Rached Ousji

Zouhaier Ksibi

Abdelhamid Ghorbel

Céline Fontaine

The effect of metal-support interactions on formaldehyde oxidation and by-product selectivities in TiO2 supported metal catalysts (Co, Cr, Mo, and Ag)

Keywords: formaldehyde, TiO2, Catalytic oxidation, Sol-Gel, Supported metal catalysts, selectivities, CO2, temperature

One of the most significant indoor air pollutants is formaldehyde, and long-term exposure to HCHO may cause health problems. Catalytic oxidation at room temperature is an effective technology for removing HCHO indoors. In this paper, a simple sol-gel synthesis method was proposed for the preparation of TiO2 support, and a series of 5%M (Co, Cr, Mo, and Ag) catalysts were prepared by impregnation process. The materials were characterized by XRD, TEM, FT-IR, BET, and H2 -TPR. The catalytic activities and the oxidation reaction of HCHO were investigated by an analytical system equipped with an infrared analyser (MKS multigas 2030) to analysis the different products. The results showed that the M/TiO2 catalysts obtained have TiO2 anatase phase diffraction peaks as well as a high surface area and porosity. The samples physicochemical, catalytic properties, and by-product selectivity's differ depending on the metal impregnated. The Ag/TiO2 catalyst was effective for the removal of formaldehyde gas at 95 °C, resulting in the selective production of carbon dioxide and water. The Co/TiO2 demonstrated complete conversion of HCHO at 244 °C and improved CO2 selectivity.

The TEM images for the Ag/TiO2 catalyst showed that the silver particles were identified and very well dispersed on the support. Finally, these results might help in the development of highperformance catalysts activities at ambient temperature.

Introduction

Indoor air pollution has become a growing concern in recent years, as people spend a significant amount of time inside buildings and structures, where the concentration of toxic substances such as volatile organic compounds (VOCs) often higher than outdoors [START_REF] Yang | Recent advancement and future challenges of photothermal catalysis for VOCs elimination: From catalyst design to applications[END_REF][START_REF] Wang | Revealing the strong interaction effect of MnOx nanoparticles and Nb2O5 supports with variable morphologies on catalytic propane[END_REF]. Various toxic substances (VOCs) have been introduced into the indoor environment, such as formaldehyde, benzene, toluene, and so on [START_REF] Zhang | Adsorption of VOCs onto engineered carbon materials[END_REF]. Formaldehyde (HCHO) is the primary indoor pollutant emitted by commonly used building and decorative materials and has been linked to various health issues, including cancer [START_REF] Costa | Occupational exposure to formaldehyde and early biomarkers of cancer risk, immunotoxicity and susceptibility[END_REF]. Although various technologies have been developed to reduce the concentration of formaldehyde in indoor air, such as physical adsorption [START_REF] Le | Bio-template-assisted synthesis of hierarchically hollow SiO2 microtubes and their enhanced formaldehyde adsorption performance[END_REF][START_REF] Arabzadeh | One dimensional CdS nanowire@TiO2 nanoparticles coreshell as high performance photocatalyst for fast degradation of dye pollutants under visible and sunlight irradiation[END_REF], photocatalytic [START_REF] Bai | Comparison of the performance for oxidation of formaldehyde on nano-Co3O4, 2D-Co3O4, and 3D-Co3O4 catalysts[END_REF][START_REF] Zhang | Catalytic performance and mechanism of a Pt/TiO2 catalyst for the oxidation of formaldehyde at room temperature[END_REF], and catalytic oxidation. However, due to its limited adsorption capacity, the adsorbent has an unstable removal impact [START_REF] Bai | Progress in research on catalysts for catalytic oxidation of formaldehyde[END_REF]. The photocatalyst's action can result in secondary toxicity pollution, such as HCHO [START_REF] Bai | Progress in research on catalysts for catalytic oxidation of formaldehyde[END_REF]. In contrast, catalytic oxidation is an effective and environmentally friendly method for formaldehyde elimination into carbon dioxide and water. Metal oxide and noble-metal catalysts have been used for formaldehyde oxidation, and their catalytic performance is closely related to their morphology, surface area, and crystal structure. At room temperature, noble-metal catalysts have very high catalytic performance for HCHO oxidation; for example, Pt/TiO2 with a Pt loading of 1% exhibited excellent activity for formaldehyde oxidation [START_REF] Zhang | Catalytic performance and mechanism of a Pt/TiO2 catalyst for the oxidation of formaldehyde at room temperature[END_REF]. Transition metal materials, on the other hand, have received widespread attention due to their low cost and high catalytic activity. Mn [START_REF] Feng | Preparation, characterization and catalytic formaldehyde oxidation at room temperature of MnOX[END_REF][START_REF] Tang | Manganese-Cerium Mixed Oxide Catalysts for Complete Oxidation of Formaldehyde: Effect of Preparation Method and Calcination Temperature[END_REF], Co [START_REF] Ma | Investigation of formaldehyde oxidation over Co3O4-CeO2 and Au/Co3O4-CeO2 catalysts at room temperature: effective removal and determination of reaction mechanism[END_REF], and Cr [START_REF] Xia | Ultrasound-assisted nanocasting fabrication and excellent catalytic performance of three-dimensionally ordered mesoporous chromia for the combustion of formaldehyde, acetone, and methanol[END_REF] have been shown to have good catalytic activity, and metals such as Ce [START_REF] Wang | Synthesis of palygorskitesupported Mn1-xCexO2 clusters and their performance in catalytic oxidation of formaldehyde[END_REF], Sn [START_REF] Lochar | study of methanol, formaldehyde and methyl formate adsorption on the surface of Mo/Sn oxide catalyst[END_REF], and Cu [START_REF] Sekine | Oxidative decomposition of formaldehyde by metal oxides at room temperature[END_REF] can be doped into the catalyst as promoters to improve activity. Titanium oxide has long been of interest to scientists as both a catalyst and support material. Its highly developed surface contains both acid-base sites and exhibits high mechanical and thermal stability, enabling the significant dispersion of active phases and providing it with exceptionally interesting properties for use in heterogeneous catalysis. Various methods have been developed to synthesize TiO2, including the sol-gel method [START_REF] Amin | Synthesis of TiO2-Ag nanocomposite with solgel method and investigation of its antibacterial activity against E. coli[END_REF]. This method has great potential for producing various material structures, such as bulk, fibres, sheets, films, and particles, at low temperatures [START_REF] Dimitriev | History of sol-gel science and technology[END_REF].

It enables the creation of materials with high purity and homogeneity, as well as the control of particle size distributions at the nanoscale level. In this study, we used sequential sol-gel and impregnation methods to synthesize titanium oxide and load metals onto it. We investigated the effect of the metal type on the catalytic performance for formaldehyde (HCHO) oxidation and detected by-products using an advanced infrared analyser (MKS multigas 2030). To investigate the physicochemical properties of the synthesized catalysts, we used a combination of X-ray diffraction (XRD), Transmission Electron Microscopy (TEM), Fourier-transform infrared spectroscopy (FTIR), Brunauer-Emmett-Teller (BET), and hydrogen temperature programmed reduction (H2-TPR).

Experimental section

Catalyst synthesis

All chemical reagents used were of the highest analytical grade. In our study, titanium oxide was synthesized using the sol-gel method and used as a support. Titanium (IV) isopropoxide (70% from S. Aldrich) was dissolved in absolute ethanol (99.8% from S. Aldrich) and stirred for 30 min. To control the hydrolysis and condensation reaction rates, ethyl acetoacetate was added to the solution in a molar ratio of Eacac (Ethyl acetoacetate): Ti =1. After 30 minutes of stirring, 1.5 mL of a 0.1M aqueous nitric acid solution (65% from S. Aldrich) was added dropwise, corresponding to a molar ratio H2O: Ti =10. The solution was then stirred until a yellow gel formed. The gel was dried in an autoclave under supercritical ethanol conditions (P = 63 bars; T = 243 °C), crushed, and then calcined under an oxygen flow for 3 hours at 500 °C with a temperature rise of 1 °C/min and a flow rate of 30 mL/min.

In the impregnation method, aqueous precursor solutions of cobalt (II) nitrate hexahydrate, chromium (III) chloride, pure molybdenum powder, and silver nitrate were added to the support material while stirring. The M/TiO2 catalysts were activated by a reduction treatment under H2 (30 mL/min) at 300 °C with a ramp of 1°C/min after drying at 100 °C for 12 hours. The impregnated solids were labelled as Co/TiO2, Cr/TiO2, Mo/TiO2, and Ag/TiO2.

Catalysts characterization

Understanding a catalyst's morphological, textural, and structural properties is critical because these properties have a direct impact on the number and accessibility of active sites, as well as the catalytic activity. In what follows, we will discuss the various techniques we used to characterize our catalysts.

The nitrogen physisorption method is commonly used to measure the specific area and porosity of catalysts produced with an ASAP 2020 Micromeritics analyser. Specifically, the BET method is used to calculate the specific surface area (SBET) from the nitrogen adsorption data, using a P/P0 ratio between 0.04 to 0.31. The desorption branch of the isotherm is then analysed using the Barret-Joyner-Halenda (BJH) model to calculate the total pore volume (Vp) and average pore size (Dp).

Transmission electron microscopy (TEM) images were obtained using an 80 kV JEOL JEM-1011 microscope to gather additional information about the composition, morphology, and structure of the catalysts. The catalysts were mixed with ethanol and dispersed in an ultrasonic bath. Subsequently, the solutions were placed on a copper plate and dried by evaporating the ethanol before the analysis.

The Perkin Elmer spectrometer was used for Fourier transform infrared spectroscopy (FTIR) to identify the molecular bonds in the samples. The samples were analysed using an IR irradiating source in the frequency range of 400-4000 cm -1 [START_REF] Uncu | Use of FTIR and UV-visible spectroscopy in determination of chemical characteristics of olive oils[END_REF].

To identify the crystalline phases and chemical composition of the catalysts, X-ray diffraction (XRD) was performed using a PANalytical X'pert PRO MPD diffractometer with a CuKα 1 radiation (1.54060 Ǻ) in reflection geometry. The diffractograms were recorded over a range of 10-70°, with a step size of 0.017° and a scan step time of 12 seconds. The crystalline phases were identified by comparing them to ICDD PDF standards. The average crystallite size of the samples (dXRD) (in nm) was calculated using Scherrer's equation:

𝑑𝑋𝑅D = 0.9 λ / β cos θ
Where K= 0.9, β is the corrected full width at half maximum (in rad), and θ is the Bragg angle of the diffraction peak (in rad).

The programmed H2 temperature reduction profiles (H2-TPR) were performed using a Micromeritics AutoChem 2920 analyser. The TPR technique can be used to characterize supported metals and oxides by determining the hydrogen consumption during metal oxide reduction as a function of temperature. A 5% H2/Ar gas mixture with a ramp rate of 5 °C/min and a flow rate of 30 mL/min was used to achieve temperatures ranging from 40 to 700 °C.

Catalytic activity measurement

The MKS Multigas 2030 infrared analyser was used to set up the oxidation of volatile organic compounds in the gas phase, enabling continuous analysis of several molecules such as formaldehyde, CO2, CO, methanol, formic acid, and water with a detection threshold of the order of parts per million (ppm).

The formaldehyde used in the tests was derived from paraformaldehyde, which was dissolved overnight with stirring at 50 °C. To stabilize the mixture, the measured mass of the solid was dissolved in 100 mL of ultrapure water and 1 mL of 0.1 mol L -1 sodium hydroxide solution.

The catalytic oxidation of HCHO over the catalysts (50 mg) was tested in a glass flow reactor using a gas mixture comprising of 100 ppm HCHO, 19.5% O2, 78% N2, and 2.5% H2O balanced at a total flow rate of 100 cm 3 min -1 , and GHSV of 84,000 h -1 .

𝐻𝐶𝐻𝑂 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 (%) = [𝐻𝐶𝐻𝑂] 𝑖 -[𝐻𝐶𝐻𝑂] 𝑇 [𝐻𝐶𝐻𝑂] 𝑖 * 100
Where [HCHO]i denotes the initial concentration and [HCHO]T denotes the concentration during the reaction.

The apparent selectivity's for carbon dioxide, carbon monoxide, methanol, and formic acid are calculated as follows:

(𝑃𝑖) 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (%) = [𝑃𝑖] ∑[𝑃𝑗] * 100
Where [Pi] is the concentration of the product and [Pj] is the sum of all reaction product concentrations.

The previous selectivity values will allow the yields of these products to be calculated as shown in the equation:

(𝑃𝑖)𝑌𝑖𝑒𝑙𝑑 (%) = 𝐻𝐶𝐻𝑂 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 * (𝑃𝑖) 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦

Results and discussion

X-Ray Diffraction analysis

Figure . 1 displays the XRD spectra of sol-gel synthesized TiO2, Co/TiO2, Cr/TiO2, Mo/TiO2, and Ag/TiO2 catalysts. The anatase phase of each catalyst exhibits prominent peaks indexed using the standard powder diffraction pattern (JCPDS 01-071-1166) with a tetragonal symmetry structure. The rutile phase is not observed since the support TiO2 was calcined at 500 °C. The anatase phase is identified by the peaks located at 2θ = 25.44°, 38.0°, 48.3°, 54.43°, and 63.4°, which correspond to the (101), ( 004), ( 200), (105), and (204) planes, respectively [START_REF] Fang | Effect of redox state of Ag on indoor formaldehyde degradation over Ag/TiO2 catalyst at room temperature[END_REF][START_REF] Bhat | Improving the thermal stability and nbutanol oxidation activity of Ag-TiO2 catalysts by controlling the catalyst architecture and reaction conditions[END_REF]. The absence of distinctive peaks corresponding to silver and cobalt in the diffraction pattern suggests that Ag was highly dispersed on the surface of anatase TiO2, while cobalt can either be inserted in the interstitial sites of the crystal or substitute Ti ions. Furthermore, the smaller ionic radius of Ti 4+ ion (0.068 nm) compared to that of Ag + ion (0.126 nm) makes it difficult for Ag + to replace Ti 4+ in the crystal lattice [START_REF] Aazam | Visible light photocatalytic degradation of thiophene using Ag-TiO2/multi-walled carbon nanotubes nanocomposite[END_REF]. However, the ionic radius of Co 2+ (0.072 nm) is slightly larger than that of Ti 4+ , making it possible for Co 2+ to substitute for Ti 4+ in the titania lattice [START_REF] Pirbazari | Co/TiO2 nanoparticles: preparation, characterization and its application for photocatalytic degradation of methylene blue[END_REF]. The XRD patterns of Mo/TiO2 exhibited two diffraction peaks assigned to the cubic molybdenum metallic at 2θ = 40.50° and 58.65°. In contrast, the Cr/TiO2 XRD patterns revealed a reduction in the intensity of the TiO2 anatase characteristic peaks and specific peaks at 2θ = 15.27°, 30.82°, 36.53°, 53.27°, and 64.18° corresponding to the monoclinic crystal system of Chromium Chloride (CrCl3). This result suggests that the reduction temperature of the chromium precursor is insufficient to remove chlorine and chromium, which were poorly incorporated into the TiO2 structure. The addition of metal increased the anatase peaks, indicating a higher degree of crystallinity, and the increase in crystallinity was strongly influenced by the type of metal present in TiO2. The increase in crystallinity resulting from the presence of metals could be due to metal ions occupying interstitial sites within the crystal or undergoing surface doping [START_REF] Ünlü | Effect of Cu and Mn amounts doped to TiO2 on the performance of DSSCs[END_REF]. Table. [START_REF] Yang | Recent advancement and future challenges of photothermal catalysis for VOCs elimination: From catalyst design to applications[END_REF] shows the crystallite sizes of the synthesized catalysts calculated using the Debye-Sherrer equation. TiO2 had the smallest crystallite size (12.4 nm), followed by Ag/TiO2 (14.6

Physisorption measurements

Figure . 2a depicts the N2 adsorption-desorption isotherms for TiO2 and various M/TiO2 samples with 5% metal loading. According to IUPAC classification, all samples resembled the type IV isotherm, a profile characteristic of mesoporous materials [START_REF] Thommes | Physisorption of gases with special reference to the evaluation of surface area and pore size distribution[END_REF]. The hysteresis loop associated with isotherms is assigned to the H2 type, which corresponds to mesoporous textures and ink-bottle shaped pores formed by aggregated spherical particles [START_REF] Yu | Effects of alcohol content and calcinations temperature on the textural properties of bimodally mesoporous titania[END_REF][START_REF] Zhang | Mesoporous TiO2 comprising small highly crystalline nanoparticles for efficient CO2 reduction by H2O. ACS Sustain[END_REF]. The BJH pore size distribution of various M-TiO2 catalysts is depicted in Fig. 2b, indicating that all samples have a monomodal size distribution. N2 adsorption-desorption measurements were used to calculate the BET surface area, pore volume, and average pore diameter of each catalyst (Table 1). Sol-gel synthesized TiO2 had the highest specific surface area of 132 m 2 /g, compared to 118 m 2 /g of Mo/TiO2, 113 m 2 /g of Co/TiO2, 104 m 2 /g of Ag/TiO2, and 91 m 2 /g of Cr/TiO2. The TiO2 exhibited a much larger surface area, and the decrease of this surface area upon addition metal (Co, Cr, Mo, and Ag) can be explained by the increase of its crystal sizes. TiO2, Mo/TiO2, Co/TiO2, Ag/TiO2, and Cr/TiO2 have pore volumes of 0.38, 0.36, 0.32, 0.28, and 0.24 cm 3 /g, respectively. The average pore diameter of Co/TiO2 (86 Ǻ) and Mo/TiO2 (85 Ǻ) was greater than TiO2 (84 Ǻ), Ag/TiO2 (77 Ǻ), and Cr/TiO2 (75 Ǻ), possibly due to a partial blockage of the pore's support entrances by cobalt and molybdenum species.

Reducibility H2-TPR analysis

According to prior research, the redox properties of the catalysts, such as low temperature reducibility, surface oxygen distributions, and oxygen mobility in the lattice, have a significant impact on their catalytic behaviour for VOC oxidation [START_REF] Zeng | Three-dimensionally macroporus MnZrOx catalysts for propane combustion: Synergistic structure and doping effects on physicochemical and catalytic properties[END_REF][START_REF] Li | Polhedral cobalt oxide supported Pt nanoparticles with enhanced performance for toluene catalytic oxidation[END_REF]. Using the H2-TPR measurement, the hydrogen absorptions could characterize the phenomenon of adsorption and dissociation of hydrogen molecules through chemical combination with active oxygen species at the surface level of metal oxide catalysts [START_REF] Tran | Defective Nb2O5-supported Pt catalysts for CO oxidation: Promoting catalytic activity via oxygen vacancy engineering[END_REF]. As a result, the information provided by this technique can also be used to evaluate the availability of surface-active oxygen and the abundance of vacant oxygen on metal oxides. The figure. S1 (from the supporting information) depicts the TPR-H2 profiles of the catalysts. The pure TiO2 profile shows a very broad and low intensity reduction peak at 536 °C, which is related to the sample's low hydrogen consumption. This could be because of resistance to the reducing process. This is due to the surface dehydroxylation of TiO2 and the reduction of Ti 4+ to Ti 3+ [START_REF] Inturi | Visible-light-induced photodegradation of gas phase acetonitrile using aerosol-made transition metal[END_REF].

The H2-TPR profile of the Co/TiO2 catalyst exhibits two reduction peaks. The first peak, which occurs at 300-400°C, corresponds to the reduction of Co3O4 to CoO, resulting in the reduction of Co 3+ to Co 2+ metal. The second peak, which occurs at 400-550°C, corresponds to the reduction of CoO to Co, resulting in the reduction of Co 2+ to Co 0 metal [START_REF] Yang | Oxygen-vacancyinduced O2 activation and electron-hole migration enhance photothermal catalytic toluene oxidation[END_REF]. For Cr/TiO2 catalysts, a single low-intensity hydrogen consumption peak was observed over the entire temperature range due to the difficulty in reducing the chromium species in the presence of chlorine. The reduction peak, which appears around 585 °C [START_REF] Rahman | Dehydrogenation of propane over chromia/alumina: A comparative characterization study of fresh and spent catalysts[END_REF], corresponds to the change in oxidation state from Cr 3+ to either Cr 2+ or the metallic state. The TPR profile of Mo/TiO2 does not exhibit any reduction peaks, indicating that the molybdenum species are in the metallic state in the supported catalyst, which is consistent with the XRD diagram [START_REF] Nilius | Activating nonreducible oxides via doping[END_REF]. On the other hand, the TPR profile of Ag/TiO2 reveals three major peaks with higher H2 consumption, observed at 85, 125, and 300 °C, respectively. As previously reported [START_REF] Wang | MOF-derived CeO2 supported Ag catalysts for toluene oxidation: The effect of synthesis method[END_REF], the thermal analysis revealed three reduction peaks. The peak observed below 100 °C was attributed to the reduction of chemisorbed oxygen on the catalyst surface. The peak observed at around 100°C was attributed to the reduction of large Ag2O clusters that had a low concentration or were highly dispersed, which made them undetectable by XRD [START_REF] Chernykh | Room-Temperature Nitrophenol Reduction over Ag-CeO2 Catalysts: The Role of Catalyst Preparation Method[END_REF]. Finally, the peak observed around 300 °C was attributed to the reduction of stable and well-dispersed Ag2O or Ag + ions. This clearly demonstrates the presence of strong support-metal interactions between Ag and TiO2, which enhances the reduction process [START_REF] Chernykh | Room-Temperature Nitrophenol Reduction over Ag-CeO2 Catalysts: The Role of Catalyst Preparation Method[END_REF].

FT-IR analysis

The FTIR spectra of (a) TiO2, (b) Co/TiO2, (c) Mo/TiO2, (d) Cr/TiO2, and (e) Ag/TiO2 nanocomposites in the 400-4000 cm -1 wavenumber range are shown in Figure . S2 (from the supporting information). All samples exhibited an absorption band in the 3800-3000 cm -1 range, which is attributed to the stretching vibrations of OH from physiosorbed water molecules. The contribution due to water proton absorption is represented by the absorption band around 1620 cm -1 . The strong band in the 900-450 cm -1 range is associated with Ti-O-Ti vibration in TiO2 [START_REF] Yu | Effects of pH on the microstructures and photocatalytic activity of mesoporous nanocrystalline titania powders prepared via hydrothermal method[END_REF][START_REF] Sakthivel | Silver doped TiO2 nano crystallites for dye-sensitized solar cell (DSSC) applications[END_REF]. The small adsorption bands 2300 cm -1 in the Mo/TiO2 and Ag/TiO2 spectra correspond to atmospheric CO2.

Catalytic activity

The Mars-Van Krevelen (MVK) mechanism has been widely used to describe the catalytic oxidation of VOCs over metallic oxides [START_REF] Pei | Critical review of catalytic oxidization and chemisorption methods for indoor formaldehyde removal[END_REF][START_REF] Popova | Toluene oxidation on chromium-and copper-modified SiO2 and SBA-15[END_REF]. The mechanism consists of two independent steps: the oxidation of VOC molecules to CO2 and H2O via surface oxygen species and the reaction between reduced sites and oxygen from a gas phase to form surface oxygen species.

Consequently, the surface oxygen species and the reducibility of the catalyst are critical for the overall oxidation of VOCs. catalysts in HCHO oxidation. All catalysts, except TiO2, were able to completely oxidize formaldehyde under the tested conditions. The highest catalytic activity was observed for Ag/TiO2, which achieved complete HCHO conversion at a relatively low temperature of 95 °C.

At 245 °C, the Co/TiO2 catalyst also achieved complete conversion of HCHO. The Mo/TiO2 catalyst exhibited much lower activity, with total elimination of formaldehyde occurring at 317 °C. Similarly, Cr/TiO2 was able to completely decompose formaldehyde, but at a higher temperature of 298 °C. To compare different materials in the field of catalysis, two key parameters are commonly studied: the T50 and T90 temperatures, which correspond to the temperatures at which 50% and 90% conversion, respectively, are achieved. The most desirable sample is one that achieves 50% or 90% conversion at the lowest possible temperatures. The activity is not the only factor to consider when selecting a catalyst; selectivity is also important. Because the most active material is also the most selective in terms of harmful byproducts, it was unsuitable for indoor HCHO removal. As a result, it is necessary to compare the product yields obtained from various materials. Three products are detected under our The yield of the different samples is in the following order:

Ag/TiO2 >Co/TiO2 > Cr/TiO2> Mo/TiO2 > TiO2.

This result shows that the redox sites created by silver species are more reactive in formaldehyde oxidation to CO2 than the sites generated by molybdenum and chromium.

Transmission electron microscopy

In order to better understand the variations in catalytic activity, the morphology and microstructure of the samples were analysed using transmission electron microscopy (TEM) techniques. 5d, the presence of Mo particles on the surface of the TiO2 support is consistent with the particle size of 19.1 nm determined from X-ray diffraction (XRD) patterns using Scherrer's equation (as shown in Table 1). The Mo particles are too large to be located within the pores of the TiO2.

Figure. 5e

shows that the distribution of Ag particles is relatively uniform. The addition of silver has resulted in some black spots with a hexagonal structure, indicating that Ag nanoparticles have been successfully loaded onto the surface of TiO2. When combined with our XRD and BET analyses, it can be concluded that the surface area of the support favours the high dispersion of the metal.

Conclusion

In summary, the addition of metals (Co, Cr, Mo, and Ag) to the TiO2 support, prepared using sol-gel and impregnation methods, significantly affected the conversion of formaldehyde (HCHO). XRD analysis revealed the presence of the anatase phase of TiO2 support, the existence of CrCl3 in the Cr/TiO2 catalyst, and metallic Mo in the solid Mo/TiO2. BET analysis showed the similarity of the isotherms characterized by a mesoporous texture. TPR confirmed the existence of reduction peaks of silver and cobalt, which had an impact on the oxidative character of the catalysts.

The catalytic tests demonstrated that the Ag/TiO2 catalysts exhibited superior catalytic activity, achieving 100% conversion of HCHO at 95°C and being the most selective for the production of CO2. An improvement in catalytic activity was attributed to the presence of Co, which showed advanced activity for the complete oxidation of HCHO and selectivity for CO2. The presence of Mo and Cr catalysts led to high production of carbon monoxide.

Figure 1 .

 1 Figure 1. X-ray diffraction of: TiO2, Co/TiO2, Cr/TiO2, Mo/TiO2 and Ag/TiO2

  Co/TiO2 (15.2 nm), Mo/TiO2 (36.8 nm), and Cr/TiO2 (61.3 nm). The increased crystal size after metal loading confirmed the higher crystallinity.

Figure. 2

 2 Figure. 2 The curves of nitrogen adsorption-desorption isotherms (a) and the corresponding pore size distribution curves (b) of TiO2, Co/TiO2, Cr/TiO2, Mo/TiO2 and Ag/TiO2

Figure. 3

 3 illustrates the catalytic properties of TiO2 and M/TiO2

Figure. 4

 4 presents a summary histogram of the T50 (in black) and T90 (in red) values for the different materials. Notably, TiO2 support exhibited a T50 of 207 °C, while the lowest T50 was observed for Ag/TiO2, which achieved 50% conversion at 79 °C. The Co/TiO2 and Mo/TiO2 catalysts exhibited T50 values of around 143 °C and 232 °C, respectively, while Cr/TiO2 had the highest T50 of 248 °C. It is worth mentioning that TiO2 conversion did not exceed 85% for T90, which is why Figure.[START_REF] Zhang | Adsorption of VOCs onto engineered carbon materials[END_REF] does not display a T90 value for this sample. Nevertheless, the T90 values for all substituted materials were measured. The most active catalyst, with a T90 of 90 °C, was Ag/TiO2, which achieved a lower T90 than the T50 values of the other modified materials. By contrast, the T90 values for Co/TiO2, Cr/TiO2, and Mo/TiO2 were found to be 224 °C, 290 °C, and 309 °C, respectively.

Figure. 3 Figure. 4

 34 Figure. 3 HCHO conversions on: (•) TiO2, (▲) Co/TiO2, (▬) Cr/TiO2, (♦) Mo/TiO2 and (■) Ag/TiO2. Reaction conditions: HCHO 100 ppm, catalyst mass 50 mg, O2 19.5 vol%, total flow rate 100 cm 3 min -1 , GHSV 84000h -1

  experimental conditions: CO2, CO, and CH3OH, with the formic acid not being observed (Figure. S3 from the supporting information). At the temperature range of 50 to 350 °C, H2O and CO2 (Fig. S3.a) were the only products for the catalyst Ag/TiO2, however, an important amount of CO (Fig. S3.b) was detected at over 200 °C produced by TiO2 support, Cr/TiO2, and Mo/TiO2. As can be seen from Fig. S3.c, methanol could be detected when the reaction temperature was 52 °C for TiO2, 60 °C for Co/TiO2, 80 °C for Cr/TiO2, and 100 °C for Mo/TiO2.

Figure. 5

 5 provides representative TEM images of the calcined TiO2 and M/TiO2 samples. Figure. 5a displays the disordered but highly mesoporous structure of the TiO2 support, which has a lattice spacing of 0.356 nm indexed as (101) and is identified as the anatase phase [43]. The Co/TiO2 sample, depicted in Figure. 5b, exhibits well-defined spherical shapes with an agglomerated structure. Figure. 5c illustrates that the chrome catalyst only contains large metal particles within the size range of 30-200 nm, with no small Cr nanoparticles detected, and the Cr particles being larger than the other metal particles. As shown in Figure.

2 Figure. 5

 25 Figure. 5 TEM images of: (a) TiO2, (b) Co/TiO2, (c) Cr/TiO2, (d) Mo/TiO2 and (e) Ag/TiO2.

Table 1 .

 1 Material properties of synthesized catalysts

	Catalyst SBET (m 2 /g) a Pore volume (cm 3 /g) a Average pore	Crystallite size
				diameter (Ǻ) a	(nm) b
	TiO2	132	0.38	84	12.4
	Co/TiO2 113	0.32	86	15.2
	Cr/TiO2 91	0.24	75	61.3
	Mo/TiO2 118	0.36	85	36.8
	Ag/TiO2 104	0.28	77	14.6

a Determined by BET, b Determined by XRD

Table 2 .

 2 TheCo/TiO2 sites have the potential to convert the HCHO and CH3OH generated into CO2 at 250 °C. Ag/TiO2 can generate more active sites for HCHO oxidation than the other catalysts, and to compare with some literature data, Table.2 showed the activities of some of the different Ag-based catalysts. Catalytic activity of silver-based catalysts in the HCHO oxidation

With GHSV: gas hourly space velocity

Table . 3

 . displays the chemical composition of each sample analysed through EDS elemental analyses. The findings indicate that the chemical composition of each impregnated element is close to that theoretically estimated.

	Catalysts	Reactions conditions	T50 (°C)	Reference
				s
				This work
	Ag/TiO2	100 ppm HCHO, O2 19.5 vol%, GHSV	79
		84000h -1
	Ag/CeO2	810 ppm HCHO, O2 20 vol%, 84000 h -1 SV	90	[41]
	Ag-HMO	400 ppm HCHO, 10 vol% O2, 30.000 ml(gh)	80	[42]
		SV

Table . 3

 . EDS analysis of the different samples

	Element TiO2 Wt%	5%Co/TiO2	5%Cr/TiO2	5%Mo/TiO2	5%Ag/TiO2
			Wt%	Wt%	Wt%	Wt%
	Ti	65.18	64.15	60.54	62.33	60.32
	O	34.82	31.36	34.45	33.00	35.12
	Co	-	4.49	-	-	-
	Cr	-	-	5.01	-	-
	Mo	-	-	-	4.67	-
	Ag	-	-	-	-	4.56
	Total	100.00	100.00	100.00	100.00	100.00

Conflict of interest

The authors declare no conflicts of interest


N Carella

Least Primitive Roots in Arithmetic Progression

Keywords: AMS MSC2020 : Primary 11A07, 11N05, Secondary 11N32 Primitive root mod p, Least prime Primitive root, Arithmetic progression, Complexity theory, Finite field

published or not. The documents may come

Introduction

The unconditional upper bounds of the least primitive root u ̸ = ±1, v 2 in the prime finite field F p seem to be exponential u ≪ p 1/4+ε , see [2, Theorem 3], and the conditional upper bounds are of the forms u ≪ (log p) 6+ε , see [7, Theorem 1.3], [START_REF] Bach | Comments on search procedures for primitive roots[END_REF]. This note proposes a new result on the theory of primitive roots in finite fields.

Theorem 1.1. Let p > 1 be a large prime number and let 1 ≤ a < q be a pair of small integers with q = O(log log p). Then there exists a primitive root u ̸ = ±1, v 2 in the prime finite field F p such that (i) u ≤ (log p) 2+ε , (ii) u ≡ a mod q, where ε > 0 is a small real number.

This innovation is made possible by a new characteristic function for primitive root described in Section 2. The proof of Theorem 1.1 appears in Section 3. Given the prime factorization of the totient p -1 an easy application of this result leads to a polynomial time algorithm for determining primitive root in the prime finite field F p . The most recent algorithm for searching for primitive roots and a survey of the literature appears in [START_REF] Shparlinski | On Constructing Primitive Roots in Finite Fields With Advice[END_REF].

Representations of the Characteristic Function

The characteristic function Ψ : G -→ {0, 1} of primitive elements is one of the standard analytic tools employed to investigate the various properties of primitive roots in cyclic groups G. Many equivalent representations of the characteristic function Ψ of primitive elements are possible, see [5, p. 258].

A new divisors-free representation of the characteristic function of primitive element is developed here. It detects the order ord p (u) ≥ 1 of the element u ∈ F p by means of the solutions of the equation τ n -u = 0 in F p , where u, τ are constants, and n is a variable such that 1 ≤ n < p -1, gcd(n, p -1) = 1. The order of an element in a finite field is defined by ord p (v) = min{k : v k ≡ 1 mod p}.

Lemma 2.1. Let p ≥ 2 be a prime and let τ be a primitive root mod p and let ψ ̸ = 1 be a nonprincipal additive character of order ord ψ = p. If u ∈ F p is a nonzero element, then

Ψ(u) = gcd(n,p-1)=1 1 p 0≤s≤p-1 ψ ((τ n -u)s) = 1 if ord p (u) = p -1, 0 if ord p (u) ̸ = p -1.
Proof. As the index n ≥ 1 ranges over the integers relatively prime to p -1, the element τ n ∈ F p ranges over the primitive roots modulo p. Ergo, the equation τ n -u = 0 has a solution if and only if the fixed element u ∈ F p is a primitive root.

Next, replace ψ(s) = e i2πks/p , where k ∈ {0, 1, 2, . . . , p}, to obtain

gcd(n,p-1)=1 1 p 0≤s≤p-1 e i2π(τ n -u)s/p = 1 if ord p (u) = p -1, 0 if ord p (u) ̸ = p -1. (2.1)
This follows from the geometric series 0≤n≤N -1 w n = (w N -1)(w -1), w ̸ = 1 applied to the inner sum. ■

Least Primitive Roots

The determination of an upper bound for the smallest primitive root in arithmetic modulo p is based on a new characteristic function for primitive roots in finite field F p developed in Section 2.

Proof. (Theorem 1.1) Let p > 2 be a large prime number and let z = (log p) 2+ε and ε > 0. Suppose the least primitive root u ∈ (z, p) and consider the sum of the characteristic function over the short interval [2, z], that is, 0 = 2≤u≤z u≡a mod q Ψ(u).

(3.1)

Replacing the characteristic function, Lemma 2.1, and expanding the nonexistence equation (3.1) yield 0 =

2≤u≤z u≡a mod q Ψ(u) (3.2) = 2≤u≤z u≡a mod q   1 p gcd(n,p-1)=1, 0≤s≤p-1 ψ ((τ n -u)s)   = c 2≤u≤z p≡a mod q 1 p gcd(n,p-1)=1 1 + 2≤u≤z u≡a mod q 1 p gcd(n,p-1)=1, 0<s≤p-1 ψ ((τ n -u)s) = M 0 (z, q, a) + E 0 (z, q, a),
where c = c(q, a) ≥ 0 is a constant depending on the integers 1 ≤ a < q.

The main term M (z, q, a) is determined by a finite sum over the trivial additive character ψ(s) = 1 is computed in Lemma 4.1, and the error term E(z, q, a) is determined by a finite sum over the nontrivial additive characters ψ(s) = e i2πks/p ̸ = 1 is computed in Lemma 5.1.

Substituting these values yield

N (z, q, a) = 2≤u≤z u≡a mod q Ψ(u) (3.3) = M (z, q, a) + E(z, q, a) = c • φ(p -1) p • (log p) 2+ε q + O(1) + [O ((log p)(log log p))] = c • φ(p -1) p • (log p) 2+ε q + O ((log p)(log log p)) .
For any prime p, the totient function is bounded away from zero, that is,

p -1 p • φ(p -1) p -1 = p -1 p r|p-1 1 - 1 r (3.4) ≫ 1 log p > 0,
where r ≥ 2 ranges over the prime divisor of p -1, see [4, Theorem 6.12]. Consequently, for small parameter q = O(log log p) the main term in (3.3) dominates the error term: The first ten least primitive roots in in each arithmetic progression modulo 3 are these.

N (z, q, a) = 2≤u≤z u≡a mod q Ψ(u) (3.5) = c • φ(p -1) p • (log p) 2+ε q + O ((log p)(log log p)) ≫ 1 log p • ( log
1.

A 1 = {u = 3n + 1 ≤ z :} = {46,

Evaluation of the Main Term

The main term defined in Section 3 is evaluated in this Section.

Lemma 4.1. Let 1 ≤ a < q be a pair of small integers and let ε > 0 be a small real number. If p ≥ 2 is a large prime and z = (log p) 2+ε , then

2≤u≤z u≡a mod q 1 p gcd(n,p-1)=1 1 = φ(p -1) p • (log p) 2+ε q + O(1),
where φ(n) is the Euler totient function.

Proof. The number of relatively integers n < p coincides with the values of the totient function. A routine rearrangement gives

2≤u≤z u≡a mod q 1 p gcd(n,p-1)=1 1 = 2≤u≤z u≡a mod q φ(p -1) p (4.1) = φ(p -1) p • (log p) 2+ε q + O(1)
.

■ 5 Estimate For The Error Term

The upper bound for the error term defined in Section 3 is estimated in this Section.

Lemma 5.1. Let p ≥ 2 be a large prime, let z = (log p) 2+ε and let q = log log p. Suppose 1 ≤ a < q is a pair of small fixed integers and ε > 0. If there is no primitive root u ≤ z = (log p) 2+ε then 2≤u≤z u≡a mod q 1 p gcd(n,p-1)=1, 0<s≤p-1 ψ ((τ n -u)s) ≪ (log p)(log log p), where ψ(s) = e i2πks/p with 0 < k < p, is an additive character.

Proof. To compute an upper bound consider the symmetric partition the triple finite sum

E(z) = 2≤u≤z p≡a mod q 1 p gcd(n,p-1)=1, 0<s≤p-1 e i2π (τ n -u)s p (5.1) = 2≤u≤z p≡a mod q 1 p gcd(n,p-1)=1,   0<s≤p/2 e i2π (τ n -u)s p + p/2<s≤p-1 e i2π (τ n -u)s p   = E 1 (x) + E 2 (x).
A geometric series summation of the inner finite sum in the first term yields This completes the verification. ■

E 1 (z) = 2≤u≤z p≡a mod q 1 p gcd(n,p-1)=1, 0<s≤p/2 e i2π (τ n -u)s p (5.2) = 1 p 2≤u≤z p≡a mod q gcd(n,p-1)=1, e i2π( τ n -u p )( p+1 2 ) -1 1 -e i2π (τ n -u) p ≤ 1 p 2≤u≤z p≡a mod q gcd(n,p-1)=1 2 | sin π(τ n -u)/

  p) 2+ε log log p + O ((log p)(log log p)) ≫ (log p) 1+ε log log p + O ((log p)(log log p)) > 0 as x → ∞. Clearly, this contradicts the hypothesis (3.1) for all sufficiently large prime numbers p ≥ p 0 . Therefore, there exists a small primitive root u = qn + a ≤ z = (log p) 2+ε . ■ Example 3.1. For the closest prime to 10 12 , the parameters are these: (a) p = 1000000000039, prime, (b) z = (log p) 2 = 763.47, range with ε = 0, (c) q ≤ log log p = 3.32, modulo, (d) N ≫ (log p)/ log log p = 8.33, predicted number N in (3.5).

1 (≪

 1 p| , see [3, p. 136] for similar geometric series calculation and estimation. The last line in (5.2) follows from the hypothesis that u is not a primitive root. Specifically, u ̸ = τ n ∈ F p for any n ≥ 1 such that gcd(n, p -1) = 1 and any u ≤ z = (log p) 2+ε . Define the sets of integersA = {(τ n -u) mod p : 1 ≤ n < p and gcd(n, p -1)} (5.3) and B = {m = ab : 1 ≤ a ≤ z and ≤ b ≤ p/z}.(5.4)The set relation A ⊂ B is utilized to obtain the next inequalityE (log z)(log p/z) ≪ (log p/z)(log log z).Similarly, the second term has the upper boundE 2 (z) = 2≤u≤z p≡a mod q 1 p gcd(n,p-1)=1, p/2<s≤p-1 e i2π (τ n -u)s p π(τ n -u)/p| ≪ (log p/z)(log log z).Adding (5.5) and (5.6) and substituting z = (log p) 2+ε yieldE(z) = E 1 (z) + E 2 (z) (5.7) ≪ (log p/z)(log log z) + (log p/z)(log log z) ≪ (log p)(log log p).


Lucas Bacheley

Rathies Ravindra

Gérard Guillamot

Phannarath Phansavath
email: phannarath.phansavath@chimieparistech.psl.eu

Virginie Ratovelomanana-Vidal
email: virginie.vidal@chimieparistech.psl.eu

Access to Enantioenriched β-Hydroxy gem-Difluorinated Heterocyclic and Acyclic Derivatives through Rh(III)-Catalyzed Asymmetric Transfer Hydrogenation

Keywords: Asymmetric transfer hydrogenation, Enantioselectivity, Homogeneous catalysis, Heterocycles, Transition metals

We report here a rapid, efficient, and easy to handle process to access a variety of enantioenriched αgem-difluorinated alcohols.

A Rh(III)-catalyzed asymmetric transfer hydrogenation method was developed in yields up to 98% and enantiomeric excesses up to >99%. The reduction proceeds under mild conditions with a range of difluorinated molecules including 3,3-difluorochromanone, 3,3difluorothiochromanone, 3,3-difluoro-dihydroquinolinone and α-difluorinated β-ketosulfone derivatives to efficiently provide the desired enantioenriched difluorinated alcohols which are valuable novel fluorinated building blocks.

Because of the distinctive characteristics of fluorine, the targeted incorporation of fluorine atom(s) or fluorine-containing groups into organic compounds frequently results in profound changes to their stability, hydrophobicity, accessibility to biological systems, and biological potency influencing the administration and processing of pharmaceuticals in the body. [1] Consequently, fluorine is emphasized as the second most commonly employed heteroelement, [2] following nitrogen, in research oriented toward the life sciences. [3] More specifically, the geminal difluoromethylated moiety can function as a bioisostere of ether oxygen, [4] leading to potential conformational shifts. [5] Additionally, in proximity to oxygen, two fluorine atoms significantly alter the fundamental properties of basicity and hydrogen bonding in alcohols. [6] Because of its significant interest in bioisosteric design, [7] the CF 2 moiety has the potential to influence physicochemical and pharmacological characteristics of a compound (Figure 1). [8] Figure 1. Examples of chiral bioactive β-hydroxy gemdifluorinated molecules.

Considering the significant characteristics of the pattern outlined earlier, and in line with our ongoing efforts focused on generating valuable enantioenriched fluorinated compounds, [9] we hereby report the synthesis of a new range of β-hydroxy gem-difluorinated heterocyclic and non-cyclic derivatives through an asymmetric transfer hydrogenation (ATH) [START_REF]Selected references on asymmetric transfer hydrogenation (ATH)[END_REF] process. Our investigations started with the preparation of a variety of α-gemdifluorinated ketones 3a-3q including 3,3difluorochromanones 3a-3i bearing diverse electrondonating or electron-withdrawing groups on the aryl ring as well as 3,3-difluorothiochromanone 3j, 3,3difluoro-dihydroquinolinones 3k-3o and αdifluorinated β-ketosulfone 3p-3q derivatives. For the 3,3-difluorochromanone series, the products 3a-3i were synthesized through a two-step sequence involving first the α-monofluorination of the ketones 1a-1i using Selectfluor in the presence of H 2 SO 4 in MeOH to deliver 2a-2i in 32-98% yield. The second fluorination reaction was performed on the corresponding silyl enol ether to afford the desired products 3a-3i in 61 to 96% yield (Figure 2a). [11] The 3,3-difluorothiochromanone derivative 3j was prepared in 64% yield by using NFSI as the fluorinating agent through sequential fluorination of thiochroman 4-one 1j with LiHMDS as a base. [12] On the other hand, the 3,3-difluoro-dihydroquinolinone derivatives 3k-3o were obtained in a single step in 45-61% yield using 6 equivalents of NaH and 4 equivalents of NFSI. [13] Finally, α-difluorinated phenylsulfonyl derivatives 3p and 3q were formed by sequential fluorination of the β-keto sulfones 1p-1q, using sodium carbonate and Selectfluor at room temperature in 51% (3p, R = Me) and 86% (3q, R = Ph) yield over 2 steps. [14] Figure 2. Synthesis of gem-difluorinated ketones.

Having those substrates in hand, we next investigated the enantioselective reduction of 3,3difluorochroman-4-one 3a as a model substrate by evaluating the catalytic properties of a series of commercially available ruthenium catalysts such as (R,R)-A, (R,R)-C, (R,R)-D or a Rh-based catalyst (R,R)-B previously developed in our group, [15] using dichloromethane as a solvent at a concentration of 0.3 M and a mixture of formic acid/triethylamine (5:2) as the hydrogen donor at 30 °C (Table , entries 1-4). All the screened complexes led to high enantioselectivities (>99% ee). However, because the rhodium-based complex allowed a full conversion with a reaction rate much shorter than the other catalysts, the optimization of the reaction parameters was performed with (R,R)-B. Thus, switching from dichloromethane to 2-MeTHF as a solvent or the catalyst loading to 0.5 mol% showed no significant impact on the yield and ee although the kinetics of the reaction was slightly improved (Table , entries 5 and6). Using the ruthenium complexes (S,S)-E and (R,R)-F under the above conditions failed to afford complete conversion even with prolonged reaction time (Table , entries 7 and8).

Table . Optimization of the reaction parameters [a]

Ent ry

Cat. mol% Solvent t (h)

Yield [b] (%) ee [c] (%)

1 (R,R)-A 1 DCM 5 94 >99 2 (R,R)-B 1 DCM 2 97 >99 3 (R,R)-C 1 DCM 6 94 >99 4 (R,R)-D 1 DCM 4 94 >99 5 (R,R)-B 1 MeTHF 1.5 95 99 6 (R,R)-B 0.5 MeTHF 1 94 99
7 (S,S)-E 0.5 MeTHF 70 91 [d] 95 8 (R,R)-F 0.5 MeTHF 70 18 [d] 31

9 [e] (R,R)-B 0.5 MeTHF 1 93 99 10 [f] (R,R)-B 0.5 MeTHF 1 90 99 11 [g]

(R,R)-B 0.1 MeTHF 2 92 97 12 (R,R)-B 0.1 neat 2 91 96 13 (R,R)-B 0.5 MeCN 1 90 98 14 (R,R)-B 0.5 AcOEt 1 90 99
[a] Reaction conditions: 3a (0.43 mmol, 80 mg), Cat. (X mol%), HCO 2 H/NEt 3 (5:2) (218 µL, 6.0 eq.), solvent (0.3 mol/L), 30 °C, t (h), under argon. Full conversion was observed except where indicated. [b] Yields were obtained after filtration on a pad of silica gel. [c] Enantiomeric excess was determined by SFC analysis with a chiral stationary phase. [d] Conversion is reported. [e] Open flask. [f] HCO 2 H/NEt 3 (1:1). [g] A concentration of 1 mol/L was used.

Interestingly, the reaction could be performed in an open flask with no effect on the catalytic performances as compared to those observed for the 1) LiHMDS (1.05 eq.), THF, 0 °C, 1.5 h 3j 64% R (a) 3,3-difluorochromanones [11] (b) 3,3-difluorothiochromanone [12] (c) 3,3-difluoro-dihydroquinolinones [13] (d) α-difluorinated β-ketosulfones [14] 1j 1p-1q

Catalyst (mol%) HCO 2 H / NEt 3 (5:2) (6 eq.) Solvent (C), 30 °C, t Rh TsN N Ph Ph Cl H MeO (R,R)-A Ru TsN N Ph Ph Cl H H (R,R)-C (R,R)-B Ru N N Ph Ph Cl H H S C 6 F 5 O O (R,R)-D Ru N TsN Ph Ph Cl H O (S,S)-E Ru TsN N Ph Ph Cl H H (R,R)-F Ru TsN N Cl H H O O F F O OH F F 3a 4a
reaction carried out under argon atmosphere ( Variously substituted 3,3-difluorochroman-4-ones 3a-3i were subjected to the asymmetric hydrogen transfer and successfully reduced in high yields (92-96%) and enantioinductions ranging from 75% to >99% ee. The lowest ee was observed for the ATH of substrate 3d having the nitro electron-withdrawing group on the phenyl ring (75% ee for 4d) whereas those bearing halogen atoms (4e-4i) or electrondonating groups such as a methyl or methoxy (4b, 4c) gave high enantioselectivities. Satisfyingly, 3,3difluorothiochroman-4-ol 4j was obtained in comparable yield (94%) and excellent enantioselectivity of 99% as those observed for the chroman-4-ol derivatives. The 3,3-difluorodihydroquinolinones were also submitted to the ATH under the optimized reaction conditions and delivered the corresponding alcohols 4k-4o in high yield (85-96%) and excellent enantioselectivities (98-99%). Finally, we turned our attention to acyclic difluorinated ketones. To this end, the ATH process was applied to the 1,1-difluoro-1-(phenylsulfonyl)propan-2-one derivative 3p, leading to 4p with an excellent 98% yield and >99% ee but a decreased ee of 52% was observed for the reduction of the parent compound 2,2-difluoro-1-phenyl-2-(phenylsulfonyl)ethan-1-one 3q. We hypothesized that the enantioselectivity observed for the reduction of the methyl ketone 3p arises from a stabilizing C(sp 3 )-H/F interaction that leads to the (R)-alcohol 4p. The lower enantioselectivity observed for the ATH of phenyl ketone 3q could be explained by a competitive C(sp 3 )-H/ interaction which would favor the (S)-alcohol (see Supporting Information). The absolute configuration of alcohol 4h was unambiguously determined as (S) through X-ray crystallographic investigation. Based on this result, we postulated that the remaining ATH heterocyclic products followed the same pattern. Scheme 1. Scope of the asymmetric transfer hydrogenation [a] On the other hand, the absolute configuration of the β-hydroxy sulfone 4p was assigned through X-ray crystallographic analysis of the corresponding p-nitro benzoyl ester 4p' whereas the configuration of alcohol 4q was attributed by comparison of the

O OH F F R (R,R)-B (0.5 mol%)
HCO 2 H / NEt 3 (5:2) (6 eq.) optical rotation value with reported literature data. [16] Of note, the enantiomers of the enantioenriched βhydroxy gem-difluorinated heterocyclic and acyclic compounds would be readily prepared by using the complex (S,S)-B instead of the (R,R)-isomer. For instance, the asymmetric reduction of 3k using the rhodium complex (S,S)-B furnished the desired alcohol (R)-4k with similar yield and ee value as expected. The effectiveness of this asymmetric transfer hydrogenation process was supported by two scale-up experiments conducted under the defined standard conditions using 3,3-difluorochroman-4-one 3a and 7-bromo-3,3-difluorochroman-4-one 3i (Scheme 2). The yields observed were slightly higher (up to 98% yield) than the ones obtained on smaller scale whereas the enantioselectivities remained unchanged. Furthermore, post-functionalization on 3,3-difluorochroman-4-ol 4a using NaH as a base and allyl bromide as the electrophile allowed the formation of the desired O-allylated product 5a in an excellent yield of 97%. Additionally, postfunctionalization of (S)-7-bromo-3,3difluorochroman-4-ol 4i was performed using a Suzuki-Miyaura coupling with Pd(OAc) 2 , cataCXium A as a ligand, K 2 CO 3 as a base, and 4methoxyphenylboronic acid as a coupling partner. This procedure provided access to the biaryl derivative 5i, with a yield of 91%.

MeTHF (0.3M) 30 °C, 1 h O R 1 F F R OH R 1 F F 4a 93%, 99% ee O OH Me F F O OH MeO F F 4b 95%, >99% ee 4c 94%, 98% ee O OH Br F F O OH F F F O OH O 2 N F F 4d 94%, 75% ee

Scheme 2. Post-functionalization reactions and scale-up experiments

In conclusion, we have developed a simple, robust and easy-to-handle method of rhodium-catalyzed asymmetric transfer hydrogenation for the preparation of a variety of enantiomerically enriched α-gem-difluorinated alcohols that are potential key building blocks. Interestingly, the reaction proceeds in an open flask, in the eco-friendly 2-MeTHF solvent at 30 °C using a low catalyst loading of 0.5 mol%, with a Rh(III) complex synthesized in our laboratory and with a mixture of formic acid/triethylamine (5:2) as the hydrogen donor source. High yields ranging from 85% to 98% alongside enantioselectivities up to >99% ee were obtained affording α-gem-difluorinated alcohols tolerating diverse electron-rich or electron-poor substituents in various positions on the aryl ring. Thus, Rh(III)catalyzed ATH enables to efficiently access under mild conditions a variety of enantioenriched βhydroxy gem-difluorinated heterocyclic and acyclic compounds which represent novel fluorinated building blocks of crucial importance in chemistry. Moreover, the ability of the ATH to proceed at scalable conditions without any adverse impact shows promises for future applications. Finally, the resulting compounds can act as valuable frameworks that can undergo subsequent functionalization on either the hydroxyl functional group or the halogenbearing phenyl ring.

Experimental Section

General procedure for the asymmetric transfer hydrogenation

A round-bottom tube was charged with the corresponding gem-difluorinated ketone (0.43 mmol, 1.0 eq.) under air. 1.65 mL (2 µmol, 0.005 eq.) of a solution of (R,R)-B (1 mg/mL in 2-MeTHF) was then introduced. The mixture was stirred for one minute before adding by syringe the necessary volume of formic acid/triethylamine (5:2) mixture (218 µL, 2.61 mmol, 6.0 eq.). The reaction was stirred at 30 °C with an oil bath for 1 h and the solvent was evaporated under reduced pressure. The remaining oil was diluted in CH 2 Cl 2 , filtered over a short pad of silica gel and concentrated under vacuum. The enantiomeric excess was determined by SFC or HPLC analysis.

  Reactions conditions: 3a (0.43 mmol, 80 mg), (R,R)-B (0.5 mol%, 1.65 mL of a 1 mg/mL solution in 2-MeTHF), HCO 2 H/NEt 3 (5:2) (218 µL, 6 eq.), 30 °C, 1 h, open-flask. Isolated yields were obtained after filtration on a pad of silica gel. Enantiomeric excesses were determined by SFC or HPLC analysis with a chiral stationary phase.

  ). L. B. is grateful to SEQENS for a grant(2021-2024). We thank G. Gontard (Sorbonne Université, Paris) for solving the X-ray structure of compounds 4h and 4p', r Fosse ( himie ParisTech -PS ), and the MS platform (Sorbonne niversité, Paris, France) for HRMS analysis.COMMUNICATIONAccess to Enantioenriched β-Hydroxy gem-Difluorinated Heterocyclic and Acyclic Derivatives through Rh(III)-Catalyzed Asymmetric Transfer Hydrogenation Adv. Synth. Catal. Year, Volume,

  Table, entries 9 vs 6). Varying the ratio of the formic acid/triethylamine mixture from 5:2 to 1:1 furnished 4a in a slightly lower yield of 90%(Table, entry 10) whereas reducing the catalyst loading to 0.1 mol% had a detrimental impact on the enantioselectivity of the reduction either in solution or neat (97% and 96% ee, respectively, Table, entries 11 and 12). Other solvents such as acetonitrile or ethyl acetate were tested, giving similar results as 2-MeTHF in terms of reaction time, yield and enantioselectivity (Table, entries 13 and 14). However, because it is considered a greener solvent, we chose to work with 2-MeTHF and the optimized reaction conditions were set as follows: 2-MeTHF at a 0.3 M concentration, in a mixture of formic acid/triethylamine (5:2) at 30 °C for 1 hour, with the rhodium-based catalyst at a 0.5 mol% catalyst loading. To further assess the scope of the reduction with these optimized conditions in hand, we next investigated the Rh-catalyzed ATH of the α-

gem-difluorinated ketones 3a-3q (Scheme 1).

Acknowledgements

This work was supported by the Ministère de l'Enseignement Supérieur et de la Recherche (MESR) and the Centre National de la Recherche


Florian Moreau

Pierre Colinet

Stéphane Dorbolo

Explosive Leidenfrost droplets

We show that Leidenfrost droplets made of an aqueous solution of surfactant undergo a violent explosion, for a wide range of initial volumes and concentrations. This unexpected behavior turns out to be triggered by the formation of a gel-like shell during the evaporation when the surface concentration of surfactant reaches some critical value. Shortly later, the temperature sharply increases above the normal boiling point leading to fast bubble growth, shell stretching and explosion. Yet, most of the droplet life is characterized by a self-similar evolution of the radial surfactant distribution during which surface and mean concentrations grow in proportion, independently of the initial conditions. The temperature rise (attributed to boiling point elevation with surface concentration) and nucleation/growth of vapor bubbles inside the shell are key features leading to the explosion, differing from the implosion (buckling) scenario reported by other authors.

I. INTRODUCTION

When a droplet is released over a plate heated above a critical temperature, it levitates above its own vapor. This so-called Leidenfrost effect [START_REF] Leidenfrost | De Aquae Communis Nonnullis Qualitatibus Tractatus[END_REF] was discovered a long time ago, yet it remains an active field of research of both fundamental [START_REF] Biance | Leidenfrost drops[END_REF][START_REF] Snoeijer | Maximum size of drops levitated by an air cushion[END_REF][START_REF] Burton | Geometry of the vapor layer under a leidenfrost drop[END_REF][START_REF] Sobac | Leidenfrost effect: Accurate drop shape modeling and refined scaling laws[END_REF][START_REF] Celestini | Take off of small leidenfrost droplets[END_REF][START_REF] Biance | Drop fragmentation due to hole formation during leidenfrost impact[END_REF][START_REF] Tran | Drop impact on superheated surfaces[END_REF][START_REF] Ma | Starshaped oscillations of leidenfrost drops[END_REF][START_REF] Gauthier | Aerodynamic leidenfrost effect[END_REF] and applied [START_REF] Kim | On the effect of surface roughness height, wettability, and nanoporosity on leidenfrost phenomena[END_REF][START_REF] Elbahri | Anti-lotus effect for nanostructuring at the leidenfrost temperature[END_REF][START_REF] Labergue | Combined three-color lif-pda measurements and infrared thermography applied to the study of the spray impingement on a heated surface above the leidenfrost regime[END_REF] interests. Recent works have for instance focused on the concave shape of the vapor film underneath the droplet [START_REF] Snoeijer | Maximum size of drops levitated by an air cushion[END_REF][START_REF] Burton | Geometry of the vapor layer under a leidenfrost drop[END_REF][START_REF] Sobac | Leidenfrost effect: Accurate drop shape modeling and refined scaling laws[END_REF], on "chimneys" observed above a certain critical size [START_REF] Biance | Leidenfrost drops[END_REF][START_REF] Snoeijer | Maximum size of drops levitated by an air cushion[END_REF], on the abscence of chimneys in particular geometries [START_REF] Hidalgo-Caballero | Leidenfrost phenomenon on conical surfaces[END_REF], on take-off regimes observed far below the capillary length [START_REF] Celestini | Take off of small leidenfrost droplets[END_REF], and on self-propelled motion on ratchets [START_REF] Linke | Self-propelled leidenfrost droplets[END_REF][START_REF] Hashmi | Leidenfrost levitation: Beyond droplets[END_REF]. In addition to the potential interest of the latter studies for droplet manipulation in microfluidics, understanding the impact of droplets on superheated substrates [START_REF] Biance | Drop fragmentation due to hole formation during leidenfrost impact[END_REF][START_REF] Tran | Drop impact on superheated surfaces[END_REF][START_REF] Labergue | Combined three-color lif-pda measurements and infrared thermography applied to the study of the spray impingement on a heated surface above the leidenfrost regime[END_REF][START_REF] Van Limbeek | Boiling regimes of impacting drops on a heated substrate under reduced pressure[END_REF] is crucial for optimizing cooling technologies.

However, most existing studies deal with pure liquids and much less is known about mixtures even though potential applications of the Leidenfrost effect exist (e.g. for nanoparticle deposition [START_REF] Elbahri | Anti-lotus effect for nanostructuring at the leidenfrost temperature[END_REF]). Generally speaking, the evaporation of droplets containing a non-volatile solute (e.g. polymers [START_REF] Pauchard | Buckling instability induced by polymer solution drying[END_REF] or colloids [START_REF] Pauchard | Invagination during the collapse of an inhomogeneous spheroidal shell[END_REF][START_REF] Tsapis | Onset of buckling in drying droplets of colloidal suspensions[END_REF]) leads to accumulation of the solute near the surface. A gel-like or glassy shell may then form, acquire elastic properties, and buckle (implode) under the internal depression resulting from compression of the shell [START_REF] Pauchard | Buckling instability induced by polymer solution drying[END_REF][START_REF] Pauchard | Invagination during the collapse of an inhomogeneous spheroidal shell[END_REF][START_REF] Tsapis | Onset of buckling in drying droplets of colloidal suspensions[END_REF].

In this Letter, we show that surfactant molecules (sodium dodecyl sulfate -SDS) in water lead to a quite different Leidenfrost dynamics. Namely, it is reported that after an initial period of gentle evaporation, the life of the droplet quite generally ends up in a sudden explosion, instead of buckling (see an example in Fig. 1a, and the movies M 1 and M 2 in the Supplemental Materials [21]). * florian.moreau@ensma.fr To begin with, free molecules and micelles are uniformly distributed. During the evaporation, the droplet shrinks and micelles accumulate at its surface, leading from t = t * to the formation of a gel-like shell. From t = tT the temperature of the droplet, T d , rises above the boiling temperature T0, leading to vapor bubble nucleation, growth, shell stretching and finally explosion of the droplet. N denotes the SDS mass fraction and ρ the density (with subscripts i, l and Σ for "initial", "liquid" and "surface", respectively).

Besides a possible impact on applications mentioned above, it is of fundamental interest to understand this unexpected yet reproducible scenario. We here focus on identifying mechanisms leading to explosion, rationalizing experiments made in a wide range of conditions thanks to a simple model based on a spherical symmetry. Formation of a gel-like shell at the droplet surface also turns out to occur with SDS, but the essential new fea-ture here is a sharp temperature increase of the droplet above the normal boiling point. This is shown to promote rapid growth of vapor bubbles in the water-rich core leading to an overpressure build-up due to the resulting shell stretching, rather than the underpressure-induced shell buckling observed in isothermal conditions [START_REF] Pauchard | Buckling instability induced by polymer solution drying[END_REF][START_REF] Pauchard | Invagination during the collapse of an inhomogeneous spheroidal shell[END_REF][START_REF] Tsapis | Onset of buckling in drying droplets of colloidal suspensions[END_REF].

II. EXPERIMENTAL SET-UP

Each droplet was placed on a curved and heated plate of aluminum. The curvature allowed to trap the droplet without contact. A heating device, a PID controller and a thermocouple placed at the surface of the plate, were used to control its temperature from T p = 200 to 450 • C. A highspeed video camera (IDT-Y4) recorded (up to 30000 fps) a side-view of the droplet evolution during the experiment, enabling extraction of the droplet volume versus time (assuming an axisymmetric shape). The droplet temperature was also followed from the top using an Infra-Red (Flir Thermovision 160) camera. Several concentrations were considered from pure water to 10 times the critical micelle concentration (CMC). Note that for SDS, CMC = 2.37 g/L.

III. RESULTS AND ANALYSIS

A. Volume and concentration evolution

In order to identify the parameters influencing the explosion, the roles of initial concentration and initial volume were analyzed first. Drops of several initial concentrations from pure water to 10 CMC, and several initial sizes from 10 to 1000 µL, were released on the plate heated at 300 • C. The corresponding volumes V (t) are plotted versus time t in Fig. 2a. Each curve is the average of 10 experiments. For clarity, curves corresponding to pure water (no explosion) are omitted from this plot.

Fig. 2a shows that for a given starting volume, the initial concentration does not affect the evaporation dynamics. Moreover, it is seen that decreasing the initial volume V i by some given factor and increasing the initial concentration ρ i by the same factor, yields nearly the same value of the volume just before explosion V f . As SDS does not evaporate, one concludes that the mean concentration ρ m,f = ρ i V i /V f at this moment is nearly the same. This suggests that an important parameter to predict the explosion is the mean concentration of surfactant ρ m (t) = ρ i V i /V (t), which is indeed confirmed by plotting ρ m versus time in Fig. 2b. Whatever the initial size and volume, the mean SDS concentration just before explosion remains in a relatively narrow range of values. Correspondingly, the total mass m i = ρ i V i of SDS inside the droplets depends linearly on the volume before explosion (Fig. 2c), with a slope equal to the value of the critical mean concentration ρ m,f = 275 ± 30 g/L.

V f (L) mi(g ) b) c) a)
FIG. 2. a. Volume vs time for water/SDS droplets of several initial sizes (Vi) and initial SDS mass concentrations (ρi):

(Vi=1000µL ρi=0.1CMC) (Vi=1000µL ρi=CMC) (Vi=1000µL ρi=10CMC) • (Vi=100µL ρi=CMC) • (Vi = 100µL ρi=10CMC) (Vi=10µL ρi=10CMC
). Filled symbols are used for the final volume just before the explosion. The plate temperature was Tp = 300 • C. In the inset, a time translation is applied to the data, so as to shift the volume just before explosion onto a reference curve (selected as the one corresponding to Vi = 1000 µL ρi = 0.1 CMC). b. Mean concentration ρm = ρiVi/V (t) versus time. The symbols are the same as in a. c. Initial mass mi = ρiVi of SDS vs final volume just before explosion V f , for all experiments at Tp = 300 • C. •: measurement and solid line: interpolation).

An additional observation is that during the droplet life, the evaporation dynamics is largely independent on the initial conditions. This is shown by the inset of Fig. 2a, obtained by horizontally translating curves of the main plot such as to superpose them on a reference curve (here selected as the one spanning the largest range of times and volumes, i.e. for V i = 1000 µL and ρ i = 0.1 CMC). All curves indeed collapse on the reference curve, showing that the drying dynamics is rather independent of the SDS concentration.

This independence with respect to initial conditions and the existence of a critical value of ρ m may be understood on the basis of scaling analysis. Assuming a small spherical droplet of radius R(t), a "full-surface" conduction-limited evaporation model (see e.g. [START_REF] Biance | Leidenfrost drops[END_REF]) yields Ṙ ∼ -χ/R, where χ = λ v θ/ρ l L, in which λ v is the vapor thermal conductivity, θ the plate superheat (difference between plate temperature T p and boiling temperature T 0 ), ρ l is the liquid density and L its latent heat. Clearly, evaporation is not affected by SDS, as long as the latter has no effect on liquid properties, and in particular on the boiling temperature. On the other hand, SDS cer-tainly does not remain uniformly distributed inside the shrinking droplet (Fig. 1b). Assuming the concentration to be above CMC, the non-volatile SDS micelles accumulate within a surface concentration boundary layer of thickness e(t)

∼ D/| Ṙ| ∼ R(t), where = ρ l LD λ v θ (1)
in which D is the diffusion coefficient of micelles. Importantly, note that therefore measures the boundary layer thickness relative to the droplet radius, and is small provided the superheat θ is sufficiently large. In this case, the volume contained inside this boundary layer at time t is of order V (t), and it can be shown by expressing the SDS mass conservation at time t that the concentration ρ Σ at the surface (i.e. in the boundary layer) scales as

ρ Σ (t) -ρ i ∼ ρ i [V i -V (t)] V (t) = ρ m (t) -ρ i (2)
as indeed, ρ i (V i -V ) is the mass of surfactant which has accumulated inside the boundary layer, at time t, as a result of droplet shrinkage from V i to V . Note also that outside the boundary layer, we assume the concentration remains equal to ρ i . Hence, if ρ m ρ i (always valid before explosion for our conditions, see Fig. 2), Eq. ( 2) yields ρ Σ ∼ ρ m / , i.e. a direct link between the mean concentration ρ m and the surface concentration ρ Σ , independent of V i and ρ i . Thus, the critical value of ρ m evidenced above corresponds to a critical value of ρ Σ , which actually makes more sense physically. On this basis, our working assumption in what follows is that the explosion sequence starts when the surface concentration reaches a well-defined critical value ρ * Σ . Hereafter, this conjecture will be reinforced by the direct observation of the formation of a gel-like shell at the droplet surface, and by pushing our modeling further.

Coming back to experiments, the influence of the superheat θ was then considered. Drops were released on the plate at several temperatures from 200 to 450 • C. The drops had the same initial size V i = 100 µL, and the same initial SDS concentration ρ i = 10 CMC. The evolution of the volume is plotted in Fig. 3a. Each curve is the average of 5 experiments. Expectedly, a higher plate temperature results in a shorter evaporation time. The values of the volume just before the explosion are plotted in Fig. 3b. They all lie in the range 9.8±1.2 µL, but increasing the plate temperature clearly results in a higher volume before the explosion. This tendency is actually coherent with the above scaling analysis, which predicts a final volume V f ∼ ρ i V i / ρ * Σ , indeed increasing with θ (but faster than in Fig. 3b, likely due to the simplicity of our model and to the fact that ρ * Σ itself may slightly increase with the evaporation rate). Note finally that below 250 • C no explosion occurs (see also [START_REF] Qiao | Experiments on adding a surfactant to water drops boiling on a hot surface[END_REF]). In this case, at the end of the droplet life, a residue made of non-evaporated products gently comes in contact with the hot surface without explosion.

B. Shell formation and temperature increase

Careful analysis of high-speed movies revealed that, at a certain time before the explosion, a shell is formed around the droplet. Just before the explosion, a capillary tube was used to remove the droplet (still in Leidenfrost state) from the hot plate to bring it on a plate at room temperature (see Fig. 4a). The liquid turns out to be encapsulated within a gel-like shell covering the whole droplet. This observation clearly demonstrates that the presence of the shell does not prevent the droplet to be in Leidenfrost state, at least for some time (typically 10 s). To understand the nature of this shell, nuclear magnetic resonance spectroscopy was used. Spectrum analysis showed that the shell is made of unaltered SDS molecules. The temperature of the droplet was also mea-sured from the top using an IR camera, averaging it all over the top surface. A camera simultaneously recorded the droplet shape and the formation of the shell. An example of temperature evolution is shown in Fig. 4b, representing the difference between the temperature at a time t and the time-averaged temperature before shell formation. Even though such IR measurements are generally delicate in the case of droplets, a sudden increase of temperature (possibly preceded by a slight decrease) is clearly detected after the shell formation. This increase generally exceeds 10 • C, and can therefore be expected to be a precursor of the explosion (given moreover that even higher temperatures are expected under the drop).

C. Self-similar concentration profile evolution

To gain further insight into this complex process, the evolution of the SDS mass fraction profile N (r, t) = ρ(r, t)/ρ l is now analyzed in more details, yet still assuming a spherical droplet of radius R(t) in its vapor at temperature T p . As for the droplet temperature T d , the sharp increase observed in Fig. 4b can be modeled by assuming that it follows the equilibrium curve T eq (N Σ ), depending on the surface mass fraction N Σ = N | r=R . This is indeed the natural generalization of the usual condition for pure liquids, namely T d = T 0 = T eq (0) (normal boiling point). However, to our knowledge the curve T eq (N ) is unknown and delicate to measure at large N . As our own experiments did not detect any such boiling point elevation up to N = 0.35, and since thermodynamics of ideal solutions shows that T eq does not deviate from T 0 = 373K before N gets very close to unity (due to the large molar weight of SDS micelles), we here stick to T d = T 0 . Then, rescaling distances by the initial radius R i and time by the evaporation time τ e = ρ l LR 2 i /2λ v θ of a SDS-free droplet, the dimensionless radius evolves according to ∂ t R = -(2 R) -1 as before, while N (r, t) satisfies the diffusion equation 2

∂ tN = r-2 ∂ r (r 2 ∂ r N ) with boundary conditions ∂ r N | r=0 = 0 (symmetry) and R N -1 ∂ r N | r= R = 1 (
no SDS flux through the surface). Note that , as defined by Eq. ( 1), is the natural dimensionless parameter characterizing this Stefan-like problem. Integrating the equation for R directly yields R = (1-t) 1/2 , and from the total SDS mass conservation we readily obtain the mean mass fraction N m = N i / R3 . This suggests a self-similar solution for N , namely

N (r, t) = N i R3 F 0 ( ) exp r2 2 R2
(3) which indeed solves the above-stated problem, and where

F 0 ( ) = 3 -1 exp[1/2 ] -π/2 3/2 erfi 1/ √ 2 -1
is a normalisation factor found from the definition of

N m = 3 R-3 R 0
r2 N (r, t)dr (solute mass conservation)

and erfi[z] is the imaginary error function erf[iz]/i. The similarity solution (3) is actually valid after a short transient, when the actual initial condition has been forgotten. In this regime, rescaling N by N m and r by R collapses all concentration profiles onto a single curve, independently of the initial volume and concentration. Moreover, Eq. ( 3) shows that the ratio

N Σ /N m = F 0 ( ) exp[1/2 ] = F 1 ( ) is a constant, i.e.
surface and mean values of N grow in proportion during the droplet evaporation. This not only confirms Eq. ( 2) for N i 1 but generalizes it to O(1) values of , and enables estimating the value N * Σ = ρ * Σ /ρ l at which a shell forms at the free surface, as conjectured above. Namely, using experimental values of N m at shell formation for various values of the plate temperature T p (and N i = 0.024, i.e. ρ i = 10 CMC), we obtain values of N * Σ between 0.37 and 0.69, i.e. a range where phase transitions of the SDS solution are indeed expected [START_REF] Kekicheff | Phase diagram of sodium dodecyl sulfate-water system: 1. a calorimetric study[END_REF]. Note that for estimating , we used Stokes-Einstein law D = kT /6πηr 0 with r 0 = 17 Å , the radius of a SDS micelle, and λ v was evaluated at (T p +T 0 )/2. Remark finally that N * Σ is found to increase with the plate temperature (hence with the evaporation rate), which might be due to faster quenching and delayed nucleation of the gel-like phase. As already mentioned, this could also be linked to the simplicity of our spherically-symmetric model, which "averages out" any non-homogeneity of concentration at the drop surface (we indeed experimentally observe that the growth of the shell is inhomogeneous). Now, a closer look at Fig. 2b interestingly reveals that the time scale of the concentration increase gets shorter at smaller values of N i , which is also captured by the self-similar solution Eq. (3). Namely, the time t * at which the shell starts to form is readily obtained from the condition N Σ = N m F 1 ( ) = N * Σ (taken equal to 0.5 hereafter). Using R = (1 -t) 1/2 , this leads to t * = 1 -[2N i F 1 ( )] 2/3 , showing that shell formation occurs closer to the evaporation time of a pure droplet (of the same initial volume and for the same superheat) when N i gets smaller. This actually also holds for the time tT > t * at which the temperature starts to increase, which as said above, corresponds to the moment where N Σ 1. Assuming the fluid properties (and in particular the diffusion coefficient D) to keep the same values in the shell, we similarly get tT = 1 -

[N i F 1 ( )] 2/3 . Hence, tT - t * ∼ [N i F 1 ( )] 2/3
, which clearly shows the acceleration of events occurring when N i decreases. Note that this is also coherent with our experimental observation of more violent explosions for less loaded droplets (see movie M3 in Supplemental Material [21]).

D. Vapor bubble nucleation/growth within shell

At time tT , the droplet temperature T d = T eq (N Σ ) sharply increases and can get extremely high given that SDS is non-volatile. In theory, T d can rise up to the plate temperature T p when the surface mass fraction N Σ gets very close to unity (quasi-pure SDS), and the droplet comes in contact with the substrate (the evaporation rate vanishing as T p -T d → 0). However, before this ultimate stage is possibly reached, conditions for nucleation of tiny vapor bubble(s) can be met inside the shell, which still contains a lot of water with a boiling temperature close to T 0 = 373 K. This water-rich core is therefore in a metastable state as soon as T d > T 0 , and homogeneous nucleation will certainly occur for T d > T k = 575 K [START_REF] Avedisian | The homogeneous nucleation limits of liquids[END_REF]. Given moreover that heterogeneous nucleation may occur earlier than that (due to impurities or even micelles themselves), and that the threshold for explosion was found between T p = 200 • C = 473 K and T p = 250 • C = 523 K (see above), a boiling-mediated explosion scenario turns out to be very likely, as now studied in more details.

Consider a spherical droplet of initial radius R 0 at temperature T d = T n , i.e. assuming that it has already heated up to the nucleation limit T n (be it homogeneous or heterogeneous). Once nucleated, any bubble grows extremely fast given the large value of the superheat ∆T = T n -T 0 200 K, and of the corresponding Jacob number Ja = ρ l c p,l ∆T /ρ v L 600, where c p,l is the liquid heat capacity and ρ v the vapor density. In these conditions, the time scale of bubble growth up to a size R 0 is of the order of τ b ∼ Ja -2 R 2 0 /κ l (where κ l is the liquid thermal diffusivity) [START_REF] Prosperetti | Vapor bubbles[END_REF], i.e. very short indeed (about 0.1µs for a 100 µL droplet). Bubble growth up to a size comparable to the containing droplet thus occurs instantaneously on the time scale τ e ∼ 10 2 s of droplet evaporation, and even on the time scale τ i ∼ τ e N 2/3 i ∼ 10 0 s of the concentration/temperature increase. Now, the droplet is confined by a SDS-rich shell which can be assumed to possess elastic properties, even though the Young's modulus of the various phases of SDS [START_REF] Kekicheff | Phase diagram of sodium dodecyl sulfate-water system: 1. a calorimetric study[END_REF] has not been measured, to the best of our knowledge. Clearly, bubble growth within the liquid stretches the shell to a certain extent which may or may not be sufficient for the shell to rupture, i.e. for explosion to occur. Indeed, two effects can limit bubble growth and lead the system to a steady state: i) the finite amount of heat available in the droplet at the moment a bubble nucleates; ii) the rise of internal pressure (induced by the shell stretching) which leads to an increase of the boiling temperature. For each of these effects separately, we may estimate the final stretching ratio δ = R s /R 0 -1, where R s is the droplet radius at steady state. For the effect i), denoting by T s the final temperature and noting that ρ v ρ l , the radius b s (or rather the volume 4πb 3 s /3) of the bubble at steady state can be obtained by dividing the excess heat in the liquid by the latent heat per unit volume of vapor. This simply yields b s = R 0 Ja s 1/3 , where Ja s = ρ l c p,l (T n -T s )/ρ v L is a Jacob number based on the temperature drop T n -T s . Expressing the conservation of mass then yields a first expression of the stretching ratio for thermally-limited growth:

δ i = (1 + Ja s ) 1/3 -1 (4)
On the other hand, for case ii), a steady state is reached when the final temperature T s equals the boiling temperature at pressure p 0 + ∆p i , where ∆p i = 4E(e 0 /R 0 )δ is the (linearized) elasticity-induced excess pressure, (as for a balloon) E is the Young's modulus and e 0 is the shell thickness. Using the Clausius-Clapeyron equation and solving for δ, this yields the stretching ratio for stiffnesslimited growth:

δ ii = p 0 4E R 0 e 0 exp - LM w R g 1 T s - 1 T 0 -1 (5)
where M w is the molar mass of water and R g is the perfect gas constant. In general, the solution lies between these two extremes, and can be found by solving δ i = δ ii for T s . A single solution is found in the interval [T 0 , T n ], the limits of which corresponding to thermally-limited growth (T s → T 0 for small values of the dimensionless stiffness σ = 4Ee 0 /R 0 p 0 ) and stiffness-limited growth (T s → T n for large values of σ). The corresponding stretching ratio is represented in Fig. 5 as a function of the plate temperature T p (which affects e 0 /R 0 ∼ , see above), for a wide range of values of E. Assuming E to be of the order of 10 3 -10 5 Pa, as for an hydrogel (given that the SDS skin contains a significant amount of water), it is seen that the shell may be considerably stretched (δ ∼ 600% is close to its maximal value obtained from Eq. ( 4) in the thermally-limited case) and therefore highly likely to rupture (hydrogels can barely withstand about 50% of strain, see e.g. [START_REF] Puleo | Mechanical and rheological behavior of pnipaam crosslinked macrohydrogel[END_REF]). In fact, it turns out that only very stiff material with moduli above 10 8 Pa could resist internal bubble growth (yet the encapsulated object would contain voids, resembling cavitation bubbles observed in isothermal situations [START_REF] Meng | Cavitation in drying droplets of soft matter solutions[END_REF]). Therefore, even though accurate measurements of E and δ would certainly be valuable, we believe that the above discussion strongly supports the proposed boiling-induced explosion scenario of Leidenfrost droplets (while thermal expansion alone cannot lead to a significant stretching of the shell).

IV. CONCLUSION

To conclude, we emphasize that the proposed scenario does not require the droplet to contact the plate (see movie M 4 in the Supplemental Materials [21], in which a vertical jet can be seen below the droplet, followed by the explosion and eventually foam formation). It thus essentially differs from contact boiling [START_REF] Tran | Drop impact on superheated surfaces[END_REF], in that it relies on the concentration contrast between surface and bulk, the latter becoming prone to nucleate and grow vapor bubbles. We also pointed out an interesting cascade of time scales (successively: droplet evaporation, concentration/temperature increase, and vapor bubble growth), each one essentially shorter than the previous one. Finally, among the many possible perspectives of this work, other types of solutes certainly need to be tested, such as polymers, or colloidal particles, for which the detailed mechanisms might considerably differ. The effect of internal flows generated by the vapor shear [START_REF] Bouillant | Leidenfrost wheels[END_REF] is also worth considering, in view of the strong effect it might have on the surfactant concentration profile. Yet, the formation of a shell and the explosion scenario proposed here should not be invalidated, given that flows are expected to remain locally tangential to the drop surface, in addition to being strongly reduced well before shell formation due to the Plateau-Marangoni-Gibbs effect.

FIG. 1

 1 FIG. 1. a. Example of an explosion of a droplet. Initial size of the drop 100 µL, initial concentration 10 CMC and temperature of the plate 400 • C. b. Schematic representation of a droplet life.To begin with, free molecules and micelles are uniformly distributed. During the evaporation, the droplet shrinks and micelles accumulate at its surface, leading from t = t * to the formation of a gel-like shell. From t = tT the temperature of the droplet, T d , rises above the boiling temperature T0, leading to vapor bubble nucleation, growth, shell stretching and finally explosion of the droplet. N denotes the SDS mass fraction and ρ the density (with subscripts i, l and Σ for "initial", "liquid" and "surface", respectively).

FIG. 3

 3 FIG. 3. a. Volume vs time for water/SDS droplets at several temperatures of the plate: 250 • C 300 • C 350 • C 400 • C 450 • C. Filled symbols are used for the final volume before the explosion. The initial concentration of the droplet is 10 CMC and the initial size of the droplet is 100 µL. b. The final volume before explosion, V f is plotted vs the temperature of the plate Tp. The line is a linear fit.

FIG. 4

 4 FIG. 4. a. Encapsulation of a Leidenfrost drop. Top: Leidenfrost droplet of SDS, methylene blue and water over a plate at 300 • C. Bottom: the Leidenfrost droplet is removed from the hot plate after the shell is formed and put on a cold plate. The whole droplet is covered by the shell, retaining water. b. Evolution of the temperature of the top part of the droplet surface. The temperature T is measured using an IR camera placed above the droplet (after a calibration procedure), and ∆T(t)=T d (t)-<T> before shell formation . The dashed line corresponds to the beginning of the formation of the shell.

E = 10 6 E = 10 7 E = 10 8 FIG. 5 .

 6785 FIG.5. The stretching ratio δ = Rs/R0 -1 the shell as a function of the plate temperature Tp, for various values of the Young's modulus E. The ratio of shell thickness e0 to droplet radius R0 is taken to , which decreases with Tp, leading to a slight increase of δ. Here, p0 = 1 atm, T0 = 373K, and the nucleation temperature is taken (for illustration) to be Tn = 525K, i.e. 50K lower than the homogeneous nucleation limit T k . The zone between E = 10 3 Pa and 10 5 Pa corresponds to hydrogels, thought to be representative of our SDS shells. Note that this diagram is independent of the values of Vi and Ni, due to the self-similarity of the concentration evolution discussed above.

ACKNOWLEDGMENTS

The authors gratefully thank C. Sun, S. Lyu, D. Quéré, A. Bouillant, B. Roman and B. Sobac for interesting discussions. This work was supported by the ODILE project (FRFC Contract No. 2.4623.11), and partly by the µ-MAST project (BELSPO IAP 7/38). SD and PC also gratefully acknowledge support of the F.R.S. -FNRS.


Dr Lucas Bacheley
email: lucas.bacheley@chimieparistech.psl.eu

Gérard Guillamot
email: gerard.guillamot@seqens.com

Dr Phannarath Phansavath
email: phannarath.phansavath@chimieparistech.psl.eu

Virginie Ratovelomanana- Vidal
email: virginie.vidal@chimieparistech.psl.eu

V Ratovelomanana-Vidal

acetal isoxazoles: application to the formal synthesis of a bioactive fluorinated isoxazole

Keywords: Fluoration, Isoxazole, Hétérocycles Fluorination, isoxazole, Heterocycles

Fluoration directe d'isoxazoles 5-(1,3-dioxane) acétal 3-substitués : application à la synthèse formelle d'un isoxazole fluoré d'intérêt biologique Direct ring fluorination of 3-substituted 5-(1,3-dioxane)

I. Introduction:

1 Heterocyclic scaffolds represent the largest 2 family of organic compounds and have a role in 3 many fields of sciences such as medicinal 4 chemistry, 1 biochemistry 2 or agrochemistry. 3 5 More specifically, the isoxazole skeleton is a very 6 important motif found in natural products or 7 synthetic products such as antibiotics, 4 8 analgesics, 5 antirheumatic, 6 anti-inflammatory 7 or 9 antidepressant compounds. 8 10 11

Furthermore, the interest of fluorine and its a Reaction conditions: (1a, 0.43 mmol, 1.0 eq.), nBuLi (0.52 mmol, 1.2 eq.), NFSI (0.86 mmol, 2.0 eq.), THF (0.4 M, 1.1 mL), -78 °C to r.t, under argon. b After NMR 1 H analysis of the crude reaction mixture. c After isolation by column chromatography. d 3.5 eq. of base were used. e 1.5 eq. of base were used. f Only degradation was observed.

Having these optimised conditions in hand, we

  Figure 1: examples of bioactive molecules containing a 4-33

  further explored the scope and limitations of the reaction with the 3,5-disubstituted isoxazole previously synthesized. This process allowed to obtain the corresponding fluorinated isoxazoles bearing various electron-donating or withdrawing substituents in the para-position of the aryl ring such as tbutyl-2b, chlorine 2c, fluorine 2d or trifluoromethyl 2e groups in 59-70% yields and compounds 2g and 2h having a 3-chloro-4fluorophenyl or a 2,6-dichlorophenyl substituentwere obtained in 44% and 21% yield, respectively (Figure3). Having a methyl in meta-position (1f) led to 75% isolated yield of the corresponding fluorinated product 2f. To extend the feasibility of our process, a bulky group such as a naphthyl-or a 2,2-difluorobenzodioxole was also investigated and yielded the products 2i in 20% and 2j in 60% respectively. The reaction was also suitable for isoxazoles bearing a non-aromatic substituent at the C-3 position and compound 2k bearing a nbutyl chain was synthesized in 25% yield.

  27 a after isolation by column chromatography b after 1 H NMR 28 analysis of the crude reaction mixture. 29 30

Figure

  Figure 3: scope of the fluorination 1

  Figure 4: formal synthesis of a bioactive compound 13

(a) J. Jampilek, Molecules,

2019, 24, 21, 3839. (b) A. Amin, T. Qadir, P. K. Sharma, I. Jeelani, H. Abe, Open J. Med. Chem., 2022, 16, e187410452209010. 2 E. Kabir, M. Uzzaman, Results Chem., 2022, 4 100606. 3 (a) C. Lamberth, Pest Manag. Sci., 2013, 69, 1106-1114. (b) E. A. Al-Harbi, W. A. Gad, Agri Res & Tech: