Gérald Lelong
email: gerald.lelong@sorbonne-universite.fr

Laurent Cormier

Louis Hennet

Florent Michel

Jean-Pascal Rueff

James M Ablett

Giulio Monaco

Lithium borates from the glass to the melt: a temperature-induced structural transformation viewed from the boron and oxygen atoms

 B conversion is observed above the glass transition temperature (T g ) from the glass to the melt from the triborate composition up to the metaborate composition. Two distinct melt structures are reported: a well polymerized borate network -with few NBOs -below the triborate composition, and a depolymerized borate network above the diborate composition with a rapid increase of the number of NBOs when Li 2 O is added. These two structurally distinct melts allow explaining the two dynamical regimes observed for lithium ion diffusion.

Introduction

Ionic transport, diffusivity and viscosity are fundamental properties of melts, whose implications are at the origin of very important processes in material and Earth sciences. The modification of glass structure with temperature is therefore of major interest for the understanding of relaxation phenomena, but also to better understand the solid-liquid transition at the local scale. The hightemperature liquid is a well-defined phase in internal thermodynamic equilibrium, with constant and fast exchanges between atomic configurations through structural relaxation and diffusion processes.

Unlike alkali silicate glasses whose properties and structure are mainly governed by the proportion of non-bridging oxygen (NBO), the behavior of alkali borate glasses is more complex. [START_REF] Wright | Borate versus Silicate Glasses: Why They Are so Different ?[END_REF] The higher level of intricacy originates from the existence of two distinct coordination states of boron atoms: the planar units BO 3 and the negatively charged tetrahedral units BO 4 , the combination of these two building blocks allowing a wide variety of tessellations of the tridimensional space. [START_REF] Wright | Borate Structures: Crystalline and Vitreous[END_REF][START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] Alkali borate glasses show an increasing fragility as the alkali oxide content increases. [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF][START_REF] Matsuda | Fragility Variation of Lithium Borate Glasses Studied by Temperature-Modulated DSC[END_REF][START_REF] Mauro | Composition Dependence of Glass Transition Temperature and Fragility. II. A Topological Model of Alkali Borate Liquids[END_REF] This fragile behaviour, characteristic of strong glass-formers, indicates a rapid raise in the configurational entropy above the glass transition temperature Tg, contrary to the strong B 2 O 3 liquid. The link between structural properties and the entropy increase is not well understood, partly due to the lack of data on the structural reorganization when going from the glass to the liquid. At room temperature, the structure of alkali borate glasses is well described in the literature in terms of short-and medium-range order. [START_REF] Wright | Borate versus Silicate Glasses: Why They Are so Different ?[END_REF][START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF][START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF][START_REF] Chryssikos | Lithium Borate Glasses: A Quantitative Study of Strength and Fragility[END_REF][START_REF] Kamitsos | Infrared Reflectance Spectra of Lithium Borate Glasses[END_REF][START_REF] Kamitsos | Borate Glass Structure by Raman and Infrared Spectroscopies[END_REF][START_REF] Majérus | Structural Modifications between Lithium-Diborate Glasses and Melts: Implications for Transport Properties and Melt Fragility[END_REF][START_REF] Cormier | Quantification of Boron Coordination Changes between Lithium Borate Glasses and Melts by Neutron Diffraction[END_REF] A temperature induced [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B to [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion has also been predicted by molecular dynamics and thermodynamic models [START_REF] Glasses | Crystals & Melts[END_REF][START_REF] Varsamis | A Molecular Dynamics Study of Li-Doped Borate Glasses[END_REF] and evidenced using in situ high-temperature sample environments coupled to Raman spectroscopy, [START_REF] Cormier | Temperature-Induced Structural Modifications Between Alkali Borate Glasses and Melts[END_REF][START_REF] Osipov | Structure of Lithium Borate Glasses and Melts: Investigation by High Temperature Raman Spectroscopy[END_REF][START_REF] Yano | High Temperature Raman Spectra of R 2 O-B 2 O 3 Glass Melts (R=Ag, Li, Na and K)[END_REF] X-ray or neutron diffraction [START_REF] Cormier | Temperature-Induced Structural Modifications Between Alkali Borate Glasses and Melts[END_REF][START_REF] Alderman | Temperature-Driven Structural Transitions in Molten Sodium Borates Na2O-B2O3 : X-Ray Diffraction, Thermodynamic Modeling, and Implications for Topological Constraint Theory[END_REF][START_REF] Herms | X ray Diffraction Studies of Structural Changes in Molten Borate Glasses[END_REF][START_REF] Majérus | Temperature-Induced Boron Coordination Change in Alkali Borate Glasses and Melts[END_REF][START_REF] Alderman | Borate Melt Structure: A Short Review[END_REF] or [START_REF] Majérus | Structural Modifications between Lithium-Diborate Glasses and Melts: Implications for Transport Properties and Melt Fragility[END_REF] B NMR. [START_REF] Sen | Temperature Dependent Structural Changes in Borate, Borosilicate and Boroaluminate Liquids: High-Resolution 11B, 29Si and 27Al NMR Studies[END_REF][START_REF] Sen | Temperature Induced Structural Changes and Transport Mechanisms in Borate, Borosilicate, and Boroaluminate Liquids: High-Resolution and High-Temperature NMR Results[END_REF] However, experimental data of the Li 2 O-B 2 O 3 system are rather sparse and mostly concern a few compositions in the range of 20-40 mol%. It is then worthwhile to study the structural properties of a wide range of compositions as a function of temperature from the glass to the melt.

Central to these problems is the bridging or non-bridging role of oxygen, the archetypal ligand in crystalline and glassy oxides. Many techniques have been used to probe the oxygen environment and in the last few years X-ray Raman scattering (XRS) spectroscopy has emerged as a powerful and versatile local probe of the electronic structure of low-Z elements under a wide range of experimental conditions. [START_REF] Lee | Probing of Pressure-Induced Bonding Transitions in Crystalline and Amorphous Earth Materials: Insights from X-Ray Raman Scattering at High Pressure[END_REF][START_REF] Sternemann | Spectroscopy of Low and Intermediate Z Elements at Extreme Conditions: In Situ Studies of Earth Materials at Pressure and Temperature via X-Ray Raman Scattering[END_REF][START_REF] Lee | Probing of Bonding Changes in B2O3 Glasses at High Pressure with Inelastic X-Ray Scattering[END_REF][START_REF] Lelong | Evidence of Fivefold-Coordinated Ge Atoms in Amorphous GeO2 under Pressure Using Inelastic x-Ray Scattering[END_REF][START_REF] Petitgirard | Magma Properties at Deep Earth's Conditions from Electronic Structure of Silica[END_REF][START_REF] Lee | Amorphous Boron Oxide at Megabar Pressures via Inelastic X-Ray Scattering[END_REF] XRS spectra are sensitive to a multitude of electronic processes related to inelastic scattering and core electron excitations. These latter ones correspond mainly to the absorption edges of the various elements present in the sample and located in the probed energy-loss window. [START_REF] Sternemann | Spectroscopy of Low and Intermediate Z Elements at Extreme Conditions: In Situ Studies of Earth Materials at Pressure and Temperature via X-Ray Raman Scattering[END_REF][START_REF] Rueff | Inelastic X-Ray Scattering by Electronic Excitations under High-Pressure[END_REF][START_REF] Sahle | Performing and Analyzing X-Ray Raman Scattering Experiments[END_REF] As for the conventional X-ray Absorption Near Edge Spectroscopy (XANES), XRS provides the opportunity to measure several absorption edges, such as the B and O K-edges, almost simultaneously, by simply selecting the energy loss range of interest. In the case of lithium borate glasses, the simultaneous measurement of both B and O K-edges is a powerful characterization method to get structural information on the local environment of every atom constituting the glassy network.

In this paper, we present a multi-edge study of the local structure of lithium borate glasses as a function of temperature -from room temperature up to 800°C. To reach the liquid state, an aerodynamic levitation device coupled to a laser heating system was inserted into the sample chamber of a XRS spectrometer, allowing to monitor both the boron coordination number and the formation of NBO atoms as a function of temperature and glass composition.

Materials and Methods

a. Synthesis

Lithium borate glasses were synthesized by melting weighed mixtures of lithium carbonate (Li 2 CO 3 -99.99% -Alfa Aesar) and boric acid (H 3 BO 3 -99.5% -Sigma Aldrich) in a Pt/Rh crucible at 1000°C during 20 minutes. The crucible was then quenched in water. Five different glasses were prepared with the following molar compositions: xLi 2 O-(1-x)B 2 O 3 , where x = 0.5, 0.33, 0.25, 0.1 and 0. The five glasses will be denoted as

LB (Li 2 O-B 2 O 3 ), LB2 (Li 2 O-2B 2 O 3 ), LB3 (Li 2 O-3B 2 O 3 ), LB9 (Li 2 O-9B 2 O 3 )
and v-B 2 O 3 , respectively. Their respective glass transition temperatures are equal to 420°C, 500°C, 487°C, 343°C and 260°C. [START_REF] Feller | Physical Properties of Alkali Borosilicates Glasses[END_REF] Spheroidal samples were prepared by melting small pieces of the as-synthesized glasses in a levitation apparatus to obtain homogeneous samples of approximately 2mm in diameter. The principle of the levitation chamber is described in detail elsewhere. [START_REF] Hennet | High-Temperature Levitated Materials[END_REF] For this experiment, the spherical sample was placed in the convergent-divergent nozzle that directed an oxygen gas jet supporting the sample. An additional regulated helium flow was also used to reduce the x-ray absorption in the chamber. Then the sample was melted using two 125 W CO 2 laser beams focused onto the sample by means of spherical mirrors. The specimen temperature was measured by an optical pyrometer operating at a wavelength of 1.625 µm at the spot on the surface illuminated by the x-ray beam.

b. XRS Spectrometers

i. ID16 Beamline -ESRF

The XRS experiments on LB2, LB3 and LB glasses were carried out at the ID16 Inelastic X-ray beamline of the European Synchrotron Radiation Facility (ESRF). [START_REF] Verbeni | Multiple-Element Spectrometer for Non-Resonant Inelastic X-Ray Spectroscopy of Electronic Excitations[END_REF] The inelastic X-ray scattering experiments previously possible on port ID16 of the ESRF are now carried out on port ID20. The incident beam was monochromatized with Si(111) and Si(220) monochromators and the beam focused to 115 (H) Í 40 (V) µm 2 . The scattered radiation was analyzed with nine bent Si(660) analyzers (R = 1 m) and detected with a photon-counting MAXIPIX bidimensional pixel detector. [START_REF] Ponchut | a Fast Readout Photon-Counting X-Ray Area Detector for Synchrotron Applications[END_REF] The spectra were collected by scanning the incident energy while keeping the analyzers energy to 9.6885 keV, so that the energy transfer was scanned around both the B K-edge at 194 eV and the O K-edge at 535 eV. The total energy resolution of the setup was 0.7-0.8 eV as measured by fitting a Gaussian profile to the quasi-elastic scattering peak. All the measurements were made at an average scattering angle of 30° in 2θ. Under these conditions all 9 analyzers are in a low exchanged momentum q configuration (q ~ 2.54 Å -1 ) and the corresponding spectra can be summed. An accumulation time of at least 2 h was necessary to achieve good statistics. A background subtraction has been achieved and each spectrum has been normalized to the area. The normalization range was taken between 185 and 218 eV for the B K-edge and between 530 and 555 eV for the O K-edge.

ii. GALAXIES Beamline -SOLEIL

The measurements of v-B 2 O 3 and LB9 glasses were performed at the GALAXIES beamline at the SOLEIL Synchrotron. [START_REF] Rueff | The GALAXIES Beamline at the SOLEIL Synchrotron: Inelastic X-Ray Scattering and Photoelectron Spectroscopy in the Hard X-Ray Range[END_REF][START_REF] Ablett | The GALAXIES Inelastic Hard X-Ray Scattering End-Station at Synchrotron SOLEIL[END_REF] The incident energy was monochromatized with a Si(111) double -crystal monochromator and the beam focused to ∼100 (H) x 30 (V) µm 2 . The scattered radiation was analyzed with 4 spherical Si(660) analyzers (R = 1m) and detected with a silicon drift diode (SDD). The spectra were collected by keeping the analyzers fixed at their quasi-backscattering energy of 9.720 keV (Bragg angle ∼ 86°) while scanning the incident X-ray energy. For example, the O K-edge at 535 eV was measured by varying the incident X-ray energy around 10.255 keV. The total energy resolution of the setup was ∼1.5 eV. All the measurements were made at an average scattering angle of 40° in 2θ.

As in the previous case, under these conditions all 4 analyzers are in a low transfer momentum q configuration (q ~ 3.4 +0.4/-0.6 Å -1 ) and the corresponding spectra can be summed. An accumulation time of at least 5h was necessary to achieve good statistics. After background subtraction each spectrum has been normalized to the area. The normalization range was taken between 185 and 218 eV for the B K-edge and between 530 and 555 eV for the O K-edge.

Results

The five glassy samples -accompanied with the L7B3 composition published elsewhere [START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF] , span an extended concentration range of Li 2 O, starting from pure vitreous v-B 2 O 3 up to 70 mol.% of Li 2 O in the case of L7B3. All the glasses were measured by XRS from room temperature up to 800-900°C depending on the Li 2 O content -the different temperature points are shown in Fig. 1. The highest temperature achieved for each composition was decided on the basis of lithium volatilization, which leads to a rapid reduction of the sphere diameter. All the measurements showed here were performed at a constant sphere diameter.

For each temperature, both the B and O K-edges XRS spectra were measured almost simultaneously.

(Fig. 2) As previously described, [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF][START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF][START_REF] Lelong | Detecting Non-Bridging Oxygens: Non-Resonant Inelastic X-Ray Scattering in Crystalline Lithium Borates[END_REF][START_REF] Lee | Structure of Alkali Borate Glasses at High Pressure: B and Li K-Edge Inelastic X-Ray Scattering Study[END_REF][START_REF] Fleet | Boron K-Edge XANES of Borate and Borosilicate Minerals[END_REF] the B K-edge spectrum, which consists of an intense π* peak at 194 eV and a broader σ* peak located around 203 eV, is mainly informative of the nature of the boron coordination polyhedron. On the other hand, the O K-edge XRS spectrum, represented by a narrow peak at 536 eV and a broader one around 545 eV, is mainly indicative of the connectivity between the boron polyhedra. ). The L7B3 composition at 450°C was measured previously. [START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF] The black stars are indicative of the glass transition temperatures. [START_REF] Feller | Physical Properties of Alkali Borosilicates Glasses[END_REF] The dashed grey line shows the subliquidus miscibility dome described by Shaw and Uhlmann 41

1 Temperature dependence of the B K-edge

Except for v-B 2 O 3 and LB9, all the studied glasses show significant spectral transformations of the B K-edge as a function of temperature. (Fig. 2) When the temperature rises, the main modifications reside in the general increase in intensity of the π* peak and the disappearance of the peak around 200 eV, which are both indicators of a temperature induced [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B to [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion. This conversion takes place gradually above T g to finally reach some kind of equilibrium around 800-900°C. Slight

2 Temperature dependence of the O K-edge

With the exception of a global broadening of the peaks related to an increase of the topological disorder when temperature is increased, the O K-edge XRS spectra do not show significant changes at low Li 2 O content, i.e. for v-B 2 O 3 and LB9 glasses. (Fig. 2) This is in line with the observations for the B K-edge spectra. The O K-edge spectra of LB3 are instead temperature dependent, as shown by the shift of the σ* peak at 543eV and the intensity increase of the π* peak around 537eV. From LB3 to LB, the spectral modifications are more and more pronounced, indicative of an increasing [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B to [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion. [START_REF] Lelong | Detecting Non-Bridging Oxygens: Non-Resonant Inelastic X-Ray Scattering in Crystalline Lithium Borates[END_REF] Additionally, an extra peak arises at low energy around 535eV, whose intensity increases with Li 2 O content. This spectral feature is related to the formation of NBOs in the melt as a consequence of the [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B to [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion. [START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF][START_REF] Lelong | Detecting Non-Bridging Oxygens: Non-Resonant Inelastic X-Ray Scattering in Crystalline Lithium Borates[END_REF]

Discussion

4.1

Temperature-induced structural modifications on the borate network Depending on the stoichiometry, both the short-and medium range orders of alkali borate glasses may be affected by temperature. The monitoring of the proportion of three-fold coordinated boron atoms using XRS is made possible since the π* peak of the B K-edge is solely related to triangular BO 3 units.

By using a data treatment procedure previously described, [START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF] it is possible to follow the proportion of [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B as a function of temperature in order to quantify the temperature-induced structural modifications (Fig. 3) [START_REF] Cormier | Temperature-Induced Structural Modifications Between Alkali Borate Glasses and Melts[END_REF] With the exception of LB9 and L7B3, all the glasses show a significant temperature induced [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B to [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion. The proportion of converted boron atoms is about 15-20% in the temperature range under study, which is in line with Raman or NMR experimental data on lithium borates. [START_REF] Cormier | Temperature-Induced Structural Modifications Between Alkali Borate Glasses and Melts[END_REF][START_REF] Osipov | Structure of Lithium Borate Glasses and Melts: Investigation by High Temperature Raman Spectroscopy[END_REF][START_REF] Yano | Structural Investigation of Sodium Borate Glasses and Melts by Raman Spectroscopy. II. Conversion between BO 4 and BO 2 O -Units at High Temperature[END_REF][START_REF] Wan | Raman Spectroscopy and Density Functional Theory Analyses of the Melt Structure in Li 2 B 4 O 7 Crystal Growth System[END_REF] The average boron coordination number n BO (x,T) is temperature dependent for intermediate compositions, i.e. LB3, LB2 and LB. In the case of LB2, n BO (x,T) decreases from 3.5 at RT to about 3.3-3.4 around 800°C, i.e.

!! !"

∆! ≈ -3. 10 !! 𝐾 !! , which agrees with the predictions of thermodynamic models and with the very few neutron diffraction experiments available at elevated temperature. [START_REF] Alderman | Borate Melt Structure: A Short Review[END_REF] This decrease of the average B-O coordination number from the glass to the melt takes place only above the glass transition temperature. Below T g , nothing really happens at the local scale, i.e. some thermal relaxations of defects/constraints on the medium range order may happen without significantly modifying the local boron environment.

Following the conversion reaction BO 4 ó BO 3 + NBO, each BO 4 unit that is converted into a planar BO 3 unit involves the formation of at least one NBO in order to maintain charge neutrality of the system. Even if the exact quantification of NBOs in borate using XRS is difficult, the intensity of the peak at 535eV in the O K-edge spectrum is a good indicator of the concentration of NBOs in the glass. [START_REF] Lelong | Detecting Non-Bridging Oxygens: Non-Resonant Inelastic X-Ray Scattering in Crystalline Lithium Borates[END_REF] By plotting the intensity of the peak at 535 eV versus temperature for different Li 2 O concentrations (Fig. 3), we clearly show the correlation between the [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B to [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion and the formation of NBOs, and that the formation of NBOs is enhanced when the Li 2 O content is increased.

NBOs start to appear around 25-30mol% Li 2 O and keep increasing up to 50mol%. Between 25 and 50mol% Li 2 O, the glass structure is mainly composed by triborate and pentaborate groups, which are gradually replaced by the di-triborate and eventually by the diborate superstructural units both characterized by the presence of a [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B-O- [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B bound unit which is energetically less favourable. [START_REF] Wright | Borate Structures: Crystalline and Vitreous[END_REF][START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF][START_REF] Wan | Raman Spectroscopy and Density Functional Theory Analyses of the Melt Structure in Li 2 B 4 O 7 Crystal Growth System[END_REF] These diborate units seem to be easily breakable upon heating moving on to the formation of BØ 2 O - and/or BØO 2 2-units in the melt, as suggested by MD simulations of Varsamis et al, [START_REF] Varsamis | Molecular Dynamics Investigation of Lithium Borate Glasses: Local Structure and Ion Dynamics[END_REF] where Ø refers to a bridging oxygen. -a more and more depolymerized borate network beyond the LB3 composition with the appearance of numerous NBOs in the melt, as revealed by the intensity increase at 535 eV in the O K-edge spectra when adding Li 2 O.

These observations indicate that the melt structure goes from a highly polymerized borate network to a more open and depolymerized structure with an increasing Li 2 O content. The transition around 25 mol% Li 2 O between these two melt structures has to be put in parallel with the persistence of the boroxol rings in the melt up to 20-25 mol%, as observed by Raman spectroscopy. [START_REF] Wright | Borate Structures: Crystalline and Vitreous[END_REF][START_REF] Osipov | Structure of Lithium Borate Glasses and Melts: Investigation by High Temperature Raman Spectroscopy[END_REF][START_REF] Yano | High Temperature Raman Spectra of R 2 O-B 2 O 3 Glass Melts (R=Ag, Li, Na and K)[END_REF][START_REF] Zheng | Structural Studies of a Li 2 O•4B 2 O 3 Melt by High-Temperature Raman Spectroscopy and Density Functional Theory[END_REF][START_REF] Wright | Borate Networks: Rigidity versus Dimensionality[END_REF] The presence of boroxol rings in the liquid state would help to stabilize the connectivity of the borate framework for low-alkali glasses. These two melt structures (polymerized vs. depolymerized) could be

Melt structure vs density at 800°C

Density is related to the atomic spatial distribution, i.e. the stacking of atoms, which will depend on the short-range order, but also on the medium-range organization via the composition in superstructural units. By plotting the structural characteristics of the melt at 800°C, i.e. the intensity of the peak at 535eV relative to the presence of NBOs and the proportion of [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B, and the variation of the density at 800°C 50 as a function of Li 2 O content, (Fig. 7) three domains emerge from the composition plot :

Domain 1 (0-30 mol% Li 2 O): a gradual [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B → [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B conversion is observed in the melt when lithium oxide is added. With the introduction of Li + cations, the electroneutrality is fulfilled by the formation of negatively charged (BO 4 ) -tetrahedral units -no or very few NBOs are observed in the 0 -30 mol% Li 2 O concentration range. The borate network is fully polymerized on the overall concentration range, but the 3D connectivity increases with the formation of the BO 4 units and the gradual disassembling of the boroxol rings into triborate and then ditriborate units. [START_REF] Osipov | Structure of Lithium Borate Glasses and Melts: Investigation by High Temperature Raman Spectroscopy[END_REF] As a consequence, the density of the melt increases.

Domain 2 (30-45 mol% Li 2 O): between 30 and 45mol%, there is a competition between the [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B → [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B conversion and the appearance of NBOs. Both processes have opposite effects on the melt density: the [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B → [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B conversion when Li supplanting the [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B → [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B conversion. A progressive depolymerization of the borate network is observed leading to a decrease of the melt density. Fig. 7: Evolution of the intensity of the peak at 535 eV related with NBOs (black colored squares), the proportion of [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B (red colored squares) and the density 50 at 800°C (grey colored circles) as a function of Li 2 O content. The dashed lines are a guide for the eyes.

Melt structure vs Li diffusion

The structural description of the melt in the section 4.4 is fully corroborated by the constant decrease of the activation energy of lithium diffusion above 20-30 mol% observed by high-temperature pulsed field gradient NMR. [START_REF] Ohkubo | Self-Diffusion Coefficient of Lithium in Molten xLi 2 O-(1-x)B 2 O 3 System Using High-Temperature PFG NMR[END_REF] This decrease is a direct consequence of the reduction of dimensionality of the borate framework with the appearance of NBOs in the melts for Li 2 O content above 45 mol%. [START_REF] Shi | Densities of Li 2 O-B 2 O 3 Melts[END_REF] Both the diffusion coefficient of the lithium ions [START_REF] Ohkubo | Self-Diffusion Coefficient of Lithium in Molten xLi 2 O-(1-x)B 2 O 3 System Using High-Temperature PFG NMR[END_REF]

Conclusions

This exhaustive study on the temperature behavior of lithium borate glasses and melts allowed us to monitor simultaneously the coordination number of boron atoms and the BO/NBO ratio as a function of both temperature and composition. Low lithium content glasses (v-B 2 O 3 and LB9) show almost no modification of their local structure with heating, probably because of the reminiscence of boroxol rings that help to stabilize the melt structure. A temperature induced [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B → [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion is observed above T g from the glass to the melt from the triborate composition up to the metaborate composition.

The non-monotonic evolution of the melt density of the melt at 800°C can be easily explained in terms of [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B → [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion and formation of NBOs.

Two distinct melt structures were evidenced: a well polymerized borate network -with few NBOsbelow the triborate composition, and a depolymerized borate network above the diborate composition with a rapid increase of the number of NBOs when Li 2 O is added. These two structurally distinct melts allow for explaining the two dynamical regimes observed for lithium ion diffusion, [START_REF] Ohkubo | Self-Diffusion Coefficient of Lithium in Molten xLi 2 O-(1-x)B 2 O 3 System Using High-Temperature PFG NMR[END_REF] and could be at the origin of the increasing fragility as the alkali oxide content increases. This study highlights also the major role of oxygen, and especially NBOs in the structural properties of the melt and its consequence on the diffusivity of atoms.

Fig. 1 :

 1 Fig. 1: Phase diagram of the Li 2 O:B 2 O 3 binary system. The colored filled circles are indicative of the measuredtemperatures for each glass composition: dark blue (room temperature), cyan (300-500°C), green (600-700°C), orange (~ 800°C) and red (~ 900°C). The L7B3 composition at 450°C was measured previously.[START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF] The black

  fluctuations of the intensity of the π* peak caused by subtraction of the Compton scattering background are not significant enough to affect the conclusions. v-B 2 O 3 and LB9 do not show marked modifications by increasing temperature: only a slight shift of the π* peak accompanied by a slight reduction of the intensity is observed with the temperature increase. A similar shift (around 0.1-0.2eV)is also observed for the metaborate composition (LB). These subtle modifications are caused by thermal fluctuations similarly to what has been experimentally observed at the Al K-edge of corundum by X-ray absorption near-edge spectroscopy.[START_REF] Manuel | Experimental Evidence of Thermal Fluctuations on the X-Ray Absorption near-Edge Structure at the Aluminum K Edge[END_REF]

Fig. 2 :

 2 Fig. 2: in situ B K-edge (left) and O K-edge (right) XRS spectra of v-B 2 O 3 , LB9, LB3, LB2 and LB glasses as a function of temperature. All the spectra were measured in the levitation chamber with the exception of the B Kedge of LB9 at room temperature, which has been measured in a standard sample holder.

Fig. 3 :

 3 Fig. 3: Evolution of the proportion of[START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B (top) and the intensity at 535eV (bottom) as a function of temperature and Li 2 O content: LB9 (cyan), LB3 (green), LB2 (orange), LB (pink) and L7B3 from reference 7 (black). The plain and dashed colored lines are a guide for the eyes, and the arrows are indicative of the glass transition temperatures of the different glasses.[START_REF] Glasses | Crystals & Melts[END_REF]

13

 13 Fig. 3: Evolution of the proportion of[START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B (top) and the intensity at 535eV (bottom) as a function of temperature and Li 2 O content: LB9 (cyan), LB3 (green), LB2 (orange), LB (pink) and L7B3 from reference 7 (black). The plain and dashed colored lines are a guide for the eyes, and the arrows are indicative of the glass transition temperatures of the different glasses.[START_REF] Glasses | Crystals & Melts[END_REF]

4 . 2

 42 Melt structure: existence of two distinct melt structuresThe present study gives access to the structure of the melt for a wide range of Li 2 O concentrations. By plotting the XRS spectra of both B and O K-edges for the five compositions at about 800°C, it is clear that the melt structure depends on the stoichiometry of the glass (Fig.4). Two sets of melts compositions can be distinguished:-a well connected borate network is observed in the melts of v-B 2 O 3 , LB9 and LB3, characterized by a strong and sharp π* peak at the B K-edge and an almost zero intensity at 535 eV at the O K-edge spectra.

  at the origin of the subliquidus miscibility dome suggested by Shaw and Uhlmann 41 and calculated by Kim and Sanders 49 which extends approximately from 2-18 mol% in the case of Li 2 O-B 2 O 3 . For a better insight, the subliquidus miscibility gap has been reproduced in figure 1. The existence of these two melt structures would explain (i) the non-existence of crystalline phases in this concentration range, and (ii) the coexistence of two sub-domains in the glass with an "alkali-rich" domain and a pure B 2 O 3 domain containing the boroxol rings.7

Fig. 4 :

 4 Fig. 4: B K-edge (Left) and O K-edge (Right) XRS spectra of LB, LB2, and LB3 glasses measured at 780°C, LB9 at 570°C and v-B 2 O 3 at 600°C.

Fig. 5 :

 5 Fig. 5: Left: O K-edge XRS spectra of LB2 melt (red points) accompanied with two crystalline phases: Li 2 B 4 O 7 (grey) and LiBO 2 (black). Right: O K-edge XRS spectra of LB melt (red points) accompanied with two crystalline phases: Li 6 B 4 O 9 (grey) and Li 3 BO 3 (black).

Fig. 6 :

 6 Fig. 6: Summary of the superstructural units found in crystalline phases (top), in glasses at room temperature (grey-shaded area) and in the melt (red-shaded area) for the Li 2 O-B 2 O 3 system.

51 Domain 3 ( 45 -

 51345 2 O is added tends towards a densification of the melt whereas the formation of NBOs leads to a depolymerization of the borate network and consequently to an increase of the melt volume. A change of slop of density at 800°C as a function of concentration is observed in this concentration domain, where the vitrification enthalpy reaches its maximum value. 70 mol% Li 2 O): from 45 up to 70mol%, the NBO content increases drastically

  and the intensity of the NBO's peak at 535eV measured at 800°C are fully correlated, as shown on the Figure 8. The disappearance of BO 4 units and the formation of NBOs are correlated with a change in the structural role of Li. In the presence of BO 4 , Li + cations play a charge compensating role around the negatively charged BO 4 tetrahedra while Li + cations are modified when associated with NBOs. This change in the Li structural role results in modifications of the local Li environment, as observed by neutron diffraction. 11The three structural domains described above are in fair agreement with the dynamical behavior of Li cations, i.e. a relatively slow translational diffusion up to 30 mol% corresponding to almost trapped ions in borate cages, followed by a steadily increase of the translational properties above 30 mol%.The role of NBOs in the mobility of Li cations is then fully pointed out, and is indicative of the presence of NBO rich-domains, whose size increases from 30 mol% up to 50 mol%, and where Li ions are free to move. This behavior seems to remain upon quenching, since the ionic conductivity of the glass is enhanced above 30-40 mol%.[START_REF] Montouillout | Ionic Conductivity of Lithium Borate Glasses and Local Structure Probed by High Resolution Solid-Sate NMR[END_REF]

Fig. 8 :

 8 Fig. 8: Comparison between the intensity of the peak at 535eV at 800°C, which is indicative of the proportion ofNBOs (red squares) and the self-diffusion coefficient of[START_REF] Lelong | Lithium Borate Crystals and Glasses: How Similar Are They? A Non-Resonant Inelastic X-Ray Scattering Study around the B and O K -Edges[END_REF] Li measured by NMR[START_REF] Ohkubo | Self-Diffusion Coefficient of Lithium in Molten xLi 2 O-(1-x)B 2 O 3 System Using High-Temperature PFG NMR[END_REF] at 975°C (grey circles) as a function of Li 2 O content.

Acknowledgements

The authors acknowledge the European Synchrotron Radiation Facility and SOLEIL for provision of synchrotron radiation facilities (Proposals HD-490 and 20141349, respectively).

Supporting Information

XRS data treatment is fully described in the electronic supporting information for both B and O Kedges.

FOR TABLE OF CONTENT ONLY

High-temperature X-ray Raman Spectroscopy has been used to determine the melt structure of five compositions of the Li 2 O-B 2 O 3 system. A temperature induced [START_REF] Angell | Relaxation in Liquids, Polymers and Plastic Crystals -Strong/Fragile Patterns and Problems[END_REF] B to [START_REF] Wright | My Borate Life: An Enigmatic Journey[END_REF] B conversion is observed above the glass transition temperature, and two distinct melt structures were evidenced for compositions below and above the diborate composition. These two structurally distinct melts allow explaining the two dynamical regimes observed for lithium ion diffusion.


Kevin M Hickson

J.-C Loison

Dianailys Nuñez-Reyes

Raphaël Méreau

Jean-Christophe Loison

Quantum Tunneling Enhancement of the C + H 2 O and C + D 2 O Reactions at Low Temperature

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

Introduction.

For many years, activated gas-phase reactions between uncharged species were thought to be unimportant in low temperature environments such as dense interstellar clouds [START_REF] Viala | Chemical Equilibrium from Diffuse to Dense Interstellar Clouds .1. Galactic Molecular Clouds[END_REF] . The rates of such processes were considered to be well described by the Arrhenius expression [START_REF] Smith | The Temperature-Dependence of Elementary Reaction Rates: Beyond Arrhenius[END_REF] , leading to larger rate constants at higher temperature as the wide distribution of reagent energies allowed the most energetic species to react. At low temperature, the reactivity of these systems was expected to become negligibly small as the reagents were no longer able to surmount the activation barrier; a prediction that was reinforced by experiments above 200 K. Recent work conducted at lower temperatures has challenged this traditional view of reactivity. Hydroxyl radical reactions with several organic molecules [START_REF] Shannon | Accelerated Chemistry in the Reaction Between the Hydroxyl Radical and Methanol at Interstellar Temperatures Facilitated by Tunnelling[END_REF][START_REF] Caravan | Measurements of Rate Coefficients for Reactions of OH with Ethanol and Propan-2-ol at Very Low Temperatures[END_REF][START_REF] Shannon | Observation of a Large Negative Temperature Dependence for Rate Coefficients of Reactions of OH with Oxygenated Volatile Organic Compounds Studied at 86-112 K[END_REF][START_REF] Shannon | A Combined Experimental and Theoretical Study of Reactions between the Hydroxyl Radical and Oxygenated Hydrocarbons relevant to Astrochemical Environments[END_REF][START_REF] Jimenez | First Evidence of the Dramatic Enhancement of the Reactivity of Methyl Formate (HC(O)OCH3) with OH at Temperatures of the Interstellar Medium: A Gas-Phase Kinetic Study between 22 K And 64 K[END_REF] and the reaction of fluorine atoms with hydrogen [START_REF] Tizniti | The Rate of the F + H2 Reaction at Very Low Temperatures[END_REF] have unequivocally demonstrated rate constants that are sometimes enhanced by several orders of magnitude compared with those derived from Arrhenius fits to higher temperature data. One plausible explanation for these dramatic results has been attributed to the possibility of tunneling through the potential energy barrier. Indeed, quantum mechanical theory demonstrates that the wavefunctions describing the reaction intermediates of such complex forming reactions only fall to zero for barriers of infinite height. As the wavefunctions decay exponentially with distance, there is a non-negligible probability that the species can be found on the product side if the barrier is sufficiently thin. For the systems mentioned above, the reagents interact initially through the formation of van der Waal's (prereactive) complexes. In the OH + CH 3 OH system for example, ab-initio calculations of the potential energy surfaces (PESs) show that the prereactive complex formed is stabilized with respect to the separated reagents by 20 kJ mol -1 9 . At high temperature, complex lifetimes are generally short due to their high internal energy, so that redissociation to reagents and/or passage over the barrier are the most probable outcomes. At low temperature, the complex lifetime increases and although passage over the barrier is inhibited, exothermic product channels may be accessible by tunneling through the barrier. In the cases mentioned above where enhanced reactivity has been observed, ab-initio calculations show that the most probable reaction pathways at low temperature involve H-atom transfer [START_REF] Shannon | Accelerated Chemistry in the Reaction Between the Hydroxyl Radical and Methanol at Interstellar Temperatures Facilitated by Tunnelling[END_REF][START_REF] Shannon | Observation of a Large Negative Temperature Dependence for Rate Coefficients of Reactions of OH with Oxygenated Volatile Organic Compounds Studied at 86-112 K[END_REF][START_REF] Shannon | A Combined Experimental and Theoretical Study of Reactions between the Hydroxyl Radical and Oxygenated Hydrocarbons relevant to Astrochemical Environments[END_REF][START_REF] Xu | Theoretical Study on the Kinetics for OH Reactions with CH3OH and C2H5OH[END_REF][START_REF] Stark | An Accurate Multireference Configuration Interaction Calculation of the Potential Energy Surface for the F+H2→HF+H Reaction[END_REF] . The tunneling efficiency decreases with the particle mass indicating that reactions involving heavier isotopes should be slower, giving rise to noticeable kinetic isotope effects (KIE) such as the one observed for the OH(OD) + CO reaction [START_REF] Frost | Reaction between OH (OD) Radicals and CO at Temperatures down to 80 K: Experiment and Theory[END_REF][START_REF] Weston | HO + CO Reaction Rates and H/D Kinetic Isotope Effects: Master Equation Models with ab initio SCTST Rate Constants[END_REF] . KIEs have also been observed in the activated C 2 H + CD 4 /CH 4 reactions [START_REF] Opansky | C2H+CH4, CD4 between 150 and 359K[END_REF] , with slower measured rates for the C 2 H + CD 4 reaction. Here, the difference is adequately explained by the larger separation between the zero-point energy (ZPE) of the reagents and the barrier heights of the respective activated complexes when deuterated methane is employed. As little deviation from Arrhenius behavior is observed for these systems [START_REF] Opansky | C2H+CH4, CD4 between 150 and 359K[END_REF] , the tunneling contribution appears negligible over the measured temperature range. Interestingly, ab-initio calculations [START_REF] Dash | Abstraction and Addition Kinetics of C2H Radicals with CH4, C2H6, C3H8, C2H4, and C3H6: CVT/SCT/ISPE and Hybrid Meta-DFT Methods[END_REF] predict that the C 2 H + CD 4 /CH 4 reactions do not involve prereactive complex formation, reinforcing the idea that such intermediates could play an important role in raising the tunneling probability [START_REF] Caravan | Measurements of Rate Coefficients for Reactions of OH with Ethanol and Propan-2-ol at Very Low Temperatures[END_REF] .

Despite the clear demonstration of large reactivity increases for several gas-phase reactions, there remains an absence of quantitative information regarding the fate of the reagents. One possibility for the processes described above could be complex stabilization rather than reaction, eliminating the need to invoke tunneling effects. Unambiguous product formation has only been demonstrated for the OH + CH 3 OH and F + H 2 reactions [START_REF] Shannon | Accelerated Chemistry in the Reaction Between the Hydroxyl Radical and Methanol at Interstellar Temperatures Facilitated by Tunnelling[END_REF][START_REF] Tizniti | The Rate of the F + H2 Reaction at Very Low Temperatures[END_REF] , with neither of these studies providing quantitative yields. Such information is crucially important for the accurate prediction of reaction rates in low temperature and low pressure environments such as interstellar space.

Building on these earlier studies of tunneling effects to include isotopic variants of the same molecule, we investigated the reactivity of atomic carbon in its ground electronic state, C( 3 P) (hereafter denoted C), with H 2 O and D 2 O down to 50 K. As gas-phase abundances of C and H 2 O are high in dense interstellar clouds [START_REF] Agúndez | Chemistry of Dark Clouds: Databases, Networks, and Models[END_REF] , this reaction could play an important role in the chemical evolution of such regions. A schematic representation of the PES for the C-H 2 O system is shown in Fig. 1, based on current and previous [START_REF] Ozkan | Reactions of 1S, 1D, and 3P Carbon Atoms with Water. Oxygen Abstraction and Intermolecular Formaldehyde Generation Mechanisms; An MCSCF Study[END_REF][START_REF] Hwang | Ab Initio Study of the Addition of Atomic Carbon with Water[END_REF] ab-initio calculations. Reaction occurs through C-atom addition to the O-atom of water forming a prereactive complex 30-40 kJ mol -1 lower than reagents. The probable exothermic products, HCO + H, are separated from the complex by a calculated energy barrier of around 11-40 kJ mol -1 [START_REF] Ozkan | Reactions of 1S, 1D, and 3P Carbon Atoms with Water. Oxygen Abstraction and Intermolecular Formaldehyde Generation Mechanisms; An MCSCF Study[END_REF][START_REF] Hwang | Ab Initio Study of the Addition of Atomic Carbon with Water[END_REF][START_REF] Schreiner | Non-Reaction" of Ground-State Triplet Carbon Atoms with Water Revisited[END_REF] . Previous room temperature experiments of the gas-phase C + H 2 O reaction [START_REF] Husain | Reactions of Atomic Carbon C(23PJ) by Kinetic Absorption Spectroscopy in the Vacuum Ultra-Violet[END_REF][START_REF] Husain | Kinetic Investigation of Ground State Carbon Atoms, C(3P)[END_REF][START_REF] Ahmed | An Experimental and Ab Initio Study of the Addition of Atomic Carbon to Water[END_REF] yielded only an upper limit for the rate constant of 1 × 10 -12 cm 3 s -1 . Consequently, a considerable barrier to product formation is likely, inhibiting reaction at lower temperature in the absence of tunneling effects. Interestingly, earlier low temperature matrix-isolation investigations [START_REF] Schreiner | Non-Reaction" of Ground-State Triplet Carbon Atoms with Water Revisited[END_REF]

Results and Discussion.

Representative decays of the C-atom emission are shown in panels (A) and (B) of Fig. for both reactions at 52 K and 106 K.

The measured second-order rate constants are summarized in Table S1. At 106 K, the reaction with deuterated water was effectively too slow to be measured and experiments performed above 106 K could not identify any supplementary C-atom losses for either system. Our experimental results are compared to previous work in Fig. 3. The rate constants for both reactions increase dramatically below 100 K, with higher values for the C-H 2 O system. At this stage it is impossible to confirm whether these rates correspond to reaction

T˚˚(K)

through tunneling, complex formation, or a combination of the two effects. Indeed, carrier gas collisions could induce C..OH 2 (OD 2 ) prereactive complex stabilization [START_REF] Weston | HO + CO Reaction Rates and H/D Kinetic Isotope Effects: Master Equation Models with ab initio SCTST Rate Constants[END_REF] ; an outcome which would be indistinguishable from reaction by following C-atom losses alone. To discriminate between reactive and non-reactive losses, we examined the product channels for these reactions by following H-or D-atom formation directly by VUV-LIF. To obtain quantitative product yields, the H-atom intensities were compared with H-atom signals generated by the C + C 2 H 4 reaction (with a H-atom yield close to unity 23 ). As the D and H line strength factors are essentially identical [START_REF] Wiese | Accurate Atomic Transition Probabilities for Hydrogen, Helium, and Lithium[END_REF] , it was also possible to obtain quantitative D-atom yields using the same reference by maintaining a fixed laser energy to probe each atomic transition. Typical H-/D-atom formation curves are presented in Fig. 4 for the three reactions at 52 K. [START_REF] Glowacki | An Open-Source Master Equation Solver for Multi-Energy Well Reactions[END_REF] .

The experimental observations (rate constants and product branching ratios) were used to constrain the initial parameters of the master equation. It was necessary to adjust the complex well depth and barrier width to reproduce the experimental results (see SI file for more details), although these modifications were consistent with those used in previous calculations of similar systems [START_REF] Shannon | Accelerated Chemistry in the Reaction Between the Hydroxyl Radical and Methanol at Interstellar Temperatures Facilitated by Tunnelling[END_REF][START_REF] Shannon | A Combined Experimental and Theoretical Study of Reactions between the Hydroxyl Radical and Oxygenated Hydrocarbons relevant to Astrochemical Environments[END_REF][START_REF] Sleiman | Pressure Dependent Low Temperature Kinetics for CN + CH3CN: Competition between Chemical Reaction and Van Der Waals Complex Formation[END_REF] .

These calculations, shown in Fig. 3 Previously, activated reactions were considered unimportant at low temperature, and such processes have mostly been discarded from reaction networks. This and other recent work demonstrate that many processes characterized by barriers could be enhanced by tunneling and that their relevance to models of cold environments needs to be reevaluated.

Experimental and Theoretical Methods.

Experiments. The continuous flow CRESU apparatus used in the present work has been described

previously [START_REF] Shannon | The Fast C(3P) + CH3OH Reaction as an Efficient Loss Process for Gas-Phase Interstellar Methanol[END_REF][START_REF] Hickson | The C(3P) + NH3 Reaction in Interstellar Chemistry. II. Low Temperature Rate Constants and Modeling of NH, NH2, and NH3 Abundances in Dense Interstellar Clouds[END_REF] . Four Laval nozzles were used in this study whose supersonic flow characteristics (temperatures, densities and velocities) are listed in Table S2. C Calculations. Rate constants and product branching ratios were calculated using the Master Equation solver MESMER [START_REF] Glowacki | An Open-Source Master Equation Solver for Multi-Energy Well Reactions[END_REF] , employing a new PES calculated here (see SI file for more details).

Briefly, the phase space for all wells on the PES was divided into grains of a set size and isoenergetic, microcanonical rate coefficients for reactive processes between different species were calculated using Rice, Ramsperger, Kassel and Marcus (RRKM) theory. Energy transfer probabilities between different grains of the same species were obtained using an exponential down model [START_REF] Troe | Theory of Thermal Unimolecular Reactions at Low Pressures. I. Solutions of the Master Equation[END_REF] . For all species, external rotations were considered to be rigid rotors whilst vibrational modes were treated as harmonic oscillators. For the current calculations, a grain size of 20 cm -1 was used above 150 K although this was reduced to 10 cm -1 at the lowest temperatures. Harmonic frequencies and rotational constants were taken from CCSD(T) calculations, but given the large range of energies for the stationary points between the different levels of theory, the energy of the complex was varied during the calculations as well as the width of the barrier connecting the complex and the HCOH adduct. During the procedure to reproduce the experimental data, the same adjustments were applied to both the C + H 2 O and C + D 2 O systems for the energies of the prereactive complexes as well as to the width of the barrier to maintain a consistent description of these two reactions. To account for quantum mechanical tunnelling, the tunnelling transmission coefficients were calculated using the semi-classical WKB method [START_REF] Garrett | Semiclassical Tunneling Calculations[END_REF] . With this method, considered to be more accurate than the one based on a parabolic Eckart-type barrier, the transmission coefficients are calculated through a one dimensional potential employing the mass-weighted intrinsic reaction coordinate (IRC) calculated at the MP2 level. Nevertheless, as this approach may underestimate the tunneling contribution as curvature could lead to an overly long tunneling path, it was necessary to reduce the barrier width to reproduce the experimental results. The barrierless complex formation step was treated using the inverse Laplace transform method to convert the high pressure limiting canonical rate coefficients for the initial association in Arrhenius form into microcanonical rate coefficients. More detailed information on the experimental and theoretical methods is given in the SI file.

Experimental Methods

The CRESU method was used in the present experiments. This technique is well suited to the study of low temperature reactions involving species in the liquid phase at room temperature. As the cold flow is isolated from the reactor walls, condensation issues are avoided and supersaturated concentrations of species with low vapour pressures are attainable. Four Laval nozzles were used in this study allowing different temperatures to be obtained using Ar or N 2 as carrier gases and experiments at 296 K were performed by removing the nozzle. All gases were passed directly from cylinders into mass flow controllers to precisely regulate the flows. Individual mass flow controllers were calibrated using the pressure rise at constant volume method. The supersonic flow characteristics (the temperatures, densities and velocities) were calculated from measurements of the impact pressure in the cold flow and the stagnation pressure in the Laval nozzle reservoir. These values are listed in Table S2. Experiments were performed at only a single fixed total density for any given temperature due to the requirement for several different nozzles to produce supersonic flows over a range of densities. C( 3 P) atoms were generated by the multiphoton dissociation of Third harmonic generation of the UV beam allowed us to produce tunable VUV radiation at 127.755 nm which was collimated by a MgF 2 lens and allowed to enter the reactor, exciting C( 3 P) atoms via the 2s 2 2p 2 3 P 2 → 2s 2 2p3d 3 D 3 ° transition within the cold supersonic flow. Atomic fluorescence was focused by a lithium fluoride lens onto the photocathode of the solar blind photomultiplier tube (PMT) and processed by a boxcar integration system. In later product formation measurements, H( 2 S) or D( 2 S) atoms were detected through VUV LIF at 121.567 nm and 121.534 nm respectively using 28.0 kPa of kryton and 72.0 kPa of argon to generate VUV radiation from a fundamental wavelength around 729 nm in this case.

H 2 O was introduced into the gas flow upstream of the Laval nozzle using a controlled evaporation mixing (CEM) system. A 1 litre reservoir maintained at 2 bar relative to atmospheric pressure was connected to a liquid flow meter allowing flows of between 0.1 and 5 g hr -1 of liquid water to be passed into an evaporation device heated to 373 K. A small flow of Ar or N 2 was also fed into the evaporation system to carry water vapour into the reactor. To determine the gas-phase water concentration, the output of the CEM was passed into a 10 cm absorption cell at room temperature.

The attenuation of the 185 nm line of a mercury pen-ray lamp was measured alternatively in the presence and absence of water vapour to yield values of the attenuated and non-attenuated intensities, I and I o respectively using a channel photomultiplier (CPM) operating in photon counting mode. A narrow band filter centred on 185 nm was placed in front of the CPM to prevent radiation from other mercury lines (notably the intense 254 nm line) from reaching the CPM. The room temperature absorption cross-section of water vapour was taken to be 6.78 × 10 -20 cm 2 37 so that its concentration could be calculated by the Beer-Lambert law. The output of the cell was connected to the reactor using a heating hose maintained at 353 K to avoid condensation. As the water vapour was diluted by at least a factor of five on entering the nozzle reservoir through mixing with the main carrier gas flow, we assume that no supplementary condensation losses occurred S1), the range of observable pseudo-first-order rate constants (the product of the second-order rate constant and the coreagent concentration) was correspondingly small, potentially leading to large errors in the second-order rate constant determinations. Indeed, the magnitude of the pseudo-first-order diffusional loss rate for C-atoms was comparable to or greater than the supplementary loss induced by reaction with H 2 O or D 2 O for most experiments, particularly at 106 K. Secondly, the product H-atom intensities were also low, a fact which could have led to large potential errors in the relative product yields. To address both of these issues, we made several improvements to the detection system to increase the signal to noise ratio and improve overall stability. A wavemeter was used to continuously monitor the laser wavelength systematically for all experiments, allowing us to limit the effects of wavelength drift for any series of experiments.

The shot to shot energy variability of the probe laser was reduced and the average pulse energy was increased for measurements of both C( 3 P) and H( 2 S) atoms, increasing the corresponding signal levels. As this energy increase also resulted in an increase in the scattered light background signal detected by the solar blind PMT, the tripling cell was displaced 60 cm further away from the reactor by mounting it on a sidearm containing a system of baffles to reduce the divergence of the )

The rate constants are measured to be (1.8 ± 0.2) × 10 -10 cm 3 s -1 and (2.1 ± 0.2) × 10 -10 cm 3 s -1 at 296 K and 127 K respectively, with the error bars quoted at the 1σ level with an added 10 % systematic uncertainty. These values show that the rate constant remains high and even increases slightly as the temperature falls. Indeed, a similar dependence is also observed for the O( 1 D) + H 2 O reaction over the 453 -227 K range [START_REF] Vranckx | Kinetics of O(1D) + H2O and O(1D) + H2: Absolute Rate Coefficients and O(3P) Yields between 227 and 453 K[END_REF] .

To check the influence of this reaction on C( 3 P) decays, we performed kinetic measurements for two of our Ar based nozzles (denoted M4Ar and M3Ar in Table S1) with a high concentration of )

[H 2 O]˚( 10 13 ˚cm -3
) order plots obtained for the C( 3 P) + H 2 O/D 2 O reactions at 106 K are displayed in Fig. S3.

Figure S3

Measured second-order rate constants for the C( 3 P) + H 2 O reaction (red solid circles) and the C( 3 P) + D 2 O reaction (blue solid triangles) at 106 K. Solid lines represent weighted linear least squares fits to the data, with the second-order rate constants derived from the slopes.

The derived second-order rate constant for the C( 3 P) + D 2 O reaction is very small indeed, with the value of 4 × 10 -13 cm 3 s -1 from a non-linear least squares fit to the datapoints. Given the small range of D 2 O concentrations used and the relatively large scatter of the measured pseudo-first-order rates, we prefer to give an upper limiting value for the rate constant of 3 × 10 -12 cm 3 s -1 at 106 K, which corresponds to the sum of the upper bound of the statistical error and the nominal rate constant.

For the C( 3 P) + H 2 O reaction at 106 K, a non-linear least squares fit to the data in Fig. S3 yields a ) second-order rate constant of (4.9 ± 1.1) × 10 -12 cm 3 s -1 where the quoted error bars represent the statistical 1σ uncertainty alone. To reflect the high scatter in the measured pseudo-first-order rates we estimate an additional systematic uncertainty of 50 % of the nominal rate, yielding a final value of (4.9 ± 2.7) × 10 -12 cm 3 s -1 . For all of the other lower temperature kinetic measurements, we apply a systematic uncertainty of 20 % on the measured rate constant values.

Relative product yields of the C( 3 P) + H 2 O/D 2 O reactions

As In this case, as it was also necessary to move between the D-atom and H-atom transitions at 121.534 nm and 121.567 nm (using the wavemeter to precisely fix the appropriate wavelength), the probe laser pulse energy was set to the same value for each product pair measurement. As the line strength factors are the same for D-and H-atoms [START_REF] Wiese | Accurate Atomic Transition Probabilities for Hydrogen, Helium, and Lithium[END_REF] , no other corrections were required to the measured intensities. Nevertheless, as an additional verification, experiments looking at the H-/D-atom yields of the C( 1 D) + H 2 /D 2 reactions resulted in ratios of unity for fixed probe laser pulse energies.

All the ratios determined from individual pairs of decays are given in Table S3 for both reactions after multiplication by 0.92 to account for the measured yield of the reference reaction. considerably larger (the C( 1 D) + N 2 quenching rate constant decreases at higher temperature), so it became difficult to extract reliable product yields under these conditions.

Theoretical Methods

Quantum chemical calculations

There have been several previous calculations of the reaction of carbon atoms with water [START_REF] Ozkan | Reactions of 1S, 1D, and 3P Carbon Atoms with Water. Oxygen Abstraction and Intermolecular Formaldehyde Generation Mechanisms; An MCSCF Study[END_REF][START_REF] Hwang | Ab Initio Study of the Addition of Atomic Carbon with Water[END_REF][START_REF] Schreiner | Non-Reaction" of Ground-State Triplet Carbon Atoms with Water Revisited[END_REF] the most complete one being the study of Schreiner & Reisenauer [START_REF] Schreiner | Non-Reaction" of Ground-State Triplet Carbon Atoms with Water Revisited[END_REF] . To perform the statistical calculations presented here, we performed new ab-initio calculations at a higher level than these earlier studies, namely at the CCSD(T)/aug-cc-pVQZ level, to describe all stationary points on the triplet surfaces. To estimate the potential uncertainties of the calculations we also performed MP2 calculations at the aug-cc-pVQZ level, DFT calculations (M06-2X level with the cc-pVQZ basis set; this highly nonlocal M06-2X functional developed by Truhlar et al. [START_REF] Zhao | The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 other Functionals[END_REF] is well suited for structures and energetics of the transition states), CASPT2 and Davidson corrected multi-reference configuration interaction (MRCI + Q) with complete active space self-consistent field (CASSCF)

wavefunctions, to take into account the eventual multi-configurational aspect of this reaction.

CASPT2, MRCI+Q and CCSD(T) calculations were carried out with the MOLPRO 2010 package whereas the MP2 and DFT calculations were performed with Gaussian09. The CASSCF and MRCI calculations were performed at full valence, namely with 8 electrons distributed in 10 orbitals with the 1s orbitals of carbon and oxygen kept doubly occupied but fully optimized. The CASSCF calculations lead to mono-configurational wavefunctions for the adduct and TS1 transition states.

Then CCSD(T) calculations should be reliable as indicated by the T1 and D1 diagnostic values (T1 values are in the 0.004-0.020 range and D1 values are in the 0.010-0.044 range). The geometries for all stationary points were fully optimized at the aug-cc-pVQZ level for each method and frequencies were calculated for each method using a smaller basis set (aug-cc-pVTZ) at the CCSD(T) and MRCI+Q levels. For each TS, characterized by one imaginary frequency (first-order saddle points) on the PES, we determined the minimum energy pathways (MEPs) performing intrinsic reaction coordinate analyses (IRC) at the MP2 and DFT levels. A schematic diagram of the PESs is shown in Figure 1 of the main article.

The calculated stationary point energies are summarized in Table S4 for the prereactive complex and TS1 at various levels. In Table S5, we list all the stationary points of the triplet PESs at the CCSD(T)/aug-cc-pVQZ level as well as the geometries, frequencies and structures of the various species.

The C( 3 P 0,1,2 ) + H 2 O(X 1 A 1 ) reaction leads to 3 surfaces in the entrance valley, one with 3 Aʹ symmetry and two with [START_REF] Shannon | Accelerated Chemistry in the Reaction Between the Hydroxyl Radical and Methanol at Interstellar Temperatures Facilitated by Tunnelling[END_REF] Aʹʹ symmetry when the C-atom approaches in C s geometry or 3 3 Aʹ surfaces in C 1 geometry (no symmetry). At the MRCI+Q level, with the CASSCF geometry optimized for non-relaxed H 2 O (the geometry of the isolated molecule), only one of the three surfaces is attractive leading to a van der Waals complex. This complex is strongly bound (between -17.9 and -48.9 kJ mol -1 depending on the calculation level), with the C-atom attached to the Oatom of water with a C-O distance between 1.76 Å and 2.45 Å depending on the method used.

Further evolution of the complex leads to the 3 HCOH intermediate through TS1 corresponding to insertion of the C-atom into the O-H bond, or directly to H + HOC through TS4. We were unable to locate the TS for the pathway leading to [START_REF] Shannon | Accelerated Chemistry in the Reaction Between the Hydroxyl Radical and Methanol at Interstellar Temperatures Facilitated by Tunnelling[END_REF] CO + H 2 . However, as these products are almost isoenergetic with the C + H 2 O reagents, if this TS exists, is likely to be at very high energy and should not play any role in the present low temperature measurements. As a result, this pathway is not considered further in these calculations.

Our results are in good agreement with previous calculations [START_REF] Ozkan | Reactions of 1S, 1D, and 3P Carbon Atoms with Water. Oxygen Abstraction and Intermolecular Formaldehyde Generation Mechanisms; An MCSCF Study[END_REF][START_REF] Hwang | Ab Initio Study of the Addition of Atomic Carbon with Water[END_REF][START_REF] Schreiner | Non-Reaction" of Ground-State Triplet Carbon Atoms with Water Revisited[END_REF] as well as with thermochemical data when they exist (-213.8 kJ mol -1 45 compared to -206.4 kJ mol -1 (this study) for the HCO + H exit channel). However, as shown in Table S4, there are significant variations in the calculated energies of the complex and TS1 depending on the method used. It should be noted that the C-O distance calculated at the CASSCF level (2.45 Å) does not correspond to the minimum energy configuration for MRCI+Q calculations so that the MRCI+Q results may not correspond exactly to the stationary point energies despite various adjustments of the C-O length in the complex. The precision of the various methods is coherent with expectations on their accuracies. Indeed, as shown by Wagner [START_REF] Wagner | The challenges of Combustion for Chemical Theory[END_REF] , DFT usually underestimates barrier energies whereas MRCI usually overestimates them. CASPT2 calculations are likely to underestimate barrier energies, as do MCQDPT2 calculations [START_REF] Ozkan | Reactions of 1S, 1D, and 3P Carbon Atoms with Water. Oxygen Abstraction and Intermolecular Formaldehyde Generation Mechanisms; An MCSCF Study[END_REF] . CCSD(T) should lead to the most accurate values considering the T1 and D1 diagnostic values [START_REF] Lee | Comparison of the T1 and D1 Diagnostics for Electronic Structure Theory: A New Definition for the Open-Shell D1 Diagnostic[END_REF][START_REF] Leininger | A New Diagnostic for Open-Shell Coupled-Cluster Theory[END_REF] in agreement with the fact that CASSCF calculations lead to monoconfigurational wavefunctions. As a result, the expected uncertainty on the complex and TS energies is difficult to estimate but it could be greater than 10 kJ mol -1 .

Master Equation Calculations

Rate constants and product branching ratios were calculated using the Master Equation solver MESMER [START_REF] Glowacki | An Open-Source Master Equation Solver for Multi-Energy Well Reactions[END_REF] , an open source program which uses matrix techniques to solve the energy grained chemical master equation for a series of unimolecular systems connected by various transitions states and local minima leading from reagents to products. Briefly, the phase space for all wells on the PES was divided into grains of a set size and isoenergetic, microcanonical rate coefficients for reactive processes between different species were calculated using RRKM theory, while energy transfer probabilities between different grains of the same species were obtained using an exponential down model [START_REF] Troe | Theory of Thermal Unimolecular Reactions at Low Pressures. I. Solutions of the Master Equation[END_REF] . For all species, external rotations were considered to be rigid rotors whilst vibrational modes were treated as harmonic oscillators.

For the current calculations, a grain size of 20 cm -1 was used above 150 K although this was reduced to values as low as 10 cm -1 at the lowest temperatures. Harmonic frequencies and rotational constants were taken from the CCSD(T) calculations but given the large range of energies for the stationary points between the different levels of theory used here, the energy of the complex was varied during the calculations as well as the width of the barrier connecting the complex and HCOH (the IRC was calculated at the MP2 level). During the procedure to reproduce the experimental data, the same adjustments were applied to both the C + H 2 O and C + D 2 O systems for the energies of the prereactive complexes as well as to the width of the barrier to maintain a consistent description of these two reactions.

The barrierless reaction step describing complex formation was treated using the inverse Laplace transform (ILT) method to convert the high pressure limiting canonical rate coefficients for the initial association in Arrhenius form into microcanonical rate coefficients. Considering the fine structure of ground state atomic carbon, only the 3 P 0 state and two levels of the 3 P 1 states of the Catom lead to reaction as mentioned above. Using capture theory, this leads to a rate constant k(T) = 7.0e -10 × (T/298) 0.17 × (1 + 2 × exp(-23.6/T))/(1 + 3 × exp(-23.6/T) + 5 × exp(-62.40/T)) for the initial complex formation step dominated by dispersion interactions.

The measured product branching ratios allowed us to provide certain additional constraints for the initial parameters of the MESMER statistical calculations. As the H-atom yield is less than unity for both the C + H 2 O and C + D 2 O reactions, some complex stabilization clearly occurs. To treat collisional energy transfer, the average downward energy transfer value, ΔE down , was taken to be equal to 400*(T/300) 0.85 cm -1 in the initial trial model although this was found to be incompatible with the experimental results (see below for details). The Lennard-Jones parameters σ and ε were set respectively to 3.47 Å and 114 cm -1 for Ar, to 3.90 Å and 82 cm -1 for N 2 and to 5.0 Å and 150 cm -1 for the C…H 2 O/D 2 O prereactive complexes. The pressures used in the calculations were set to be equal to the experimental values (see Table S2).

When using the CCSD(T) well depth for the complex, the WKB method for tunneling using the IRC calculated at the MP2 level (adjusted to take into account the ZPE variation) and the standard energy transfer value, the master equation calculations predict that some complex stabilization occurs, but bimolecular product formation is negligible. In order to increase the yield of the reactive pathway leading to bimolecular product formation (H + HCO), it was necessary to either substantially decrease the TS1 barrier height or decrease its width. Decreasing the barrier height leads to a rate constant which presents little temperature dependence, with a significantly greater value than the upper limit measured by Husain and Young [START_REF] Husain | Kinetic Investigation of Ground State Carbon Atoms, C(3P)[END_REF] . Consequently, we maintained this barrier height at the calculated value (+32.9 kJ mol -1 for H 2 O and +35.1 kJ mol -1 for D 2 O) and varied the barrier width instead. To reproduce the experimental results, it was necessary to reduce the width by a factor close to 2. Moreover, it was also necessary to increase either the prereactive complex well depth and/or the collisional energy transfer efficiency. Both of these adjustments lead to longer complex lifetimes, thereby enhancing the tunneling process at low temperature as well as increasing the probability for complex stabilization through three body collisions. In the absence of either of these adjustments, the major fate of the prereactive complex is dissociation back to reagents, even at low temperature. This is almost certainly due to the fact that the C + H 2 O system is relatively small with a low density of rovibrational levels. Increasing only the complex well depth, to -60.0 kJ mol -1 (instead of -28.9 kJ/mol at the CCSD(T) level), allows reasonable agreement to be obtained between the calculations and the measured reaction rates/branching ratios. Good agreement could also be obtained by adjusting the well depth to -46 kJ mol -1 and by using a temperature independent ΔE down value of 400 cm -1 . These values were the ones used to obtain the calculated rates presented in Figure 3 of the main article. As a comparison, in the recent study by Sleiman et al. [START_REF] Sleiman | Pressure Dependent Low Temperature Kinetics for CN + CH3CN: Competition between Chemical Reaction and Van Der Waals Complex Formation[END_REF] of the CN + CH 3 CN reaction, a temperature independent value of 800 cm -1 was used for the ΔE down parameter.

Using these parameters, the branching ratio between complex stabilization and H-atom product formation is not completely reproduced for the experimental conditions at 52 K for the C + H 2 O reaction (92% for the calculated product formation instead of the measured value of 58%) while it is well reproduced for the C + D 2 O reaction (30% for the calculated product formation instead of the measured value of 29%). The calculated values were predicted to decrease with increasing pressure, due to an increase of the total rate constant arising from more efficient complex stabilization (with only a weak corresponding effect on the bimolecular product formation rate).

As mentioned in the main article, we do not consider the possible contributions of HCO or DCO fragmentation in the calculated H-/D-atom branching ratios. As the observed H-/D-atoms are clearly identified as products of the C + water reaction (and not from competing secondary reactions) with well-defined yields, this strongly suggests that statistical theory can only provide semi-quantitative explanations for the experimental observations in this instance.

It is interesting to compare our calculations with other recent studies of OH radical reactions with various oxygenated volatile organic compounds 3-4, 6, 49 as well as the CN + CH 3 CN reaction 26 at low temperature. All these processes are characterized by prereactive complex formation associated with a notable barrier on the reactive pathways. Moreover, all these reactions show similar behavior with a strong increase of the rate constant at low temperature. However, the actual mechanisms are considered to be different in many of these systems. In some cases, (notably for the OH + CH 3 OH reaction 3 ) the main process was thought to be tunneling through the barrier leading to reaction. In other cases (the OH + acetone reaction [START_REF] Shannon | A Combined Experimental and Theoretical Study of Reactions between the Hydroxyl Radical and Oxygenated Hydrocarbons relevant to Astrochemical Environments[END_REF] , the OH + dimethylether reaction [START_REF] Shannon | A Combined Experimental and Theoretical Study of Reactions between the Hydroxyl Radical and Oxygenated Hydrocarbons relevant to Astrochemical Environments[END_REF] , and OH + ethanol and propan-2-ol 4 ) the experimental conditions were considered to favor complex stabilization rather than bimolecular product formation. It should be noted that in many of these previous studies, the RRKM calculations were generally unable to reproduce the experimental results without large adjustments. For their study of the OH + acetone reaction, Shannon et al. [START_REF] Shannon | A Combined Experimental and Theoretical Study of Reactions between the Hydroxyl Radical and Oxygenated Hydrocarbons relevant to Astrochemical Environments[END_REF] increased the well depth for the prereactive complex by 50% to reproduce the experimental data.

In their investigation of the OH + methanol reaction to temperatures and pressures more representative of dense interstellar clouds although it was not possible to extend these calculations below 30 K due to numerical difficulties. While the statistical calculations predict that complex stabilization is a pressure dependent process, the bimolecular product channel is found to depend only slightly on the total pressure. Indeed, three body collisions increase the complex lifetime, thereby increasing the possibility of tunneling through the barrier.

Here the experimental total rate constant at 52 K is multiplied by the H-atom branching ratio of 0.58 to yield the reactive (tunneling) rate alone. The calculations predict that the total rate constants measured at 77 and 106 K are essentially the same as the tunneling rate already (complex association is negligible at these temperatures). We also use the experimental upper limit of Husain and Young at 300 K 20 of 1 × 10 -12 cm 3 s -1 to further constrain the fit. These data are fitted using an expression of the type a × (T/300) b leading to a = 1.26 × 10 -12 cm 3 s -1 and b = -1.59 in the 52 -300 K range. Then, as the RRKM calculations show that the tunneling rate constant has a small pressure dependence, we multiply the fitted rate constant expression by the ratio between the calculated zero pressure value and the calculated value at the pressure used in the 52 K experiment.

This ratio is equal to 0.74 leading to a modified formula with a = 9.3 × 10 -13 and b= -1.59. At 10 K, this expression yields a rate constant of 2 × 10 -10 cm 3 s -1 . Given the predicted high abundance of atomic carbon in dense interstellar clouds and the large rate constant, this process should become the most efficient mechanism for H 2 O loss in current models. *The errors on the Mach number, temperature and mean flow velocity, cited at the level of one standard deviation from the mean are calculated from separate measurements of the impact pressure using a Pitot tube as a function of distance from the Laval nozzle and the stagnation pressure within the reservoir.

Figure 1 .

 1 Figure 1. Potential energy diagram for the C + H 2 O reaction on the triplet surface. Calculations

1 )

 1 of this reaction observed the formation of Energy (kJ mol -

Figure 2 .D

 2 Figure 2. Kinetics of atomic carbon removal in the presence of H 2 O and D 2 O. (A) Exemplary C-

Figure 3 .

 3 Figure 3. Rate constants as a function of temperature. The C + H 2 O reaction: (green diamond) Husain and Kirsch 19 ; (solid blue circles) these experiments; (solid blue line) calculated total rate

Figure 4 .

 4 Figure 4. Relative yields of atomic hydrogen and atomic deuterium products. H/D-atom temporal

( 3 P

 3 ) atoms were generated by the multiphoton dissociation of CBr 4 molecules at 266 nm by aligning the photolysis laser along the supersonic flow axis. Previous studies[START_REF] Shannon | The Fast C(3P) + CH3OH Reaction as an Efficient Loss Process for Gas-Phase Interstellar Methanol[END_REF] under similar conditions have shown that excited state carbon atoms C( 1 D) are also produced, at the level of 10-15% with respect to C( 3 P). Rate constants for the C( 3 P) + H 2 O reaction were measured by detecting C( 3 P) atoms directly by on-resonance VUV LIF at 127.755 nm. In later product formation measurements, H( 2 S) or D( 2 S) atoms were detected through VUV LIF at 121.567 nm and 121.534 nm respectively. H 2 O was introduced into the gas flow upstream of the Laval nozzle using a controlled evaporation mixing (CEM) system. Flows of liquid water were passed into an evaporation device heated to 373 K along with a small flow of Ar or N 2 to carry water vapour into the reactor. The gas-phase water concentration was determined by absorption using the 185 nm line of a mercury lamp upstream of the reactor. D 2 O could not be introduced into the experiments in this way, given the need for a large volume of D 2 O in the CEM reservoir. Moreover, the absorption cross-section of D 2 O is almost an order of magnitude smaller than the H 2 O one at 185 nm, so it was no longer possible to determine its concentration spectroscopically. Instead, D 2 O vapour was carried into the reactor using a room temperature bubbler connected to a cold trap held at 288 K to precisely control the concentration of D 2 O in the flow[START_REF] Harvey | Correlation for the Vapor Pressure of Heavy Water From the Triple Point to the Critical Point[END_REF] . The pseudo-first-order approximation was used in all experiments with [H 2 O]/[D 2 O] >> C( 3 P) so that the temporal dependence of the C( 3 P) LIF signal was given by a simple exponential function of the form A × e -Bt . For experiments monitoring the formation of product H/D-atoms, a biexponential function of the form A × (e -Bt -e -Ct ) was used to describe the initial production and eventual loss of these atoms.

CBr 4

 4 molecules at 266 nm with approximately 20 mJ of pulse energy. Previous studies[START_REF] Shannon | The Fast C(3P) + CH3OH Reaction as an Efficient Loss Process for Gas-Phase Interstellar Methanol[END_REF] under similar conditions have shown that excited state carbon atoms C( 1 D) are also produced, at the level of 10-15% with respect to C( 3 P). A column of carbon atoms of uniform density was thus created by aligning the photolysis laser along the supersonic flow axis. CBr 4 was carried into the reactor using a small carrier gas flow over solid CBr 4 . The gas-phase concentration of CBr 4 was estimated to be lower than 1.1 × 10 13 cm -3 from its saturated vapor pressure. Rate constants for the C( 3 P) + H 2 O reaction were measured by detecting C( 3 P) atoms directly by on-resonance VUV LIF. A pulsed narrow band dye laser operating at 766.5 nm was frequency doubled to produce UV radiation at 383.3 nm which was focused into a cell containing 13.3 kPa of xenon and 48.0 kPa of argon for phase matching mounted on a sidearm of the reactor at the level of the observation axis.

  VUV probe radiation in the reactor. To avoid supplementary losses of VUV light within the sidearm through absorption by residual gases within the reactor, the sidearm was also continuously flushed with N 2 during the experiments. Influence of the C( 1 D) + H 2 O/D 2 O reactions It the present experiments, it was clear that the reactions of C( 1 D) atoms with both H 2 O and D 2 O might interfere with both the kinetic and product measurements of the corresponding C( 3 P) reactions. As the C( 1 D) + H 2 O/D 2 O reactions are barrierless processes 18 , their rate constants could be several orders of magnitude larger than the C( 3 P) ones, although no experimental measurements are available in the literature. To improve our overall understanding of the present experiments, we studied the kinetics of the C( 1 D) + H 2 O reaction at two temperatures, 300 K and 127 K, by following the production of H-atoms. The carrier gas for both of these temperatures was Ar, allowing us to maintain a high concentration of C( 1 D) atoms in the flow 40 . At these temperatures H-atom production from the C( 3 P) + H 2 O tunneling reaction was negligible. The second-order plots obtained in these experiments are shown in Fig. S1.

Figure S1

 S1 Figure S1 Measured second-order rate constants for the C( 1 D) + H 2 O reaction obtained at 296 K

N 2

 2 added ([N 2 ] > 9 × 10 15 cm -3 ) to rapidly relax C( 1 D) atoms. Measurements at 106 K were performed with N 2 as the carrier gas. While the nominal temperatures for the M3Ar and M4Ar nozzles are calculated to be (75 ± 2) K and (50 ± 1) K, the use of such large [N 2 ] values shifts the calculated temperatures higher by 2 K. Recent measurements of the quenching of C( 1 D) by N 2 down to low temperatures have shown that the rate constants for this process increase to values of around 1.5 × 10 -11 cm 3 s -1 at 50 K[START_REF] Hickson | An Experimental and Theoretical Investigation of the C(1D) + N2 → C(3P) + N2 Quenching Reaction at Low Temperature[END_REF] . The results of such experiments are compared to the results of measurements performed in the absence of N 2 in Fig.S2for the M3Ar nozzle.

Figure S2

 S2 Figure S2Measured second-order rate constants for the C( 3 P) + H 2 O reaction obtained in the presence (blue solid squares, [N 2 ] = 9 × 10 15 cm -3 ) and absence (green solid circles) of N 2 at 77 K

2 ×

 2 the C( 1 D) + H 2 O/D 2 O reactions are much faster than the corresponding C( 3 P) ones, quantitative measurements of H/D-atom production by C( 3 P) reactions were only possible when N 2 was added to the flows. N 2 concentrations around 2.1 × 10 16 cm -3 were used to rapidly quench C( 1 D) atoms at 52 K. The pseudo-first-order rate constant for C( 1 D) loss under these conditions is equal to 3.10 5 s -1 , indicating that C( 1 D) atoms are entirely removed from the flow within the first 10 microseconds. A typical H-atom formation curve is shown in Fig. S4 for experiments performed at 52 K, alongside the corresponding reference reaction (C( 3 P) + C 2 H 4 ) one with a known H-atom yield of 0.92 ± 0.04 at 300 K 23 .

Figure S4 H

 S4 Figure S4 H-atom formation curves for the target C( 3 P) + H 2 O (red solid circles) and reference C( 3 P) + C 2 H 4 reaction (green solid triangles) recorded at 52 K with [H 2 O] = 1.8 × 10 13 cm -3 and [C 2 H 4 ] = 1.5 × 10 12 cm -3 . The solid red line represents the biexponential fit used to determine the instantaneous H-atom signal from the C( 1 D) + H 2 O reaction. The dashed red line represents the

Figure S5

 S5 Figure S5 Ratio of the H-atom signals from the target C( 3 P) + H 2 O and reference C( 3 P) + C 2 H 4

FigureFigure S7

 S7 Figure S6 H-/D-atom formation curves for the target C( 3 P) + D 2 O (red solid circles) and reference C( 3 P) + C 2 H 4 reaction (green solid triangles) recorded at 52 K with [D 2 O] = 2.0 × 10 13 cm -3 and [C 2 H 4 ] = 1.5 × 10 12 cm -3 . The solid red line represents the biexponential fit used to determine the instantaneous D-atom signal from the C( 1 D) + D 2 O reaction. The dashed red line represents the

  D-atom product yields were only derived from data recorded at low H 2 O or D 2 O concentrations (< 3.8 × 10 13 cm -3 ) for three main reasons. Firstly, such low values allowed us to neglect the potential absorption of the VUV excitation laser and VUV fluorescence emission by residual gas in the reactor. Secondly, it allowed us to minimize the contributions of the C( 1 D) + H 2 O/D 2 O reactions to the H-/D-atom formation curves. Thirdly, any small contributions to the H-/D-atom signals from H 2 O/D 2 O clusters that might be present in the flow (which may or may not be able to react rapidly with ground state atomic carbon) were entirely negligible. The average H-and Datom product yields given in the main article were derived from 11 and 9 individual pairs of formation curves respectively.While efforts were made to record relative product yields at higher temperatures, these measurements were hampered by several issues. At 106 K in particular, comparison of the extremely weak H-/D-atom formation curves with H-atom yields from the reference C( 3 P) + C 2 H 4 reaction led to large product yield variations. As these measurements rely on the use of identical pseudo-first-order production rates for the target and reference reactions, given the large errors on the measured second-order rate constants, such variations were not unexpected. Indeed, further attempts to overcome these problems by using much larger concentrations of H 2 O and D 2 O also failed with these measurements potentially being affected by cluster formation in the supersonic flow. At 77 K, the instantaneous production of H-/D-atoms from the C( 1 D) + H 2 O/D 2 O was

  CO, although the products were attributed to water reactions with excited state carbon and carbon clusters. To investigate the C + H 2 O/D 2 O reactions in this work, we employed the CRESU technique[START_REF] Bergeat | CRESU stands for Cinétique de Reaction en Ecoulement Supersonique Uniforme or Reaction Kinetics in a Uniform Supersonic Flow 23[END_REF] (see the Supplementary Information file (SI) for more information). In these experiments, C-atoms were generated by pulsed laser photolysis of carbon tetrabromide (CBr 4 ) and detected by vacuum ultraviolet laser-induced fluorescence (VUV-LIF).

	species such as H 2
				3 CO+H 2
	C+H 2 O	H 2 O...C	HCOH	HCO+H

  upstream of the Laval nozzle. D 2 O could not be introduced into the experiments in this way, given the need for a large volume of D 2 O in the CEM reservoir. Moreover, as the absorption cross-section of D 2 O is almost an order of magnitude smaller than the H 2 O one at 185 nm, it was no longer possible to determine its concentration spectroscopically. Instead, D 2 O vapour was carried into the reactor by passing a small flow of Ar or N 2 through room temperature liquid D 2 O held in a bubbler at a known pressure.The output of this bubbler was then passed into a cold trap held at 288 K to ensure that the saturated vapour pressure of D 2 O at 288 K was attained in the gas flow[START_REF] Harvey | Correlation for the Vapor Pressure of Heavy Water From the Triple Point to the Critical Point[END_REF] . The output of the cold trap was then fed into the Laval nozzle reservoir, allowing us to accurately determine D 2 O concentrations in the supersonic flow. He as the bath gas[START_REF] Bourgalais | Low Temperature Kinetics of the First Steps of Water Cluster Formation[END_REF] . To determine whether water cluster formation might have an influence on the present experiments, we performed numerical simulations of our experimental system, including the association rate constants derived in this recent study and all other competing processes. As our carrier gases Ar and N 2 are likely to be more efficient than He at promoting cluster formation, we also ran simulations with H 2 O association rate constants two times higher than the nominal values. The results obtained suggest that cluster formation is negligible at all temperatures for the H 2 O/D 2 O concentration ranges used here. The requirement to use low [H 2 O]/[D 2 O] values had important consequences for the present measurements. Firstly, as the second-order rate constants for the C + [H 2 O]/[D 2 O] reactions are small (Table

H 2 O and D 2 O concentrations The range of [H 2 O]/[D 2 O] that could be used in the experiments was severely limited by the formation of clusters in the supersonic flow. Our earlier work on the kinetics of the CH + H 2 O reaction 38 allowed us to establish the exploitable range of [H 2 O]/[D 2 O] in these experiments, listed in Table

S2

. The kinetics of water cluster formation has recently been investigated at low temperature, using

  [START_REF] Shannon | Accelerated Chemistry in the Reaction Between the Hydroxyl Radical and Methanol at Interstellar Temperatures Facilitated by Tunnelling[END_REF] , one imaginary frequency was divided by 4.6 leading only to qualitative agreement between the calculated and experimental rate constant values. In a recent study of the CN + CH 3 CN reaction, Sleiman et al.[START_REF] Sleiman | Pressure Dependent Low Temperature Kinetics for CN + CH3CN: Competition between Chemical Reaction and Van Der Waals Complex Formation[END_REF] used a large value for the ΔE down parameter to stabilize efficiently the prereactive complex. Nevertheless, they were unable to reproduce the rate constant temperature dependence below 100 K. In the context of this previous work, where large deviations from the initial ab-initio values and standard parameters were required, the modifications applied in the present work appear to be quite reasonable.The C( 3 P) + H 2 O/D 2 O reactions display large negative temperature dependences which can be reproduced theoretically by increasing the prereactive complex lifetime as described above. As the experimental H-/D-atom yields demonstrate that complex stabilization is non-negligible, the statistical calculations have been used to extrapolate the rate constant of the C( 3 P) + H 2 O reaction

Table S1

 S1 Measured rate constants for the C( 3 P) + H 2 O and C( 3 P) + D 2 O reactions Number of individual measurements. †Concentration range (10 13 cm -3 ). ‡Second-order rate constant (10 -12 cm 3 s -1 ). §Errors are cited at the 1σ level with an added systematic uncertainty (see text for details). Mach3 Ar Mach3 Ar Mach4 Ar Mach4 Ar Mach number 2.0 ± 0.03* 3.0 ± 0.02 3.0 ± 0.1 3.0 ± 0.1 3.9 ± 0.1 3.9 ± 0.1

	T (K)	N*	[H 2 O] †	k C+H2O ‡, § T (K)	N*	[D 2 O] †	k C+D2O ‡, §
	50	22	0-8.5	34.7±7.4 52	26	0-8.6	30.1±7.8
	52	28	0-8.3	37.0±7.8 52	26	0-8.4	30.4±7.4
	75	30	0-8.3	10.9±2.7 77	50	0-8.5	9.7±2.7
	77	25	0-7.4	12.8±3.4 106	23	0-5.1	< 3.0
	106	28	0-13.6	4.9±2.7
	Table S2 Continuous supersonic flow characteristics
	Laval nozzle Mach3 N 2 Carrier gas Mach2 N 2 (using Ar) Ar N 2	Ar (7% N 2 )	Ar	Ar (7% N 2 )	Ar
	Density (10 16 cm -3 )	12.6	10.3	14.7	14.7	25.9	25.9
	Temperature (K) 127 ± 2 a	106 ± 1	77 ± 2	75 ± 2	52 ± 1	50 ± 1
	Mean flow velocity (ms -1 )	419 ± 3 a	626 ± 2	479 ± 3	479 ± 3	505 ± 1	505 ± 1

*

Table S3

 S3 Individual product yields for the C( 3 P) + H 2 O and C( 3 P) + D 2 O reactions at 52 K [H 2 O] (cm -3 ) H-atom yield C + H 2 O / H-atom yield C + C 2 H 4 [D 2 O] (cm -3 ) D-atom yield C + D 2 O / H-atom yield C + C 2 H 4 *Individual product yields obtained from fits to the temporal H-/D-atom yields such as those shown in Figs.S5 and S7. The uncertainties are quoted at the 1σ level. †Mean product yields with uncertainties quoted at the 95% confidence level including the errors associated with the reference reaction.

		0.65±0.01*		0.31±0.01*
		0.54±0.01		0.29±0.01
		0.55±0.01	3.8 × 10 13	0.32±0.01
	3.3 × 10 13	0.56±0.01		0.29±0.01
		0.52±0.01		0.25±0.01
		0.55±0.01
		0.58±0.01		0.32±0.01
	1.8 × 10 13	0.60±0.01 0.60±0.01 0.61±0.01	2.0 × 10 13	0.25±0.01 0.29±0.01 0.28±0.01
		0.62±0.01
		0.58±0.04 †		0.29±0.02 †

Table S4

 S4 Calculated energies of the H 2 O…C prereactive complex and TS1 by different methods (at 0 K including ZPE with respect to the C + H 2 O reagent asymptote).TableS5Energies (in kJ/mol at 0 K including ZPE with respect to the C + H 2 O energy at the CCSD(T)/aug-cc-pVQZ level), geometries and frequencies (in cm -1 , unscaled, calculated at the CCSD(T)/aug-cc-pVTZ level) of the various stationary points of the C + H 2 O reaction on the triplet surface as well as the stationary points of the C + D 2 O reaction used in the RRKM calculations.

	Species	Energies	Geometries		Frequencies
		(kJ/mol)				(cm -1 )
	H 2 O	0	O 0.00000000 0.00000000 -	1645, 3810, 3920
			0.06578856
			H 0.00000000 0.75754244
			0.522142971
			H 0.00000000 -0.75754244
			0.5221429713
	D 2 O	0	identical to H 2 O		1204, 2747, 2872
			O -0.06649886 0.00000014		293, 534, 546,
		-28.9	0.73931770		1628, 3755, 3862
			H 0.47330244 0.76821292
	H 2 O…C		0.95626321
			H 0.47329692 -0.76822168
			0.95624485	Complex	TS1
	MRCI+Q/av5z//CASCCF/av5z C 0.00914383 0.00000054 --17.9	+33.6
	CASPT2/av5z//CASCCF/av5z 1.14531122	-48.9	+0.2
	MP2/vqz			-33.2	+29.8
	CCSDT/avqz D 2 O…C	identical to H 2 O…C	-28.9	+32.9 290, 397, 401,
	M06/vqz	-30.3		-48.4	+6.8	1191, 2706,

Acknowledgments.

The authors acknowledge support from the Agence Nationale de la Recherche (ANR-15-CE29-0017-01) and from the French INSU/CNRS programs 'Physique et Chimie du Milieu Interstellaire' (PCMI) and 'Programme National de Planétologie' (PNP).

Author information

Corresponding author *E-mail: kevin.hickson@u-bordeaux.fr

Supporting Information Available:

The supporting information file includes details of the experimental and theoretical methods used, supplementary figures S1 to S7 and supplementary tables S1 to S5.

Supplementary Information for

Quantum