Louwanda Lakiss

Jean-Pierre Gilson

Valentin Valtchev

Svetlana Mintova

Alexandre Vimont

Robert Bedard

Suheil Abdo

Jeffery Bricker

Probing the Brønsted acidity of the external surface of Faujasite type zeolites

Keywords: Faujasite, Triphenylphosphine oxide, 2, 4, 6 Tri-tert-butylpyridine, phosphorous NMR spectroscopy, Infrared spectroscopy

We outline two methodologies to selectively characterize the Brønsted acidity of the external surface of FAU-type zeolites by IR and NMR spectroscopy of adsorbed basic probe molecules. The challenge and goal are to develop reliable and quantitative IR and NMR methodologies to investigate the accessibility of acidic sites in the large pore FAU-type zeolite Y and its mesoporous derivatives often referred to as ultrastable Y (USY). The accessibility of their Brønsted acid sites to probe molecules (n-alkylamines, n-alkylpyridines, n-alkylphosphine-and phenylphosphineoxides) of different molecular sizes is quantitatively monitored either by IR or 31 P NMR spectroscopy. It is now possible, for the first time to quantitatively discriminate between the Brønsted acidity located in the microporosity and on the external surface of large pore zeolites.

 )

 )

 ) but it is often challenging to prove that either reactants, intermediates or some products do not penetrate their microporosity at reaction temperatures.

 ) So far, all methodologies describing the acidity of the external surface of zeolites fail when applied to the FAU structure, in its purely microporous form (Y) and even more on its mesoporous derivatives (USY). A 31 P NMR study of rare earth zeolite Y using TMPO and TBPO reported that TBPO does not access zeolite Y microporosity and estimated its concentration of external acidic sites at 120 µmol/g, i.e. about 3 % of the total acid sites.( 45 ) However, this zeolite, with a Si/Al ratio of 3.7, was certainly dealuminated, i.e. already possessed some mesoporosity as well as extraframework species potentially restricting the accessibility of some probe molecules; this could raise doubts on the accessibility of TBPO to the native microporosity of zeolite Y.

The FAU type structure is by far the most widely used zeolite in industrial processes: i) the so-called Y or USY (Si/Al  2.5) mostly as a catalyst (Hydrocracking, Fluid Catalytic Cracking [FCC], Aromatics alkylation...) ( 6 ), ii) the so-called X (Si/Al  1.0) mostly as an adsorbent (aromatics separations…). Its crystalline structure, made of sodalite

INTRODUCTION

Zeolite catalysts are currently widely used in oil refining and petrochemical processes and their applications are set to grow further in these classical and other more emerging applications. [START_REF] Rigutto | Introduction to Zeolite Science and Practice[END_REF][START_REF] Kulprathipanja | Zeolites in Industrial Separation and Catalysis[END_REF][START_REF] Marcilly | Acido-Basic Catalysis -Application to Refining and Petrochemistry[END_REF][START_REF] Sheldon | Fine Chemicals Through Heterogeneous Catalysis[END_REF][START_REF] Ennaert | Potential and challenges of zeolite chemistry in the catalytic conversion of biomass[END_REF][START_REF] Vermeiren | Impact of Zeolites on the Petroleum and Petrochemical Industry[END_REF] ) Their high surface areas and micropore volumes, tunable acidity, active sites located in confined spaces, unique shape selectivity and many other easily adjustable properties make them often the catalysts or adsorbents of choice for various industrial processes. [START_REF] Kulprathipanja | Zeolites in Industrial Separation and Catalysis[END_REF][START_REF] Marcilly | Acido-Basic Catalysis -Application to Refining and Petrochemistry[END_REF][START_REF] Sheldon | Fine Chemicals Through Heterogeneous Catalysis[END_REF] ) These desired properties come at a price, internal mass transport limitations lowering their potential catalytic performances,( 7 ) although such limitations can also be effective tools to engineer unique selectivities. [START_REF] Chen | Molecular Transport and Reaction in Zeolites[END_REF] The interplay between internal mass transport and chemical kinetics in zeolite catalysis is often described using the Thiele modulus (Φ) approach.( 7 ) However, as it explicitly does not take into account the external surface of zeolites, the approach might become less relevant when effective particle size decreases during top-down (biased or unbiased demetallation generating intracrystalline mesoporosity) or bottom-up (direct synthesis of nanosized zeolite crystals generating intercrystalline mesoporosity) hierarchization procedures.( 9) When the external surface of zeolites, where confinement differs from inside the microporosity, is explicitly taken into account in computing the Thiele modulus, it was shown recently that its effect on catalyst effectiveness (η) decreases.( 10) Although impressive advances in the last few years enabled a better description of the micro-and meso-porous volumes and surfaces of zeolites by physisorption of cages (cuboctahedral units) linked by hexagonal prisms (double six rings), generates a microporosity in supercages of about 1.2 nm in diameter accessible to relatively bulky molecules; ( 60 ) the sodalite cages remain inaccessible to most probe molecules unless opened by chemical treatment. ( 61) As-synthesized Y zeolite is usually in its sodium form and acidity generated by ammonium exchange(s) followed by calcination(s). During calcination, partial dealumination and/or amorphisation can occur. Zeolite Y is often dealuminated by steaming at high temperatures and/or acid leaching to prepare a more stable form, the so-called ultrastable Y (USY). During this process, some aluminum is expelled from the framework and mesoporosity added to its native microporosity creating a hierarchical material, provided microand meso-porosity are sufficiently connected. The acidic (number, strength, location, accessibility, distribution…) and textural properties of the zeolite are therefore modified during this process. In particular, the confinement in a significant proportion of acid sites will change as the microporosity will decrease and intracrystalline mesoporosity will be added, i.e. the internal/external acidity ratio will increase. This ratio is also substantially increased, with the formation of intercrystalline mesoporosity, when small crystals (< 100 nm) of zeolites are synthesized, the so-called nanozeolites.( [START_REF] Mintova | Advances in nanosized zeolites[END_REF][START_REF] Awala | Template-free nanosized Faujasite-type zeolites[END_REF] In IR spectroscopy, the preferred methodology to quantify acid properties, the stepwise addition of calibrated doses of a basic probe molecule is the norm. It is however a challenge to find suitable probe molecules (liquid with a vapor pressure of about 0.1 torr) not entering the zeolite Y microporosity due to the dimension (0.74 nm) of the windows (12 MR, twelve T atoms delineating a ring) leading to its supercages. Two criteria need consideration when selecting such suitable probe molecules: their kinetic diameter and the adsorption temperature. A trusted rule of thumb states that molecules with a kinetic diameter 20 % larger than a zeolite pore will enter the porosity as temperature increases.( [START_REF] Kunkeler | The use of Bulky Molecules as Probes for Investigating the Contributions of the External and Internal Pore-wall Activities of Zeolite Catalysts[END_REF][START_REF] Van Koningsveld | Single crystal structure analysis of zeolite H-ZSM-5 loaded with naphthalene[END_REF] ) Accordingly, a molecule probing the external surface of FAU type structures should have a kinetic diameter superior to 0.9 nm. ( 55 ) 2,4 dimethylquinoline (2,4 DMQ) is a potential candidate and was already used to probe the external acidity of some zeolites.( 31 ) As it accesses, at 423 K, the microporosity of BEA and FAU structures, lowering its adsorption to room temperature might prevent or significantly delay its diffusion in the FAU microporosity.

We screened other basic molecules using these criteria to monitor the FAU external surface acidity by IR (2,4 dimethylquinoline [DMQ, 0.91 nm], 2,6 di-tert-butylpyridine [DTBPy, 0.8 nm], 2,4,6 tri-tert-butylpyridine [TTBPy, 1.1 nm]) or [START_REF] Corma | 2, 6-Di-tert-butyl-pyridine as a probe molecule to measure external acidity of zeolites[END_REF] P NMR (triphenylphosphine oxide [TPhPO, 1.1 nm]) spectroscopies. In addition, as trimethylamine (TMA) was already used to measure the strength of acid sites in zeolite Y, we selected two bulkier alkylamines (tributylamine [TBA, 1.1 nm] and trihexylamine [THA, 1.3 nm]). 30 The more classical probes, Pyridine (IR) and TMPO (NMR) were used to quantify the maximum accessible acidity of zeolite Y and its USY derivatives. These probe molecules along with some selected properties are described in Table S.1.

EXPRIMENTAL SECTION

Three commercial zeolites were investigated: i) Y: LZY-64 supplied by UOP, ii) USY's: CBV720 and CBV760 purchased from Zeolyst. Some typical physicochemical properties are summarized in Table 1. USY's are typical of steamed (CBV720) and steamed/acid leached (CBV760) Y zeolites. Their Si/Al ratios range from 2.3 to 28 and they differ significantly by their acidic and textural properties. As expected, USY's display higher mesoporosity than their Y parent.

Probe molecules with different sizes and basicities, namely Pyridine (Py, 99.8 %), 2,6 Di-tert-butylpyridine (DTBPy, >97 %), 2,4 Dimethyl quinoline (DMQ, 95%), Tributylamine (TBA, 99.5 %), Trihexylamine (THA, 96 %) and 2,4,6 Tri-tert-butylpyridine (TTBPy, 99%) were purchased from Sigma-Aldrich and used without further purification.

With the exception of Py, DTBPy and TTBPy, the molar absorption coefficients of bands characteristic of the protonated probe molecules were not determined. Instead, the Brønsted acid site concentrations were measured by integrating the (OH) bands at 3630 cm -1 (OH HF , located in the supercages) and 3550 cm -1 (OH LF , located in the sodalite cages) before and after adsorption of the probe molecules. Their respective molar absorption coefficients ( OH HF = 6.76 cm.mol -1 and  OH LF = 5.39 cm.mol -1 ) were determined, very accurately, earlier in a homemade setup (AGIR), by monitoring simultaneously weight gains/losses on a thermobalance (AG) fitted with a cell recording the IR spectra of the adsorbed probes.( 24)

IR spectra were recorded with a Nicolet Magna 550-FT-IR spectrometer at 4 cm -1 optical resolution. Prior to the measurements, the zeolites were pressed into self-supporting discs (diameter: 1.6 cm, 18 mg) and pretreated in the IR cell attached to a vacuum line (10 -6 Torr), first at 393 K for 2 hours followed by a ramp to 723 K (3 K /min) held for 2 h. The adsorption temperature of Pyridine (1 torr at equilibrium) and 2,6 Di-tert-butylpyridine (0.2 torr at equilibrium) were 373 K and 423 K, respectively. DMQ, TBA, THA, and TTBPy (0.1-0.2 torr) adsorptions were performed at 298 K. After equilibration with the probe molecules, the cell was outgassed to remove the physisorbed species. All spectra were normalized to the same mass (20 mg wafers). The amounts of pyridine adsorbed on the Brønsted and Lewis acid sites were determined by integrating the area of the characteristic bands corresponding to pyridinium ions (1545 cm -1 ) and coordinated pyridine (1454 cm -1 ) using their respective molar absorption coefficients (1545 =1.35 and 1454 = 1.8 cm.mol -1 ).( 24) As TTBPy is solid at room temperature (melting point: 343 K and boiling point: 393 K), an alternative procedure was followed for its adsorption. A self-supported wafer of solid TTBPy was first prepared and transferred to a small calibrated volume enclosed between 2 valves in the IR cell (Figure S1). After evacuation under vacuum, this volume is isolated during the activation of the zeolite; the valve is then opened to start the TTBPy adsorption.

A homemade cell was used to perform the NMR experiments (Figure S.2). As outlined above, two different molecules were selected: i) Trimethylphosphine oxide (TMPO) to access both the internal and external acidity, ii) Triphenylphosphine oxide (TPhPO) to access only the external acidity. The samples were first dehydrated under vacuum (10 -6 Torr) at 723 K (reached at 3 K /min) for 2 h, a solution of TMPO (4 mmol/l) or TPhPO (0.4 mmol/l) in CH 2 Cl 2 then poured on the zeolite in a glove box filled with argon and equilibrated for 15 min under ultra-sonication. The cell was then connected to a vacuum line (Pressure = 10 -4 torr) and evacuated at 298 K for 2 hours, the product recovered transferred to an argon filled glove box and loaded in an NMR rotor. The NMR spectra were recorded on a Bruker Avance 500 and the samples spun at the magic angle at a frequency of 12 kHz with a single pulse width of 8.5 µs and a recycle delay of 10 s. The 31 P chemical shifts were measured relative to an aqueous H 3 PO 4 (85 %).

RESULTS AND DISCUSSION

Adsorption of basic probe molecules monitored by IR

Internal and external acidity of the FAU structure: Pyridine (Py)

Figure1a shows the IR spectra of LZY-64 activated at 723 K before and after pyridine adsorption. After activation, three absorption bands are observed in the (OH) region:

-3740 cm -1 : silanol groups -3640 cm -1 and 3545 cm -1 : bridging hydroxyl groups (Brønsted acid sites, BAS) respectively located in the supercages (OH HF ) and sodalite cages (OH LF ).

After pyridine adsorption and evacuation at 523 K, the supercages BAS (3640 cm -1 ) disappear almost completely while those in the sodalite cages (3545 cm -1 ) are unaffected, Figure 1. The number of BAS determined by this procedure is reported in Table 2. As expected, the majority of acidic sites accessible to pyridine are located in the supercages (1260 µmol/g) and the proportion of acidic sites accessible to pyridine in sodalite cages is negligible. The difference in the number of acid sites estimated by IR and [START_REF] Vimont | Analysing and understanding the active site by IR spectroscopy[END_REF] Si NMR for LZY-64 is a direct consequence of the presence of residual sodium cations (ca. 3 % determined by ICP analysis). The ACI of pyridine in LZY-64 is 0.4 and implies that only 40% of the acidic sites, all located in in the supercages, are accessible to molecules with a kinetic diameter of about 0.55 nm.

The same procedure is applied to CBV760, Figure 1b. In contrast to LZY-64, the acidic sites in the sodalite cages become accessible to pyridine as both OH HF and OH LF bands disappear after pyridine adsorption. While the number of Brønsted acid sites is much lower on CBV760, their accessibility to pyridine is higher (0.5), although the presence of extraframework aluminum could hinder access to some acid sites. The Brønsted acid site concentration expected from the [START_REF] Vimont | Analysing and understanding the active site by IR spectroscopy[END_REF] Si NMR derived framework composition (520 µmol/g) is significantly higher than those detected (320 µmol/g) and accessible (240 µmol/g) by IR spectroscopy.( 65 This bulky molecule (kinetic diameter: 0.8 nm) is already used to probe the external acidity of different zeolite types such as MOR, ZSM-5.( [START_REF] Corma | 2, 6-Di-tert-butyl-pyridine as a probe molecule to measure external acidity of zeolites[END_REF][START_REF] Gora-Marek | 2,6-Di-tert-butylpyridine Sorption Approach to Quantify the External Acidity in Hierarchical Zeolites[END_REF] ) However, on LZY-64 and CBV760, the OH HF band (supercages) decreases upon DTBPy adsorption and evacuation at 523 K, while the OH LF (sodalite cages) remains intact or slightly broadened, Figure 2. New bands appear at 3360, 1616 and 1530 cm -1 , characteristic of protonated DTBPy. The IR spectra of LZY-64 after exposure to DTBPy for 0-64 minutes are shown in Figure 3a and the variation of the integrated intensity of the 3360 cm -1 band (DTBPyH+) with the amount of OH HF consumed (molar absorption of 6.76 µmol cm -1 ) in Figure 3b. An excellent linear correlation (r 2 = 0.99) with a zero intercept allows to calculate the molar absorption coefficient ( 5.22 cm.µmol -1 ) of the 3360 cm -1 band of DTBPyH + assuming DTBPy adsorbs specifically on OHHF. The resulting number of acidic sites (1013 µmol/g) probed by 2,6 DTBPy is reported in Table 3.

While this demonstrates an expected lower accessibility of DTBPy than Py to both LZY-64 and CBV760 acid sites, DTBPy nevertheless interacts with internal acidity, including sodalite cages in CBV760. Therefore it cannot be considered a suitable probe for the external surface of FAU structures. External acidity of the FAU structure: a quest for the right molecule n-Tributylamine (TBA), 2,4 dimethylquinoline (DMQ), n-trihexylamine (THA) and 2,4,6 tri-tert-butylpyridine (TTBPy) are selected as their adsorption/diffusion in the microporosity at 298 K might become slow enough to discriminate between internal and external acidity during IR monitored uptake experiments. As discussed above, the amount of adsorbed probe molecules is determined by following the consumption of the OH bands (molar absorption coefficients from Ref. 24) assuming one probe molecule adsorbs per acid site. Figure 4 shows the disappearance of the OH HF (3640 cm -1 ) band of LZY-64 as a function of (t = exposure time, in s) at 298 K for these candidates. Except for TTBPy and THA, a monotonous uptake of the probe molecule is observed.

DTBPy, often used to probe the external acid sites of large pore zeolites (MOR, BEA…) zeolites, enters the microporosity of LZY-64, and reaches about 16 % of the acid sites within 20 min. Both TBA and DMQ behave similarly, albeit slower. DMQ, for instance reaches 16 % of the acidic sites, after 1 hour at 298 K. THA on the other hand first adsorbs slowly, reaching a plateau after consuming about 2 % of the acid sites, to finally reach 14 % of the Bronsted sites after 2 hours. The plateau corresponds to the expected quantity of THA adsorbed on the external surface sites, in good agreement with earlier computed geometric external surface of zeolite Y.( 67 ) In the case of this particular LZY-64, its geometric surface evaluated assuming spherical crystallites (500 nm diameter) and no Al zoning, as described elsewhere, ( [START_REF] Chen | Type and catalytic activity of surface acid sites of medium and large pore zeolites Their deactivation with bulky organophosphorus compounds[END_REF][START_REF] Obenaus | Generation and Properties of Brønsted Acid Sites in Bifunctional Rh-, Ir-, Pd-, and Pt-Containing Zeolites Y Investigated by Solid-State NMR Spectroscopy[END_REF] ) amounts to 10 m 2 /g, i.e. the external acid sites contribute to about 1.3 % of the total acidity, i.e. 45 µmol/g of zeolite.

In contrast to the above probes, liquid at room temperature, the TTBPy uptake is slow and progressive reaching a final plateau when about 2 % of the acid sites are neutralized (inset in Figure 4) indicating that it never accesses the microporosity at 298 K and interacts only with the external Brønsted acidity. Again, assuming that one molecule is adsorbed per acid site, the external acid sites of zeolite is estimated to 50 µmol/g. However, at a higher temperature, 373 K, TTBPy penetrates zeolite Y microporosity. In order to better quantify the TTBPy adsorbed on the BAS of the USY zeolites, with higher Si/Al, the molar extinction coefficient of its protonated form, TTBPy + , is determined, vide infra. Figure 5 shows the spectra of TTBPy vapor (a), 1 wt % TTBPy dispersed in KBr (b) and a difference spectrum i.e. the pristine LZY-64 spectra substracted form TTBPY adsorbed on LZY-64 (c). The latter displays new bands at 3365, 3350, 1612 and 1373 cm -1 . The 3365 and 3350 cm -1 are assigned to (N-H+) vibrations of protonated TTBPy.( 68 ) The molar absorption coefficient of the (N-H+) band at 3365 cm -1 is determined as for 2,6 DTBPy, vide supra. The TTBPyH + (3370-3350 cm -1 ) integrated area correlates (r 2 = 0.99) well with the intensity decrease of the OH HF , (Figure 6 b). The derived molar absorption coefficient, ε, is 5.74 cm.µmol -1 . TTBPy is also adsorbed on CBV720 and CBV760 (298 K followed by evacuation under vacuum at RT for 15 min) and compared with LZY-64 (Figure 7). This confirms that on LZY-64, as with Py and DTBPy, only the OH HF band decreases while the OH LF broadens. Table 4 summarizes the TTBPy results on the three zeolites and the associated accessibilities (ACI).

On that basis, we conclude that THA and TTBPy are suitable molecules to probe the external surface of FAU; TTBPy should be preferred as it does not enter the zeolite microporosity, even after upon prolonged exposure. LZY-64 and CBV760 zeolites are loaded with an excess of TMPO to guarantee a complete titration of all acid sites (4 mmol of TMPO/g zeolite, dissolved in 1 ml of CH 2 Cl 2 ). When all acid sites are titrated, a peak due to physisorbed (solid) TMPO emerges between 39-43 ppm and serves as an internal standard. The first is assigned to crystalline TMPO while the second is due to interaction between P=O and traces of water.( [START_REF] Zheng | 31P Chemical Shift of Adsorbed Trialkylphosphine Oxides for Acidity Characterization of Solid Acids Catalysts[END_REF][START_REF] Zheng | 31 P NMR Chemical Shifts of Phosphorus Probes as Reliable and Practical Acidity Scales for Solid and Liquid Catalysts[END_REF][START_REF] Zheng | 31P Chemical Shift of Adsorbed Trialkylphosphine Oxides for Acidity Characterization of Solid Acids Catalysts[END_REF][START_REF] Begimova | Effect of Hydrogen Bonding to Water on the 31P Chemical Shift Tensor of Phenyl-and Trialkylphosphine Oxides and α-Amino Phosphonates[END_REF] ) Figure 8 shows the 31 P NMR spectra of TMPO adsorbed on LZY-64 and CBV760. On LZY-64, three signals in the 55-80 ppm range are assigned to Brønsted acid sites.( [START_REF] Yu | Acidity characterization of rare-earth-exchanged Y zeolite using 31 P MAS NMR[END_REF][START_REF] Rakiewicz | Characterization of Acid Sites in Zeolitic and Other Inorganic Systems Using Solid-State 31 P NMR of the Probe Molecule Trimethylphosphine Oxide[END_REF][START_REF] Karra | NMR Characterization of Bronsted Acid Sites in Faujasitic Zeolites with Use of Perdeuterated Trimethylphosphine Oxide[END_REF][START_REF] Wiper | Multinuclear solid-state NMR characterization of the Brønsted/Lewis acid properties in the BP HAMS-1B (H-[B]-ZSM-5) borosilicate molecular sieve using adsorbed TMPO and TBPO probe molecules[END_REF] ) Obenaus et al. assigned the 55 ppm resonance to TMPO interacting with Brønsted acid sites in the sodalite cages, while those at 65 and 78 ppm to the Brønsted acid sites located in the supercages.( 71) The 31 P NMR spectrum of CBV760 shows similar features to LZY-64, except the 78 ppm resonance. The number of acid sites measured by TMPO in LZY-64 is therefore 3046 µmol/g showing that, as expected, TMPO interacts with almost all acid sites, including those located in sodalite cages (ACI = 0.85).

External acidity of the FAU structure: Triphenylphosphine oxide (TPhPO)

TPhPO is a bulky molecule (kinetic diameter of of 1.1 nm) previously used by Ryoo et al. to measure the external acidity of highly mesoporous MFI structures.( [START_REF] Zheng | 31 P NMR Chemical Shifts of Phosphorus Probes as Reliable and Practical Acidity Scales for Solid and Liquid Catalysts[END_REF][START_REF] Kyungsu | Directing Zeolite Structures into Hierarchically Nanoporous Architectures[END_REF] ) As it should have a highly restricted access to the zeolite Y microporosity, it is a potential candidate to interact specifically with its external acidic sites. The 31 P NMR spectrum of pure TPhPO, displays two resonances, 24 ppm and 28 ppm, assigned respectively to crystalline TPhPO and hydrated TPhPO due, as for TMPO, to interactions between P=O and traces of water as, Figure 9. Upon adsorption on LZY-64 and CBV760, its 31 P NMR spectra display three resonances around 24, 28 and 30 ppm. On -alumina, the 28 ppm resonance of adsorbed TPhPO is attributed to its interaction with Lewis acid sites (Figure S.4). However, on a zeolite, TPhPO is too sterically hindered to interact with Lewis acidic sites. By analogy with TMPO, vide supra, we assign the 28 ppm resonance to physisorbed TPhPO and the 30 ppm one to TPhPO adsorbed on Brønsted acidic sites. The amount of Bronsted sites accessible to TPhPO on LZY-64 (53 µmol/g) and CBV760 (19 µmol/g) are consistent with those obtained by IR with TTBPy, a molecule of similar size (Table 5).

CONCLUSIONS

For the first time, the Brønsted acidity of the external surface of the FAU type structure, the archetype large pore zeolite, is measured. It is quantified by titration with probe molecules monitored by readily available and proven spectroscopic techniques, IR and NMR. Some bulky but flexible molecules (Tri-hexylamine, 1.3 x 1.4 nm) access both its external and internal acidity even when adsorption takes place at room temperature while others, less flexible (Tritert-butyl pyridine and Tri-phenylphosphine oxide, both 1.1 x 1.1) probe only the external acidity. The room temperature adsorption of tri-tert-butylpyridine monitored by IR spectroscopy indicates that 2 w% (Y) and 4 w% (USY) of the total acid sites, i.e. 60 µmol/g and 20 µmol/g respectively are located on the external surface. [START_REF] Corma | 2, 6-Di-tert-butyl-pyridine as a probe molecule to measure external acidity of zeolites[END_REF] P NMR spectroscopy of adsorbed triphenylphosphine oxide (TPhPO) leads to very similar conclusions.

This advance opens the door to a more quantitative and deeper understanding of the catalytic performances of zeolites, in particular, the nanosized and hierarchical ones where the external surface plays an even more important role.( 43 ) It will participate to a better description of structure-reactivity using the Thiele modulus approach and bring more insights in the structural and chemical changes occurring during the shaping of zeolites in technical bodies as this operation affects mainly the external surface, as reported recently.( 16)

More insight is however required to establish better structure-activity correlations and design superior zeolitic catalysts. For instance, advanced NMR techniques ( 69 ) should bring more knowledge on the exact nature of the external acid sites while recent methodologies where calorimetric data are acquired together with the IR spectra of adsorbed probe molecules could provide information on the strength and the environment (confinement) of these acid

)Figure 1 .Table 2 : 5 a

 125 Figure1a shows the IR spectra of LZY-64 activated at 723 K before and after pyridine adsorption. After activation, three absorption bands are observed in the (OH) region:-3740 cm -1 : silanol groups -3640 cm -1 and 3545 cm -1 : bridging hydroxyl groups (Brønsted acid sites, BAS) respectively located in the supercages (OH HF ) and sodalite cages (OH LF ).After pyridine adsorption and evacuation at 523 K, the supercages BAS (3640 cm -1 ) disappear almost completely while those in the sodalite cages (3545 cm -1 ) are unaffected, Figure1. The number of BAS determined by this procedure is reported in Table2. As expected, the majority of acidic sites accessible to pyridine are located in the supercages (1260 µmol/g) and the proportion of acidic sites accessible to pyridine in sodalite cages is negligible. The difference in the number of acid sites estimated by IR and[START_REF] Vimont | Analysing and understanding the active site by IR spectroscopy[END_REF] Si NMR for LZY-64 is a direct consequence of the presence of residual sodium cations (ca. 3 % determined by ICP analysis). The ACI of pyridine in LZY-64 is 0.4 and implies that only 40% of the acidic sites, all located in in the supercages, are accessible to molecules with a kinetic diameter of about 0.55 nm.The same procedure is applied to CBV760, Figure1b. In contrast to LZY-64, the acidic sites in the sodalite cages become accessible to pyridine as both OH HF and OH LF bands disappear after pyridine adsorption. While the number of Brønsted acid sites is much lower on CBV760, their accessibility to pyridine is higher (0.5), although the presence of extraframework aluminum could hinder access to some acid sites. The Brønsted acid site concentration expected from the[START_REF] Vimont | Analysing and understanding the active site by IR spectroscopy[END_REF] Si NMR derived framework composition (520 µmol/g) is significantly higher than those detected (320 µmol/g) and accessible (240 µmol/g) by IR spectroscopy.([START_REF] Almutairi | Influence of Extraframework Aluminum on the Brønsted Acidity and Catalytic Reactivity of Faujasite Zeolite[END_REF]

6 Figure 2 .

 62 Figure 2. IR spectra before and after adsorption of 2,6 Di-tert-butylpyridine (DTBPy) and after evacuation at 523 K under vacuum: a) LZY-64 and b) CBV760.

Figure 3 .Table 3 .a

 33 Figure 3. a) Time evolution of the IR spectra of LZY-64 in contact with 2,6 DTBPy, b) integrated band area at 3360 cm -1 as a function of the OH HF consumed.

Figure 4 .

 4 Figure 4. Consumption of the LZY-64 Brønsted acidity as a function of the square root of exposure time , at 298 K for various basic probe molecules (inset: zoom on TTBPy).

2 Figure 5 .

 25 Figure 5. IR spectra of a) gas phase (TTBPy) in the cell (x 40), b) 1% TTBPy/KBr pellet, c) difference spectrum between TTBPY adsorbed on LZY-64 and the pristine LZY-64 (298 K).

Figure 6 .

 6 Figure 6. a) IR spectra of LZY-64 before and after 120 min contact with TTBPY vapor at 298 K, b) integrated intensity of the 3360 cm -1 band as a function of OH HF consumed.

Figure 7 .Table 4 .a

 74 Figure 7. IR spectra of TTBPy adsorbed at 298 K and evacuated under vacuum at room temperature for 15 min on a) LZY-64, b) CBV720, c) CBV760.

Figure 8 .

 8 Figure 8. 31 P MAS NMR spectra of TMPO adsorbed on a) LZY-64, b) CBV760 (*: spinning side bands). It is well established that TMPO accesses the microporosity of zeolite Y.( 46 ) The 31 P NMR MAS spectrum of pure TMPO, Figure S.3, displays two signals at 39 and 43 ppm. The first is assigned to crystalline TMPO while the second is due to interaction between P=O and traces of water.( 69,33,69,70 ) Figure 8 shows the 31 P NMR spectra of TMPO adsorbed on LZY-64 and CBV760. On LZY-64, three signals in the 55-80 ppm range are assigned to Brønsted acid sites.( 45,48,49,50 ) Obenaus et al. assigned the 55 ppm resonance to TMPO interacting with Brønsted acid sites in the sodalite cages, while those at 65 and 78 ppm to the Brønsted acid sites located in the supercages.( 71 ) The 31 P NMR spectrum of CBV760 shows similar features to LZY-64, except the 78 ppm resonance. The number of acid sites measured by TMPO in LZY-64 is therefore 3046 µmol/g showing that, as expected, TMPO interacts with almost all acid sites, including those located in sodalite cages (ACI = 0.85). External acidity of the FAU structure: Triphenylphosphine oxide (TPhPO)

Figure 9 .a

 9 Figure 9. 31 P MAS NMR spectra of TPhPO a) pure, b) adsorbed on LZY-64, c) adsorbed on CBV760Table 5. External acidity of LZY-64, CBV720 and CBV760 zeolites probed by TTBPy and TPhPO bulky basic molecules.

Table 1 . Physico-chemical properties of the parent zeolite powders

 1

	Zeolite		LZY-64	CBV720	CBV760
	Unit cell parameter (Å) a	24.7	24.3	24.2
	Si/Al Framework	b	2.3	16	28
	V Micro ( cm 3 /g) c	0.34	0.27	0.27
	V Meso ( cm 3 /g) c	0.05	0.23	0.27
	S BET ( m 2 /g) c		754	840	805
	S Ext (m 2 /g) c		60	267	261
	Crystallinity (%) d	100	70	70

a unit cell parameter; b determined by

[START_REF] Vimont | Analysing and understanding the active site by IR spectroscopy[END_REF]

Si MAS NMR; c determined by nitrogen sorption at 77K; d relative to LZY-64

Funding sources

Honeywell UOP

ACNOWLEDGMENT

Honeywell UOP for funding and permission to publish

SYNOPSIS TOC

12

sites.( 73 ) Last but not least, advances in computational modelling will become ever more helpful to better understand the role of the external surface of zeolites, the compulsory ports of entry to their micropores.( 19)

ASSOCIATED CONTENTS

Supporting Information is available free of charge via the Internet at http://pubs.acs.org : Physical properties and molecular dimensions of the basic probe molecules, schemes of the infrared and NMR cells and 31 P NMR spectra of the phosphorous based probe molecules.

AUTHOR INFORMATION

Corresponding Author * Email: jean-pierre.gilson@ensicaen.fr. * Email: suheil.abdo@honeywell.com.


Antonino Sferlazza
email: antonino.sferlazza@unipa.it

Luca Zaccarian
email: zaccarian@laas.fr

Giovanni Garraffa
email: giovanni.garraffa01@unipa.it

Filippo D'ippolito
email: filippo.dippolito@unipa.it

Localization from Inertial Data and Sporadic Position Measurements

Keywords: Localization, sampled data observer, sporadic measurements, hybrid systems

A novel estimation strategy for inertial navigation in indoor/outdoor environments is proposed with a specific attention to the sporadic nature of the non-periodic measurements. After introducing the inertial navigation model, we introduce an observer providing an asymptotic estimate of the plant state. We use a hybrid dynamical systems representation for our results, in order to provide an effective, and elegant theoretical framework. The estimation error dynamics with the proposed observer shows a peculiar cascaded interconnection of three subsystems (allowing for intuitive gain tuning), with perturbations occurring either on the jump or on the flow dynamics (depending on the specific subsystem under consideration). For this structure, we show global exponential stability of the error dynamics. Hardware-in-the-loop results confirm the effectiveness of the proposed solution.

INTRODUCTION

Navigation and localization of mobile vehicles represents an important research field witnessing significant efforts in the study of Inertial Navigation Systems (INSs) [START_REF] Hamel | Attitude estimation on SO(3) based on direct inertial measurements[END_REF]; [START_REF] Fossen | Handbook of marine craft hydrodynamics and motion control[END_REF]; [START_REF] Zhang | Mathematical model and matlab simulation of strapdown inertial navigation system[END_REF]. The growing interest in this field mainly arises from the increasing use of autonomous vehicles to accomplish certain tasks that can be dangerous or that require special effort from the human operator. However, autonomous vehicles need precise knowledge of their position and orientation for trajectory tracking or more general navigation and positioning tasks [START_REF] Fossen | Guidance and control of ocean vehicles[END_REF][START_REF] Fossen | Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs and Underwater Vehicles[END_REF]; [START_REF] Paull | AUV navigation and localization: A review[END_REF].

Most INSs are based on a 9 degrees of freedom (DOF) Inertial Measurement Unit (IMU). IMUs are indeed typically equipped with three accelerometers for the acceleration measurements in the body frame, three gyros for the measurement of the angular velocity vector, referred to as the Earth Centered Inertial (ECI) frame, three magnetometers allowing for attitude estimation, and a micro-controller in charge of processing the measurement data acquired from the above sensors. A common data fusion process is the strap-down method, consisting in transforming the body frame accelerometer measurements into inertial frame coordinates, by means of the attitude measurements (coming from the estimation of the gravity vector fused with the magnetometers) and then performing an open-loop double integration to estimate the speed and position of Research supported in part by the Agence Nationale de la Recherche (ANR) via grant Hybrid And Networked Dynamical sYstems (HANDY), number ANR-18-CE40-0010.

the vehicle [START_REF] Woodman | An introduction to inertial navigation[END_REF]; [START_REF] Zhang | Mathematical model and matlab simulation of strapdown inertial navigation system[END_REF]; [START_REF] Grip | Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation[END_REF]). It is well known that the strap-down method provides inaccurate estimates, due to the noise and sensor biases combined with the open-loop integration of the acceleration signals. In particular, drifts in the speed and position estimates must be suitably compensated. Consequently, the IMU-based INS works correctly for short time windows, but its behavior degrades rapidly as the integration time increases [START_REF] Grip | Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation[END_REF]).

In order to cope with this estimation problem, besides the IMU measurements, further position sensors are typically required. In particular, outdoor localization is based on the Global Positioning System (GPS), since it allows for tracking of a mobile object on the Earth, whenever the object can receive the satellite signals. While GPS systems are based on Time-of-Flight (ToF) algorithms, for indoor scenarios different techniques can be used, such as the Received Signal Strength Indicator (RSSI), the Time Difference of Arrival (TDoA) and the ToF distance measurements. Moreover, for indoor scenarios, many communication methods between fixed and mobile devices can be used, like WiFi networks, ultrasonic waves, optical lasers or UltraWideBand radio signals. The recent surveys [START_REF] Liu | Survey of wireless indoor positioning techniques and systems[END_REF]; [START_REF] Yassin | Recent advances in indoor localization: A survey on theoretical approaches and applications[END_REF]) describe different technologies and methods for indoor localization.

In this context, the main challenge is the sensor fusion between the inertial and position measurements coming from various sensors implementing different technologies, operating at different sampling frequencies. Several works have been published to address this challenge. For example [START_REF] Vik | A nonlinear observer for GPS and INS integration[END_REF]) presents one of the first nonlinear observers for GPS and IMU sensor data fusion. In [START_REF] Zhao | Discrete nonlinear observers for inertial navigation[END_REF]), based on contraction theory, a deterministic nonlinear observer is proposed, which takes into account the sampled-data and sporadic nature of the measurements, but using additional velocity measurements (not used in this paper). When these velocity measurements are available, a nonlinear observer for inertial navigation is proposed in [START_REF] Grip | Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation[END_REF], which uses a quaternion-based attitude representation. That work was then extended in [START_REF] Bryne | Nonlinear observer with time-varying gains for inertial navigation aided by satellite reference systems in dynamic positioning[END_REF] by introducing time-varying observer gains. Similar results relying on velocity measurements are given in [START_REF] Fusini | A uniformly semiglobally exponentially stable nonlinear observer for GNSS-and camera-aided inertial navigation[END_REF], which addresses nonlinear position, velocity and attitude estimation for Unmanned Aerial Vehicles (UAVs).

In this paper we propose a novel estimation strategy for inertial navigation in indoor/outdoor environments, with specific attention to the sporadic nature of position-only measurements (namely we do not assume the presence of any velocity sensors). The motivation for our work is that, especially when operating with beacons and non-periodic or unreliable communication channels, it is well known that the sampled position measurements are far from being available at a fixed frequency. To rigorously represent this scenario, we adopt the hybrid dynamical systems modeling framework of [START_REF] Goebel | Hybrid Dynamical Systems: modeling, stability, and robustness[END_REF], which provides an effective and elegant notation, in addition to a number of useful well-posedness results. This hybrid framework has been already used in other works dealing with the design of observers with sporadic measurements [START_REF] Ferrante | State estimation of linear systems in the presence of sporadic measurements[END_REF]; [START_REF] Li | Robust distributed estimation for linear systems under intermittent information[END_REF]; [START_REF] Sferlazza | Time-varying sampled-data observer with asynchronous measurements[END_REF]; [START_REF] Ferrante | L 2 state estimation with guaranteed convergence speed in the presence of sporadic measure-ments[END_REF], due to its suitability for obtaining accurate models of systems with sampled measurements and non-periodic time-of-arrival. While those approaches can solve the estimation problem addressed here, the explicit solution that we build in this paper is more effective in terms of the tunability of the estimation error dynamics due to its peculiar cascaded structure.

The structure of this paper is as follows. After introducing the inertial navigation model in Section 2, we illustrate the dynamics of the proposed observer in Section 3, first discussing the implementation and then deriving the error dynamics and their cascaded structure. Finally, in Section 4, we present some experiments carried out using a hardware-in-the-loop method. The experiments confirm the effectiveness of the proposed solution in providing accurate estimates also in the presence of measurement noise.

Notation: R n denotes the n-dimensional Euclidean space. R ≥0 denotes the set of nonnegative real numbers. Z denotes the set of all integers, while Z ≥0 denotes the set of nonnegative integers. B denotes the closed unit ball, of appropriate dimensions, in the Euclidean norm. I q denotes the identity matrix of dimension q ∈ Z ≥0 . λ m (S) and λ M (S) denote, respectively, the minimum and the maximum eigenvalues of a symmetric matrix S. x + denotes the state of a hybrid system after a jump. |x| denotes the Euclidean norm of a vector x ∈ R n . B, and N denote the BODY and NED (North-East-Down) reference frames, respectively.

SPORADIC POSITION MEASUREMENTS IN AN INERTIAL NAVIGATION SYSTEM

Consider the strap-down model of an Inertial Navigation System (INS) given by: (Bryne et al., 2014, Eq.s (2)-( 3)):

vn = V (ξ n b )γ b + g, (1) ṗn = v n .
(

) 2
where p n := [p x p y p z ] and v n := [v x v y v z ] are respectively the position and velocity vectors expressed in N coordinates (x, y, z), g := [0 0 g] is the gravity acceleration referred to the N -frame, γ b := [γ x γ y γ z ] is the acceleration measurement provided by the IMU expressed in the B-frame, ξ n b := [ξ 0 ξ 1 ξ 2 ξ 3 ] is the quaternion vector, describing the orientation of the B-frame relative to the N -frame, and matrix V (ξ n b ) is the rotation matrix from the B-frame to the N -frame, as a function of the associated quaternion, corresponding to

V(ξ n b ) := ξ 2 0 +ξ 2 1 -ξ 2 2 -ξ 2 3 2(ξ1ξ2-ξ0ξ3) 2(ξ1ξ3+ξ0ξ2) 2(ξ1ξ2+ξ0ξ3) ξ 2 0 -ξ 2 1 +ξ 2 2 -ξ 2 3 2(ξ2ξ3-ξ0ξ1) 2(ξ1ξ3-ξ0ξ2) 2(ξ2ξ3+ξ0ξ1) ξ 2 0 -ξ 2 1 -ξ 2 2 +ξ 2 3 .
The inertial model ( 1), ( 2) is obtained under the assumption that the Earth angular velocity about the z-axis of the Earth-Centered Inertial (ECI) frame is small, so that it can be neglected (Grip et al., 2013, Remark 2). For further details about (1), ( 2) the reader is referred to (Alonge et al., 2019, Section II).

The strap-down inertial navigation algorithm [START_REF] Zhao | Discrete nonlinear observers for inertial navigation[END_REF]; Grip et al. ( 2013)) is not robust, because the speed and the position vectors are obtained by openloop integration of the acceleration and this leads to drift problems. To solve these observability problems, a position measurement is used, provided by a Global Positioning System (GPS), for outdoor navigation, or beacons, for indoor navigation. Consequently, problems arise because these position measurements are available with a significantly lower sampling rate, as compared to the IMU signals. Moreover the time between two consecutive position measurements is not constant, thus providing a so-called sporadic position measurements situation [START_REF] Ferrante | State estimation of linear systems in the presence of sporadic measurements[END_REF][START_REF] Ferrante | L 2 state estimation with guaranteed convergence speed in the presence of sporadic measure-ments[END_REF]. In order to formalize the above described setting, we assume in this paper that no velocity measurement is available and that the only output of system (1)-( 2) is represented by the vector y = p n , only accessible at discrete instants of time, resulting in a sequence of 3dimensional vectors y k , k ∈ Z ≥1 , defined as:

y k = p n k := p n (t k ), (3)
where t k , k ∈ Z ≥1 , is a sequence of increasing non-negative real numbers that satisfies the following assumption: Assumption 1. There exist scalars T m and T M , with 0 < T m ≤ T M , such that:

T m ≤ |t k+1 -t k | ≤ T M , ∀ k ∈ Z ≥1 . (4)
Assumption 1 essentially requires that the sporadic measurements y k be available with intersample times that are lower and upper bounded by positive constants T m ≤ T M whose knowledge is not required by the estimation algorithm proposed here. As a consequence, Assumption 1 appears to be an extremely mild assumption ruling out the defective cases of Zeno behaviors (because T m is greater than zero) and the situation of sporadic measurements whose occurrence becomes increasingly rare as time grows.

Using the hybrid systems formalism of [START_REF] Goebel | Hybrid Dynamical Systems: modeling, stability, and robustness[END_REF], it is possible to represent the sampled-data system associated with setting (1)-(3) as follows:

   vn = V (ξ n b )γ b + g, ṗn = v n , τ = 1, (v n , p n , τ ) ∈ C, (5a)
   v n+ = v n , p n+ = p n , τ + = 0, (v n , p n , τ ) ∈ D, (5b)
y = p n , (5c)
where the timer τ is an additional state variable keeping track of the elapsed time since the last measurement, while sets C and D are respectively the so-called flow set and jump set, defined as:

C :=R 3 × R 3 × [0, T M ], (6) D :=R 3 × R 3 × [T m , T M ].
(7) The impulsive nature of the available measurement is represented by the extra property that y = p n is only available at the jump times.

CONTINUOUS-DISCRETE OBSERVER ARCHITECTURE

Observer dynamics

In this paper, we propose an observer whose structure implicitly complies with the restriction specified in Assumption 1 about the available measurements. Our observer is capable of providing an asymptotic estimate of the plant state, for any sequence of sampling times t k at which the sampled output is available, as long as these times satisfy Assumption 1 for some (not known) values of 0 < T m ≤ T M .

The hybrid structure of the proposed observer is the following one

         vn = V (ξ n b )γ b + g, ṗn = vn , τ = 1, ṗ = 0, (v n , pn , τ, p) ∈ C ×R 3 , (8a)            vn+ = vn +(1-α v ) p n -pn - p τ , pn+ = pn +(1-α p )(p n -pn ), τ + = 0, p+ = α p (p n -pn ) (v n , pn , τ, p) ∈ D×R 3 , (8b
) where p is an auxiliary "zero-order hold" state vector propagating the last position correction term across the intersample interval, and α v and α p are two positive gains that may be tuned to suitably adjust the estimation error transient. Note that the measurement y = p n is only used in the jump dynamics of our observer, which is then compliant with the measurement constraints imposed by Assumption 1. As compared to the architecture used in [START_REF] Alonge | A hybrid observer for localization of mobile vehicles with asynchronous measurements[END_REF], observer (8) considers a different jump map with an extra auxiliary state vector p. This is necessary because [START_REF] Alonge | A hybrid observer for localization of mobile vehicles with asynchronous measurements[END_REF] addresses a simpler problem where both the position and the speed are simultaneously measured. In the setting addressed here, where only the sampled position measurement is available, a more sophisticated dynamic correction is required.

Error Dynamics and Main Result

The main result of this work proves stability and convergence of the estimation error in the extended error space corresponding to the error variables

e := e v e p := v n p n - vn pn (9a) ẽv := e p -p -τ e v (9b)
and provides design rules to select the tuning gains α v and α p in (8). In particular, with the error variables (9), the corresponding error dynamics issued from ( 5)-( 8) is well represented by the cascaded structure schematically shown in Figure 1. In this figure, the upper subsystem, governed by the dynamics of ẽv , converges to zero in finite time at the first measurement instant; the middle subsystem, governed by the velocity error dynamics e v , provides a constant continuous-time behavior in the inter-measurement periods and a discretely converging dynamics (tunable by adjusting α v ) at the measurement instants, perturbed by input ẽv . Finally, the third subsystem, governed by the position error dynamics e p , provides a constant continuoustime behavior perturbed by the velocity error e v in the inter-measurement periods, and a discretely converging dynamics (tunable by adjusting α p ) at the measurement instants.

For clarity of exposition, we write the three dynamics represented in Figure 1 as three different systems, even though it is emphasized that the variable τ governing the jumps is the same one for all of them. By considering ( 5) and ( 8), the hybrid position error dynamics can be written as:

ėp = e v , τ = 1, (e p , τ ) ∈ R 3 × [0, T M ], (10a)
e p + = α p e p , τ + = 0, (e p , τ ) ∈ R 3 × [T m , T M ], (10b)
while, the speed error dynamics can be written as:

ėv = 0, τ = 1, (e v , τ ) ∈ R 3 ×[0, T M ], (11a)
e v + = α v e v + α v -1 τ ẽv , τ + = 0, (e v , τ ) ∈ R 3 ×[T m , T M ]. (11b)
Finally, the dynamics of ẽv is governed by

ėv = 0, τ = 1, (ẽ v , τ ) ∈ R 3 ×[0, T M ], ( 12a
) ẽv + = 0, τ + = 0, (ẽ v , τ ) ∈ R 3 ×[T m , T M ]. ( 12b
)
Remark 1. The cascaded interconnection represented in Figure 1 and whose dynamics correspond to ( 10), ( 11) and ( 12) is somewhat peculiar because: 1) the upper subsystem converges to zero in finite time (at the first jump); 2) the middle subsystem converges asymptotically to zero being perturbed by the upper subsystem across jumps; 3) the lower subsystem converges asymptotically to zero being perturbed by the upper subsystem along flows. This somewhat peculiar continuous-discrete cascaded interconnection naturally emerges from the continuous-discrete nature of the observer.

Our main result provides necessary and sufficient conditions for the gains α p and α v in the observer dynamics (8) to ensure global exponential stability (GES) of the compact set (the attractor):

A := (e, ẽv , τ ) : e = 0, ẽv = 0, τ ∈ [0, T M ] ,

for the error dynamics (10), ( 11) and ( 12). The attractor in (13) corresponds to the set where the estimation error is zero, therefore our main result establishes necessary and sufficient conditions for exponential estimation of the unmeasured states p n and v n . Theorem 1. Set A in ( 13) is globally exponentially stable for the error dynamics (10), ( 11) and ( 12) if and only if the gains α p and α v satisfy |α p | < 1 and |α v | < 1. In particular, those conditions hold if and only if there exist positive scalars κ and λ such that all solutions to (5)-( 8) satisfy

v n (t, j)-vn (t, j) p n (t, j)-pn (t, j) = e v (t, j) e p (t, j) ≤ κe -λ(t+j)
e v (0, 0) e p (0, 0) ẽv (0, 0) .

While the proof of Theorem 1 is omitted for lack of space, we emphasize here that the error dynamics (10), ( 11) and ( 12) satisfies the hybrid basic assumptions of (Goebel et al., 2012, As. 6.5) (which in this single-valued case corresponds to checking that the flow and jump sets are closed and the flow and jump maps are continuous in these respective sets). Therefore, since the attractor A in ( 13) is compact, according to (Goebel et al., 2012, Ch. 7), the established GAS property is uniform, namely the proposed observer (8) provides uniformly convergent asymptotic estimates of p n and v n under the stated assumptions on the gains. Finally, due to (Goebel et al., 2012, Ch. 7), sufficiently small modeling and measurement errors do not destroy such a stability property, but provide a graceful performance degradation in a semiglobal practical sense.

HARDWARE-IN-THE-LOOP RESULTS

We test observer (8) by running some hardware-in-theloop experiments. To this end, the hybrid dynamics (8) has been implemented in a Raspberry-PI 3 with a sampling frequency of 100 Hz. While, by means of Matlab Rsimulink R , a suitable realistic scenario has been simulated resembling a possible path associated to the motion of a mobile vehicle. The corresponding trajectory is shown in Figures 2(a) and 2(b), which display the reference position and yaw angle, respectively. In the hardware-in-theloop setup, sampled measurements of this trajectory, as well as accelerations and attitude angles are sent to the Raspberry. In particular, the IMU data corresponding to the accelerations and attitude angles are provided to the Raspberry periodically with a fixed frequency coinciding with its operating frequency (100 Hz), while the sporadic position measurements are available at random instants of time satisfying Assumption 1 for some small enough T m and some large enough T M . Even though these values are not important (the observer dynamics is independent of them), here we selected T m = 0.5s and T M = 1.5s. The evolution of the timer variable τ is reported in Fig. 2(c), showing that the measurements occur randomly in the interval [T m , T M ], according to the described dynamics. The parameters of the observer have been fixed at α v = 0.9 and α p = 0.9 and the initial conditions are p n 0 = [10 10 10] and v n 0 = [-0.85 -0.85 -0.85]. Two tests have been performed: in test 1 (noise-free case) the position trajectory of Fig. 2(a) has been exactly sampled, at the sporadic times discussed above, and fed to the observer. Similarly, the accelerations γ b and the attitude angles ξ n b have been fed to the observer in a noise-free scenario. In test 2 (noisy case) for the same values of the observer parameters and initial conditions, the measurements have been corrupted by noise. In particular, the accelerations have been corrupted by a Gaussian zero mean white noise having standard deviation equal to 0.04 m/s 2 , while the position has been corrupted by a Gaussian zero mean white noise having standard deviation equal to 0.5 m.

The results of the noise-free test 1 are shown in Figures 345. In particular Figures 3 and4 show the real and the estimated positions and velocities. It is apparent that the estimated variables exponentially converge to the corresponding state variables (all the errors exponentially converge to zero). The hybrid behavior of the estimate is clearly visible, especially during the initial transient. Indeed, in Fig. 5 the velocity error is constant during flowing, and decreases across jumps, as expected from the theoretical results Theorem 1, while the position error respects the bound given in Theorem 1. Figure 5 provides further insight by showing suitably zoomed (transient and steady-state) areas from Figure 5.

Similar tests have been provided for test 2 (noisy case), and are reported in Figures 678. These noisy tests confirm that the observer is able to cope with noisy measurements, since both the position and the velocity are well estimated by a suitable filtering action of the measurement noise.

Finally Figure 9 shows the position error e p and the velocity error e v for different values of α p and α v . As one may expect from the error dynamics characterized in Theorem 1, the closer α p and α v are to zero, the higher the convergence rate of the estimation error will be, but a higher convergence rate leads to a reduced filtering action on the measurement noise. The choice of α p and α v then should be carried out as a trade-off between these two goals. Note also that the convergence rate is influenced by the values of T m and T M . Indeed, if the measurements are accessible less frequently, then the convergence rate results to be slower.

CONCLUSIONS

In this paper, a novel estimation strategy for inertial navigation in indoor/outdoor environments has been proposed with specific attention to the sporadic nature of the sampled-data measurements. After introducing the inertial navigation model, an observer providing exponentially converging position and velocity estimates has been proposed. A hybrid dynamical systems framework has been used for presenting our results. The main theorem proves uniform exponential convergence to zero of the estimation error, together with an intuitive selection of the observer gains. Hardware-in-the-loop experiments confirmed the effectiveness of the proposed approach and the capability of the described observer to also deal with measurement noise.

Fig. 1 .

 1 Fig. 1. Block diagram of the speed and position error dynamics.

Fig. 2 .

 2 Fig. 2. Reference position trajectory (a). Reference yaw angle (b). Evolution of the timer variable τ showing the sporadic nature of the sampled position measurements (c).

Fig. 3 .

 3 Fig. 3. Actual and estimated positions in test 1 (noise-free).

Fig. 4 .

 4 Fig. 4. Actual and estimated velocities in test 1 (noise-free).

Fig. 5 .

 5 Fig. 5. Position errors ep (upper plot) and velocity errors ep (bottom plot) in test 1 (noise-free).

Fig. 6 .

 6 Fig. 6. Actual and estimated positions in test 2 (noisy).

Fig. 7 .

 7 Fig. 7. Actual and estimated velocities in test 2 (noisy).

Fig. 8 .

 8 Fig. 8. Position errors ep (upper plot) and velocity errors ep (bottom plot) in test 2 (noisy).

Fig. 9 .

 9 Fig. 9. Waveforms of the position error ep (upper plot) and of the velocity error ep (bottom plot) for different values of αp and αv.


Zhengxing Qin

Leila Hafiz

Yanfeng Shen

Stijn Van Daele

Philippe Boullay

Valerie Ruaux

Svetlana Mintova

Jean-Pierre Gilson

Valentin Valtchev

Stijnvan Daele

Defect-engineered zeolite porosity and accessibility

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Porosity and acidity are two of the most essential properties of zeolites, which are microporous crystalline aluminosilicates comprising well-defined channels and/or cages of molecular dimension [1]. The location of well-defined acid sites in microporous space makes zeolite particularly appropriate for applications in the field of heterogeneous catalysis thanks to its unrivalled shape-selectivity [2]. On the other hand, however, the micropore confinement imposes diffusion limitations when bulky molecules are to be processed [3].

To circumvent the intra-crystalline mass transfer problem, the partial removal of framework atoms has long been employed to introduce auxiliary porous paths into the inner part of zeolite crystals [4]. This can be achieved through either dealumination or desilication [5,6], noting that both dealumination and desilication, as the name indicates, are element-selective methods. A non-biased chemical etching approach, NH4F etching, was also developed by us recently [7]. This is a method able to partially dissolve zeolite crystals without changing the framework composition [START_REF] Qin | [END_REF][9][10].

Moreover, the removal of framework atoms begins always from extended and localized grain boundaries [10][11][12]. Thanks to these unique advantages, we revealed the "mosaic" architecture of zeolite crystals [10], and we prepared a "house-of-cards"like zeolite by a top-down approach for the first time [11]. Such a narrowing of the thickness of the microporous domains shortens the diffusion path length of reactants and products and increases the catalytic performance of zeolites dramatically.

One the other hand, however, the decrease of microporous domain size improves only the accessibility to the domains, but not necessarily the diffusion efficiency in a micropore. Actually, the intrinsic microporosity remains intact when the dissolution of zeolite follows a reverse "layer-by-layer" mechanism [11]. In order to face the new industrial challenges, there are continuous efforts to obtain zeolite materials with enhanced micropore diffusion. Several new zeolite structures with extra-large micropores were obtained [13][14], but none of them offer industrial potential due to cost and low (hydro)thermal stability.

In the present study, we present a simple chemical approach to enhance the pore volume of zeolite and increase the number of active sites accessible to molecules with a kinetic diameter larger than the micropore opening of zeolite. Our approach is based on two key factors: i) the in-situ generation of a small amount of HF2 -, which extracts both framework cations (Si and Al); and, ii) the dissolution of zeolite crystals starts preferentially from framework weak points, i.e. defect sites [10][11][12].

Defects are ubiquitous in crystalline materials. Zeolites, similarly to other crystalline materials, contain structural defects such as vacancies, dislocations, grain boundaries… It is known that defect sites in the zeolite framework are prone to retain coke precursors [11,15]. Therefore, defects are often considered as something that deteriorates the intrinsic zeolite properties. For this reason, the synthesis of zeolites in fluoride media was invoked to decrease the number of framework defects [16,17]. In fact, "Crystals are like people: it is the defects in them which tend to make them interesting" [START_REF] Humphreys | Introduction to Analytical Electron Microscopy[END_REF]. Indeed, our approach is fundamented on the rational use of existing and generated defects that allow us to obtain zeolite crystals with superior properties.

In the present work, we report a simple and potentially universal strategy for hierarchical zeolite design that highlighting the impact of chemical induced defects in zeolite framework, which make zeolite dissolution going beyond the limit set by zeolite structure and synthesis conditions. We will discuss in detail the structural descriptors that dictate the dissolution behavior of zeolite crystals leading to materials with a multi-model pore structure. The feasibility of this approach is exemplified by the treatment of the MOR-type zeolite [START_REF] Simoncic | [END_REF], an essential active component in a number of catalytic reactions, such as carbonylation [20][21][22], conversion of methane into methanol [23], selective conversion of syngas [24], selective catalytic reduction of NOx [25], hydroisomerization [26] and others. Besides the 12-member ring (MR) channel running along the c axis, mordenite contains an 8-MR side pocket that could contribute substantially to its performance [27][28]. However this space is not readily accessible due to the minimal diameter of the pore openings [29]. Besides, the quasione-dimensional channel system of this zeolite is very prone to coke [29]. The successful engineering of the micro-environment around the active sites of mordenite can be very informative and useful for the fine-tuning of the structure of other channel-type zeolites.

Experimental section

Oxalic acid and fluoride treatment of mordenite

The parent NH4-form mordenite (MOR, Si/Al = 6.5) was purchased from Zeolyst [10]. The acid treatment of MOR was performed as follows; 24 g of the zeolite powder was dispersed in 500 g of 6 wt.% aqueous oxalic acid solution and reacted at 90 °C for 24 h under stirring (ca. 400 rpm). The solid product was recovered by suction filtration. The sample was washed thoroughly with water and dried at 100 °C overnight. This oxalic acid treated sample was named as MOR-A.

The method used for the fluoride etching of MOR and MOR-A is reported in ref. 10. In a typical experiment, 2.5 g of MOR or MOR-A was dispersed in 40 g of 40 wt.% NH4F aqueous solution and allowed to react. The reaction was carried out at 50 °C for 2 min under mechanical stirring and ultrasonication (USC 600 TH, 45 kHz, VWR).

The etched products were collected by suction filtration, washed thoroughly with distilled water and allowed to dry at 100 °C over night. The samples derived from MOR and MOR-A respectively were labelled as follows: i) MOR-AF for the NH4F treated sample, ii) MOR-A-AF for the sample prepared by consecutive oxalic acid and NH4F treatment.

Characterization methods

X-ray diffraction measurements were performed on an X'pert Pro/PANalytical Diffractometer using Cu Kα radiation (λ = 1.5418 Å, 45 kV, 40mA). The samples were studied in the 5-50° 2θ range with a scanning step of 0.0167° s -1 . Electron micrographs were taken on a JSM-7900F (JEOL) low-voltage high-resolution scanning electron microscope (SEM) equipped with a field emission gun, and a FEI LaB6 TECNAI G2 30UT transmission electron microscope (TEM) operated at 300 kV.

Elemental analysis was performed by inductively coupled plasma-atomic emission spectroscopy (ICP-AES) using an OPTIMA 4300 DV (Perkin-Elmer) instrument.

Nitrogen adsorptions were performed with a Mircomeritics ASAP 2020 automated gas adsorption analyzer. Prior to analysis, the samples were out gassed at 100 °C for 1 h and 300 °C for 10 h. Specific surface areas were determined from the BET equation applied to the 0.01 -0.06 P/P0 range. The total volume was taken from nitrogen adsorbed volume at P/P0 = 0.97. The t-plot method, applied in the 0.4 -0.8 thickness range, was used to distinguish the micropores from the mesopores in the samples. 27 Al and 29 Si MAS NMR spectra were recorded on a Bruker Advance 500 MHZ spectrometer using a 4 mm rotor. The 27 Al MAS NMR spectra were recorded at 104.3 MHz with a 12 pulse length of 2.2 µs, a spinning rate of 14 kHz and a recycle delay of 1 s. 1 M Al(NO3)3 was used as reference for chemical shifts of 27 Al. Infrared spectra were recorded using a Nicolet Magna 550-FT-IR spectrometer with 2 cm -1 optical resolution. Prior to the measurements, the samples were pressed into self-supporting discs (diameter: 1.6 cm, ~17 mg) and preheated in the IR cell attached to a vacuum line at 450 °C (2 °C/min) for 5 h down to 10 -6 Torr. The adsorption of 2,4,6trimethylpyridine (collidine) was also performed at room temperature. After reaching a pressure of 1 Torr, the sample was heated at 200 °C in the collidine atmosphere for 30 -210 min to improve the diffusion and absorption of collidine inside micropores.

After establishing equilibrium at this condition, the cell was evacuated at increasing temperatures, in steps of 50 °C from 50 to 450 °C. The amount of collidine adsorbed on the samples after degassing at 250 °C was used for the measure of zeolite acidity.

All Spectra were normalized to the weight of wafers. The absorption bands at ca. 1637 and 1648 cm -1 were used for the quantification of the accessibility of acid sites.

The extinction coefficient ε(collidine)1632-1648 = 10.1 cm.µmol -1 was used for collidine adsorption [30].

Catalytic test

The dealkylation of 1,3,5-triisopropylbenzene (TiPBz) was performed in a tubular flow reactor operating in the gas phase at atmospheric pressure. For each experiment, 25 mg of zeolite was loaded in the reactor enclosed between two layers of inert SiC (200 ~ 400 µm size range). The samples were activated in a dry-air stream (50 mL min -1 ), first at 100 °C for 5 h, and then the temperature raised to 450 °C (ramp of 2.5°C•min -1 ) and maintained 3 h at this final temperature. N2 was subsequently introduced and the reactor cooled-down to the reaction temperature, 350 °C. A stream of 200 mL min -1 N2 was diverted to a saturator filled with TiPBz maintained at 71 °C (PTiPBz = 180 Pa). A space time of 95 kg•s•mol -1 was used. Stable conditions were established in less than 5 minutes; the first effluent was collected after 5 min, thereafter at 15 min intervals and analyzed quantitatively on a CPG (VARIAN Cp 3800; HP-Pona 50 m, 0.2 mm, 0.5 µm column), fitted with a FID detector.

Results and Discussion

Defect sites in the zeolite framework induced by oxalic acid leaching

The recent research results of our group showed that the formation of secondary porosity is directly related to the intrinsic structural properties of zeolites [START_REF] Qin | [END_REF][9][10][11][12].

Namely, the dissolution behavior of zeolites is preset by zeolite synthesis history.

Following this line, a mordenite zeolite (MOR) with an initial Si/Al ratio of 6.5 was treated by using oxalic acid, in order to introduce defect sites in the zeolite framework by selective removal of framework Al atoms [31]. The oxalic acid leaching resulted in the removal of ca. 75% of the framework Al. The Si/Al ratio of the acid leached sample, MOR-A, increased to 29.0 (Table 1). Despite the substantial loss of framework aluminum atoms, MOR-A remained highly crystalline and microporous (Figure 1, Figure 2A). However, its N2 adsorption isotherm slightly differs from that of the parent zeolite. The isotherm of MOR is type-I(a), characteristic of a microporous material (Figure 2A [32]. The subtle change in isotherms shape serves, therefore, as the first sign of a change of the microstructure of zeolite framework, as the occurrence of type-I(b) is an indication of materials with wider micropores and possibly narrow mesopores. The pore size distribution of this sample in the 2-3 nm range also raises slightly (Figure 2B). MOR-A shows a total increase of 0.03 cm 3 /g in (Vmic + Vsec) in comparison to MOR (Table 1), noting that the larger micropores and/or small mesopores are difficult to be distinguished at this critical 2 nm pore size. Clearly, the removal of framework Al (Table 1) has resulted in the formation of some additional void space, which is large enough for the accommodation of N2 molecules (kinetic diameter: 0.36 nm). Another proof of the removal of framework Al and the resultant formation of framework vacancies as a result of acid leaching comes from the 27 Al and 29 Si MAS NMR results (Figure 3). The quantitative 27 Al MAS NMR experiment shows clearly the loss of framework Al caused by acid leaching (Figure 3A). It also shows that both MOR and MOR-A are free of non-framework Al species. The 29 Si MAS NMR spectrum of MOR shows clearly three peaks centered at -99, -105 and -112 ppm (Figure 3B), which are attributed to the Si(2Al), Si(1Al) and Si(0Al) atoms in the zeolite framework, respectively [33]. The Si/Al ratio of this sample determined by the Pore diameter / nm deconvolution of the 29 Si MAS NMR spectrum is 6.2, which is quite close to the ICP and EDS analysis results (Table 1). The 29 Si MAS NMR spectrum of MOR-A shows only two peaks sitting around -104 and -112 ppm (Figure 3C). The Si/Al ratio of this sample determined by the NMR method is 10.2, which is much lower than the ICP and EDS data (Table 1). Apparently, defect sites assigned to Q3 groups corresponding to nonbonded defects (silanol) are present in the framework of MOR-A. Such signals increase the -104 ppm peak intensity and, as a result, the NMR analysis underestimates substantially the Si/Al ratio of the oxalic acid dealiminated zeolite (MOR-A) [34].

Figure 4 The IR spectra showing the ν(OH) region of MOR, MOR-A and MOR-A-AF:

(A) the 3000-4000 cm -1 region, (B) the 3600-3800 cm -1 region highlighting the hydroxyl groups related to defective sites.

The structure characteristics of MOR and MOR-A were further studied by IR. For MOR, the bridging hydroxyl groups are characterized by a sharp asymmetric band centered at ca. 3609 cm -1 in the ν(OH) region (Figure 4A). A small IR band at 3746 cm -1 representing the silanol groups on the external surface of zeolite can also be clearly identified (Figure 4). The number of bridging hydroxyl groups decreases substantially after acid treatment (Figure 4A). On the contrary, the number of internal silanol groups, characterized by an IR band at ca. 3734 cm -1 , increases obviously upon SEM observation shows that MOR zeolite has a particle morphology consisting of intergrown small boulder-like particles (Figure 5A). These small crystals exhibit a rather homogeneous contrast under TEM (Figure 6A), reflecting the absence of mesoporosity. The SEM image of MOR-A shows a very similar aggregative morphology like MOR (Figure 5B). The small particles also show a homogeneous contrast with distinct grain boundaries under TEM observation (Figure 6B). The darkto-light contrast, a sign of the presence of intra-particle mesopores, is absent.

Apparently, the selective removal of framework aluminum only results in the formation of some localized defective sites that are documented by IR, NMR and N2 adsorption analysis (Figure 234), but are difficult to be visualized by SEM or TEM analysis.

NH4F etching of MOR and MOR-A

NH4F etching of MOR

Treating MOR with NH4F does not change the Si/Al ratio of the sample (MOR-AF, Table 1). This result is in agreement with our previous studies performed on MFI, FAU, and FER type zeolites [START_REF] Qin | [END_REF][9][10][11]. The crystalline characteristic and micropore volume of zeolite are retained (Table 1, Figure 1). There is little increase in the fraction of narrow mesopores (Figure 2). Furthermore, the surface morphology of MOR-AF (Figure 5C) looks similar to the parent mordenite (Figure 5A). On the other hand, the NH4F treatment results in a substantial increase in the mesopore volume (Table 1 and Figure 2). TEM reveals the formation of visible "cracks" in large platelike zeolite grains (Figure 6C). We have interpreted such splits as the gradual separation of small crystals with intergrowth interface [START_REF] Qin | [END_REF][9][10]. Besides the diassembly of the aggregates, some large, isolated intra-particle mesopores are also formed in some crystals (Figure 7A). While the number of such pores is small at the stage of etching, an extension of NH4F etching from 2 min to 25 min increases the number of mesopores with straight, clear-cut edges substantially (Figure 7B). These pores are spatially oriented and aligned themselves to the crystallographic axis (Figure 7B, inset). We attribute the formation of these intra-particle mesopores specifically to the mosaic structures in zeolite framework,i.e., the selective removal of hidden nanocrystalline domains [10].

NH4F etching of MOR-A

The NH4F treatment of MOR-A results in a substantial decrease in the Si/Al ratio (MOR-A-AF, Table 1). This is in sharp contrast to the case of MOR-AF, which shows that it is a consequence of the preliminary oxalic acid etching.

The MOR-A-AF sample remains highly crystalline (Figure 1). The micropore volume determined by t-plot is the same as the precursor, MOR-A (Table 1). Nitrogen adsorption analysis also revealed that a certain amount of mesoporosity was introduced by the fluoride treatment (MOR-A-AF, Table 1 and Figure 2). The TEM inspection shows that the MOR-A-AF is highly segmented along the interfaces between the crystals building the aggregates (Figure 6D,E), and the dark-to-light contrast is densely distributed throughout the whole particle volume. This profile contrasts sharply with the intact appearance of MOR (Figure 6A) and MOR-A (Figure 6B). Based on a careful comparison of the SEM and TEM images, one can get the impression that the mesopore density in the case of MOR-A-AF is substantially higher than that of MOR-AF (Figure 5C, D and Figure S2). This visual observation was also quantitatively confirmed by nitrogen adsorption data (Table 1 and Figure 2).

The significant difference in mesoporosity (pore size, density, and morphology) between MOR-AF and MOR-A-AF samples is even more evident through the comparison of the corresponding isolated fragments. For the MOR-AF samples, only few mesopores can be observed in the bulk of the separated crystals (Figure 7A,B).

Most of the mesopore size is larger than 20 nm along the long direction, while pores with sides shorter than 10 nm are rare. In the MOR-A-AF case, the number of mesopores cannot be counted accurately due to the substantially higher mesopore density (Figure 7C). Also the clear identification of the mesopore periphery is difficult. Based on a careful investigation of the TEM images, however, one can still distinguish between two types of pores. One type possesses a rectangle periphery or has at least some right angles (indicated with rectangles in Figure 7C, and Figure S3A), the other is generally ill-defined in shape and much smaller in size than the regularly shaped pores (Figure 7D and Figure S3B).

While the presence of mesopores with rectangular shapes or right angles is considered as the removal of the spatially distributed hidden nano-crystalline domains, the formation mechanism of the much more irregular-shaped and smaller mesopores (Figure 7D and Figure S3B) are not related with a particular type of growth or structure-related particularities.

Acid sites accessibility: an IR study of pyridine and collidine adsorption

Pyridine adsorption

The adsorption of pyridine was conducted at room temperature (RT). The adsorption reached equilibrium within 15 min for all mordenite samples. The kinetic diameter of the probe molecule is 0.57 nm and is much smaller than the 0.7 nm large 12-MR channel of mordenite and thus no diffusion limitation is expected.

The treatment of MOR using NH4F does not change the zeolite acidity. Both MOR and MOR-AF show similar Brønsted and Lewis acidity (Table 2). This is in line with the fact that NH4F etching does not change Si and Al composition or produce extraframework Al species (Figure 3A). It is also a clear indication that the treatment does not change the microporous properties of mordenite. This is in line with our previous observation that the intrinsic microporosity remains intact when the dissolution of zeolite follows a reverse "layer-by-layer" mechanism [11]. The acidity is calculated on the basis of the Al content by assuming that each Al contributes to an acid site. b The Brønsted (B) and Lewis (L) acid amount determined by using pyridine as the probe molecular. c The acid amount determined by using collidine as the probe molecular. d Acid sites accessibility were calculated based on the total Al content and the amount of acid sits accessible to pyridine and collidine. MOR: the parent mordenite; MOR-A: the oxalic acid treated mordenite, MOR-AF: the NH4F treated mordenite, MOR-A-AF: the sequential oxalic acid and NH4F treated mordenite.

The leaching of MOR using oxalic acid decreases the total amount of acid sites substantially, in agreement with the decrease of the aluminum content (Table 1).

Noteworthy, the sum of Brønsted and Lewis acidity is very close to the acid amount calculated based on the Al content (Table 2). If we assume that each Al contributes an acid site, either Brønsted or Lewis type, then it can be speculated that almost all the acid sites in MOR-A are accessible to pyridine. This is in agreement with previous finding that some of the acid sites in the side pockets of mordenite become accessible upon dealumination [35].

MOR-A-AF shows higher acid stes content than MOR-A, in line with its higher Al content. The sum of Brønsted and Lewis acidity is also very close to the acidity calculated based on the Al content (Table 2), indicating that the acid sites are also almost fully accessible to pyridine.

Collidine adsorption

The initial adsorption of collidine was also conducted at RT. We noticed that this molecule, with a kinetic diameter of 0.74 nm [36] that is larger than the pore size of mordenite, was very difficult to penetrate through the micropores of this zeolite. This can be seen from the fact that the adsorption of collidine on Brønsted acid sites at RT is slow for all mordenites (1637-1648 cm -1 bands, lines "RT" in Figure S4). The 3610 cm -1 bands intensity remains almost unchanged before and after the adsorption of collidine (lines "RT" in Figure S4). The adsorbed collidine mainly interacts with the silanol groups (1573 and 1616-1618 cm -1 ) [15] on the external surface of the zeolite (lines "RT" in Figure S4). As a result, the amount of collidine adsorbed on parent mordenite is the lowest due to the poor acid site accessibility and to the limited amount of surface silanol groups (Figure 8A, black solid). The collidine adsorption increases after acid or fluoride etching (Figure 8A, blue and red solid). The highest amount of collidine is adsorbed after a consecutive oxalic acid and fluoride etching (Figure 8A, pink solid), which is unambiguous proof of the higher accessibility achieved (Table 2).

Figure 8. (A)

The increase of the peak intensity (the integration of 1573, 1617, 1637 and 1648 cm -1 bands, see Figure S4) with time during the adsorption of collidine on mordenite zeolites. (B) The negative peaks show the portion of silanol groups (3745 cm -1 ) and acidic hydroxyl groups (3585-3610 cm -1 ) that are interacting with physical or chemical adsorbed collidine at the state of steady adsorption (Figure 8C). (C) IR spectra of collidine adsorbed on the mordenite zeolites at the state of steady adsorption.

After reaching a collidine pressure of 1 torr at RT, the sample was heated at 200 °C in the collidine atmosphere until reaching a steady adsorption state. In general, the heating helps the diffusion of molecules with a kinetic diameter close to the zeolite pore to diffuse. However, the adsorption of collidine on MOR increased only a little after 15 min of activation (Figure 8A). The comparison of the spectra reveals that the adsorption of collidine on this sample reached already a steady state within 15 min (Figure 8A and Figure S4A,S5A). The 3610 cm -1 band of this sample remained strong (Figure S4A), and the corresponding collidine adsorption band is very weak (Figure 8C). Obviously, it is difficult for collidine to reach the acidic groups inside MOR zeolite framework even under activation at 200 °C.

The adsorption of collidine on MOR-A increased slightly after activation at 200 °C (Figure 8A, blue open), as the adsorbed collidine mainly interacts with Brønsted acid sites (Figure S4B, S5B). Interestingly, MOR-A keeps adsorbing collidine, slowly but steadily (slope 0.021), until reaching a steady state after 105 min of activation (Figure 8A). Finally, the 1637-1648 cm -1 band intensity of this sample is higher than that of MOR at the equilibrium adsorption state (Figure 8C). This information, combined with the fact that the Si/Al ratio of MOR-A is more than 4 times higher than that of MOR (Table 1), shows unambiguously that the oxalic acid leaching has improved the diffusion of collidine towards the microporous channels of MOR-A. As a result, much more collidine can be adsorbed on its external surface (Figure 8B, C), Furtherly, bulky molecules like collidine can penetrate easily and be absorbed in the micropores of MOR-A.

The impact of heating on the sorption of collidine on MOR-AF and MOR-A-AF samples is much more pronounced. The 1637-1648 cm -1 band intensity of MOR-AF increases sharply after the first 15 min of activation at 200 °C (Figure 8A and Figure S4C), then the sorption increases continuously (slope 0.072) in the following 75 min (Figure 8A, red open). The amount of collidine absorbed on MOR-AF at steady state is 12 times higher than that on MOR (Figure 8A, red open). The presence of the very strong negative 3610 cm -1 band (Figure 8B), coupled with the presence of the very strong 1637-1648 cm -1 peaks (Figure 8C), shows clearly that a large portion of the Brønsted acid sites inside zeolite crystals are perturbed by collidine (Figure S5C). In the case of MOR-A-AF, the intensity of the 1637-1648 cm -1 bands also increases obviously after heating at 200 °C for 15 min (Figure 8A and Figure S4D, S5D). The sorption of collidine on this sample continuously increases in the next 120 min, with the highest slope (slope 0.123) amongst all samples (Figure 8A, pink open).

After establishing a steady absorption state, the collidine was desorbed under vacuum upon increasing the temperature. During the process, the 1573 and 1617 cm -1 bands disappear first (Figure S6). Meanwhile, the 1637-1648 cm -1 bands loss intensity progressively (Figure S6). Based on the spectra collected after desorption at 250 °C (Figure S6D), the acid amount of MOR, MOR-A, MOR-AF, and MOR-A-AF were quantified as 49, 82, 418 and 326 µmol g -1 , respectively (Table 2). Based on the Si/AlICP ratio, however, the estimate acid amount of these samples is 2222, 556, 2222 and 800 µmol g -1 , respectively (Table 2). Accordingly, the portions of acid sites that are accessible for collidine in the case of MOR, MOR-A, MOR-AF, and MOR-A-AF are 2, 15, 19 and 41%, respectively (Table 2). This result highlites what level of accessibility for a bulky molecule such as collidine could be acheived by oxalic acid, NH4F and combined oxalic acid -ammonium fluoride treatment. Noticeably, even the acid sites inside the side pockets of MOR-A-AF are accessible to collidine. A strong argument is the asymmetric nature of the negative peaks (3610 cm -1 , Figure 8B) in the case of MOR-A-AF. The deconvolution of the negative peak of MOR-A-AF shows that about 40% of acidic hydroxyl groups interacting with collidine is situated in the side pockets, i.e., corresponds to the band at 3590 cm -1 .

Defect engineered mesopore formation

The introduction of mesopores in a microporous zeolite crystal requires partial removal of framework atoms. Whatever the post-synthesis method employed, desilication [37], dealumination [38] or demetallation [9], the introduction of secondary porosity involves a partial breakage of framework Si-O-Al and/or Si-O-Si bonds. The features of the added porosity (pore size, shape, volume, interconnectivity, spatial distribution…) are therefore determined by the ease of breaking the T-O-T bonds [5].

The crystallographically imperfect zones are rich in coordination unsaturated or strained framework sites, which bear much higher internal energy and hence are much more vulnerable to chemical attack. Naturally, this serves as the origin for the development, through the partial dissolution of zeolite framework, of interstitial and intra-particle secondary porosity in zeolite framework [10]. Because of this, the dissolution of mordenite zeolites in NH4F solution results in the formation of interparticle "cracks" and intra-crystalline mesopores (Figure 6, 7). Specifically, the interface between intergrown crystallites leads to separated nano crystals (Figure 6C-E). And the presence of the hidden mosaic structures allows the engineering of zeolite poorsity at meso sized scales, which lead directly to intra-particle mesopores formation (Figure 7A-C). At the same time, this also shows that the primary dissolution behavior of a zeolite crystal has already been preset by zeolite synthesis history [10,11,[39][40][41].

The acid-leaching induced defects, introduced by oxalic acid extraction of framework aluminium, changed the dissolution behavior of zeolite crystals substantially. This is evidenced by the fact that the mesoporosity of MOR-AF and MOR-A-AF is very different from each other, as revealed by electron microscopy and quantified by high resolution nitrogen physisorption analysis (Figure 2, Figure 567and Table 1). Although the removal of framework Al by oxalic acid does not increase substantially the pore volume of zeolite (Table 1), it results in a remarkable improvement of the inter-/intra-particle absorption and diffusion of chemical molecules [42]. In the present study, this has been demonstrated unambiguously through the collidine absorption experiment (Figure 8A).

As a result of the significant presence of framework defects and the substantially improved intra-particle diffusion efficiency, the dissolution of MOR-A is much faster the parent mordenite due to the improved uptake of reactive species and presence of defects that favor the dissolution of the framework. In line with this, the MOR-A is more deeply etched and shows 14% lower product yield than the parent zeolite (Table 1). Also as a result of the improved diffusion and dissolution, more mesopores with much smaller pore size are formed in the MOR-A-AF sample as compared to the MOR-AF (Figure 5C, D and Figure 7A,C,D).

Figure 9 A high resolution TEM image of MOR-A-AF demonstrating the presence of a defect-induced mesopore.

Besides, the framework defects left by the selective Al removal function as starting points for framework dissolution. These defects are spatially more accessible and energetically more favorable sites for dissolution. We have observed that the number of internal silanols (3734 cm -1 on the OH-IR spectra, Figure 4) on MOR-A-AF decreased with respect to its precursor, MOR-A (Figure 4 and Figure S7), which supports our interpretation of the role of defect sites in NH4F etching. We have also analyzed the small and ill-defined pores by high resolution TEM and found intensive and localized dissolution of zeolite framework (Figure 9). Furthermore, the Si/Al ratio of MOR-A-AF decreased (ca. 20) in respect to MOR-A (ca. 29) (Table 1). This apparent "desilication" behavior sharply contrasts the general observations that fluorides, especially the concentrated NH4F solutions, remove Si and Al equally from zeolite frameworks [START_REF] Qin | [END_REF][9][10][11]43]. Hence, the only plausible explanation is that during the NH4F etching of MOR-A, the dissolution starts preferentially at the defect sites left by Al removal, i.e., the Si-rich and highly defected by the Al extraction regions.

Accordingly, these artificial defects function as independent embryo of small and irregular mesopores, as shown in Figure 7D and Figure 9. Thanks to the presence of these chemically induced defects, small mesopores can now be conveniently introduced to the framework of nano-sized separate particles that are most likely coherent crystal domains in nature (figure 7D).

The set of our experimental data shows that the formation of mesopores under the present conditions involves two independent and synergistic pathways. The defects already present in MOR lead to the fragmentation of previously aggregated domains and the selective removal of hitherto hidden nano-crystals; this is the so-called mosaic structure of the zeolite [10]. The artificial defects introduced by partial removal of framework Al serve as additional sites versatile for the enhanced dissolution of zeolite structure. Thus by carrying out a pretreatment on the as-synthesized zeolite before implementing the intended changes, one can effectively overcome the chemical or structural limitation predefined by zeolite synthesis history. In this way, it allows us to further explore the potential of post-synthesis modification in engineering and designing advanced zeolite materials for various applications.

Dealkylation of 1,3,5-Triisopropylbenzene on the parent and modified mordenite zeolites

In the dealkylation of 1,3,5-triisopropylbenzene (TiPBz, kinetic diameter 9.5 Å), a bulky molecule reacting mainly on the external surface of zeolites, MOR shows an initial conversion of 66% followed by a fast deactivation (Figure 10). MOR-AF samples start with a 10% higher initial conversion than MOR, and the activity stability is substantially improved. Considering that the intrinsic microporosity is not impacted by NH4F etching, the improved conversion of TiPBz is therefore attributed to more exposure of crystal external surface (Table 1) as a result of the decrease of the microporous domain size. The initial TiPBz conversion on MOR-A is only about 10% (Figure 10), although this sample shows almost twice higher collidine acidity than MOR. Apparently, although the acid leaching is helpful for the intraparticle diffusion of pyridine and collidine (Table 2, Figure 8A), it is not enough to improve the diffusion of a bulkier molecular such as TiPBz. The drop in the activity is also due to the extraction of aluminium from the external surface of zeolite. The initial TiPBz conversion on MOR-A-AF increases to 67% (Figure 10), more than 6 times higher than its counterpart MOR-A, and comparable to the parent mordenite. It is worth mentioning that the Al content of MOR sample is three times higher than that of MOR-A-AF (Table 1). This result suggests that some of the active sites located inside the MOR-A-AF crystals are accessible to TiPBz. These data illustrate the potential of defect-induced dissolution of zeolite framework to control and improve the catalytic performances of zeolites.

Conclusions

An in-depth study of the dissolution behavior of MOR-type zeolite under consequtive oxalic acid and NH4F treatment is carried out. The role of framework defects in the process of formation of inter-and intra-particle mesopores is identified.

The interface between intergrowths is a place for a fast dissolution that leads to separated crystals or inter-particle mesopore formation, revealing the intrinsic hidden mosaic structures of zeolite crystals. These intrinsic defects allow the engineering of zeolite crystals at meso scales and fragmentation of zeolite aggregates of their building parts.

The set of experimentak data reveals that the extrinsic defects, induced by chemical leaching in oxalic acid, generates different type of mesoporosity and can be used to control zeolite accessibility and activity at nanoscale. More precisely, the contribution of the extrinsic defects is twofold. First, they improve the intra-particle diffusion and absorption of chemicals substantially. Second, the defects themselves serve as the initial points for the preferential dissolution of a zeolite framework. As a result, the dissolution of the defect-containing framework is more efficient and uniform. The resultant hierarchical zeolite shows superior mesoporosity in terms of mesopore distribution and available mesopore volume and thus substantially improved accessibility to the active sites located inside the micropores. Derived catalysts show outstanding catalytic performance in the catalytic conversion of bulky molecules, as exemplified in the dealkylation of 1,3,5-triisopropylbenzene.

Herein, a simple and potentially universal method for post-synthesis zeolite engineering, which makes zeolite dissolution going beyond the limits set by zeolite structures and synthesis chemistry, is developed. This approach can be extended to other zeolites providing zeolite catalyst and molecular sieves with substantially improved performance.

  and Figure Sl). The N2 isotherm of MOR-A remains type I, but it is closer to type-I(b) (Figure 2A and Figure Sl) according to the new IUPAC classification of physisorption isotherms

  b EDS. c The weight percentage yield of MOR-AF (71 wt%) and MOR-A-AF (57 wt%) calculated based on the mass of MOR and MOR-A, respectively. d BET surface area. e t-plot. f Vtotal -Vmic (Vtotal: the volume adsorbed at P/P0 = 0.97). MOR: the parent mordenite; MOR-A: the oxalic acid treated mordenite, MOR-AF: the NH4F treated mordenite, MOR-A-AF: the sequential oxalic acid and NH4F treated mordenite.

Figure 1

 1 Figure 1 XRD patterns of the parent mordenite (MOR), the sample treated by oxalic

Figure 2

 2 Figure 2 N2 physisorption isotherms (A) and pore size distribution (B) of MOR,

Figure 3

 3 Figure 3 The 27 Al MAS NMR spectra of MOR, MOR-A, MOR-AF, and MOR-A-AF

  dealumination (Figure4). Besides, there are broad bands in the region of 3650-3710 cm -1 (Figure4A, indicated by arrow). These data show clearly that defect sites, most probably in the form of isolated silanol groups, have been introduced into the mordenite zeolite framework as desired[35].

Figure 5

 5 Figure 5 The high-resolution low-voltage SEM images of MOR (A), MOR-A (B),

Figure 6

 6 Figure 6 The TEM images of MOR (A), MOR-A (B), MOR-AF (C), and MOR-A-AF (D, E).

Figure 7

 7 Figure 7 Representative TEM images of MOR-AF (A), a mordenite sample prepared

Figure 10 .

 10 Figure 10. Conversion of 1,3,5-triisopropylbenzene as a function of the catalyst time

Table 1 .

 1 Chemical composition, product yield, specific surface area, and porosity data of the parent and modified mordenite samples.

	Samples	Si/Al a Si/Al b	Yield c wt%	SBET d m 2 /g	Sext e m 2 /g	Vmic e cm 3 /g	Vsec f cm 3 /g
	MOR	6.5	6.8	̶	489	25	0.18	0.06
	MOR-AF	6.5	̶	71	490	67	0.17	0.16
	MOR-A	29.0	26.5	̶	512	39	0.19	0.08
	MOR-A-AF	19.8	20.1	57	558	93	0.19	0.27

a ICP.

Table 2 .

 2 Acidity and accessibility of the active sites of the parent and modified mordenite samples measured by IR using pyridine (Py) and collidine (Co) as probe molecules (The unit for acid amount: µmol g -1 ).

	Samples	Acidity a	B	Acidity b L	B+L	Acidity c	Accessibility d Py Co
	MOR	2222	992	73	1065	49	48	2
	MOR-AF	2222	909	82	991	418	45	19
	MOR-A	556	355 157	513	82	92	15
	MOR-A-AF	800	422 348	770	326	96	41
	a

Acknoweledgements

The authors acknowledge funding from the Sino-French joint laboratory "Zeolites". Zhengxing Qin acknowledge the support from NSFC21706285, Qingdao Applied Basic Research Project (19-6-2-70-cg), the Fundamental Research Funds for the Central Universities (18CX02013A), ZQ and SM acknowledge the support from NSFC21991091.