Zichun Wang

Kuizhi Chen

Yijiao Jiang

Julien Trébosc

Wenjie Yang

Jean-Paul Amoureux

Ivan Hung

Zhehong Gan

Alfons Baiker

Olivier Lafon

Jun Huang

Revealing Brønsted Acidic Bridging SiOHAl Groups on Amorphous Silica-Alumina by Ultra-high Field Solid-state NMR

Keywords: Amorphous silica-alumina, Brønsted acidity, Ultra-high-field solid-state NMR, bridging SiOHAl acid sites

ABSTRACT: Amorphous silica-aluminas (ASAs) are important acidic catalysts and supports for many industrially essential and sustainable processes. The identification of surface acid sites with their local structures on ASAs is of critical importance for tuning their catalytic properties, but still remains a great challenge and under debate. Here, ultra-high magnetic field (35.2 T) [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC (dipolar-mediated hetero-nuclear multiple-quantum correlation) twodimensional NMR experiments demonstrate two types of Brønsted acid sites in ASA catalysts. In addition to the known pseudo-bridging silanol acid site, the use of ultra-high field NMR provides the first direct experimental evidence for the existence of bridging silanol (BS: SiOHAl) acid sites in ASAs, which has been hotly debated in the past few decades. This discovery provides new opportunities for scientists and engineers to develop and apply ASAs in various reaction processes, due to the significance of BS in chemical and fuel productions based on its strong Brønsted acidity.

To realize green and sustainable energy and chemical productions, eco-friendly and cost-effective silicaalumina catalysts are extensively utilized for driving versatile acid-catalyzed hydrocarbon conversion reactions in drug and fine chemistry, petrochemical, and bio-refining industries. [START_REF] Li | Applications of Zeolites in Sustainable Chemistry[END_REF][START_REF] Corma | Inorganic solid acids and their use in acidcatalyzed hydrocarbon reactions[END_REF] Compared to microporous zeolites, amorphous silica-aluminas (ASAs) offer unconstrained mass transfers and thus exhibit excellent performances in reactions involving large molecules as both acid catalysts and supports for metal active species. These properties render ASAs particularly interesting for applications in the conversion of biomass and derivatives for renewable energy and chemicals. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF][START_REF] Wang | Palladium-doped silica-alumina catalysts obtained from double-flame FSP for chemoselective hydrogenation of the model aromatic ketone acetophenone[END_REF][START_REF] Wang | Efficient acidcatalyzed conversion of phenylglyoxal to mandelates on flame-derived silica/alumina[END_REF][6][START_REF] Wang | Flame-spray-pyrolysis amorphous alumina-silica for tailoring the product distribution of Fischer-Tropsch synthesis[END_REF][START_REF] Yun | Mechanistic study of glycerol dehydration on Brønsted acidic amorphous aluminosilicate[END_REF] Moreover, ASAs are widely utilized in large-scale hydrocracking processes to balance the acidity for the selective production of middle distillates, such as diesel and kerosene fractions. [START_REF] Aitani | Oil Refining and Products[END_REF] So far, several models for the formation of catalytically active Brønsted acid sites (BASs) in ASAs have been proposed. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF][START_REF] Chizallet | Toward the atomic scale simulation of intricate acidic aluminosilicate catalysts[END_REF][START_REF] Busca | Silica-alumina catalytic materials: A critical review[END_REF][START_REF] Wang | Engineering the distinct structure interface of subnano-alumina domains on silica for acidic amorphous silica-alumina toward biorefining[END_REF] Two models are commonly considered for the formation of BASs on ASAs: 1) pseudo-bridging silanols (PBS: SiOH•••Al) [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF][START_REF] Chizallet | Pseudo-bridging silanols as versatile Brønsted acid sites of amorphous aluminosilicate surfaces[END_REF][START_REF] Perras | Shedding light on the atomic-scale structure of amorphous silica-alumina and its Brønsted acid sites[END_REF][START_REF] Wang | Brønsted acid sites based on penta-coordinated aluminum species[END_REF] with silanol groups tilting towards Al atoms with weak interaction; and 2) silanols weakly bounded to neighboring Al sites via electrostatic interactions. [START_REF] Luo | Using trimethylphosphine as a probe molecule to study the acid states in Al-MCM-41 materials by solidstate NMR spectroscopy[END_REF][START_REF] Wang | Acidity enhanced [Al]MCM-41 via ultrasonic irradiation for the Beckmann rearrangement of cyclohexanone oxime to ɛ-caprolactam[END_REF] In these models, there is no covalent bond between silanols and aluminium atoms. The acidic strength of these protons depends on Al sites coordinating to the hydroxyl oxygen of neighboring silanols as well as the SiOH•••Al distance. Due to their amorphous nature, ASAs exhibit average SiOH•••Al distances in the range of 2.94-4.43 Å, which are significantly longer than for bridging OH groups (SiOH-Al) in crystalline zeolites (1.88-2.0 Å). [START_REF] Chizallet | Pseudo-bridging silanols as versatile Brønsted acid sites of amorphous aluminosilicate surfaces[END_REF][START_REF] Perras | Shedding light on the atomic-scale structure of amorphous silica-alumina and its Brønsted acid sites[END_REF] These elongated SiOH•••Al distances could weaken the polarization of the hydroxyl oxygens by neighboring Al sites, accounting for the much lower Brønsted acidity and catalytic performance of ASAs compared to zeolites. [START_REF] Xu | Metal active sites and their catalytic functions in zeolites: Insights from solid-state NMR spectroscopy[END_REF][START_REF] Jiang | Solid-state nuclear magnetic resonance investigations of the nature, property, and activity of acid sites on solid catalysts[END_REF] In contrast, the weak acidity and poor activity of ASAs have been ascribed to the small amount of strong BASs existing in ASAs compared to zeolites. [START_REF] Bevilacqua | Are the active sites of protonic zeolites generated by the cavities?[END_REF] However, the existence of strong BASs in ASAs has been reported by using reactivity measurements in propane cracking [START_REF] Xu | Strong Brønsted acidity in amorphous silica-aluminas[END_REF] and H/D exchange reactions. [START_REF] Poduval | Brønsted acid sites of zeolitic strength in amorphous silica-alumina[END_REF] Zeolite-like bridging SiOHAl acid sites in short-range order have also been proposed by theoretical calculations for the strong BASs in ASAs. [START_REF] Chizallet | Toward the atomic scale simulation of intricate acidic aluminosilicate catalysts[END_REF] However, no direct spectral evidence has been reported so far for these strong BASs owing to their low density and their potentially broad signal due to their hydrogenbond donor nature. Therefore, whether strong BASs are formed via PBS or SiOHAl, or both, is still strongly under debate.

Identifying the surface acid sites and their structureproperty relationship is crucial for the rational design and performance optimization of ASAs. Various diffraction techniques, particularly X-ray diffraction (XRD), are powerful for studying the structure of crystalline zeolites. However, they fail to determine unambiguously the local structures of ASAs due to their absence of long-range ordering, resulting in strong line broadenings. IR spectroscopy could identify the surface sites but does not allow distinguishing between PBS and SiOHAl sites. Solid-state NMR spectroscopy is a powerful tool for characterizing surface acid sites and their local structures on silica-alumina materials. [START_REF] Jiang | Solid-state nuclear magnetic resonance investigations of the nature, property, and activity of acid sites on solid catalysts[END_REF][START_REF] Xu | Solid-state NMR characterization of acid properties of zeolites and solid acid catalysts[END_REF] In 1 H 1D spectra under magic-angle spinning (MAS), NMR signals at d1H = 1.2-2.2 ppm for PBS and terminal SiOH groups have been observed. [START_REF] Wang | Acidity enhanced [Al]MCM-41 via ultrasonic irradiation for the Beckmann rearrangement of cyclohexanone oxime to ɛ-caprolactam[END_REF][START_REF] Wang | Strongly enhanced acidity and activity of amorphous silica-alumina by formation of pentacoordinated Al V species[END_REF][START_REF] Wang | One-step room-temperature synthesis of [Al]MCM-41 materials for the catalytic conversion of phenylglyoxal to ethylmandelate[END_REF] However, the signals at d1H = 3.6-5.2 ppm, typical for bridging SiOHAl acid sites in zeolites, [START_REF] Jiang | Solid-state nuclear magnetic resonance investigations of the nature, property, and activity of acid sites on solid catalysts[END_REF] have never been detected so far. Indeed, even when suppressing the strong SiOH signal with a 1 H-{ [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al} TRAPDOR (transfer of population in double resonance) filter, [START_REF] Deng | 1 H/ 27 Al TRAPDOR NMR studies on aluminum species in dealuminated zeolites[END_REF][START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] only the PBS signal at d1H  1.8 ppm has been probed. [START_REF] Wang | Strongly enhanced acidity and activity of amorphous silica-alumina by formation of pentacoordinated Al V species[END_REF] The SENS-DNP technique (surface-enhanced NMR spectroscopy using dynamic nuclear polarization) can significantly enhance the 1 H sensitivity by one or two orders of magnitude. [START_REF] Perras | Natural abundance 17 O DNP two-dimensional and surface-enhanced NMR spectroscopy[END_REF][START_REF] Liao | Dynamic nuclear polarization surface enhanced NMR spectroscopy (DNP SENS): Principles, protocols, and practice[END_REF] It has been used on ASAs, but still, no SiOHAl sites could be detected. [START_REF] Perras | Shedding light on the atomic-scale structure of amorphous silica-alumina and its Brønsted acid sites[END_REF] The analysis of the dephasing curves obtained from DNP-enhanced [START_REF] Wang | Acidity enhanced [Al]MCM-41 via ultrasonic irradiation for the Beckmann rearrangement of cyclohexanone oxime to ɛ-caprolactam[END_REF] O-{ [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al} TRAPDOR experiments have shown that in ASAs the average distances between Al and neighboring SiOH groups are well in line with the theoretical value of PBS. 14 In the same work, the signal at d1H = 5 ppm besides that of PBS at d1H = 1.3 ppm correlates with [START_REF] Wang | Acidity enhanced [Al]MCM-41 via ultrasonic irradiation for the Beckmann rearrangement of cyclohexanone oxime to ɛ-caprolactam[END_REF] O nuclei with slower de-phasing than in [START_REF] Wang | Acidity enhanced [Al]MCM-41 via ultrasonic irradiation for the Beckmann rearrangement of cyclohexanone oxime to ɛ-caprolactam[END_REF] O-{ [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al} TRAPDOR experiments. This hints at a significantly longer distance between Al-O for the OH signal at d1H = 5 ppm, and hence, it was assigned to hydrogen-bonded OH groups other than bridging OH groups.. Therefore, the direct observation of SiOHAl on ASAs remains a great challenge. [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC (Dipolar-mediated hetero-nuclear multiple-quantum correlation between [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al and 1 H with [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al observation) two-dimensional (2D) NMR experiments provide information on 1 H- [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al proximities. [START_REF] Wang | Brønsted acid sites based on penta-coordinated aluminum species[END_REF][START_REF] Chen | Structure and catalytic characterization of a second framework Al(IV) site in zeolite catalysts revealed by NMR at 35[END_REF] This experiment has notably allowed the observation of PBS sites at B0 = 18.8 T on the surface of ASAs. Recently, an [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC experiment at B0 = 20.0 T has been applied to detect the acid sites of aluminum oxide films grown on a silica support. [START_REF] Kaushik | Atomic-scale structure and its impact on chemical properties of aluminum oxide layers prepared by atomic layer deposition on silica[END_REF] A very broad signal centered at d1H = 4.3 ppm was obtained from the simulation of the indirect 1 H dimension of the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC spectra, but the indirect 1 H dimension of the corresponding [START_REF] Liao | Dynamic nuclear polarization surface enhanced NMR spectroscopy (DNP SENS): Principles, protocols, and practice[END_REF] Si-{ 1 H} spectra shows only a strong signal at d1H = 2.5 ppm without a signal at d1H = 4.3 ppm. Therefore, it is still under debate whether the broad signal at d1H = 4.3 ppm is due to the presence of bridging SiOHAl groups or mainly a combination of various bridging AlOHAl groups. [START_REF] Yang | Qualitative and quantitative analysis of acid properties for solid acids by solid-state nuclear magnetic resonance spectroscopy[END_REF] Here, we report that this experiment carried out at the ultra-high magnetic field of B0 = 35.2 T provides direct evidence for the presence of bridging SiOHAl acid sites on the surface of ASAs. To the best of our knowledge, these sites have never been observed directly so far. This detection is possible since higher B0 fields increase the resolution along both 1 H and [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al dimensions and thus allow identifying sites that are undetectable at lower magnetic fields. [START_REF] Chen | Structure and catalytic characterization of a second framework Al(IV) site in zeolite catalysts revealed by NMR at 35[END_REF] This is particularly the case of [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al nuclei bonded to bridging OH groups, which are broadened by large quadrupole interactions and hence, which are largely 'invisible' at magnetic fields up to 18.8 T. [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF][START_REF] Jiao | Characterization of framework and extra-framework aluminum species in non-hydrated zeolites Y by 27 Al spin-echo, high-speed MAS, and MQMAS NMR spectroscopy at B-0=9[END_REF] Conversely, the reported [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC spectra at 35.2 T allow resolving a new correlation signal between tetra-coordinated Al (Al IV ) species (d27Al = 55-58 ppm) and bridging OH groups (d1H = 4.6 ppm), demonstrating the presence of bridging silanol groups linked to Al. A similar correlation is also firstly observed with penta-coordinated Al (Al V ) species (d27Al = 31-35 ppm), revealing the formation of SiOHAl BASs based on Al V species, which have never been probed hitherto. Moreover, we demonstrate that the SiOHAl formation and the distribution of Al species in ASAs depend on the Al/Si ratio. The detailed insights into surface acid sites and the discovery of new SiOHAl in ASAs pave the way for generating strong SiOHAl in ASAs, which facilitates the optimization of their performance for acid catalysis and multifunctional catalysis in various fields. Amorphous silica-alumina (ASA) catalysts were prepared within microseconds at extremely high temperature (ca. 2000 K) by the flame-spray pyrolysis (FSP) technique. [START_REF] Huang | Increasing the Brønsted acidity of flame-derived silica/alumina up to zeolitic strength[END_REF] Aluminum(III) acetylacetonate (99%, ABCR), tetraethoxysilane (99%, Fluka) acetic acid (analytical grade, Fluka), and methanol (analytical grade, Fluka), were used as received. In brief, the appropriate amounts of the Al and Si precursor materials were dissolved in a 1:1 (vol.) mixture of acetic acid and methanol. The resulting solution was filtered using a glass filter, pumped through a capillary at a rate of 5 mL.min -1 , nebulized by using an O2 flow rate of 5 L.min - 1 . The resulting spray was ignited by an annular supporting methane/oxygen flame (1.5/0.9 L.min -1 ) to generate ASA nanoparticles with a large amount of Al V species. The ASA samples with different atomic ratios of Al/Si are designated as ASA/X, where X represents the percentage of Al atoms with respect to the total amount of Al and Si atoms in the precursors. The nitrogen isotherms, specific surface areas, concentrations of OH groups, and the densities of BAS and Lewis acid sites (LAS) of these ASA materials were determined in our previous works. [START_REF] Wang | Efficient acidcatalyzed conversion of phenylglyoxal to mandelates on flame-derived silica/alumina[END_REF][START_REF] Huang | Increasing the Brønsted acidity of flame-derived silica/alumina up to zeolitic strength[END_REF][START_REF] Wang | NMR spectroscopic characterization of flamemade amorphous silica-alumina for cyclohexanol and glyceraldehyde conversion[END_REF] All 2D NMR experiments were performed on the 35.2 Tesla ( 1 H 1.5 GHz) Series-Connected Hybrid (SCH) magnet operated at the National High Magnetic Field Laboratory (NHMFL, Tallahassee, USA), equipped with a Bruker Avance NEO console. A 2.0 mm triple resonance probe designed and built at the NHMFL was used in double resonance mode and with a sample spinning frequency of R = 30 kHz. The 1 H and [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al isotropic chemical shifts were referenced indirectly by using a D2O sample at room temperature ( 17 O δiso = -2.8 ppm) and the IUPAC reference sample frequencies in Ref. 36.

The [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al Triple-Quantum Magic-Angle Spinning (3QMAS) spectra of ASAs were recorded with a shiftedecho pulse sequence, [START_REF] Massiot | Two-dimensional magic-angle spinning isotropic reconstruction sequences for quadrupolar nuclei[END_REF] and sheared with the QSHEAR program using Matlab. [START_REF] Hung | Q-shear transformation for MQMAS and STMAS NMR spectra[END_REF] Proximities between [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al nuclei were probed using 2D [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al through-space double-quantum to single-quantum (DQ-SQ) homo-nuclear correlation experiments using π/2 and π-pulses of 10 and 20 s CT-selective with 1 = 8.3 kHz. The 27 Al two-spin DQ coherences were excited and reconverted by applying the BR2 2 1 pulse sequence, 39 which reintroduces the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al- [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al dipolar interactions under MAS. The lengths of the excitation and reconversion times were optimized on ASA/50 as exc = rec = 800 s. The rf amplitude applied during the BR2 2 1 pulse sequence was 5 kHz, which corresponds to a nutation frequency of 15 kHz for the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al CT, which matches the HORROR (homo-nuclear rotary resonance) condition. Furthermore, a WURST (wideband, uniform rate, smooth truncation) adiabatic pulse with a frequency sweep equal to the MAS frequency and an offset of 300 kHz with respect to the CT was applied before the BR 2 2 1 excitation, [START_REF] Siegel | Signal enhancement of NMR spectra of half-integer quadrupolar nuclei in solids using hyperbolic secant pulses[END_REF] to enhance the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al CT polarization by inverting/saturating the satellite transitions. [START_REF] Yao | Sensitivity enhancement of the central transition NMR signal of quadrupolar nuclei under magicangle spinning[END_REF][START_REF] Kwak | Enhancing sensitivity of quadrupolar nuclei in solid-state NMR with multiple rotor assisted population transfers[END_REF] The 2D [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al DQ-SQ spectra resulted from averaging 2048 transients for SA/10 and SA/30, and 3072 transients for ASA/50, respectively, with t1 = 33.33 s, 20 t1 increments, TRD = 0.1 s, resulting in a total experimental time of 2.5 and 3.75 h, respectively.

To enhance the sensitivity, the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al nuclei were observed since its rapid longitudinal relaxation allows the use of short recovery delays. The 1 H- [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al dipolar couplings were reintroduced by applying an SR 4 1 2 recoupling on the 1 H channel. [START_REF] Brinkmann | Proton-selective 17 O-1 H distance measurements in fast magic-anglespinning solid-state NMR spectroscopy for the determination of hydrogen bond lengths[END_REF] The 1 H rf amplitudes for the 90° pulses and the SR4 1 2 recoupling were equal to 1  60 kHz. The CT-selective pulse lengths on [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al were equal to 10 and 20 µs for π/2 and π pulses, respectively, i.e. an rf-field amplitude 1 = 8.3 kHz. The total dipolar recoupling time was optimized at rec = 3.2 ms. The 2D spectra resulted from the accumulation of NS = 1024 transients with States-TPPI acquisition of 16 complex t1 increments with t1 = 33.33 s and TRD = 0.1 s, i.e. a total experiment time of about 1 h.

The formation of BASs strongly depends on the coordination number of Al species in dehydrated ASAs, which could be determined at 35.2 T from 1D MAS (Fig. S1 in Supporting Information) and 2D 3QMAS [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al NMR spectra (Fig. 1). The 2D 3QMAS spectra of these catalysts are dominated by the Al IV and Al V signals, while a weaker signal ascribed to hexa-coordinated Al sites (Al VI ) is also visible, in agreement with previous reports. [START_REF] Wang | Brønsted acid sites based on penta-coordinated aluminum species[END_REF][START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] Then the simulation of corresponding 1D [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al MAS NMR spectra were performed. The obtained quadrupole parameters and concentration of each Al species are summarized in Table S1. With increasing Al/Si ratio from 10/90 to 30/70 and 50/50, called ASA/10, /30 and /50, the content of Al V is remarkably raised. The high temperature and fast cooling rate under oxygen-rich atmosphere could promote the generation of intermediate Al V species in ASAs, which may be caused by the local structure reformation under the harsh synthesis conditions. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF][START_REF] Wang | Strongly enhanced acidity and activity of amorphous silica-alumina by formation of pentacoordinated Al V species[END_REF][START_REF] Kim | Tailoring highperformance Pd catalysts for chemoselective hydrogenation reactions via optimizing the parameters of the double-flame spray pyrolysis[END_REF] Unlike bridging OH groups on zeolites, [START_REF] Jiao | Effects of adsorbate molecules on the quadrupolar interaction of framework aluminum atoms in dehydrated zeolite H, Na-Y[END_REF] only a slight decrease of quadrupole coupling constant (CQ) was detected for ASA/50 before and after ammonia loading (Table S1). A direct comparison of their 1D [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al MAS NMR spectra (Fig. S1e) shows an increase of the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al signal intensity with small line narrowing. In zeolites, a significant line narrowing for bridging OH groups could be observed even at magnetic field of 9.4 T. This reduced effect is attributed to the wide chemical shift distribution of Al sites in ASA compared to those in crystalline zeolites. Furthermore, for PBS on ASAs, the ammonia loading has limited effect on the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al spectra recorded at magnetic field of 16.4 T, [START_REF] Wang | Brønsted acid sites based on penta-coordinated aluminum species[END_REF] which is attributed to the much longer Al-OH distance than in zeolites. The effect upon ammonia loading of the possible bridging SiOHAl groups in ASA could be masked by the signals of other Al sites. Therefore, [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D NMR experiments were applied to probe selectively surface protons in connection with Al sites. In SA10, the dominant Al IV and Al V species are highly dispersed in the silica networks on the surface, [START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] which is proposed to promote the formation of moderate BASs. 15 27 Al-{ 1 H} D-HMQC 2D spectra at B0 ≤ 18.8 T only exhibit a broad [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al signal at 60-20 ppm correlated to the 1 H signal at 1.9 ppm (see Fig. S2). When the width of the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al resonance is dominated by the second-order quadrupolar interaction, the resolution of the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al 1D spectra is proportional to (B0) 2 , and hence is improved at higher magnetic fields. Here, cross-peaks between both Al IV (d27Al = 55 ppm) and Al V (d27Al = 31 ppm) species interacting with neighboring SiOH groups (d1H = 1.9 ppm) are clearly resolved at B0 = 35.2 T (Fig. 2a and2b), and confirmed by the corresponding [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al 1D slices (Fig. 2d and2e). These cross-peaks are ascribed to PBSs generated in ASA/10 (Fig. 2f), responsible for the moderate Brønsted acidity of ASAs with low Al/Si ratios.

Moreover, an additional weak 1 H signal at d1H = 3.4 ppm correlates with both Al IV and Al V species (Fig. 2a and2c) has been assigned to AlOH groups. [START_REF] Jiang | Solid-state nuclear magnetic resonance investigations of the nature, property, and activity of acid sites on solid catalysts[END_REF] Since terminal AlOH groups are often observed at d1H shifts ranging from -0.5 to 0.7 ppm, the strong observed deshielding indicates that these AlOH are either polarized by neighboring sites or bridged another Al sites, as in doubly bridging (μ2) AlOHAl sites. [START_REF] Jiang | Solid-state nuclear magnetic resonance investigations of the nature, property, and activity of acid sites on solid catalysts[END_REF][START_REF] Wang | Mapping the oxygen structure of γ-Al2O3 by high-field solid-state NMR spectroscopy[END_REF] The 27 Al DQ-SQ 2D spectrum of ASA/10 (Fig. S3a) exhibits Al IV -Al IV , Al IV -Al V , and Al V -Al V correlations, which were undetectable in previous works at 18.8 T due to their concentration and strong line broadening. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF] Since no strong BASs could be detected in ASA/10, 34 these proximities between Al are not accompanied by a significant synergistic effect on the same SiOH group. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF] The detected proximities between Al sites are proposed to be existing in a few nearby Al species, requiring AlOH groups to balance the local structure as supported by DFT calculation studies. [START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] These AlOH groups produce the deshielded 1 H signal at d1H = 3.4 ppm. In addition to the SiOH•••Al IV sites, the presence of Al IV -O-SiOH species has been constructed by DFT calculations from the silication of the (100) γ-Al2O3 surface, [START_REF] Valla | Atomic description of the interface between silica and alumina in aluminosilicates through dynamic nuclear polarization surface-enhanced NMR spectroscopy and First-Principles calculations[END_REF] which could be centred at d1H = 1.9 ppm as well. After loading with NH3, the 1 H peak of acidic SiOH•••Al IV sites is shifted to ca. 6.7 ppm for NH4 + , while the 1 H peak of non-acidic Al IV -O-SiOH species remains at around 1.9 ppm. Upon NH3 loading, the 1 H peak at 1.9 ppm in Fig. 2a was disappeared and replaced by a peak at d1H = 6.7 ppm, [START_REF] Wang | Brønsted acid sites based on penta-coordinated aluminum species[END_REF] demonstrating the absence of Al IV -O-SiOH species. 3a). Physisorbed and hydrogen-bonded water molecules on ASAs show 1 H signals at ca. d1H = 4.6-4.8 ppm, which could be probed by [START_REF] Li | Applications of Zeolites in Sustainable Chemistry[END_REF] H MAS NMR even at low magnetic fields (7.0 T). [START_REF] Hunger | Magic-angle spinning nuclear-magnetic-resonance studies of watermolecules adsorbed on Brønsted-acid and Lewis-acid sites in zeolites and amorphous silica-aluminas[END_REF] However, these signals are undetectable in 1 H DQ-SQ 2D spectra at 18.8 T for dehydrated ASAs as used here. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF] Hence, the presence of water molecules with signals at d1H = 4.6 ppm can be ruled out. The formation of bridging AlOH groups at similar 1 H chemical shifts (d1H = 3-4.5 ppm) has been reported recently for Al2O3 at 35.2 T. [START_REF] Wang | Mapping the oxygen structure of γ-Al2O3 by high-field solid-state NMR spectroscopy[END_REF] On the other hand, the signal at d1H = 4.6 ppm is typical for bridging OH groups in crystalline zeolites. [START_REF] Yang | Qualitative and quantitative analysis of acid properties for solid acids by solid-state nuclear magnetic resonance spectroscopy[END_REF] In ASAs, BASs originate from Al IV or Al V sites interacting with neighboring SiOH groups in the alumina-silica interphase region or inside the silica networks, whereas Al VI species are typically in the alumina phase and do not contribute to the formation of BASs. The 27 Al DQ-SQ 2D spectrum of dehydrated ASA/30 (Fig. S3b) does not exhibit any correlation with Al VI signal, suggesting that no significant alumina phase exists in ASA/30, which is in line with a previous report. [START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] The D-HMQC spectrum shows cross-peaks between Al VI species (d27Al = 7 ppm) and either SiOH (d1H = 1.9 ppm) or bridging AlOH (d1H = 3.4 ppm) groups (see the slices shown in Figs. 3b, 3c and3g). The NMR observations suggest that some Al VI species are isolated on the silica surface, whereas other ones are located in the proximity of AlOH groups in Figs. 3c and3g. However, the Al VI species are not in connection with the signal at d1H = 4.6 ppm in ASA/30 (Fig. 3d),

demonstrating that this signal is not associated with the alumina phase. The signal at d1H = 4.6 ppm mainly correlates with Al IV or Al V signals, and thus, is considered to be located either in the alumina-silica interphase region or inside the silica networks, contributing to BASs (Fig. 3h). Similar structures are also detected for ASAs with higher Al/Si ratios (Fig. 4). However, the signals at d1H = 4.6 and 3.4 ppm are overlaid by the intense one at d1H = 1.9 ppm in the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D spectrum of dehydrated ASA/50 (Fig. 4a). The cross-peaks between Al IV and Al V sites and the 1 H signal at 1.9 ppm are ascribed to PBSs interacting with one or two Al atoms. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF][START_REF] Wang | Brønsted acid sites based on penta-coordinated aluminum species[END_REF] The first case leads to moderate BASs, which can catalyze the dehydration of cyclohexanol. 6 However, we have recently shown that the presence of an additional Al atom in the vicinity of PBSs can enhance their Brønsted acidity. [START_REF] Wang | Acidity enhancement through synergy of penta-and tetra-coordinated aluminum species in amorphous silica networks[END_REF] This increased intensity of the 1 H signal at 1.9 ppm at high Al/Si ratio indicates an increased amount of PBSs, which is consistent with a homogeneous distribution of Si atoms into the alumina matrix or on the alumina surface of ASAs at high Al/Si ratios. [START_REF] Chizallet | Pseudo-bridging silanols as versatile Brønsted acid sites of amorphous aluminosilicate surfaces[END_REF][START_REF] Perras | Shedding light on the atomic-scale structure of amorphous silica-alumina and its Brønsted acid sites[END_REF] The D-HMQC 2D spectrum of dehydrated ASA/50 shown in Fig. 4a exhibits cross-peaks between Al IV and Al V sites and the 1 H signal at d1H = 5.2 ppm. This 1 H chemical shift has been ascribed to aluminols, bridging OH groups, or hydrogen-bonded hydroxyls. [START_REF] Jiang | Solid-state nuclear magnetic resonance investigations of the nature, property, and activity of acid sites on solid catalysts[END_REF] Similar to bridging AlOH groups observed at d1H = 3.4 ppm (Figs. 2c, 3c, andS4b), the OH groups at d1H = 5.2 ppm is in proximity to Al VI species, but the chemical shift is significantly higher than that of triply-bridging AlOH groups in alumina resonating at d1H = 3.4 ppm. [START_REF] Wang | Mapping the oxygen structure of γ-Al2O3 by high-field solid-state NMR spectroscopy[END_REF] Hence, the cross-peaks at d1H = 5.2 ppm could be ascribed to triply-bridging AlOH in strong electrostatic interaction with neighboring oxygen atoms, similar to hydrogenbonded hydroxyls observed in zeolites. The acidic properties of surface protons could be identified using NH3 as probe molecule because the protonation of NH3 at BASs results in NH4 + ions producing a 1 H signal at d1H = 6.5-7.0 ppm, which can clearly be distinguished from other OH groups in silicaaluminas. NH3 coordinated to Lewis acidic Al sites on Al2O3 and ASA leads to 1 H signals in the range d1H = -0.5  4.6 ppm. [START_REF] Wang | NMR spectroscopic characterization of flamemade amorphous silica-alumina for cyclohexanol and glyceraldehyde conversion[END_REF][START_REF] Lang | Novel approach for the characterization of Lewis acidic solid catalysts by solid-state NMR spectroscopy[END_REF][START_REF] Yin | NH3 as a probe molecule for NMR and IR study of zeolite catalyst acidity[END_REF][START_REF] Ma | An investigation of the roles of surface aluminum and acid sites in the zeolite MCM-22[END_REF] AlOH groups are generally inactive in protonating NH3. Although a recent report shows protonation of NH3 on Al2O3, the amount of potential acidic OH groups is very small compared to LASs. [START_REF] Lang | Novel approach for the characterization of Lewis acidic solid catalysts by solid-state NMR spectroscopy[END_REF] Since AlOH groups are inactive for the protonation of ammonia, the increase in the signal intensity of the cross-peaks between Al V resonance and 1 H signals at 3.4 and 5.2 ppm upon ammonia loading is attributed to the adsorption of ammonia at LASs (Figs. S4b,g andS4d,h). [START_REF] Wang | NMR spectroscopic characterization of flamemade amorphous silica-alumina for cyclohexanol and glyceraldehyde conversion[END_REF] In the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D spectrum shown in Fig. 4b, the cross-peaks at d1H = 1.9 and 4.6 ppm, have ,g andS4d,h) indicate that the proton donation arises mainly from the peaks at d1H = 1.9 and 4.6 ppm. These spectral modifications demonstrate that these two proton species are surface BASs. The complete deprotonation (disappearance) of the peak at d1H = 1.9 ppm in Fig. 4b is because that mainly acidic SiOH groups with neighboring Al centers can be selectively detected in [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC experiments, while non-acidic SiOH groups are still observed upon ammonia adsorption using conventional [START_REF] Li | Applications of Zeolites in Sustainable Chemistry[END_REF] H 1D experiments (Fig. S5). [START_REF] Wang | Brønsted acid sites based on penta-coordinated aluminum species[END_REF][START_REF] Huang | Increasing the Brønsted acidity of flame-derived silica/alumina up to zeolitic strength[END_REF] The signal at d1H = 1.9 ppm is widely accepted for PBS sites in ASAs. DFT calculations shows that the interaction between SiOH groups and local Al sites in ASAs is very weak compared to bridging SiOHAl groups, unless deprotonation upon the adsorption of probe molecules. [START_REF] Chizallet | Acidity of amorphous silicaalumina: From coordination promotion of Lewis sites to proton transfer[END_REF] Therefore, both moderate and strong PBS sites denote similar signals at d1H = 1.9 ppm, without strong deshielding on the nearby silanol protons. Therefore, the signal at d1H = 4.6 ppm does not arise from the PBS and the bridging AlOH in alumina. The acidic hydroxyl groups with d1H = 4.6 ppm can correlate with Al IV and Al V sites (Figs. S4c,e,f,j,k). In zeolites, Al IV sites lead to a significant deshielding of the 1 H resonance on neighboring OH groups, like in bridging SiOHAl IV groups. Therefore, the cross peaks between the signal at d1H = 4.6 ppm and Al IV and Al V peaks are ascribed here to bridging SiOHAl IV and SiOHAl V moieties. These two groups transfer protons to ammonia. To the best of our knowledge, SiOHAl V acid sites have never been observed so far.

As the hetero-nuclear coherence transfer in [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC experiments are only effective up to a few Å, the 1 H signal of ammonium ions only correlates with [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al signals involved in the conjugated base of BASs. Hence, the cross-peaks of the 1 H signal of ammonium ions in D-HMQC spectra demonstrate that BASs contain both Al IV and Al V sites. The structures of PBS and BS involving Al IV and Al V sites and their reactions with ammonia are shown in Figs. 4e and4f. Both PBS and BS act as BASs. To determine the population densities of BASs based on PBS and BS, we assume that they have comparable transfer efficiencies in the D-HMQC experiments. Then the population densities of PBS and BS are determined from the integrated intensities of their signal in the 1 H projection of D-HMQC spectra (Figs. 3h, 4c and4d), and the as-derived molar fractions are given in Table 1. The fraction of SiOHAl amounts to the range of 9.2-24 % of the total number of BASs, and PBS are predominant in ASAs. With increasing Al/Si ratio from 30/70 to 50/50, the molar fraction and the number of SiOHAl were significantly reduced. 34. b Molar fractions of BS were determined by the ratios (BS)/(BS+PBS) of the integrated intensities obtained from simulations of the 1 H projections of [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D spectra of dehydrated ASA.

Bridging OH groups are widely accepted to be generated based on framework Al IV species in crystalline zeolites, but are rarely probed in ASAs. Generally, Al IV species involved in SiOHAl IV groups are subject to very large CQ values, e.g. up to 15 ± 1 MHz for framework Al IV species in zeolite H-Y, [START_REF] Jiao | Characterization of framework and extra-framework aluminum species in non-hydrated zeolites Y by 27 Al spin-echo, high-speed MAS, and MQMAS NMR spectroscopy at B-0=9[END_REF] causing significant line broadenings, and thus are 'invisible' at low to medium magnetic fields. Increasing the magnetic field strength and the spinning rate may significantly narrow the [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al signal, and allow recovering this 'invisible' signal. Moreover, [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D spectra allow the selective detection of SiOH groups with different neighboring Al sites, while removing the 1 H signal of non-acidic terminal SiOH groups.

With this in mind, the newly observed signals at d1H = 4.6 ppm in proximity to Al IV species demonstrate the formation of SiOHAl groups in ASAs, which are similar to those observed in zeolites with the same [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D experiments. [START_REF] Chen | Structure and catalytic characterization of a second framework Al(IV) site in zeolite catalysts revealed by NMR at 35[END_REF] These [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al and 1 H correlations are undetectable when using a magnetic field of 18.8 T (Fig. S2), but could be detected at 35.2 T. This observation confirms that these Al species are subject to large quadrupolar interactions. Large values of CQ = 13-16.6 MHz, similar to those reported for framework Al IV species, have been calculated in ASAs by DFT for Al IV with neighboring silanols. [START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] These SiOHAl environments of ASAs exhibit similar 1 H chemical shifts and acidic properties as bridging OH groups in zeolites.

More interestingly, Al V species exhibit similar proximity to bridging OH groups at d1H = 4.6 ppm, as observed with Al IV species. Al V species interacting with SiOH groups can exhibit CQ  12-16 MHz, according to DFT calculations, [START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] similar to those reported for framework Al IV species in zeolite H-Y. 33 27 Al-{ 1 H} D-HMQC 2D spectra, recorded before and after ammonia loading (Figs. 4a and4b), demonstrate that Al V species are in proximity to protons at d1H = 4.6 ppm and ammonium ions (Figs. S4f,k), and are thus acting as SiOHAl. The cross-peaks with Al V signal in D-HMQC 2D spectra have intensities similar to those with Al IV resonance (Figs. 3d andS4c). Therefore, bridging sites interacting with Al V sites represent a significant fraction of the total amount of the bridging sites and not only some extra sites in the structure. Furthermore, the reaction of ASAs with ammonia (Fig. 4b) indicates that Al IV and Al V are unsaturated species with similar properties to promote the acid strength of neighboring silanols (d1H = 1.9 ppm).

The formation of bridging SiOHAl groups in ASAs has been proposed by DFT calculation studies, constructed from the silication of the (100) γ-Al2O3 surface upon hydrothermal treatment. [START_REF] Chizallet | Toward the atomic scale simulation of intricate acidic aluminosilicate catalysts[END_REF][START_REF] Chizallet | Pseudo-bridging silanols as versatile Brønsted acid sites of amorphous aluminosilicate surfaces[END_REF][START_REF] Chizallet | Acidity of amorphous silicaalumina: From coordination promotion of Lewis sites to proton transfer[END_REF][START_REF] Chizallet | Density functional theory simulations of complex catalytic materials in reactive environments: Beyond the ideal surface at low coverage[END_REF] The presence of bridging SiOHAl groups requires a high hydroxyl coverage (≥ 5.4 OH nm -2 ), [START_REF] Chizallet | Pseudo-bridging silanols as versatile Brønsted acid sites of amorphous aluminosilicate surfaces[END_REF] much higher than that (ca. 2.8~3.0 OH nm -2 ) on flame-made ASAs. [START_REF] Huang | Increasing the Brønsted acidity of flame-derived silica/alumina up to zeolitic strength[END_REF] The surface density of SiOHAl groups in ASA/30 is ca. 0.5 nm -2 at 2.8 OH nm -2 , which is similar to that reported for DFT model at 7.5 OH nm -2 , indicating a promotion of SiOHAl formation using FSP. In the DFT model, the bridging SiOHAl groups are formed based on Al V species, other than the well accepted Al IV species in zeolites. [START_REF] Chizallet | Density functional theory simulations of complex catalytic materials in reactive environments: Beyond the ideal surface at low coverage[END_REF] However, SiOHAl groups based on both Al IV and Al V species are observed in this work. The DFT obtained structural parameters of SiOHAl groups in ASAs are like those reported for zeolites, such as bond distances (Al-O, Si-O and O-H) and Si-O-Al angle. [START_REF] Chizallet | Pseudo-bridging silanols as versatile Brønsted acid sites of amorphous aluminosilicate surfaces[END_REF] With the similar structure, similar large CQ values of SiOHAl in ASAs and zeolites can be expected and are reported in DFT calculation studies as discussed above. [START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] Therefore, our observations of SiOHAl groups in ASAs can be supported by the existing DFT calculation studies.

To the best of our knowledge, the bridging silanol groups SiOHAl V have never been reported experimentally so far and the above results represent the first direct observation of bridging silanol groups in ASAs, in which a PBS local environment dominates. These observations well support the strong BASs probed in ASAs in previous works. [START_REF] Bevilacqua | Are the active sites of protonic zeolites generated by the cavities?[END_REF][START_REF] Xu | Strong Brønsted acidity in amorphous silica-aluminas[END_REF][START_REF] Poduval | Brønsted acid sites of zeolitic strength in amorphous silica-alumina[END_REF] The formation of BS could depend on the wide distribution of Al species in ASAs, leading to BASs with versatile strengths and structures. For ASAs prepared at milder conditions, mainly moderate BASs based on Al IV sites are generated, and thereby observing directly the structure of a few strong BASs is quite difficult. Likewise, distinguishing the structure of strong BASs from PBS with an Alsynergistic effect and a BS site is impossible using other techniques, such as FTIR. In flame-spray pyrolysis, the high flame temperature (∼ 2000 K) and oxygen-rich atmosphere promote the formation of Si-O-Al bonds, leading to highly populated surface Al V species and much higher BAS density than in ASAs prepared at milder conditions. [START_REF] Wang | Strongly enhanced acidity and activity of amorphous silica-alumina by formation of pentacoordinated Al V species[END_REF][START_REF] Wang | High population and dispersion of pentacoordinated Al V species on the surface of flame-made amorphous silicaalumina[END_REF] The harsh synthesis conditions using FSP provide a more homogeneous distribution of Al and Si atoms even at high Al loading, which tends to promote the formation of bridging silanol groups based on either Al IV or Al V sites in flame-derived ASAs. Hence, we could directly observe here that the formation of bridging SiOHAl is not a unique property of zeolites featuring long-range order, but is also possible in amorphous materials, such as ASAs.

As the formation and the amount of SiOHAl sites depend on the Al/Si ratio and Al distribution, it may be possible to tune the acidity of ASAs for the selective production of middle distillates from hydrocracking. In addition, the strong SiOHAl BASs can cooperate with other sites on the surface of ASAs for the catalysis of multi-step reactions, including bifunctional Brønsted-Lewis acid-catalytic glucose dehydration for 5hydroxymethylfurfural. [START_REF] Wang | Cooperativity of Brønsted and Lewis acid sites on zeolite for glycerol dehydration[END_REF][START_REF] Wang | Extra-framework aluminum-assisted initial C-C bond formation in methanol-to-olefins conversion on zeolite H-ZSM-5[END_REF][START_REF] Wang | Insight into threecoordinate aluminum species on ethanol-to-olefin conversion over ZSM-5 zeolites[END_REF] Moreover, bridging OH groups could result in strong metal-support interactions, [START_REF] Mojet | Metal-support interactions in supported platinum catalysts: zeolites and amorphous supports[END_REF] enhancing the catalytic activity and stability of active metal species for removing hazardous gases, such as NO, NO2, NH3, and volatile organic compounds, [START_REF] Ma | In situ DRIFTS and temperature-programmed technology study on NH3-SCR of NOx over Cu-SSZ-13 and Cu-SAPO-34 catalysts[END_REF][START_REF] Zhang | Selective transformation of various nitrogen-containing exhaust gases toward N2 over zeolite catalysts[END_REF] with benefits to the environment and human health. Therefore, our discovery of SiOHAl formation in ASAs could significantly expand their applications in various fields.

In summary, the formation of Al IV -based bridging OH groups in ASAs, together with a new type of Al V -based bridging OH groups, are directly observed by [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D NMR spectroscopy. So far, bridging OH groups, as the key catalytic active sites, have been widely accepted to be formed with framework Al IV species in crystalline zeolites. Compared to zeolites, the formation of bridging OH groups in ASAs is strongly under debate due to the lack of long-range order in these materials, longer Al-O distance, significantly lower Brønsted acidity, and rare spectral evidence. Here, we proved the formation of bridging OH groups in ASAs based on Al IV and Al V species in proximity to SiOH groups, showing similar 1 H isotropic chemical shifts and acidic properties as those in zeolites. We demonstrated that the formation of bridging OH groups is general in silica-aluminas and virtually independent from the longrange order of the local structure. This could be achieved by reducing the distance between Al IV /Al V species and SiOH groups in compact structure in ASAs by using a suitable synthesis approach. Our findings, which are related to the use of a very high magnetic field (35.2 T), show promise for the development of ASAs populated with bridging OH groups, enhancing their acidity and catalytic activity for a wide range of acid and multifunctional catalysis for energy and chemical production in key industrial chemical processes.

ASSOCIATED CONTENT

The Supporting Information is available free of charge via the Internet at http://pubs.acs.org.

Method for simulating the 1D [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al MAS NMR spectra 1D [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al and 1 H MAS NMR spectra [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al-{ 1 H} D-HMQC 2D spectrum of ASA/10 27 Al and 1 H DQ-SQ 2D spectrum of ASAs [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] Al and 1 H slices from Fig. 4 XRD patterns, STEM and EDX images of ASAs Nitrogen adsorption/desorption isotherms of ASAs

  Excitation and reconversion pulses lasted tp = 3.75 and 1.25 s, respectively, with a radiofrequency (rf) field strength of 1 = 96 kHz, and central-transition (CT) selective π/2 and π pulses of 10 and 20 µs at 1 = 8.3 kHz. The 2D 3QMAS spectra were acquired with complex acquisition using t1 = 33.33 s, NS = 1920 transients, 20 t1 increments, and a recovery delay TRD = 0.1 s.

Figure 1 .

 1 Figure 1. 27 Al 3QMAS ASA spectra recorded at 35.2 T with R = 30 kHz of (a) ASA/10, (b) ASA/30, and (c) ASA/50, dehydrated at 723 K under vacuum for 12 h, as well as (d) ASA/50 loaded with ammonia and evacuated at 373 K for 1 h.

Figure 2 .

 2 Figure 2. Correlation spectra of dehydrated ASA/10. (a) 2D 27 Al-{ 1 H} D-HMQC spectrum acquired using rec = 3.2 ms, along with the 27 Al and 1 H 1D slices displayed in subfigures (b,c) and (d,e), respectively. (f) Proposed structure of PBSs corresponding to the dominant crosspeaks in the 27 Al-{ 1 H} D-HMQC spectrum. ASA/10 was dehydrated at 723 K for 12 h under vacuum and the spectra were recorded at 35.2 T with R = 30 kHz. At higher Al concentration, besides the signals of moderate BASs and AlOH groups at d1H = 1.9 and 3.4 ppm, an additional signal at d1H = 4.6 ppm was detected in dehydrated ASA/30 (Fig. 3a). Physisorbed and hydrogen-bonded water molecules on ASAs show 1 H

Figure 3 .

 3 Figure 3. Correlation spectra of dehydrated ASA/30. (a) 27 Al-{ 1 H} D-HMQC 2D spectrum acquired using rec = 3.2 ms, along with the 27 Al and 1 H 1D slices displayed in subfigures (b-d) and (e-g), respectively. (h) Simulation of the 1 H projection of (a) and the proposed local environments of silanol groups based on spectrum (a) and corresponding slices. ASA/30 was dehydrated at 723 K for 12 h under vacuum and spectra were recorded at 35.2 T with R = 30 kHz.

19

 19

Figure 4 .

 4 Figure 4. 27 Al-{ 1 H} D-HMQC spectra of ASA/50: (a) dehydrated at 723 K for 12 h under vacuum, and (b) upon ammonia loading. (c,d) Simulation of the 1 H projection of (a) and (b). (e,f) Proposed structures of PBS and BS sites before and after their reaction with ammonia. Spectra were recorded at 35.2 T with R = 30 kHz and rec = 3.2 ms.

  Fig.4a, while concomitantly a signal at d1H = 6.7 ppm appears. The large intensity of the ammonium signal and the very limited change in the signals of AlOH groups (Figs. S4b

Table 1 .

 1 Molar fraction and concentration of BS and PBS BASs on ASAs. a

		Molar	Density of	Density of
		fraction of	BS /	PBSs /
		BS b / %	mmol/g	mmol/g
	ASA/10	0	0	9.8 × 10 -2
	ASA/30	18.3	2.0 × 10 -2	9.1 × 10 -2
	ASA/50	9.2	1.2 × 10 -2	12.2 × 10 -2
	a Total densities of BASs in ASAs are obtained from
	ref.

Table S1 .

 S1 Summary of parameters and deconvolution results

Table S2 .

 S2 Surface areas and acidic properties of ASA catalysts

ACKNOWLEDGMENT J.H. and Z.W. acknowledge the financial supports from Australian Research Council Discovery Projects (DP150103842, DP180104010, and DE190101618). J.H. thanks the University of Sydney SOAR fellowship, Sydney Nano Grand Challenge, and the International Project Development Funding. O.L., J.L. and J.-P.A. are grateful for funding provided by the Region Nord/Pas de Calais (France), Europe (FEDER), CNRS, Ministère de l'Enseignement Supérieur et de la Recherche, CPER, Chevreul Institute (FR 2638), Infrastructure de Recherche en Résonance Magnétique Nucléaire à Très Haut Champ (IR-RMN, FR 3050), ENSCL, and contracts ANR-18-CE08-0015-01 (ThinGlass) and T-UEPEARL-20-005-LAFON-HAMDOUNA (NMR-MECA-DRUG). OL acknowledges financial support from Institut Universitaire de France (IUF). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1644779 and the state of Florida. Development of the 36 T SCH magnet and NMR instrumentation was supported by NSF (DMR-1039938 and DMR-0603042) and NIH (BTRR 1P41 GM122698).

AUTHOR INFORMATION

Corresponding Author * olivier.lafon@univ-lille.fr; jun.huang@sydney.edu.au

Author Contributions

All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.


Thomas Duminy
email: thomas.duminy@insa-lyon.fr

Aurélien Doitrand

Sylvain

Sylvain Meille

Fracture parameter identification by Digital Image Correlation and Finite Fracture Mechanics for millimeter-scale samples

Keywords: Finite fracture mechanics, Digital Image Correlation, small-scale

come

Fracture parameter identification by Digital Image

Correlation and Finite Fracture Mechanics for millimeter-scale samples

Introduction

Wedge splitting test (WST) [START_REF] Brühwiler | The wedge splitting test, a new method of performing stable fracture mechanics tests[END_REF] consists of the insertion of a wedge in a notched sample. WST is often used in the study of concrete [START_REF] Guan | Wedge-splitting tests for tensile strength and fracture toughness of concrete[END_REF] and of refractories with sample dimensions approximately equal to hundreds of millimeters [START_REF] Brochen | Investigation of fracture behavior of typical refractory materials up to service temperatures[END_REF] [START_REF] Yu | Fracture behavior of Al2O3-SiO2 castables by the wedge splitting test and digital image correlation technique[END_REF], as illustrated in Fig. 1 (a). The wedge acts on two rollers that generate a mode I loading, leading to stable crack propagation under imposed displacement.

Feilden et al. [START_REF] Feilden | ≪ 3D Printing Bioinspired Ceramic Composites ≫[END_REF] studied ceramic samples at the millimeter scale, using WST. At this scale, WST is slightly different from the apparatus used in [START_REF] Brochen | Investigation of fracture behavior of typical refractory materials up to service temperatures[END_REF][START_REF] Yu | Fracture behavior of Al2O3-SiO2 castables by the wedge splitting test and digital image correlation technique[END_REF] since no rollers can be inserted to ensure the mode I loading (sse Fig. 1 (b)). Sernicola et al. [START_REF] Sernicola | ≪ In Situ Stable Crack Growth at the Micron Scale ≫[END_REF] performed in-situ WST using a nano-indentor in a scanning electron microscope on SiC single crystal and SiC bi-crystal micro-scale samples machined using a focused ion beam. They observed cracks initiating slightly offset from the notch 10 tip. They correlated this phenomenon with asymmetry in the testing sample and in the sample -nano-indentor alignment, more and more prominent as the sample downsizes. It ultimately increased scattering in results. WST has thus been implemented across the scales, the macro-scale being subjected to less experimental uncertainty but the micro-scale being able to capture local phenomena, such as single interface delamination. Recently, in-situ WST has been instrumented using digital image correlation (DIC) [START_REF] Doitrand | Fracture and Cohesive Parameter Identification of Refractories by Digital Image Correlation Up to 1200°C[END_REF][START_REF] Mathieu | Identification of a crack propagation law by digital image correlation[END_REF][START_REF] Vargas | ≪ Analysis of a castable refractory using the wedge splitting test and cohesive zone model ≫[END_REF][START_REF] Doitrand | ≪ Fracture and Cohesive Parameter Identification of Refractories by Digital Image Correlation Up to 1200°C ≫[END_REF]. Coupling the capability of WST to initiate a crack that propagates stably with displacement field measurement using DIC, fracture parameters [START_REF] Doitrand | Fracture and Cohesive Parameter Identification of Refractories by Digital Image Correlation Up to 1200°C[END_REF] or traction-separation profile [START_REF] Mathieu | Identification of a crack propagation law by digital image correlation[END_REF] can be identified. Several methods exist to model fracture using

WST tests and DIC. The most commonly used is cohesive zone models (CZM). They have been successfully coupled with DIC to determine fracture properties of refractories with sample dimensions in the order of tens of millimeters, both at room [START_REF] Vargas | ≪ Analysis of a castable refractory using the wedge splitting test and cohesive zone model ≫[END_REF] and elevated temperatures [START_REF] Doitrand | ≪ Fracture and Cohesive Parameter Identification of Refractories by Digital Image Correlation Up to 1200°C ≫[END_REF]. Efforts have been made to study the influence of the DIC acquisition zone on the identified parameters [START_REF] Alfano | ≪ Global Sensitivity Analysis in the Identification of Cohesive Models Using Full-Field Kinematic Data ≫[END_REF][START_REF] Réthoré | ≪ Identification of a cohesive zone model from digital images at the micron-scale ≫[END_REF]. Alfano et al. [START_REF] Alfano | ≪ Global Sensitivity Analysis in the Identification of Cohesive Models Using Full-Field Kinematic Data ≫[END_REF] studied the influence of temporal and spatial discretization on CZM parameters identification of a double-cantilever beam test using a global DIC approach. On the one hand, the more pre-fracture images were used in DIC, the enhanced the evaluation of the tensile strength σ c was. On the other hand, the estimate of the critical energy release rate G c was more accurate, provided more images acquired during stable crack propagation phase were used in DIC.

Similarly, the dimensions of the DIC region of interest (ROI) have an opposite influence on σ c and G c . Enhanced sensitivity in the estimation of σ c was observed for smaller ROI, whereas larger ROI gave higher sensitivity to the estimation of G c . Rethoré et al. [START_REF] Réthoré | ≪ Identification of a cohesive zone model from digital images at the micron-scale ≫[END_REF] studied crazing in PMMA, which is associated with a fracture process zone of tens of micrometers. To adequately capture this phenomenon, DIC data were acquired on a 1 mm 2 zone on a 1000 mm 2 sample surface. As no macroscopic loading information was directly available, crack tip stress intensity factors were extracted [START_REF] Hild | ≪ Measuring stress intensity factors with a camera: Integrated digital image correlation (I-DIC) ≫[END_REF]. It allowed tracking the position of the crack tip during the test and deriving a traction-opening profile and, thus, determining the cohesive zone parameters. Further use of DIC for fracture parameter or fracture model identification was applied for instance in conjunction to the Boundary Element Method for concrete [START_REF] Ferreira | On the analysis of notched concrete beams: From measurement with digital image correlation to identification with boundary element method of a cohesive model ≫[END_REF] or with cohesive zone model to identify fracture properties of composites [START_REF] Shen | ≪ Identification of cohesive zone model and elastic parameters of fiber-reinforced cementitious composites using digital image correlation and a hybrid inverse technique ≫[END_REF] or refractories [START_REF] Vargas | Cohesive properties of refractory castable at 600 • . Effect of sintering and testing temperature ≫[END_REF].

CZM are nonlinear models, thus generally time-consuming when employed for fracture property inverse identifications. They require numerous computations before converging towards adequate results [START_REF] Khosrozadeh | ≪ Inverse identification of material constants of various cohesive laws for delamination of composites using experimental results ≫[END_REF]. The coupled criterion (CC) [START_REF] Leguillon | ≪ Strength or toughness? A criterion for crack onset at a notch ≫[END_REF] is another method to study the initiation and propagation of a crack, thus going beyond classical linear elastic fracture mechanic (LEFM) [START_REF] Griffith | VI. The phenomena of rupture and flow in solids[END_REF] which can assess crack propagation based on an energy criterion for an infinitesimal crack advance. In a more general framework, including LEFM, the CC is based on a simultaneous fulfillment of both stress and energy criteria, inducing a finite initiation crack extension. The CC has been successfully implemented in both 2D [START_REF] Martin | ≪ Prediction of Interfacial Debonding between Stiff Spherical Particles and a Soft Matrix with the Coupled Criterion ≫[END_REF] and 3D [START_REF] Doitrand | ≪ 3D Application of the Coupled Criterion to Crack Initiation Prediction in Epoxy/Aluminum Specimens under Four Point Bending ≫[END_REF]. In addition, it has proven to be a successful method to study a wide range of crack initiation configurations, e.g. mode mixity in elastic isotropic materials [START_REF] Yosibash | ≪ A Failure Criterion for Brittle Elastic Materials under Mixed-Mode Loading ≫[END_REF] [23], nonlinear material behavior [START_REF] Doitrand | ≪Nonlinear Implementation of Finite Fracture Mechanics: A Case Study on Notched Brazilian Disk Samples ≫[END_REF], and dynamic crack initiation [START_REF] Doitrand | ≪ Dynamic Crack Initiation Assessment with the Coupled Criterion ≫[END_REF], among others. Under the assumption of linear elasticity and small deformations, fracture parameter inverse identification using the CC is much faster than using CZM since it only requires some linear elastic finite element (FE) computations. The major advantage of the CC is that the fracture parameters are only required during the post-processing step, which makes the inverse identification procedure numerically efficient. Both CC and CZM fracture parameters inverse identification procedure converge to similar values [26] [27] provided that the studied material exhibits a brittle behavior at crack initiation. Fracture parameter identification using the CC generally relies on idealized boundary conditions of the experiments. Nevertheless, the actual boundary conditions may differ from such idealized prescribed forces or displacements. The latter can actually be estimated using DIC to measure the displacement fields at the surface sample during the test and better represent the loading applied to the specimen.

The objective of this work is to implement the CC using boundary conditions based on displacement fields measured by DIC to determine the tensile strength and critical ERR from WST on PPMA millimeter-sized samples. The experimental procedure is presented in Section 2. Section 3 presents the CC and its implementation using boundary conditions from displacement fields measured using DIC. In addition, a parametric study is conducted to determine the methodology limitations of such an approach. Finally, fracture parameters are identified (Section 4).

Definition of the test

Sample preparation

Cast PMMA samples are laser-cut from a 3-mm plate using a Trotec Speedy 100 machine (Trotec Laser GmbH, Marchtrenk, Austria). Dimensions are given in A freckle is applied to perform DIC. First, a homogeneous white layer is applied using acrylic spray paint. Then, black speckles are deposited using another acrylic spray paint.

Wedge splitting test

WST is performed using a Microtest 2 kN machine from Deben UK Ltd (London, UK). A homemade module carrying a tungsten carbide wedge is progressively inserted in the sample notch (Fig. 2). To ensure quasi-static loading conditions, a prescribed displacement rate of 33 µm.min -1 is applied. Tests are conducted either up to the complete fracture of the sample or 20 seconds after crack initiation. Fig. 3 shows the force-displacement curves for the five tested samples. The material exhibits a linear-elastic behavior up to crack initiation. Crack initiation is followed by unstable crack propagation, both phenomena inducing a sudden force drop. After unstable crack propagation following initiation, the imposed displacement must be increased for further crack propagation, which means that stable crack propagation occurs.

Digital image correlation

DIC is a contactless technique to measure displacement on a sample surface. Images are acquired over time. Let f be the reference image grey level field, g be the deformed image grey level field, and u be estimations of the searched displacement field u m that transforms the deformed image into the reference image. An algorithm is used aiming to minimize the sum of the squared grey pin wedge 40°y x level difference between the reference image and the deformed image corrected by the displacement field estimation [START_REF] Hild | ≪ Damage Measurements via DIC ≫[END_REF]:

u m = Argmin u ROI [f (x) -g(x + u(x))] 2 , (1)
The minimization is performed using a FE-based nonlinear least-squares algorithm with a global approach implemented in the software Ufreckles [START_REF] Rethoré | ≪ UFreckles ≫[END_REF]. The image acquisition device is an optical microscope (Hirox Japan Co Ltd, Tokyo, Japan) with a 8 µm physical pixel size. Images are acquired every two seconds.

Undesired acquisition noise is inherent to DIC. This noise is a function of the experimental setup, e.g. acquisition apparatus, lightning, speckle quality, DIC mesh size, and ROI contour shape.

Consequently, the displacement should be null on the whole sample surface. The maximum error is found to be 0.23 ± 0.06 pixels, or equivalently 1.86 ± 0.53 µm. DIC mesh size element equals 50 pixels, or approximately 400 µm corresponding to a good trade-off between measurement noise and spatial segmentation. Moreover, to reduce the noise, the DIC FE mesh is taken slightly inside

DIC-based coupled criterion implementation

The coupled criterion 105

The CC is a model dedicated to studying the initiation of a crack. It is based on the simultaneous fulfillment of stress and energy conditions. The stress criterion states the opening stress σ nn must be larger than the material tensile strength σ c over the whole area corresponding to a putative crack before initiation. The energy criterion requires that the incremental energy release rate (IERR) G inc , defined as -∆W ℓ in 2D, where ∆W (ℓ) is the elastic strain energy variation due to crack opening and ℓ the crack length, must be equal to or larger than the critical energy release rate G c . These two conditions write:

   σ nn (ℓ, U c ) ≥ σ c , ∀ ℓ ≤ ℓ c , G inc (ℓ c , U c ) ≥ G c , (2)
where ℓ c is the crack initiation length and U c is the applied displacement. which both conditions given in Eq. 2 are fulfilled for a length corresponding to ℓ c . As a consequence, the CC predicts that crack initiation occurs as a sudden event with a crack length jumping from 0 to ℓ c for an imposed displacement U c . After initiation, the crack propagation can be assessed based on LEFM using the energy release rate (ERR) G. The stable crack propagation condition is defined as G = G c , with G = -δW δℓ . In configurations where G inc exhibits a maximum, ℓ c is smaller than or equal to the length maximizing G inc [START_REF] Weißgraeber | ≪ Crack Nucleation in Negative Geometries ≫[END_REF], denoted ℓ (see Fig. 5). If ℓ c maximize G inc , i.e.

ℓ c = ℓ, after initiation:    G(ℓ c ) = G inc (ℓ c ) = G c , dG(ℓ) dℓ < 0 ∀ℓ > ℓ c . (3)
As a consequence, stable crack propagation occurs after initiation. Otherwise, if ℓ c is smaller than ℓ, after initiation:

   G(ℓ c ) > G inc (ℓ c ) = G c , dG(ℓ) dℓ > 0 . (4)
It means that unstable crack propagation occurs just after initiation until an arrest length ℓ arr verifying G(ℓ arr ) = G c , where ℓ arr is the arrest length schematically defined on Fig. 5.

Full-field measurement techniques such as DIC allow to have direct access to the displacement field u m , from which FE boundary conditions (BC) can be extracted. The methodology to convert u m in FE BC is detailed in Section 3.2. The FE calculation using the BC extracted from DIC thus provides σ nn before initiation, and G inc as a function of ℓ for the initiation-imposed displacement.

As a consequence, three unknowns remain: ℓ c , σ c and G c . These parameters can be determined since Eq. 2 is fulfilled at crack initiation, which provides (G c , σ c , ℓ c ) so that:

   σ c = σ nn (ℓ c ), G c = G inc (ℓ c ). with ℓ c ∈ [0, ℓ] (5)
Only crack lengths from 0 to ℓ are considered, otherwise, crack initiation at a smaller imposed displacement would be possible [START_REF] Weißgraeber | ≪ Crack Nucleation in Negative Geometries ≫[END_REF].

It must be emphasized that Eq. 5 yields an infinite number of admissible fracture parameter couples (σ c , G c ), corresponding to initiation lengths between 0 and ℓ. As a consequence, the sole knowledge of the initiation loading is not sufficient to determine both the tensile strength and critical energy release rate, which requires additional data. It is not trivial to measure ℓ c experimentally since, in most configurations, unstable crack propagation follows crack initiation.

However, the arrest crack length after unstable crack propagation can be measured experimentally and compared to that obtained using the CC, ℓ arr (see Fig. 5). Finally, the final stable crack propagation can also be used to determine the material critical energy release rate based on LEFM crack propagation condition G(ℓ exp ) = G c , where ℓ exp is the crack length measured experimentally.

It is done by calculating the energy release rate using the displacement measured using DIC as BC.

Ultimately, coupling DIC with a full-FE implementation of the CC amounts to:

Influence of the boundary conditions

DIC provides the displacement fields at the surface of the specimen, from which BC of the FE model can be determined. In the literature, different approaches are used to extract BC from displacement fields obtained by DIC. The displacement acquired over the contour of a given ROI can be used. Such an approach has been implemented by Fedele et al. [START_REF] Fedele | ≪ Identification of Adhesive Properties in GLARE Assemblies Using Digital Image Correlation ≫[END_REF] to determine CZM parameters from a debonding test. The ROI was two orders of magnitude smaller than the corresponding experimental testing sample (i.e. ROI dimensions in the order of the millimeter). DIC displacements inside the ROI were incorporated in the material parameter identification algorithm objective function. Similarly, Vargas et al. [START_REF] Vargas | ≪ Comparison of two full-field identification methods for the wedge splitting test on a refractory ≫[END_REF] prescribed BC on a ROI contour and compared the resulting displacement field to the full-field results inside the ROI to determine elastic properties using a finite element model updating approach. In both approaches, the BC are applied along a closed contour. Another approach is to apply BC in the FE model at the same position where the testing apparatus applies loading on the testing sample. However, these exact locations might not be encompassed by DIC. To tackle this issue, Vargas et al. used a local measurement of WST notch opening displacement to extrapolate the BC [START_REF] Vargas | ≪ On the Calibration of Cohesive Parameters for Refractories from Notch Opening Displacements in Wedge Splitting Tests ≫[END_REF]. This extrapolation was made after a relationship was established in a previous study [START_REF] Vargas | ≪ Fracture Energy Evaluation of Refractories in Wedge Splitting Tests from Notch Opening Displacements ≫[END_REF] between the notch opening displacement (NOD) and the crack mouth opening displacement (CMOD), on a test where both locations were encompassed by DIC. Then, the CMOD was applied as BC. Using such an approach, they identified fracture energies in agreement with reference values from experimentally determined work of fracture.

To assess the influence of the type of BC on the determination of fracture parameters, a parameter study is conducted. Three different BC application methodologies are tested, namely:

• the point method is the direct application of u pm , the displacement at the contact between the testing apparatus and the sample. This displacement is directly measured from the DIC displacement (see Fig. 6 -a).

• the contour method consists of applying BC along a contour taken inside the sample, near the sample free edges. This displacement data is denoted u con . The BC are directly extracted from DIC. The contour is defined by a parameter δ, which defines the distance of the contour from the sample outer edges. Polynomial interpolations convert these discrete values into a continuous contour displacement.

• the adjusted point method (AP method ) is the BC application of a displacement u ap at the contact between the sample and the apparatus, i.e. as for u pm . However, u ap differs from u pm , since a gradient descent algorithm is used to determine the value of u ap that results in a contour displacement as close as possible from u con .

The reliability of the three methods is evaluated by generating virtual experimental data from a numerical FE simulation. A point displacement u ref is imposed at the contact location between the wedge and the specimen, which enables calculating σ nn and G inc that will be considered as reference values for the analysis. These values will thus be referred to as σ ref nn and G ref inc .

Point method

In the absence of DIC acquisition noise, point method should provide the actual displacement at the contact between the wedge and the specimen. DIC acquisition noise has been estimated as explained in Section 2.3. In addition to DIC noise, an error can be committed on wedge-specimen contact coordinate identification from DIC data. Wrong identification of the contact zone can cause an error up to 0.4 pixels, or 3.2 µm, i.e. twice the DIC acquisition noise. There is no acquisition noise in the virtual experiments, thus the point method provides the reference configuration.

Contour method

In the current section, the influence of the choice of contour is assessed. Different contours are extracted from the reference configuration, with varying δ (see Section 3.2). Then, gaussian noise is added to the displacement on the contour. The normal distribution associated with this noise exhibits a mean value of 0 and a standard deviation equal to 2 %, which is the ratio between the DIC acquisition noise (see Section 2) and the maximum observed opening displacement. The resulting displacement is applied as BC in different simulations. The opening stress and incremental energy release rate are computed. Fig. 7 shows the variation of

|G inc -G ref inc | max(G ref inc ) and |σnn-σ ref nn | max(σ ref nn )
for increasing δ, i.e. for a contour defined further and further from the specimen free edges. In this figure, the crack length is normalized by the maximum computationally admissible crack length, i.e. W -a -δ (see Section 2 for definitions of a and δ). The computation of σ nn is in good agreement with the reference configuration (Fig. 7 -c). It can be observed a slight influence of δ on the opening stress, even though the maximum relative observed error, i.e. for short crack lengths and δ = 0.0 is only 1.8 %. The error made on G inc is larger, as shown on Fig. 7 -a & b. Indeed, the relative error becomes larger than 5 % as soon as

|G inc -G ref inc | max(G ref inc )
is larger when δ is increases, i.e. when the subdomain size becomes smaller.

Consequently, using the contour method, CC resolution is expected to remain accurate for crack length smaller than 2 % of the sample ligament. As explained in Section 3.1, provided that full-field data are acquired at crack initiation (thus fulfilling the CC), FE model allows the determination of σ c -G c corresponding to ℓ c smaller than ℓ. Fig. 8 shows the evolution of ℓc W -a-δ as a function of Irwin's length E ′ .Gc σc 2 with E ′ = E 1-ν 2 . The critical value ℓc W -a-δ = 0.02 corresponds to ℓ mat ≈ 2 mm, with Young's modulus E and Poisson's ration ν equal to 2200 MPa and 0.37 respectively. The inequality ℓ mat < 2 mm assesses that no methodological bias comes from the contour method in the study of crack initiation from full-field data. ℓ mat is a priori unknown for the PMMA under study since G c and σ c are both to be determined. However, it is in the range of tens of µm [START_REF] Doitrand | ≪ Comparison between Cohesive Zone and Coupled Criterion Modeling of Crack Initiation in Rhombus Hole Specimens under Quasi-Static Compression ≫[END_REF].

Adjusted point method

To assess the efficiency of the AP method, the displacement applied in the reference configuration is corrupted by noise following a normal law with a standard deviation equal to 12.5 %, which overestimates the actual error. Note that virtual tests were also conducted with a noise having a standard deviation similar to the one applied when assessing the contour method noise robustness, see Section 3. . This value is chosen to assess the efficiency of the method. The resulting displacement along a contour as defined for the contour method is extracted. Then, the input displacement is iteratively adjusted using a gradient descent algorithm to minimize in a least-squares sense the difference of the displacement taken along the contour when the reference and corrupted BC are applied. This procedure is repeated 5 times to evaluate statistical effects.

Fracture property identification

In the present section, the three methods depicted in Section 3 for fracture parameter identification are compared on five experimental WST (sample geometries given in Table 2).

Reference configuration

To compare the methods relying on the use of DIC BC in a FE model, reference values for G c and σ c are first determined from 3PB tests on notched (SENB) and plain beams. The dimensions of the plain beams can be found in Table 3, whereas SENB dimensions are given in Table 4. The bending sample dimensions are close to the WST sample dimensions, allowing to perform the bending tests with the same load cell and the same loading rate. For each testing sample type, an inverse identification routine based on the CC is conducted (see [START_REF] Doitrand | ≪ Determination of interface fracture properties by micro-and macro-scale experiments in nacre-like alumina ≫[END_REF]

Crack process

The DIC data can be divided into four categories: in the linear elastic regime, at crack initiation, during unstable crack propagation that follows crack initiation, and finally during stable crack propagation, if any. The presence of stable crack propagation is required to identify a single G c value (see Section 3). The transition between unstable and stable crack propagation can be arduous to determine optically. Consequently, for each DIC frame after crack initiation, FE simulations are conducted to determine G c from crack propagation. Similarly to FE simulations for crack initiation assessment, the BC are extracted from the displacement fields measured using DIC on a contour and the corresponding ERR is calculated. Since stable crack propagation occurs at this stage, the obtained ERR provides an estimate of the material critical ERR. For sample S 3 , G c equals 400 J.m -2 . For this value, the CC does not predict crack initiation, thus, no σ c can be determined. The determined strength value strongly diverges from the tensile strength value estimated with 3PB (i.e. relative error of -59%). However, stable crack propagation is adequately modeled with the point method, as the error lies below 2 %. Computing the crack arrest lengths linked to G inc and G determined at crack initiation also allows to define upper and lower bounds for G c as explained in Section 3.1. The computation of G from crack initiation gives G c (ℓ arr ) equal to half the reference value.

Contour Method

An example of applied displacement u conx and u cony (see Fig. 6 for the axis definition) at crack initiation with δ = 0.5 mm can be found on Fig. 12 -a thus the effect of u cony dominates over u conx . Results from the fracture parameter identification using the contour method are presented in Fig. 11 -b. This method gives G c = 337 ± 101 J.m -2

and σ c = 135 ± 32 MPa, see the green hatched rectangle on Fig. 11 -b. As for the point method, the contour method allows for an acceptable determination of G c (i.e. relative error of 6 %). However, the contour method identifies a strength value with a relative error of 16 %, which is almost 4 times lower than the error committed using the point method. This behavior can be explained by the displacement field on the surface sample, and especially the displacement observed near the wedgesample contact. gives an incremental energy release rate one order of magnitude below the reference G c .

Adjusted point method

It can be observed from Fig. 13 that the AP method results in a contour displacement closer to the one from the contour method with respect to the point method. The AP method gives 307 ± 23 J.m -2 and 74 ± 28 MPa for G c and σ c respectively (see the green hatched rectangle on Fig. 11 -c), which corresponds to relative errors of -3 % and -36 % respectively as compared to the reference values identified in bending. For similar reasons as the point method (see Section 4.3), the AP method fails to predict accurately the strength. However, the AP method gives a better G c determination with respect to the two other methods, by reducing the scattering in the results.

As for the point method, G c determined from crack initiation is half the reference value.

Discussion

Influence of the sample geometry

Two sets of notch radii have been tested (see Table 2). Under the present testing condition, this difference in notch radii does not have an influence on F init . It seems, however, to have an influence on the determination of fracture parameters when crack initiation BC are applied. Indeed, Fig. b,c show that the values determined for samples with larger notch radii (S 3 , S 4 , S 5 ) are systematically lower than values determined for samples with smaller notch radii. As the notch radius difference is accounted for in the FE models, fracture parameter identification should be insensitive to this parameter. Thus, this difference might be explained by the FE model, which does not account for the presence of a process zone ahead of the notch tip. Moreover, this difference might also emphasize a limitation of the 2D model, i.e. the measured BC may not be constant along the sample thickness, and/or the laser cutting process may have resulted in non-parallel faces.

It is in agreement with results reported by Vargas et al. [START_REF] Vargas | ≪ On the Calibration of Cohesive Parameters for Refractories from Notch Opening Displacements in Wedge Splitting Tests ≫[END_REF]. They reported a 10 % variation in the computation of G c and σ c if evaluated from the front or the back face on centimeter size refractories using DIC, WST, and CZM. The testing apparatus used in the present study does not allow for in-situ image acquisition on both faces. The determination of σ c considering only samples with small notch radius and using the contour method gives a relative error on the strength of 3 %. It is 10 times lower than the error committed when considering samples with a big notch radius.

Nevertheless, the difference in notch radii does not have an influence on G computed with BC taken from stable crack propagation.

Full-field data

Virtual experiments performed in Section 3 enabled determining the validity of the different approaches tested to apply boundary conditions. Defining BC by extracting displacements over a contour remains valid to calculate the stress and the IERR provided the crack length remains small with respect to the contour width. Otherwise, the applied BC provides an erroneous estimate of the IERR and ERR. As a consequence, the contour method based on the displacement field measured by DIC just before initiation is accurate for crack initiation assessment since the obtained initiation crack length is small. Nevertheless, the crack arrest length cannot be estimated using the BC based on the displacement field measured just before initiation but requires using the displacement field measured after unstable crack propagation following initiation. The difference in fracture properties obtained using either the point or adjusted point methods compared to the reference fracture properties may indicate that the way the BC are applied in these FE models is not representative of the actual BC applied to the specimen. As a consequence, the choice of the applied BC appears to be crucial for inverse identification of fracture properties based on crack initiation results. A way to better estimate the BC would consist in measuring the displacement fields on the two opposite specimen surfaces, as sample asymmetry (possibly arising from the sample cutting process) or misalignment of the sample with respect to the wedge and the pin (see Fig. 2) could induce a non-constant displacement variation through the sample thickness.

Comparison between the methods

Table 5 sums up the identified parameters from the different methods. Among all methods, the contour method provides the best agreement with the reference values. The adjusted point method improves the point method as it gives more reliable results on the determination of σ c , even though the determined value is lower than the reference one. It should be noted that the AP method decreases the dispersion of the results with respect to the other methods, especially on the critical incremental energy release rate.

Conclusion

Boundary conditions from displacement fields measured by DIC during a WST can be implemented by a pointwise application at the wedge-specimen contact location or through application at the contour of a subdomain. While there is no a priori crack size limitation for the former, the latter is valid provided the initiation length remains small enough compared to the subdomain size. Based on the measured BC just before crack initiation, the CC provides admissible strength and critical ERR couples corresponding to initiation lengths smaller than the initiation length maximizing the incremental ERR. Among these admissible fracture properties, the optimal couple can be selected by measuring the critical ERR during stable crack propagation. Both pointwise or contour BC application provides critical ERR estimate close to that measured based on three-point bending specimen testing. The contour BC application also provides an accurate estimate of the material tensile strength, whereas it is underestimated using a pointwise BC application. Finally, an accurate modeling of boundary conditions seems to be of primary importance for a reliable determination of fracture parameters using the CC.

Aknowledgement

Figure 1 :

 1 Figure 1: Schematic of (a): WST specimen with dimensions in the range of hundreds of millimeters. The wedge pushes two rollers that generate a mode I loading; (b): WST specimen at the millimeter scale with the wedge being in direct contact with the specimen.

Figure 2 : 5 Figure 3 :

 253 Figure 2: Tested sample, wedge, and pin from the testing apparatus. The scale bar is 1.5 mm long.

100Figure 4 :

 4 Figure 4: (a): Displacement and (b) strain fields at the surface of specimen S2 just before crack initiation.

Fig. 5 Figure 5 :

 55 Figure 5: Schematic explanation of the coupled criterion when used with DIC. Ginc and σnn normalized by their respective critical values as a function of the crack length. As the BC of the FE model corresponds to a situation of crack initiation, each couple Ginc-σnn is a possible Gc-σc couple if ℓ < ℓ. G and Ginc define the minimum and maximum crack arrest lengths up to which unstable crack propagation happens.

Figure 6 :

 6 Figure 6: Graphical illustration of: (a) the point method boundary condition extraction, where the three white points represent the location where BC are extracted. (b) the contour method boundary condition extraction. The exact displacement values are taken at DIC mesh nodes along a contour that encompasses the notch (dashed white line).

Figure 7 :

 7 Figure 7: Variation of (a-b) the IEER and (c) the stress relative error as a function of the normalized crack length for different contour sizes, with a zoomed view on errors below 5 %.

ℓW

  -a-δ > 0.02. Moreover, it can be noticed that contrary to |σnn-σ ref nn | max(σ ref nn ) where deviation from the reference values decreases with increasing δ, deviation of

Figure 8 :

 8 Figure 8: Evolution of the normalized critical crack length ℓc W -a-δ as a function of ℓmat.

2 . 2 .

 22 For this noise level both G inc

Fig. 9 W

 9 -a-δ for one of the tests. The presented configuration is the one showing the highest deviation with respect to

Figure 9 :

 9 Figure 9: Assessment of the AP method in the computation of (a) G inc G ref inc

  for methodology details) leading to different G c -σ c relationships. The reference values G ref c and σ ref c are determined as the values fulfilling both relationships from plain and SENB samples. The G c -σ c relationships obtained for each specimen evidence experimental scattering, thus an average G c -σ c relationship is calculated among all samples of a given geometry. It gives G ref c = 318 ± 77 J.m -2 , and σ ref c = 116 ± 5 MPa.

Fig. 10 (Figure 10 :

 1010 Figure 10: (a) Evolution of Gc and ℓexp with time after crack initiation computed with the contour method for samples S2 and S3 ,in solid and dashed line respectively. (b) Comparison of the computation of Gc on sample S5 for the contour and point methods.

4. 3 .

 3 Point MethodResults from point method parameter identification are shown in Fig.11 -a. The diamond markers show the G c values determined with stable crack propagation BC. The point method gives G c = 324 ± 84 J.m -2 and σ c = 40 ± 22 MPa, see the green hatched rectangle on Fig. 11 -a.

5 Figure 11 :

 511 Figure 11: Parameter identification results. Solid lines depict the results obtained from studying the crack initiation. The unique value extracted from the crack propagation study is depicted with a diamond marker. The green hatched zones represent the identified Gc and σc for each method, i.e. maximum and minimum values. The reference values are represented by the red-hatched zones.

Figure 12 :

 12 Figure 12: Displacement along S4 contour for δ = 0.5 mm.

Figure 13 :

 13 Figure 13: Displacement applied as BC in contour method (solid line), displacement along the same contour resulting from point method (dashed line) and AP method (dotted line), (a) at crack initiation; (b) during stable crack propagation.

  This work was supported by the LABEX MANUTECH-SISE (ANR-10-LABX-0075) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). Moreover, we thank the French Ministry of Education and Research for funding this work, through a PhD scholarship. Finally, we thank the GM-Factory (Univ Lyon, INSA Lyon) for laser-cutting our sample.

Table 1 :

 1 List of variables and associated units used in the article.

	Variable	name

Table 2

 2

	, i.e. with L, H,

Table 2 :

 2 Sample geometrical dimensions and experimental forces at crack initiation.

Table 3 :

 3 Sample L (mm) W (mm) B (mm) F init (N) Sample geometrical dimensions and force to failure for plain specimens in bending.

	3P B 1	14.95	4.3	2.91	438
	3P B 2	15.06	3.2	2.95	417
	Sample L (mm) W (mm) B (mm) e (mm) F init (N)
	3P B n 1	14.8	3.49	2.90	0.594	46
	3P B n 2	14.95	3.54	2.90	0.604	52
	3P B n 3	15.07	3.2	2.97	0.692	58

Table 4 :

 4 Sample geometrical dimensions and force to failure for notched specimens in bending.

  Methodσ c (MPa) G c (J.m -2 )

	3PB	116 ± 5	318 ± 77
	point	48 ± 36	324 ± 84
	contour	135 ± 31	337 ± 92
	adjusted point	74 ± 28	307 ± 23

Table 5 :

 5 Couples σc-Gc identified for all the presented methods.

This noise is assessed prior to WST by acquiring images of the sample without applying any load.