A Zhadan

V Sarou-Kanian

L Del Campo

L Cosson

M Malki

C Bessada

Speciation and transport properties in molten alkali carbonates at high temperature

Keywords: Molten alkali carbonates, high temperature, PFG NMR, electrical conductivity, CO2, selfdiffusion

We study structural and transport properties of different eutectic mixtures of molten carbonate used for the capture and valorization of CO2. Different techniques: NMR, PFG NMR, electrical impedancemetry, were used to study Li2CO3-Na2CO3 (52:48 %mol), Li2CO3-K2CO3 (62:38 %mol), Li2CO3-K2CO3 (40:60 %mol), Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 %mol) compositions at high temperature. The NMR measurements confirmed only the presence of anionic species CO . No effect of composition or temperature on speciation was detected. From electrical conductivity and self-diffusion coefficients measurements, we have shown that the electrical 2 conductivity of carbonates does not only depend on the radius of the cations, but also depends on the electrostatic interaction between ions. With the addition of K2CO3 in the carbonate mixture, the interaction between the charge carriers present in the liquid increases and results in a decrease of electrical conductivity. We have shown that the high solubility of CO2 in compositions with high lithium carbonate content is associated with a high mobility of Li + cations.

Introduction

The global warming has become a strong problem for humanity. Every year billions tons of CO2 are produced. [START_REF] Benson | Carbon Dioxide Capture and Storage[END_REF] This pollution increases the temperature on earth and some places become uninhabitable. Nowadays it is possible to store the carbon dioxide [START_REF] Caprile | Carbon Capture: Energy Wasting Technologies or the MCFCs Challenge?[END_REF] and to produce electricity, using for example the Molten Carbonate Fuel Cells (MCFCs) [START_REF] Carter | The Fuel Cell Today Industry Review[END_REF]4 . In this case, humanity will win on the both aspects: first-one, decreasing the pollution by CO2 and second-one, producing electricity. These fuel cells work at high temperature, at about 800 K, 4 and suffer from difficulties in the study of physicochemical properties, which are needed for a better understanding of their operation. In these cells, the electrolyte is molten alkali carbonates. [START_REF] Frangini | Molten Carbonates for Advanced and Sustainable Energy Applications: Part I. Revisiting Molten Carbonate Properties from a Sustainable Viewpoint[END_REF] These molten salts are very corrosive at high temperature, and require careful selection of materials for analysis using experimental techniques.

To define the optimal conditions for CO2 consumption in MCFCs the solubility mechanism of CO2 in molten carbonates at high temperature has to be understood. Some Molecular Dynamic (MD) simulations have proved the presence of different species such as CO2, CO , C O , C O and CO. [START_REF] Carof | Carbon Species Solvated in Molten Carbonate Electrolyser Cell from First-Principles Simulations[END_REF] Nevertheless, some of these species are very scarce and have a very low lifespan, certainly too low to be detected by experimental techniques.

In this study, we explore Li2CO3-Na2CO3-K2CO3, Li2CO3-Na2CO3, Li2CO3-K2CO3 systems over a large temperature range (670-1020 K) using two experimental techniques: Nuclear Magnetic Resonance (NMR), [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] which allow measuring self-diffusion coefficients D, [START_REF] Rollet | Measuring Self-Diffusion Coefficients up to 1500 K: A Powerful Tool to Investigate the Dynamics and the Local Structure of Inorganic Melts[END_REF] and chemical shifts, [START_REF] Zhadan | Transport Properties in Molten Carbonates: Self-Diffusion and Conductivity Measurements at High Temperature[END_REF] and Electrical Impedance Spectroscopy (EIS) to measure electrical conductivity, [START_REF] Gaillard | Carbonatite Melts and Electrical Conductivity in the Asthenosphere[END_REF] both in the liquid state at high temperature. The aim is to study the structure and dynamics in these melts as a function of temperature and composition. In a previous publication in LiCO3-NaCO3 system, we have combined the measurements of [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na and [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li self-diffusion coefficients with the electrical conductivity to explain the speciation and transport mechanism at high temperature. [START_REF] Zhadan | Transport Properties in Molten Carbonates: Self-Diffusion and Conductivity Measurements at High Temperature[END_REF] In this paper, we investigate the effect of the nature of alkali cation and the composition in such carbonates mixtures.

Self-diffusion coefficients in molten carbonates were measured with radioactive tracers methods by Spedding et al. 11 This technique does not allow to study some chemical elements with a low half-life time of radioactive isotopes, such as lithium.

In this work we have measured self-diffusion coefficients D by pulsed field gradients (PFG) NMR technique. This method allows to obtain the values of D in a wide diffusion time range (10 - 9 -10 -10 m 2 /s) without using radioactive isotopes. Other advantages are the selectivity toward the isotope and the possibility to provide in situ experiments at high temperature up to 1020 K.

Taking into account the high corrosiveness of molten carbonates, a special set up with double containers was developed [START_REF] Zhadan | Transport Properties in Molten Carbonates: Self-Diffusion and Conductivity Measurements at High Temperature[END_REF] and allows working up to 1020 K with different gases during the experiment. [START_REF] Zhadan | Transport Properties in Molten Carbonates: Self-Diffusion and Conductivity Measurements at High Temperature[END_REF] To analyse carbonaceous species in molten salts we have obtained results on the [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C and [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O nucleus by NMR spectroscopy, the only isotopes observables for this two nuclei. Both nuclei have very low natural abundance: 1.07% and 0.038% respectively. Commercial powders of alkali carbonates enriched by [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C were used in our experiments. It significantly reduced the time of analysis. In the case of [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O, we did not find commercial carbonates enriched by [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O exist and the synthesis of [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O-enriched carbonates was difficult. So we have decided to show in this paper [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O spectra obtained in natural abundance, with a very high number of acquisitions, to improve the resolution. Among the other nuclei observable in these systems by NMR, we have studied all the alkali metals [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na, [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li and 39 K by NMR at high temperature.

The conductivity cell used for these measurements consists of 4 platinum electrodes [START_REF] Zhadan | Transport Properties in Molten Carbonates: Self-Diffusion and Conductivity Measurements at High Temperature[END_REF] which is specifically adapted for measurements at high temperature in corrosive molten salts under different atmospheres.

Experimental

Samples preparation

For NMR experiments, Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 %mol), Li2CO3-Na2CO3 (52:48 %mol), Li2CO3-K2CO3 (62:38 %mol), Li2CO3-K2CO3 (40:60 %mol) eutectics were synthetized from dried Li2CO3 (99.998%), Na2CO3 (99.997%), K2CO3 (99.997%) powders [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C enriched (99%) (Sigma-Aldrich). Sodium and potassium carbonates are sensitive to moisture, so all mixtures were prepared and stored in a glove box under dried argon. The salt was firstly pressed in an alumina (Al2O3) crucible of 4 mm diameter and 4 mm height, and then placed inside a second magnesium oxide (MgO) crucible of 7 mm diameter and 15 mm height with a lid, which were glued using an alumina paste for better tightness. This system of crucibles has already been described in a previous paper. [START_REF] Zhadan | Transport Properties in Molten Carbonates: Self-Diffusion and Conductivity Measurements at High Temperature[END_REF] For electrical conductivity measurements, the same mixtures of carbonates were prepared from Alfa Aesar, with no [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C enrichment and stored in glove box. The salt was then melted in an alumina crucible of 40 mm diameter and 60 mm height, under air, and then cooled down to be stored in an electric oven at 423 K to prevent from any hydration of samples.

Characterization techniques NMR

High-temperature NMR experiments were performed with the laser heating system developed at CEMHTI, Orleans (France). [START_REF] Machado | Study of NaF-AlF3 Melts by Coupling Molecular Dynamics, Density Functional Theory, and NMR Measurements[END_REF] A Bruker AVANCE I NMR spectrometer (magnetic field of 9.4 T) associated with high temperature probe and two CO2 lasers (λ = 10.6 µm, 250 W) were used. It allows heating the sample crucible from top and bottom sides, insures a good homogeneity of temperature inside the crucible. The power of the lasers is increased slowly to avoid thermal shock of the sample during the experiments.

The spectra at high temperature were recorded on Bruker AVANCE I NMR (9.4 T) spectrometer using single pulse excitation consisting of 15 -90 µs pulses, recycle delays of 0.1 -35 s and 8 -18432 scans to obtain a reliable signal-to-noise ratio for the [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na, 39 K, [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C and [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O nucleus.

The acquisition conditions and Larmor frequencies are presented in Table 1. [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na, 39 K, [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C and [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O NMR measurements were realised at high temperature for Li2CO3-Na2CO3-K2CO3, Li2CO3-Na2CO3, Li2CO3-K2CO3 eutectics mixtures under CO2. [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C chemical shifts were referenced to silicone oil (C6H18OSi2). For 23 Na, [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li and 39 K, 1M aqueous solutions of NaCl, LiCl and KCl were used respectively and water was selected as [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O chemical shits reference.

The silicon oil (PDMS) was used as a secondary reference equal to 0 ppm relative to TMS. Using of PDMS is related to the design features of the high temperature NMR probe and volatility of TMS. Samples were heated up to 1010 K. For each experiment, the acquisition started after 6 min of heating to be sure that the thermal equilibrium inside the crucible was reached.

Self-diffusion coefficients were measured by PFG NMR technique specially adapted for molten salts at high temperature. [START_REF] Rollet | Measuring Self-Diffusion Coefficients up to 1500 K: A Powerful Tool to Investigate the Dynamics and the Local Structure of Inorganic Melts[END_REF][START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] To realise these measurements, a Bruker Diff30 probe adapted for high temperature experiments combined with laser heating was used. High gradient strengths (up to 1000 G/cm for this work) connected with convection-free NMR pulse sequence proposed by Jerschow et al. [START_REF] Jerschow | Suppression of Convection Artifacts in Stimulated-Echo Diffusion Experiments. Double-Stimulated-Echo Experiments[END_REF] were used for self-diffusion coefficient measurements. An example of the attenuation curves is presented in the Supporting Information (Figure S4). This technique is not destructive and does not need any additional treatment of the obtained data.

The self-diffusion coefficients were obtained for [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na and [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C nuclei at different temperatures from the melting temperature up to 1010 K. Short duration of experiment was fixed in order to avoid any overheating of the probe and the spectrometer. For 17 O, the self-diffusion measurements were not possible because of the low abundance of this isotope, and time needed for the experiment. We could not observe the 39 K, with the probe used for PFG NMR, not accessible for it's very low Larmor frequency (18,66MHz).

The measured self-diffusion coefficients versus temperature allows calculating the corresponding activation energies, to explain the mechanism of movement of ions in a molten carbonate.

Electrical conductivity

The electrical conductivity of molten carbonates was measured in the temperature range (373 K to 1023 K) under CO2 at 1 atm. A four-probe technique [START_REF] Simonnet | Electrical Conductivity Measurements of Oxides from Molten State to Glassy State[END_REF] using platinum electrodes combined to a Solartron SI 1260 impedancemeter working in the frequency range from 1 Hz to 1 MHz was used.

The four-probe technique consists of two platinum plates applying a current flow between which two platinum wires measure the voltage drop. This system is well adapted to obtain the electrical conductivity in molten salts at high temperature. [START_REF] Gaillard | Carbonatite Melts and Electrical Conductivity in the Asthenosphere[END_REF][START_REF] Pomier | Methodological Re-Evaluation of the Electrical Conductivity of Silicate Melts[END_REF] To minimize the leakage of molten salt and to protect the oven during the experiments, a system of three crucibles was specially designed for the analysis of molten alkali carbonates at high temperature. [START_REF] Zhadan | Transport Properties in Molten Carbonates: Self-Diffusion and Conductivity Measurements at High Temperature[END_REF] The principal advantages of the four-electrode method as compared to the classical twoelectrode method are that the polarization effects are minimized, especially at high temperature and low frequencies and that the method does not take into account the contribution of the platinum wires at the measured impedance, which is important for highly conductive solutions. [START_REF] Pomier | Methodological Re-Evaluation of the Electrical Conductivity of Silicate Melts[END_REF] The conductivity cell is calibrated using 1 M aqueous solution KCl at room temperature for a depth of immersion of 8 mm of the electrodes in the melt. [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF][START_REF] Lair | Theoretical Predictions vs experimental measurements of the electrical conductivity of molten Li2CO3-K2CO3 modified by additives[END_REF] As an example, Figure 1 shows the complex impedance obtained at 930 K. The first few points where omitted because they are too noisy. This figure shows the Cole-Cole or Nyquist diagram [START_REF] Abelard | Dielectric Relaxation in Alkali Silicate Glasses: A New Intepretation[END_REF] where the opposite of the imaginary part of the impedance is plotted as a function of its real part, and as seen, it presents a semicircle arc at low frequencies followed by a vertical line at high frequencies. The arc of the semicircle corresponds to the residual electrode polarization effects and not to the sample response itself. The negative part at high frequencies is due to inductive phenomena linked to the measuring wires [START_REF] Yoshino | Effects of Pressure and Water on Electrical Conductivity of Carbonate Melt with Implications for Conductivity Anomaly in Continental Mantle Lithosphere[END_REF] . The intersection of this semicircle with the horizontal (real) axis, shown by the red arrow, gives the direct electrical resistance Rdc, which is linked to the direct electrical conductivity by the simple relation 𝜎 = 𝐾/𝑅 , where K is the cell factor [START_REF] Simonnet | Electrical Conductivity Measurements of Oxides from Molten State to Glassy State[END_REF] .

The electrode inductance effects on impedance are calculated for this cell and impedance is corrected using the method detailed in reference. 15 In the literature, we did not find any study on NMR in molten carbonates, but some NMR solid state studies have been published for alkali carbonates at room temperature. Dunstan et al. [START_REF] Dunstan | Ion Dynamics in Li2CO3 Studied by Solid-State NMR and First-Principles Calculations[END_REF] studied the [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O and [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li chemical shifts in lithium carbonate. In their study on solid

Li2CO3 the structure indicates one lithium site and two oxygen sites that are attributed to δ( 7 Li) = 0 ppm and δ( 17 O) at 171.9 and 154.8 ppm. At high temperature, the bond lengths as well as the density can vary, which leads to a slight modification of the chemical shift (~2 ppm). The chemical shifts that we obtained in the liquid state of the four molten eutectic compositions, for [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na, [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, 39 K and [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C, [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O correspond to CO unit at high temperature. The variation of [START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] Transport properties [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na, [START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li and [START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C PFG NMR

As far as we know, this is the first time that the self-diffusion coefficient for Li + , Na + and CO ions in molten alkali carbonates mixtures are reported in the literature. Previous measurements of self-diffusion coefficients were performed by radiotracer techniques. [START_REF] Spedding | Trace-Ion Diffusion in Molten Alkali Carbonates[END_REF] This technique does not allow measuring diffusivity of lithium in molten carbonates, because of the short life-time of radioactive isotopes of lithium. The most recent diffusivity data in molten carbonates were calculated by molecular dynamics simulations by Desmaele et al. [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] In Figure 4, we present a comparison between self-diffusion coefficients measured in our work, for Li + , Na + and CO ions in different mixtures of molten alkali carbonates such as Li2CO3-Na2CO3 (52:48 mol%), Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 mol%), Li2CO3-K2CO3 (62:38 mol%), Li2CO3-K2CO3 (40:60 mol%) with data found in literature. [START_REF] Spedding | Trace-Ion Diffusion in Molten Alkali Carbonates[END_REF][START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF][START_REF] Spedding | Tracer Diffusion Measurements in Mixtures of Molten Alkali Carbonates[END_REF][START_REF] Spedding | An Interpretation of the Concentration Dependence of Mobilities in Fused Alkali Carbonate Mixtures[END_REF] The self-diffusion coefficients increase with temperature in all carbonates compositions. Li + cations diffuse faster regardless of composition. This can be explained simply by the small value of the ionic radius of the Li + cation. Conversely, the lowest diffusion coefficients are obtained for the "large" CO anions. We can thus state that the diffusivity values for Na + are always lower than those for Li + but higher than those for CO , fact that can be explained by their respective sizes.

For lithium, the highest values of self-diffusion coefficient correspond to compositions with the highest percentage of lithium carbonate. Self-diffusion coefficients decrease as: Li2CO3-K2CO3

(62:38 mol%) ˃ Li2CO3-Na2CO3 (52:48 mol%) ˃ Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 mol%) ˃ Li2CO3-K2CO3 (40:60 mol%). In the case of CO it is very difficult to make a correlation with the composition because the diffusivity values are too small (10 -10 m 2 /s). Concerning the sodium cation, a clear difference between the compositions is observed. As in the case of Li + , the autodiffusion coefficients of Na + increase for the compositions where the percentage of lithium carbonate is higher. From these observations, we can conclude that the self-diffusion coefficients are higher when the percentage of lithium carbonate in the mixture increases. Some authors claimed that the CO2 solubility also increases with the temperature and with the percentage of Li2CO3 in the molten carbonates [START_REF] Meléndez-Ceballos | Input on the Measurement and Comprehension of CO2 Solubility in Molten Alkali Carbonates in View of Its Valorization[END_REF] . This fact could be related to the high mobility of Li + cations in liquid carbonates. Self-diffusion coefficients of Li + , Na + and CO were fitted with Arrhenius equation ( 1) to calculate the activation energy, Ea. The results are presented and compared to data obtained by Spedding et al. [START_REF] Spedding | Tracer Diffusion Measurements in Mixtures of Molten Alkali Carbonates[END_REF] in the table 2.

𝐷 = 𝐷 𝑒𝑥𝑝(-) (1)
where D (m 2 .s -1 ) is the self-diffusion coefficient, D0 (m 2 .s -1 ) a pre-exponential factor, Ea (eV) is the activation energy, R (J.K -1 .mol -1 ) the gas constant and T (K) is the absolute temperature. For binary mixtures, the activation energies are quite close for cations and anions given the error bars. This finding was also reported by Spedding et al. [START_REF] Spedding | Tracer Diffusion Measurements in Mixtures of Molten Alkali Carbonates[END_REF] has been explained by the presence of a cooperative mechanism between the cations (Li + , Na + , K + ) and the CO anion in the diffusion process. For ternary mixture, there is a significant difference between the activation energies of Na + , K + and CO showing non negligible increase from Na + to K + , and from K + to CO . Actually, for the CO anion, Ea is approximately twice the activation energy of Li + .

Electrical conductivity measurements

The obtained results of static conductivity for different mixtures of alkali carbonates as a function of temperature are presented in Figure 5 and compared with previous experimental results obtained by Kojima et al. [START_REF] Kojima | Surface Tension, and Electrical Conductivity of Ternary Molten Carbonate System Li2CO3-Na2CO3-K2CO3 and Methods for Their Estimation[END_REF][START_REF] Kojima | Physical Properties of Molten Li2CO3-Na2CO3 (52:48 Mol%) and Li2CO3-K2CO3 (62:38 Mol%) Containing Additives[END_REF][START_REF] Kojima | Electrical Conductivity of Molten Li2CO3-X2CO3 (X: Na, K, Rb, and Cs) and Na2CO3-Z2CO3 (Z: K, Rb, and Cs)[END_REF] Figure 5. Electrical conductivity at 1 bar CO2 from experimental results obtained in this study (squares) and those measured by Kojima et al. [START_REF] Kojima | Surface Tension, and Electrical Conductivity of Ternary Molten Carbonate System Li2CO3-Na2CO3-K2CO3 and Methods for Their Estimation[END_REF][START_REF] Kojima | Physical Properties of Molten Li2CO3-Na2CO3 (52:48 Mol%) and Li2CO3-K2CO3 (62:38 Mol%) Containing Additives[END_REF][START_REF] Kojima | Electrical Conductivity of Molten Li2CO3-X2CO3 (X: Na, K, Rb, and Cs) and Na2CO3-Z2CO3 (Z: K, Rb, and Cs)[END_REF] (dashed lines).

All studied compositions show high electrical conductivities as compared to other molten salts.

The lowest conductivity is observed for the Li2CO3-K2CO3 (40:60 mol%) mixture: at ~1000 K it is about 2.5 times lower than the most conductive Li2CO3-Na2CO3 (52:48 mol%) composition. We can also note the decrease of electrical conductivity with the addition of potassium, effect already observed by Kojima et al. [START_REF] Kojima | Surface Tension, and Electrical Conductivity of Ternary Molten Carbonate System Li2CO3-Na2CO3-K2CO3 and Methods for Their Estimation[END_REF][START_REF] Kojima | Physical Properties of Molten Li2CO3-Na2CO3 (52:48 Mol%) and Li2CO3-K2CO3 (62:38 Mol%) Containing Additives[END_REF][START_REF] Kojima | Electrical Conductivity of Molten Li2CO3-X2CO3 (X: Na, K, Rb, and Cs) and Na2CO3-Z2CO3 (Z: K, Rb, and Cs)[END_REF] We can conclude that the addition of cations with larger radius to the composition of alkali carbonates, decreases the electrical conductivity.

The activation energies and the pre-exponential factors were determined by fitting the Arrhenius equation ( 2) to the electrical conductivity:

𝜎𝑇 = 𝜎 𝑒𝑥𝑝(-) (2)
where σ (Sˑcm -1 ) is the conductivity of molten carbonate, σ0 (Sˑcm -1 ) the pre-exponential factor, Ea (eV) is the activation energy, kb (JˑK -1 ) the Boltzmann constant and T (K) the absolute temperature.

Table 3 shows the obtained results for these two parameters. It can be seen that the activation energies of the four eutectic compositions are very close and in good agreement with those of Kojima et al. [START_REF] Kojima | Surface Tension, and Electrical Conductivity of Ternary Molten Carbonate System Li2CO3-Na2CO3-K2CO3 and Methods for Their Estimation[END_REF][START_REF] Kojima | Physical Properties of Molten Li2CO3-Na2CO3 (52:48 Mol%) and Li2CO3-K2CO3 (62:38 Mol%) Containing Additives[END_REF][START_REF] Kojima | Electrical Conductivity of Molten Li2CO3-X2CO3 (X: Na, K, Rb, and Cs) and Na2CO3-Z2CO3 (Z: K, Rb, and Cs)[END_REF] . The same observation can be noted for the pre-exponential factor 𝜎 . The fact that 𝜎 is nearly constant with composition means that the conductivity is driven by the activation energy Ea in these systems.

Discussion

The electrical conductivity of molten carbonates is related to the transport properties such as self-diffusion. To compare these two properties, we use the concept of the ideal or Nernst-Einstein conductivity (σ NE ) which assumes that the ions move independently in the molten salt, without interacting with each other. This parameter can be calculated using the equation (3).

𝜎 = ∑ 𝑁 𝑧 𝐷 ( 3
)
where q is the elementary charge, s concerns the conduction species (Li , Na + and CO ), Ns is the number of s ions contained in the volume V, zs the conduction charge and Ds the experimental self-diffusion coefficients for the chemical species s. To calculate the molar volume V, we used the densities provided by Kojima et al. [START_REF] Kojima | Surface Tension, and Electrical Conductivity of Ternary Molten Carbonate System Li2CO3-Na2CO3-K2CO3 and Methods for Their Estimation[END_REF] , [START_REF] Kojima | Physical Properties of Molten Li2CO3-Na2CO3 (52:48 Mol%) and Li2CO3-K2CO3 (62:38 Mol%) Containing Additives[END_REF] .

The ideal conductivities were calculated for the different compositions: Li2CO3-Na2CO3 (52:48 mol%), Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 mol%), Li2CO3-K2CO3 (62:38 mol%), Li2CO3-K2CO3 (40:60 mol%) at different temperatures using the self-diffusion coefficients Li + , Na + and CO measured by PFG NMR. The results of the ideal conductivity (σ NE ) compared to the conductivities (σ) measured by impedance spectroscopy are presented in table 4. As we were not able to measure the self-diffusion coefficient of the K + cation by PFG NMR, we have used the simulation results of Corradini et al. [START_REF] Corradini | Insight into the Li2CO3-K2CO3 Eutectic Mixture from Classical Molecular Dynamics: Thermodynamics, Structure, and Dynamics[END_REF] for the mixture Li2CO3-K2CO3 (62:38 mol%) and those obtained by Spedding et al. [START_REF] Spedding | Tracer Diffusion Measurements in Mixtures of Molten Alkali Carbonates[END_REF] by the radio-tracer method for the composition Li2CO3-K2CO3 (40:60 mol%).

From a microscopic point of view, the electrostatic interactions between the different ions plays a major role on the electrical conductivity in molten carbonates. In the absence of these electrostatic interactions, the ionic conductivity would be identical to the Nernst-Einstein conductivity. [START_REF] Gheribi | First-Principles Determination of Transference Numbers in Cryolitic Melts[END_REF] So, the Haven ratio, 𝐻 = (4) defines the total effect of the electrostatic interactions on the conductivity. If this factor is equal to 1, it means that the movements of ions are not correlated and therefore the charge transport must strictly obey the Nernst-Einstein law. In general, in molten salts, H is greater than 1 because of the electrostatic interactions which attenuate the ionic mobility. The results of calculations for Haven ratios are presented in the table 4. [START_REF] Kojima | Electrical Conductivity of Molten Li2CO3-X2CO3 (X: Na, K, Rb, and Cs) and Na2CO3-Z2CO3 (Z: K, Rb, and Cs)[END_REF] , but also depends on the electrostatic interaction between ions in these molten carbonates.

Using Equation 3we can calculate the contribution of each type of ion to the ideal conductivity as a function of composition and temperature. Table 5 presents the results of these calculations.

Recall that the diffusion coefficients of potassium were taken from the literature. [START_REF] Spedding | Tracer Diffusion Measurements in Mixtures of Molten Alkali Carbonates[END_REF][START_REF] Corradini | Insight into the Li2CO3-K2CO3 Eutectic Mixture from Classical Molecular Dynamics: Thermodynamics, Structure, and Dynamics[END_REF] It is interesting to note that the Nernst-Einstein conductivity concerning the carbonate ions (CO ) is less than the sum of the conductivities concerning all the cations, even if the overall negative charge is equal to the overall positive charge (electrical neutrality). Additionally, we see that the electric current is mainly carried by the cations in these alkaline carbonates. [START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] and Carof et al. [START_REF] Carof | Carbon Species Solvated in Molten Carbonate Electrolyser Cell from First-Principles Simulations[END_REF] were not detected by used experimental techniques. These calculated species have a very short lifespan, of the order of a few femtoseconds (10 -15 s), with a very low concentration in the molten carbonate (around 1%), so NMR technique (10 -9 s) and the same for Raman spectroscopy (10 -13 s) do not make it possible to observe species with a much smaller lifespan.

In this work we coupled the electrical conductivity measurement with self-diffusion coefficients to better understand the transport mechanism in eutectic mixtures. Using the Nernst-Einstein relation, we propose that the electrical current is mainly carried by the cations in molten carbonates. Considering the Haven ratio (H), we suggest that the electrical conductivity does not only depend on the radius of cations as reported by Kojima et al. [START_REF] Kojima | Electrical Conductivity of Molten Li2CO3-X2CO3 (X: Na, K, Rb, and Cs) and Na2CO3-Z2CO3 (Z: K, Rb, and Cs)[END_REF] but that the electrostatic interaction between the ions also plays an important role. Finally, we showed that this interaction increases with the amount of K2CO3 in the mixture of carbonates.

Last but not least, we have measured for the first time the self-diffusion coefficients of Li + cations in the different compositions of alkali carbonates in the molten state using the pulse field gradient NMR technique.

Supporting Information

Figure 1 .

 1 Figure 1. Cole-Cole representation of the complex impedance of the Li2CO3-Na2CO3 (52:48 %mol) eutectic point at 930 K. Measured impedance (Z*meas, solid symbols) and corrected impedance (Z*meas -Z"induct, open symbols). The Rdc is indicated by the red arrow.Results and discussion23 Na,[START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, 39 K and 13 C,[START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O NMR spectra At high temperature, when the salt is completely melted, the different ionic species present in the system are in fast exchange (few picoseconds) as compared to the time scale of the NMR measurements (10 -9 s). As a result, a single line is obtained instead of several narrow signals from each chemical species (Figure2and Supporting Information: FiguresS1, S2, S3). Theoretically, the NMR line shape should be Lorentzian, but it is in some cases distorted due to magnetic field inhomogeneities (imperfect 'shims'). The position of this signal or its chemical shift in ppm

Figure 2 .

 2 Figure 2. Evolution of[START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, 39 K and[START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C,[START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O spectra with the temperature for the composition Li2CO3-K2CO3 (40:60 %mol).[START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na,[START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, 39 K and 13 C,[START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O chemical shifts obtained for the eutectic compositions Li2CO3-Na2CO3 (52:48 %mol), Li2CO3-K2CO3 (62:38 %mol), Li2CO3-K2CO3 (40:60 %mol), Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 %mol) at different temperatures are presented in Figure 3. For the different compositions we do not observe any significant changes of the chemical shifts with

Figure 3 .

 3 Figure 3. Evolution of 23 Na (△), 7 Li (◇), 39 K (○) and 13 C (□), 17 O (✱) chemical shifts for the

  O chemical shift with composition indicates only a change of environment (cations) around the oxygen. It can be caused by the different atomic radius of Li + , Na + and K + which in turn effects on the distance O-Cation.

Figure 4 .

 4 Figure 4. Self-diffusion coefficients in eutectic mixtures a) Li2CO3-Na2CO3 (52:48 %mol) , b) Li2CO3-K2CO3 (62:38 %mol) and Li2CO3-K2CO3 (40:60 %mol), c) Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 %mol) obtained by PFG NMR in this work (squares) and measured by Spedding et al. 11,23-25

Table 1 .

 1 Spectrometer's Larmor frequencies and typical acquisition conditions used for high

	temperature NMR experiments.
	Nucleus	Frequency (MHz) at 9.4 T	Natural abundance (%)	Pulse length (µs)	Recycle delay (s)	Number of scans
	7 Li	155.44	92.41	15	35	8

  [START_REF] Papenguth | 13 C MAS NMR Spectroscopy of Inorganic and Biogenic Carbonate[END_REF][START_REF] Dunstan | Ion Dynamics in Li2CO3 Studied by Solid-State NMR and First-Principles Calculations[END_REF] δ( 13 C) is observed at 168.4 ppm for lithium carbonate and 169.8 ppm for sodium carbonate. These values are attributed to CO species and are in good agreement with the values measured in this work in solid carbonates: δ( 13 C) = 169.4 ppm for Li2CO3, 170.8 ppm for Na2CO3 and 170.6 ppm for K2CO3. The difference of 1 ppm could be explained by some impurities in the used carbonates.

Table 2 .

 2 Activation energies (Ea) of the NMR self-diffusion coefficients for the eutectic compositions of carbonates and the values of Ea reported in the literature[START_REF] Spedding | Tracer Diffusion Measurements in Mixtures of Molten Alkali Carbonates[END_REF]

	Composition	Ea(Li + ) (eV)	Ea(Na + ) (eV) Ea(K + ) (eV) Ea(CO ) (eV)
	Li/Na (52:48 mol%)	0.34 ± 0.05	0.30 ± 0.04	-	0.48 ± 0.07
	Li/Na (53.3:46.7 mol%) 24	-	0.48	-	0.50
	Li/K (62:38 mol%)	0.28 ± 0.05	-	-	0.40 ± 0.06
	Li/K (40:60 mol%)	0.37 ± 0.06	-	-	0.30 ± 0.05
	Li/K (42.7:57.3 mol%) 24	-	-	0.50	0.52
	Li/Na/K (43.5:31.5:25 mol%)	0.25 ± 0.04	0.39 ± 0.06	-	0.60 ± 0.09
	Li/Na/K (43.5:31.5:25 mol%) 24	-	0.48	0.44	0.44

Table 3 .

 3 Fit parameters of equation (2) and comparison with Kojima et al. values.[START_REF] Kojima | Surface Tension, and Electrical Conductivity of Ternary Molten Carbonate System Li2CO3-Na2CO3-K2CO3 and Methods for Their Estimation[END_REF][START_REF] Kojima | Physical Properties of Molten Li2CO3-Na2CO3 (52:48 Mol%) and Li2CO3-K2CO3 (62:38 Mol%) Containing Additives[END_REF][START_REF] Kojima | Electrical Conductivity of Molten Li2CO3-X2CO3 (X: Na, K, Rb, and Cs) and Na2CO3-Z2CO3 (Z: K, Rb, and Cs)[END_REF]

	Li/Na (52/48)	This work	Kojima et al. 27-29
	Ea (eV)	0.28	0.29
	ln(𝜎 ) (Ω -1 ˑcm -1 ˑK)	11.92	11.29
	Li/Na/K (43.5/31.5/25)
	Ea (eV)	0.32	0.33
	ln(𝜎 ) (Ω -1 ˑcm -1 ˑK)	11.37	11.32
	Li/K (62/38)
	Ea (eV)	0.32	0.34
	ln(𝜎 ) (Ω -1 ˑcm -1 ˑK)	11.22	11.36
	Li/K (40/60)
	Ea (eV)	0.34	0.31
	ln(𝜎 ) (Ω -1 ˑcm -1 ˑK)	11.13	10.78

Table 4 .

 4 Ideal conductivity (σ NE ), experimental conductivity (σ) and Haven ratio (H) of the molten carbonates at different temperatures. and having a direct effect on the electrical conductivity, despite the high contents of Li2CO3 in the composition. So, the electrical conductivity of alkali carbonates does not only depend to the radius of cations as reported byKojima et al.

	In Li2CO3-Na2CO3 (52:48 mol%) and Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 mol%)
	compositions the values of Haven ratio are close to 1. This allows us suggesting that the ions move
	independently of each other in both salts, which can be directly related to the fact that the electrical
	conductivity values are the highest among the studied compounds. But when adding potassium
	carbonate in the mixture, the H factor increases. For the two compositions of lithium and potassium
	carbonates, we obtained high values of H (1.1 to 1.5), suggesting that the ions in the Li2CO3-
	K2CO3 (62:38 mol%), Li2CO3-K2CO3 (40:60 mol%) mixtures interact with each other hindering

Table 5 .

 5 Ideal conductivities calculated from equation 3 for the different charge carrier's Na + , Li + , K + and CO depending on the composition and the temperature. In this paper, we presented experimental results obtained for molten eutectic compositions of alkali carbonates. From high temperature NMR results we determined the melt speciation in eutectic compositions Li2CO3-Na2CO3 (52:48 mol%), Li2CO3-Na2CO3-K2CO3 (43.5:31.5:25 mol%), Li2CO3-K2CO3 (62:38 mol%), Li2CO3-K2CO3 (40:60 mol%). Only the presence of CO species has been detected whatever composition and temperature. The other carbonate species proposed in theoretical approaches (C O , C O ) by Desmaele et al.

	Composition	T(K)	σ Li + NE (S/m)	σ Na + NE (S/m) σ K + NE (S/m) σ CO 3 2-NE (S/m)
	Li/Na (52:48 mol%)	861 952 1003	57 87 101	51 71 72	---	53 113 138
	Li/K (62:38 mol%)	861 952 1003	70 80 124	---	35 47 55	75 103 99
	Li/K (40:60 mol%)	861 952 1003	25 40 52	---	29 45 61	45 59 76
		861	36	15	15	42

Na,[START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li, 39 K and 13 C,[START_REF] Miyazaki | An Apparatus for Electrical Conductance Measurements with Molten Carbonates[END_REF] O NMR spectra at high temperature; attenuation curves of[START_REF] Bessada | Structural and Dynamic Approaches of Molten Salts by High Temperature Spectroscopies[END_REF] Li,[START_REF] Desmaele | Atomistic Simulations of Molten Carbonates: Thermodynamic and Transport Properties of the Li2CO3 -Na2CO3 -K2CO3 System[END_REF] Na and[START_REF] Rollet | Self-Diffusion Coefficient Measurements at High Temperature by PFG NMR[END_REF] C from PFG NMR at 1003 K (PDF)

ACKNOWLEDGMENT

This work was funded by the French National Research Agency (ANR-17-CE05-0025 project MCEC). Financial support from the IR-RMN-THC FR 3050 CNRS for conducting the research is gratefully acknowledged.

Corresponding Author

Notes

The authors declare no competing financial interest. 2020, 59 (29), 13305-13314. DOI: 10.1021/acs.iecr.0c02281

Table of Contents

SYNOPSIS

Speciation and transport properties in molten alkali carbonate eutectic mixtures were investigated using a combination of high temperature NMR, pulse field gradient NMR and electrical impedancemetry. Electrostatic interactions in molten carbonates are observed and discussed.


Lang Shen

Yifan Zhu

Feilong Mao

Siyuan Gao

Zihao Su

Zhitao Luo

Hui Zhang
email: seuzhanghui@seu.edu.cn

Badreddine Assouar
email: badreddine.assouar@univ-lorraine.fr

Broadband Low-Frequency Acoustic Metamuffler

Keywords: acoustic metasurfaces and metamaterials, acoustic insulation, noise control

In this research, we propose and design an acoustic metamuffler (AMM) by coupling a micro-perforated plate and a composite waveguide formed by a main waveguide and a Helmholtz resonator. The proposed mechanism and the deliberately designed structure are conducive to generating multimode resonances which help to improve the coupling absorption effect and lead to a broadband (4 octaves) sound insulation. We develop an effective circuit model to analytically predict the insulation bandwidth and put forward numerical and experimental measurements that demonstrate the effectiveness of the proposed concept. The designed AMM produces sound insulation with an average of 20 dB of sound transmission loss at a low frequency range extending from 100 to 1600 Hz while having an ultrathin thickness of 6.2 cm (1/55λ for the lowest working frequency). Our findings could have pragmatic applications for acoustic insulators or absorbers.

I. Introduction

In acoustic engineering, it is a key scientific problem to understand how to achieve low frequency and broadband noise cancellation with small thickness, while maintaining air circulation or ventilation. Traditional sound-absorbing materials and sound barriers not only need huge structural sizes (windows, walls, etc.) to eliminate low frequency noise, but also cannot guarantee air circulation while eliminating noise [START_REF] Yu | A numerical investigation on the sound insulation of ventilation windows[END_REF]. Acoustic metamaterials [START_REF] Cummer | Controlling sound with acoustic metamaterials[END_REF][START_REF] Ma | Acoustic metamaterials: From local resonances to broad horizons[END_REF] and acoustic metasurfaces [START_REF] Assouar | Acoustic metasurfaces[END_REF] can achieve the regulations of low-frequency acoustic waves with subwavelength structural sizes, such as negative refraction, acoustic stealth, acoustic abnormal reflections, etc. [START_REF] Li | Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces[END_REF][START_REF] Zhao | Manipulating acoustic wavefront by inhomogeneous impedance and steerable extraordinary reflection[END_REF][START_REF] Zhao | Redirection of sound waves using acoustic metasurface[END_REF]. Thanks to the great success of acoustic metamaterials and acoustic metasurfaces for low-frequency acoustic wave manipulations, various meta-structures have been applied to the design of sound absorbers for the application of the noise control field [START_REF] Li | Acoustic metasurface-based perfect absorber with deep subwavelength thickness[END_REF][START_REF] Huang | Acoustic perfect absorbers via spiral metasurfaces with embedded apertures[END_REF][START_REF] Donda | Extreme low-frequency ultrathin acoustic absorbing metasurface[END_REF]. By employing local resonance and Fano resonance [START_REF] Wu | High-efficiency ventilated metamaterial absorber at low frequency[END_REF][START_REF] Li | Broadband compact acoustic absorber with high-efficiency ventilation performance[END_REF][START_REF] Ghaffarivardavagh | Ultra-open acoustic metamaterial silencer based on fano-like interference[END_REF], sound waves within a certain frequency range can be dissipated and absorbed in the structures, and such designs make it possible for the subwavelength meta-structure to regulate low-frequency sound waves, which provides a different strategy for low frequency acoustic wave manipulations.

Considering that noise is usually broadband, the realization of low frequency broadband noise cancellation has always been the focus and difficulty of research. The emergence of the coupling structure of multiple resonant modes with optimized structural resonance and acoustic interference provides a different design methodology for broadband sound cancellation [START_REF] Huang | Compact broadband acoustic sink with coherently coupled weak resonances[END_REF][START_REF] Zhu | Broadband ultra-thin acoustic metasurface absorber with coiled structure[END_REF][START_REF] Zhu | Nonlocal acoustic metasurface for ultra-broadband sound absorption[END_REF][START_REF] Dong | Ultra-broadband acoustic ventilation barriers via hybrid-functional metasurfaces[END_REF]. Even so, achieving low frequency and broadband sound cancellation under airflow conditions [START_REF] Wu | High-efficiency ventilated metamaterial absorber at low frequency[END_REF][START_REF] Li | Broadband compact acoustic absorber with high-efficiency ventilation performance[END_REF][START_REF] Ghaffarivardavagh | Ultra-open acoustic metamaterial silencer based on fano-like interference[END_REF][START_REF] Dong | Ultra-broadband acoustic ventilation barriers via hybrid-functional metasurfaces[END_REF][START_REF] Zhang | Omnidirectional ventilated acoustic barrier[END_REF][START_REF] Lee | Ultrasparse acoustic absorbers enabling fluid flow and visible-light controls[END_REF][START_REF] Sun | Broadband acoustic ventilation barriers[END_REF] remains a challenge.

In this paper, we propose and demonstrate an acoustic metasurface muffler (AMM) to achieve low-frequency wideband noise elimination. In a prior study [START_REF] Zhang | Tunable acoustic filters assisted by coupling vibrations of a flexible Helmholtz resonator and a waveguide[END_REF], it was illustrated that the tunable acoustic filters can be realized by a composite waveguide consisting of a Helmholtz resonator and the main waveguide. Here, we combine the composite waveguide [START_REF] Zhang | Tunable acoustic filters assisted by coupling vibrations of a flexible Helmholtz resonator and a waveguide[END_REF] with micro-perforated plate [START_REF] Maa | Potential of microperforated panel absorber[END_REF][START_REF] Yu | Hybrid silencers with micro-perforated panels and internal partitions[END_REF][START_REF] Kang | Feasibility of applying micro-perforated absorbers in acoustic window systems[END_REF] as the building block of the AMM to improve the bandwidth of sound insulation. The designed coupled structure helps to increase the resonant mode density of the system [START_REF] Yang | Optimal sound-absorbing structures[END_REF], especially at very low frequencies. Based on the principle of acoustic absorption interaction and multi-parameter resonance units, a low-frequency broadband noise elimination is achieved. We first analyze the coupled structure theoretically by developing effective circuit models (acoustic-electric analogy [START_REF] Kinsler | Fundamentals of Acoustics[END_REF]). Then, the effectiveness of the proposed theory is verified through simulation and experiment. Through theory, simulation and experiment, it is proved that this structure can achieve broadband noise cancellation within the range of 100-1600 Hz (the average noise cancellation amount is higher than 20 dB), and its thickness is only 6.2 cm. The proposed mechanism based on the coupled structure can lead to an ultra-broadband (4 octaves) sound insulation, that outperforms previous broadband designs [START_REF] Huang | Compact broadband acoustic sink with coherently coupled weak resonances[END_REF][START_REF] Zhu | Broadband ultra-thin acoustic metasurface absorber with coiled structure[END_REF][START_REF] Zhu | Nonlocal acoustic metasurface for ultra-broadband sound absorption[END_REF][START_REF] Dong | Ultra-broadband acoustic ventilation barriers via hybrid-functional metasurfaces[END_REF]. In addition, putting a micro-perforated panel in a series connections introduces an additional trade-off between ventilation performance and sound insulation, since the microperforated plate may block part of the fluid under flowing-fluid-filled circumstances [START_REF] Dong | Ultra-broadband acoustic ventilation barriers via hybrid-functional metasurfaces[END_REF]. We therefore have evaluated and optimized the ventilation performance in our case. The most critical factor affecting the ventilation performance of AMM is the ventilation area. Through calculation, it can be concluded that the minimum ventilation area of the AMM designed in this work is about of 81 mm 2 , accounting for about 13% of the cross-section area.

II. RESULTS

A. The coupled silencing structure

As shown in Fig. 1 (a), we draw a conceptual diagram of AMM, that consists of a coupled structure connected by a micro-perforated plate layer and a composite waveguide layer. The structure is a square with a side length a=70 mm and total thickness 𝑯 = 𝒉 𝟏 + 𝒉 𝟐 + 𝒉 𝟑 . Here 𝒉 𝟏 = 𝟐 mm is the thickness of the micro-perforated plate. 𝒉 𝟐 = 𝟐𝟎 mm is the thickness of the mid-air layer. 𝒉 𝟑 = 𝟒𝟎 mm is the thickness of the composite waveguide layer. The pore diameter of the top micro-perforated plate is r=0.3 mm, and the perforation rate is 𝝈 = 𝝅𝒓 𝟐 𝒑 𝟐 ⁄ = 0.4%. The outer parameters of the four units (four units) at the bottom are the same.

For clarity, the composite waveguide layer is detached to show the details of its inner structure.

It has four kinds of composite waveguide units with different parameters. In each unit, the cross-sectional area of the acoustic main waveguide and the length of the neck is S1 = 4×30 mm 2 and l=4 mm respectively. The other parameters for four units are shown in Table 1 (S2 is the cross-sectional area of the necks, V is the volume of the Helmholtz cavity). To make the AMM have a broadband muffling effect, each unit has a different sound absorption and isolation frequency band. In addition, on the surface of the structure, we also designed a micro-perforated plate structure whose anechoic frequency band is just complementary to the composite waveguide layer. As it will be shown in Fig. 1(b), four composite waveguides are conceived explicitly so that each one has its contribution (highefficient dissipation or resonance), and they collectively provide a remarkable sound blocking over a wide frequency range, while the whole structure features a subwavelength thickness.

B. Theoretical model

The coupled silencing structure is shown in Fig. 1(a). Based on the theoretical analysis, the impedance of the micro-perforated plate is calculated according to the acoustic-electrical analogy method, and then the acoustic transmission characteristics of the resonant structure are calculated by using the local analysis method, to obtain the sound transmission loss (STL) of the whole structure. The STL of the coupling structure is determined by the following formula:

𝑆𝑇𝐿 = 10 log $% 1 𝑡 & (1) 𝑡 & = 4 4𝑐𝑜𝑠 ' (𝑘 ' 𝐷) + ? 𝑍 ' + 𝑍 % ' 𝑍𝑍 % A ' 𝑠𝑖𝑛 ' (𝑘 ' 𝐷) (2)
where 𝑡 & is the transmission coefficient of sound intensity, 𝑘 ' = 2𝜋𝑓/𝑐 % is wave number, 𝐷 is the width of the structure, 𝑓 is the frequency of the incident sound wave, 𝑍 = 𝜌 % 𝑐 % is the characteristic impedance of air, 𝑍 % is structural impedance, where 𝜌 % =1.21 kg/m 3 , 𝑐 % =343 m/s represent air density and sound velocity in air, respectively.

By using the acoustic-electric analogy, we can calculate the relationship between the acoustic impedance of the structure and the parameters of each structure. It can be seen from Fig. 2(a) that the whole structure satisfies the conditions.

𝑃 % = 𝑃 $ + 𝑃 ' (3)
The complex impedance of each part is assumed to be 𝑍 $ and 𝑍 ' .

𝑍 % = 𝑍 $ + 𝑍 ' (4)
We can figure out the magnitude of 𝑍 $ and 𝑍 ' .

𝑍 $ = 𝑅 $ + 𝑗X ($ -𝑗𝑋 )$ (5)
where the waveguide and micro-perforation plate can be regarded as an inductor 𝐿 in series For the micro-perforated plate structure, we can simply calculate its acoustic transmission loss curve. When the aperture of the micro-perforated plate is small, its impedance 𝑍 $ can be expressed as [START_REF] Maa | Potential of microperforated panel absorber[END_REF]:

𝑍 $ ≈ 4 3 𝑗𝜔𝜌𝑡 + 32𝜌𝜇𝑡 𝑑 ' (7)
The acoustic transmission loss of the micro-perforated plate structure can be calculated by the following formula.

𝑆𝑇𝐿 = -20 lg ?1 + 𝑍 $ 𝜎 2𝜌𝑐 A ( 8
)
The green circles line in Fig. 2(b) can be obtained by numerical calculation. The results show that the designed micro-perforated plate structure has good noise reduction performance, and the sound reduction effect is significantly improved within the wider frequency range from 0 to 2000 Hz, theoretically.

For the composite waveguide structure, the calculation formula of the acoustic transmission loss can be obtained as follows.

𝑡 & = 1 1 + 𝜌 ' 𝑐 ' 4𝑆 ' ' 𝑋 0 ' (9)
where 𝑋 0 = 𝜔𝜌𝑙 𝑆 ' ⁄ -𝜌𝑐 ' 𝜔𝑉 ⁄ . The STL of the composite waveguide structure can be obtained by combining Eq. ( 9) with Eq. ( 2). Based on Eq. (1) to Eq. ( 9), we find that the sound transmission loss of AMM highly depends on the parameters of both the micro-perforated panel and the waveguide. Thus, the reasonable design structure parameter can lead to a planar and optimized sound insulation spectrum, considering the coupling effect between structures. This is due to the resonance of the composite waveguide. As the frequency of the noise increases, the effect of micro-perforated plates becomes even more dramatic. According to our design, when the frequency exceeds 1100 Hz, the micro-perforated plate plays a major role in sound absorption and insulation in the coupling structure.

In brief, the AMM can realize the broadband noise elimination because of the existence of the resonance peak for the composite waveguide and the assist of the micro-perforated plate.

Through the above analysis, it is proved that broadband acoustic suppression comes from the coaction of the four coupled resonant chambers. Empowered by the coupling effect, our muffler has a wide noise attenuation bandwidth. Compared with the noise cancellation structure designed solely by interference [START_REF] Yang | Slow-wave metamaterial open panels for efficient reduction of low-frequency sound transmission[END_REF] or dissipation [START_REF] Kumar | Labyrinthine acoustic metastructures enabling broadband sound absorption and ventilation[END_REF] mechanism, our advantage lies in making full use of the synergistic effect of resonance and dissipation to achieve low frequency and broadband noise cancellation.

C. Numerical simulation and experimental demonstration

The designed coupled silencing structure is numerically simulated by using the "Pressure Acoustics, Frequency Domain" module of COMSOL Multiphysics, in which the frequency domain study is performed to calculate the sound transmission through the coupled silencing structure. To be consistent with experimental conditions and estimate its low-frequency behavior under plane wave incidence, the designed coupled silencing structure is emplaced in a cylindrical waveguide, both the waveguide wall and coupled silencing structure are considered acoustically rigid in the physical field settings. To avoid the effects of reflected waves, both ends of the waveguide are set as plane-wave radiation boundaries while the incident wave is plane wave and acoustic pressure amplitude is set as 1 Pa. Because there are tiny structures inside, we choose these regions as "Narrow Region Acoustics" in COMSOL, which can simulate the acoustic structures considering visco-thermal loss. caused by coupling resonance of different composite waveguides, respectively, and the additional cavities formed by micro-perforated and composite waveguides. In addition, it can be seen from Fig. 3(a) that the composite waveguide structures play a major role in different vibration modes, which is related to our parameter design. For mode 4 (1104 Hz) in Fig. 3, we find that the acoustic pressure amplitude is large not only in the third composite waveguide but also in the mid-air layer. It means the cavity of the mid-air layer between the micro-perforated plate and the composite waveguide is also resonant at 1104 Hz. Mode 4 is caused by the coupling resonant of the mid-air layer and the composite waveguide. For mode 5 (1300 Hz) in Fig. 3, we find that the composite waveguide is no longer resonant. The resonance only occurs in the mid-air layer. This is consistent with the theoretical results of the acoustic-electric analogy analysis. Figure 3(b) shows that improper selection of the parameters will reduce the STL of the structure, and the selection of the aperture of the micro-perforated plate has a great influence on the middle and high frequencies (mode 4 and mode 5). A comparison for parameters r=0.3 mm and r=0.6 mm show that r=0.3 mm has higher efficiency, that we choose this optimized radius as the final design. We also plot the curve for the structure with only micro-perforated plate in Fig. 3(b) as a reference. The comparison shows that the designed AMM has higher STL efficiency than micro-perforated plate. Meanwhile, the standard impedance tube system was used for the experimental measurement, and the double load method [START_REF] Sun | Broadband acoustic ventilation barriers[END_REF] was used for the measurement, where the sample is fixed firmly with clamps in the impedance tube. The experimental setup, consistent with that adopted in numerical modeling, is schematically illustrated in Fig. 4 As can be seen from Fig. 4(c), the theoretical prediction shows excellent agreement with numerical and experimental results, demonstrating the effectiveness of our design. The designed AMM sample blocks more than 90% of incident sound energy in the range of 100-1600 Hz (experimental data). In Fig. 4(c), caused by the resonance of the composite waveguide, there are multiple peaks within 100-1600 Hz. Meanwhile, the dissipation effect of the micro-perforated plate makes the coupling muffler structure keep a high muffler capacity.

More specifically, harnessing the power of dissipation in combination with resonance remarkably lowers the onset frequency in the current design. It is noted that the 'sampled' frequencies do not exactly coincide with the peaks. This is because modes 1-5 are inevitably affected by the coupling resonances between composite waveguides and mid-air layer.

However, we consider that this effect is not obvious in the case of very low sound frequency (modes 1-3), because the resonance frequency for the mid-air layer is between modes 4-5.

For the optimization of the frequency band, the design of the fine-distributed composite waveguide is critical in the proposed AMM. In the current study, we theoretically choose 200 Hz, 400 Hz, 700 Hz, and 1100 Hz as four targeted resonant frequencies as shown in Fig. 3

(b).

From mode 5 in Fig. 3, the resonant frequency for the mid-air layer is 1300 Hz. These five frequencies lead to the final broadband absorption spectrum from 100 Hz to 1600 Hz. Different unit cells are deliberately designed to have a continuous bandwidth. The resonant frequency of the composite waveguide is mainly decided by the parameters of Table 1.

III. Conclusion

We have theoretically and experimentally introduced an analytical model to design an acoustic metamuffler. The acoustic-electrical analogy method has been applied to the theoretical analysis, and the FEM results have shown a good agreement with the experimental measurements. We have investigated an alternative metastructure composed of a composite waveguide and a micro-perforated plate. To illustrate the proposed concept and underlying physical mechanism, we have combined theory and experiment to achieve a broadband ventilated metamuffler operating at the low frequency of 100-1600 Hz, featuring a deepsubwavelength thickness. We have shown that the designed metastructure helps to enlarge the bandwidth and strengthen the effectiveness of the sound insulation at a low frequency regime.

FIG. 1 .

 1 FIG. 1. (a) Schematic diagram of AMM and the unit composition. (b) The composite waveguide units have a different internal size and are divided into three parts: the waveguide, the neck, and the Helmholtz cavity. (c) The composite waveguide layer is composed of four units.

  with a resistor 𝑅 at low frequencies, Meanwhile, the Helmholtz resonator (HR) cavity and the cavity-backed are equivalent to a capacitor 𝐶. 𝑋 ( = 2𝜋𝑓𝐿 and 𝑋 ) = $ '+,) express inductive and capacitive reactance. 𝑗 represents the imaginary unit. Analogous to acoustics and electricity: 𝐿 = 𝜌𝑙/𝑆 ' , 𝐶 = -! . ! / ! " , 𝑉 % is the volume of the Helmholtz cavity.

FIG. 2 .

 2 FIG. 2. (a) Acoustic-electrical analogy of acoustic metasurface muffler. The left figure is for acoustic metasurface muffler. The middle one is for micro-perforated plate. The right one is for composite waveguide. (b) The relation of transmission loss and the frequency for the microperforated plate with different mid-air layer thickness (rhombus, circle, and square correspond to h2=10 mm, 20 mm, and 30 mm, respectively.) and different composite waveguides of units 1-4, corresponding to blue, orange, yellow, purple lines, respectively.To further explore the underlying working mechanism, as shown in Fig.2(a), we established the acoustic-electric analogy model of the coupled anechoic structure and obtained the changing relationship of the sound transmission loss of each part of the structure with frequency according to the acoustic local analysis method. In Fig.2(b), here we focus on the following four frequency points of 202 Hz, 403 Hz, 698 Hz, and 1104 Hz corresponding to units 1-4, at which the capability of the coupled muffler is dominated by sound absorption induced by the visco-thermal loss and also reflection by the effective impedance mismatching.

FIG. 3 .

 3 FIG. 3. (a) Sound field distribution in the structure at the frequencies of 202 Hz, 403 Hz, 698 Hz, 1104 Hz, and 1300 Hz, respectively, denoted as modes 1-5. Incident directions are marked by arrows and incident pressure is marked by Pi in the figure. (b) Simulation diagram of the STL curve of the AMM (r=0.3 mm and r=0.6 mm) and micro-perforated (r=0.3 mm). Modes 1-5 are marked in the figure. (c) The simulations considering the mid-air layer with different thicknesses of h2=20 mm and h2=30 mm, respectively.

Figure 3 (

 3 Figure 3(a) shows the acoustic pressure amplitude distributions for different modes (modes 1-5). Incident directions are marked by arrows and the incident pressure is marked by Pi in the figure. According to the previous analysis, modes 1-3 (202 Hz, 403 Hz, 698 Hz) are mainly

Figure 3 (

 3 c) shows the simulation considering the mid-air layer with different thicknesses with h2=30 mm and h2=20 mm, respectively. Combining the results in Fig.3(c) and Fig.2(b), we find that the STL is increasing with the mid-air layer thickness. Considering the tradeoff of sample thickness and the sound insulation, we choose h2=20 mm in the sample fabrication.

FIG. 4 .

 4 photosensitive resin via 3D printing is shown by the inset in Fig.4(b). The relevant results are shown in Fig.4(c). The parameters of the structure are consistent with those used in theoretical calculation.

Table 1 .

 1 Structural parameters of the composite waveguide

		Unit 1	Unit 2	Unit 3	Unit 4
	S2 (mm2)	1×1	2×2	3×5	5×7.5
	V (mm3)	18000	18000	22500	22500

Acknowledgments

The authors acknowledge the financial support provided by the National Natural Science Foundation of China (No. 11874110).


Virginie Privas-Bréauté

Maud Ciekanski

Nicolas Molle

Carmenne Kalyaniwala

Kossi Seto

Presentation at Eurocall

Introduction

In the last decade, Virtual Reality (VR) has been increasingly studied and used for educational purposes [START_REF] Mellet-D'huart | Réalité virtuelle et apprentissage[END_REF][START_REF] Gobin Mignot | Former avec la réalité virtuelle[END_REF]. Whilst this technology is highly adapted for technical skills training such as flying an aircraft or performing surgery, simulations through VR with language learners seem less relevant at first sight.

However, previous work has highlighted numerous potentials, especially for the development of language skills which requires a rich contextualisation to ensure the necessary input and intake processes for aural/oral skills acquisition [START_REF] Pekarek Doehler | L2 Interactional Competence as Increased Ability for Context-sensitive Conduct: A Longitudinal Study of Story-openings[END_REF]. First, the human/machine interactivity allows to give the illusion of reality via sensory-motor elements [START_REF] Fuchs | Virtual reality headsets: a theoretical and pragmatic approach[END_REF]. Then, VR provides immersion, which refers to the stimuli produced by the VR device and their perceived degree of faith to reality. Finally, VR triggers a feeling of presence which is very specific [START_REF] Steuer | Defining virtual reality: dimensions determining telepresence[END_REF][START_REF] Slater | Taking steps: the influence of a walking technique on presence in virtual reality[END_REF][START_REF] Bouvier | La présence en réalité virtuelle, une approche centrée sur l'utilisateur[END_REF]. For [START_REF] Sheridan | Musing on Telepresence and Virtual Presence[END_REF], virtual presence refers to the feeling of being physically present in a synthetic environment.

These three affordances combined, if they are not hindered by latency and sensory-motor inconsistencies, are a strong catalyst for learning by developing a total commitment from the user [START_REF] Molle | La réalité virtuelle comme vecteur d'immersion pour apprendre les langues[END_REF], physically, emotionally, and cognitively, since the learner is totally engaged in the accomplishment of a task. Therefore, the benefits for learning are major: the sensory information input places the learner in an authentic situation which, instead of being a simple observer of his/her learning, will then become the actor of it, without having to resort to his/her imagination. VR also makes it possible to test the reality of a situation without taking any risks, thus building confidence [START_REF] Borona | The use of 3D multi-user virtual environments in computer-assisted second language learning: a systematic literature review[END_REF]. At last, the recording and reversibility of actions are training elements because they allow both feedback and the possibility of (re)testing other strategies under the same conditions. However, unlike specific resources designed for the development of technical vocational skills, there are few VR resources aimed at professions with a significant language component (eg.

tourism trade, real estate trade, rights trade...). We were therefore interested in free mainstream resources that provide a sufficiently rich vocational context for students with specific language objectives. In such situations, specialized discourses are of utmost importance. Our understanding of the expression "specialized discourses" relies upon the definition by Moirand & Tréguer-Felten as discourses constrained by an enunciation situation, which can be related to a professional social place1 and which imply the transmission or exchange of theoretical or practical, declarative or procedural, or even experiential information or knowledge, between enunciators or interactants who have a socio-professional status or a defined social position, and whose message has a precise pragmatic aim2 .

We have sought to identify professional social places virtualized by VR applications, the results of which are presented as a taxonomy for teachers in English Professional Purposes (EPP). As mainstream VR applications are mostly designed for leisure purposes, we will discuss their integration into formal learning through the predominant role of educational scenarios that some applications require if they are used in a language teaching/learning context. We will show the value of VR in supporting situated learning specific to professional situations, as well as their potential for soft skills development. The results open the floor for questions that discuss whether VR applications are indeed a complementary resource among other authentic resources used in the classroom and whether they lead to a renewal of language learning practices.

Specificities of VR settings for EPP

VR may allow students to better immerse themselves in a professional situation by requiring their full attention, with the 360° view facilitated by the wearing of a VR headset [START_REF] Berti | You can almost feel like you are in the place presented': Implementing Virtual Reality in the Language Classroom[END_REF] as described below.

Multimodal professional situated language learning

Beyond the exposure to the language, the communicative situation and the type of discourse influence the "learning opportunities" that learners can seize. Professional situations can constitute in themselves an enabling environment for the development of skills, particularly language skills. If [START_REF] Lave | Situated Learning: Legitimate peripherical participation[END_REF] emphasise the importance of guidance from peers or experts for learning to take place in a situation, [START_REF] Rogoff | Apprenticeship in Thinking[END_REF] shows that situated learning is based on three particular learning modalities: observation, participation and imitation (we will illustrate these learning modalities later on using the example of tourism students in Tables 2 and3).

Moreover, [START_REF] Larsen-Freeman | Complex Systems and Applied Linguistics[END_REF] and [START_REF] Tomasello | Constructing a Language: A Usage-Based Theory of Language Acquisition[END_REF] highlight the fundamental role of cognitive, metacognitive, and social strategies at work in language immersion: focusing attention, understanding the communicative intention of speakers, mobilising formal categories of language, detecting language structures, imitating, identifying novelty, using the support of other interactants (Larsen-Freeman & Cameron, 2008: 118).

VR affordances can support the learner's attention because they sustain the development of language professional skills in a very relevant way as explained in [START_REF] Molle | La réalité virtuelle comme vecteur d'immersion pour apprendre les langues[END_REF] by means of interactivity, immersion and the sense of presence provoked by the VR device. VR resources allow learners to use a variety of modes to explore the virtual space: textual, verbal, visual, iconic, graphic, to which are added the haptic and spatial modes which contribute to the feeling of presence. Communication is thus highly multimodal since it mobilises between five and seven different modes depending on the resource. Multimodality favours perceptual-motor activities and contributes to the understanding of the explored place, by placing learners at the centre of their experience. As Norris (2020: 17) reminds us of, the different modes and modalities are interrelated in the users' perception of them ("chains of modes and modalities") and act in support of linguistic and language intakes. Multimodality would participate in users' attention according to different combinations specific to individual strategies and according to communication situations during which learners can modify their "modal density" [START_REF] Norris | Multimodal discourse analysis: a conceptual framework[END_REF], by favouring certain modes and modalities at a given moment of their simulation.

The multimodality of VR settings can particularly enhance the complex aural comprehension process, which is highly cognitive, but also very volatile and based on immediate reactivity.

Aural skills depend on a semantic representation which is very context-dependent and rely on the use of different memory capacities. Those skills also require a significant amount of extralanguage knowledge (ideological, cultural, and encyclopaedic). The contextualization of the learner in the professional setting via hedonomic affordances may then sustain the use of appropriated strategies, in particular socio-affective strategies such as self-reinforcement, cooperation, and so on. Thus, the contextualization that VR environments promote facilitates memory, stimulates gestural and body activity, and arouses emotions. Soft skills thus may enable a better use of cognitive and metacognitive strategies and favour the control of the affective dimension accompanying all learning.

Being engaged in a highly sensory and emotional experience

The bodily experience that users have refers to the stimuli produced by the VR device and their perceived degree of fidelity to reality. This produces an embodied experience which associates images and feelings with the more objective elements that are the information to which one is exposed. Recent work in neuroscience shows the interrelation between cognition, emotion, and behavior, with the concepts of emotional thinking and embodiment (Immordino-Yang, 2016).

Although these three elements influence one another, emotion remains the main element as a mediator of cognition and behavior. Furthermore, for embodied cognition theories, the knowledge to be acquired is related to the learner's physical experiences. Cognition would be anchored in the experiences of individuals and their appropriation of the environment in which they are situated. There is thus a very strong link between the body, perception, and action [START_REF] Chaker | User Experience of a 3D Interactive Human Anatomy Learning Tool[END_REF][START_REF] Gadille | The Embodiment Dimension while Learning and Teaching in a Virtual World[END_REF].

Taxonomy of the VR apps and their use in EPP

Context of the study

Many applications found with Oculus (the device we have used in the context of this present study) refer to numerous categories (such as entertainment or games for example) sorted out depending on their genres: educational, documentary and history, simulation, exploration, art and creativity, adventure, action, puzzle, shooter, social, casual, travel. Our choice of an app.

for an English/language course is always guided along two criteria: the application must a.be free of charge, and b. offer authentic communication situations that we can use for professionalizing purposes in humanities and social sciences. The professionalizing courses we provide at the University of Lorraine and in which we have introduced VR settings are, for instance, History, Geography, Tourism, Real estate and Heritage law, Art history, Business and management.

Genres

Numerous applications have been used to facilitate training in both language and communication competences and soft skills. We identified more than 25 resources 12 of which are presented in Table 1, classified along the genres defined by Oculus.

Documentary and history

Simulation

Art All these applications are mainly used individually. Yet, since communication involves having people to interact with, as language teachers, it is important for our team to use these apps differently to imply verbal and non-verbal interactions. In such contexts, users can adopt three kinds of postures: spectators, actors, and spect-actors. It is crucial for us that they adopt all these postures and not only one among them. Furthermore, our goal being professionalizing students, we choose apps that permit to reach this purpose. Indeed, there are very few apps that can both enable students to learn the language and use it in a professional context. So, we choose free and accessible entertaining resources that involve social practices, and we often incorporate an educational scenario, a course design that helps us reach the objectives: professionalize our students and teach/learn English at the same time. Some apps can be considered as modelresources, others as resources that need to be enriched (in this case, we resort to multimodality and scaffolding) and a last category can be seen as resources to produce. Table 3 presents the development of skills through the same apps after course design, therefore after being enriched. Table 3: Applications as regards language and soft skills development after course design.

Development of language, communication, and soft skills

Applications

These possible course designs enable to enrich the resources and train the students in language/communication and soft skills that would serve them in their future jobs. As a matter of fact, we think that it is crucial for language teachers to train students to developing language skills as well as soft skills. In an even more competitive world, employers are particularly sensitive to the capacity of recruits to empathize, lead, take initiatives, collaborate and so on.

Therefore, VR apps provide us with quasi real-life situations in which students/ users can imitate a discourse that might then be reproduced.

Discussion

Our The effects that are targeted with the apps as seen in the example with students in tourism mainly revolve around:

understanding the guided tour as a social practice to be experienced (as both a tourist and a guide)

highlighting the important elements of the guide's discourse: mentioning the names of monuments in both languages, at what moment, how to attract attention, the role of anecdotes and the link with them getting a better understanding of the eco-drive learning elements So, not only does VR allow to create a context in which to act but it also develops an embodiment associating emotions and cognition, essential to a tourist guide as developed here.

Virtual reality, once it has been refashioned, repurposed, and managed by users, VR becomes a catalyst for language learning and even more. The users can act in and on the environment since they can collaborate and interact with the space to transform it. So, they develop soft skills.

Limitations

Our study has shed light on the potentials of VR (triggered by its contextualizing power) as well as its limitations. For instance, the scenarios provided for by the creators of the apps are often poor because they are based on a linear unfolding. So, we need to enrich them and incorporate tasks and problem-solving activities to help students reach professionalizing goals in English.

Our recommendations

Considering what we observed, our recommendations for language teachers aiming at using VR in their courses are as follows:

repurposing the apps to require more agency from the learner/ user and encourage interaction implementing a strong educational scenario depending on what and why we want to use the apps (this is task-dependent, therefore enriching the types of tasks is crucial)

-Using their creativity and relying on their students' creativity

Conclusion

To conclude, Virtual Reality is seen as an asset in language learning: learners are placed in realistic communication situations and have the chance to live extraordinary adventures. As a simulated experience, VR increases learners' cognitive, emotional, and physical engagements.

Despite the limitations to the use of VR in education [START_REF] Chateau | Adding virtual reality to the university self-access language centre: brave new world or passing fad?[END_REF], VR is a promising

  research team has been working on IVE and VR in language training contexts since 2018 and since 2019 we have been looking to integrate the use of VR in the professional paths of LANSOD students in English (law in particular). The interest in terms of research and training is to reflect on the nature of the simulations linked to professions in humanities and in which oral communication skills in context are central. VR thus makes it possible to literally project oneself into the communication situation to be mastered, whether it is a real estate visit or a guided tour as in the example we have developed. It is in this perspective that we have made an inventory of the existing resources on Sansar. The proposed resources are very heterogeneous in their nature, especially in terms of what the user can do (passive user/consumer or active user/actor). Based on what the resource allows the user to do, we have selected a progression articulating the three postures mentioned above: the spectator posture (step 1), the spect-actor posture (step 2) and the actor posture (step 3), as shown in the table.

Table 1 :

 1

	and creativity	Exploration

Genre typology for virtual resources

Genres are not mutually exclusive. For instance, Blitz, in which you board on a plane during the Blitz in 1943, has a documentary and historical objective but can also be classified as an exploration tool.

Table 2

 2

	Applications	Language/	Soft skills developed
		communication skills developed
	Nefertari: Journey to	Listening skills	Management of emotions:
	Eternity		astonishment, anxiety,
	This app. enables users		empathy. As soon as students
	to visit Queen Nefertari's		are equipped with VR
	tomb and listen to		helmets, they are
	explanations in English		overwhelmed with emotions
	about its history.		(be they positive or negative,

presents the apps that any teacher can use with students in tourism classified along the skills we think they develop before course design. They are given as examples for how they can be used in EPP.

Table 2 :

 2 Applications as regards language and soft skills development before course design.

Our emphasis. This so-called "professional social place" is meaningful in a context of VR since Immersive Virtual Environments (IVEs) can simulate such places.

" Les discours spécialisés sont des discours contraints par une situation d'énonciation, que l'on peut rapporter à un lieu social professionnel, et qui supposent la transmission ou l'échange d'informations ou de connaissances théoriques ou pratiques, déclaratives ou procédurales, voire expérientielles, entre énonciateurs ou des interactants qui ont un statut socio-professionnel ou une position sociale définie et dont le message a une visée pragmatique précise"(Moirand & Tréguer-Felten, 2007 : 12)

device to develop and practice linguistic, cultural, socio-linguistic, pragmatic, and soft skills, so it appears as a good simulation device to add to the teacher's toolbox.

Our present study has also put to the fore the emergence of new competences in language learning/teaching (not developed here) that we can conceptualize as interactive listening and interactive reading (e.g. Amaze), which sheds light to the ongoing developments of VR used in educational contexts and the need to develop other apps for educational purposes.