Camila Flores

Vladimir L Zholobenko

Bang Gu

Nuno Batalha

Valentin Valtchev

Walid Baaziz

Ovidiu Ersen

Nilson R Marcilio

Vitaly V Ordomsky
email: vitaly.ordomsky@univ-lille.fr

Andrei Y Khodakov
email: andrei.khodakov@univ-lille.fr

Versatile Roles of Metal Species in Carbon Nanotube Templates for the Synthesis of Metal-Zeolite Nanocomposite Catalysts

Keywords: nanocomposite, hard template, replicas, catalyst, promotors, metal nanoparticles, acidity

Metal-zeolite nanocomposites are extensively used in heterogeneous catalysis. The small size of zeolite micropores and non-uniform distribution of the metal component within the zeolite structure can severely reduce the efficiency of these catalysts. In this work, we propose a new single-pot synthesis strategy for the design of metal-zeolite nanocomposites with specific shape, enhanced mesoporosity and uniform distribution of highly dispersed metals such as cobalt, nickel, and magnesium within the zeolite crystals. The strategy involves using metal carbon nanotubes as a secondary hard template. The presence of metal species in carbon nanotube templates is crucial and indispensable for the synthesis of metal zeolite nanocomposites. The multiple roles of the metal carbon nanotubes in the zeolite synthesis are revealed. First, they serve as a replica to create zeolites with specific fibrous morphology.

Second, they fulfill the role of a mesoporogen and markedly increase the zeolite secondary porosity. Finally, they act as a vehicle to uniformly introduce the metal functions inside the mesoporous zeolites. Nanocomposites prepared using metal carbon nanotubes have shown enhanced catalytic performance in Fischer-Tropsch synthesis, hydrogenation of aromatics and anisole acylation.

Introduction

Zeolites are microporous crystalline solids with a regular pore system, which have found numerous applications in industrial processes such as oil refining, organic synthesis, adsorption and separation. The zeolite crystal structure determines the size and geometry of the micropores. They are very specific for a given type of the zeolite [START_REF] Corma | From Microporous to Mesoporous Molecular Sieve Materials and Their Use in Catalysis[END_REF][START_REF] Schüth | Microporous and mesoporous materials[END_REF] and often are comparable with the size of the reacting molecules. Small and uniform pores lead to stronger interaction between the zeolite and reacting molecules, and thus, introduce geometric and electronic confinement as well as shape selectivity phenomena in catalytic reactions involving bulky molecules [START_REF] Egeblad | Templating Mesoporous Zeolites[END_REF] . Zeolites can be tailored to specific catalytic applications by controlling their Brønsted and Lewis acidity as well as by introducing new catalytic functions, such as metal cations, clusters, metal oxides, metalorganic complexes and enzymes [START_REF] Egeblad | Templating Mesoporous Zeolites[END_REF] .

Zeolites in their hydrogen form are considered as acid catalysts, while metal-containing zeolites can be bifunctional catalysts that exhibit complex behavior. The concentrations and intrinsic activity of the metal and acid sites, and in particular, their localization within the zeolite structure are of utmost importance for the catalyst activity, selectivity and stability [START_REF] Ertl | Preparation of solid acids[END_REF][START_REF] Weisz | Polyfunctional heterogeneous catalysis[END_REF][START_REF] Subramanian | The Role of Steric Effects and Acidity in the Direct Synthesis of iso-Paraffins from Syngas on Cobalt Zeolite Catalysts[END_REF] .

Ion exchange, impregnation, or the introduction of a metal precursor into the zeolite synthesis gel have been often used for synthesis of metal-zeolite nanocomposites, including isomorphously substituted materials [START_REF] Barrer | Hydrothermal Chemistry of Zeolites[END_REF] , [START_REF] Ma | A review of zeolite-like porous materials[END_REF] . In the metal-zeolite nanocomposites, metals can be present either in the form of isolated cations in the cationic sites, or in the form of tetrahedrally coordinated cations isomorphously substituting silicon or aluminum atoms in the zeolite framework, or as small metal or oxide nanoparticles localized within the zeolite microor mesopores. The distribution of metal component within the zeolite is of paramount importance for the resulting catalytic performance, which can be strongly affected by the distance between metal nanoparticles and acid sites, the so-called "site intimacy" [START_REF] Ertl | Preparation of solid acids[END_REF] and by diffusion of the intermediates during their transport from one site to another. [START_REF] Zečević | Nanoscale intimacy in bifunctional catalysts for selective conversion of hydrocarbons[END_REF][START_REF] Samad | The controlled synthesis of metal-acid bifunctional catalysts: The effect of metal:acid ratio and metalacid proximity in Pt silica-alumina catalysts for n-heptane isomerization[END_REF][START_REF] Prins | Hydrogen Spillover. Facts and Fiction[END_REF][START_REF] Im | Maximizing the catalytic function of hydrogen spillover in platinum-encapsulated aluminosilicates with controlled nanostructures[END_REF] The very small pore size of zeolites (~1 nm) imposes diffusional limitations for many catalytic reactions, in particular, for those involving bulky molecules. In order to overcome these, numerous efforts have made to synthesize nano-sized zeolite crystals [START_REF] Tosheva | Nanozeolites: synthesis, crystallization mechanism, and applications[END_REF] , extra-large pore zeolites [START_REF] Jiang | Extra-large-pore zeolites: bridging the gap between micro and mesoporous structures[END_REF] , or mesoporous zeolites [START_REF] Tao | Mesopore-modified zeolites: preparation, characterization, and applications[END_REF][START_REF] Van Donk | Generation, characterization, and impact of mesopores in zeolite catalysts[END_REF] , the latter are often referred to as hierarchical zeolites.

The hierarchical zeolites contain, in addition to the well-defined micropore system, mesopores with the diameters in the range of 2-50 nm. Different to zeolite micropores, the size, shape and orientation of these mesopores are not directly related to the zeolite crystalline structure.

The methods used for the preparation of hierarchical zeolites could be divided into two main groups. (i) Bottom-up methods, where sacrificial templates of desired size and dimensions are incorporated into the zeolite crystals during crystallization. These templates are then eliminated by combustion or extraction. (ii) Top-down methods, including post-synthesis chemical treatment of zeolite crystals leading to the extraction of aluminum or silicon atoms and partial dissolution of the zeolite framework. Note that it is usually much more difficult to maintain zeolites with good crystallinity and to generate uniform mesopores using top-down methods such as steam treatment, acid and alkaline leaching [START_REF] Chen | Hydroconversion of jatropha oil to alternative fuel over hierarchical ZSM-5[END_REF] compared to the bottom-up strategies.

Both hard [START_REF] Schmidt | Carbon Nanotube Templated Growth of Mesoporous Zeolite Single Crystals[END_REF][START_REF] Boisen | TEM stereo-imaging of mesoporous zeolite single crystals[END_REF] and soft templates [START_REF] Meng | Templating route for synthesizing mesoporous zeolites with improved catalytic properties[END_REF][START_REF] Zhou | The comparison of mesoporous HZSM-5 zeolite catalysts prepared by different mesoporous templates and their catalytic performance in the methanol to aromatics reaction[END_REF] have been utilized to synthetize hierarchical zeolites using the bottom-up approach. The hard templates usually include carbon nanoparticles, nanotubes and polymer beads, whilst various cationic surfactants, organosilanes, cationic polymers, and ionic liquids [START_REF] Sachse | Ordered Mesoporous ZSM-5 Employing an Imidazolium-Based Ionic Liquid[END_REF][START_REF] Sachse | Mesoporous Y zeolite through ionic liquid based surfactant templating[END_REF] are considered as soft secondary templates. Both hard and soft templates could be removed by calcination. Among the hard templates, carbon nanotubes (CNT) have attracted particular attention in the literature. CNT are very versatile materials [START_REF] Zhai | Carbon-based nanostructures for advanced catalysis[END_REF][START_REF] Liu | Synthesis and characterization of graphene and carbon nanotubes: A review on the past and recent developments[END_REF] as their properties are strongly affected by the presence of hydrophobic or hydrophilic functional groups, metals, oxides and other dopants. As a result, the properties of hierarchical zeolites prepared using CNT as secondary templates are strongly affected by the features of CNT and zeolite synthesis conditions. Carbon nanotubes often contain traces of metal catalysts, which are used for their synthesis. For these reasons, the literature about the use of carbon nanotubes as templates for the synthesis of hierarchical zeolites is rather contradictory.

In this work, we found that when metal impurities had been carefully removed from the synthesized carbon nanotubes, hierarchical zeolites could not be obtained using carbon nanotubes as secondary templates. Importantly, intentional addition of CNT with metal oxides to the synthesis gel, results in excellent hierarchical zeolites. This implies that the presence of metal sites in carbon nanotubes (which can be residual metal catalysts or added metal species) is crucial for using these materials for the synthesis of hierarchical zeolites. Moreover, we uncovered multiple roles of metal-CNT in the zeolite synthesis. Firstly, they strongly affect the shape of the synthesized zeolites, which seem to be replicas of CNT and show distinct fibrous morphology. Secondly, the metal-CNT act as mesoporogen and strongly enhance the zeolite mesoporous volume. Finally, zeolite synthesis in the presence of metal-CNT offers an opportunity to simultaneously introduce new catalytic functions leading to bifunctional metalzeolite nanocomposites. The introduced metals are uniformly distributed within the zeolite crystals. The presence of metal species in CNT is essential for the synthesis of hierarchical ZSM-5 zeolites with enhanced properties and catalytic performance. Indeed, only a very limited impact on zeolite porous structure was observed by using metal-free CNT as secondary hard templates. The metal-zeolite nanocomposites prepared using metal-CNT templates exhibited improved catalytic performance in Fischer-Tropsch synthesis, hydrogenation of aromatics and anisole acylation with hexanoic acid.

Experimental

CNT impregnation with metal precursors

Two multi-wall CNT samples (Iolitec nanomaterial, 95%) of different size, i.e. 10-20 nm and 20-40 nm, were used. The CNT were pretreated with nitric acid in order to remove all metal contaminations. This treatment also converted CNT into their hydrophilic forms. Typically, 3 g of CNT was pretreated in 210 mL of concentrated HNO 3 (68%) for 14 h under reflux. Next, the samples were filtered, washed with distilled water until pH = 7 and dried at 100 ºC overnight.

Metals were added to CNT via the wet impregnation method using Co(NO 3 ) 2 6H 2 O (Sigma-Aldrich) and Pt(NH 3 ) 4 (NO 3 ) 2 (Sigma-Aldrich), Mg(NO 3 ) 2 6H 2 O (Sigma-Aldrich) and Ni(NO 3 ) 2 6H 2 O (Sigma-Aldrich) as precursors. Co-impregnation with small amounts of platinum was solely used for the preparation of cobalt catalysts. Platinum is commonly used as a promoter in the preparation of cobalt catalysts containing small metal nanoparticles in order to improve cobalt reducibility [START_REF] Diehl | Promotion of cobalt Fischer-Tropsch catalysts with noble metals: A review[END_REF] . Typically, the precursor amount for impregnation was calculated to obtain 20 wt. % of the metal in the final catalyst. The mixture was exposed to ultrasonic treatment for 30 min and dried at 80 °C. The samples were calcined at 400 °C for 4 h under nitrogen atmosphere.

After calcination in nitrogen, the hydrophilic properties of CNT were partially lost. In order to restore the CNT hydrophilicity, the samples were treated with H 2 O 2 . Typically, 30 mL of 1:1 H 2 O 2 (Sigma-Aldrich, 35%) and distilled water mixture were added to 2.56 g of impregnated CNT, sonicated for 30 min and dried at 80 °C. The metal supported CNT catalysts are denoted as Metal/CNT (x) (where Metal=Co, Ni or Mg) and x is the CNT diameter in nm.

Synthesis of metal-ZSM-5 nanocomposites

The ZSM-5 zeolite was synthesized by using a synthesis gel with the initial composition of 2.7NaCl:1Al 2 O 3 :12.5TPAOH:55.8SiO 2 :7500H 2 O. The synthesis of the zeolite was carried out by mixing sodium chloride (0.380 g, Janssen Chimica, P.A.), tetrapropylammonium hydroxide (3.0 g, Sigma-Aldrich, 1 M in H 2 O), sodium aluminate (0.040 g, Sigma-Aldrich) and distilled water until a clear solution was obtained. Metal/CNT (0.24 g) and tetraethylorthosilicate (TEOS, 2.8 g, Sigma-Aldrich, 99%) were added to this solution and the resulting synthesis gel was aged for 1 h at room temperature under stirring. Next, the zeolite crystallization was performed in a Teflon-lined autoclave (40 mL) under static condition at 170 °C for 24 h. After cooling down, the solid was recovered by filtration and washed until pH=7 was achieved. The final solid was calcined at 600 °C for 4 h in air. Further details relevant to the introduction of cobalt with CNT into ZSM-5 zeolite are available elsewhere [START_REF] Flores | Direct production of iso-paraffins from syngas over hierarchical cobalt-ZSM-5 nanocomposites synthetized by using carbon nanotubes as sacrificial templates[END_REF] .

For comparison, the zeolite syntheses using metal-free CNT were performed under the same conditions using a similar gel composition. The resulting zeolites were then impregnated using incipient wetness method with cobalt, nickel and magnesium nitrates as precursors.

In order to obtain the zeolite acid form, two successive exchanges using 2 M NH 4 NO 3 aqueous solution at 80 °C for 1 h (1 g of zeolite per 50 mL of solution) were performed. The ammonium forms were converted into the protonic forms by calcination at 450 °C for 4 h in air. The synthesized samples were denoted as metal-CNT (x) /ZSM-5 (where metal= Co, Ni or Mg) for the samples synthesized using metal impregnated CNT (x represents the CNT diameter, i.e. 10-20 or 20-40 nm) and CNT (x) /ZSM-5 for the samples synthesized with pure CNT as secondary templates. Metal/ZSM-5 stands for the zeolite synthesized without any secondary template and conventionally impregnated after its synthesis with a metal nitrate followed by the nitrate decomposition via calcination in air at 500°C.

Catalyst characterization

The textural properties of the samples were determined by N 2 physisorption on a Micromeritics ASAP 2000 apparatus. Prior to the analysis, the samples were degassed under vacuum (10 µmHg) at 350 °C for 4h. The total pore volume (TPV) was calculated from the amount of vapor adsorbed at a relative pressure P/P 0 = 0.97. The apparent sample surface area was estimated by the BET method, while the micropore volume was calculated using the deBoer t-plot method.

The samples were characterized by X-ray diffraction (XRD) utilising a D8 Advance diffractometer equipped with an energy dispersive type detector and a monochromatic CuK α radiation source. The samples were analyzed using a step size of 0.02° with an acquisition time of 0.5 s.

The sample chemical composition was determined by X-ray fluorescence (XRF) using a M4 TORNADO (Bruker) spectrometer. This instrument was equipped with 2 anodes, a rhodium X-ray tube 50 kV/600 mA (30 W) and a tungsten X-Ray tube 50 kV/700 mA (35 W). For sample characterization, the rhodium X-ray tube with a poly-capillary lens enabling excitation of an area of 200 μm was utilised. A silicon-drift Si(Li) detector with Peltier cooling (253 K) and a resolution <145 eV at 100000 cps (Mn Kα) was used. The measurements were conducted under vacuum (20 mbar). Quantitative analysis was carried out using fundamental parameter (standardless).

The catalyst reducibility was studied using an Autochem II (Micrometrics) temperatureprogrammed reduction (TPR) system. The samples were reduced under a flow of 5% H 2 in argon (50 mL/min) and heated up to 800 °C at a rate of 5°C/min. The catalyst Brønsted and Lewis acidities were monitored by infrared spectroscopy (IR) with pyridine adsorption. The IR spectra were recorded using a Thermo iS10 spectrometer (DTGC detector, 64 scans at 4 cm -1 resolution). The samples were pretreated under vacuum (10 -5 Torr) at 450°C for 5h.

After pre-treatment, pyridine was adsorbed on the sample at 150 °C and the excess of pyridine was then removed under vacuum (10 -5 Torr). The spectra before and after the Py adsorption were collected at ambient temperature. The amounts of Brønsted and Lewis acid sites were calculated using the intensity of bands at ~1545 cm -1 and ~1455 cm -1 , respectively. The absorption coefficients ε(B)=1.08 for Brønsted acid sites (peak at ~1545 cm -1 ) and ε(L)=1.71 cm mol -1 for Lewis acid sites (peaks at ~1455-1445 cm -1 ) were used for quantification of the zeolite acid sites.

The TEM observations of the samples were obtained by using a Jeol 2100F instrument operated at 200 kV. Before the analysis, the samples were dispersed by ultrasound in ethanol for 5 min and a drop of the suspension was deposited onto a carbon membrane on a 300 mesh copper grid. The STEM-HAADF tomographic analysis was carried out on a Jeol 2100F (field emission gun) microscope operating at 200 kV by using a spot size of 1.1 Å with a current density of 0.5 pA Å -1 . Selected Area Electron Diffraction (SAED) patterns were recorded using a US1000XP CCD camera with an exposure time of 2 s on circular areas of 200 nm in diameter.

Catalytic tests

Hydrogenation of aromatics: Toluene or triisopropylbenzene hydrogenations were carried out in a fixed-bed reactor. The catalyst (50 mg) was placed into the stainless-steel reactor and then activated in a H 2 gas flow (10 cm 3 /min, atmospheric pressure) at 400 °C for 4h with a heating rate of 2 °C/min. The reactor was cooled down to 50 °C and a hydrogen flow with a pressure of 20 bar was introduced into the reactor. The temperature was increased at 1 °C/min to the required reaction temperature (250 °C). The liquid reagents (toluene or triisopropylbenzene) were injected by a PHD ULTRA 4400 pump (Harvard Apparatus) with a flow rate of 0.8 mL/h). The products were collected in a cold trap and analyzed by a gas chromatograph (Bruker GC-450) equipped with thermal conductivity (TCD) and flame ionization (FID) detectors.

Fischer Tropsch synthesis: the experiments were performed in a fixed-bed reactor. Prior to testing, the samples were reduced in situ in a flow of pure H 2 (3 cm 3 /min) at 400 °C for 4 h with a heating rate of 3°C/min. Next, the reactor was cooled down to room temperature, the flow was switched to syngas (H 2 /CO = 2) and the pressure adjusted to 20 bar. Nitrogen (5% relative to CO) was used as the internal standard. After achieving the desired pressure, the temperature was increased to the reaction temperature, i.e. 250 °C, at a rate of 3 °C/min. The gas space velocities were adjusted to obtain the CO conversion of 30-40% for all catalysts.

The gaseous reaction products, i.e. up to C 5 , were analyzed on-line using a GC equipped with FID and TCD (Varian, CP-3800). The remaining products (wax) were condensed under pressure and analyzed ex situ on a Shimadzu GC using an FID (2010-Plus-AF).

Anisole acylation: the activity of all catalysts was evaluated in the acylation reaction between anisole and hexanoic acid according to the following protocol. The catalyst (20 mg) was added to a mixture of anisole (2 g) and hexanoic acid (0.3 g) in a reflux reactor system. The reactor was heated at 180 °C for 2 h. The products were analyzed by gas chromatography.

Results and Discussion

The nitrogen adsorption-desorption isotherms for the catalysts prepared by impregnation and synthesized using the Metal/CNT templates are shown in Figure 1. The ZSM-5 sample displays a type I isotherm exhibiting a sharp uptake at low relative pressure followed by a plateau with a hardly visible hysteresis at P/P 0 >0.5. This type of isotherm is usually observed for microporous materials with textural mesoporosity generated by aggregation of small zeolite crystallites. Similar isotherms have been observed for the CNT (10-20)/ ZSM-5 and CNT (20-40) /ZSM-5 samples synthesized using metal-free CNT as secondary hard templates (Figure 1a). Table 1 shows that the addition of metal-free CNT (10-20) during the ZSM-5 zeolite synthesis results only in a slight increase in the BET surface area and pore volume.

The use of CNT (20-40) during the ZSM-5 zeolite synthesis does not change substantially the porous characteristics of the zeolite. This suggests that CNT without metals are poor templates for synthesis of hierarchical zeolites.

Introduction of metals (Co, Mg, Ni) via conventional impregnation without using CNT as a secondary template, has only a minor effect on the zeolite porosity and specific surface area resulting in a decrease in the zeolite pore volume and specific surface area (Table 1). The difference between the surface area and pore volume of the parent zeolite and its counterparts containing metals may be assigned to the effect of zeolite "dilution" by metals and partial pore blocking by the metal species. Only minor changes are observed in the microporous and mesoporous zeolite volume after the impregnation with metals. In agreement with the literature, this indicates that the metal cations are preferentially located in the zeolite micropores, whereas metal oxides species are located on the external surface of ZSM-5 [START_REF] Subramanian | The Role of Steric Effects and Acidity in the Direct Synthesis of iso-Paraffins from Syngas on Cobalt Zeolite Catalysts[END_REF][START_REF] Peron | Nickel-zeolite composite catalysts with metal nanoparticles selectively encapsulated in the zeolite micropores[END_REF] .

Remarkably, rather different isotherms and textural properties have been observed for the ZSM-5 zeolites synthesized in the presence of the Metal/CNT templates. The zeolites prepared in the presence of Co/CNT, Ni/CNT and Mg/CNT exhibit a combination of type I and IV isotherms with a significant N 2 uptake at low relative pressure and a hysteresis loop at a high relative pressure (P/P 0 > 0.5, Figures 1b-d). Adsorption of nitrogen in the range of P/P 0 = 0.5 -1.0 and relevant hysteresis can be explained by mesoporosity developed in the presence of cobalt, nickel or magnesium oxides supported on CNT. Note that almost no increase in the zeolite mesoporosity has been observed when metal-free CNT (10-20) or CNT (20- 40) were used as mesoporous hard templates (Table 1). The presence of metal species on CNT is therefore essential for the synthesis of ZSM-5 zeolite with enhanced mesoporous volume. A slight increase in the BET surface area has been observed for CoCNT (10-20) /ZSM-5, NiCNT (10- 20) /ZSM-5 and MgCNT (10-20) /ZSM-5, while the BET surface area slightly decreases when using the MeCNT (20-40) templates. Thus, the most significant effect of using CNT containing cobalt, nickel and magnesium is the substantial increase in the mesoporous volume. The zeolite mesoporous volume increases 2.5-4 times, when using CoCNT (10-20) and CoCNT (20-40) , 4.5-5 times, when using MgCNT (10-20) and MgCNT (20-40) and 2.2-3 times for NiCNT (10-20) and NiCNT (20-40) (Table 1). Note that the zeolite micropore volume (between 0.09-0.13 cm 3 /g) is only slightly affected by CNT supported metals used as secondary templates. NiCNT (20-40) /ZSM-5 catalysts prepared using NiCNT (10-20) and NiCNT (20-40) as hard templates show no peaks characteristic of the nickel oxide phases. No XRD peaks of Mg-containing phases have been detected in either Mg/ZSM-5 prepared via aqueous impregnation or in MgCNT (10-20) /ZSM-5 and MgCNT (20-40) /ZSM-5 catalysts prepared using hydrothermal synthesis with the MgCNT hard template. The absence of XRD peaks attributed to the metal oxide phases can be explained by smaller metal oxide particle size in the Mg-and Ni-containing samples, which are below the XRD detection limits. It should be noted that the observed difference in the metal loading must be related to the differences in solubility of the respective metal hydroxides. Indeed, the solubility product of magnesium hydroxide is ~3 orders of magnitude greater than that for nickel and cobalt hydroxides, which is in accord with the significantly lower Mg content (c.a. 2.5%) in the nanocomposite metal-zeolites.

Figure 2 shows the TEM images of the Co, Ni and Mg containing ZSM-5 catalysts prepared using metal-CNT templates. They are very different from those usually observed for the conventional ZSM-5 zeolite. The zeolite crystallites obtained in the presence of metal CNT templates exhibit a rather irregular fibrous morphology leading to the development of zeolite mesoporosity. TEM images suggest zeolite crystallization over CNT. This morphology arises from CNT partially encapsulated inside the zeolite crystals during the zeolite synthesis. The synthesized zeolite seems to be replicas of Metal/CNT. They reproduce almost exactly the shape of the secondary templates. Importantly, the presence of metal containing CNT seems indispensable for obtaining these fibrous zeolite crystallites. The TEM images for all prepared metal-zeolite catalysts also display small metal oxide nanoparticles with the diameter between 1 and 5 nm. The presence of zeolite phase in these fibrous structures was further confirmed by selected area electron diffraction (SAED). techniques reveal the important function of small metal oxide clusters in CNT for the formation of mesopores in zeolite crystals. Note that no significant enhancement of the zeolite mesoporosity has been observed by using metal-free CNT as secondary templates (Table 1).

The ZSM-5 zeolite nucleation seems to occur on the metal oxide sites located on CNT producing a hierarchical material with enhanced mesoporosity. It is important to emphasize that the stability of metal oxide nanoparticles supported on CNT in the basic medium used for zeolite synthesis is essential for obtaining hierarchical zeolites with enhanced mesoporosity.

The resulting zeolite replicates the fibrous shape of CNT. The mesopores are created when CNT are removed from the zeolite by calcination. A schema illustrating the formation of hierarchical zeolite during the synthesis utilizing Metal/CNT as secondary hard templates is shown in Figure 4.

Cobalt and nickel temperature programed reduction (TPR) profiles are presented in Figure S3, SI. The reduction patterns of the cobalt zeolite catalysts are consistent with the presence of several types of cobalt species and two-step Co 3 O 4 reduction to metallic cobalt. Previous reports [START_REF] Subramanian | The Role of Steric Effects and Acidity in the Direct Synthesis of iso-Paraffins from Syngas on Cobalt Zeolite Catalysts[END_REF][START_REF] Van't Blik | Characterization of supported cobalt and cobalt-rhodium catalysts: III. Temperature-Programmed Reduction (TPR), Oxidation (TPO), and EXAFS of Co-Rh/SiO 2[END_REF][START_REF] Hong | Impact of sorbitol addition on the structure and performance of silica-supported cobalt catalysts for Fischer-Tropsch synthesis[END_REF][START_REF] Khodakov | Pore-size control of cobalt dispersion and reducibility in mesoporous silicas[END_REF] suggest that Co 3 O 4 is first reduced to CoO at a lower temperature, whereas CoO is reduced to metallic Co at higher temperatures (Figure S3a). The Co/ZSM-5 sample, with cobalt added by impregnation, exhibits a TPR peak at 280°C with shoulders at 150-220°C. The shoulders at 150-220°C in the TPR profile of Co/ZSM-5 can be therefore attributed to the reduction of the Co 3 O 4 nanoparticles to CoO, while the major TPR peak at 280°C corresponds to the reduction of CoO to metallic cobalt. Previously, we showed [START_REF] Subramanian | The Role of Steric Effects and Acidity in the Direct Synthesis of iso-Paraffins from Syngas on Cobalt Zeolite Catalysts[END_REF][START_REF] Peron | Nickel-zeolite composite catalysts with metal nanoparticles selectively encapsulated in the zeolite micropores[END_REF][START_REF] Carvalho | Design of nanocomposites with cobalt encapsulated in the zeolite micropores for selective synthesis of isoparaffins in Fischer-Tropsch reaction[END_REF] that ZSM-5 catalysts prepared by impregnation contained a large fraction of cobalt or nickel oxide nanoparticles on the zeolite outer surface. Because of a larger solvating shell, diffusion of multi-charged ions such as cobalt or nickel, inside the ZSM-5 micropores can be rather slow [START_REF] Stakheev | Localization of polyvalent cations in pentasil catalysts modified by metal oxides[END_REF] . In all catalysts prepared by impregnation, a considerable amount of divalent metal ions are present on the zeolite external surface. The CoCNT (10-20) /ZSM-5 and CoCNT (20- 40) /ZSM-5 samples exhibite two groups of TPR peaks at 150-420°C and at 600 -800 °C.

Similar to the Co/ZSM-5 zeolite, the low temperature peaks are attributed to the reduction of small Co 3 O 4 nanoparticles to metallic cobalt via the intermediate formation of CoO. The shift of these peaks to higher temperature can be explained by smaller Co 3 O 4 particle sizes [START_REF] Khodakov | Reducibility of cobalt species in silica-supported Fischer-Tropsch catalysts[END_REF] and their localization inside the zeolite meso-and micropores. In agreement with previous studies [START_REF] Puskas | Activity decline and diffusional changes in a magnesium-promoted cobalt-silica catalyst[END_REF][START_REF] Jong | Reduction behavior and catalytic properties of cobalt containing ZSM-5 zeolites[END_REF] , the peaks at higher temperature are assigned to cobalt silicates or aluminates.

These mixed compounds form because of the interactions between the small metal oxide nanoparticles located on CNT and the zeolite being synthesized under the hydrothermal conditions. The TPR data are consistent with the suggestions that cobalt species supported on CNT act as nucleation sites in the synthesis of the hierarchical ZSM-5 zeolite.

The reduction profiles of the nickel catalysts prepared by impregnation with nickel nitrate and synthesized using Ni/CNT as secondary templates are shown in Figure S3b, SI. They exhibit broad hydrogen consumption peaks in the temperature range from 350 to 750°C. A single hydrogen consumption peak at about 400°C [START_REF] Tomiyama | Preparation of Ni/SiO 2 catalyst with high thermal stability for CO 2 -reforming of CH 4[END_REF][START_REF] Soghrati | Zeolite-supported nickel phyllosilicate catalyst for CO hydrogenolysis of cyclic ethers and polyols[END_REF] is usually observed in the TPR profiles of bulk NiO. It corresponds to the reduction of NiO to metallic nickel. Thus, the low temperature peaks observed between 400 and 500 °C in the TPR profiles of nickel-zeolite catalysts may correspond to the reduction of small NiO particles. Note that the Ni/ZSM-5 zeolite prepared by impregnation usually contains 28 a significant concentration of NiO on the zeolite outer surface. These NiO nanoparticles are detected in Ni/ZSM-5 by XRD (Figure S1, SI). Similar to cobalt zeolite nanocomposites, the shift of the TPR peaks to a higher temperature can be due to the smaller NiO particle size and some diffusional limitations during their reduction arising from the localization of these small NiO nanoparticles in the porous material [START_REF] Maia | Ni-ZSM-5 catalysts: Detailed characterization of metal sites for proper catalyst design[END_REF] . The area of the low temperature TPR peaks between 400 and 500 °C significantly decreases for the catalysts prepared using Ni/CNT as secondary templates. This corresponds to a decrease in the concentration of the NiO particles on the zeolite outer surface. The TPR profiles of the NiCNT (10-20) /ZSM-5 and NiCNT (20-40) CNT/ZSM-5 catalysts exhibit low intensity peaks at 500-700°C. High temperature TPR peaks can be attributed to the reduction of highly dispersed nickel species [START_REF] Maia | Ni-ZSM-5 catalysts: Detailed characterization of metal sites for proper catalyst design[END_REF][START_REF] Romero | Bifunctional catalyst Ni/HZSM-5: effects of the nickel incorporation method[END_REF] or to the presence of nickel silicate (phyllosilicate) species [START_REF] Soghrati | Zeolite-supported nickel phyllosilicate catalyst for CO hydrogenolysis of cyclic ethers and polyols[END_REF][START_REF] Chen | Towards a full understanding of the nature of Ni(ii) species and hydroxyl groups over highly siliceous HZSM-5 zeolite supported nickel catalysts prepared by a deposition-precipitation method[END_REF][START_REF] Chen | A simple and convenient approach for preparing core-shell-like silica@ nickel species nanoparticles: highly efficient and stable catalyst for the dehydrogenation of 1, 2-cyclohexanediol to catechol[END_REF] .

In agreement with other characterization methods, the TPR results clearly show that the introduction of nickel and cobalt species with CNT during the zeolite hydrothermal synthesis leads to a higher metal dispersion. In cobalt catalysts, metal nanoparticle localization within the zeolite meso-and micropores also leads to the formation of mixed compounds between the metal oxide and silica or alumina.

The acidity of metal-zeolite catalysts has been characterized by FTIR using adsorption of pyridine (Py) as a probe for Brønsted (BAS) and Lewis acid sites (LAS). The FTIR spectra recorded after Py adsorption on the reduced catalysts are displayed in Figure 5. The parent ZSM-5 zeolite exhibits characteristic bands at ~1545 and 1455-45 cm -1 assigned to the pyridinum ion (PyH + ) formed on BAS and to Py adsorbed on LAS (which may also include metal ions such as Co 2+ , Ni 2+ or Mg 2+ ), respectively. Py adsorbed on both the LAS and BAS also displays a band at 1490 cm -1 . The concentrations of BAS and LAS calculated from the intensities of the bands at ~1545 and 1455-45 cm -1 are shown in Table 1. Impregnation of the ZSM-5 zeolite with the Co 2+ , Ni 2+, and Mg 2+ cations leads to a significant decrease in the concentration of BAS. The effect is more pronounced for the Mg 2+ impregnated ZSM-5. A much lower concentration of BAS in the impregnated catalysts can be explained by the ion exchange of the protons of the zeolite bridging OH groups with the Mg 2+ , Ni 2+ and Co 2+ ions.

Small metal oxide clusters can also block some zeolite micropores, thus making some of BAS inaccessible for Py adsorption. Interestingly, at the same metal content in the zeolites, the decrease in the concentration of BAS is less significant, when the cations are introduced with the Metal/CNT hard templates. This suggests that a significant fraction of the metal species added with Metal/CNT are probably not localized in the cationic zeolite sites but present as small oxide clusters in the zeolite micro-and mesopores. This explains a less significant decrease in the number of BAS in the zeolites synthesized using the Metal/CNT hard templates with the same metal contents.

The number of LAS is considerably higher in all metal containing ZSM-5 as compared to their metal-free ZSM-5 counterpart (Table 1). The addition of the metals results in the generation of news types of LAS such as coordinatively unsaturated Co 2+ , Ni 2+ or Mg 2+ cations. Some of these cations can occupy zeolite cationic sites. Interestingly, a much lower concentration of LAS is generated in the metal zeolite catalysts prepared using zeolite crystallization in the presence of metal CNT secondary templates as compared to the sample prepared by zeolite impregnation with nitrates. This can be due to a lower concentration of Co 2+ , Ni 2+ and Mg 2+ in the cationic sites of the hierarchical zeolites. This also indicates the formation of metal oxide clusters and is consistent with a smaller decrease in the number of BAS in the zeolites prepared using the Metal/CNT hard templates. Overall, both metal oxide nanoparticles and ion-exchanged metal cations are formed in the synthesised metal-zeolite nanocomposite catalysts, as demonstrated by a combination of characterisation techniques.

However, the number of isolated M 2+ cations in the Metal-CNT/ZSM-5 samples is considerably lower as compared to the Metal/ZSM-5 samples prepared via "conventional" impregnation.

Catalytic Performance in Fischer-Tropsch Synthesis, Hydrogenation and Acylation Reactions

The results of catalytic tests of cobalt zeolite catalysts in Fischer-Tropsch synthesis are presented in Table S1, SI. Hydrocarbons and water are major reaction products of carbon monoxide hydrogenation. Extremely small amounts of CO 2 have been observed. By varying GHSV between 20 and 70 L/h g Co , the CO conversion of 30-40% has been obtained for all catalysts. The reaction rate normalized by the total amount of cobalt in the catalysts slightly increases for CoCNT (10-20)/ ZSM-5 and decreases in CoCNT (20-40) /ZSM-5 compared to the Co/ZSM-5 sample prepared by conventional impregnation. Note however, that TPR (Figure S3a, SI) is indicative of very different cobalt reducibility in different samples. The addition of the Co/CNT hard templates during the zeolite synthesis results in the formation of barely reducible cobalt silicate or cobalt aluminate species, which exhibit TPR peaks at 600-800 °C.

The peaks at 600-800 °C are absent in the TPR profiles of Co/ZSM-5. This suggests a low concentration of cobalt silicates or aluminates in the Co/ZSM-5 catalyst prepared by impregnation. Interestingly, the activity per reducible cobalt increased 5-10 times over CoCNT/ZSM-5 prepared using CoCNT as secondary templates in comparison with Co/ZSM-5 prepared by impregnation [START_REF] Flores | Direct production of iso-paraffins from syngas over hierarchical cobalt-ZSM-5 nanocomposites synthetized by using carbon nanotubes as sacrificial templates[END_REF] . The higher activity (per reducible cobalt) over CoCNT (10- 20 )/ZSM-5 can be explained by enhanced mesoporosity and more uniform distribution of cobalt nanoparticles within the zeolite. The enhanced diffusion of the reagents, intermediates between metal and zeolite acid sites in combination with easy removal of the reaction products result in higher catalytic activity of the metal zeolite nanocomposites.

The methane selectivity varies between 13-33%. Previous data [START_REF] Iglesia | Selectivity Control and Catalyst Design in the Fischer-Tropsch Synthesis: Sites, Pellets, and Reactors[END_REF] suggest that the higher methane selectivity over zeolite-based catalysts can be due to more significant diffusion limitations for carbon monoxide molecules compared to hydrogen. Slower diffusion of CO relative to hydrogen results in the CO deficiency the zeolite pores. The resulting higher H 2 /CO ratio in the narrow zeolite pores leads to a higher contribution of methanation reaction and higher methane selectivity. Importantly, lower methane selectivity was observed over CoCNT (10-20) /ZSM-5 and CoCNT (20-40) /ZSM-5 with larger mesoporous volume. These catalysts may have less significant diffusion limitations compared to mostly microporous Co/ZSM-5, where cobalt was added by impregnation. The catalysts prepared using the CoCNT (10-20) and CoCNT (20-40) hard templates also exhibit a higher selectivity to the C 5 + products (around 74%) as compared to the conventional Co/ZSM-5 catalysts which shows C 5+ selectivity of 48% (Table S1, SI).

Nickel catalysts have been tested in the toluene and 1,3,5-triisopropylbenzene hydrogenation (Table 2). These reactions have been used to evaluate the activity and accessibility of nickel metal sites in the hierarchical zeolites. The mesoporosity developed in the nickel-zeolite catalysts synthesized in the presence of Ni/CNT secondary templates results in a significantly higher hydrogenation rate in both toluene and 1,3,5-triisopropylbenzene reactions. The reaction rate increases in the order: Ni/ZSM-5< NiCNT (10-20)/ ZSM-5<NiCNT (20-40)/ ZSM-5. This is indicative of a better nickel dispersion and enhanced accessibility of nickel metallic sites in the zeolites prepared using the Ni/CNT hard templates. Noteworthy, the zeolite prepared using NiCNT (20-40) with larger CNT diameter exhibited higher reaction rate in both toluene and 1,3,5-triisopropylbenzene hydrogenation reactions.

Zeolites usually contain a significant number of acid sites. Acylation of anisole with hexanoic acid has been selected as a model reaction to characterize the catalytic performance of the acid sites on the outer surface and in the mesopores of the hierarchical zeolites (Schema, SI).

On all catalysts evaluated in the present work, the reaction results in the formation of orthomethoxy-hexyl-phenone with the selectivity higher than 90%, while the selectivity to the para-isomer was less than 10%. Only traces of the meta-isomer have been detected. Note that the size of the ortho-isomer is much larger than the diameter of micropores in the ZSM-5 zeolite. The higher selectivity to the larger ortho-methoxy-hexyl-phenone is consistent with the critical role of the zeolite acid sites on the zeolite outer surface and mesopores in this reaction. The hexanoic acid conversion and reaction rate are shown in Table 3. For all the catalysts, the conversion increases when Metal/CNTs have been added as hard templates during the zeolite synthesis. The conversion increases by a factor of 2-4 over CoCNT (10- 20) /ZSM-5 and CoCNT (20-40) /ZSM-5, 1.3-1.6 over NiCNT (10-20) /ZSM-5 and NiCNT (20-40) /ZSM-counterparts prepared via impregnation. The effect is more pronounced when CNT had a relatively large (20-40 nm) diameter. The highest conversion has been achieved over NiCNT (20-40) /ZSM-5. Figure 6 shows the relation between the conversion of hexanoic acid and the number of Brønsted acid sites in the catalysts. Both the concentration of Brønsted acid sites and the presence of mesopores created in the ZSM-5 zeolite in the presence of metal supported CNT affect the catalytic performance in the anisole acylation. Interestingly, at a similar concentration of BAS, the higher acylation rates are observed for the catalysts with higher mesoporosity. Indeed, zeolites with larger mesopores obtained using Metal/CNT with the diameter of 20-40 nm are the most active in this reaction. This suggests a better accessibility of both BAS and metal sites in the hierarchical ZSM-5 prepared using the Metal/CNT templates. Hence, the strategy for the synthesis of hierarchical zeolites using metal supported CNT as secondary hard templates seems promising. It produces hierarchical zeolites replicating the shape of CNT with enhanced mesoporosity and highly dispersed, accessible and uniformly distributed metal nanoparticles and acid sites, which would be beneficial for a number of important catalytic reactions.

Conclusion

Our paper provides a new synthesis strategy for the preparation of hierarchical zeolites. It involves metal supported carbon nanotubes as secondary templates. The Metal/CNT templates play three roles in the synthesis of hierarchical zeolite. These templates are (i) a zeolite synthesis replica, (ii) a mesoporogen and (iii) a tool to introduce uniformly distributed metal species into zeolites.

The metal oxide species seem to be nucleation sites and crystallization modifiers leading to the fibrous zeolite morphology, which largely replicates the CNT. Using Metal/CNT as templates leads a several-fold increase in the zeolite mesoporous volume. The dispersed metal species, which are present as small metal oxide nanoparticles, are uniformly distributed within the crystallites of the synthesized zeolites. The concentration of Brønsted acid sites in the zeolites synthesized using Metal/CNT as secondary templates is higher than in the zeolites with the same amount of metal species prepared via impregnation.

Owing to the enhanced diffusion of the reacting species and uniform distribution of metal nanoparticles in the zeolite, the resulting materials have shown improved catalytic performance in three catalytic reactions: Fischer-Tropsch synthesis, hydrogenation of aromatics and anisole acylation.

Our data also explain the discrepancies in the literature relevant to synthesis of hierarchical zeolites using carbon nanotubes as templates. Indeed, when nickel or other metals are removed from the carbon nanotubes utilized in zeolite synthesis, hierarchical materials cannot be obtained. In contrast, intentional addition of carbon nanotubes containing metal oxides to the synthesis gel results in successful synthesis of hierarchical zeolites with enhanced mesoporosity. V tot (cm 3 g -1 )

V mic (cm 3 g -1 )

V meso (cm [START_REF] Egeblad | Templating Mesoporous Zeolites[END_REF]

Figure S1 (

 S1 Figure S1 (see Supporting information (SI)) displays XRD patterns of all samples included

  Figure S2, SI displays well defined diffraction patterns and clearly indicates zeolite crystalline phase in the areas containing a larger quantify of fibrous zeolite replicas of the Metal/CNT templates. TEM images and STEM-HAADF electron tomography of the CoCNT (20-40) /ZSM-5 sample have confirmed localization of metal oxide nanoparticles within the zeolite (Figure 3). Co nanoparticles have been observed as bright spots with the size in the range 2-5 nm. STEM-HAADF images and tomography video (see Supporting information) show that nanoparticles are located inside the pores of CoCNT (20-40) /ZSM-zeolite. Thus, electron microscopy, electron diffraction and tomography in combination with other characterization

Figure 1 .Figure 2 .

 12 Figure 1. Low temperature nitrogen adsorption-desorption isotherms on the HZSM-5 zeolite synthesized with and without addition of CNT (a) cobalt (b), nickel (c) and magnesium (d) ZSM-5 catalysts. (The P/P 0 region below 0.01 is not shown for clarity.)

Figure 3 .Figure 4 .Figure 5 .Figure 6 .

 3456 Figure 3. STEM-HAADF electron tomography analysis of CoCNT (20-40) /ZSM-5 clearly showing the presence of cobalt nanoparticles inside the zeolite structure

Table 1 .

 1 Catalyst characterization data

	*determined by pyridine adsorption at 150°C

Table 2 .

 2 Hydrogenation reaction (H 2 =20 mL/min, liquid flow=0.8 mL/h, T=250 °C, P=20 bar, reaction time 6 h)

		Lewis	Brønsted
	g -1 )	(µmolg -1 )	(µmolg -1 )

Table 3 .

 3 Acylation reaction (2 g of anisol, 0.3 g hexanoic acid, 20 mg of the catalyst, T=180°C; reaction time 2 h)

	Catalyst	Conversion (%)	Reaction rate (μmol/g min)
	Co/ZSM-5	0.43	4.63
	CoCNT (10-20) /ZSM-5	1.00	10.78
	CoCNT (20-40) /ZSM-5	1.79	19.29
	Ni/ZSM-5	1.53	16.49
	NiCNT (10-20) /ZSM-5	1.92	20.69
	NiCNT (20-40) /ZSM-5	2.46	26.51
	Mg/ZSM-5	0.26	2.80
	MgCNT (10-20) /ZSM-5	1.18	12.72
	MgCNT (20-40) /ZSM-5	1.31	14.12

*time at 6 h.

Acknowledgements

The authors are grateful to Olivier Gardoll, Laurence Burylo and Joelle Thuriot for help with TPR, XRD and XRF measurements. The authors thank International Cooperation Program CAPES/COFECUB Foundation funded by CAPES -Brazilian Federal Agency for Support and Evaluation of Graduate Education within the Ministry of Education of Brazil for providing a PhD stipend for C.F. and financial support for this work. Chevreul Institute (FR


Augustin Vernay

Lucas Bonnet-Gamard

Veronique Boutou

Sivan Trajtenberg-Mills

Ady Arie

Benoit Boulanger
email: benoit.boulanger@neel.cnrs.fr

Véronique Boutou

Benoît Boulanger

High efficiency cascaded third-harmonic generation in a quasi-periodically poled KTiOPO 4 crystal

Introduction

Extending the bandwidth of laser sources is a huge field of application of parametric nonlinear optics starting from the pioneering work on Second-harmonic Generation (SHG) [START_REF] Franken | Generation of Optical Harmonics[END_REF] and Optical Parametric Oscillators (OPO) [START_REF] Giordmaine | Tunable coherent parametric oscillation in LiNbO3 at optical frequencies[END_REF]. Third-Harmonic Generation (THG) is also of strong interest in this frame of frequency conversion since it is often used as a pump source of OPO [START_REF] Fan | Visible BaB2O4 optical parametric oscillator pumped at 355nm by a singleaxialmode pulsed source[END_REF], but it is also at the heart of nuclear reactions [START_REF] Simakin | Initiation of nuclear reactions under laser irradiation of Au nanoparticles in the aqueous solution of Uranium salt[END_REF] and optical processing [START_REF] Schmid | Optical processing on a femtosecond time scale[END_REF] for example. Quantum optics is another area of interest for THG since it can lead to the generation of squeezed light [START_REF] Dmitriev | Generation of polarization squeezed light in PPNC[END_REF][START_REF] Belinsky | Simultaneous nonlinear conversion of light in periodically poled crystals[END_REF].

THG can be performed using a direct third order nonlinear process, i.e. ω + ω + ω → 3ω that is governed by the third-order nonlinear electric susceptibility χ (3) [START_REF] Gravier | Third order frequency generation in TiO2 rutile and KTiOPO4[END_REF]. While third-order susceptibility is present in all materials, it is usually very small, causing conversion efficiency of THG to be low and requires very high pump intensities. Another approach is by cascading two processes driven by the second-order susceptibility χ (2) : ω + ω → 2ω, which corresponds to SHG, and THG it-self , i.e. 2ω + ω → 3ω creating the third harmonic. These two steps can be successive [START_REF] Simakin | Initiation of nuclear reactions under laser irradiation of Au nanoparticles in the aqueous solution of Uranium salt[END_REF] or simultaneous [START_REF] Belinsky | Simultaneous nonlinear conversion of light in periodically poled crystals[END_REF][START_REF] Zhu | Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice[END_REF][START_REF] Qi | Cascaded third-harmonic generation with one KDP crystal[END_REF][START_REF] Marangoni | Simultaneously phase-matched second-and third-harmonic generation from 1.55 μm radiation in annealed proton-exchanged periodically poled lithium niobate waveguides[END_REF].

The second-order susceptibility is available only for non-centrosymmetric materials, but it can be a few orders of magnitude higher than the third-order susceptibility, so that the secondorder processes are generally more efficient. Direct as well as cascaded THG can be achieved in phase-matched birefringent crystals of volume [START_REF] Gravier | Third order frequency generation in TiO2 rutile and KTiOPO4[END_REF][START_REF] Qi | Cascaded third-harmonic generation with one KDP crystal[END_REF][START_REF] Boulanger | Cubic optical nonlinearity of KTiOPO4[END_REF] or waveguide [START_REF] Marangoni | Simultaneously phase-matched second-and third-harmonic generation from 1.55 μm radiation in annealed proton-exchanged periodically poled lithium niobate waveguides[END_REF][START_REF] Boutou | Phase-matched second-harmonic generation in a flux grown KTP crystal ridge optical waveguide[END_REF] dimensions. But periodically-poled nonlinear crystals are also a good alternative because of their relatively high non-linearity and their phase-matching flexibility [START_REF] Dmitriev | Generation of polarization squeezed light in PPNC[END_REF][START_REF] Belinsky | Simultaneous nonlinear conversion of light in periodically poled crystals[END_REF][START_REF] Banks | High-intensity third-harmonic generation[END_REF]. Note that the simultaneous cascading configuration had led to the highest THG conversion efficiencies using birefringent phase-matching [START_REF] Qi | Cascaded third-harmonic generation with one KDP crystal[END_REF] as well as quasi-phase-matching [START_REF] Zhu | Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice[END_REF][START_REF] Marangoni | Simultaneously phase-matched second-and third-harmonic generation from 1.55 μm radiation in annealed proton-exchanged periodically poled lithium niobate waveguides[END_REF].

The present study deals with this latter configuration. We developed theoretical and experimental methods for designing an efficient cascaded THG using a single quasiperiodically poled KTiOPO4 crystal (QPPKTP). KTP crystals are widely used for frequency conversion and quantum optics, they have a high second-order susceptibility and are commercially available. Quasi periodic structures in KTP have shown to be strong contenders for achieving high conversion efficiencies [START_REF] Zhu | Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice[END_REF][START_REF] Fradkin-Kashi | Multiple Nonlinear Optical Interactions with Arbitrary Wave Vector Differences[END_REF][START_REF] Bahabad | Nonlinear photonic quasicrystals for novel optical devices[END_REF]. Our objective is then to go beyond these pioneering works by developing a model of THG in the depleted pump regime and by experimentally optimizing the conversion efficiency, in particular in the visible around 0.5 μm. This last point is of prime importance in the more general framework of the generation of new quantum states of light, where the exact reverse of cascaded THG, i.e. 3ω → ω + 2ω coupled with 2ω → ω + ω, is a way to produce three highly correlated photons at ω [START_REF] Hübel | Direct generation of photon triplets using cascaded photon-pair sources[END_REF]. The target is then to perform this Triple-Photon Generation (TPG) in the telecom range for quantum information, which means λω around 1.5 μm and so λ3ω around 0.5 μm. Since TPG and THG exhibit the same phase-matching properties, the optimization of one then leads to the optimization of the other.

Crystal design

Tailoring the second-order susceptibility of nonlinear crystals can be performed by electric field poling, a process that can flip the sign of some 𝜒 (2) coefficients. The most common use of this is for quasi-phase matching, where a periodic change in the sign of the susceptibility with period Λ can compensate phase mismatch, leading to high conversion efficiencies in crystals and processes that were inefficient otherwise. But not only periodic structures can be created, also 2D modulations have been shown to be useful for beam shaping [START_REF] Trajtenberg-Mills | Shaping light beams in nonlinear processes using structured light and patterned crystals[END_REF] as well as for general frequency control [START_REF] Leshem | Experimental realization of spectral shaping using nonlinear optical holograms[END_REF].

One interesting way of designing nonlinear crystals is by imposing a quasi-periodic structure [START_REF] Lifshitz | Photonic Quasicrystals for Nonlinear Optical Frequency Conversion[END_REF][START_REF] Bahabad | Experimental confirmation of the general solution to the multiple-phase-matching problem[END_REF], where multiple periods are combined in the same crystal. This enables to phase-match multiple processes simultaneously through different Fourier components of the crystal modulation. These crystals are designed to have a few discrete peaks in their Fourier spectrum, each corresponding to the phase-matching requirements of each process. This concept was originally based on a Fibonacci tiling of the crystal [START_REF] Zhu | Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice[END_REF][START_REF] Vardeny | Optics of photonic quasicrystals[END_REF], although only specific wave-vectors, whose ratio depends on the Fibonacci golden ratio, are available for phase matching in this type of system. The theory was later extended to provide an arbitrary set of wave vectors with the use of the De Brujin's Dual-Grid Method [START_REF] Lifshitz | Photonic Quasicrystals for Nonlinear Optical Frequency Conversion[END_REF][START_REF] De Brujin | Algebraic theory of Penrose's non-periodic tilings of the plane[END_REF], which enables to phase-match an arbitrary combination of multiple nonlinear processes, in one dimension [START_REF] Lifshitz | Photonic Quasicrystals for Nonlinear Optical Frequency Conversion[END_REF][START_REF] Bahabad | Experimental confirmation of the general solution to the multiple-phase-matching problem[END_REF] as well as two dimensions [START_REF] Bahabad | Engineering two-dimensional nonlinear photonic quasicrystals[END_REF]. In order to simultaneously phase-match SHG and THG, we used a quasiperiodic modulation in a KTP crystal. We chose the third-harmonic to be 𝜆 3𝜔 = 527 𝑛𝑚, so that the lower harmonics are 𝜆 2𝜔 = 790.5 𝑛𝑚, and 𝜆 𝜔 = 1581 𝑛𝑚. We considered the following cascading processes: type 0 SHG (all fields are z-polarized) 1581 (𝑧) + 1581 (𝑧) → 790.5 (𝑧) followed by type II THG (input signal is (z) polarized and the rest are (y) polarized) 790.5 (𝑧) + 1581 (𝑦) → 527 (𝑦) where y and z stand for the direction of polarization of the waves propagating along the x-axis, (x, y, z) being the crystalline axes. We then calculated the corresponding phase-mismatch values, i.e.:

2 2 SHG k k k   -  = and 3 2 THG k k k k    - -  =
, where 2 ( ) /

i i i k n    =
is the wave vector. Using the refractive indices of KTP as a function of temperature [START_REF] Emanueli | Temperature-dependent dispersion equations for KTiOPO4 and KTiOAsO4[END_REF][START_REF] Kato | Parametric Oscillation at 3.2 µm in KTP Pumped at 1.064 µm[END_REF] at 100°C, we obtained  -  =

. The flexibility of our design method [START_REF] Lifshitz | Photonic Quasicrystals for Nonlinear Optical Frequency Conversion[END_REF][START_REF] Bahabad | Experimental confirmation of the general solution to the multiple-phase-matching problem[END_REF] allows us to tailor the nonlinear response of the crystal so that it will provide phase-matching at these two spatial frequencies, with the tiling vectors / 14.1836

SHG k m    = and / 12.7849 THG k m    =
, respectively. We fabricated a 1cm-long QPPKTP crystal, where the width of the poled zone is 1mm. A microscopy image of the selectively etched surface of the fabricated crystal and the associated Fourier spectrum are shown in Fig. 1.

Phase-matching conditions

We experimentally determined the phase-matching wavelengths and the corresponding temperatures of the SHG and THG steps in the 1-cm-long QPPKTP sample described in the previous section. The fundamental beam at 𝜆 𝜔 , that is used for pumping the QPPKTP crystal, was emitted by a tunable TOPAS Optical Parametric Generator (OPG) with a repetition rate of 10 Hz, a pulse duration of 𝜏 𝜔 = 15𝑝𝑠 (Full-width at 1/e 2 ), and a wavelength tunability with an accuracy of ± 1 nm. The QPPKTP was placed in an oven whose temperature can be tuned from room temperature to 140°C with an accuracy of ± 0.5°C. The longitudinal thermal gradient between the center of the crystal and the entrance or exit face is equal to 0.7°C, while the transverse gradient was estimated to be 0.3 °C. The temperature of the QPPKTP crystal can be assumed to be nearly homogeneous since such a gradient may affect the fifth decimal place of the refractive indices, which cannot modify the phase-matching conditions. The fundamental pump beam is focused inside the crystal with a focal lens f = 50 cm; its waist radius measured at the center of the crystal is then equal to 𝑤 𝜔 = 205 ± 21 µ𝑚 (Full-width at 1/e 2 ), which leads to a Rayleigh length of ~15 cm, much longer than the crystal length, ensuring propagation in the parallel beam limit. The experiment design enabled to independently measure the energy of the second-harmonic and third-harmonic (TH) waves. The two corresponding beams were separated using a HR 800 mirror: the energy at λ2ω was measured by a J3S10 Molectron Joulemeter (MJ) placed behind a notch filter at 532-nm, and the energy at λ3ω using also a J3S10 MJ behind a prism. The energy of the incident beam at λω was measured before the QPPKTP crystal using a J305 MJ behind a flip mirror. A half-waveplate installed in the input beam path before the QPPKTP allowed us to adjust the polarization of the beam at λω according to the required phase-matching condition, i.e. that of a pure SHG or that of THG.

By tuning the OPG wavelength λω and the QPPKTP temperature T, we identified several situations for which SHG and THG were phase-matched simultaneously, as shown in Fig. 2(a). In this example, the temperature of the QPPKTP crystal was fixed at T = 90.7 °C, and the 2ω and 3ω peaks are centered at λω = 1587 nm and λω = 1586 nm, respectively. The shift between these two wavelengths was within the measurement accuracy, i.e. ± 1 nm. There is also a satisfying agreement at the level of the wavelength acceptance,   , that is defined as the full width of the phase-matching peak at 0.405 of its maximum. The experimentally measured bandwidths of 𝛿𝜆 𝜔 𝑒𝑥𝑝 𝑆𝐻𝐺 = 3.4 𝑛𝑚 and 𝛿𝜆 𝜔 𝑒𝑥𝑝 𝑇𝐻𝐺 = 2.3 𝑛𝑚, according to Fig. 2   = =

.

A final optimization led to a maximal THG conversion efficiency reached for λω = 1587 nm and T = 95°C. The corresponding polarization curves are shown in Fig. 2(b) where α is the angle between the polarization of the fundamental wave and the y-axis of the QPPKTP crystal. There is a perfect agreement between calculation and measurement, the optimal angle for a Type 0 SHG being found at α = 90°, while it is α = 54° for THG. Note that these two values of angle can be easily calculated in the Undepleted Pump Approximation (UPA) because the SH intensity is simply proportional to the square of the fundamental intensity, which gives ( ) . These values of optimal polarization angles obviously remain the same in the depleted pump regime. These latter experimental conditions of temperature, wavelength and polarization were kept for measuring the SHG and THG conversion efficiencies, as described in the next section.

Conversion efficiencies

The conversion efficiencies, expressed as the power ratios    = , were measured using the experimental setup described in the previous section. First, we considered SHG alone, so the polarization angle α was fixed at 90°. Second, we performed THG, which can be achieved for α=54°. In this situation, while ηSHG decreased to the value of 17% as shown in Fig. 3(a), whereas THG was optimized, the conversion efficiency ηTHG reaching a maximal value of 40% from a fundamental intensity of about 1.5 GW/cm 2 that corresponds to a fundamental energy of 20µJ. The normalized conversion efficiency with respect to the peak power defined as ( )

2 3 ( ) / (0) L L P P       is 43.1 % /MW.cm 2 .
Figure 3(a) shows that the SH wave was depleted when the THG was optimized since the corresponding SHG energy conversion efficiency dropped from 45%, to 17%. The comparison with theory was performed using a numerical calculation of the following coupled system of equations relative to real amplitudes, i.e. the moduli of the complex amplitudes of the electric fields of the interacting waves written |𝐸 𝜔,2𝜔,3𝜔 |. It is assumed that SHG and THG are quasi-phase-matched along the x-axis of the QPPKTP crystal. Therefore, we consider only a single Fourier component for each one of these two processes, so that the effective nonlinear coefficient is given by the product of the material's second-order susceptibility 𝜒 (2) with the corresponding Fourier coefficient F. This system of equations can be written as:

(2) 33 2

(2)

* 24 3 2 2 (2) 33 2 2 (2) 24 3 2 2 () ( 2 ) ( ) . ( ) () () ( 3 2 ) ( ) . ( ) () () (2 ) ( ) . ( ) ( ) (2 3 ) ( ) ( ) z SHG z z z y y THG z y z SHG z z z y THG z EX F E X E X X n EX F E X E X X n E X F E X E X X n F E X n                                                 = - = -   = - = -   = + = +  - = - * 3 (2) 24 2 3 3 . ( ) () (3 2 ) ( ) . ( ) ( )
y y y THG z y EX E X F E X E X X n                                    = + = +  (1)
Here the quantity X is the longitudinal coordinate along the x-axis, the superscripts y and z stand for the directions of the electric fields, and the wavelengths are the optimal ones derived experimentally, i.e. 𝜆 𝜔 = 1587.0𝑛𝑚, 𝜆 2𝜔 = 793.5𝑛𝑚 and 𝜆 3𝜔 = 529.0𝑛𝑚. The values of the principal refractive indices 𝑛 𝑦 (𝜆 𝜔/3𝜔 ) and 𝑛 𝑧 (𝜆 𝜔/2𝜔 ) are given in Table 1; they are calculated according to the considered wavelengths at the working temperature from the dispersion equations of references [START_REF] Emanueli | Temperature-dependent dispersion equations for KTiOPO4 and KTiOAsO4[END_REF][START_REF] Kato | Parametric Oscillation at 3.2 µm in KTP Pumped at 1.064 µm[END_REF]. The second-order nonlinear coefficients 𝜒 24 [START_REF] Giordmaine | Tunable coherent parametric oscillation in LiNbO3 at optical frequencies[END_REF] and 𝜒 33 [START_REF] Giordmaine | Tunable coherent parametric oscillation in LiNbO3 at optical frequencies[END_REF] , also given in Table 1, are calculated from the data at room temperature of reference [START_REF] Boulanger | Relative sign and absolute magnitude of d (2) nonlinear coefficients of KTP from second-harmonic-generation measurements[END_REF] using Miller rule. The Fourier amplitudes 𝐹 𝑆𝐻𝐺 and 𝐹 𝑇𝐻𝐺 can be calculated using the method outlined in ref [START_REF] Lifshitz | Photonic Quasicrystals for Nonlinear Optical Frequency Conversion[END_REF], but here they are adjustment parameters for fitting the experimental data. Since there is no analytical solution to Eqs. ( 1), the comparison with theory was performed using a parametric numerical resolution based on the Runge-Kutta method.

The study of the wavelength acceptances described in the previous section shows that the effective interaction length is slightly smaller than the geometrical length of the QPPKTP crystal, and that this effective length is not the same for SHG and THG. Then the numerical integration of Eqs. The electric fields in Eqs.( 1) are the internal fields inside the QPPKTP crystal. The values of the moduli of the complex amplitudes of the fundamental electric fields at the entrance of the crystal, i.e. |𝐸 𝜔 𝑦 (𝑋 = 0)| and |𝐸 𝜔 𝑧 (𝑋 = 0)| that have to be taken for the integration of Eqs.( 1) are linked to the total experimental energy of the incident fundamental beam 𝜀 𝜔 𝑡𝑜𝑡 (𝑋 = 0) by the following equations (assuming plane waves with temporal and transverse Gaussian profiles):

2 0 2 0 ( 0) cos ( ) ( 0) () ( 0) sin ( ) ( 0) () yy tot y z z tot z c E X T X n c E X T X n                      = = = = = = (2) with , , 2 , 3/2 2 4 ( ) [1 ( )] 22 yz yz yz n T n w                     = + = (3)
The quantities 𝑇 𝜔 𝑦,𝑧 correspond to the Fresnel transmission in normal incidence, the light being polarized along the y-axis or z-axis respectively, and α=90° for the SHG alone and α=54° for the optimized THG. The quantity 𝜏 𝜔 corresponds to the pulse duration and 𝑤 𝜔 to the beam radii.

In the same way, the calculated energy of the generated SH and TH waves at the exit of the QPPKTP crystal, i.e. 𝜀 2𝜔 (𝑋 = 𝐿) and 𝜀 3𝜔 (𝑋 = 𝐿), are linked to the moduli of the calculated SH and TH complex amplitudes, i.e. |𝐸 2𝜔 𝑧 (𝑋 = 𝐿)| and |𝐸 3𝜔 𝑦 (𝑋 = 𝐿)|, by:

2 2 2 2 2 2 0 2 3 3 3 3 3 0 () ( ) ( ) () ( ) ( ) zz z y yy n X L T E X L c n X L T E X L c                        = = = = = = (4) with 2 2 2 2 3/2 2 2 2 2 3 3 2 3 3/2 2 3 3 3 4 ( ) [1 ( )] 2 2 4 ( ) [1 ( )] 2 2 z z z y y y n T n w n T n w                                              = + = = + = (5)
where the Gaussian relations apply regarding the pulse durations 𝜏 𝜔 ,𝜏 2𝜔 and 𝜏 3𝜔 as well as the beam radii 𝑤 𝜔 , 𝑤 2𝜔 and 𝑤 3𝜔 , i.e.: , 33

w w w w                == == (6)
The numerical values of the Fresnel transmissions, beam waist radii and pulse durations are given in Table 1.

The system of Eqs. (1) was first solved for the SHG case only by taking α=90°. We performed a parameter adjustment on the Fourier coefficient 𝐹 𝑆𝐻𝐺 . The best fit was found for 𝐹 𝑆𝐻𝐺 = 0.28, which is 30% lower than the theoretical value. The shape of the fitting curve is in excellent agreement with the experimental data as shown by the red curve of Fig. (3)a. Afterwards, this value of 𝐹 𝑆𝐻𝐺 was taken for the second step of integration where the whole system has been considered, i.e. for α=54°. The Fourier coefficient 𝐹 𝑇𝐻𝐺 was then taken also as a fitting parameter and ended up only 8% smaller than its theoretical value, i.e. 𝐹 𝑇𝐻𝐺 = 0.368. These deviations from the theoretical Fourier coefficient are thought to be due to fabrication defaults. But the agreement remains very good between the theoretical and experimental curves as shown by the black curves of Fig. 3

Conclusion

We demonstrated a 40% THG energy conversion efficiency in a quasi-periodically poled KTP crystal pumped with an energy as low as 20 µJ. This is the highest THG efficiency ever reported to the best of our knowledge. Previous records using also a quasi-periodic poling structure were 23% [START_REF] Zhu | Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice[END_REF], and 30.7% in a single KDP crystal allowing simultaneous birefringent phase-matching [START_REF] Boulanger | Cubic optical nonlinearity of KTiOPO4[END_REF]. Note that using 𝜒 (3) interactions for THG results in efficiencies of single percent only [START_REF] Gravier | Third order frequency generation in TiO2 rutile and KTiOPO4[END_REF]. Our work opens the way to exciting developments regarding frequency up-conversion for numerous applications, in particular for the generation in the ultra-violet range around 330 nm starting from a laser around 1 μm. Moreover, it opens new possibilities in quantum optics for TPG by a 𝜒 (2) cascaded spontaneous parametric down conversion [START_REF] Hübel | Direct generation of photon triplets using cascaded photon-pair sources[END_REF] of a 527 nm pump for generating a three-photon state at 1581 nm in a compact single nonlinear crystal, which is an alternative of using a 𝜒 (3) process in a birefringent crystal [START_REF] Douady | Experimental demonstration of a pure third-order optical parametric downconversion process[END_REF]. Intracavity quasi-phasematching may also be interesting in this context [START_REF] Kravtsov | Intracavity quasiphase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3crystal[END_REF].

Fig. 1 .

 1 Fig. 1. (a) A schematic picture of the cascaded processes; (x,y,z) refers to the dielectric frame ; kω,2ω,3ω stands for the wave vectors and 𝛥𝑘 𝑆𝐻𝐺,𝑇𝐻𝐺 for the phase-mismatches, with no metric matching between the vector sizes and the pattern in the background. (b) Microscopy picture of the PPQKTP crystal exhibiting the poling pattern; the yellow scale bar is 28 µm long. (c) Far field diffraction pattern from the crystal. In orange are the peaks that correspond to the designed peaks. (d) Fourier Transform of the nonlinear modulation pattern, exhibiting two peaks at the mismatch frequencies, i.e.

Fig. 2 (

 2 a) shows that a concomitant phase-matching exists in the QPPKTP crystal on the one hand, and that the corresponding values of the phase-matching parameters are close to the theoretical ones, i.e. λω = 1581 nm and T = 100°C, on the other hand. This agreement between calculations and experiments validates the design of the quasi-periodic grating as well as of the values of the refractive indices as a function of wavelength and temperature.

Fig. 2 .

 2 Fig. 2. (a) Normalized intensities of the second-harmonic (SH) wave and third-harmonic (TH) waves as a function of the QPPKTP temperature when the waves propagate along the x-axis, the quantities (y) and (z) referring to the polarization directions of the interacting waves; the dots correspond to experimental data and the dashed lines to fits. (b) Normalized intensities of the SH and TH waves as a function of the polarization angle α defined in the right insert. The fundamental intensity was lower than 0.5 GW.cm -2 , hence pump depletion is negligible here.

  cascaded TH intensity depends on the product of the fundamental and SH intensities, i.e.

  [START_REF] Franken | Generation of Optical Harmonics[END_REF] was made from 𝑋 = 0, i.e. the entrance of the crystal, and 𝑋 = 𝑙 𝑒𝑓𝑓 𝑆𝐻𝐺 = 6.6 𝑚𝑚 for SHG, and 𝑋 = 𝑙 𝑒𝑓𝑓 𝑇𝐻𝐺 = 7.8𝑚𝑚 for THG.

Fig. 3 .

 3 Fig. 3. SHG (a) and THG (b) energy conversion efficiencies as a function of the total incident fundamental intensity. The dots correspond to experimental data and the continuous lines stand for the interpolations.

  (a) and by Fig.3(b). Note that the high values of the conversion efficiency for both SHG and THG are well corroborated by the behaviors of the curves of Figs.[START_REF] Fan | Visible BaB2O4 optical parametric oscillator pumped at 355nm by a singleaxialmode pulsed source[END_REF], which undoubtedly indicate that SHG as well as THG are achieved in the depleted pump regime.

  (a), are slightly wider than the theoretical values, i.e. 𝛿𝜆 𝜔𝑐𝑎𝑙𝑐 𝑆𝐻𝐺 = 2.2 𝑛𝑚 and 𝛿𝜆 𝜔𝑐𝑎𝑙𝑐

																			𝑇𝐻𝐺 =
	1.8 𝑛𝑚. This weak discrepancy is probably mainly due to some small imperfections in
	fabrication. Since the product of the interacting length by the acceptance is constant, we
	conclude that the effective interaction length for the SHG and THG, 𝐿 𝑒𝑓𝑓 𝑆𝐻𝐺	and 𝐿 𝑒𝑓𝑓 𝑇𝐻𝐺
	respectively, are slightly smaller than the geometrical length = 1𝑐𝑚 , i.e.
	SHG eff L	=	L	(   SHG calc	/	exp SHG  	)	=	6.6 mm	and	THG eff L	L	(	THG calc 	/	exp THG 	)	7.8 mm

Table 1 .

 1 Wavelengths 𝛌 𝛚 𝐢 where 𝛚 𝐢 stands for the frequencies 𝛚, 𝟐𝛚 or 𝟑𝛚, pulse durations 𝛕 𝛚 𝐢 , principal refractive indices𝐧 𝐲 (𝛌 𝛚/𝟑𝛚 ) and 𝐧 𝐲 (𝛌 𝛚/𝟑𝛚 ) [26], beam wait radii 𝐰 𝛚 𝐢 , Fresnel transmissions 𝐓 𝛚 𝐢 𝐲,𝐳 and nonlinear

			coefficients 𝛘 𝐢𝐣 (𝟐) used for the numerical integration of Eqs. (1) [27].
		𝝀 𝝎 𝒊 [nm]	𝝉 𝝎 𝒊 [ps]	𝒏 𝒚 (𝝀 𝝎 𝒊 )	𝒏 𝒛 (𝝀 𝝎 𝒊 )	𝒘 𝝎 𝒊 [µm]	𝑇 𝜔 𝑖 𝑧	𝑇 𝜔 𝑖 𝑦	𝜒 33 (2) [pmV -1 ]	(2) 𝜒 24 [pmV -1 ]
	𝝎	1587	15.0	1.7363	1.8150	205	0.917	0.929	16.1	3.8
	𝟐𝝎	793.5	10.6	-	-	145	0.912	-	19.2	4.8
	𝟑𝝎	529	8.7	1.7907	1.8445	118	-	0.920	-	5.3

Funding

A. Vernay is supported by the ANR/FNS PRCI France-Switzerland (16707). A. Arie wishes to thank the Israel Science Foundation (1415/17). S. Trajtenberg-Mills is supported by the ministry of science women in science scholarship.

Acknowledgments

All the authors wish to thank Imaginano (the France Israël Associated International Laboratory with CNRS -Weizmann Institute of Science -Tel Aviv University -Hebrew University of Jerusalem).

Disclosures

The authors declare no conflicts of interest.