatometric study

The relative linear shrinkage of Nd 1-2x Th x Ca x PO 4 •n H 2 O was analyzed by dilatometric measurements (Figure 7) and revealed a three-step variation. The first dehydration step leading to the stabilization of the hemihydrate form was not observed. However, a slight swelling of about 1% took place around 200°C and was assigned to the complete dehydration of the rhabdophane compounds. Then a transition was observed from 600°C to 850°C and corresponds to the irreversible transformation from rhabdophane-type structure into monazite-cheralite which appears in good agreement with the results obtained from in situ HT-PXRD. The final step occurred at higher temperatures (i.e. for T > 850°C)

and was correlated to the sintering of the samples.

The temperature of the phase transition, deduced from the maximum shrinkage rate, was found to increase with the Ca-Th coupled substitution rate from 693 ± 1°C (x = 0) to 762 ± 1°C (x = 0.1). It agreed well with the temperatures reported by Jonasson and Vance (500 -900°C) and by Kijkowska (717 -910°C) regarding to the formation of monazite endmembers [START_REF] Jonasson | DTA STUDY OF THE RHABDOPHANE TO MONAZITE TRANSFORMATION IN RARE-EARTH (LA-DY) PHOSPHATES[END_REF][START_REF] Kijkowska | Thermal decomposition of lanthanide orthophosphates synthesized through crystallisation from phosphoric acid solution[END_REF] . Moreover, both studies showed an increase of the transformation temperature with the atomic number. Reviewing the reported data and the results of this work, it might have an interest to investigate the variation of this temperature versus ionic radius. Indeed, as shown in Figure 8, such temperature of transformation was found to increase with the shrinkage of ionic radius. 44

Influence of coupled substitution on crystal structures

According to the TGA results, the first three temperature set points of the in situ HT-PXRD study, i.e.

30°C, 100°C and 300°C, were corresponding to three distinct phases, i.e. Nd 9.

At 30°C, the rhabdophane crystallizes in the monoclinic system in C2 space group in the LnPO 4 .0.667 H 2 O structure type. The refined volume of the unit cell was found to increase when the thorium and calcium contents increase within the structure. If we consider the ionic radius of Nd 3+ , Th 4+ and Ca 2+ reported in the Shannon tables (Table 4), the refined volume of the rhabdophane structure should decrease when smaller atoms are inserted. Such behavior could be explained by the preference of thorium and calcium to be coordinated by the water molecules leading to a 9-fold coordination. In this case, the volume of the unit cell should increase because the average r Ca-Th (CN =9) value is larger than the ionic radius of Nd (CN = 8), on the one hand, and because of the impact of larger amounts of water molecules within the channels, on the other hand. This assumption is justified also by the water content measured by TGA. Moreover, theoretically, if we consider that all the cationic sites are coordinated by water molecules, the structure should have 1.5 water molecule per formula unit. (TGA results, Table 3). According to the data viewed in Figure 9, after the first dehydration step, the unit cell volume seemed to decrease in agreement with the ionic radius of Th 4+ , Ca 2+ and Nd 3+ reported in literature [START_REF] Shannon | Revised effective inonic-radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF] . Regarding the structural features of the hemihydrate form (Figure 1), we could assume that there is no ordering of thorium and calcium on a specific site (i.e. specific coordination number), and thus the distribution of water molecules respects the crystal structure properties published previously by Mesbah et al. [START_REF] Mesbah | In pursuit of the rhabdophane crystal structure: from the hydrated monoclinic LnPO 4 .0.667H 2 O to the hexagonal LnPO4 (Ln = Nd, Sm, Gd, Eu and Dy)[END_REF] . Moreover, the same observation was made for the structure refined at 300°C when considering the anhydrous form of the rhabdophane structure. It is worth noting that the unit cell volume variations at 100°C and 300°C were consistent with that expected. Therefore, there is more reason to believe that the increase of the unit cell volume of Nd 1-2x Th x Ca x PO 4 •n H 2 O compounds collected at 30°C could be associated to the increase of water amounts within the channels.

Conclusions

In this study, rhabdophane-type precursors with general formula Nd 1-2x Th x Ca x PO 4 •n H 2 O (x = 0 to 0.15) were prepared by hydrothermal synthesis. Single phase monazite-cheralite Nd 1-2x Th x Ca x PO 4 solid solutions were obtained by direct heating of such precursors from x = 0 to x = 0.1. For x > 0.1, the composition of the rhabdophane precursor appeared to be non-stoichiometric and α-ThP 2 O 7 was found as a secondary phase in the final product. The combination of TGA analyses, HT-PXRD and dilatometry experiments allowed the description of the thermal conversion of rhabdophane-type precursor to the final monazite-cheralite wasteform. The temperatures associated to the dehydration and to the rhabdophane to monazite conversion were determined. The Ca-Th coupled substitution rate seemed to affect these transformation temperatures as the change of ion radii would influence the structure stability. In the case of the as-synthesized powders, the refined unit cell volume was found to increase when smaller atoms are incorporated within the structure. This unexpected trend is impacted by the insertion of extra water molecules in a slightly variable amounts within the channels. Accurate determination of the temperature associated to the stabilization of the hemihydrate form was not possible. However, above 100°C, we assume all the samples prepared to be under the form Nd 1- 2x Th x Ca x PO 4 •0.5 H 2 O (x = 0 to 0.10). Under these circumstances, the unit cell volume decreases linearly in agreement with the average size of Ca-Th incorporated in the structure. At higher temperature (≥ 210°C), the anhydrous form is observed and above 650°C the monazite-cheralite structure is irreversibly stabilized. In agreement with the previous studies, the temperature of transition rhabdophane-monazite was found to increase with the average ionic size of cations. Based on this thermal behavior and aiming at the use of such ceramics for the long-term conditioning of radioactive waste, further experiments will be focused on the sintering properties as well as on the chemical durability of the prepared materials.

FOR TABLE OF CONTENTS USE ONLY

Authors: Danwen Qin , Adel Mesbah, Nicolas Clavier, Stéphanie Szenknect, Nicolas Dacheux Synopsis. Nd 1-2x Th x Ca x PO 4 •n H 2 O (x = 0 -0.15) solid solutions were prepared under hydrothermal conditions (110°C, t = 4 days). The combined in situ high temperature PXRD, TGA and dilatometry investigations showed that the dehydration process follows the same trend than the NdPO 4 •0.667 H 2 O end-member. The incorporation of Ca/Th was found to increase slightly the dehydration temperature (210±3°C to 214±3°C) as well as that corresponding to the irreversible conversion into monazite at higher temperature (693±1°C to 762±1°C).

Figure 1 .

 1 Figure 1. Representation of the chains and channels present in LnPO 4 •0.667 H 2 O (top) and LnPO 4 •0.5 H 2 O (bottom).35

3 (

 3 Nd 3+ ) + 4 (Th 4+ ) + 2 (Ca 2+ ) equals 3.03 ± 0.21 while the total negative charge, i.e. 3 (PO 4 3-), reaches 3.21 ± 0.51. Both values are thus not significantly different considering the associated uncertainties. One explanation of the slight difference between Th and Ca contents could result from the formation of the presence of vacancies in the structure. Additionally, it is worth noting that during the synthesis of Pr 1- 2x Th x Ca x PO 4 •n H 2 O samples, XRD analysis revealed the formation of crystallized Th 2 (PO 4 ) 2 (HPO 4 )•H 2 O (TPHPH)[START_REF] Brandel | Hydrothermal synthesis and characterization of the thorium phosphate hydrogenphosphate, thorium hydroxide phosphate, and dithorium oxide phosphate[END_REF] as a secondary phase for x ≥ 0.20. Such an additional thoriumenriched phase was not detected by PXRD in this work which also argue in favor of a nonstoichiometric substitution.[START_REF] Brandel | Hydrothermal synthesis and characterization of the thorium phosphate hydrogenphosphate, thorium hydroxide phosphate, and dithorium oxide phosphate[END_REF]

Figure 2 . 3 . 2 .

 232 Figure 2. PXRD patterns obtained for Nd 1-2x Th x Ca x PO 4 •nH 2 O samples (with 0  x  0.15)

Figure 3 .

 3 Figure 3. PXRD patterns obtained after conversion of Nd 1-2x Th x Ca x PO 4 •n H 2 O rhabdophanes at 1100°C for 6 hours (air atmosphere). PXRD patterns reported for monazite NdPO 4 (black vertical bars) 40 and for -ThP 2 O 7 (red vertical bars) 41 .

Figure 4 .

 4 Figure 4. In situ HT-PXRD patterns of Nd 0.8 Th 0.1 Ca 0.1 PO 4 •nH 2 O: initial rhabdophane (black line), hemihydrate rhabdophane (red line), anhydrous rhabdophane (blue line), mixture of rhabdophane and monazite-cheralite (yellow line) and single phase monazite-cheralite (green line).

Figure 5 .

 5 Figure 5. Variation of refined unit cell volume of Nd 0.8 Th 0.1 Ca 0.1 PO 4 •nH 2 O versus heating temperature, the volume of each phase was normalized to three formula units per cell for better understanding.

Figure 6 .

 6 Figure 6. TGA curves obtained for Nd 1-2x Th x Ca x PO 4 •nH 2 O samples.

Figure 7 .

 7 Figure 7. Dilatometric curves obtained during the sintering of Nd 1-2x Th x Ca x PO 4 •n H 2 O samples.

Figure 8 .

 8 Figure 8. Variation of the the temperature ofconversion from rhabdophane to monazite-cheralite depending on the ionic radius.

Figure 9 .

 9 Figure 9. Refined unit cell volume obtained for Nd 1-2x Th x Ca x PO 4 •n H 2 O samples prepared at 30°C, 100°C, 300°C and those corresponding to the monazite-cheralite samples collected at 30°C after thermal treatment at 1100°C.

32

 32

  Nd and Th amounts. The mixture was stirred for 15 minutes then the Teflon ® container was sealed and placed in an oven at 110°C for 4 days. The obtained precipitate was washed (twice with

	3 •6 H 2 O, CaCl 2 •n H 2 O, Th(NO 3 ) 4 •4-5 H 2 O; while acid
	solutions were diluted from concentrated H 3 PO 4 (85% Sigma-Aldrich), HCl (37% Carlo-Erba), and
	HNO 3 (69.5% Carlo-Erba). In order to avoid any problem of stoichiometry due to the hygroscopic
	character of the salts and thus to prevent potential lack of accuracy in weighing the amount of
	reactants, NdCl 3 and CaCl 2 were dissolved in 0.1M HCl and Th(NO 3 ) 4 •4-5 H 2 O in 4M HNO 3 . The
	final concentrations were typically ranging from 0.5 to 1.5 M. They were further determined by ICP-
	AES. As already described, the synthesis proceeded through mixing stoichiometric amounts of
	neodymium and thorium into a 30 mL Teflon ® container, with ten times the stoichiometric amount of
	calcium compared to thorium. Afterwards, 5M H 3 PO 4 was added dropwise with a 3 mol.% excess with
	regards to

Table 1 .

 1 Chemical composition of Nd 1-2x Th x Ca x PO 4 •n H 2 O rhabdophane-type compounds obtained by ICP-AES analysis after complete dissolution of the powdered samples

	x (target value)	Nd (1-2x)	Th (x)	Ca (x)	P/(Nd+Ca+Th)
	0.00	1.00 ± 0.01	---	---	1.04 ± 0.01
	0.05	0.90 ± 0.01	0.05 ± 0.01	0.05 ± 0.01	1.0 ± 0.1
	0.10	0.80 ± 0.03	0.11 ± 0.01	0.10 ± 0.01	1.0 ± 0.1
	0.15	0.71 ± 0.03	0.17 ± 0.02	0.11 ± 0.02	1.1 ± 0.2

Table 2 .

 2 Results

	x (target value)	Nd	Th	Ca	P/(Nd+Ca+Th)
	0.05	0.86 ± 0.02	0.06 ± 0.01	0.07 ± 0.01	0.92 ± 0.05
	0.10	0.76 ± 0.01	0.12 ± 0.01	0.11 ± 0.01	1.05 ± 0.03
	0.15	0.67 ± 0.02	0.19 ± 0.02	0.14 ± 0.01	1.01 ± 0.05
	3.3.

of X-EDS analysis obtained on Nd 1-2x Th x Ca x PO 4 monazite-cheralite solid solution samples prepared after thermal conversion of rhabdophanes

Structural evolution followed by in situ HT-PXRD.

In order to get a better understanding of dehydration and conversion processes of Nd 1-2x Th x Ca x PO

4

•n H 2 O (x = 0.0 -0.10), in situ HT-PXRD experiments were performed. The collected powder patterns recorded for Nd 0.8 Th 0.1 Ca 0.1 PO 4 •n H 2 O are viewed in Figure

Table 3 .

 3 Results of TGA obtained on Nd 1-2x Th x Ca x PO 4 •n H 2 O solid solutions

	x	T min derivative (°C)	H 2 O per unit formula (2 nd step)	H 2 O per unit formula (total amount)
	0.00	210 ± 3	0.46 ± 0.01	0.68 ± 0.01
	0.05	213 ± 3	0.47 ± 0.01	0.88 ± 0.01
	0.10	214 ± 3	0.46 ± 0.01	0.79 ±0.01

  1-2x Th x Ca x PO 4 •n H 2 O (0.68 ± 0.01 to 0.88 ± 0.01), Nd 1-2x Th x Ca x PO 4 •0.5 H 2 O and Nd 1-2x Th x Ca x PO 4 , respectively. Based on such structural models, these collected PXRD patterns were refined by the Rietveld method. The variation of the unit cell volume of the Nd 1-2x Th x Ca x PO 4 •nH 2 O compounds are reported in Figure

Table 4 .

 4 Selected Crystal Radius reported for Ca 2+ , Nd 3+ and Th 4+ in the eight and nine fold coordination numbers[START_REF] Shannon | Revised effective inonic-radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]

	Coordination	r Ca Å 2+	r Th 4+ Å	r Ca-Th Å	r Nd 3+ Å	Δ r d	r d	r Ca Th X
	VIII IX	1.26 1.32	1.19 1.23	1.225 1.275	1.249 1.303		
	Despite the difficulties to determine the exact temperature of the first structural transition leading to
	the hemihydrate form, we can suggest that its stabilization occurs below 100°C. Therefore, the
	difference of the relative weight between 100°C and over 250 °C is corresponding to about 0.5 H 2 O

Acknowledgements

The authors would like to express their gratitude to Bruno Corso (ICSM) for the PXRD measurement; Renaud Podor and Joseph Lautru (ICSM) for X-EDS analyses. PhD salary of Danwen Qin was funded by the China Scholarship Council (CSC).

AUTHORS INFORMATION

*E-mail: adel.mesbah@cea.fr (A. MESBAH) Nicolas.clavier@icsm.fr (N. Clavier)

Notes

The authors declare no competing financial interest.


Alice Marcotte

Timothée Mouterde

Antoine Niguès

Alessandro Siria
email: alessandro.siria@ens.fr

Lydéric Bocquet
email: lyderic.bocquet@ens.fr

Mechanically activated ionic transport across single-digit carbon nanotubes

come

Mechanically activated ionic transport across single digit carbon nanotubes

Alice Marcotte, Timothée Mouterde, Antoine Niguès, Alessandro Siria , Lydéric Bocquet Laboratoire de Physique de l'Ecole normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France * Fluid and ionic transport at nanoscale recently highlighted a wealth of exotic behaviours [START_REF] Bocquet | Nanofluidics, from bulk to interfaces[END_REF][START_REF] Faucher | Critical knowledge gaps in mass transport through single-digit nanopores: a review and perspective[END_REF][START_REF] Bocquet | Nanofluidics coming of age[END_REF][START_REF] Majumder | Enhanced flow in carbon nanotubes[END_REF][START_REF] Holt | Fast mass transport through sub-2-nanometer carbon nanotubes[END_REF][START_REF] Tunuguntla | Ultrafast proton transport in sub-1-nm diameter carbon nanotube porins[END_REF][START_REF] Tunuguntla | Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins[END_REF][START_REF] Secchi | Massive radius-dependent flow slippage in carbon nanotubes[END_REF][START_REF] Siria | New avenues for the large-scale harvesting of blue energy[END_REF][START_REF] Walker | Extrinsic cation selectivity of 2D membranes[END_REF][START_REF] Yang | Carbon nanotube membranes with ultrahigh specific adsorption capacity for water desalination and purification[END_REF][START_REF] Feng | Single-layer MoS2 nanopores as nanopower generators[END_REF][START_REF] Feng | Observation of ionic Coulomb blockade in nanopores[END_REF][START_REF] Siria | Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube[END_REF] . However, the artificial nanofluidic devices [START_REF] Esfandiar | Size effect in ion transport through angstrom-scale slits[END_REF][START_REF] Radha | Molecular transport through capillaries made with atomic-scale precision[END_REF][START_REF] Fumagalli | Anomalously low dielectric constant of confined water[END_REF][START_REF] Mouterde | Molecular streaming and voltage-gated response in Angström scale channels[END_REF] are still far from the advanced functionalities existing in biological systems, such as electrically and mechanically activated transport [START_REF] Anishkin | Feeling the hidden mechanical forces in lipid bilayer is an original sense[END_REF][START_REF] Cox | Biophysical Principles of Ion-Channel-Mediated Mechanosensory Transduction[END_REF]. Here we focus on the ionic transport through 2 nm-radius individual multiwalled carbon nanotubes (CNT), under the combination of mechanical and electrical forcings. Our findings evidence mechanically activated ionic transport under the form of an ionic conductance which depends quadratically on the applied pressure. Our theoretical study relates this behaviour with the complex interplay between electrical and mechanical drivings, and shows that the superlubricity of CNT [START_REF] Majumder | Enhanced flow in carbon nanotubes[END_REF][START_REF] Holt | Fast mass transport through sub-2-nanometer carbon nanotubes[END_REF][START_REF] Tunuguntla | Ultrafast proton transport in sub-1-nm diameter carbon nanotube porins[END_REF][START_REF] Tunuguntla | Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins[END_REF][START_REF] Secchi | Massive radius-dependent flow slippage in carbon nanotubes[END_REF][START_REF] Pang | Origin of giant ionic current in carbon nanotube channels[END_REF]] is a prerequisite to attain mechanically activated transport. The pressure sensitivity shares similarities with the response of biological mechanosensitive ion channels [START_REF] Anishkin | Feeling the hidden mechanical forces in lipid bilayer is an original sense[END_REF][START_REF] Cox | Biophysical Principles of Ion-Channel-Mediated Mechanosensory Transduction[END_REF] observed here for the first time in an artificial system. This paves the way to build new active nanofluidic functionalities inspired by the complex biological machinery.

Nanofluidics, the field studying transport of fluids at the nanoscales, has now reached a stage of maturity. The manifold systems which have been developped over the recent years, from nanopores, nanotubes, to angström scale channels, together with the new instrumentation developped, now allow investigating fluid transport at the frontier of hydrodynamics. This points to key knowledge gaps in the so-called single digit nanopores with size below ten nanometers [START_REF] Faucher | Critical knowledge gaps in mass transport through single-digit nanopores: a review and perspective[END_REF].

Still, such artificial systems remain far from the impressive complexity of the biological ionic machinery, which exhibits a plethora of advanced transport functionalities. In particular, the recent identification of mechanotransduction channels has highlighted complex response involving excitatory mechanically activated ionic current under mechanical pressure or stretching [START_REF] Anishkin | Feeling the hidden mechanical forces in lipid bilayer is an original sense[END_REF][START_REF] Cox | Biophysical Principles of Ion-Channel-Mediated Mechanosensory Transduction[END_REF]. Reproducing such advanced response in artificial systems was up to now unreachable.

In the quest to reproduce such advanced response, we investigate here the non-linear transport in individual 'single-digit' CNT with radius ≈ 2 nm and explore how mechanical pressure does affect the ionic transport in these channels. CNT are unique materials in that they highlight ultra-low water friction on their surface [START_REF] Secchi | Massive radius-dependent flow slippage in carbon nanotubes[END_REF] and electro-dynamic couplings are accordingly expected to be exalted. However, probing transport in individual CNT with nanometric radius under coupled voltage and pressure drops has been so far a considerable challenge, notably in terms of fabrication and sensitivity, and most experimental studies in such tiny NT have been restricted up to now to electric forcings [START_REF] Pang | Origin of giant ionic current in carbon nanotube channels[END_REF][START_REF] Yazda | Voltage-activated transport of ions through single-walled carbon nanotubes[END_REF][START_REF] Choi | Diameter-dependent ion transport through the interior of isolated single-walled carbon nanotubes[END_REF][START_REF] Liu | Translocation of Single-Stranded DNA Through Single-Walled Carbon Nanotubes[END_REF]. To overcome this bottleneck, we build on the transmembrane nanotube methodology, initially developed for the measurement of the ionic transport with larger 10 -50 nm radii nanotubes, [START_REF] Siria | Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube[END_REF], but here applied to 2 nm nanotubes. The experimental set-up is shown in Fig. 1b: an individual arc-discharge CNT (SIGMA ALDRICH, Product number: 406074) connects two macroscopic fluid reservoirs through a 50 nm thick silicon-nitride (SiN) membrane (NORCADA). We investigated CNTs with inner radii of R ≈ 2.0 ± 0.6 nm and lengths of L ≈ 1 µm. The length of the CNTs is measured during the fabrication procedure under Scanning Electron Microscope (SEM) imaging (see Fig. 1a) and the inner radii distribution for the CNT has been obtained by Transmission Electron Microscopy (TEM) observations and is displayed on Fig. 1b. Transmembrane individual CNT (t-CNT) devices are realized by in situ SEM nanomanipulation, using the method previously described in [START_REF] Siria | Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube[END_REF] (see Methods for more details). The membrane is then sealed between two reservoirs, which are filled with a potassium chloride (KCl) solution at various con-centrations (denoted as c) and pHs. One Ag/AgCl electrode is immersed in each reservoir, and connected to a patch-clamp amplifier (Axopatch 200B) which allows for ionic current measurements with a current resolution of 0.1 pA. Both reservoirs can be connected to a pressure controler, enabling us to impose a pressure drop (± 0 -2 bar) in both directions across the membrane. This setup allows measuring the ionic current driven by a pressure drop ∆P and the combined effect of additional forcing ∆V applied along the t-CNT. In this study, three independent t-CNT devices with similar geometries were studied, and gave the same response as described below. Their IV characteristics at c = 1 M and pH 5.5 are given by Supplementary Figure 1.

In a typical experiment, we measured the pressure-driven component of the ionic current I, referred to as the streaming current and defined here as I str = I(∆P, ∆V ) -I(∆P = 0, ∆V ), see Methods. This current results from the transport of (excess) ions carried by a pressure-induced flow (inset Fig. 1c) and probes the interplay between ion and mass transport. A pressure drop between 50 mbar and 1.5 bar is applied in both directions across the t-CNT. We do not observe a temporal evolution of the system and the conductance is the same before and after pressure measurements are performed. Let us focus first on the pressure-response of the system in the absence of voltage bias (∆V = 0). As shown on Figure 1c and on Supplementary Figure 2 for c = 1 M and ∆V = 0, once the pressure drop is applied, the streaming current overshoots and then quickly relaxes to a stationary value.

We report in the Figure 1d, the stationary value reached by I str as a function of the applied pressure ∆P . As usually expected for such measurements without applied voltage, the streaming current varies linearly with the applied pressure, I str ∝ ∆P , see Fig. 1d, and the slope increases with pH. The sign of the current is furthermore consistent with an excess transport of positive charges flushed by water flow. This response is in agreement with results obtained for CNT with larger diameters [26] and was explained in terms of hydroxide adsorption on the CNT walls. Another contribution can originate from the differential mobility of the ions in confinement, as discussed recently [START_REF] Mouterde | Molecular streaming and voltage-gated response in Angström scale channels[END_REF].

In the present study, we rather focus on the pressure response in the presence of a constant bias voltage ∆V , typically ∆V ∈ [-100 mV; 100 mV]. Figure 2a shows the time-dependent response of the streaming current while applying pressure drops of ±200 mbar and ±400 mbar, when a bias voltage of 25 mV and of -25 mV is imposed along the CNT. We measure that for a given bias voltage, the streaming current is of the same sign independently of the sign of the pressure drop. This is best illustrated in Fig. 2b, which shows that the streaming is now a non-linear function of the pressure drop. This response is evidenced for all investigated systems, salt concentrations and pHs, see Supplementary Figures 3, 4 and5. The experimental data is very well described by a second order polynomial function of the pressure drop:

I str (∆P ) = µ EO ∆P + β(∆V ) × ∆P 2 , ( 1
)
where the first term is the (linear) electro-osmotic term with mobility µ EO and the second quadratic term is the dominant contribution to the current, Fig. 2b. Furthermore, the coefficient β(∆V ) is shown to depend linearly on the gating voltage, ∆V , as indicated on the inset of Fig. 2c.

Gathering the streaming and bare conductance contributions to the ionic current, one finds that the total current can be rewritten as

I ∆P (∆V ) = µ EO × ∆P + G(∆P ) × ∆V (2)
where the conductance is now a quadratic function of the applied pressure, G(∆P ) =

G 0 + G 2 × ∆P 2 .
This result highlights that narrow carbon nanotubes display mechanosensitive ionic conduction, with a conductance which is tuned by the mechanical pressure.

Figure 2c represents the conductance G(∆P ) as a function of the pressure drop ∆P , here for a solution of salt concentration of 1 M and pH 5.5. The collapse of the G curves for various ∆V shows that the pressure-dependent conductance is the physically relevant quantity here. This behaviour was measured for all investigated pHs and salt concentrations. Supplementary Figure 6 shows that G 2 increases with salt concentration (for both pH 5.5 and pH 10.5) with only a weak dependence on pH. This suggests that this result does not stem from a surface charge effect contrary to the case of the -much smallerstreaming currents without applied bias displayed in the Figure 1c. In the latter case, the pH-dependent surface charge of the CNT is expected to be the main contribution to the bare streaming current. Furthermore, both the effects of the stretching of the supporting membrane, and the change of radius of the CNT can be discarded as the origin of this phenomenon, since both are negligible due to the high stiffness of the materials (in contrast to explanations for the mechano-sensitive response of biological channels [START_REF] Anishkin | Feeling the hidden mechanical forces in lipid bilayer is an original sense[END_REF][START_REF] Cox | Biophysical Principles of Ion-Channel-Mediated Mechanosensory Transduction[END_REF]). Interestingly the observed response in CNT is also very different from that observed recently in 2D

Angström slits with carbon confinement [START_REF] Mouterde | Molecular streaming and voltage-gated response in Angström scale channels[END_REF], where only a linear dependence of the ionic current as a function of pressure drop could be observed whatever the applied voltage.

Here the response reveals a robust, quadratic, pressure-dependence of the conductance.

Interestingly, such pressure-sensitive behaviour shares similarities with the mechanosensitive response of biological channels [START_REF] Anishkin | Feeling the hidden mechanical forces in lipid bilayer is an original sense[END_REF][START_REF] Cox | Biophysical Principles of Ion-Channel-Mediated Mechanosensory Transduction[END_REF]. In the latter systems, a pressure drop converts into a ionic current, showing a non-linear dependence on the applied pressure.

In order to rationalize this behaviour, we have developed a theoretical model capturing the main ingredients of ionic transport in narrow carbon nanotubes. A key feature is the low friction expected for water on the CNT surface, which results in fast flows inside the CNT under imposed pressure drop. We anticipate that this is at the root of the strong interplay between the ionic transport and mechanical forcings.

The theoretical description proceeds with a modified Poisson-Nernst-Planck-Stokes (PNPS) description for the ion transport inside the CNT, building on the framework introduced in [START_REF] Mouterde | Molecular streaming and voltage-gated response in Angström scale channels[END_REF]; the details of the derivation are provided in the Supplementary Note 1. In short, we consider the 1-dimensional transport of ions inside the CNT, under the combined effects of the local electric field and (fast) flow of water. Ion mobilities are not necessarily equal and we account for the friction of ions on both water and surface walls.

Last but not least, water slippage on the CNT surface is assumed. The PNPS framework writes the conservation equations for each specie and water along the channel.

Under limited approximations, this extended PNPS model can be solved analytically in 1D and one obtains an analytical prediction for the ionic current under the combined effects of pressure and voltage drops. Remarkably the theory predicts that the conductance is a function of a Péclet number Pe, defined as

Pe = Q w D × L πR 2 0 ( 3
)
where Q w is the water flow rate and D a typical ion diffusion coefficient. Note that the definition of the Péclet number involves the length L (and not the radius R) of the channel.

To linear order in ∆V as in the experiments, but keeping the full dependence on the Péclet number, one predicts

I = µ EO × ∆P + G(Pe) × ∆V + . . . ( 4
)
where µ EO is an electro-osmotic mobility, which is a function of the various kinetic parameters -see Supplementary Information for details -, and G(Pe) is a Péclet-dependent conductance. The theory predicts a transparent expression for the conductance as:

G(Pe) = G 0 × Pe 2 tanh Pe 2 (5)
which can be expanded as G(Pe) = G 0 × (1 + Pe 2 12 + . . . ). One expects the pressuredriven contribution to the flow to be the main contribution to the Péclet number, so that Pe = Q w L/DπR 2 0 = Kapp D × ∆P , with K app the apparent permeance of the CNT. The ionic conductance G(Pe) is now a function of the pressure drop, varying quadratically for low ∆P . This is in full agreement with experimental measurements, see Fig. 2 and Eq. ( 2). Physically, this square-like dependence of the conductance on the Péclet number results from the balance between electric and mechanical forces. This leads to an overall increase of the ionic concentration in the nanotube for both ∆P > 0 and ∆P < 0 -as can be verified from the direct calculation of the ionic density profiles in the channel, see Supplementary Note 1. -, hence an increase in the conductance of the nanotube which is symmetric for positive and negative pressure drops. A key remark is that the Péclet number (hence flow) cannot be neglected here to describe ionic transport in tiny CNTs, in strong contrast to usual channels: typical values for the Péclet number may be inferred from the current-pressure characteristics such as in Fig. 2b, yielding Pe ∼ 1-10 depending on the conditions and nanotube size. In contrast, a Poiseuille flow prediction with no-slip boundary condition on the surface would yield a Péclet number in the range Pe ∼ 10 -2 (considering a 2 nm-radius channel under a maximum pressure drop of 0.5 bar as applied here). But this estimate for Pe is amplified by a factor 1+8b/R when surface slippage, with slip length b, occurs on the CNT surface. Hence, large slippage, i.e. low surface friction on the CNT surface, leads to a strong sensitivity of the conductance on the pressure drop, as highlighted in Eq.( 5). This makes the slippery carbon nanotube unique to obtain the mechanosensitive conductance.

In order to further assess these predictions, we solved numerically the full PNPS ionic transport model using a finite-element approach (COMSOL) (see Supplementary Note 2). Overall, these numerical calculations fully confirm the results of the analytical model described above. A linear dependence of the streaming current on the pressure drop is recovered when no bias voltage is applied, and the magnitude of the streaming current is as expected much larger in the low friction regime than in the high friction regime, see Supplementary Figure 7. Now, applying simultaneously voltage and pressure drops, the numerical calculations highlight a quadratic response of the conductance as a function of the pressure drop, Fig. 3, and furthermore show that this response is intimately connected to a low surface friction (i.e. strong slippage); see the high versus low friction response in Supplementary Figure 8, and the G 2 dependency on the slip length b on Supplementary Figure 9. A linear response in ∆P is recovered in the high friction regime, and is reminiscent of the results reported in [START_REF] Mouterde | Molecular streaming and voltage-gated response in Angström scale channels[END_REF] in Angström slits (slippage was shown to be larger in nanotubes than on flat graphite [START_REF] Secchi | Massive radius-dependent flow slippage in carbon nanotubes[END_REF]). But a quadratic response in ∆P is obtained for the low friction surface as observed here for the CNT.

Overall we unveil that the conductance of the CNT is quadratically modulated by the applied pressure. It is interesting to remark that this result is reminiscent of the response of mechanosensitive biological channels. However, in the case of mechano-sensitive biological channels the mechanism at stake rather involves the sensing of changes in membrane tension coupled to conformational changes in the channel protein structures. As discussed above, such mechanism does not occur for the transmembrane CNT considered here. Our results rather point to the unique properties of the 'single digit' CNTs to obtain such pressure-sensitive response, whereby a pressure-dependent accumulation of ionic species occurs in the CNT under a voltage bias. The low friction of water on the carbon surface is accordingly shown to be a prerequisite to the quadratic pressure dependence of the ionic response in the CNT. Single digit CNTs are thus able to respond to very local pressure signal, with nanometric spatial resolution.

Hence, this artificial system reproduces a pressure-sensitive response. Since the device properties are robust and well calibrated, it provides a unique platform to study such advanced response in an artificial system. In addition, the possibility of inserting CNTs into lipid membranes, as developed in Refs [START_REF] Tunuguntla | Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins[END_REF]25], provides promising applications to conceive new types of ultra-local pressure sensors using e.g. assemblies of vesicles as electric compartments with pressure-modulated potential. This would constitute a promising building-block to fabricate sensitive soft materials, enabling one to reproduce artificial sensing devices for (light) touch or proprioception. Such hybrid devices offer manifold perspectives in the development of iontronic systems for which the response intensity can be tuned. Finally, our discovery should benefit to the flourishing field of bottom-up artificial cells fabrication for synthetic ion channels design, which mechanosensitive response can be rationally engineered, via our theoretical model, by tuning the nanochannel nature, length or size.

Figure 2 . 11 -Figure 3 .

 2113 FIGURES

Acknowledgements A.S. acknowledges funding from the EU H2020 Framework Programme/ERC Starting Grant agreement number 637748-NanoSOFT. L.B. acknowledges funding from the EU H2020 Framework Programme/ERC Advanced Grant agreement number 785911-Shadoks and ANR project Neptune. L.B. and A.S. acknowledge support from the Horizon 2020 program through Grant No. 766972-FET-OPEN-NANOPHLOW.

Data availability

The data that support the plots within this paper and other findings of this study are provided with this paper as source data and in Supplementary Information.

Author contributions

L.B. and A.S. designed and directed the project. A.M., A.S., and A.N. fabricated the devices. A.M. performed the measurements with inputs from the other authors. All authors analyzed the data and contributed to discussions. L.B. performed the theoretical analysis and A.M. the numerical modelling. A.M., A.S and L.B. wrote the manuscript with inputs from T.M.

Competing interests

The authors declare no competing interests.

z a g t f R M l N q h X T x 6 Y 1 I y H J E m p L q Y s N y N q X y q n C W 7 y H u i P O X Z x v S 3 M y + f W I E 7 Y v / S z S v / q 5 O 9 C P R x p n p w q a d I M b I 7 J 3 N J 1 a 3 I k 7 M f X Q l y i I i T u E f 5 m L C j l P N 7 Z k q T q N 7 l 3 V o q / 6 k q J S v X T l a b 4 k u e k g Y 8 n y J b D B o n u m n o 5 t V p q X q e j T q P A x z i m O Z Z R h W X q K F O 3 v d performed in the chamber of a Scanning Electron Microscope using a built-in nano manipulator consisting in three axis piezo-inertial step motors of nanometric precision controlled by an outside joystick. The sealing of the tube in the membrane nanohole is ensured by localized cracked naphthalene deposition. Eventually, the sealed nanotube is cut free from the tungsten tip by highly energetic electron beam exposure in water vapor. The centimetric Si/SiN chip is then squeezed between two macroscopic reservoirs filled with a potassium chloride (KCl) solution of various concentrations. All steps of this procedure follow those described in detail in the Supplemental Materials of [START_REF] Siria | Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube[END_REF].

Streaming current measurements. Ag/AgCl electrodes are immersed into the reservoirs and connected to an external patch-clamp amplifier (Axopatch 200B, Molecular Devices) which allows for electrical forcing as well as for electrical measurements, with a resolution in the tenths of picoamperes. The ionic current is measured versus time, while steps of pressure ranging from 50 mbar to 1.5 bar are applied via a pressure pump (AF1, Elveflow). Each step typically lasts 15 s, and the delay between two successive steps is 15 s. The streaming current is defined as the difference between the plateau value reached by the ionic current while the pressure is applied, and its value when the pressure is released. For each drop of pressure, this measurement is performed between 2 and 25 times. Supplementary Figure 2 gives an example of an ionic current measurement as a function of time, when no bias voltage is applied.

[26] E. Secchi, A. Niguès, L. Jubin, A. Siria and L. Bocquet, Scaling Behavior for Ionic Transport and its Fluctuations in Individual Carbon Nanotubes, Phys. Rev. Lett. 116, 154501 (2016)


Jean Keller & Pierre-Marc Delaux LRSV, Université de Toulouse, CNRS, UPS, Castanet-Tolosan, France Title: Evolution of plant metabolism: A (bio)synthesis Studying the evolution of metabolism is technically challenging. A novel study combining in silico metabolic maps and phylogenomics allows reconstructing the diversification of plant metabolism across one billion years of evolution.

Text:

Following the initial primary endosymbiotic event leading to the evolution of the chloroplast approximately a billion years ago, plants (Viridiplantae or Chloroplastida) have evolved into a tremendous diversity of organisms such as green algae, mosses or ferns [START_REF] Leebens-Mack | One thousand plant transcriptomes and the phylogenomics of green plants[END_REF]. Each of these lineages has evolved prominent developmental and physiological innovations linked to the colonization of new ecological niches. Although roots and flowers will come to everyone's mind when asked for plant innovations, one can hardly argue against specific metabolites, say caffeine, as iconic lineage-specific novelties. Besides such recent evolution, metabolic novelties that evolved at deep nodes in the plant phylogeny may have played essential roles in the evolution of extremely diverse and successful plant lineages such as the land plants. However, while scoring for the presence or absence of a given macroscopic traitsuch as roots or flowersis relatively straightforward, determining the distribution of metabolites requires the use of sophisticated and time-consuming approaches, hindering the description of the plant metabolism in an evolutionary perspective.

In their work published in this issue of Current Biology Cannell et al. [START_REF] Cannell | A comparative survey of chloroplastid genomes reveals metabolic innovations and losses associated with major transitions in plant evolution[END_REF] overcome these limitations and propose a comprehensive view of the plant metabolism evolution. To do so, the authors first computed metabolic maps on eight focal taxa belonging to the major plant lineages. Rather than reflecting the presence or absence of a given enzymatic property, reconstructing biosynthesis pathways allow inferring whether the "modules" are present and thus the metabolic end-product. Mapping these predictions on the plant phylogeny, the authors were able to propose gains and losses of specific metabolic pathways in an untargeted manner. The initial set of eight species, although covering a large diversity of lineages, made the approach very sensitive to misannotation or assemblies. To strengthen their conclusions the authors included a total of 72 diverse plant genomes in an OrthoFinder run, identifying orthologs across all the species, and later added 305 transcriptomes. With these orthogroups, the authors were able to predict the evolution of the plant metabolism. Some of these predictions reflected the known evolutionary pattern of well-described metabolic pathways, such as the gain of thalianol biosynthesis in the Arabidopsis thaliana lineage [START_REF] Field | Metabolic diversification -Independent assembly of operon-like gene clusters in different plants[END_REF] others turned out to be much more surprizing.

Revisiting the evolution of plant hormones

Gibberellins (GAs) are plant hormones regulating multiple developmental processes. Their biosynthesis is well described in angiosperms. Initial phylogenetic studies conducted on the biosynthetic enzymes on the model moss Physcomitrella patens, and metabolomics survey, suggested that active GAs (derivative of GA12) were not produced in mosses, suggesting that their evolution was specific to the vascular plants [START_REF] Miyazaki | An Ancestral Gibberellin in a Moss Physcomitrella patens[END_REF]. Here the authors discovered in liverworts and hornworts, the other two bryophyte clades, the entire suit of enzymes necessary to produce bioactive GA implying a much earlier evolution of this class of compounds. According to the author's reconstruction, both liverworts and hornworts should be able to produce GA4. Comparing the metabolome of wild-type and mutants in the responsible enzyme (kaurenoic acid oxidase -KAO) in, for instance, the liverworts Marchantia polymorpha should allow determining whether GA4 is indeed produced in these species and whether it actually depends on the same pathway than in angiosperms. Alternatively, it could reveal the involvement of KAO in the biosynthesis of other compounds.

Beside the presence of a near-complete GA biosynthesis pathway in bryophytes, the absence of multiple enzymes required in angiosperms for the biosynthesis of another plant hormone, the brassinosteroids (BRs), came as another surprise. Indeed, these compounds have been detected in most plant lineages including bryophytes and algae. Such discrepancy between the inferred biosynthetic abilities and the actual presence of metabolites may result from either of two evolutionary processes: convergence, where BRs would have evolved independently in all the investigated lineages, or diversification. Given the distribution of BRs, the most parsimonious hypothesis would be that BR biosynthesis evolved once and then diversified independently in multiple lineages. Here, a parallel can be drawn with observations made on the diversification of gene regulatory networks. Selection acts on the output of these networks, which is the activation of target genes in response to a given environmental or developmental clue, and not on the topology of the network itself that may vary over time via intermediate, redundant, stages [START_REF] Sorrells | Making sense of transcription networks[END_REF][START_REF] Sayou | A promiscuous intermediate underlies the evolution of LEAFY DNA binding specificity[END_REF]. Similarly, while BRs production seems conserved across plants (the output) the structure of the biosynthetic pathway can be predicted to be under lower selective constraint, resulting in different enzymes contributing to the biosynthesis. In the future, it would be of interest to determine whether evolutionary mechanisms contributing to the diversification of gene regulatory networks may be transposed to the diversification of metabolic pathways across large evolutionary timescale. The predictions reported by Cannell et al. provide the framework for such future studies. Beyond diversification, a number of rules for the evolution of metabolic pathways in the plants can be proposed based on these predictions.

Evolutionary principles of plant metabolism evolution

Exaptation, the process by which an existing character is recruited for a novel function it was not initially selected for, is becoming a common theme in plant evolution [START_REF] De Vries | Plant evolution: landmarks on the path to terrestrial life[END_REF][START_REF] Nishiyama | The Chara Genome: Secondary Complexity and Implications for Plant Terrestrialization[END_REF]. For instance, the perception of the plant hormone abscisic acid (ABA), which is playing multiple roles in the biology of land plants including the responses to biotic and abiotic stresses, evolved by exaptation. In land plants, the perception of ABA is mediated by receptors of the PYL protein family. Homologs are present in Zynematophyceae [START_REF] Sun | A ligand-independent origin of abscisic acid perception[END_REF][START_REF] Cheng | Genomes of subaerial provide insights into land plant evolution[END_REF] where they are, however, activated in absence of ABA, indicating that ABA-binding evolved in land plants by exaptation of this ancient protein family [START_REF] Sun | A ligand-independent origin of abscisic acid perception[END_REF]. In their study, Cannell et al. identified a number of examples of metabolic exaptation. The authors found that all the plantboth algal and land plantgenomes and transcriptomes investigated harboured the pathway for the biosynthesis of precursors of biopolymers such as cutin and suberin while lacking a number of enzymes for their subsequent modification and polymerization. Another example of metabolic exaptation is the biosynthesis of flavanol in seed plants, which branches out of the phenylpropanoid metabolism that the authors found present in all investigated land plants, via the gain of three enzymes. Although without biochemical analyses it cannot be ruled out that Zygnematophyceae or other streptophyte algae produce cutin, or that non-seed plants produce flavanol, the data suggest that both chemicals evolved by exaptation of ancestral pathways. This is in line with previous report focusing on specialized metabolism, such as caffeine [START_REF] Huang | Convergent evolution of caffeine in plants by co-option of exapted ancestral enzymes[END_REF], and demonstrates that, as for signalling pathways, exaptation is a major player in defining the diversity of the plant metabolism even at deep evolutionary nodes.

The role played by the loss of traits in shaping biodiversity is becoming more and more prominent, with the loss of genes often found as causal for these losses. This is for instance the case for the diversification of leaf shapes [START_REF] Vlad | Leaf shape evolution through duplication, regulatory diversification and loss of a homeobox gene[END_REF]. Whether trait loss is adaptive (the more-isless hypothesis) or the result of relaxed selection depends on the lineage and the trait being investigated [START_REF] Albalat | Evolution by gene loss[END_REF]. In their study, Cannell et al. found at least three clear examples of metabolic losses. Among them the biosynthesis of diacylglyceryl-N,N,N trimethylhomoserine and GAs seem to have been lost in seed plants and in mosses respectively. Interestingly, both losses perfectly illustrate cases of trait loss due to relaxed selection. Indeed, diacylglyceryl-N,N,N trimethylhomoserine and GA have been functionally substituted in seed plants and in mosses by phosphatidylcholine and ent-3β-hydroxy-kaurenoic acid respectively. Due to functional redundancy the selection acting on the ancestral metabolites would have been relaxed, leading to their loss. Interestingly, metabolic redundancy with the metabolism of their hosts is often the cause of gene and pathway losses in obligate parasites or symbionts. As compare to the loss of multiple other traits that may be adaptive [START_REF] Albalat | Evolution by gene loss[END_REF] the loss of metabolic pathway seems to be predominantly the result of relaxed selection. Functional studies on pathway found by Carnell et al. to be lost, for instance the biosynthesis of L-selenocysteine in land plants, should allow testing this hypothesis further.

By proposing a kingdom-wide evolution of the plant metabolism, this study perfectly illustrates the power of combining approaches at different scales (metabolic maps with orthogroups) to address complex questions, and provide the framework for further experimental approaches to understand the evolutionary processes building (metabolic) diversity.