Pamela Ramirez-Vidal

Rafael L S Canevesi

Giuseppe Sdanghi

Sébastien Schaefer

Gaël Maranzana

Alain Celzard

Vanessa Fierro
email: vanessa.fierro@univ-lorraine.fr

A Step Forward in Understanding the Hydrogen Adsorption and Compression on Activated Carbons

Keywords: hydrogen storage, activated carbons, adsorption modelling, high-pressure adsorption, isosteric heat, adsorption entropy

come

Introduction

Hydrogen is an attractive energy vector to replace fossil fuels because it has the highest gravimetric energy density among all non-nuclear fuels (i.e., 120 MJ kg -1 compared to oil, 47 MJ kg -1 ). However, hydrogen is also the lightest element in the universe. Therefore, several technological challenges need to be overcome in order to plan its large-scale implementation, such as environmentally friendly production and efficient distribution, storage and use [START_REF] Sinigaglia | Storage, Fuel Stations of Hydrogen and Its Utilization in Automotive Applications-a Review[END_REF][START_REF] Méndez | A New Insight into Au/TiO2-Catalyzed Hydrogen Production from Water-Methanol Mixture Using Lamps Containing Simultaneous Ultraviolet and Visible Radiation[END_REF][START_REF] Berry | Onboard Storage Alternatives for Hydrogen Vehicles[END_REF][START_REF] Sdanghi | Review of the Current Technologies and Performances of Hydrogen Compression for Stationary and Automotive Applications[END_REF] . In order to meet the storage targets to power a fuel cell vehicle and cover a distance of 500 km, 5 kg of hydrogen should be stored at 298 K and 0.1 MPa, [START_REF] Berry | Onboard Storage Alternatives for Hydrogen Vehicles[END_REF] for a total storage volume of 61 m 3 .

To solve this problem, three approaches have been considered: (i) compression in gas cylinders [START_REF] Sdanghi | Review of the Current Technologies and Performances of Hydrogen Compression for Stationary and Automotive Applications[END_REF][START_REF] Moreno-Blanco | The Storage Performance of Automotive Cryo-Compressed Hydrogen Vessels[END_REF][START_REF] Law | Cost Analyses of Hydrogen Storage Materials and On-Board Systems[END_REF] ; (ii) liquefaction in cryogenic tanks [START_REF] Andersson | Large-Scale Storage of Hydrogen[END_REF][START_REF] Meneghelli | 4 Integrated Insulation System for Automotive Cryogenic Storage Tanks[END_REF] and; (iii) absorption or adsorption in solids (metal hydrides [START_REF] Bellosta Von Colbe | Application of Hydrides in Hydrogen Storage and Compression: Achievements, Outlook and Perspectives[END_REF] , metallic organic frameworks [START_REF] Farha | Metal-Organic Framework Materials with Ultrahigh Surface Areas: Is the Sky the Limit?[END_REF][START_REF] Liu | Entropy Prediction for H2 Adsorption in Metal-Organic Frameworks[END_REF] , nanostructured carbons [START_REF] Schaefer | Rice Straw-Based Activated Carbons Doped with SiC for Enhanced Hydrogen Adsorption[END_REF][START_REF] Tellez-Juárez | Hydrogen Storage in Activated Carbons Produced from Coals of Different Ranks: Effect of Oxygen Content[END_REF][START_REF] Sdanghi | Hydrogen Adsorption on Nanotextured Carbon Materials[END_REF] , hypercrosslinked polymers [START_REF] Cousins | Highly Porous Organic Polymers for Hydrogen Fuel Storage[END_REF] ).

Compression is the most widely used method for hydrogen storage [START_REF] Sdanghi | Review of the Current Technologies and Performances of Hydrogen Compression for Stationary and Automotive Applications[END_REF] , although very high pressures have to be used to achieve a significant increase in hydrogen density. Indeed, a density of 42.9 g L -1 is obtained by compressing hydrogen to 70 MPa and 298 K, which results in a four order of magnitude increase in density compared to ambient conditions. Highpressure hydrogen storage requires heavy and bulky tanks. Type IV tanks, which are made of carbon fibers and a polymer inner lining, are the most commonly used for storing hydrogen at high pressure [START_REF] Sdanghi | Towards Non-Mechanical Hybrid Hydrogen Compression for Decentralized Hydrogen Facilities[END_REF] . The cost of a Type IV tank has been estimated at approximately $ 633 kg -1 6 .

Nevertheless, high-pressure systems require safety measures that may alarm public opinion.

Another proposed approach for storing hydrogen is its liquefaction in cryogenic tanks. The estimated cost of a liquid hydrogen tank is $ 386 kg -1 for a 100L internal volume reservoir for automotive applications [START_REF] Meneghelli | 4 Integrated Insulation System for Automotive Cryogenic Storage Tanks[END_REF] . In addition, it should be considered that the most modern hydrogen liquefaction plants have a specific energy demand of approximately 10 kWh kg -1 17 , a third of the energy contained in hydrogen.

Having a similar expected cost that the liquefaction of hydrogen in cryogenic tanks (390 $ kg -1 ) [START_REF] Meneghelli | 4 Integrated Insulation System for Automotive Cryogenic Storage Tanks[END_REF] , the cryo-compression is a viable alternative for storing hydrogen. In fact, cryocompression needs less strength materials compared to a 70MPa room compression and can overcome the gas lost associated to the boil-off in the H 2 liquefaction systems [START_REF] Ahluwalia | Supercritical Cryo-Compressed Hydrogen Storage for Fuel Cell Electric Buses[END_REF][START_REF] Ahluwalia | Technical Assessment of Cryo-Compressed Hydrogen Storage Tank Systems for Automotive Applications[END_REF] . The volume of the hydrogen storage system can be significantly reduced by introducing a porous material to promote hydrogen adsorption. Indeed, it has been observed that the use of activated carbons (ACs) can reduce the volume needed for hydrogen storage by 23% compared to pure compression at 20 MPa and room temperature [START_REF] De La Casa-Lillo | Hydrogen Storage in Activated Carbons and Activated Carbon Fibers[END_REF][START_REF] Fierro | Adsorption and Compression Contributions to Hydrogen Storage in Activated Anthracites[END_REF] . Hydrogen storage in ACs is achieved by physisorption, which is a physical phenomenon since no chemical bonding between the hydrogen molecules and the carbon surface is involved. It is widely known that hydrogen interacts with the carbon surface through charge density fluctuations, i.e., van der Waals interactions [START_REF] Sdanghi | Hydrogen Adsorption on Nanotextured Carbon Materials[END_REF][START_REF] Andreas | Hydrogen: The Future Energy Carrier[END_REF] . ACs have, on average, the highest hydrogen adsorption capacities among currently known nanotextured carbon materials (up to 7 wt. % at 4 MPa and 77 K) [START_REF] Sdanghi | Hydrogen Adsorption on Nanotextured Carbon Materials[END_REF][START_REF] Fierro | Experimental Evidence of an Upper Limit for Hydrogen Storage at 77K on Activated Carbons[END_REF] .

The amount of hydrogen that can be physisorbed on a porous material, at a given pressure and temperature, depends essentially on its textural properties. Hydrogen storage is enhanced in materials with an adequate micropore size distribution and high surface area. Furthermore, hydrogen adsorption on ACs is thermodynamically favored at low temperature and high pressure because it is an exothermic process. Thus, hydrogen uptake at 77 K is assumed to increase by 1 wt. % per 500 m 2 g -1 of BET area, a behavior known as "Chahine's rule" [START_REF] Bénard | Storage of Hydrogen by Physisorption on Carbon and Nanostructured Materials[END_REF] .

In the framework of hydrogen adsorption modeling, the Ono-Kondo theory proved to be in very good agreement with hydrogen adsorption isotherms measured up to 6 MPa and over a wide temperature range (77 -298 K) [START_REF] Ahluwalia | Automotive Hydrogen Storage System Using Cryo-Adsorption on Activated Carbon[END_REF] . The modeling of hydrogen adsorption isotherms with the Sips equation, also called Langmuir-Freundlich isotherm, also gave very good predictions [START_REF] Lam | Modeling and Predicting Total Hydrogen Adsorption in Nanoporous Carbon Materials for Advanced Nuclear Systems[END_REF] , although the Toth equation proved to be better adapted than the Sips equation at low pressure [START_REF] Tedds | Characterisation of Porous Hydrogen Storage Materials: Carbons, Zeolites, MOFs and PIMs[END_REF] . The modified Dubinin-Astakhov (MDA) equation also proved to fit accurately N 2 , CH 4 and H 2 adsorption isotherms on ACs [START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 1: Modified Dubinin-Astakhov Model[END_REF][START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 2: Conservation of Mass and Energy[END_REF] . However, the physical significance of the MDA parameters is not completely understood and is of primary importance for the design of hydrogen storage systems.

In our previous study [START_REF] Sdanghi | Application of the Modified Dubinin-Astakhov Equation for a Better Understanding of High-Pressure Hydrogen Adsorption on Activated Carbons[END_REF] , we determined hydrogen adsorption on two commercial ACs, MSC30 and MSP20X from Kansai Coke and Chemicals TM (Japan), and used the MDA equation to fit the experimental hydrogen adsorption over a wide range of pressures and temperatures. We found that the parameters of the MDA model were related in some way to the textural properties of the ACs used. However, as the panel of ACs was reduced to only two, we could not draw indisputable conclusions. The MDA equation was also used to evaluate the heat of adsorption as an alternative to other well-known methods, such as isosteric sorption and calorimetric-volumetric methods [START_REF] Kloutse | Isosteric Heat of Hydrogen Adsorption on MOFs: Comparison between Adsorption Calorimetry, Sorption Isosteric Method, and Analytical Models[END_REF][START_REF] Giraldo | Isosteric Heat: Comparative Study between Clausius-Clapeyron, CSK and Adsorption Calorimetry Methods[END_REF] . As the heat of adsorption can significantly affect the hydrogen storage capacity of ACs, the usable hydrogen uptake in an adsorption system can be enhanced when the heat of adsorption is effectively removed from the system [START_REF] Broom | Concepts for Improving Hydrogen Storage in Nanoporous Materials[END_REF] . A good knowledge of the variation of the heat of adsorption with the textural properties of the AC is therefore essential to design an appropriate thermal management of a hydrogen storage system.

In this study, we used six ACs with very different textural characteristics to better understand hydrogen adsorption on ACs and to elucidate the dependence of the MDA parameters. We have shown that four out of the five parameters of the MDA equation are correlated (R 2 between 0.95 and 0.99) to the textural properties of the CACs.

Experimental

Carbon materials

Six commercial activated carbons (CACs) were studied, namely: MAXSORB® (i) MSC30 and (ii) MSP20X from Kansai Coke and Chemicals TM (Japan); (iii) SA1500 and (iv) SA20 from Nunchar Ingevity® (USA); (v) TH90I from Silcarbon® (Germany) and (vi) Filtrasorb400 from Chemviron® (Belgium).

Textural characterization

Textural characterization of the samples was determined by adsorption of N 2 (77 K) and CO 2 (273 K) in two automatic adsorption apparatus from Micromeritics-Particulate Systems®, ASAP 2020 and ASAP 2040, respectively. Outgassing was carried out at 383K under secondary vacuum for more than 48h, before sample weight determination, and further outgassing was carried out at the measuring port at 383K and under secondary vacuum for at least 6h. More details are given elsewhere [START_REF] Schaefer | Rice Straw-Based Activated Carbons Doped with SiC for Enhanced Hydrogen Adsorption[END_REF][START_REF] Schaefer | Assessment of Hydrogen Storage in Activated Carbons Produced from Hydrothermally Treated Organic Materials[END_REF] . Data treatment of the adsorption isotherms was performed with the Microactive software® provided by Micromeritics. We calculated the BET areas, A BET , in the adequate range of relative pressures of the N 2 adsorption data (see Table S1 of the Supporting Information), taking into consideration the Rouquerol criterion 23,[START_REF] Rouquerol | Is the Bet Equation Applicable to Microporous Adsorbents[END_REF] . Micropore volumes were obtained by applying the Dubinin-Radushkevich (DR) equation to either N 2 , V , DR-N2 , or CO 2 , V , DR-CO2 , adsorption data. For the determination of the pore size distributions (PSDs), the SAIEUS ® software provided by Micromeritics was used [START_REF] Jagiello | Dual Gas Analysis of Microporous Carbons Using 2D-NLDFT Heterogeneous Surface Model and Combined Adsorption Data of N2 and CO2[END_REF] . Combining N 2 and CO 2 sorption data by the non-local density functional theory (NLDFT), we obtained the surface areas, S NLDFT , and the pore size distributions (PSDs). For that purpose, we applied the two-dimensional version of the heterogeneous carbon surface model, 2D-NLDFT-HS [START_REF] Jagiello | Carbon Slit Pore Model Incorporating Surface Energetical Heterogeneity and Geometrical Corrugation[END_REF] , to the N 2 and CO 2 adsorption data in the entire range of relative pressures. By integration of the PSDs, we obtained the total pore volumes, V T , and the volumes of pores having diameters: (i) under 0.7 nm (V <0.7,NLDFT ), i.e., ultramicropores; (ii) between 0.7 and 2 nm (V 0.7-2,NLDFT ), i.e., supermicropores; (iii) under 2 nm (V micro ), i.e., micropores; and (iv) between 2 and 50 nm (V mes ), i.e., mesopores, calculated as V T -V micro .

Micropore ( ) and total ( ) average pore sizes were calculated taking into account the PSDs and were volume-weighted.

Determination of hydrogen adsorption isotherms

The determination of the hydrogen adsorption isotherms was carried out in an automatic adsorption equipment HPVAII from Micromeritics-Particulate Systems® coupled with a single-stage closed cycle cryogenic refrigerator. Before hydrogen adsorption at high pressure, the AC was outgassed first in a vacuum oven at 373K overnight under primary vacuum. Then, the AC was transferred to the high-pressure device: a 10 cm 3 cell was filled with about 1.2 g of AC and submitted to further outgassing at 373K for 48h under secondary vacuum.

Measurements were performed in a range of temperatures from 77 to 273 K with an accurate temperature control (margin of error ± 0.005 K). We fixed the pressure steps for hydrogen adsorption at 0.1, 0.5, 0.8, 1, 2, 3, 5, 7.5, 10, 12.5 and 14 MPa, whereas we took desorption data at 11.5, 8, 4.5, 1.5 and 0.5 MPa. Outgassing between adsorption and desorption experiments was carried out overnight under secondary vacuum at room temperature. The first isotherm was repeated twice to confirm the good repeatability of the results.

In addition, the determination of high-resolution hydrogen isotherms at 77 K and up to 0.1 MPa was carried out in a 3-Flex automatic device (Micromeritics) after outgassing the sample at 383K for at least 24h. Further outgassing of the samples was carried out in the analysis ports for at least 8h. The measurement of the cold and warm volumes was performed after the adsorption-desorption experiments to avoid helium entrapment in narrow pores.

Modeling

Application of the MDA equation

Hydrogen storage capacities can be measured by both gravimetric and volumetric devices.

Gravimetric devices provide values of absolute hydrogen adsorption, which is defined as the amount of gas confined in a volume that has a higher concentration than the bulk free gas.

The volume associated with absolute adsorption is defined by that of the adsorbed layer, a non-empirical parameter [START_REF] Hurst | An International Laboratory Comparison Study of Volumetric and Gravimetric Hydrogen Adsorption Measurements[END_REF] . Volumetric devices provide values of excess hydrogen adsorption, n exc , defined as the difference between the hydrogen uptake on the surface of the adsorbent at a specific temperature and pressure, and the amount that would be present in the same volume and under the same conditions in the absence of adsorption forces. n exc [mol kg - 1 ] on ACs can be properly represented by the MDA equation [START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 1: Modified Dubinin-Astakhov Model[END_REF][START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 2: Conservation of Mass and Energy[END_REF][START_REF] Richard | Preliminary Evaluation of the Performance of an Adsorption-Based Hydrogen Storage System[END_REF][START_REF] Hardy | Modeling of Adsorbent Based Hydrogen Storage Systems[END_REF][START_REF] Jakubov | Modified Dubinin-Radushkevich/Dubinin-Astakhov Adsorption Equations[END_REF][START_REF] Momen | Experimental and Numerical Investigation of the Thermal Effects during Hydrogen Charging in Packed Bed Storage Tank[END_REF] , which reads as follows: (1) where n max [mol kg -1 ] is the amount of adsorbed hydrogen corresponding to the saturation of the entire available pore volume, R [8.314 J mol -1 K -1 ] is the universal gas constant, α [J mol - 1 ] is the "enthalpy" factor, β [mol J -1 K -1 ] is the "entropy" factor [START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 2: Conservation of Mass and Energy[END_REF] , P 0 [MPa] is the pseudosaturation pressure according to Dubinin's definition [START_REF] Dubinin | Adsorption in Micropores[END_REF] , ρ g [mol m -3 ] is the hydrogen bulk phase density and V a [m 3 kg -1 ] is the volume of the adsorbed phase. As far as we know, only one study considered the variation of V a with the temperature and the amount adsorbed [START_REF] Dreisbach | Highest Pressure Adsorption Equilibria Data: Measurement with Magnetic Suspension Balance and Analysis with a New Adsorbent[END_REF] . V a is usually considered as constant under supercritical conditions by several authors [START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 1: Modified Dubinin-Astakhov Model[END_REF][START_REF] Do | Adsorption of Supercritical fluids in Non-Porous and Porous Carbons: Analysis of Adsorbed Phase Volume and Density[END_REF][START_REF] Czerny | Adsorption of Nitrogen on Granular Activated Carbon: Experiment and Modeling[END_REF] . We also consider that the adsorbed phase occupies the available porosity and that its average density increases gradually to an asymptotic value during hydrogen adsorption [START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 1: Modified Dubinin-Astakhov Model[END_REF] .

For the determination of the absolute amount of hydrogen adsorbed, n abs [mol kg -1 ], we used the following expression:

(2)

The adsorption data obtained for each CAC at the nine temperatures chosen in this study were fitted simultaneously. This solution allowed obtaining a set of only five parameters (n max , α, β, P0 and Va ) valid for the entire temperature range considered and for a given CAC.

ρg was calculated by using the REFPROP-7 software.

The Levenberg-Marquardt algorithm [START_REF] Levenberg | A Method for the Solution of Certain Non-Linear Problems in Least Squares[END_REF] was used to solve the non-linear fitting of the curves and get the MDA parameters for each AC. Then, we established the relationships between the MDA parameters and the textural properties of the ACs.

Determination of the isosteric heats of adsorption

The isosteric heat of adsorption, Q st [kJ mol -1 ], can be deduced from the MDA equation using the following expression: (3) where n abs /n max is the fractional filling on the surface of the AC, usually referred to as .

Q st was also calculated by the Clausius-Clapeyron equation as follows: (4) The Clausius-Clapeyron equation was applied to groups of three adsorption isotherms in order to get Q st as a function of both temperature and absolute amount of hydrogen adsorbed. In order to calculate the Q st of the six CACs by the classical Clausius-Clapeyron equation, we applied the Sips equation, which is the most appropriate for studying the thermodynamics of hydrogen adsorption [START_REF] Lam | Modeling and Predicting Total Hydrogen Adsorption in Nanoporous Carbon Materials for Advanced Nuclear Systems[END_REF] , to calculate the absolute adsorbed amounts (n abs ) in the equilibrium pressure range of the study. According to the Sips equation, n abs is calculated as follows: (5) where N is the maximum adsorption capacity of the material at a given temperature, b is the equilibrium constant related to the Langmuir adsorption coefficient and k is the coefficient related to the Freundlich equation. When P or b approaches 0, the Sips expression reduces to that of Freundlich, whereas if k is equal to 1, Eq. ( 5) becomes the Langmuir equation [START_REF] Rouquerol | 2 -Thermodynamics of Adsorption at the Gas/Solid Interface[END_REF] . The hydrogen absolute isotherms were calculated from the excess isotherms by means of Eq. ( 2).

V a was estimated for each temperature assuming asymptotic behavior at high fugacity values.

The specific pressures, P, to apply the Clausius-Clapeyron equation were calculated by Eq. ( 6): (6) In the present study, fugacity was used instead of pressure because of the deviation from ideal conditions, and was calculated as a function of temperature and pressure using the REFPROP-7 software. In this way, Eq. ( 4) can be expressed as a function of fugacity according to: (7)

Determination of adsorption entropies

The entropy of the adsorbed hydrogen with respect to the entropy of the perfect gas phase at 0.1 MPa and the same temperature, [J kg -1 K -1 ], can be calculated from the MDA equation 30 : (8) where s g 0 is the entropy of the perfect gas phase at 0.1 MPa and at the same temperature as the adsorbed phase, Erf is the error function and P 0 is the pressure of the reference state, i.e., 0.1 MPa.

According to the second law of thermodynamics, and once the adsorption equilibrium is reached, the variation of entropy due to hydrogen adsorption, ΔS ads [J mol -1 K -1 ], can be related to as follows:

ΔS ads was calculated from (Eq. ( 7)), and correspond to a given filling; it is therefore not directly comparable to calculated by Eq. ( 8) because the latter corresponds to the total hydrogen adsorbed and refers to the amount of carbon and not to the amount of hydrogen adsorbed.

Results and discussion

Textural characterization

Figures 1a and 1b show the N 2 and CO 2 isotherms of the CACs studied, respectively. We determined their PSDs by applying the 2D-NLDFT-HS model to both adsorption isotherms simultaneously. This approach gives a more accurate view of the textural properties of the selected ACs, and especially of the narrowest pores. Although the kinetic diameters of N 2 and CO 2 are quite similar (3.6 and 3.3 nm, respectively), CO 2 physisorption at 273 K is a much faster process than that of N 2 at 77 K because molecular diffusion is highly temperaturedependent [START_REF] Jagiello | Enhanced Resolution of Ultra Micropore Size Determination of Biochars and Activated Carbons by Dual Gas Analysis Using N2 and CO2 with 2D-NLDFT Adsorption Models[END_REF][START_REF] Grau-Marin | Evaluation of the Textural Properties of Ultramicroporous Carbons Using Experimental and Theoretical Methods[END_REF] . CO 2 adsorption isotherms give a reliable indication of porosity with a diameter of less than 1 nm because CO 2 is adsorbed in pores where N 2 cannot enter, within the set equilibrium times [START_REF] Jagiello | Enhanced Resolution of Ultra Micropore Size Determination of Biochars and Activated Carbons by Dual Gas Analysis Using N2 and CO2 with 2D-NLDFT Adsorption Models[END_REF][START_REF] García-Díez | Novel Porous Carbons Derived from Coal Tar Rejects: Assessment of the Role of Pore Texture in CO2 Capture under Realistic Postcombustion Operating Temperatures[END_REF] .

The six investigated CACs presented very different textural properties, with A BET ranging from 983 to 3310 m 2 g -1 . A high percentage of mesoporous volume was observed for MSC30 (40%), SA1500 (50%) and SA20 (59%), while MSP20X, TH90I and Filtrasorb400 were essentially microporous with fractions of micropores of 94, 94 and 80%, respectively. The volume of pores narrower than 1 nm, given by CO 2 isotherms (Figure 1b), decreased in the order TH90 > MSC30  MSP20X > SA1500 > Filtrasorb400 > SA20.

According to the IUPAC classification 23 , the N 2 isotherm measured for MSC-30 has a type Ib shape without hysteresis loop (see Figure 1a), which is characteristic of ACs with a large fraction of supermicropores and narrow mesopores. MSC-30 exhibited more developed textural properties than all the ACs selected for this study: A BET = 3310 m 2 g -1 , S NLDFT = 2216 m 2 g -1 and V T = 1.60 cm 3 g -1 (Figure 1d). An important difference is observed when comparing A BET and S NLDFT values. The BET method is indeed known to underestimate the surface area when ultramicropores, i.e., with a pore diameter less than 0.7 nm, exist. This is because a single monolayer of N 2 is adsorbed in very narrow pores, while the presence of two pore walls should be taken into account to give a more realistic value of the surface area. In addition, the BET method also overestimates the surface area in ACs having a large fraction of supermicropores, since N 2 uptake proceeds by pore filling [START_REF] De Lange | Assessing the Surface Area of Porous Solids: Limitations, Probe Molecules, and Methods[END_REF] . For these reasons, reported A BET values are sometimes higher than 3000 m 2 g -1 , although it is well known that the specific surface area of an AC should be always smaller than the theoretical surface area of a graphene sheet, i.e., 2630 m 2 g -1 54,55 .

Samples SA1500 and SA20 showed a combination of type Ib and type IVa isotherms with an H4 hysteresis loop in the P/P 0 range of 0.4-0.8, indicating the presence of both micropores and mesopores (50 and 59%, respectively). They both had relatively high A BET , equal to 2204 and 1737 m 2 g -1 , and S NLFT equal to 1621 and 1305 m 2 g -1 , respectively. Filtrasorb400, TH90I

and MSP20X presented N 2 isotherms type Ia without hysteresis loop, which are characteristic of microporous materials with narrow porosity. MSP20X presented the largest surface area of the aforementioned samples (A BET = 2363 m 2 g -1 and S NLDFT = 2007 m 2 g -1 ), followed by TH90I (A BET = 1204 m 2 g -1 and S NLDFT = 1256 m 2 g -1 ) and Filtrasorb400 (A BET = 983 m 2 g -1

and S NLDFT = 996 m 2 g -1 ). MSP20X and TH90I had a higher percentage of micropores (94%) than FiltraSorb400 (80%). The higher surface area of MSP20X is due to supermicropores (0.7-2 nm), which produce the widening of the isotherm elbow. Figure 1c shows the PSDs of all the CACs studied and Figure 1d shows their pore volumes corresponding to the ultramicropore, supermicropore and mesopore ranges. Figure 1d also shows the A BET and S NLDFT . As expected, the specific surface area is proportional to the micropore volume. Full details on the textural properties of the six CACs studied are reported in the Supporting Information, Table S1. The CACs with a high percentage of mesopores i.e., MSC30X, SA1500 and SA20, presented average micropore sizes of 1.28, 1.27 and 1.26 nm (in the supermicropore range) and average pore sizes of 1.95, 3.21 and 3.80 nm (near or in the mesopore range), respectively. On the other hand, the microporous CACs had narrower average micropore sizes: 1.05, 0.87 and 0.92 nm for MSP20X, TH90I and Filtrasorb400, respectively.

Hydrogen adsorption

Hydrogen adsorption on all six CACs was found to be completely reversible. The desorption isotherms overlapped those of adsorption without any hysteresis loop throughout the 0.1 to 15 MPa pressure range. Figure 2 shows the hydrogen adsorption-desorption isotherms at the lowest temperature, i.e., 77 K (Figure 2a) and at the highest one, i.e., 273 K (Figure 2b), for all materials. A maximum of excess hydrogen adsorption was observed at 77 K and 3-4 MPa, due to the increased density of the adsorbed phase as the temperatures were lowered [START_REF] Rouquerol | 2 -Thermodynamics of Adsorption at the Gas/Solid Interface[END_REF] . Although this maximum is reached at lower pressures when increasing the fraction of narrower pores 75 , Filtrasorb400 has the highest fraction of narrow pores and reached a maximum hydrogen uptake of 2.34 wt.% at 3 MPa. For his reason, we have chosen to report hydrogen capacities at 4MPa for all the CACs except for Filtrasorb400. This value was 5.78, 4.74, 4.04, 3.24, 2.90 and 2.31 wt. % for MSC30, MSP20X, SA1500, SA20, TH90I and Filtrasorb400, respectively.

Figure 2b shows that the excess hydrogen adsorption increases steadily with pressure at 273 K; the values obtained at 14 MPa were 1.04, 0.95, 0.86, 0.72, 0.67 and 0.55 wt. % for the same carbons and in the same order of adsorption capacity as mentioned for the adsorption data at 77K (Figure 2a).

Figure 3 shows the 3D plot of excess hydrogen adsorbed as a function of both temperature and pressure (a, b and c) as well as the corresponding T-P contour lines (d, e and f) for the CACs MSC30, SA20 and Filtrasorb400, respectively. The use of lower temperatures allows reducing the pressure to get maximum hydrogen storage. The slope of the contour lines increases as the temperature is lowered, due to the increased density of adsorbed hydrogen [START_REF] Do | Adsorption of Supercritical fluids in Non-Porous and Porous Carbons: Analysis of Adsorbed Phase Volume and Density[END_REF][START_REF] Müller | Technologies for the Storage of Hydrogen Part 1: Hydrogen Storage in the Narrower Sense[END_REF][START_REF] Kadono | Dense Hydrogen Adsorption on Carbon Subnanopores at 77[END_REF] , which is the most important contribution to hydrogen storage under supercritical conditions [START_REF] Murata | A New Determination Method of Absolute Adsorption Isotherm of Supercritical Gases under High Pressure with a Special Relevance to Density-Functional Theory Study[END_REF] . Figures 3d, 3e and 3f show that the values of the excess hydrogen adsorbed are higher than 5, 3 and 2 wt. % for MSC30, SA20 and Filtrasorb400, respectively, at temperatures lower than 93 K and pressures between 2 and 8 MPa. Figure 4 shows the excess hydrogen adsorbed, n exc , as a function of A BET and S NLDFT at 77 and 273 K for the six CACs. In Figure 4a, the fitting of n exc as a function of the surface area with a straight line forced to pass through (0,0), showed determination coefficients (R 2 ) of 0.88 and 0.98 for A BET and S NLDFT , respectively, at 77 K. Therefore, the fit of the data was more accurate when using S NLDFT . Indeed, hydrogen adsorption at 77 K was found to increase by 1.25 wt. % per 500 m 2 g -1 of S NLDFT , which could be proposed as an alternative to the Chahine rule [START_REF] Sdanghi | Hydrogen Adsorption on Nanotextured Carbon Materials[END_REF][START_REF] Bénard | Storage of Hydrogen by Physisorption on Carbon and Nanostructured Materials[END_REF] . Figure 4b shows that the difference between the determination coefficients obtained at the linear fitting of n exc as a function of S NLDFT and A BET at 273 K and 14 MPa were even higher. The R 2 obtained by the linear regression passing though (0,0) were 0.20 and 0.88 for A BET and S NLDFT , respectively. The higher R 2 obtained using S NLDFT at both 77 K and 273 K clearly shows that a more accurate characterization of the textural properties was achieved using both CO 2 and N 2 adsorption isotherms.

Figure 5a and 5b show the excess hydrogen adsorption at 77 K up to 100 and 1.5 kPa, respectively. The excess hydrogen adsorbed was found to be higher in the CACs having both high microporosity and very narrow pores, i.e., Filtrasorb400, MSPX 20 and TH90I. Indeed, Van der Waals interactions are stronger in the ACs with narrow pores, as they overlap when hydrogen molecules are in contact with both pore walls [START_REF] Yurduşen | A Remarkable Increase in the Adsorbed H2 Amount: Influence of Pore Size Distribution on the H2 Adsorption Capacity of Fe-BTC[END_REF] . According to this, the Henry's constant linearly increases when reducing the average micropore size (Figure 5c), confirming that hydrogen adsorption is enhanced in very narrow pores where adsorption is stronger due to overlapping adsorption potentials.

Fitting with the MDA equation

Figure 6 shows that the MDA equation is a good analytical tool to describe hydrogen adsorption data over a wide range of pressures and temperatures. Data were reported for two of the six CACs studied in the present paper, i.e., SA20 and SA 1500. The five parameters of the MDA equation (i.e., n max , α, β, P 0 and V a ) obtained by non-linear regression of the hydrogen adsorption data are listed in Table S2 of the Supporting Information. R 2 coefficients ranging from 0.96 to 0.99 were obtained for all six CACs. Figure 7a shows the almost perfect linear variation of V a with A BET (R 2 = 99). V a ranged from 1.50 cm 3 g -1 for MSC30 to 0.362 cm 3 g -1 for Filtrasorb400. The linear correlations between V a and S NLDFT , micropore volume and total pore volume, were also calculated and showed lower determination coefficients, i.e., 0.90, 0.91 and 0.7, respectively (see Table S3).

The fact that V a is more dependent on A BET than on S NLDFT clearly suggests that hydrogen storage is not exclusively a surface phenomenon; hydrogen storage also takes place by pore filling as it occurs during nitrogen adsorption at 77 K. Since A BET is an apparent area that takes into account not only the surface coverage but also the pore filling, V a and A BET evolve in the same way [START_REF] Sdanghi | Characterization of Carbon Materials for Hydrogen Storage and Compression[END_REF] . Figure 7a also shows the variation of n max as a function of A BET : a linear relationship was found (R 2 = 0.98). n max varied between 72.5 and 20.8 mol kg -1 . Figure 7b shows the "enthalpy" factor, α, as a function of the average micropore size. α decreases linearly as the average micropore diameter increases (R 2 =0.97). This behavior is due to the fact that the interactions between hydrogen molecules and the walls of narrower pores in the AC are stronger. Indeed, α is related to the heat of adsorption as shown by Eq.

(3). Thus, the more hydrogen is adsorbed in a pore, the higher the heat released will be, due to the exothermic nature of hydrogen adsorption on ACs. Figure 7b also shows the linear (R 2 =0.95) and direct relationship of the "entropy" factor, β, with the total pore volume, V T . In contrast to α, β was found to increase with the average pore size. This behavior can be explained by the higher degree of disorder of hydrogen molecules, and therefore by a higher entropy, in wider pores.

Concerning the pseudo-saturation pressure, P 0 , the highest value was found for MSC30:

1013 MPa, and values ranging from 616 to 700 MPa were obtained for other CACs. Richard et al. [START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 1: Modified Dubinin-Astakhov Model[END_REF] reported values of 71.6 mol kg -1 and 1470 MPa for n ads and P 0 , respectively, with the AC AX-21 (former name of the MSC30), which are close to those obtained in this study, 72.5 mol kg -1 and 1013 MPa for MSC30. Nevertheless, these differences may be explained by the different maximum pressures reached for the measurements (14 MPa in this study, 6 MPa by the aforementioned authors), which inevitably affects the non-linear regression giving a lower coefficient of determination, R 2 . In addition, it is important to highlight that even though they are supposed to be the same, they had different values of BET area (A BET of 3300 m 2 g -1 and 2800 m 2 g -1 for MSC30 and AX-21, respectively).

In the original model proposed by Dubinin, P 0 represented the saturation pressure [START_REF] Dubinin | Adsorption in Micropores[END_REF] .

Indeed, Dubinin's model was developed to describe adsorption of gases under subcritical conditions. However, hydrogen adsorption generally occurs under supercritical conditions, and the original definition of P 0 therefore loses its physical meaning. Do and Do support a concept of quasi-saturated vapor pressure based on the assumption that supercritical fluids might form clusters when confined in narrow micropores, and these clusters might be large enough to exert a P 0 in the same way as a subcritical fluid [START_REF] Do | Adsorption of Supercritical fluids in Non-Porous and Porous Carbons: Analysis of Adsorbed Phase Volume and Density[END_REF] . According to this, P 0 should be temperature-dependent and be a characteristic property of any adsorbent material. Amankwab and Schwakz [START_REF] Amankwab | A Modified Approach for Estimating Pseudo-Vapor Pressures in the Application of the Dubinin-Astakhov Equation[END_REF] proposed that P 0 can be defined as:

P 0 = P c (T / T c ) k ( 10
)
where P c and T c are critical pressure and temperature, respectively, T is the process temperature, and k is a factor that depends on the adsorbate-adsorbent interactions and is generally set at 2 for H 2 adsorption on ACs [START_REF] Richard | Gas Adsorption Process in Activated Carbon over a Wide Temperature Range above the Critical Point. Part 1: Modified Dubinin-Astakhov Model[END_REF][START_REF] Hardy | Modeling of Adsorbent Based Hydrogen Storage Systems[END_REF][START_REF] Jakubov | Modified Dubinin-Radushkevich/Dubinin-Astakhov Adsorption Equations[END_REF] . Other authors have suggested that P 0 depends not only on the adsorbed gas, but also on the nature of the adsorbent, and values of k ranging between 2 and 4 have been commonly obtained 62,[START_REF] Srinivasan | A Method for the Calculation of the Adsorbed Phase Volume and Pseudo-Saturation Pressure from Adsorption Isotherm Data on Activated Carbon[END_REF] . Presently, due to the lower values of determination coefficients (see Table S3), it is not possible to elucidate the dependence of P 0 with texture, probably because we should also take into account its variation with T. This approach will be addressed in further studies.

Determination of the isosteric heat of adsorption

Figure 8a shows the isosteric heat of adsorption calculated from α by Eq. ( 3), , as a function of the fractional filling, Θ = n abs /n max . At low Θ, the first sites to be occupied are those where there are the strongest interactions between the AC surface and the gas, mainly ultramicropores. As Θ increases, hydrogen adsorption occurs in wider pores where the interaction is less strong [START_REF] Czerny | Adsorption of Nitrogen on Granular Activated Carbon: Experiment and Modeling[END_REF][START_REF] Bhatia | Optimum Conditions for Adsorptive Storage[END_REF] . Eq. ( 3) is not appropriate for calculating when Θ approaches 0 and 1, since increases indefinitely or becomes zero, respectively.

Figure 8b shows as a function of the average micropore size and for different Θ, from 0.01 to 0.94. A linear dependence (R 2 =0.98) of on the average micropore size was observed for all values of Θ. The is more dependent on the average micropore size than on the pore volume, as shown in Figure S1 of the Supporting Information. The dependency of on the average micropore size is much higher at low Θ because almost the whole surface and micropores are available. At Θ = 0.001, decreased from 11.37 to 8.52 kJ mol -1 when the average micropore size increased from 0.86 to 1.26 nm. At Θ = 0.94, decreased from 1.01 to 0.75 kJ mol -1 in the same range of average micropore size. This small variation is due to the fact that the narrowest pores, giving the highest adsorption energies, are already occupied. The maximum absolute H 2 adsorbed at 77 K was 7.5, 6.2, 5.6, 3.9, 3.5, 3.3 wt. % for MSC30, MSP20X, SA1500, SA20, TH90 and Filtrasorb400, respectively. As an example, Figure S2 of the Supporting Information shows the isotherms of absolute hydrogen adsorbed for SA20 and SA1500 as a function of fugacity. The Sips parameters for all the CACs are reported in Table S4. These isotherms were used to calculate Q st using the Clausius-Clapeyron equation (Eq. ( 7)). Figures 9a and9b show the Q st obtained for SA20 and SA1500.

In general, the Q st ranged from 4 to 10 kJ mol -1 for the six CACs. These values are in good agreement with the results obtained with the MDA equation and presented in Figure 8.

Figures 9c and9d show the Q st at the lowest (93 K) and highest (253 K) temperatures for the six CACs. In general, it can be observed that for each isotherm, Q st is initially high at nearzero filling and decreases with increasing n abs to a plateau value, which is different for each temperature. The Q st remains constant with the increase of hydrogen adsorption until a given fractional filling (range of pore diameters available at this temperature) is reached. At high Θ, the Q st increases strongly due to the repulsion forces between the hydrogen molecules in the gas phase and the already adsorbed hydrogen molecules . This increase is not predicted by the MDA equation.

Determination of the entropies of adsorption

For all six CACs, the values of -ranged from 0 to 4.5 kJ kg -1 K -1 when Eq. ( 8) was used. The negative values of are consistent with the exothermic nature of hydrogen adsorption [START_REF] Sdanghi | Application of the Modified Dubinin-Astakhov Equation for a Better Understanding of High-Pressure Hydrogen Adsorption on Activated Carbons[END_REF] . Figure 10a shows the linear increase of -as a function of fractional filling due to the higher density of the molecules adsorbed in the pores, increasing their filling. The possibilities of movement (disorder) in the pore space decrease, and thusincreases. Figure 10b shows that -is directly proportional to the micropore volume, and the slope of the lines become steeper as the fractional filling increases. The proportionality with A BET is due to the fact that high-pressure adsorption is mainly by pore filling, so with increasing A BET , adsorption increases and therefore more molecules pass from the gas phase to the adsorbed phase, which is a more ordered state. The MDA equation is not suitable for determining the temperature dependence of the adsorption entropy [START_REF] Czerny | Adsorption of Nitrogen on Granular Activated Carbon: Experiment and Modeling[END_REF][START_REF] Myers | Adsorption in Porous Materials at High Pressure: Theory and Experiment[END_REF] . Thus, -ΔS ads was also calculated using the Clausius-Clapeyron (Eq. ( 9)), considering averaged Q st . Figure S3 shows the average isosteric entropy of adsorption of the six CACs as a function of temperature, considering small amounts of adsorbed hydrogen (0-3.5 mmol g -1 ). -ΔS ads values obtained for the six carbons are in good agreement with those reported in the literature for hydrogen adsorption on: ACs 42,64 , MOFs 11,66 and zeolites [START_REF] Garrone | Enthalpy-Entropy Correlation for Hydrogen Adsorption on Zeolites[END_REF] . For all the CACs, the value of -ΔS ads decreased when the temperature increased. This can be attributed to the fact that there is no significant change in Q st at low filling, 5-10 kJ mol -1 , as observed in Figure 9, so the decrease in the Q st / T ratio is almost entirely due to the increase in temperature, in good agreement with the results reported in the literature [START_REF] Bhatia | Optimum Conditions for Adsorptive Storage[END_REF][START_REF] Che | Rigid Ladder-Type Porous Polymer Networks for Entropically Favorable Gas Adsorption[END_REF] . Higher values of -ΔS ads were found for mostly microporous CACs (TH90I, Filtrasorb400 and MSP20X) due to the higher Q st in narrow pores compared to CACs with a large mesopore fraction (MSC30, SA1500 and SA20).

Implementation of the MDA equation in practice

In this study, we showed for the first time the relationship between MDA parameters and the textural properties of ACs. Although scientifically this may be interesting and intellectually rewarding for the authors of this manuscript, one may question the applicability of the knowledge gained on the dependence of MDA parameters in practice. While we have clearly shown that α and β are well correlated with and V T , we will now show the effect of each parameter on n abs /n max when the temperature varies, and its practical implications.

Figures 11a and11b show the effect of α and β on the fractional filling, Θ = n abs /n max , when the temperature increases from 77 to 273 K, P/P 0 being set to 0.02. In Figure 11a, α was set to 4.2 kJ mol -1 ( around 1.0 nm) and β varied from 0.02 to 0.01 kJ mol -1 K -1 (equivalent to V T between 2.0 and 0.5 cm 3 g -1 ). Since n max is directly proportional to A BET and V micro [START_REF] Sdanghi | Characterization of Carbon Materials for Hydrogen Storage and Compression[END_REF] , comparing different values of β (proportional to V T ) is equivalent to comparing carbons with similar V micro but with different values of V meso . In Figure 11b, β was set to 0.01 kJ mol -1 K -1 (equivalent to V T equal to 0.5 cm 3 g -1 ) and α varied from 5.8 to 2.5 kJ mol -1 (equivalent to between 0.5 and 1.5 nm). Comparing the effect of the two parameters on the decrease in fractional filling with the temperature (Figures 11a and11b), the changes in β (function of V T

) were found to be less relevant than the changes in α (function of ). According to Myres and Monson [START_REF] Myers | Adsorption in Porous Materials at High Pressure: Theory and Experiment[END_REF] , the characteristic energy of adsorption can be obtained by the sum of enthalpy and entropy contributions, α + βT, which can be interpreted as an average excess of adsorption energy in the pores compared to the open surface [START_REF] Czerny | Adsorption of Nitrogen on Granular Activated Carbon: Experiment and Modeling[END_REF][START_REF] Pera-Titus | On an Isotherm Thermodynamically Consistent in Henry's Region for Describing Gas Adsorption in Microporous Materials[END_REF][START_REF] Bickford | On the Adsorption Affinity Coefficient of Carbon Dioxide in Microporous Carbons[END_REF] .

Bickford et al. [START_REF] Bickford | On the Adsorption Affinity Coefficient of Carbon Dioxide in Microporous Carbons[END_REF] associated this parameter with the influence of the adsorbent surface chemistry in the adsorption of CO 2 and N 2 . Figure 11c shows α + βT as a function of the temperature for the six CACs. Due to its very high V T , MSC30 exhibited the largest variation in the function α + βT when increasing the temperature from 77 to 273K.

Since  is inversely proportional to and  is proportional to V T , the adsorption of hydrogen on a carbon material with a high V T , basically consisting of narrow micropores, would be less temperature-dependent. In this way, and V T play a role not just on the total adsorption capacity [START_REF] Sdanghi | Characterization of Carbon Materials for Hydrogen Storage and Compression[END_REF] but also on the reduction of the effect of temperature on adsorption, which is highly desirable for hydrogen storage where desorption is achieved by lowering the pressure. However, this is far from being the best option for temperature-driven hydrogen compression where the pressure increase is mainly due to changes in adsorption capacity with the temperature. In conclusion, for ACs having equivalent values of A BET , and taking into account hydrogen capacities on a weight basis (g H 2 /g AC), those with high V T and narrow should be chosen for hydrogen storage while those with a larger and lower V T and V meso are better suited to hydrogen compression. Finally, this study should help researchers working on hydrogen storage in ACs to have a preliminary estimation of the hydrogen capacities, after a correct textural characterization of their materials, at different temperatures and pressures.

Conclusions

The Modified Dubinin-Astakhov (MDA) equation has been successfully used to fit the hydrogen excess adsorption over a wide range of pressures and temperatures and on six commercial activated carbons (CACs): MSC30, MSP20X, SA20, SA1500, Filtrasorb400 and TH90I. Four out of the five parameters of the MDA equation, i.e., n max , V a , α and β were correlated to the textural properties of the CACs. n max and V a are directly proportional to the BET area. The "entropy" factor, β, linearly increased with the total pore volume whereas the "enthalpy" factor, α, was inversely proportional to the average micropore diameter.

The isosteric heat of adsorption, Q st , was calculated using the Clausius-Clapeyron equation. Values between 5 and 10 kJ mol -1 were obtained for all six CACs, consistent with those obtained using the MDA equation. The adsorption entropy was found to be higher in materials with narrower pores and higher BET areas.

As the variation of hydrogen adsorption capacity with temperature is controlled by the parameters α and β, we can conclude that hydrogen adsorption on carbon materials with high pore volumes and narrow micropore sizes would be less temperature-dependent. For ACs having equivalent BET areas and taking into account hydrogen capacities on a weight basis (g H 2 /g AC), those with higher pore volumes and narrower micropores should be chosen for hydrogen storage, while those with wider micropores and lower mesopore volumes are better suited for hydrogen compression. Finally, this study should help researchers working on hydrogen storage on ACs to have a preliminary estimation of the hydrogen capacities, after a correct textural characterization of their materials, at different temperatures and pressures.

Supporting Information

Textural characteristics of the CACs; MDA parameters of each CAC; determination coefficient when linearly fitting the MDA parameters, the isosteric heat or entropy of adsorption to the textural parameters; SIPS parameters; evolution of Q st as a function of total pore volume for several fractional fillings; absolute hydrogen adsorption isotherms of: (a) SA20; and (b) SA1500 fitted by the Sips equation; average isosteric entropy of adsorption of the six CAC's as a function of the temperature at low amount adsorbed hydrogen; evolution of the average isosteric entropy of adsorption as a function of the average micropore size over the temperature range 93-253K.

Figure 1 .

 1 Figure 1. Textural characteristics of the CACs: (a) N 2 adsorption-desorption isotherms at

Figure 2 .

 2 Figure 2. Excess hydrogen isotherms: (a) at 77 K; and (b) at 273 K, for the 6 CACs. Filled

Figure 3 .

 3 Figure 3. Excess hydrogen adsorbed plotted as a function of pressure and temperature for: (a)

Figure 4 .

 4 Figure 4. Hydrogen excess adsorbed as a function of A BET or S NLDFT at: (a) 77 K and 4 MPa

Figure 5 .

 5 Figure 5. Hydrogen isotherms for the six CACs at 77 K: (a) up to 100 kPa; and (b) up to 1.5

Figure 6 .

 6 Figure 6. Hydrogen isotherms on: (a) SA20; and (b) SA1500, and their fitting with the MDA

Figure 7 .

 7 Figure 7. MDA parameters plotted as a function of several textural parameters: (a) V a and

Figure 8 .

 8 Figure 8. Evolution of as a function of: (a) fractional filling; and (b) average micropore

Figure 9 .

 9 Figure 9. Isosteric heat of adsorption for the studied temperatures for: (a) SA20; and (b)

Figure 10 .

 10 Figure 10. -

Figure 11 .

 11 Figure 11. Effect of the parameters: (a) β; and (b) α on the H 2 adsorption capacity at P/P 0 =

Acknowledgements

The financial support of the CONACYT-SENER scholarship 708651/ 739301 is gratefully acknowledged. This study was partly supported by the French PIA project "Lorraine Université d'Excellence", reference ANR-15-IDEX-04-LUE, the TALiSMAN project funded by FEDER (2019-000214) and the Research Fund for Coal and Steel (RFCS) of the European Union (EU) under grant agreement No 709741 (PROMOTEE project). Ingevity™ and Silcarbon Aktivkohle™ are gratefully acknowledged for providing activated carbons. The authors thank Philippe Gadonneix for his technical assistance in the laboratory measurements.


Corentin Jouault
email: jouaultc0@gmail.com

André Nel
email: anel@mnhn.fr

A new genus and species of Aulacidae (Hymenoptera: Evanioidea) from mid-Cretaceous Burmese amber

Keywords: Hymenoptera, Evanioidea, Aulacidae, Cenomanian, fossil record 1. Introduction

The mid-Cretaceous amber from Kachin State of Myanmar provides a well-diversified fauna of aulacid wasps. Here we describe a new aulacid genus and species Paleoaulacus minutus. This discovery highlights the underestimated diversity of aulacid wasps in Burmese Ablian-Cenomanian amber.

Interestingly, Paleoaulacus minutus gen. et sp. nov. shares wing venation and body characters with the tribes Electrofoenini and Aulacini, challenging a clear placement. Future discoveries of additional specimens are necessary to precise its position or erect a new tribe to accommodate this peculiar genus. This fossil shows a developed wing venation, similar to that of the extant genus Aulacus Jurine, 1807.

The superfamily Evanioidea comprises the families Aulacidae, Evaniidae, Gasteruptiidae, †Praeaulacidae, †Anomopterellidae, †Andreneliidae, †Baissidae, and †Othniodellithidae. These wasps were clearly more diverse during the Mesozoic than in the extant fauna, with records of fossils of all these families. Notice that Engel et al. (2016), [START_REF] Engel | New evanioid wasps from the Cenomanian of Myanmar (Hymenoptera: Othniodellithidae, Aulacidae), with a summary of family-group names among Evanioidea[END_REF], and [START_REF] Turrisi | New aulacid wasps from the mid-Cretaceous of Myanmar (Hymenoptera: Evanioidea)[END_REF] considered the praeaulacid subfamily †Nevaniinae as a different family but did not provide a clear phylogenetic argument or synapomorphy justifying such a placement. Thus we prefer to follow [START_REF] Zhang | Nevaniinae subfam. n., a new fossil taxon (Insecta: Hymenoptera: Evanioidea: Praeaulacidae) from the Middle Jurassic of Daohugou in Inner J o u r n a l P r e -p r o o f[END_REF] and [START_REF] Li | Phylogeny of Evanioidea (Hymenoptera, Apocrita), with descriptions of new Mesozoic species from China and Myanmar[END_REF], keeping the †Nevaniinae as a subfamily of †Praeaulacidae.

Among the Evanioidea, the aulacid wasps are easily recognizable by an anterior margin of metasomal segment 1 distinctly separated from metanotum, and metatibia at most slightly widened toward apex (vs. metasomal segment 1 with anterior margin almost touching metanotum, and metatibia gradually enlarged or markedly swollen toward apex, appearing club-shaped) according to [START_REF] Goulet | Hymenoptera of the world: An identification guide to families[END_REF]. The Aulacidae comprise extant and fossil species, distributed in two subfamilies †Hyptiogastritinae [START_REF] Engel | Two ensign wasps in Cretaceous amber from New Jersey and Myanmar (Hymenoptera: Evaniidae)[END_REF][START_REF] Engel | New evanioid wasps from the Cenomanian of Myanmar (Hymenoptera: Othniodellithidae, Aulacidae), with a summary of family-group names among Evanioidea[END_REF] and Aulacinae (Shuckard, 1841). Furthermore, the monophyly of the family is well-supported [START_REF] Jennings | Higher-level phylogeny of the Aulacidae and Gasteruptiidae (Hymenoptera: Evanioidea)[END_REF][START_REF] Smith | World catalog of the family Aulacidae (Hymenoptera)[END_REF][START_REF] Turrisi | Revision of the Afrotropical species of Pristaulacus Kieffer, 1900 (Hymenoptera: Aulacidae)[END_REF][START_REF] Turrisi | Revision of the Palaearctic species of Pristaulacus Kieffer, 1900 (Hymenoptera: Aulacidae)[END_REF][START_REF] Turrisi | A new species of Pristaulacus Kieffer, 1900 from Laos (Hymenoptera: Aulacidae)[END_REF][START_REF] Turrisi | Phylogeny and generic concepts of the parasitoid wasp family Aulacidae (Hymenoptera: Evanioidea)[END_REF][START_REF] Turrisi | Addition to the revision of the Pristaulacus comptipennis speciesgroup: description of two new species from Laos and Thailand (Hymenoptera: Aulacidae)[END_REF]. Mesozoic Aulacidae are not uncommon but only known from Burmese amber (burmite, Kachin, northern Myanmar) inclusions [START_REF] Turrisi | New aulacid wasps from the mid-Cretaceous of Myanmar (Hymenoptera: Evanioidea)[END_REF] with 11 described species (Cockerell, 1917a(Cockerell, , 1917b;;[START_REF] Engel | New evanioid wasps from the Cenomanian of Myanmar (Hymenoptera: Othniodellithidae, Aulacidae), with a summary of family-group names among Evanioidea[END_REF][START_REF] Li | Phylogeny of Evanioidea (Hymenoptera, Apocrita), with descriptions of new Mesozoic species from China and Myanmar[END_REF][START_REF] Turrisi | New aulacid wasps from the mid-Cretaceous of Myanmar (Hymenoptera: Evanioidea)[END_REF][START_REF] Jouault | New evanioid wasps (Hymenoptera: Praeaulacidae, Aulacidae) from Cenomanian Burmese amber[END_REF]. Cockerell (1916aCockerell ( , 1916bCockerell ( , 1917aCockerell ( , 1917bCockerell ( , 1920aCockerell ( , 1920b) ) provided the first scientific studies on this amber. This resin is now renowned for its plethoric insect inclusions (Ross, 2019[START_REF] Ross | Supplement to the Burmese (Myanmar) amber checklist and bibliography[END_REF]. One more time, it has delivered a new genus and species which is described an illustrated herein.

Material and methods

The amber piece containing the specimen studied herein derives from the deposits of Noije Bum in the Hukawng Valley (26° 29′ N, 96° 35′ E), Kachin State, northern Myanmar (Fig. 1). Radiometric J o u r n a l P r e -p r o o f data established an early Cenomanian age (98.79 ± 0.62 Ma) for Kachin amber, based on zircons from volcanic clasts found within the amber-bearing sediments [START_REF] Shi | On the Aulacidae, a family of Hymenoptera pupivora; and that Trigonalys is one of its components: with the description of a British species of this genus, and incidental remarks upon their collateral affinities[END_REF]. Some ammonites found in the amber-bearing bed and within amber corroborate a late Albian-early Cenomanian age [START_REF] Cruickshank | Geology of an amber locality in the Hukawng Valley, northern Myanmar[END_REF][START_REF] Yu | An ammonite trapped in Burmese amber[END_REF].

The new aulacid specimen is embedded in a piece of clear yellow amber. It is a nearly complete individual but with damaged antennae, with the apical flagellomeres missing on right antenna and left antenna broken. The type specimen is housed in the amber collection of the Geological Department and Museum (IGR) of the University of Rennes, France. The specimen was examined and photographed with a Nikon SMZ25 with an attached Nikon D800 camera. All images were digitally stacked photomicrographic composites of several individual focal planes, which were obtained using HeliconFocus 6.7. The figures were composed with Adobe Illustrator CC2019 and Photoshop CC2019 softwares. The wing venation terminology follows [START_REF] Jouault | New evanioid wasps (Hymenoptera: Praeaulacidae, Aulacidae) from Cenomanian Burmese amber[END_REF].

Published work and nomenclatural acts are registered in ZooBank (http://www.zoobank.org/, last access: 07/12/2020), with the following LSID (reference): urn:lsid:zoobank.org:pub:478D05C9-6F3D-4395-A7B0-45030873215B

Systematic paleontology

Order Hymenoptera Linnaeus, 1758 Suborder Apocrita Gerstaecker, 1867 Superfamily Evanioidea Latreille, 1802 Family Aulacidae Shuckard, 1841 Subfamily Aulacinae Shuckard, 1841 See summary of fossil species in Table 1 Genus Paleoaulacus gen. nov. Etymology. From the Latin word minutus meaning 'small', referring to the small size of the species.

The specific epithet is to be treat as an adjective in a genitive case.

Diagnosis. As for the genus.

Description. Head globulous, practically hypognathous, higher than wide (in full face view); occipital carina absent; malar space narrow, almost inexistant; gena angled and slightly protruding; compound eye very large, prominent, ovoid, without circum-ocular carina, inner margins slightly angled (maximal distance between eyes near upper margin); ocelli small, arranged in a small triangle on top of vertex above compound eyes and separated by at least their diameter. Antennal toruli broadly separated, situated above head mid-length, distinctly separated from clypeus, near eyes apex; scape robust, 0.13 mm long, longer than wide, more than twice as long as pedicel, enlarged medially, slightly longer than or sub-equal to first flagellomere; pedicel almost as long as wide, 0.06 mm long;

J o u r n a l P r e -p r o o f flagellum filiform, with nine preserved flagellomeres, all longer than wide and cylindrical. Mandibles present but closed and not projected forward; palpal formula not clearly visible, at least composed by maxillary palps six-segmented and labial palps bi-segmented. Mesosoma longer than high; pronotum short, smooth, without defined, raised posterior dorsal surface bordering mesoscutum, posterior border concave; propleuron projected into a conspicuous neck; mesoscutum flat in lateral view, with conspicuous edge along anterior border, with notauli not connected; mesosctellum with slightly developed axilla; tegula visible; mesopleuron short.

Legs long compared to mesosoma, with slender podites; protibial spur clearly curved; tibial spur formula 1-2-2; meso-and metacoxae closer to each other than to procoxa; trochantellus distinct but fused to associated femur; profemur shortest; basitarsus elongate but sub-equal to combined lengths of remaining tarsomeres; pretarsal claws small, simple; arolium minute.

Forewing with moderately wide costal space of comparatively consistent width along its length, slightly narrower than pterostigma; pterostigma longer than wide, expanded in width medially, tapering gradually in width to acute apex; r-rs vein originating at widest part of pterostigma (slightly distad pterostigmal midlength); cell 1Cu long, separated from cell 2Cu by angled and curved vein 1cu-a; cell R slightly wider than 1Cu; cell 1R1 large compared to other cells, vein 1Rs slightly longer than 2Rs, both slightly curved, vein 2Rs+M short (more than twice as short as 2Rs), vein 1Rs+M straight and parallel to 1Cu, more than twice as long as 2Rs+M and enclosing cell 1M rectangular shaped, conspicuously longer than wide; cell 1M separated from 2M by a small vein 1m-cu sub-parallel to 2Rs and as long as 1M; cell 2Cu wider than long, slightly elongated basally with presence of vein 2cu-a and separated from 2M by vein 2Cu; cell 2M elongated, enclosed by vein 2m-cu and 3Cu; cell 2R1 broad and elongated (twice as long as wide), with greatest width near vein 2rs-m; vein 1rs-m and 2rs-m spectral and subequal, slightly curved; cell 1Rs shorter but as wide as 2Rs. Hind wing hidden under forewing, without visible venation except C+R.

Metasoma elongated in profile, cylindrical, longer than mesosoma; inserted well after metanotum; first metasomal segment long with anterior part modified into a petiole, remaining part cone J o u r n a l P r e -p r o o f shaped; first tergite and sternite longer than remaining ones; tergites and sternites equal to sub-equal in lengths and separated by conspicuous sutures; last segment shorter than preceding ones. Hypopygium divided ventrally to form an elongate, apically rounded lobe on each metasomal side. Apex of gaster projected apically into rounded parameres.

Measurements (in mm). Total length as preserved (excluding antennae) 3.1; head length (excl. mandibles) 0.37; compound eye 0.31 long, 0.24 wide; mesosomal length 1.0, maximum height 0.47; dorsal length of propodeum (between metanotum and petiolar insertion) 0.19; metasomal length 1.35; profemur length 0.46, protibial length 0.43, probasitari length 0.31, combined lengths of remaining tarsomeres 0.23; mesofemur length 0.53, mesotibial length at least 0.5, mesobasitarsus length 0.27, combined lengths of remaining tarsomeres not measurable; metafemur length 0.53, metatibial length 0.62; metabasitarsus length 0.27, combined lengths of remaining tarsomeres 0.35; forewing length 2.1; hind wing length 1.2.

Discussion.

Paleoaulacus gen. nov. is assigned to the Aulacidae based on the geniculate antenna with a distinct elbow between scape and pedicel, which differentiates it from Baissidae. Also its propleuron is extending forward to form a pronounced 'neck' (not present in †Bassidae). However, the current family rank of Baissidae might be challenged since lacking clear apomorphies [START_REF] Rasnitsyn | Vectevania vetula Cockerell, 1922 from the uppermost Eocene of Bembridge Marls, England, and the system of the family Gasteruptiidae s.l. [Vespida (= Hymenoptera), Evanioidea][END_REF] and retaining several plesiomorphies (listed in [START_REF] Engel | New evanioid wasps from the Cenomanian of Myanmar (Hymenoptera: Othniodellithidae, Aulacidae), with a summary of family-group names among Evanioidea[END_REF]. With 11 preserved antennomeres, and a reduced hind wing venation (viz. without 1r cell closed by tubular vein). Paleoaulacus gen. nov. vs. cannot be assigned to the †Praeaulacidae that have more than 20 flagellomeres. The family †Praeaulacidae is currently considered as the 'ancestral' group of Evanioidea and is characterized by a complete wing venation, except for some species of the subfamily †Cretocleistogastrinae [START_REF] Rasnitsyn | An outline of evolution of the hymenopterous insects (order Vespida)[END_REF][START_REF] J O U R N A L P R E -P R O O F Li | Anomopterellidae restored with two new genera and its phylogeny in Evanioidea (Hymenoptera)[END_REF]. Hence, Paleoaulacus gen. nov. cannot be assigned to this family since it has not such a wing venation. Paleoaulacus gen. nov. has not the typical horn with toruli, the long scape and the high number of antennomeres (20-21) proper to the †Othniodellithidae. It cannot be J o u r n a l P r e -p r o o f assigned to the †Anomopterellidae because it has only 12(?) antennomeres vs. at least 18 for the latter family.

Following [START_REF] Goulet | Hymenoptera of the world: An identification guide to families[END_REF], the extant Aulacidae differ from the Gasteruptiidae sensu Engel (2017) (= †Kotujellitinae + Gasteruptiinae + †Hypselogastriinae + Hyptiogastrinae) in having an anterior margin of metasomal segment 1 distinctly separated from metanotum, and metatibia at most slightly widened toward apex (vs. metasomal segment 1 with anterior margin almost touching metanotum, and metatibia gradually enlarged or markedly swollen toward apex, appearing clubshaped in Gasteruptiidae). Paleoaulacus gen. nov., thereby, keys out as an aulacid wasp. Following the key to suprageneric groups of Aulaciformes of [START_REF] Engel | New evanioid wasps from the Cenomanian of Myanmar (Hymenoptera: Othniodellithidae, Aulacidae), with a summary of family-group names among Evanioidea[END_REF], Paleoaulacus gen. nov. keys out near the tribes Aulcini and Electrofoenini. [START_REF] Engel | New evanioid wasps from the Cenomanian of Myanmar (Hymenoptera: Othniodellithidae, Aulacidae), with a summary of family-group names among Evanioidea[END_REF] proposed to use the relative positions of the eyes and antennae to separate Gasteruptiidae (see. Engel, 2017: Appendix: 'toruli never at or bordering ventral tangent of compound eyes') and Aulacidae (see. Engel, 2017: Appendix: 'toruli usually at or near ventral tangent of compound eyes'). Following this character Paleoaulacus gen. nov. also keys out as an Aulacidae. Paleoaulacus gen. nov. has a forewing venation developed as in some other Aulacidae, with the veins 1rs-m, 2rs-m and 2m-cu present (absent in Hyptiogastritinae). In view of all these characters, we assigned Paleoaulacus gen. nov. to the subfamily Aulacinae.

Following the key proposed by [START_REF] Engel | New evanioid wasps from the Cenomanian of Myanmar (Hymenoptera: Othniodellithidae, Aulacidae), with a summary of family-group names among Evanioidea[END_REF], Paleoaulacus gen. nov. would key out in the Aulacini because of the forewing with 2Rs+M shorter than 1Rs+M, and shorter than 2Rs plus short mandibles. However, Paleoaulacus gen. nov. clearly lacks the mesoscutum transversely carinate, challenging a confident placement within the tribe Aulacini. Moreover, Paleoaulacus gen. nov. has a metasoma with narrow tube-like petiole, sharply segregated from a cone-like base of the gaster. This character is unknown in Aulacini but occurs in some early diverged Aulacidae (e.g., Archeofoenus Engel, 2017 and some †Electrofoenini).

Similarly, Paleoaulacus gen. nov. could fall in the †Electrofoenini because of the mesoscutum not transversely carinate. It also shares with the recently described Electrofoenia jehani Jouault J o u r n a l P r e -p r o o f sent in Paleoaulacus gen. nov.). Paleoaulacus gen. nov. would rather display the 'groundplan' venation features of Evanioidea [START_REF] Basibuyuk | The limits of the family Evaniidae (Insecta: Hymenoptera) and a new genus from Lebanese amber[END_REF]. [START_REF] Chen | A revision of the Chinese Aulacidae (Hymenoptera, Evanioidea)[END_REF] proposed to separate Aulacus and Pristaulacus on the basis of the following characters: occipital carina absent in Aulacus vs. present in Pristaulacus; forewing with crossvein 2r-m, with 2Rs+M long in Aulacus vs. short in Pristaulacus; hind coxa of female without groove or notch on inner lateral surface in Aulacus vs. present in Pristaulacus; pretarsal claw not pectinate, without tooth-like processes along inner margin in Aulacus vs. pectinate, with tooth-like processes along inner margin in Pristaulacus. Even if we cannot discern the presence of a 'groove or notch on inner lateral surface of hind coxa', all the others characters allow us to assume that Paleoaulacus gen. nov. shares more characters with Aulacus than with Pristaulacus. However, Paleoaulacus gen. nov. differs from Aulacus in having more developed eyes (completely occupying the sides of head); cylindrical metasoma; cell 1M narrow with parallel to sub-parallel sides; and 2Rs+M short.

Conclusion.

The present description of Paleoaulacus gen. nov. suggests that the diversity of aulacid wasps in mid-Cretaceous Burmese amber is underestimated. Paleoaulacus gen. nov. possesses characters of the †Electrofoenini and of the Aulacini, challenging a clear placement in one of these two tribes.

Paleoaulacus gen. nov. could belong to a new tribe, maybe 'intermediate' between extant and extinct tribes. By sharing with the extant genus Aulacus a similar wing venation, Paleaoaulacus gen.

nov. shows an atypical stability of the wing venation though time; while the evolutionary tendency in the Aulacidae, and Hymenoptera as a whole, seems to have been towards a reduction and a simplification of the wing venation during geological time.

  Figs 1-2.

Acknowledgment

J o u r n a l P r e -p r o o f

We sincerely appreciate critical reviews and comments from the editor (Dr. Eduardo Koutsoukos), an anonymous reviewers, and Prof. Alexandr Rasnitsyn in improving our manuscript. We are grateful to Dr. Valérie Ngô-Muller (ISYEB, MNHN) who has kindly imaged the specimen.

J o u r n a l P r e -p r o o f