Keywords: uranyl(VI), plutonyl(VI), N-(1-adamantyl)acetamide, precipitation study, coordination complex, single-crystal X-Ray diffraction, thermal analysis

The reactivity of the N-(1-adamantyl)acetamide ligand (L = adam) has been evaluated as precipitating agent for the hexavalent uranyl cation ([U] = 20-60 g.L -1 ) in concentrated nitric acid aqueous solution (0.5-5 M). It results in the formation of a crystalline complex (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (1), in which the uranyl center is eight-fold coordinated to two chelating nitrate groups and two N-(1-adamantyl)acetamide (= adam) ligands through the oxygen atom of the amide function. Two other non-coordinating adam moieties are also observed in the crystal structure packing and interact through a hydrogen bond scheme with the uranyl-centered species. A similar molecular assembly has been obtained with the plutonyl(VI) cation, in the complex (PuO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (2).

Precipitation studies indicate high (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) formation yields (up to 99 % U for L/U molecular ratio of 5/1) for HNO 3 concentration in the 0.5-5 M range. However, the precipitation kinetics is rather slow and the reaction is completed after several hours (3-4 h). The calcination of the resulting solid under air atmosphere led to the formation of the U 3 O 8 oxide from 400 °C, through a transient phase UO 2 fluorite-type (from 200 °C).

Introduction

The research of organic molecules for the actinides conversion into a solid form from the aqueous solution resulting from the dissolution of the spent nuclear fuel in nitric acid has been intensively investigated during the last decades. One of the current industrial process, PUREX 1,[START_REF]Tributyl Phosphate in Nuclear Fuel Processing[END_REF] , is based on the utilization of oxalate anion as a non-selective precipitating agent of actinides(III and IV). This process requires a redox adjustment before the conversion and leads to the quantitative precipitation of trivalent and/or tetravalent actinides into solid actinide oxalates used as oxide precursors (precipitation yield > 99%) but is not efficient for hexavalent uranium precipitation. [START_REF]Reprocessing and Recycling of Spent Nuclear Fuel[END_REF][START_REF] Abraham | Actinide Oxalates, Solid State Structures and Applications[END_REF][START_REF] Grandjean | Method for Co-Precipitation of Actinides in Different Oxidation States and Method for Preparation of Mixed Actinide Compounds[END_REF] Alternative reprocessing routes have been studied and based on a precipitation without redox of uranyl by new organic molecules, which chemically interact specifically with the targeted actinides. In this context, a family containing pyrrolidone derivatives has been explored for their properties as precipitating agent toward the uranyl species. Indeed, in 2000, Ikeda and co-workers [START_REF] Varga | New Uranyl Nitrate Complex with N-Cyclohexyl-2-Pyrrolidone: A Promising Candidate for Nuclear Fuel Reprocessing[END_REF] described the selective precipitation of UO 2 2+ cation with a yield of 68 % U by the N-cyclohexyl-2-pyrrolidone (NCP) molecule [START_REF] Varga | Molecular and Crystal Structure of Bis(N-Cyclohexyl-2-Pyrrolidone)Dioxouranium(VI) Nitrate[END_REF] in concentrated nitric acid solutions, and opened a new investigation path for the research of novel precipitating agents with actinides. This NCP molecule has been found to be one of the most efficient ligands for the precipitation of uranyl solution and could be considered in a new process for recovering the actinides from spent nuclear fuel. [START_REF] Koshino | Using Selective Precipitant for Uranyl Ions -Fundamental Studies for Evaluating the Precipitant Performance[END_REF] The combination of a -butyrolactam group, with a cyclohexyl chain, is likely a good compromise that allows a good solubility of the free ligand in water and a relatively high hydrophobicity once the amide group is coordinated to metallic cations. The nature of the functionalization of the -butyrolactam has been examined in order to optimize the uranyl cation precipitation in concentrated nitric acid aqueous solution. These investigations gave rise to many reports of the structural characterizations of several pyrrolidone-based nitrate complexes with uranyl(VI). [START_REF] Varga | Molecular and Crystal Structure of Bis(N-Cyclohexyl-2-Pyrrolidone)Dioxouranium(VI) Nitrate[END_REF][START_REF] Ikeda | A Study on Pyrrolidone Derivatives as Selective Precipitant for Uranyl Ion in HNO3[END_REF][START_REF] Kazama | Molecular and Crystal Structures of Uranyl Nitrate Coordination Polymers with Double-Headed 2-Pyrrolidone Derivatives[END_REF] The reactivity of plutonyl(VI) cations has been also studied in order to analyze the formation of such pyrrolidone molecular assemblies, which may co-crystallize with the analogous uranyl(VI) element. [START_REF] Morita | Development of Advanced Reprocessing System Based on Precipitation Method Using Pyrrolidone Derivatives as Precipitants: -Precipitation Behavior of U(VI), Pu(IV), and Pu(VI) by Pyrrolidone Derivatives with Low Hydrophobicity[END_REF][START_REF] Kim | Molecular and Crystal Structures of Plutonyl(VI) Nitrate Complexes with N -Alkylated 2-Pyrrolidone Derivatives: Cocrystallization Potentiality of U VI and Pu VI[END_REF] The family of the alkylamides, to which pyrrolidone belongs, has also shown a potential interest as a specific extractant of the cationic uranyl (UO 2 2+ ) and plutonium (Pu 4+ ) species for the separation of actinides from fission products. [START_REF] Ansari | Chemistry of Diglycolamides: Promising Extractants for Actinide Partitioning[END_REF][START_REF] Musikas | Solvent Extraction for the Chemical Separations of the 5f Elements[END_REF] In this context, many investigations reported the formation of monoamide uranyl (UO 2 (NO 3 ) 2 L 2 ) complexes or diamides (UO 2 (NO 3 ) 2 L) complexes, in which the organic molecules L act as monodentate or polydentate ligands toward the actinide metallic center. The modification of the alkyl group (length and branching of the carbon chain) of the amide as well as functionalization offers the possibility to tune their extracting abilities.

In the present study, we studied another relative of monoamide to be considered in conversion processes. We report the efficient precipitation of uranyl cation in nitric acid aqueous solution by an acetamide-based molecule bearing an adamantyl group called N-(1adamantyl)acetamide. With a cyclohexyl fragment completed by two other connected cyclohexane groups in an "armchair" configuration, the nitrogen atom is still functionalized by a non polar aliphatic cycle, as for the NCP. To counter balance the increase of the molecule hydrophobicity, the butyrolactam is removed (Figure 1).

Experimental Section

Reagents. Caution! Uranium and plutonium precursors are radioactive and chemically toxic reactants, so precautions with suitable care and protection for handling such substances have been followed. S1b). Due to the highly plutonium radiotoxicity, limited characterizations have been carried out with this element: they included single-crystal X-ray diffraction, powder X-ray diffraction (Figure S2b) and one batch of precipitation (from [Pu] = 20g.L -1 ) analyses.

Single-crystal X-ray diffraction

Crystal of compound 1 was selected under polarizing optical microscope and glued on a glass fiber for a single-crystal X-ray diffraction experiment. X-ray intensity data were collected on a Bruker DUO-APEX2 CCD area-detector diffractometer using Mo-K  radiation ( = 0.71073 Å) with an optical fiber as collimator. Several sets of narrow data frames (20 s per frame) were collected with  scans. A crystal of 2 was mounted on MicroMount patented by MiTeGen, inserted into a goniometer base. For confinement purpose, a MicroRT capillary was then drawn over the sample and onto the base, where it was sealed by adhesive. The single-crystal XRD intensities were measured on a Nonius four-circle diffractometer equipped with an Apex II detector. The instrument was equipped with a fine-focus Mo-target X-ray tube (λ = 0.71073 Å) operated at 1500 W. Data reduction was accomplished using SAINT V7.53a. [START_REF]SAINT Plus Version 8.34a, Bruker Analytical X-Ray Systems[END_REF] The substantial redundancy in data allowed a semi-empirical absorption correction (SADABS V2.10 38 ) to be applied, on the basis of multiple measurements of equivalent reflections. The structure of 1 was solved by direct methods, developed by successive difference Fourier syntheses, and refined by full-matrix least-squares on all data using SHELX program suites, [START_REF] Sheldrick | A Short History of SHELX[END_REF] implemented in the OLEX2 [START_REF] Dolomanov | OLEX2 : A Complete Structure Solution, Refinement and Analysis Program[END_REF] interface. Crystals of compound 2

were systematically twinned (merohedral twinning) and were treated by means of the JANA2006 software suite. [START_REF] Petříček | Crystallographic Computing System JANA2006: General Features[END_REF] For this compound 2, the orientation matrix for the two domains was 1 0 0; -0.1172 -1 0; -0.47 0 -1, with 49.6(7) % of domain I, and consequently 50.4(7) % of domain II.

The crystal data are given in Table 1. Supporting information is available in CIF format.

CCDC numbers: 1987462 for 1, 1987465 for 2, contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

ICP-AES (Inductively Coupled Plasma Atomic Emission Spectroscopy).

The supernatant aqueous solutions after reaction of the uranyl nitrate precursor with the organic adam ligand have been analyzed by using a Vista-PRO VARIAN spectrometer. A fraction of the supernatant solution (10 L) was extracted, then diluted 1000 times with deionized water. The remaining uranium concentration was then directly analyzed with the ICP-AES technique. The ICP measurement was accumulated routinely three times and then merged. The uranium contents are given with uncertainties of 5%.

Powder XRD

X-ray powder diffraction was performed on Bruker D8 Advance diffractometer (LynxEye detector) in a Bragg-Brentano - mode using Cu-K  radiation. Each powder pattern was recorded within an angular range of 5-50° in 2, with steps of 0.02° and counting time of 0.5 s per step.

Scanning electron microscopy

The SEM analyses of uranium compound were performed on a Hitachi-S3400N microscope, equipped with a tungsten filament (acceleration voltage = 15 kV, secondary electron mode, working distance = 5 to 10 mm). Plutonium compound was studied on a Zeiss Supra 55/55VP field-emission scanning electron microscope (acceleration voltage = 5 kV, secondary electron mode, working distance 5 to 10 mm, diaphragm= 30 µm). Both with uranium and plutonium based samples, powders were coated with gold prior to the analysis.

Specific surface area measurement

The specific surface area was measured at 77 K by the BET method with a MICROMERITICS ASAP 2020 (surface area and porosity analyzer). About 100 mg of sample has been used and degassed at 200°C under vacuum. For surface area calculations, we used krypton gas adsorption and BET model was applied in the p/p 0 range of 0.01-0.2.

Thermal analysis

Thermogravimetric analysis was performed on a thermoanalyzer 92 SETARAM TGA up to 800 °C, in air, with a heating rate of 5 °C.min -1 .

X-ray thermodiffractometry was performed under 5l.h -1 air flow in an Anton Paar HTK1200N of a D8 Advance Bruker diffractometer (- mode, CuKα radiation) equipped with a Vantec1 linear position sensitive detector (PSD). Each powder pattern was recorded in the range 5-60° (2) (at intervals of 20°C up to 800°C) with a 0.5 s/step scan, corresponding to an approximate duration of 30 mn.

Visible spectroscopy

The plutonium solutions were determined by Vis spectroscopy using a spectrophotometer VARIAN CARY 6000i, the optical signal is transmitted through optical fibers (10 m length, Hellma) from the disposable UV-cuvette (PMMA, 1 cm optical path) inside the glove-box to the spectrophotometer placed outside. Solution is scanned from 350 to 900 nm with a speed of 300 nm/min, a measuring range of 1 nm and a gap width of 1.5 nm. Uncertainties of the uranium content are estimated to be 10%.

Results and discussion

Structure Description

The association of the N-(

Precipitation study of the actinyl N-(1-adamantyl)alkylamide nitrate complexes

The precipitation yield of uranyl nitrate with N-(1-adamantyl)acetamide (L) was firstly investigated in nitric acid aqueous solution. The initial uranium and nitric acid concentrations were adjusted to 20 g.L -1 and 0.5 M, respectively. The molar ratio of amide over uranium concentrations L/U range from 0.25 to 6. The precipitation process followed the synthetic route described in the experimental section for the preparation of complex 1 under static conditions (without magnetic stirring), after heating at 50 °C for 24 hours. The supernatant solution at the end of the precipitation was separated from the solid and analyzed by ICP-AES to measure the concentration of non-converted uranyl species, and thus the quantitative yield of the precipitation reaction for the formation of complex 1. For each synthesis, the composition of the solid was analyzed by powder X-Ray diffraction to ensure it is singlephased. One example of the comparison of the experimental XRD pattern to the calculated one (from the single-crystal study) is given Figure S2a of the supporting information. The solid was also analyzed by IR spectroscopy (see Figure S8 of the supporting information).

Figure 4 indicates the evolution of the yield of the formation of (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam)

(1) precipitate as a function of L/U molar ratio. It shows a linear increase of the yield between L/U = 0.25 and L/U = 4 (yield reaction 92 % U ), and then a slight increase for L/U>4, 96 % and 99 % U for L/U = 5 and 6 respectively. The optimum ratio L/U = 4 is expected since it is directly related to that of the stoichiometry observed in the crystal structure of complex 1. For the U/L = 6 ratio value, the remaining uranium concentration in the supernatant solution is lower than 0.2 g.L -1 . Due to the structural similarities observed for the complex (AnO 2 )(adam) 2 (NO 3 ) 2 •2(adam) involving uranium(VI) (1) or plutonium(VI) (2), the same experiment has been performed from an aqueous solution containing plutonyl nitrate species with a concentration of 20 g.L -1 at ambient temperature. For safety reasons, it was not possible to carry out the experiment at 50 °C as for uranium. Moreover, the nitric acid concentration was set to 1 M to preclude plutonium hydrolysis reaction. The molar ratio of the N-(1-adamantyl)acetamide (L) over Pu contents was ranging from 1 to 5, and the mixture was left static for 16 hours. The comparison of the experimental XRD pattern to the calculated one (from the single-crystal study) given

Figure S2b of the supporting information indicates the formation of the same phase as the one described previously. The reaction yield for the formation of complex (PuO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (2) was estimated on the basis of the concentration of plutonium remaining in the aqueous solution, by using UV-Vis spectroscopy. The evolution of the plutonium precipitation yield is alike the uranyl one: linear progression between L/Pu = 1 and L/Pu = 4 ratios (Figure 4), with a upper value up to 88 % Pu with a slight increase for higher ratio than stoichiometry (L/Pu = 5, 95 % Pu ).

For the formation of the uranyl N-(1-adamantyl)acetamide nitrate complex (1), the influence of the acidity of the aqueous solution has been then examined for nitric acid concentrations ranging from 0 to 5 M with L/U molar ratio of 5 (after reaction at 50°C for 24 hours). Without HNO 3 , the precipitation yield is found to be about 88 % U . The addition of nitric acid favors the crystallization of compound 1 resulting in increasing acidity, and by providing an excess of nitrate anion to the reaction medium. An increase of the precipitation yield up to 99 % U for HNO 3 above 1 M, (Figure 5). This result as well as the conservation of the XRD patterns indicate that such uranyl N-(1-adamantyl)acetamide nitrate complex (1) exhibits a very good stability toward nitric acidity, as it is required in the actinide recycling process. The concentration of uranium in aqueous solution with nitric acid 0.5 M was then studied for 20, 40 and 60 g.L -1 . For the L/U ratio of 5, the precipitation yield remains approximately stable even if it slightly increases with the uranium concentration, from 96 up to 98 % U (Figure S5).

Precipitation kinetics of the uranyl N-(1-adamantyl)acetamide nitrate complex (1)

The kinetics of the precipitation of the complex 1 was analyzed for three uranium concentrations, 20, 40 and 60 g.L -1 in HNO 3 0.5 M. The ligand was added at t=0 to the uranyl nitrate aqueous solution and then a 10 L sample of supernatant liquid was withdrawn at different times in order to measure by ICP the remaining uranium concentration in the liquid phase. The Avrami-Erofe'ev equation [START_REF] Charushnikova | Crystal Structure of a Complex of Pu(VI) Nitrate with Triphenylphosphine Oxide[END_REF][START_REF] Finney | Is There a Minimal Chemical Mechanism Underlying Classical Avrami-Erofe'ev Treatments of Phase-Transformation Kinetic Data?[END_REF] involving an exponential evolution of type  = 1exp[-(kt) n ] was used to help rationalize the data. For this model,  is the reaction rate (in our case, related to the precipitation yield of uranyl complex 1), k is a kinetics constant and n is an Avrami coefficient. Although this kinetics model was initially used for the specific case of solid-solid transitions, it is now widely used to describe the crystalline formation of different types of materials (for instance: zeolites, [START_REF] Jensen | In Situ Studies of Solvothermal Synthesis of Energy Materials[END_REF][START_REF] Thompson | Mathematical Analyses of Zeolite Crystallization[END_REF] organically templated metal phosphates, [START_REF] Norby | Hydrothermal Conversion of Zeolites: An in Situ Synchrotron X-Ray Powder Diffraction Study[END_REF][START_REF] Francis | Time-Resolved In-Situ Energy and Angular Dispersive X-Ray Diffraction Studies of the Formation of the Microporous Gallophosphate ULM-5 under Hydrothermal Conditions[END_REF][START_REF] Vistad | Identification of a Key Precursor Phase for Synthesis of SAPO-34 and Kinetics of Formation Investigated by in Situ X-Ray Diffraction[END_REF] coordination polymers, metal-organic frameworks, 50-52 …). The expression is quite convenient to extract kinetics constants of the formation of crystalline products. However, the significance of the fitted Avrami parameter could be questionable and then considered with caution, if one considers the heterogeneous crystallization from a solution to a solid, as it occurs in our precipitation experiment of uranyl N-(1-adamantyl)acetamide nitrate complex.

The fit accuracy of kinetics curves has been evaluated using the Sharp-Hancock method, [START_REF] Cravillon | Formate Modulated Solvothermal Synthesis of ZIF-8 Investigated Using Time-Resolved in Situ X-Ray Diffraction and Scanning Electron Microscopy[END_REF] corresponding to the linear transformation of the Avrami-Erofe'ev equation, as ln[-ln(1 -)]

= nln(k) + nln(t). The kinetics parameters obtained for the different precipitations with various conditions (static/stirring; [U] varying from 20 to 60 g.L -1 ) are summarized in the Table 3.

The Avrami-Erofe'ev and Sharp-Hancock plots are presented in the Figure 6 only for [U] = 20 g.L -1 . Other kinetics curves for [U] = 40 and 60 g.L -1 , are given in the Supplementary

Information (Figures S6 & S7).
At [U] = 20 g.L -1 , under static condition (without magnetic stirring; Figure 6), the maximum precipitation yield is not reached after 10 hours, since only 87% of uranium crystallized. The corresponding fitted values k and n are 0.0049(3) min -1 and 0.71 (5), respectively. The influence of stirring the aqueous solution mixture has been evaluated by means of rotating magnet (rotation speed: 750 rpm). The precipitation kinetics increases drastically under magnetic stirring reaching the maximum yield value of 99% U after 4 hours of reaction at 50°C. The corresponding k and n values are 0.0168(7) min -1 and 0.99 (7), respectively. The effect of stirring increases the precipitation kinetics by a factor 3.5 in these conditions. The same behavior is observed for higher uranium concentrations, but less contrasted. The k parameters are 0.0101(4) min -1 (static) and 0.0203(6) min -1 (stirring) for [U] = 40 g.L -1 , and are a factor of 2. They are 0.0214(7) min -1 (static) and 0.0230(8) min -1 (stirring) for [U] = 60 g.L -1 , and are only a factor of 1.07. For the latter, the influence of the magnetic stirring is quite limited, since the kinetics gain is about 7%. The kinetics of the precipitation is thus directly correlated to the concentration of uranium in the aqueous nitric acid solution. Without stirring, this result is not surprising as for a greater concentration, the reagent put in touch is less limited by diffusion. The maximum precipitation yield (99% U ) is reached after 3 hours for [U] = 40 and 60 g.L -1 , under stirring conditions. However, we notice that the kinetics of precipitation remains quite slow and requires a reaction time of 3-4 hours for getting the maximal yield. The Avrami parameters are in the range 0.7-1.1 (Table 3), with higher values for the stirring conditions (in the range 0.9-1.1) and lower values for the static conditions (in the range 0.7-0.9). According to previous data from literature, [START_REF] Finney | Is There a Minimal Chemical Mechanism Underlying Classical Avrami-Erofe'ev Treatments of Phase-Transformation Kinetic Data?[END_REF][START_REF] Hancock | Method of Comparing Solid-State Kinetic Data and Its Application to the Decomposition of Kaolinite, Brucite, and BaCO 3[END_REF] the crystallization mechanisms would be controlled by the diffusion of species for an Avrami exponent in the range 0.6-0.8, whereas it is controlled for reaction of species on the crystal surface if the Avrami exponent is in the range 1.0-1.1. This study confirms these two mechanisms: under static conditions, the kinetics of precipitation would be limited by a diffusion-controlled mechanism, and under stirring conditions, it would be limited by phase-boundary-controlled reaction. This study shows that the acetamide bearing an adamantyl group (i.e N-(1adamantyl)acetamide) could be a good candidate for precipitating uranyl nitrate from highly acidic nitric acid aqueous solutions. When the adam/U ratio reaches to 5/1, one observes high yields for uranium precipitation with values in the range 96-99% U for nitric acid concentrations 1-5M. It is well-known that the classical precipitating agent used in the spent nuclear fuel recycling is the oxalic acid molecule, which is very efficient for its rapid reaction with tetravalent actinide, such as plutonium(IV) with very high yields (>99% Pu ).

Unfortunately, in the case of uranyl nitrate aqueous solution, the precipitation yield was observed to decrease drastically. For instance, previous investigations, [START_REF] Leturcq | Uranyl Oxalate Solubility[END_REF] [START_REF] Leturcq | Uranyl Oxalate Solubility[END_REF] By comparison, our study indicates a precipitation of uranyl nitrate complex within roughly the same reaction time but, with a better precipitation yield (up to 99% U ).

Nevertheless, this slow precipitation kinetics drawback is not reported when using Ncyclohexyl-2-pyrrolidone (NCP), for which a pioneering work describes the formation of an uranyl nitrate coordination complex UO 2 (NO 3 ) 2 (NCP) 2 with reaction yield of 68 % U , from an initial NCP/U = 3.6 and [U] = 50 g.L -1 . [START_REF] Varga | Molecular and Crystal Structure of Bis(N-Cyclohexyl-2-Pyrrolidone)Dioxouranium(VI) Nitrate[END_REF] Further investigations on this NCP-U(VI) system have shown a robust precipitation route since high specifications with reaction yields > 99% U have been described from highly concentrated uranyl nitrate solution, i.e 238 g.L -1 , NCP/U ratio >3 in HNO 3 3M. [START_REF] Morita | A Study on Precipitation Behavior of Plutonium and Other Transuranium Elements with N-Cyclohexyl-2-Pyrrolidone for Development of a Simple Reprocessing Process[END_REF] The main difference is the kinetics of the precipitation of uranyl cation between the NCP and adam systems. Indeed, the precipitation of the NCP uranyl nitrate complex is complete after a few minutes at room temperature only, [START_REF] Morita | A Study on Precipitation Behavior of Plutonium and Other Transuranium Elements with N-Cyclohexyl-2-Pyrrolidone for Development of a Simple Reprocessing Process[END_REF] but requires a reaction time for several hours for the production of the complex 1 with adam ligand from solutions containing [U] = 40 or 60 g.L -1 at 50°C (with HNO 3 0.5M). The solubility of the organic complexing agent in water might be considered for explaining such different kinetic reactivities. The NCP molecule is a viscous liquid, which possesses a high miscibility with water, [START_REF] Ikeda | A Study on Pyrrolidone Derivatives as Selective Precipitant for Uranyl Ion in HNO3[END_REF] whereas oxalic acid and N-(1-adamantyl)acetamide) reactants are powdered compounds. The water solubility of oxalic acid is known to be quite high (90-100 g.L -1 at room temperature) and we estimated that of N-(1-adamantyl)acetamide), which was found to be very low ( 1-2 g.L -1 at room temperature). These ligand solubility considerations may thus control the slow formation of the (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (1) complex, compared to that of the NCP uranyl complex. This drastic kinetics difference strongly limits the potential use of the N-(1-adamantyl)acetamide molecule as precipitating agent for industrial applications.

Thermal analysis

The thermal treatment under air atmosphere has been analyzed, only for the complex 1, in order to study the thermal transition of this uranyl complex under its oxide form. The thermal decomposition of complex 1 has been characterized by in-situ powder X-ray diffraction (Figure 7). This experiment shows multiple phase transformation steps. Bragg peaks of the phase 1 persist up to 200°C. At this temperature, a new transient crystalline product (red diffraction patterns -Figure 7) appeared with a new set of peaks located at d = 10.03, 8.96, 6.67 and 7.62 Å, for the lowest angle values. This structural transformation is related to a first weight loss of 3 %, after heating up to 170°C, reported on the thermogravimetric curve (Figure S9). Between 200 and 400°C, new broad Bragg peaks (blue diffraction patterns -Figure 7) are visible with d = 3.33, 2.86 and 1.99 Å, indicating the crystallization of a second badly crystalline product, related to the formation of UO 2 fluorite type compound (Figure S11). A remarkable and unexpected transient reduction of the uranium is observed during the decomposition of the coordination organic-inorganic complex. Indeed, previous thermal decompositions have been reported for some uranyl coordination complexes, such as uranyl terephthalate, [START_REF] Mihalcea | Six-Fold Coordinated Uranyl Cations in Extended Coordination Polymers[END_REF] uranyl pyromellitates [START_REF] Mihalcea | Uranyl-Pyromellitate Coordination Polymers: Toward Three-Dimensional Open Frameworks with Large Channel Systems[END_REF] or uranyl mellitate, [START_REF] Volkringer | Uranyl and/or Rare Earth Mellitates in Extended Organic-Inorganic Networks: A Unique Class of Heterometallic Cation-Cation Interaction with UVI=O-LnIII Bonding (Ln = Ce, Nd)[END_REF] for instance. The thermal transformation of these initial complexes went directly to the formation of the uranium oxide U 3 O 8 under air atmosphere, without through the generation of a transient UO 2 phase. For the present study, the appearance of the UO 2 oxide could be correlated to the air combustion of the organic part (which is present with a larger L/U ratio compared to the previous examples), [START_REF] Mihalcea | Six-Fold Coordinated Uranyl Cations in Extended Coordination Polymers[END_REF][START_REF] Mihalcea | Uranyl-Pyromellitate Coordination Polymers: Toward Three-Dimensional Open Frameworks with Large Channel Systems[END_REF][START_REF] Volkringer | Uranyl and/or Rare Earth Mellitates in Extended Organic-Inorganic Networks: A Unique Class of Heterometallic Cation-Cation Interaction with UVI=O-LnIII Bonding (Ln = Ce, Nd)[END_REF] likely into transient CO species, inducing high concentration of these evacuating gases and provoking the temporary reduction of uranium, crystallizing with the fluorite structure. This intermediate uranium reduction during thermal treatment is therefore quite specific of the degradation of compound 1. The fluorite phase is then classically transformed when further heating under air into the U 3 O 8 form. [START_REF] Rousseau | A Detailed Study of UO 2 to U 3 O 8 Oxidation Phases and the Associated Rate-Limiting Steps[END_REF] Indeed, from 400°C, the crystallization of -U 3 O 8 is clearly observed with peaks intensity increasing with temperature.

The thermogravimetric curve of this complex (Figure S9) presents weight loss events between 120 and 500 °C. The remaining weight value is 24.1 %, in good agreement with the expected one (24.0 %wt.), for U 3 O 8 as final phase at 800°C.

BET surface area (using krypton adsorption) of the resulting uranium oxide after heating at 800°C, was measured at 3.9 (±0.5) m 2 .g -1 . This value strongly depends on the calcination conditions but seems to be a bit high compared to previous studies on U 3 O 8 compounds. [START_REF] Chazel | Effect of U3O8 Specific Surface Area on In Vitro Dissolution, Biokinetics, and Dose Coefficients[END_REF][START_REF] Smith | Atmospheric Contamination of Uranium Dioxide Powder[END_REF] Scanning electron microscopy of the calcined complex 1 at 800°C indicates the preservation of large blocks (50 m), but cracks and holes are visible, due to the gaseous evacuation of the degradation products from the organic ligand (Figure S10).

Conclusion

In summary, the ability of the N-(1-adamantyl)acetamide molecule to precipitate the uranyl cation has been examined in the view of a general actinide recycling process. In a wide range of highly concentrated nitric acid solutions (0.5-5 M), this organic species is able to react with the actinyl cation, to form a crystalline coordination complex, (AnO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (An = U(1) or Pu(2)), obtained with high yield (up to 99% An , when L/An ratio is 5). The The N-(1-adamantyl)acetamide ligand has thus showed interesting properties for the quantitative precipitation of uranyl(VI) cation in nitric acid, which can be extended to the use of the analogous element, plutonyl(VI) cation (2). This chemical reactivity have been restricted to the use of hexavalent state of actinide and further investigations will be required in order to examine the precipitation behavior with tetravalent actinide elements.

Figure 1 :

 1 Figure 1: Schematic representation of the studied monoamide N-(1-adamantyl)acetamide (left) and Ncyclohexyl-2-pyrrolidone (right). The common carbon backbone of the two ligand types is indicated in red.

[

  diff. peak and hole/e.Å -3 1.151 and -0.419 1.15 and -1.43

are 1 .

 1 257(3) and 1.268(3) Å, for the oxygen atoms involved with the uranyl center in 1. The terminal N-O bonding distance is shorter, with a value of 1.215(3) Å, as expected. 7,16 The distances within the nitrate group in 2, are 1.270(4) Å for the oxygen atoms linked to the plutonyl center and 1.219(6) Å for the terminal N-O bonding.

Figure 2 :

 2 Figure 2: Representations of the molecular complex of the uranyl N-(1-adamantyl)acetamide UO 2 (adam) 2 (NO 3 ) 2 •2(adam) (1). Yellow circle: uranium(VI); red circle: oxygen; blue circle: nitrogen; grey circle: carbon; light grey circle: hydrogen. The molecular complex of the plutonyl analog (2) is identical and shown in Figure S4.

Table 2 : 2 .Figure 3 :

 223 Figure 3: View of the hydrogen bond network (dotted red line) in compound AnO 2 (adam) 2 (NO 3 ) 2 •2(adam) (1-2), with the connection modes between free N-(1adamantyl)acetamide molecules and the coordination molecular complex [AnO 2 (adam) 2 (NO 3 ) 2 ] via N-H•••O nitrate and N-H•••O-C bonding. Yellow circle: uranium(VI) or plutonium(VI); red circle: oxygen; blue circle: nitrogen; grey/black circle: carbon; light grey circle: hydrogen.

Figure 4 :

 4 Figure 4: Yields of the formation of (AnO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (U (1): red lozenge; Pu (2): blue triangles) precipitates as a function of L/U molar ratio in HNO 3 0.5 M for uranyl aqueous solution and HNO 3 (1 M) for plutonyl aqueous solution ([U] = [Pu] = 20 g.L -1 ).

Figure 5 :

 5 Figure 5: Yield of the formation of (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (1) precipitate as a function of the HNO 3 concentration for L/U molar ratio 5/1.

Figure 6 :

 6 Figure 6: (top) Kinetics curve of formation of the (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (1) precipitate for U concentration at 20 g.L -1 under static conditions (red) and magnetic stirring (blue) in HNO 3 0.5 M (at 50°C), with molar ratio ligand/U =5. (bottom) Sharp-Hancock plot from linear regression of the Avrami-Erofe'ev equation (ln[-ln(1-)] = nln(k) + nln(t)).

Figure 7 :

 7 Figure 7: Evolution of the powder XRD patterns as a function of temperature for the (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (1) (heating rate 5°C.min -1 and scans collected every 50°C, air atmosphere). XRD patterns in green: (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (1) phase; red: unknown phase; blue: transient fluorite-like UO 2 phase; black: -U 3 O 8 phase.

  kinetics investigations have shown that the precipitation reaction is rather slow and completed after several hours (3-4 h) for the compound 1 even under stirring. This could be related to the rather weak solubility of the powdered N-(1-adamantyl)acetamide molecule in water, which inhibits the rapid reaction with the uranyl cations. The thermal degradation of the (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) compound (1) showed a decomposition in three steps with the transient formation of an crystalline unidentified phase, followed by a reduction process from 200°C, with the crystallization of fluorite-type UO 2 , and finally transformed into uranium oxide U 3 O 8 from 400°C, under air atmosphere.

Compounds 1 & 2 syntheses (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (1):

  Initially, Pu(IV) nitrate solution ( 239 Pu) was prepared by dissolving the corresponding oxide, PuO 2 , in a nitrofluorhydric solution (HNO 3 10 M-HF 0.05 M) followed by a purification step on a DOWEX resin. Then, the resulting Pu(IV) nitrate solution was oxidized to Pu(VI) nitrate solution by addition of silver oxide AgO (molar ratio Ag/Pu = 2/1).

	The reduced form of Ag + ion was eliminated by precipitation with one equivalent of
	hydrochloric acid to form AgCl. The resulting plutonyl(VI) nitrate aqueous solution was
	filtrated under vacuum and characterized by UV-Vis spectroscopy in order to determine the
	final plutonium concentration.
	The other following reactants were used: uranyl nitrate hexahydrate (UO 2 (NO 3 ) 2 •6H 2 O,
	Merck, 99 %), N-(1-adamantyl)acetamide (C 12 H 19 NO, noted adam, Alfa Aesar, 98 %), nitric
	acid (HNO 3 , 68 %, VWR) and deionized water. The chemical reactants were commercially
	available and were used without any further purification.
	A mixture of 200 mg (0.4 mmol) UO 2 (NO 3 ) 2 •6H 2 O, 75
	mg (0.4 mmol) N-(1-adamantyl)acetamide and 10 mL aqueous HNO 3 (0.5 M) was placed in a
	glass tube and then heated at 50°C for 24 hours. The resulting yellow crystalline powder was
	then filtered off, washed with water and dried at room temperature in air atmosphere. Yield
	reaction was 24.4 % U from these synthetic conditions (here, initial Ligand/U ratio of 1/1). 1
	was analyzed by scanning electron microscope showing well-shaped multi-facetted bulky
	crystals of 10-150 m size (Figure S1a).

The manipulation of plutonium reactant has been carried out at the ATALANTE facility (CEA-Marcoule, France). Because of the highly radioactive nature of plutonium, the experiments involving this element were carried out in glove box with very restrictive protocols.

(PuO 2 )(adam) 2 (NO 3 ) 2 •2(adam) (2): A mixture of

	162 mg (0.84 mmol) N-(1-
	adamantyl)acetamide and 5mL plutonyl(VI) nitrate aqueous solution ([Pu] = 0.084 M;
	[HNO 3 ] = 1 M) was placed in a glass tube and then left at room temperature for 16 hours.
	Yield reaction was 49 % Pu . 2 was analyzed by scanning electron microscope showing well-
	shaped multi-facetted bulky crystals of 5-50 m size (Figure

Table 1 .

 1 Crystal data and structure refinement for compounds 1 & 2.

		1	2
	Formula	C48H76N6O12U	C48H76N6O12Pu
	Formula weight	1167.17	1173.2
	Temperature/K	296	293
	Crystal type	yellow block	yellow block
	Crystal size/mm	0.25 x 0.20 x 0.16	0.06 x 0.05 x 0.04
	Crystal system	triclinic	triclinic
	Space group	P-1	P-1
	a/Å	10.1363(3)	10.0759(3)
	b/Å	11.5945(3)	11.5308(3)
	c/Å	12.8737(4)	12.5976(4)
	α/°	65.038(1)	65.646(1)
	β/°	70.866(1)	71.250(1)
	γ°	79.406(1)	79.151(1)
	Volume/Å 3	1294.05(7)	1259.99(6)

  Figure 2). Within this discrete entity, the actinyl center sits on a special position ½ ½ 0 (inversion center, 1e) and holds an eight-fold hexagonal bipyramidal coordination, with the typical double trans uranyl (U=O = 1.763(2) Å), or plutonyl (Pu=O = 1.736(3) Å) bondings.

	The two nitrate groups are placed in trans position within the equatorial hexagonal plane,
	adopting a chelating connection mode, with U-O bonding lengths of 2.514(2) and 2.536(2) Å
	in 1, and Pu-O bonding lengths of 2.492(3) and 2.519(3) Å in 2. The two remaining An-O
	bondings correspond to the monodentate linkage with the amide oxygen atom of the organic
	ligand (U-O = 2.366(1) Å; Pu-O = 2.368(2) Å). It is interesting to notice that the An-O nitrate
	bond lengths decrease from uranyl to plutonyl as expected with the radius contraction, but the
	An-O

1-adamantyl)acetamide ligand with actinyl(VI) cations gives rise to the formation of a coordination complex of type (AnO 2 )(adam) 2 (NO 3 ) 2 •2(adam), where An is U in 1, and Pu in 2. Their crystal structures are similar and composed of a molecular moiety containing actinyl center bonded to two N-(1-adamantyl)acetamide and two bidentate nitrate groups (amide bond length is almost identical. For complex 1, the U-O nitrate ( 2.52 Å) and U-O amide ( 2.36 Å) bond distances are typical for uranyl, according to the Cambridge Structural Database (Release v.5.41 November 2019). For the plutonyl complex 2, only three compounds have been referenced in the presence of chelating nitrate groups, with the Pu-O nitrate bond distances in the range 2.472-2.519 Å

[START_REF] Kim | Molecular and Crystal Structures of Plutonyl(VI) Nitrate Complexes with N -Alkylated 2-Pyrrolidone Derivatives: Cocrystallization Potentiality of U VI and Pu VI[END_REF][START_REF] Charushnikova | Crystal Structure of a Complex of Pu(VI) Nitrate with Triphenylphosphine Oxide[END_REF][START_REF] Gaunt | Structural and Spectroscopic Characterization of Plutonyl(VI) Nitrate under Acidic Conditions[END_REF]

and Pu-O amide bond distance equal to 2.377 Å,

[START_REF] Kim | Molecular and Crystal Structures of Plutonyl(VI) Nitrate Complexes with N -Alkylated 2-Pyrrolidone Derivatives: Cocrystallization Potentiality of U VI and Pu VI[END_REF]

close to what is observed here. Within the nitrate groups, the N-O bond distances

Table 3 :

 3 Kinetics parameters extracted from the curve fits from the Avrami-Erofe'ev equation and Sharp-Hancock plots describing the crystallization of (UO 2 )(adam) 2 (NO 3 ) 2 •2(adam)(1). The fitting was performed using Kaleidagraph 4.5.

		[U] = 20 g.L -1	[U] = 40 g.L -1	[U] = 60 g.L -1
	Avrami-	no stirring	stirring	no stirring	stirring	no stirring	stirring
	Erofe'ev
	k (min -1 )	0.0049(3)	0.0168(7)	0.0101(4)	0.0203(6)	0.0214(7)	0.0230(8)
	n	0.71(5)	0.99(7)	0.71(4)	1.00(5)	0.88(4)	1.08(7)
	* R 2	0.970	0.988	0.986	0.994	0.993	0.989
	Sharp-Hancock	no stirring	stirring	no stirring	stirring	no stirring	stirring
	k (min -1 )	0.0049(5)	0.0168(3)	0.0109(6)	0.0219(5)	0.02286(5)	0.0242(7)
	n	0.71(4)	1.10(4)	0.77(4)	1.05(6)	0.93(4)	0.90(5)
	* R 2	0.966	0.989	0.963	0.969	0.976	0.966

* R 2 : correlation coefficient from the kinetics curves fittings.

  have shown the formation of a powdered product of hydrated uranyl oxalate type (UO 2 [C 2 O 4 ](H 2 O)2H 2 O) after mixing oxalic acid in a nitric acid aqueous solution containing uranyl nitrate. Optimal precipitation yield was found to be less than 83% U (remaining [U] = 4.0 g.L -1 ), from an uranyl nitrate concentration [23.8 g.L -1 ] in HNO 3 (2M) aqueous solution at ambient temperature. If the precipitation of UO 2 [C 2 O 4 ](H 2 O)2H 2 O appeared after a few minutes, the maximal yield is obtained after several hours.

Acknowledgements

The authors would like to thank Mrs. Nora Djelal, Laurence Burylo, Philippe Devaux and Pr Lydie Pelinski for their assistances with the synthesis, SEM images, XRD powder patterns measurements (UCCS). The "Fonds Européen de Développement Régional (FEDER)", "CNRS", "Région Hauts de France" and "Ministère de l'Education Nationale de l'Enseignement Supérieur et de la Recherche" are acknowledged for the funding of X-ray diffractometers and ICP-AES apparatus from the Chevreul Institute platform. This work was part of the French National Research Agency (ANR) through the project "ASTUTE" (contract ANR-15-CE08-0011-01).

Associated Content

Supporting Information

Supplementary data (powder XRD pattern, thermogravimetric curves, IR spectra) associated with this article can be found in the online version.

Accession Codes

Crystallographic data for the structural analysis have been deposited with the Cambridge Crystallographic Data Centre, CCDC No. 1987462 for 1, 1987465 for 2. Copies of the data can be obtained free of charge on application to CCDC, 12 Union Road, Cambridge CB2 1EZ (fax: +44-1223-336-033; e-mail: data_request@ccdc.cam.ac.uk).


Christian Ben Lakhdar
email: christian.ben-lakhdar@univ-lille.fr

Xavier Elharrar
email: xavierelharrar@hotmail.com

Karine Gallopel-Morvan
email: karine.gallopel-morvan@ehesp.fr

François-Charles Wolff

Tobacco sales to underage buyers in France: findings from a mystery shopping study

Keywords: tobacco, underage sales, mystery shopper, France

Objectives:

In 2017, one in four French 17-year-olds was a daily smoker, even though France prohibited the sale of tobacco to under-18 minors in 2009. This research aims to evaluate the retail violation rate for sale to minors (RVRm) and the associated factors.

Study design:

Observational mystery shopping study.

Methods:

We conducted a mystery shopping study enlisting 12-year-old and 17-year-old youths in a representative sample of 527 tobacco outlets during three weeks in spring 2019.

Multinomial Logit and Probit regressions were estimated on the data collected.

Results:

The law is not respected. Two out of three sellers (65.2%) were willing to make an illegal sale to a 17-year-old minor, and almost one in 12 (8.1%) were willing to sell to a 12-year-old child attempting to buy tobacco. Illegal sales were more likely to be made by male sellers, retailing in big cities, when there were no in-shop queues, and to 17-year-old females. The absence of the mandatory enforcement poster flagging up the ban on the sale of tobacco to minors appears to be a strong factor associated with RVRm.

Conclusions:

These findings show that progress needs to be made to better enforce tobacco control legislation in order to help decrease underage smoking in France. Rate of compliance with A c c e p t e d m a n u s c r i p t the law could be improved by stronger enforcement measures and tougher sanctions, but also by training and the provision of age-verification tools for sellers, as demonstrated by experiments in other countries.

Introduction

Smoking is the leading cause of preventable death worldwide. Every year, more than 8 million people die from tobacco use, and a billion premature deaths attributable to smoking are expected over the course of this century [START_REF] Who | Tobacco -Key Facts[END_REF]. However, smoking is still prevalent in many European countries, and particularly France, even after having implemented the main measures of the World Health Organization's Framework Convention on Tobacco Control (WHO FCTC) and despite the effectiveness of these measures [START_REF] Gravely | A c c e p t e d m a n u s c r i p t Implementation of key demand-reduction measures of the WHO Framework Convention on Tobacco Control and change in smoking prevalence in 126 countries: an association study[END_REF]. Even though smoking rates have started to decline in recent years, 32% of French people were smokers in 2018 [START_REF] Andler | Baisse de la prévalence du tabagisme quotidien parmi les adultes : résultats du Baromètre de Santé publique France[END_REF], which is still twice as high as in Australia or the United States and higher than Belgium (19%), Germany (25%) and Spain (28%), and above the European average (26%) [START_REF] Eurobarometer | Attitudes of Europeans towards tobacco and electronic cigarettes[END_REF].

Controlling youth access to tobacco is one of the most crucial tobacco control measures to curb this epidemic. As emphasized by the WHO FCTC and others, the ban on the sale of tobacco to minors aims to prevent young people starting smoking and help the youngest smokers to quit [START_REF] Dent | Relation between access to tobacco and adolescent smoking[END_REF][START_REF] Rigotti | The Effect of Enforcing Tobacco-Sales Laws on Adolescents' Access to Tobacco and Smoking Behavior[END_REF][START_REF] Difranza | Reducing youth access to tobacco[END_REF][START_REF] Hinds | Impact of a local ordinance banning tobacco sales to minors[END_REF]. Every intervention that has successfully disrupted the sale of tobacco to minors has been associated with an observed reduction in tobacco use by youth [START_REF] Difranza | Which interventions against the sale of tobacco to minors can be expected to reduce smoking?: Table 1[END_REF]. With that vision, in 2009, France opted to strengthen the blanket ban on the sale of tobacco to minors by increasing the minimum age from 16 up to 18 years old. This law ushered in various obligations for retailers, including asking for proof of age (ID) if the seller has any doubt about the age of a customer. Sellers were also required to have a clearly visible poster stating the ordinance and law prohibiting sales of tobacco to under-18s [START_REF] Elharrar | Interdiction de vente de tabac aux mineurs en France et au Québec. Comparaison du cadre législatif, de son application, et du tabagisme des adolescents[END_REF].

However, the most recent adolescent population survey still reported a high prevalence of smoking among under-18s in France. In 2017, 59% of 17-year-olds reported having smoked at least one cigarette in their lifetime, 34.1% admitted tobacco use in the 30 days preceding A c c e p t e d m a n u s c r i p t the survey, and one in four reported being daily smokers. Despite the law banning tobacco sales to minors, easy access for young people to tobacco products remains an issue in France, with 94% of 17-year-old French smokers reporting that they can easily buy tobacco from official retailers [START_REF] Nézet | Les comportements tabagiques à la fin de l'adolescence[END_REF].

In order to assess enforcement of this law, the national tobacco control fund (Fonds de Lutte contre le Tabac) commissioned a French NGO called Comité National Contre le Tabagisme (National Committee for Tobacco Control) to conduct a mystery shopping study. The study was designed to evaluate the retail violation rate for sale to minors (RVRm) and the associated factors. This methodology was selected due to its effectiveness in checking compliance with the law and its control of known biases. Mystery shopper methodology is a well-established and evaluated market research tool commonly used to study selling agerestricted products to young people [START_REF] Hinds | Impact of a local ordinance banning tobacco sales to minors[END_REF][START_REF] Difranza | Legislative Efforts to Protect Children From Tobacco[END_REF][START_REF] Difranza | Is the standard compliance check protocol a valid measure of the accessibility of tobacco to underage smokers?[END_REF][START_REF] Forster | Perceived and measured availability of tobacco to youths in 14 Minnesota communities: the TPOP Study. Tobacco Policy Options for Prevention[END_REF][START_REF] Forster | Youth Access To Tobacco: Policies and Politics[END_REF][START_REF] Carruthers | The availability of cigarettes to minors in Perth, Western Australia[END_REF][START_REF] Difranza | What Is the Potential Cost-Effectiveness of Enforcing a Prohibition on the Sale of Tobacco to Minors?1[END_REF][START_REF] Rimpela | The effectiveness of tobacco sales ban to minors: the case of Finland[END_REF][START_REF] Levinson | Assessment of the US Federal Retailer Violation Rate as an Estimate of the Proportion of Retailers That Illegally Sell Tobacco to Adolescents[END_REF][START_REF] Gosselt | Mystery Shopping and Alcohol Sales: A c c e p t e d m a n u s c r i p t Do Supermarkets and Liquor Stores Sell Alcohol to Underage Customers[END_REF][START_REF] Van Hoof | Selling alcohol to underage adolescents in Romania: compliance with age restrictions in Pitesti[END_REF][START_REF] Moore | Implementing a Reward and Reminder Underage Drinking Prevention Program in Convenience Stores Near Southern California American Indian Reservations[END_REF][START_REF] Dorji | Increasing compliance with alcohol service laws in a developing country: intervention trial in the Kingdom of Bhutan: Alcohol outlet intervention in Bhutan[END_REF][START_REF] Van Hoof | The role of consumer age and financial profit in vendor compliance for underage alcohol sales[END_REF]. This approach could usefully inform public policy by highlighting key characteristics of tobacco outlets and underage buyers for control, training and prevention policy to prioritize.

Methods

A mystery shopping study was designed to estimate the RVRm and the associated factors.

Design

Cross-sectional data were collected over a three-week period in spring 2019. Sampling was stratified by type of tobacco outlet (tobacconist, tobacconist-newsagent, bar-tobacconist, bar-tobacconist-newsagent), size of town and region (the study covered every region of mainland French except Corsica) to obtain a representative sample of French tobacco A c c e p t e d m a n u s c r i p t outlets. In France, tobacco outlets have a monopoly on the sale of tobacco products. No other stores (like supermarkets) can sell cigarettes, and cigarette vending machines are prohibited. We selected 527 tobacco outlets from a total of 14,000 tobacco vendors listed by the Ministry of Economy and Finance to conduct 527 purchase attempts by either 12-yearold (N=260) or 17-year-old (N=267) male or female mystery shoppers.

Sample size was determined using 2019 figures for the number of French young adults aged 12 (N=848,005) and 17 (N=841,386). Using a 95% confidence level and a margin of error of six gives approximate sample sizes of N=260 for 12-year-olds and N=267 for 17-year-olds. BVA, a market research and consultancy institute that has no competing interests with the tobacco industry, conducted the mystery shopping study. The steering committee (including agents from the French public health authorities) validated that the ethics and methodology of the study were sound. Parental consent to participate was obtained for all minors, who received a financial incentive for their participation.

BVA purpose-trained and assigned experienced adult mentors to discreetly accompany the mystery shoppers (minors aged either 12 or 17 yo). Their role was to ensure that the purchase attempt went smoothly and to note the existence of a sign flagging the ban of tobacco sales to minors. Before the attempt, the adults recruited and trained young people to participate in the compliance checks. During the purchase attempt, the adults bought confectionary or chewing gum in order to look like ordinary customers. Minors were instructed to not wear makeup or clothes that would make them appear older, to take their ID card with them, and to make their purchase attempts in unfamiliar tobacco outlets.

Minors never completed the tobacco purchase, even if the seller was willing to sell-they simply claimed they did not have enough money, and left the shop. The mystery shopping procedure is described in Figure 1. Immediately after the attempted purchase of a cigarette pack, the minor and the mentor completed a questionnaire compiling various items including location of the tobacco outlet, type of outlet, presence/absence of the legal ban enforcement poster, whether or not the seller asked for the minor's age and/or ID card, and whether or not the sale was about to be completed.

The law clearly stipulates that tobacconists are to request ID if they are in any doubt as to a customer's age. Nevertheless, due to ignorance of the law, some sellers may only ask for age without requiring proof of ID, which is why the questionnaire also captured this information.

Table 1 reports descriptive data on the main variables used in the empirical analysis.

[Table 1]

Data analysis

RVRms were calculated as the ratio of sellers willing to sell tobacco to total number of attempted purchases. As the results focused on both the seller's reaction (as the law obliges the seller to ask for the buyer's age and ID) and his/her decision-making (as cigarette sale to minors is forbidden), we ran two econometric analyses. The first analysis used multinomial Logit regressions to get the odds ratios of factors associated with the seller asking for age only, ID only, or both age and ID (the reference category is no age-check effort). The second

Results

RVRm

Faced with an underage mystery shopper, 62.2% of sellers made no effort to check age, [START_REF] Rimpela | The effectiveness of tobacco sales ban to minors: the case of Finland[END_REF].2% asked the customer their age without requiring ID, and only 19.6% asked for proof of ID. After the minor had responded to their request and, if necessary, given a false pretence (making the purchase for their mother or father) in an attempt to buy the cigarettes, 62.6% of sellers refused to sell cigarettes to the minor while 37.4% agreed to make the illegal sale.

Among the 328 sellers who did not ask for any confirmation of age, 46.3% sold cigarettes and 53.7% declined.

Results differed according to the age of the minors. When the mystery shopper was a 12year-old, 68.9% of sellers did not ask for the shopper's age or ID, 16.9% asked for the shopper's age without requiring ID, and 14.2% asked for ID. After the minor either presented his/her ID card or lied by claiming he/she was 18 years old or tried to buy the cigarettes under a false pretence, 8.1% of sellers agreed to sell cigarettes to the minor, and the other 91.9% refused to sell in all cases.

When the mystery shopper was a 17-year-old, 55.8% of sellers did not ask for the shopper's age or ID, 19.5% asked for the shopper's age without requiring ID, and 14.2% asked for ID.

Still following the protocol, either after claiming to be 18 years old or having presented A c c e p t e d m a n u s c r i p t his/her ID and tried to buy the cigarettes under a false pretence, 65.2% of tobacco sellers agreed to sell cigarettes to the minor, and the other 34.8% refused to sell.

Factors associated with RVRm

The sellers' reactions differed according to several factors (Table 2). Sellers were twice as likely to ask for age, 3.4 times more likely to ask for ID, and almost 6 times more likely to ask for age and ID from a 17-year-old shopper compared to a 12-year-old shopper. Sellers were less likely to ask for age and ID when the tobacco outlet was in a city of 15,000 inhabitants or more. Mystery shoppers who were smokers also got asked much less for their age and ID.

[Table 2]

Concerning the sellers' reactions to 12-year-old mystery shoppers, age and ID checks decreased very sharply when the attempted purchase was made after 4 pm compared to in the morning. Conversely, age and ID checks increased very strongly when the outlet was located in a 'priority neighbourhood' (socio-economically deprived area). The factor that seemed to most influence asking for ID or for both age and ID is seller gender: frequency of age and ID checks increased very strongly when the seller was a woman.

Concerning sellers' reactions to 17-year-old mystery shoppers, female sellers asked for the shopper's age significantly more but asked for ID significantly less. Being a smoker also significantly reduced the likelihood of a minor being asked for age and ID. Time of purchase had an influence, since shoppers were more often asked for their age in mid-afternoon compared to morning.

A c c e p t e d m a n u s c r i p t

For both groups of underage shoppers, the type of outlet, presence of the mandatory ban enforcement poster, proximity of a middle/high school, and presence of a queue did not influence the behaviour of the sellers.

The final sale decision partially followed the factors associated with the sellers' reactions (Table 3). Sellers were more willing to sell to a 17-year-old minor, especially to girls, and less willing to sell to 12-year-old girls. Furthermore, when the mystery shopper was a smoker (no 12-year-old smokers in our sample), it significantly increased the seller's readiness to sell them cigarettes. Female sellers were less likely than male to sell cigarettes to a 12-year-old shopper. Size of the town is a factor: the bigger the city, the more the sellers were willing to sell cigarettes to minors. The decision to sell was not affected by time of the attempted purchase. Sellers were less likely to sell cigarettes to minors when there were other people waiting in the queue.

[Table 3]

Type of outlet, proximity of a school, or being located in a priority neighbourhood had no effect on the seller's decision. However, the presence of the mandatory ban enforcement poster appeared to be strongly associated with refusal to sell tobacco to a minor.

Discussion

Results from this mystery shopping study show that the law is not respected in France. Two out of three sellers were willing to sell cigarettes to a 17-year-old minor, and one in 12 were willing to sell to a 12-year-old child. These RVRm are associated with various factors.

A c c e p t e d m a n u s c r i p t

Many characteristics of the mystery shoppers influenced the results, including smoking status, gender, and age. Other influential covariates included whether the seller was a woman, whether or not the outlet was located in a small town, and whether or not there was a queue in the shop. These variables impacted not only the reactions of sellers but also their final sale decision. Finally, sales were more likely to be made when the mandatory enforcement poster citing the ban on selling tobacco to minors was not visible in the store.

There are several potential explanations for this non-compliance with the law. The penalty for this offense in France may not be enough of a deterrent. Currently, a tobacco seller who fails to comply with the law risks a €135 fine, which is well below penalty levels established in other countries. In the UK, for example, first-time offenders are fined around €3,000 and repeat offenders are fined up to €23,000 and may lose their license or their right to work in a tobacco outlet for 12 months. Ireland has also introduced deterrent punishments, with fines of €400 to €3,000, suspensions of sales licenses and up to 3 months in prison. Both the seller and the storeowner can be sanctioned, and the list of sanctioned retailers is made public. Compared with these neighbouring countries, the French sanction appears to be weak and, consequently, not dissuasive. Furthermore, the probability of a compliance check in France is very low [START_REF]Cour des comptes. Rapport d'évaluation -Les politiques de lutte contre le tabagisme[END_REF]. French law specifies that it is essentially the role of the police to enforce the underage smoking law compliance checks, but after 10 years in existence, only a few sellers have ever been fined for illegal sales. French police are clearly reluctant to carry out this task. Systematic random unannounced inspections by mystery shoppers headed by the Ministry of Health (as in A c c e p t e d m a n u s c r i p t Quebec) or a public health authority (as in Australia or the USA) may be a policy measure to increase compliance. In the USA, for example, the FDA performs more than 130,000 compliance checks annually. It has been shown that effectively enforcing laws against tobacco sales to minors through regular compliance checks and penalizing retailers that sell to minors can significantly reduce youth smoking [START_REF] Stead | Interventions for preventing tobacco sales to minors[END_REF][START_REF] Dai | The effects of tobacco control policies on retailer sales to minors in the USA[END_REF] and is cost-effective [START_REF] Difranza | What Is the Potential Cost-Effectiveness of Enforcing a Prohibition on the Sale of Tobacco to Minors?1[END_REF].

A qualitative study posits that sellers may be uncomfortable carrying out their legal duty [START_REF] Gomez | Evaluation de l'interdiction de vente d'alcool et de tabac aux mineurs[END_REF]. Indeed, as our results show, many French sellers do not ask for age or ID. There are many ways to dispel the potential unease surrounding the legal obligation to ask for ID in France. As already done in Ireland (see www.showmeid.ie), the association of French tobacco sellers could organize specific training and awareness campaigns to facilitate execution of the law. For instance, fear appeal campaigns that depict very young people who start smoking because the law is under-enforced could prompt a reaction from tobacco retailers. Such campaigns have been shown to be effective in increasing awareness and behavioural compliance [START_REF] Tannenbaum | Appealing to fear: A meta-analysis of fear appeal effectiveness and theories[END_REF]. French health authorities could take the FDA's lead and propose specific online training for sellers. Furthermore, the implementation of ageverification systems (AVS) could facilitate age control and improve compliance, as found in the Netherlands. AVS are technical supports for cashier, such as pop-up windows that indicate the minimum accepted date of birth when an age-restricted product is scanned, date-of-birth key-in systems where the seller has to key the customer's date of birth into the cash register system, ID swiper/checkers, or even remote age verification with live video [START_REF] Van Hoof | Shop Floor Compliance with Age Restrictions for Tobacco Sales: Remote Versus In-Store Age Verification[END_REF][START_REF] Roodbeen | Alcohol and Tobacco Sales to Underage Buyers in Dutch Supermarkets: Can the Use of Age Verification Systems Increase Seller's Compliance?[END_REF].

A c c e p t e d m a n u s c r i p t

However, even if this non-compliance with French law by tobacco sellers can be partly explained by a lack of training and control tools, there are almost certainly other explanatory factors not highlighted here. Qualitative research using retailer interviews could serve to further explore these barriers to enforcement of underage smoking law. Also, the results of mystery shopper studies also depend on the mystery shoppers recruited: enlisting smokers in our sample clearly influenced the results obtained, which confirms findings from previous studies [START_REF] Difranza | Is the standard compliance check protocol a valid measure of the accessibility of tobacco to underage smokers?[END_REF]. As underage smokers who behaved normally were more likely to be sold tobacco, the rate of non-compliance may be underestimated, as most underage customers attempting to buy cigarettes are current smokers.

In this study, only 16% of all mystery shoppers were smokers, and all were 17-year-old customers (32%). This proportion is higher than the prevalence of this age group in the general population, where 25% self-report as daily smokers [START_REF] Nézet | Les comportements tabagiques à la fin de l'adolescence[END_REF]. In other words, while our sample was representative of tobacco stores, it was not representative of youth smoking status, as 17-year-old smokers were over-represented.

Other factors could pose limitations to our results. We found that female sellers were less willing to sell tobacco to a 12-year-old client. Our study had a roughly 50/50 split between male and female tobacco sellers, but the actual gender split among tobacco sellers in France remains unknown. Likewise, we found that the presence of a queue in the shop impacts the sales decision: social control and the fear of being reported to the police could explain why sellers are more reluctant to accept a sale in these situations, but it may also be viewed more as a random event than a limitation.

A c c e p t e d m a n u s c r i p t

Another limit lies in the fact that we did not account for other possible sources of procuring tobacco, such as the black market, Internet purchases, or through adult acquaintances.

Again, this limit warrants some perspective, as a recent representative survey of French teenagers found that 94% of 17-year-old smokers reported that they buy their tobacco in official tobacco outlets [START_REF] Nézet | Les comportements tabagiques à la fin de l'adolescence[END_REF]. Finally, two important issues may be seen either as limits or as a research agenda. First, we did not study e-cigarettes and e-liquids, even though France prohibits the sale of vaping products to under-18s. Second, as shown for alcohol, compliance at outlet level can misrepresent the real availability of products to minors. The time required by an underage shopper to buy the risky product may be another informative indicator, in addition to compliance rate, to describe the availability of age-restricted products [START_REF] Van Hoof | Underage Alcohol Sales-It Only Takes a Minute: A New Approach to Underage Alcohol Availability[END_REF].

In conclusion, the RVRm in France is still high. Even today, retailers continue to supply adolescent smokers with tobacco products. France still requires effective and efficient implementation of existing enforcement measures in order to curb tobacco sales to minors and thus bring down underage smoking.

A

  c c e p t e d m a n u s c r i p t analysis used a Probit model to investigate the factors associated with the seller's decision to sell or refuse cigarettes.

Figure 1 .

 1 Figure 1. Mystery shopping study protocol.

A

  c c e p t e d m a n u s c r i p t

Table 1 . Descriptive statistics (%)

 1

	Variables

Table 2 . Econometric analysis of the seller's reaction (multinomial logit, reference = no demand -odds ratios)

 2 CNTC Mystery Shopper Study. Note: odds ratios from multinomial logit models. Significance levels are 1% (***), 5% (**) and 10% (*), respectively.

	Variables

Table 3 . Econometric analysis of the seller's decision (probit model -marginal effects)

 3 CNTC Mystery Shopper Study. Note: estimates from probit models. Significance levels are 1% (***), 5% (**), 10% (*), respectively. Decisions after the mystery shopper's pretexted excuse are not included in the probit models on 12-yo and 17-yo youths, but they are included in the full sample.

	Variables

Acknowledgements

We thank Pr. Yves Martinet, president of CNCT, and Emmanuelle Béguinot, executive director of CNCT, for their implication and their outstanding work in this and other projects.

We also thank the National Health Insurance Fund for funding this research. The authors take responsibility for any remaining errors.

Statements of ethical approval

We did not seek ethics committee approval for this research, as our study method is not deemed medical research. Subjects were not manipulated or negatively affected in any way.

For this reason, this study is exempted under the French "Loi Jardé" (law 2012-300 of 5

March 2012 concerning research involving human subjects) which incorporates the Declaration of Helsinki principles.

Funding

This study was supported by the French Tobacco Control Fund under a multi-year funding agreement from the National Health Insurance Fund (Caisse Nationale d'Assurance Maladie) -Project: Ban on the sale of tobacco products to minors: Mobilization of civil society and stakeholders to enhance its effectiveness.

Conflicts of interest

None


Maxime Bourgain

C Sauret

Thibault Marsan

M J Perez

Olivier Rouillon

Patricia Thoreux

Philippe Rouch

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Influence of the projection plane and the markers choice on the X-factor computation of the golf swing X-factor: a case study

Influence of the projection plane and the markers choice on the X-factor computation of the golf swing X-factor: a case study

Introduction

X-factor seeks to account for the dissociation between the shoulder and the pelvis girdles. It has been believed to be a key parameter for golf swing performance. However, several computational methods have been used and there is currently no consensus. Even if some comparison studies were performed, they remain incomplete. Methodologies used for its computation are based on pelvic markers on the one hand, and either on acromions markers [START_REF] Kwon | Validity of the X-factor computation methods and relationship between the X-factor parameters and clubhead velocity in skilled golfers[END_REF] or thorax ones [START_REF] Brown | The X-Factor: An evaluation of common methods used to analyse major inter-segment kinematics during the golf swing[END_REF] on the other hand. These markers permit to define an upper and a lower lines. These lines are then projected either in the horizontal plane or in the swing plane. Then, this factor could be defined either as the angle at the beginning of the downswing phase (or top of the backswing), or as the maximal value of this separation angle. In the latter case, it is named the X-factor stretch [START_REF] Cheetham | The importance of stretching the "X-factor" in the downswing[END_REF].

The objective of this study was to evaluate if the methodological choice, i.e., based on acromion versus thorax markers, and depending on the plane of projection, have a significant influence on both the X-factor and X-factor stretch estimations.

Methods

Subject

One professional male golfer was recruited for this experiment. He was informed and gave his written consent before the experiment. This protocol was approved by an independent ethics committee (2015-A01760-49, Ile de France X).

Acquisitions

The volunteer was equipped with 65 reflective markers with 4 additional markers for the golf club. Markers were tracked by a 12-cameras optoelectronic motion capture system (Vicon system, Oxford metrics, UK; 200 Hz). The volunteer performed a series of 10 swings with his own driver club. Swing performance was assessed with a dedicated ball flight radar (TrackMan 3, TrackMan, USA) by considering the club head speed at impact. The five best swings were retained and processed in this study.

Processing

The swing plane was computed based on the clubhead marker by computing the best fit plane with a root mean square criterion, during the last part of the downswing [START_REF] Morrison | Changes in club head trajectory and planarity throughout the golf swing[END_REF].

Markers positions were used to animate a rigid bodies model [START_REF] Bourgain | Effect of shoulder model complexity in upper body kinematics analysis of the golf swing[END_REF], based on a multi-body kinematic optimization algorithm, on OpenSim software [START_REF] Delp | OpenSim opensource software to create and analyze dynamic simulations of movement[END_REF]. Resulting markers were used to compute two computational methods used to define the X-factor:

The upper body markers were either the thorax ones (7th cervical and manubrium) or both acromions. The plane of projection was either the horizontal plane (HP), or the functional swing plane (FSP).

An estimation of the shoulder/pelvis dissociation was performed based on markers of the acromions and pelvis. The thorax/pelvis based on the markers of the thorax and pelvis. For each method, the X-factor (XF) was defined as the angle at the top of backswing and the Xfactor stretch (XFS) was defined as the maximum angle.

The correlation between each computed X-factor and the performance was estimated by computing the linear correlation coefficient (R).

Results and discussion

The clubhead speed at impact varied from 45.1 to 46.3 m/s. As it could have been expected, both X-factor and X-factor stretch were higher for shoulder/pelvis dissociation than for thorax/pelvis dissociation, with an overall average difference of 19 and 14 for horizontal and swing planes projection, respectively. This indicates that the shoulder complex contributed noticeably to the XF, which is in accordance with a previous study [START_REF] Bourgain | Effect of shoulder model complexity in upper body kinematics analysis of the golf swing[END_REF]. Values of XF and XFS with the different methods, and their linear correlation with clubhead speed, were reported in Table 1.

Values of XF and XFS in the thorax/pelvis method were in accordance but slightly higher of previously reported results [START_REF] Brown | The X-Factor: An evaluation of common methods used to analyse major inter-segment kinematics during the golf swing[END_REF]). As they considered elite amateurs and not professionals, this is in accordance with the idea of increasing the XF and XFS with golfer skills. Values of XF and XFS in the shoulder/pelvis method were in accordance with a previous study [START_REF] Kwon | Validity of the X-factor computation methods and relationship between the X-factor parameters and clubhead velocity in skilled golfers[END_REF].

It can also be noticed that the consistency of those angles, i.e., the standard deviation, is less than 2 , which represent less than 3% of the nominal value. The influence of the chosen plane for the projection depends on the methodology: with the thorax/pelvis method the mean value variated of 2 and 4% for XFS and XF respectively, whereas, for shoulder/pelvis methods it was 4 and 11% for XFS and XF respectively.

According to the linear coefficient of correlation, this subject appeared to have a better performance when he increased his thorax/pelvis dissociation.

However, this is only a case study, and those tendencies should be confirmed on more subjects.

Table 1 .

 1 values in degrees of XF, XFS according to the methodology chosen. S/P: shoulder/pelvis dissociation method, T/P: thorax/pelvis method.

		Horizontal plane	Swing plane
	XF( )	S/P	T/P	S/P	T/P
	Mean (SD)	56,5 (1,4)	37,8 (0.9)	50,2 (1.8)	36,4 (1.0)
	Range	55.3	37.3	47.9	35.3
		58.6	39.4	52.3	38.1
	Correlation (R)	0.86	0.98	0.74	0.94
	XFS( )	S/P	T/P	S/P	T/P
	Mean (SD)	56.7 (1.2)	38.0 (0.8)	54.4 (0.9)	38.8 (0.6)
	Range	55.8	37.5	53.6	37.9
		58.6	39.5	55.6	39.6
	Correlation (R)	0.87	0.96	0.50	0.81

Acknowledgements

The author would like to thank the volunteer who performed this experiment, the French Federation of Golf for his support and the companies: TrackMan who borrow the radar, and Titleist for the balls.

Conclusions

The method chosen for computing the X-factor highly influences its value and its correlation to performance. The main element influencing its computation is the upper anatomical region taken into account. The plane chosen for the projection had a limited influence. The authors recommend to explicitly indicate the methodology used for X-factor computation, in particular the markers used, the plane of projection and the instant of computation to help comparison between studies.

Disclosure statement

No potential conflict of interest was reported by the authors.