Pedro S F Mendes

João M Silva

M Filipa Ribeiro

Antoine Daudin

Christophe Bouchy
email: christophe.bouchy@ifpen.fr

From powder to extrudate zeolite-based bifunctional hydroisomerization catalysts: zeolite integrity and Pt location

Keywords: hydroisomerization, zeolite shaping, HUSY, metal-acid balance, metal-acid intimacy

The development of zeolite-based hydroisomerization catalysts in the powder form is widely spread in scientific literature but shaped bodies are the ones being employed in industry. This work aims at bridging that gap. The shaping procedure for HUSY zeolite in presence of an alumina binder disclosed herein achieved a full conservation of zeolite properties, e.g. porosity and Brønsted acidity. When Pt was located inside the zeolite and an homogeneous Pt distribution along the extrudate was ensured, shaped Pt-containing catalysts had similar hydroisomerization performances to those of powder Pt/zeolite in terms of turnover frequency per Brønsted acid site and maximal feed isomers yield. Conversely, non-uniform distribution of Pt along the extrudates diameter (macroscale) was observed to reduce the feed isomers yield. This was tentatively explained by the lower local metal to acid sites ratio in the core of the extrudates. Optimal performance of shaped bifunctional catalysts requires, hence, an adequate metal to acid sites ratio throughout the whole catalyst (i.e. at macroscale), even if full intimacy between catalytic functions is ensured at the nanoscale by the selective deposition of Pt inside the zeolite.

Introduction

Bifunctional catalysts comprising acid and hydrogenation-dehydrogenation functions are of utmost important in industrial relevant processes. In the petroleum refining industry, the hydroisomerization of C 5 -C 6 n-paraffins to produce high-octane [START_REF] Primo | Zeolites as catalysts in oil refining[END_REF][START_REF] Vogt | Zeolites and Zeotypes for Oil and Gas Conversion[END_REF] gasoline and the production of diesel by hydrocracking of heavy oil cuts (e.g. vacuum gas oil) [START_REF] Primo | Zeolites as catalysts in oil refining[END_REF][START_REF] Vogt | Zeolites and Zeotypes for Oil and Gas Conversion[END_REF][START_REF] Bertoncini | Hydrocracking[END_REF][START_REF] Weitkamp | Catalytic Hydrocracking-Mechanisms and Versatility of the Process[END_REF] is achieved thanks to bifunctional catalysts. In the context of diversification of liquid fuels sources, bifunctional catalysts have also a key role to play either on biodiesel production by hydrotreatment and hydroisomerization of vegetable oils [START_REF] Furimsky | Hydroprocessing challenges in biofuels production[END_REF][START_REF] Daudin | Hydrotreatment of Vegetable Oils[END_REF][START_REF] Galadima | Catalytic upgrading of vegetable oils into jet fuels range hydrocarbons using heterogeneous catalysts: A review[END_REF] or synthetic diesel production by the Low Temperature Fischer-Tropsch process [START_REF] Sousa-Aguiar | The main catalytic challenges in GTL (gas-to-liquids) processes[END_REF][START_REF] Liu | Technical review on jet fuel production[END_REF][START_REF] Khodakov | Advances in the development of novel cobalt Fischer-Tropsch catalysts for synthesis of long-chain hydrocarbons and clean fuels[END_REF][START_REF] Bouchy | Fischer-Tropsch Waxes Upgrading via Hydrocracking and Selective Hydroisomerization[END_REF].

The hydroisomerization of long chain n-paraffins involves a bifunctional catalyst typically consisting of a noble metal finely dispersed over a zeolite (usually mixed with alumina). The choice of the adequate zeolite depends on acid-basic properties and on its pore architecture combining micro and mesopores [START_REF] Akhmedov | Recent advances and future aspects in the selective isomerization of high n-alkanes[END_REF][START_REF] Mccusker | Zeolite structures[END_REF]. The ultrastabilized Y (USY) zeolite is the most studied and industrially employed zeolite [START_REF] Bertoncini | Hydrocracking[END_REF] but BEA zeolite [START_REF] Park | Comparison of Pt/zeolite catalysts for n-hexadecane hydroisomerization[END_REF][START_REF] Gutiérrez | Preliminary studies on fuel production through LCO hydrocracking on noble-metal supported catalysts[END_REF][START_REF] Martens | Relation Between Paraffin Isomerisation Capability and Pore Architecture of Large-Pore Bifunctional Zeolites[END_REF][START_REF] Zhang | Effect of zeolite structure and acidity on the product selectivity and reaction mechanism for n-octane hydroisomerization and hydrocracking[END_REF][START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF] as well as some medium-pore frameworks have also revealed promising results [START_REF] Souverijns | Hydrocracking of isoheptadecanes on Pt/H-ZSM-22: An example of pore mouth catalysis[END_REF][START_REF] Mota | IZM-2: A promising new zeolite for the selective hydroisomerization of long-chain n-alkanes[END_REF][START_REF] Zhang | Shape Selectivity in Hydroisomerization of Hexadecane over Pt Supported on 10-Ring Zeolites: ZSM-22[END_REF][START_REF] Mendes | A systematic study on mixtures of Pt/zeolite as hydroisomerization catalysts[END_REF]. For a given zeolite and operating conditions, the reaction rates are hence determined by the balance between the hydrogenatingdehydrogenating (HDH) and acid functions [START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF][START_REF] Alvarez | Hydroisomerization and hydrocracking of alkanes -Influence of the balance between acid and hydrogenating functions on the transformation of n-decane on PtHY catalysts[END_REF][START_REF] Guisnet | Ideal" bifunctional catalysis over Pt-acid zeolites[END_REF], and the distance between these functions (Weisz's intimacy criterion) [START_REF] Weisz | Polyfunctional Heterogeneous Catalysis[END_REF][START_REF] Batalha | n-Hexadecane hydroisomerization over Pt-HBEA catalysts. Quantification and effect of the intimacy between metal and protonic sites[END_REF]. Specifically, most of the studies have shown that maximal intimacy between metal and acid sites enhances the selectivity in feed isomers [START_REF] Weisz | Polyfunctional Heterogeneous Catalysis[END_REF][START_REF] Batalha | n-Hexadecane hydroisomerization over Pt-HBEA catalysts. Quantification and effect of the intimacy between metal and protonic sites[END_REF].

However, recent reports reopened the debate about the ideal proximity between both functions for optimal performances [START_REF] Zecevic | Nanoscale intimacy in bifunctional catalysts for selective conversion of hydrocarbons[END_REF]. Designing a bifunctional catalyst is thus a complex process where numerous parameters play a role requiring careful study. In order to reduce the degree of complexity, usually the studies on hydroisomerization catalysts are carried out over zeolitebased catalysts in the powder form. Consequently, studies focusing catalyst scale-up, and in particular shaped bifunctional catalysts, are lacking in open literature, in spite of the great number of patents in this field [START_REF] Gallei | Development of Industrial Catalysts[END_REF][START_REF] Schüth | Catalyst Forming[END_REF].

In the case of zeolites, the most common method of shaping is mulling-extrusion method. This requires the use of a binder, typically alumina or silica, due to the very poor mechanical resistance of shaped zeolites [START_REF] Bedard | Synthesis of Zeolites and Manufacture of Zeolitic Catalysts and Adsorbents[END_REF]. Shaping is commonly described as a complex process during which the zeolite active sites can be drastically modified [START_REF] Mitchell | From powder to technical body: the undervalued science of catalyst scale up[END_REF]. The existing reports focus on catalytic cracking catalysts and point out either beneficial or detrimental effects of shaping.

The shaping of ZSM-5 zeolite with different binders, particularly boehmite, has been described to result in the neutralization of the most acidic Brønsted sites [START_REF] Martin | Neutralization of HZSM-5 Brönsted acid sites by shaping with boehmite[END_REF][START_REF] Martin | Effect of Si: Al ratio and type of binder on the catalytic properties of HZSM-5 catalysts[END_REF][START_REF] Michels | Effects of Binders on the Performance of Shaped Hierarchical MFI Zeolites in Methanol-to-Hydrocarbons[END_REF][START_REF] Lucas | Liquid-Phase Hydroisomerization of n -Octane over Platinum-Containing Zeolite-Based Catalysts with and without Binder[END_REF]. In the case of catalytic cracking, the reduction of the zeolite acidity can be beneficial conducing to a reduction of catalyst deactivation and so longer catalyst lifetimes [START_REF] Martin | Neutralization of HZSM-5 Brönsted acid sites by shaping with boehmite[END_REF][START_REF] Martin | Effect of Si: Al ratio and type of binder on the catalytic properties of HZSM-5 catalysts[END_REF]. Some cases of improved acidity following shaping processes are also documented in literature [START_REF] Lucas | Liquid-Phase Hydroisomerization of n -Octane over Platinum-Containing Zeolite-Based Catalysts with and without Binder[END_REF][START_REF] Lee | Influence of Catalyst Binders on the Acidity and Catalytic Performance of HZSM-5 Zeolites for Methanol-to-Propylene (MTP) Process: Single and Binary Binder System[END_REF][START_REF] Du | Influence of binder on catalytic performance of Ni/HZSM-5 for hydrodeoxygenation of cyclohexanone[END_REF][START_REF] Ito | Catalysis at the interface of nano-oxides and nanozeolites[END_REF]. The characteristics of the binder and the shaping procedure play, hence, a vital role on the final properties of the zeolite [START_REF] Whiting | The curious case of zeolite-clay/binder interactions and their consequences for catalyst preparation[END_REF], but for the same binder and shaping procedure different behaviours can also occur depending on the zeolite [START_REF] Lucas | Effect of the metal loading in the hydroisomerization of n-octane over beta agglomerated zeolite based catalysts[END_REF]. It is also worth mentioning that full preservation of the structure and porous network of zeolites can also be achieved but it is scarcely reported [START_REF] Gueudré | Superior Mass Transfer Properties of Technical Zeolite Bodies with Hierarchical Porosity[END_REF].

Up to now, the shaping process of zeolites and its impact on the behaviour of hydroisomerization catalysts has been scarcely considered in the open literature despite their industrial relevance. This work is a means of reducing this gap. Firstly, the properties of a HUSY zeolite will be studied throughout the scale-up, e.g. before and after shaping. The performances of a series of shaped bifunctional HUSY catalysts will be compared to that of powder HUSY ones in the hydroisomerization of n-hexadecane. Pt will be the hydrogenating function of both catalyst series. In order to compare the intrinsic behaviour of both catalysts, the metal to acid sites ratio will be varied while keeping, tentatively, a comparable metal-acid sites distance through the selective deposition of Pt particles inside the zeolite crystals.

Materials and Methods

Catalysts preparation

A commercial HUSY zeolite (CBV720) from Zeolyst, with a sodium to framework aluminium ratio of 0.01, was employed without any further treatment. The shaped zeolite was prepared by a mulling-extrusion method. The binder used was a commercial boehmite (Pural SB-3) from Sasol which does not contain any cationic impurities. The zeolite, boehmite and Methocel powders (17:83:1 weight proportion on a dry basis) were mixed with an aqueous solution (57 g of water per 100 g of dry powder) containing 7.6 wt.% of nitric acid (i.e. 3.6 g of HNO 3 per 100 g of dry boehmite). After kneading this mixture during 30 min, an aqueous solution (59 g of water per 100 g of dry powder) containing 1 wt.% of ammonium was added. The kneading of the paste proceeded for 15 min. The paste was extruded through a die having a trilobal shape with an diameter of 1.6 mm. Extrudates were then dried at 353 K overnight and calcined at 873 K over 2 h (heating rate of 5 K min -1 ) under dry air (1.5 NL h -1 g support -1

). The extrudates length was kept between 3 and 6 mm. A reference sample containing only boehmite was prepared employing the same procedure in absence of zeolite.

The introduction of platinum in the unshaped zeolite was performed by incipient wetness . Three plateaux at 423, 523 and 623 K over 1 h each and a final plateau at 773 K over 2 h were performed. A heating rate of 5 K min -1 was used.

Solids characterization

Quantitative elemental analysis was performed by x-ray fluorescence. Samples were grinded and sieved into a granulometry under 200 µm. Measurements were carried out directly over powder samples in a Thermofischer Scientific Advant-X instrument. The identification of crystalline phases was achieved by x-ray powder diffraction (XRD). The diffraction patterns were acquired by a PANalytical X'Pert Pro diffractometer, in a Bragg-Brentano configuration with a stationary x-ray source and a movable detector. The analysis range employed was from 2θ = 2 to 70°, with a step of 0,05° and a counting time of 12 seconds per step. The XRD patterns were treated with the software EVA by Bruker and compared with database of ICDD (Figures S1 andS2).

Nitrogen adsorption measurements were carried out at 77 K on a Micrometrics ASAP 2010 apparatus. Before adsorption, zeolite samples were degassed under vacuum at 363 K for 1 h and then at 623 K for 4 h. The total pore volume (V total ) was calculated from the adsorbed volume of nitrogen for a relative pressure P/P 0 of 0.97 whereas the microporous volume (V micro )

and surface area (S micro ) were determined using the t-plot method [START_REF] Leofanti | Surface area and pore texture of catalysts[END_REF]. The mercury porosimetry was carried out in a Micrometrics Autopore IV 9500 apparatus under vacuum (30-50 mmHg).

The sample was first pre-treated in a kiln at 523 K during 2 h. The relationship between Hg pressure and pore diameter was obtained through the surface tension of mercury [START_REF] Giesche | Mercury Porosimetry: A General (Practical) Overview[END_REF].

The size and morphology of the zeolite crystals in powder zeolite samples and in shaped zeolitic supports were studied by Scanning Electron Microscopy (SEM), using a SEM ZEISS Supra 40 equipped with a field emission gun and an Everhart-Thornley secondary electron detector. Local Si/Al ratios in zeolite crystals were measured by Energy Dispersive X-ray Spectrometry (TEM-EDX), in a JEOL JEM 2100F equipped with a Si-Li detector. Before observation, the powders were embedded in an epoxy resin and thin slices (about 70 nm) were cut by ultramicrotomy and transferred onto a copper grid covered by a holey carbon membrane.

Platinum dispersion of shaped supports was determined by oxygen titration of chemisorbed hydrogen in a homemade apparatus with a thermal conductivity detector. The pre-reduced saturated samples were pre-treated under H 2 . Two cycles of hydrogen titration of chemisorbed oxygen and oxygen titration of chemisorbed hydrogen were consecutively performed at room temperature. The results presented correspond to the average O 2 consumption in the two cycles; relative deviation between measures was inferior to 10%. The metal dispersion was calculated by means of a 0.75 O 2 :Pt stoichiometric coefficient [START_REF] Bartholemew | H2 adsorption on supported noble metals and its use in determining metal dispersion[END_REF][START_REF] Prasad | Stoichiometry of Hydrogen-Oxygen Titrations on Supported Platinum Catalysts[END_REF].

The investigation of metal location implies the use of microscopic techniques. For powder samples, the most comprehensive technique is electron tomography which enables a 3dimensional visualization of the zeolite crystals exceeding thus the 2-dimension information routinely obtained by transmission electron microscopy. For Pt/HUSY samples in particular, electron tomography measurements revealed a homogeneous distribution of Pt inside the zeolite crystals [START_REF] Mendes | Nanoscale insights into Pt-impregnated mixtures of zeolites[END_REF]. In the case of shaped materials, the lack of studies in literature goes along with underdeveloped analytical tools for the study of such materials. Techniques that have been successfully used to assess the location of elements in shaped materials is the electron probe micro analysis (EPMA) and TEM-EDX [47]. For noble metals at low concentration, TEM-EDX is not sensitive enough to detect the metal in the zeolite and in the binder. Despite its lower spatial resolution, the sensitivity of EPMA allows to extrapolate the concentration of metal in binder and zeolithe.

The electron probe micro analysis (EPMA) were carried out in a JEOL JXA 8100 equipment.

The extrudates were embedded in an Specifix-40 epoxy resin (Struers, Ballerup) that was prepolymerized to prevent carbon contamination [START_REF] Sorbier | Microanalysis of porous materials[END_REF] and polished to obtain a flat section. A thin conductive carbon layer was deposited to prevent surface charging effects. Samples were analysed using a 20 keV and 100 nA electron beam. Al was analysed on the Kα (2) line, Si on the Kα line, Pt on the Mα line and O was calculated assuming Al 2 O 3 and in SiO 2 stoichiometry.

For each sample, five profiles were measured on five different catalyst grains along a 3-fold symmetry axis of the extrudates (from a hollow to the lobe), further called the diameter in the paper. Each profile was acquired with 25 points resulting in a constant step of about 56 µm.

Local measured concentrations were then processed using the method of the distance transform [START_REF] Sorbier | Use of the Distance Transform for Integration of Local Measurements: Principle and Application in Chemical Engineering[END_REF] to obtain the overall concentration of each element in the extrudate.

In order to condense the elemental profiles into a single parameter, a distribution coefficient can be used. The distribution coefficient element is the ratio of the mean concentration along the extrudate to overall concentration assuming a spherical grain of diameter 2 equal to the length of the profile [START_REF] Sorbier | Determining the Distribution of Metal by Electron Probe Micro Analysis[END_REF] (Eq. 1). By these means, a distribution coefficient close to 1 means a uniform distribution of the element along the extrudate diameter. Otherwise, the coefficient will be higher than 1, if the concentration is greater in the core than at the edges (so-called egg-yolk distribution); and lower than 1 if the concentration is greater at the edges than in the core (socalled egg-shell distribution) [START_REF] Sorbier | Determining the Distribution of Metal by Electron Probe Micro Analysis[END_REF].

To calculate the concentration of Pt in alumina and zeolite phases, the approach described by Kasztelan et al. was applied [47]. For all the analysis points in all the extrudates EPMA gave

!"!#!$% = & ' ( !"!#!$% ) * * 3 ' ( !"!#!$% & ) * * Equation 1 zeolite = SiO 2 1 + SiO 2 + Al 2 O 3
Equation 2

The plot of Pt , the local concentration of Pt, as function of zeolite was fitted to a straight line.

Extrapolation of the line for zeolite = 0 and for zeolite = 1 gave the concentrations of Pt on the alumina phase and zeolite phase respectively.

Details on the characterization of Pt/HUSY samples can be found elsewhere in literature [START_REF] Mendes | Nanoscale insights into Pt-impregnated mixtures of zeolites[END_REF][START_REF] Mendes | Hydrogenating activity of Pt/zeolite catalysts focusing acid support and metal dispersion influence[END_REF].

Catalytic tests

The m-xylene isomerization was used as a model reaction to characterize the Brønsted acidity of zeolite and alumina-shaped zeolite. The reaction was carried out at 623 K under atmospheric pressure using a pyrex glass down-flow reactor. All catalysts were tested at the same granulometry (0.2-0.5 mm). Shaped samples were grinded into 0.2-0.5 mm pellets whereas powder samples were first pressed into wafers (ρ wafer =10 mg cm -2

) and then grinded. Before reaction, samples were pre-treated under air flow (150 NL h -1 g zeolite -1

) at 623 K over 4 h (heating rate of 5 K min -1

). Reaction took place under nitrogen flow (160 NL h -1 g zeolite -1

), using a weight hourly space velocity of 5.6 g m-xylene g zeolite -1 s -1

. This space velocity ensured conversion levels below 20 % for all catalysts. The reactor effluent was heated at about 413 K to prevent product condensation and was analysed on-line in an apparatus for gas-chromatography coupled with a flame ionization detector (GC-FID) equipped with a 50 m HP-FFAP capillary column from

Agilent. An analysis was performed at every 20 min. At each time, the catalytic activity was calculated as the amount of m-xylene converted per zeolite mass and per unit of time. The deactivation curve (i.e. catalytic activity vs. time-on-stream) was fitted to a logarithmic equation and the activity at 1 min of reaction was extrapolated by means of such equation.

The hydroisomerization of n-hexadecane took place in high-throughput catalytic test unit with fixed-bed downflow reactors described elsewhere [START_REF] Mota | High-throughput experimentation for the discovery of new hydroconversion catalysts[END_REF]. The catalytic testing was fully automated, with the operating conditions of the catalytic bed of each reaction being monitored individually. As for m-xylene isomerization, all catalysts were tested at the same granulometry (0.2-0.5 mm) in order to prevent any diffusional limitations. The catalyst was then pre-treated using a hydrogen flow rate of 4 NL/h/g and heated at 5 K/min to a final reduction temperature of 723 K for one hour. The tests were performed at 1.1 MPa total pressure, a molar H 2 to n-C 16 ratio of 10. The weight hourly space velocity (WHSV) ranged between 0.14 and 1.1 mg n-hexadecane g catalyst -1 s -1 and the reaction temperature ranged from 483 to 498 K in order to modify the conversion level. Products were analysed on-line by a GC-FID apparatus equipped with low polarity capillary columns from Agilent (DB-1 and CP-Sil-5-CB). Deactivation of all samples was negligible at the end of the catalytic tests. Catalytic performances were calculated by mass balance to the carbon atoms at the outlet. n-C 16 conversion was calculated as the amount of carbon atoms of the products divided by total amount of carbon atoms (uncertainty ±5% for conversion). The yield of a given product was calculated as the amount of carbon atoms of that product divided by total amount of carbon atoms (uncertainty ±2% for i-C 16 yield). Activity was calculated as the apparent kinetic constant for first-order consumption of n-hexadecane per catalyst mass per unit of time. The average turnover frequency per Brønsted sites was defined as the activity per mole of Bronsted acid site of the zeolite, Al IV (see Table 1).

Results

Characterization of the supports

Physico-chemical properties

The samples were firstly characterized by Scanning Electron Microscopy (SEM) to get hold of the extrudates macroscopic organization. The micrographs for shaped HUSY extrudates are depicted in Figure 1. The shaped support consisted in a dense and homogeneous matrix presenting a number of morphological features (Figure 1a). The main population was composed of assemblies of some well-defined crystals dispersed in a homogeneous way in the support (Figure 1c). Porous clusters of crystals in the 1-20 µm size range were also detected (Figure 1b). Crystals were in the 300-1000 nm range matching that observed for parent zeolite [START_REF] Mendes | Nanoscale insights into Pt-impregnated mixtures of zeolites[END_REF]. The white spots correspond to dense agglomerates of HUSY crystals (Figure 1d). These agglomerates were also observed in parent zeolite (Figure S3) and, according to TEM-EDX have a Si/Al atomic ratio (3.5) to that typically attained in as-synthesized Y zeolite (2.1-3.0) [START_REF] Lutz | Zeolite Y: Synthesis, Modification, and Properties-A Case Revisited[END_REF].

Therefore, the dense particles observed should correspond to Y zeolite that did not undergo any subsequent post-treatments. For the main population of HUSY crystals, a Si/Al atomic ratio of 18.6 was measured. This composition is analogous to that of the bulk sample (16.7), determined by X-Ray Fluorescence (Table 1), confirming that the dense particles observed were minor in the HUSY sample. The physico-chemical properties of the HUSY zeolite as well as the shaped extrudates are presented in Table 1. The commercial HUSY ((atomic Si/Al) global =16.7) sample employed herein has been previously characterized in detail [START_REF] Mendes | Nanoscale insights into Pt-impregnated mixtures of zeolites[END_REF][START_REF] Mendes | Hydrogenating activity of Pt/zeolite catalysts focusing acid support and metal dispersion influence[END_REF]. The diffractogram disclosed a purely crystalline zeolite (Figure 2) with the typical diffraction pattern of FAU framework. In terms of pore topology, FAU framework has a 3-dimensional channel with an equivalent minimum pore size of 0.74 nm and supercages of 1.4 nm in the channel intersections [START_REF] Baerlocher | Atlas of Zeolite Framework Types[END_REF]. The framework Si/Al atomic ratio amounted to 18.4, resulting in a concentration of framework aluminium Al IV of 820 µmol g -1 [START_REF] Mendes | Hydrogenating activity of Pt/zeolite catalysts focusing acid support and metal dispersion influence[END_REF]. As these aluminium atoms generate negatively charged oxygen atoms in zeolites framework [START_REF] Primo | Zeolites as catalysts in oil refining[END_REF], n Al(IV) is an estimation of Brønsted acid sites concentration for zeolites in the protonic form. The trilobe extrudates were characterized after calcination. The only phase detected in the shaped support based exclusively on binder matched with γ-Al 2 O 3 transition phase (Figure 2).

This phase is known to occur after calcination of boehmite in the 773-1073 K range [START_REF] Wefers | Oxides and hydroxides of aluminum[END_REF]. This result was thus in agreement with the calcination temperature of the support (873 K). The diffractograms of HUSY, alumina, and shaped HUSY (Figure 2) only revealed γ-Al 2 O 3 and FAU framework phases. Moreover, the width of the peaks was similar pointing to a comparable level of crystallinity in both parent HUSY and shaped HUSY samples. The fraction of zeolite in the Al 2 O 3 +HUSY sample was thus estimated based on the amount of silicon detected (Table 1).

The zeolitic extrudate comprised roughly 83.5% of alumina and 16.5% of HUSY zeolite.

Accordingly, the concentration of Al IV sites in the extrudate is expected to be around 135 µmol g The textural properties of all samples were compiled on Table 1. The HUSY sample is characterized by a large micropore volume due to its large pores as well as the presence of supercages. At the origin of the mesoporosity of HUSY sample are 10 nm pores obtained by dealumination of the original aluminium-rich zeolite [START_REF] Mendes | Nanoscale insights into Pt-impregnated mixtures of zeolites[END_REF]. Macropores were not detected in any of the samples excluding. Thus, for the shaped supports, the presence of defects generated during the shaping process (e.g. cracks and large cavities). Intensity (a.u.)

2θ (°)

zeolite and Al 2 O 3 in the support (Figure 3). After shaping, 83% of the micropore volume was preserved. Zeolite can be considered responsible for all the microporosity in extrudates as Al 2 O 3 did not hold any pores with less than 5 nm. Therefore, the similar microporous volume of shaped supports to that of parent zeolites hints at the preservation of zeolite structure after shaping in agreement with the XRD measurements. It furthermore reveals that the alumina platelets did not block the access to the zeolite micropores to a significant extend. The

Acidic properties

Assessing the Brønsted acidity of shaped zeolitic support is not straightforward. Some authors have used NH 3 -TPD [START_REF] Zecevic | Nanoscale intimacy in bifunctional catalysts for selective conversion of hydrocarbons[END_REF][START_REF] Michels | Hierarchically Structured Zeolite Bodies: Assembling Micro-, Meso-, and Macroporosity Levels in Complex Materials with Enhanced Properties[END_REF] but, as this technique is not sensitive to the nature of the acid sites, the Lewis acidity of γ-Al 2 O 3 can complicate the interpretation of the experimental results.

Consecutive pyridine adsorption and thermodesorption followed by in situ FTIR has been also performed in shaped supports [START_REF] Michels | Effects of Binders on the Performance of Shaped Hierarchical MFI Zeolites in Methanol-to-Hydrocarbons[END_REF] and it is the most common method to characterize zeolite acidity. In this case, the pyridine-acid sites interaction leads to two differents IR bands [START_REF] Lercher | Infrared studies of the surface acidity of oxides and zeolites using adsorbed probe molecules[END_REF] enabling a separate quantification of Brønsted and Lewis. In Figure S4, the spectra of HUSY zeolite is compared to those of shaped support and the corresponding mechanical mixture of HUSY zeolite with grinded γ-Al ) or V meso (mL g sup -1

) Calculated Measured stake. To overcome such problem, the Brønsted acidity of shaped HUSY was compared to that of parent zeolite through a model reaction catalyzed by such acid sites.

The selected reaction was the isomerization of m-xylene [START_REF] Morin | Influence of the framework composition of commerical HFAU zeolites on their activity and selectivity in m-xylene transformation[END_REF][START_REF] Guisnet | Model Reactions for Characterizing the Acidity of Solid Catalysts[END_REF]. All samples were tested in powder form, at a similar m-xylene/zeolite space velocity, and the activity was expressed per zeolite mass. The catalytic activity decreased with time-on-stream and this evolution was well described by a logarithmic equation (Figure S5). The activity at 1 min of reaction was extrapolated by these means and represented in Figure 4for the HUSY-based samples. The activity per zeolite mass was about 1.1 mmol g -1 s -1

, for shaped and unshaped USY. This confirms that grinding and shaping procedures used herein have no impact on the intrinsic Brønsted activity of zeolite. Besides the shaping procedure in itself, the absence of cationic impurities in the boehmite employed is also believed to be of prime importance to preserve the Brønsted activity during shaping.

Characterization of the Pt-based bifunctional catalysts

Metal properties

The metal properties of the samples are presented on Table 2. The Pt loading of bifunctional shaped catalysts was selected in order to cover a comparable range of n Pt /n Al to that of Pt/HUSY. The Pt content of all solids was determined by XRF. For the unshaped Pt/zeolite catalysts, the measured content was in agreement with the expected content within the experimental error (±10 %). In contrast, for the the shaped support obtained by ionic exchange, the deviation increased along with the metal loading. sample. The impact of Pt introduction on zeolite acidity should remain limited, due to the relatively small loading of Pt (< 1 wt.%) introduced by incipient wetness impregnation. Hence, the concentration of Brønsted acid sites in the catalysts was considered similar to that of parent HUSY zeolite. In this way, the metal to acid sites ratio (n Pt /n Al ) was estimated for each catalyst.

In general, the shaped catalysts cover superior n Pt /n Al . The low zeolite content in the shaped supports (ca. 17 wt.%) as well as their superior Pt dispersions were at the origin of such difference.

Metal location

The average elemental profiles of Pt, Si and Al along the diameter of extrudates are depicted in Figure 5 for Pt/(zeolite+Al 2 O 3 ) samples. Most of the profiles revealed an uniform distribution of Pt all along the diameter of the extrudate. The exception was the Pt profile for 0.07Pt/(HUSY+Al 2 O 3 ) sample in which a lower concentration of Pt was noticeable at the core of the extrudate. In order to condense the elemental profiles into a single parameter, a distribution coefficient can be used. The distribution coefficient is the ratio of the mean concentration along the extrudate to overall concentration [START_REF] Sorbier | Determining the Distribution of Metal by Electron Probe Micro Analysis[END_REF] (vide Section 2.2). In the case of platinum (Figure 6a), according to the distribution coefficient, the metal was uniformly distributed along the extrudates of samples 0.11Pt/(HUSY+Al 2 O 3 ) and 0.25Pt/(HUSY+Al 2 O 3 ) but not for those of 0.07Pt/(HUSY+Al 2 O 3 ) sample. In this case, the coefficient was markedly below one (0.72) confirming the egg-shell like distribution previously qualitatively reported. The distribution coefficient for silicon was close to 1 for all samples (Figure 6a) revealing hence a uniform distribution of the zeolite along the extrudates diameter. This result corroborates the previous observations by SEM which pointed out a homogenous distribution of zeolite in the alumina. can be differentiated. The Pt content in zeolite was thus estimated (vide Section 2.2 for calculations details) and compared to the Pt content deposed in the whole support (Figure 6b).

For all three samples, the Pt content deposed in the HUSY zeolite nearly matched with the whole Pt deposed on the support. In other words, the Pt was preferentially introduced in the zeolite crystals with only a negligible amount of Pt located in the alumina in agreement with the selected procedure for metal introduction. In fact, the selective deposition of Pt in the zeolite has been reported to be due to the ionic exchange of the counter-ions of the zeolite Bronsted sites by the Pt(NH 3 ) 4 2+ precursor ions, in a solution with a pH above the point of zero charge of the zeolite but below that of the alumina [START_REF] Ribeiro | Étude de la technique d'échange ionique avec compétition. Cas du dépôt de platine sur support solide acide par échange cationique[END_REF]. As compared to Pt/HUSY, in Pt/(HUSY+Al 2 O 3 ) the Pt was also located in the zeolite crystals. However, there is a second scale in terms of Pt location that arises: the macroscopic scale, induced by the extrudate diameter. The macroscopic distribution of Pt was different among the shaped samples, with the lowest Pt loading leading to a local concentration of Pt in the extrudate edges of 0.089 % whereas that in the centre amounted to 0.026%. The local concentration of Pt in the edges was hence more than three times greater than in the centre of the extrudate. As the solution starts penetrating in the extrudates, the Pt precursors can be exchanged into the zeolite. Whenever the ionic exchange occurs faster than the solution diffusion, the metal will be first deposed in the edges of the

Hydroisomerization of n-hexadecane

As the catalytic results for Pt/HUSY series were discussed in detail in a previous work [START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF], the focus herein will be held at those of Pt/(HUSY+Al 2 O 3 ) series and the pertinent comparisons.

Catalytic activity

The consumption of n-paraffins in hydroconversion reactions has been shown to be first-order in the paraffin concentration [START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF][START_REF] Calemma | Hydroisomerization and hydrocracking of long chain n-alkanes on Pt/amorphous SiO2-Al2O3 catalyst[END_REF][START_REF] Girgis | Impact of catalyst metal acid balance in n-hexadecane hydroisomerization and hydrocracking[END_REF]. The first-order plots for the hydroisomerization of nhexadecane over Pt/(HUSY+Al 2 O 3 ) (Figure S5) reveal an excellent fit regardless of reaction temperature or catalyst confirming the abovementioned observations in literature. Using the apparent kinetic constant, the catalytic activity was determined for each catalyst at 483 K (Table 3). In Figure 7a), the catalyst series are compared. Regardless of Pt loading, as awaited, Pt/HUSY catalysts revealed a superior activity than Pt/(HUSY+Al 2 O 3 ) ones. The difference in catalytic activity corresponds, at iso-conversion, to a gap in reaction temperature of about 30 K.

Some practical implications arise as the reaction temperature may affect the catalytic performance, particularly the product selectivity. In order to have a comparable working temperature range for both catalyst series, slower space velocities were employed when testing the shaped catalysts (0.1-1.1 vs. 0.6 mg n-hexadecane g catalyst -1 s -1

). 0.11Pt/(HUSY+Al2O3) 0.39 2.9 58.6 0.25Pt/(HUSY+Al2O3) 0.39 2.9 60.6

Evolution of turnover frequency with n Pt /n Al

In order to fully understand the causes of the lower activity of shaped catalysts, the turnover frequency over the protonic sites of both catalyst series should be compared. As the turnover frequency depends also on the metal to acid sites ratio [START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF][START_REF] Alvarez | Hydroisomerization and hydrocracking of alkanes -Influence of the balance between acid and hydrogenating functions on the transformation of n-decane on PtHY catalysts[END_REF], the average turnover (TOF Al )

was plotted as function of n Pt /n Al ratio in Figure 7b). This evolution has been modelled previously for Pt/HUSY [START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF] and so the model results for Pt/HUSY were also included in the comparison.

The TOF Al obtained over Pt/(HUSY+Al 2 O 3 ) catalysts was strikingly comparable to those of Pt/HUSY catalysts. The underlying implication is that the available Brønsted sites hold a similar intrinsic activity regardless of the differences in catalyst formulation. Furthermore, as the TOF Al was independent of n Pt /n Al , according to the classical bifunctionnal mechanism, this implies that the dehydrogenation rate over the HDH function should have been sufficient to feed all the Brønsted sites in the HUSY+Al 2 O 3 support with intermediate olefinic species [START_REF] Alvarez | Hydroisomerization and hydrocracking of alkanes -Influence of the balance between acid and hydrogenating functions on the transformation of n-decane on PtHY catalysts[END_REF].

Product selectivity and yield

The lumped product distribution as function of conversion for different reaction temperatures is depicted in Figure 8 for 0.25Pt/(HUSY+Al 2 O 3 ) catalyst. Considering the evolution of product selectivity at low conversion, monobranched (MB) and multibranched (MTB) isomers appear as primary products. MB products were predominant up to 50% of conversion and MTB products for conversions between 50% and 90%. Cracking products (CP) selectivity stays below 5% for conversions lower than 40% and increase steadily with conversion. All in all, this is an indication of a rather consecutive apparent reaction scheme: n-C 16 MB MTB CP [START_REF] Alvarez | Hydroisomerization and hydrocracking of alkanes -Influence of the balance between acid and hydrogenating functions on the transformation of n-decane on PtHY catalysts[END_REF]. Additionally, the evolution of the products selectivities with conversion were the same, irrespectively of the reaction temperature. In other words, a 25 K shift in the reaction temperature did not modify the catalyst selectivity in the lumped products. It has been reported in literature that, for wellbalanced catalysts, the same product selectivity can be obtained over relatively wide ranges of operating conditions [START_REF] Steijns | Hydroisomerization and Hydrocracking. 2. Product Distributions from n-Decane and n-Dodecane[END_REF][START_REF] Thybaut | Acid-metal balance of a hydrocracking catalyst: Ideal versus nonideal behavior[END_REF] (giving rise to the so-called unique curve of feed isomer yield).

From the practical point of view, this means that the catalysts can be compared in terms of product yield even if discrepancies in the reaction temperature are present, as in this case. The C 16 isomer yield, i.e. the sum of MB and MTB yields, was represented as function of the conversion for Pt/(HUSY+Al 2 O 3 ) catalysts (Figure 9a). For catalysts loaded with 0.11 and 0.25%

Pt, the evolution of C 16 isomer yield with conversion were similar whereas that of 0.07Pt/(HUSY+Al 2 O 3 ) was clearly below the other two. The maximal C 16 isomer yield was thus lower for 0.07Pt/(HUSY+Al 2 O 3 ) as well as the conversion level at which it occurred. Both observations point to a more parallel reaction scheme over the 0.07Pt/(HUSY+Al 2 O 3 ) catalyst which can be associated with a longer residence time of intermediate olefins promoting consecutive acid-catalysed reactions and so cracking products, according to the classical bifunctional mechanism [START_REF] Weitkamp | Catalytic Hydrocracking-Mechanisms and Versatility of the Process[END_REF][START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF][START_REF] Alvarez | Hydroisomerization and hydrocracking of alkanes -Influence of the balance between acid and hydrogenating functions on the transformation of n-decane on PtHY catalysts[END_REF]. The high number of experimental points (due to a simultaneous change of reaction temperature and catalyst contact time) enabled the direct determination of the maximum of C 16 isomer yield (Table 3). On the contrary, those of Pt/HUSY catalysts were previously determined with the help of a macrokinetic model [START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF].

Figure 9b) compares the catalysts with the highest Pt loading of each series (i.e. unshaped and shaped HUSY). The evolution of C 16 isomer yield with conversion over 0.25Pt/(HUSY+Al 2 O 3 )

catalyst matched remarkably the one obtained with 0.7Pt/HUSY catalyst. The two catalysts series revealed hence the same selectivity towards isomerisation for sufficiently high Pt loadings. In such case, the intrinsic performance of Pt/HUSY and Pt/(HUSY+Al 2 O 3 ) catalysts was noticeably alike. To get hold at the full picture, the metal to acid sites ratio should be also taken into account. For a given zeolite, a unique relation between the maximal C 16 isomer yield (Y i-C16,max ) and n Pt /n Al can be established for Pt/zeolite catalysts [START_REF] Mendes | Quantification of metal-acid balance in hydroisomerization catalysts: a step further towards catalyst design[END_REF]. This relationship will be then analysed for the Pt/(zeolite+Al 2 O 3 ) catalysts. Therefore, in such case, the acid function of the shaped catalysts was "well-balanced" by its HDH function. In other words, the hydrogenation/dehydrogenation reactions were much faster than the acid-catalysed ones becoming those the rate-limiting steps [START_REF] Coonradt | Mechanism of hydrocracking -reactions of paraffins + olefins[END_REF]. For well-balanced catalysts, the apparent reaction scheme is thus governed by the zeolite properties and thereby intrinsic to the zeolite. Above all, this result confirms the similarity in the intrinsic selectivity of Pt/HUSY and Pt/(HUSY+Al 2 O 3 ) catalysts to C 16 isomers firstly revealed in the previous section.

Strikingly, for low n Pt /n Al , specifically for the 0.07Pt/(HUSY+Al 2 O 3 ) catalyst, the shaped catalysts were not as selective as Pt/HUSY ones for similar n Pt /n Al ratio (around 0.02). This significant reduction in the Y i-C16,max cannot therefore be explained by a lack of the amount of hydrogenating sites for the catalyst as whole. At this point, the heterogeneity of Pt distribution in the extrudates should be taken into consideration because the catalytic behaviour depends not only on the zeolite intrinsic properties and on the overall metal to acid sites ratio but also on the distance between metal and acid sites [START_REF] Weisz | Polyfunctional Heterogeneous Catalysis[END_REF][START_REF] Batalha | n-Hexadecane hydroisomerization over Pt-HBEA catalysts. Quantification and effect of the intimacy between metal and protonic sites[END_REF].

The role of Pt macroscopic distribution

The estimation of an average distance between Pt and Brønsted acid sites is virtually impossible due to the complexity of the system. As a result, we will focus on the calculation of a maximal Pt-acid sites distance taking into account well-known properties of the samples at question.

As abovementioned, an homogeneous distribution of Pt inside the zeolite crystal has been revealed for Pt/HUSY samples [START_REF] Mendes | Nanoscale insights into Pt-impregnated mixtures of zeolites[END_REF]. For such case, the maximal distance between Pt and acid sites (d Pt-acid ) would correspond to half of the distance between two consecutive Pt particles (d Pt- Pt ). Considering that Pt particles are homogenously dispersed throughout the support, we assume that each particle covers a cubic volume of support (V Pt-sup ). The distance between Pt particles can be hence calculated from that support volume that surrounds a given particle from its neighbours. The volume of zeolite per zeolite gram corresponds to the bulk density (ρ bulk =0.6 g cm -3 for HUSY zeolite). The number of Pt particles per gram of zeolite (n particles ) can be estimated by the volume of Pt per gram of zeolite divided by the volume of each particle.

Considering cubic particles and the particle diameter obtained by H 2 -O 2 titration (d Pt ), the density of Pt (21.45 g cm -3

) and the Pt loading (x Pt ), d Pt-acid can be ultimately calculated. In the case of shaped catalysts, as the platinum particles were also located inside the zeolite, the circumstances are therefore similar to those of Pt/HUSY with x Pt corresponding to the mass of Pt per mass of zeolite. The results for the Pt-acid sites distance calculations are presented in Table 4. It ranged from 30 to 10 nm from 0.1Pt/HUSY to 0.7Pt/HUSY sample. For the shaped Pt-catalysts, the distance was even shorter due to higher Pt concentration in the zeolite crystals (x Pt ). It is also however mentioning that a 15-fold increase in x Pt led only to a 3-fold reduction in the maximal Pt-acid site distance. This can be explained by the cubic root factor on Pt loading (Equation 1) ruling out hence the use of Pt loading to tune the metal-acid sites distance in a bifunctional catalyst. In all cases, the maximal Pt-acid sites was in a narrow range 10-30 nm. According to literature reports, a distance shorter than a few micrometers is required to ensure that diffusion of olefinic intermediates is not rate-limiting [START_REF] Weisz | Polyfunctional Heterogeneous Catalysis[END_REF][START_REF] Batalha | n-Hexadecane hydroisomerization over Pt-HBEA catalysts. Quantification and effect of the intimacy between metal and protonic sites[END_REF] pointing to an adequate intimacy between catalytic functions at the scale of zeolite crystals.

Meanwhile, when the shaped catalysts were crushed and sieved before the catalytic test, powder particles with a granulometry of 0.2-0.5 mm were formed. For 0.11Pt/(HUSY+Al 2 O 3 ) and 0.25Pt/(HUSY+Al 2 O 3 ) samples, as the metal was homogeneous distributed throughout the whole support, all the particles should have a comparable metal to acid sites ratio, similar to the overall ratio. Conversely, when 0.07Pt/(HUSY+Al 2 O 3 ) was crushed, the heterogeneous distribution of Pt throughout the extrudate should have resulted in different metal to acid sites ratios over the powder particles. As the particle size is about 100 times longer than required for the absence of diffusion limitations between the catalytic functions, this means that the olefins formed on one catalyst particle will not diffuse to another particle without reacting. In other words, the Pt of one particle will not balance the Brønsted acid sites located in another particle.

Therefore, in such case, the overall metal to acid sites ratio of the catalyst is not representative of the local metal to acid sites ratios. The local n Pt /n Al ratios should be therefore considered when evaluating the catalytic behaviour of the catalyst.

Discussion

As mentioned in the introduction, the shaping of zeolites is barely studied in the open literature.

It is frequently described as a complex process during which the zeolite can be significantly modified. In this work, zeolites were extruded with boehmite free of cationic impurities and fully characterized after the adequate thermal treatments. The same features in terms of zeolite structure, texture and Brønsted acidity were observed before and after shaping hinting to a full preservation of the zeolite properties in the extrudates. Our results differ from most of the literature reports that describe zeolite-binder interactions resulting, frequently, in the neutralization of the Brønsted acid sites [START_REF] Martin | Neutralization of HZSM-5 Brönsted acid sites by shaping with boehmite[END_REF][START_REF] Martin | Effect of Si: Al ratio and type of binder on the catalytic properties of HZSM-5 catalysts[END_REF][START_REF] Michels | Effects of Binders on the Performance of Shaped Hierarchical MFI Zeolites in Methanol-to-Hydrocarbons[END_REF][START_REF] Lucas | Liquid-Phase Hydroisomerization of n -Octane over Platinum-Containing Zeolite-Based Catalysts with and without Binder[END_REF]. However, those are beneficial effects to the reactions under study. In the case of hydroconversion, the main goal of zeolite shaping is to retain the intrinsic properties of the acidic function as designed for an optimal performance (i.e.

as in the powder form) and no reports exist up to now, to our knowledge. The procedure herein executed met, hence, that criterion proving that shaping of zeolites can be carried out with full preservation of its properties.

The repercussions of the scale-up from powder to shaped bodies are not restrained however to the properties of the zeolite, when bifonctionnal catalysts are at stake. Modifications on the properties of the metal phase, that was previously deposed directly in the zeolite and it is now introduced in the extrudates, are also expected. For Pt/zeolite samples, platinum was introduced directly in the zeolite by incipient wetness impregnation whilst, Pt introduction in the extrudates was carried out by ionic exchange with competition. In the latter, improved metal dispersions were obtained (50% vs. 73%) and, as the zeolite is diluted by the binder when shaped, remarkably greater metal to acid sites ratios can be obtained over shaped catalysts as compared to powder zeolites. On the other hand, a lower catalytic activity per gram of catalyst is to be always expected due to the lower zeolite content in shaped catalysts.

In the shaped samples, two special scales have to be considered: the nanoscale and the macroscale. At the nanoscale, the Pt was preferentially located in the zeolite, like in Pt/zeolite samples. At the macroscale, however, Pt was not always uniformly distributed along the extrudates diameter. For the lowest Pt loading in the shaped extrudates, it was preferentially deposed in external surface of the trilobe extrudates. When crushed to powder catalyst, the catalyst behaves as a mechanical mixture of catalysts holding different metal to acid sites ratio.

The consequence is, at the same overall n Pt /n Al , a lower C 16 isomers yield for catalysts with poor macroscopic Pt distribution. It is also worth mentioning that the reduction of the granulometry of the shaped catalysts before the catalytic test ensured both the fulfilment of the criteria for a plug-flow reactor operation and the direct comparison of catalytic behaviour to unshaped catalysts. Concomitantly, the critical macroscopic dimensions, i.e. half of the smallest particle dimension, remained in the same order of magnitude: 0.1-0.3 mm for crushed and 0.6 mm for non-crushed shaped catalysts enabling the observation of catalytic phenomena similar to those occurring when the shaped catalyst are not crushed.

Our results agree with the first study on the importance of the macroscopic Pt distribution [START_REF] Ribeiro | Influence of the macroscopic distribution of platinum in PtHFAU catalysts on their activity for n-hexane isomerization[END_REF] offering now an insight into the metal-acid sites distance in such case as well as evidence for the poor balance between metal and acid functions. This also agrees generically with the criterion deduced by Weisz for the minimal distance between metal and acid sites [START_REF] Weisz | Polyfunctional Heterogeneous Catalysis[END_REF] which can be converted as the number of acid steps undergone by olefinic intermediates during their diffusion between two Pt sites [START_REF] Batalha | n-Hexadecane hydroisomerization over Pt-HBEA catalysts. Quantification and effect of the intimacy between metal and protonic sites[END_REF]. Most of the studies have shown hence that the maximal intimacy between metal and acid sites enhances the selectivity in feed isomers. In contrast, it has been suggested recently that improved selectivity in feed isomers when Pt is deposed in the alumina binder instead of the zeolite [START_REF] Zecevic | Nanoscale intimacy in bifunctional catalysts for selective conversion of hydrocarbons[END_REF]. Herein a poor distribution of Pt throughout the extrudates has been demonstrated to have a significant detrimental effect in the catalyst selectivity. Further studies are still required but most of the evidence so far seems to uphold the importance of intimacy between metal and acid sites in the development of bifunctional catalysts for the hydroisomerization of long chain n-paraffins. Finally, n-hexadecane hydroconversion test can be conveniently used to check the homogeneous distribution of the metallic function within a shaped catalyst. Similar conclusions were drawn in the past for the nhexane hydroconversion test [START_REF] Ribeiro | Influence of the macroscopic distribution of platinum in PtHFAU catalysts on their activity for n-hexane isomerization[END_REF].

Conclusion

This work aimed at shedding light on the parameters to be controlled during the scale-up of bifunctional catalysts from powder to shaped bodies. The focus was held both at the impact of shaping on the zeolite properties and at the metal properties of Pt-containing samples.

The employed shaping procedure enabled the full preservation of zeolite framework and its properties. The structural features of zeolites in the shaped supports were analogous to those of parent zeolites and the microporous volume was mostly retained after shaping. Likewise, the activity of Brønsted acid sites was similar before and after shaping. Modifications on the metal phase location, that was previously deposed on the zeolite and it is now introduced in the extrudates, were observed. The nanoscale location was similar (Pt deposed in the zeolites also for shaped support), but the macroscale location depended on the Pt loading. For the lowest Pt content, the Pt was mostly deposed in the edges of the extrudate instead of uniformly distributed.

In hexadecane hydroisomerization, Pt-shaped catalysts revealed similar catalytic features to Pt/zeolite catalysts, including comparable turnover frequency per protonic site, for high metal to acid sites ratio. These results corroborated the full preservation of zeolite properties. In contrast, a reduction in the feed isomers selectivity, comparing to Pt/zeolite, was disclosed for shaped catalysts with similar metal to acid sites ratio but poor macroscopic distribution of Pt. As the diffusion of intermediates throughout the whole catalyst is much slower than the reaction rate, the catalyst behaves as a mechanical mixture of catalysts holding different metal to acid sites ratio. This leads, at the same overall metal to acid sites ratio, to a lower feed isomers yield.

Therefore, the behaviour of a shaped bifunctional catalyst depends not only on the overall metal to acid sites ratio but also on the local metal to acid sites ratios, which are only equal to the bulk one if the metal is homogeneously distributed throughout the shaped body.

In summary, the shaping of zeolites can be achieved with a full conservation of zeolite properties according to procedure herein. In such way, the development or modification of zeolites is fully reproduced in the industrial catalysts. Nevertheless, the repercussions of the scale-up from powder to shaped bodies are not restrained to the properties of the zeolite. An optimal catalytic behaviour can only be ensured by achieving an adequate balance between catalytic functions at the microscale.

  impregnation of [Pt(NH 3 ) 4 NO 3 ]•6H 2 O in a water solution. Aiming at a selective deposition of Pt in the zeolite crystals, the introduction of platinum in the shaped zeolite support was carried out by excess impregnation of the shaped zeolite with an aqueous solution containing [Pt(NH 3 ) 4 Cl 2 ]•H 2 O and NH 4 NO 3 . The NH 4 NO 3 /Pt(NH 3 ) 4 Cl 2 molar ratio of 120 ensured the adequate pH in solution. Typically, 10 grams of shaped zeolite were immersed into 80 ml of aqueous solution and gently stirred for 24 h. Afterwards the extrudates were rinced with 160 ml of distillated water. The same thermal treatments were performed for all materials. The impregnated materials were dried overnight at 383 K and then calcined in an air flow of 4 L h 1

Figure 1 :

 1 Figure 1: a), b), c) SEM micrographs for HUSY extrudates after a),b) mechanical polishing, and c) ionic cross section polishing (diamonds denote porous clusters of HUSY crystals and circles denote small aggregates of zeolite). d) SEM micrograph for a dense HUSY zeolite agglomerate (direct observation from HUSY sample).

a

  Measured by x-ray fluorescence. b Using the amount of Si measured by x-ray fluorescence in parent zeolites. c Using nAl(IV) determined for the parent zeolite.

- 1 .Figure 2 :

 12 Figure 2: Diffraction patterns of HUSY+Al 2 O 3 , Al 2 O 3 , and HUSY (from bottom to top).

  Such defects could lead to a lack of mechanical strength and heterogeneous distribution of zeolite crystals throughout the extrudates. Further insight can be acquired by comparing the measured properties of shaped HUSY sample to those of HUSY zeolite and pure shaped Al 2 O 3 , weighed by the fraction of

  mesopore volume of Al 2 O 3 +HUSY sample also corresponded to the weighted sum of the Al 2 O 3 and HUSY solids. It revealed that alumina crystallites stacking was not modified by the HUSY presence during the shaping process.

Figure 3 :

 3 Figure 3: Calculated and measured volumes of micropores and mesopores for unshaped and shaped samples by N 2 adsorption-desorption.

  2 O 3 support. In presence of alumina, the IR contribution corresponding to zeolite Brønsted acid sites was clearly reduced. This can be easily explained by a dilution effect: zeolite corresponded to only 16.5 wt.% of the shaped sample and the alumina does not have any Brønsted acidity, as probed by pyridine at 423 K. Unfortunately, this resulted in band intensities too weak to enable an estimation of the BAS concentration of after mechanical mixing or shaping. This should mean that a specific procedure should be used in order to probe the acidity of zeolites when diluted with a binder, even if the same solids are at

Figure 4 :

 4 Figure 4: Activity per zeolite mass at t=1 min for HUSY, HUSY mechanically mixed with Al 2 O 3 , and shaped HUSY zeolite in m-xylene isomerization.

Figure 5 :

 5 Figure 5: Average electron probe microanalysis profiles of Al (red), Si (purple), and Pt (blue) elements along the diameter of the extrudate for a) 0.07Pt/(HUSY+Al 2 O 3 ), b) 0.11Pt/(HUSY+Al 2 O 3 ), and c) 0.25Pt/(HUSY+Al 2 O 3 ). Full ordinates scale is 100% for Al, 50% for Si, and a) 0.1%, b) 0.2%, c) 0.5% for Pt.

  shaped material and then proceed to the core of the extrudate. For low concentrations of precursor in solution, this can lead to the consumption of most of the Pt in the first contact of the solution with shaped bodies creating then a gradient of concentration from the edges to the core of the extrudate. The egg-shell Pt distribution for 0.07Pt/(HUSY+Al 2 O 3 ) sample is therefore explained by low Pt concentration in solution and the rapid ionic exchange of the Pt precursor ions into the Brønsted acid sites of the zeolite despite the presence of the ammonium competitor.

Figure 6 :

 6 Figure 6: a) Distribution coefficient of Pt ( ) and Si ( ) measured by electron probe micro analysis as a function of the Pt content. b) Pt content deposed in the alumina vs. overall Pt content deposed in the support. Pt/(HUSY+Al 2 O 3 ) samples

Figure 7 :

 7 Figure 7: a) n-C 16 hydroconversion activity as function of Pt loading and b) turnover frequency per protonic site as a function of n Pt /n Al ratio. Pt/HUSY ( ) [18] and Pt/(HUSY+Al 2 O 3 ) ( ) catalyst series. Symbols stand for experimental data and lines for model fitting results.

Figure 8 :

 8 Figure 8: Monobranched ( ) and multibranched ( ) C 16 isomers, and cracking ( ) products selectivity as function of conversion at 483 K (closed symbols), 488 K (cross symbols), and 498 K (open symbols), for 0.25Pt/(HUSY+Al 2 O 3 ).

Figure 9 :

 9 Figure 9: Yield of feed isomers as function of conversion. a) Pt/(HUSY+Al 2 O 3 ) series with different Pt loadings: 0.07% ( ), 0.11% ( ), and 0.25% ( ). b) 0.7Pt/HUSY ( ) and 0.25Pt/(HUSY+Al 2 O 3 ) ( ) catalysts.

Figure 10 :

 10 Figure 10: Maximal C 16 isomer yield as a function of the overall n Pt /n Al ratio. Pt/HUSY ( ) [18] and Pt/(HUSY+Al 2 O 3 ) ( ) catalyst series. Symbols stand for experimental data and lines for model fitting results.

Table 1 :

 1 Zeolite fraction, Al IV concentration, micro and mesopores properties by N 2 adsorptiondesorption, and macropores properties by Hg porosimetry for supports.

	Sample	Si (wt.%) a	Zeolite (wt.%)	nAl(IV) (µmol g	-1 )	Vmicro (mL g -1 )	Smicro (m 2 g -1 )	Vmeso (mL g -1 )	Smeso (m 2 g -1 )	Vmacro (mL g -1 )
	HUSY	43.9	100	820		0.33	813	0.21	101	n.d.
	Al2O3	-	-	-		n.d.	n.d.	0.62	263	n.d.

  decreased with increasing metal loadings. Taking into account the concentration of zeolite framework AlIV sites in the shaped support (Table1), the theoretical Pt ion exchange capacity of the HUSY-based extrudate is 2.6 wt.%. The percentage of exchanged Al IV sites was thus only 10%. However, about 30% of a HUSY are inaccessible to Pt precursors, due to the small pore aperture of sodalite cages[START_REF] Ribeiro | Étude de la technique d'échange ionique avec compétition. Cas du dépôt de platine sur support solide acide par échange cationique[END_REF]. Furthermore, the presence of a competitor ion (NH 4 + ) decreases the equilibrium amount of exchanged Pt.The accessible metal on the samples was determined by oxygen titration of chemisorbed hydrogen. The very low Pt content in the 0.07Pt/(HUSY+Al 2 O 3 ) precluded the evaluation of Pt dispersion by O 2 -H 2 titration. For the other two samples, the Pt dispersions were comprised in a narrow range with a mean value of 73%. The amount of accessible metal per gram of catalyst was then calculated and the average value of dispersion was used for the 0.07Pt/(HUSY+Al 2 O 3 )

	)
	s -1	1.2
	Activity t=1 min @ 623 K (mmol g -1	0 0.2 0.4 0.6 0.8 1	Zeolite	Mechanical	Shaped
				mixture	support
				The efficiency of ionic exchange has

Table 2 :

 2 Pt loading and dispersion, accessible Pt and metal to acid sites ratio for bifunctional catalysts.

	Catalyst	Nominal Pt loading (wt.%)	Measured Pt loading (wt.%)	Dispersion (%)	nPt (µmol g	-1 )	nPt/nAl	Pt distribution coefficient
	0.1Pt/HUSY	0.10	0.10	53	3		0.003	-
	0.4Pt/HUSY	0.40	0.42	53	11		0.013	-
	0.7Pt/HUSY	0.70	0.73	52	19		0.023	-
	0.07Pt/(HUSY+Al2O3)	0.063	0.065	<MDL	2	a		0.018	0.72
	0.11Pt/(HUSY+Al2O3)	0.125	0.11	71	4		0.030	0.95
	0.25Pt/(HUSY+Al2O3)	0.375	0.25	76	10		0.071	0.99

a Assuming a Pt dispersion of 73% (average of Pt/(HUSY+Al2O3) solids).

Table 3 :

 3 Catalytic activity, turnover frequency over protonic sites at 483K and maximum isomer yield.

	Sample	Activity @ 483 K (µmol g -1 s -1 )	TOFAl @ 483 K (10 3 s -1 )	Maximal C 16 isomers yield (%)
	0.1Pt/HUSY	1.62	2.0	46.5
	0.4Pt/HUSY	2.26	2.8	59.3
	0.7Pt/HUSY	1.71	2.1	62.1
	0.07Pt/(HUSY+Al2O3)	0.28	2.1	47.4

Table 4 :

 4 Metal to acid sites ratio for the whole sample (overall) and in the centre of the extrudate (core) for bifunctional shaped catalysts. Pt /n Al in the core of the extrudates was then calculated for each catalyst through the Pt content measured by EPMA in a radius of 50 µm from the centre of the extrudate and assuming the same metal dispersion throughout the whole extrudate (Table4). In the case of 0.07Pt/(HUSY+Al 2 O 3 ), the metal to acid sites ratio at the core of the extrudate was less than half the overall ratio. Comparing to the edge of the extrudate, the n Pt /n Al in the core was 3.4 times lower. The heterogeneous macroscopic distribution of Pt resulted, hence, in catalyst particles with clearly different metal to acid sites ratios after crushing and sieving. In order to investigate the catalytic implications of such differences, one can consider a model case. In this hypothetical catalyst, only two populations of particles with different metal to acid sites ratio exist: one holding n Pt /n Al =0.001 and another holding (n Pt /n Al )=0.015. The maximal C 16 isomer yield of the catalyst would correspond to weighed average of the Y i-C16,max at the core and at the edge of the extrudate. In other words, the Y i-C16,max of the catalyst would lie on a straight line unifying the two particle populations with the coordinates (n Pt /n Al ;Y i-C16,max ). Regardless of weight giving to each population, the catalyst performance would be always lower than that of a catalyst with the same overall n Pt /n Al lying in the simulated Y i-C16,max curve. The result is a positive effect on the isomerization yield when Pt is homogeneously distributed. The inferior performance of the 0.07Pt/(HUSY+Al 2 O 3 ) catalyst can be thus tentatively explained by the heterogeneous macroscopic distribution of Pt resulting in a poorer balance between the metal and acid sites as compared to that of a homogeneous Pt distribution for the same overall n Pt /n Al ratio. Simulation results for the maximal C 16 isomer yield as a function of n Pt /n Al ratio for mixtures Pt/(HUSY+Al 2 O 3 ).

	d Pt-Pt	) ,% -./0 =	1 2	) 123,% =	1 2	45 ,% 678 9	=	1 2	: 9	; <7"= > 8-*%/."!6	=	Equation 3
					=	1 2	: 9	; <7"= ,% ; ,% ) ,% ? ⁄
	Catalyst		(nPt/nAl)overall	xPt (10 2 gPt gzeolite -1 )	Maximal Pt-acid site (nm) distance	Pt coefficient distribution	(nPt/nAl)core
	0.1Pt/HUSY		0.003				0.10			30	-	-
	0.4Pt/HUSY		0.013				0.42			19	-	-
	0.7Pt/HUSY		0.023				0.73			16	-	-
	0.07Pt/(HUSY+Al2O3)	0.018				0.39			19	0.72	0.007

Acknowledgements

Authors would like to thank to M. Moscovici-Mirande, V. Delattre and C. James for the work on n-C 16 hydroisomerization, I. Clemençon and C. Deville for the work with x-ray powder diffraction, A.-L. Taleb and A.-S. Gay for the work on the microscopic techniques, and L. Sorbier for the work on electron microprobe. Financial support was provided by Fundação para a Ciência e Tecnologia through CQE (Project UID/QUI/00100/2013) and PhD grant (SFRH/BD/87927/2012).


Mutsuo Ito

Naoyuki Hesegawa

Ryusuke Egawa
email: egawa@archi.is.tohoku.ac.jp

Ken-Ichi Suzuki
email: suzuki@archi.is.tohoku.ac.jp

Tadao Nakamura
email: nakamura@archi.is.tohoku.ac.jp

An Adaptive-Grain Thermal Simulation Method to Evaluate Effects of Spatio-Temporal Analysis Granularity upon The Thermal Behavior of VLSIs

Recent advanced processors become more and more power-hungry and face adverse effects caused by the nonuniform thermal distribution generated by itself. The effects have not only an impact on the performance but also the logical and physical reliability. In the near future, circuit designers have to consider and estimate the effects during all design stages appropriately. In this paper, we propose an adaptive-grain thermal simulation on Very Large Scale Integrated Circuits(VLSIs), and by use of the proposal, we investigate and estimate the effects of changing analysis granularities on forming temperature profiles in digital circuits from the spatio-temporal viewpoint. Furthermore, from the simulations, focusing on the complication among some parameters; chip area, power, variation of power density distribution, etc., and the effects upon temperature profiles, we summarized the complication as a kind of curved surfaces. Consequently, we can say that the appropriate time resolution should be determined depending on required accuracy in terms of temperature, and tolerable computation cost.

1.

INTRODUCTION

The power density of recent VLSIs increases rapidly as CMOS process technology evolution heads toward practical use of the nano-scale process technology. For example, at the presence moment, the power density of high-performance microprocessors has already reached 50W/cm 2 at the 100nm technology node, and it is said that next generation chips will soon reach 100W/cm 2 at the technologies below 50nm [START_REF]The international technology roadmap for semiconductors(ITRS)[END_REF]. As a result, the average temperature of the die also increases rapidly. Furthermore, local hot spots on the die usually have significantly higher power densities than the average, making the local temperatures much higher.

High temperature and hot spots have significant impacts on performance and reliability of VLSIs [START_REF] Cheng | ILLIADS-T: An Electrothermal Timing Simulator for Temperature-Sensitive Reliability Diagnosis of CMOS VLSI Chips[END_REF] [START_REF] Pedram | Analysis and Optimization of Thermal Issues in High-Performance VLSI[END_REF].

Accordingly, across the entire stages of a circuit design, circuit designers require detailed on-chip temperature profiles inevitably so as to accurately estimate temperature-dependent power, performance and reliability. Similarly, in order to precisely investigate effectiveness of Dynamic Thermal Management techniques(DTMs), it is essential that DTM designers hold spatio-temporal information about dynamic on-chip thermal behavior in more detail. For near future VLSI design, it is critical to find a way of properly addressing the temperature-related aspects of the design flow, and using temperature straightforward as a design policy in the entire design stages. Therefore, temperature-aware design has been becoming one of the major challenges in further updated design stages such as microprocessors, ASICs or System-on-a-Chip(SoC) [START_REF] Huang | Compact Thermal Modeling for Temperature-Aware Design[END_REF] [START_REF] Stan | HotSpot: a Dynamic Compact Thermal Model at the Processor-Architecture Level[END_REF].

In view of the current temperature-aware design and performance management, a lot of chiparchitecture level thermal simulation methods have been proposed from the various points of view of spatio-temporal analysis granularity [START_REF] Cheng | ETS-A: A New Electrothermal Simulator for CMOS VLSI Circuits[END_REF]- [START_REF] Ito | SIMULATING FINE-GRAIN THER-MAL BEHAVIORS ON VLSIS[END_REF]. In general, as a design stage progresses, an extremely large amount of specific data can be obtained and available from the advanced design stage. It is very important for temperature-aware design methodology to be able to easily handle and apply the larger spatiotemporal data to more effective and accurate thermal simulation in compliance with the design stages. In order to realize it, it goes without saying that it is essential to have knowledge about the effects of various analysis granularities on thermal simulation, and find appropriate analysis granularity in advance. Unfortunately, all the methods mentioned above do not seem to be able to realize the effective and accurate thermal simulation throughout the temperatureaware design flow, because, to the best of our knowledge, no research has a discussion about the effects and accuracy of analysis granularity.

In this paper, for the purpose of addressing the problem, firstly, we define analysis granularity in view of thermal modeling and simulation. Then, we propose a simulation method which can deal with var-Figure 1: The constituition of the defined granularities. ious analysis granularities. Finally, by use of the proposed method, we extensively investigate the effects on forming temperature profiles dependent on the analysis granularity and summarize the results comprehensively.

The rest of this paper is organized as follows. The next section describes a definition of analysis granularity and explains our proposed adaptive-grain thermal simulation method. Thermal modeling and numerical procedure exploited by the proposed are explicated in Section 3. Then Section 4 provides some simulation results of our specific simulation for several circuits and evaluates the results from the viewpoint of spatio-temporal granularity. Section 5 concludes the paper.

ANALYSIS GRANULARITY

As mentioned previously, we see that it is very important to estimate temperature at different granularities and at different design stages, especially early in the design flow. In this section, we define the keyword of analysis granularity in thermal simulations.

When we simulate temperature behavior on a chip, we have to model the physical phenomena in order to reconstruct it on a computer, discretizing a continuous governing equation of the phenomena. We call the degree of target size "analysis granularity" along the series of the process. Chiefly the analysis granularity consists of two parts: model granularity and computation granularity. The model granularity means the minimum scale or size of a heat source we can deal with in an analysis. And, the computation granularity represents a kind of computational scale.

In our proposed approach, the concept of these two granularities is used as a kind of indicator which is a tradeoff between effectiveness and accuracy. Furthermore, each granularity is represented by two phases: spatial and temporal granularity. In summary, the model granularity is composed of spatial model granularity and temporal model granularity. Likewise the computation granularity consists of mesh resolution granularity and time resolution granularity. The relation among the granularitiesis is shown in Fig. 1 illustratively.

In the following subsections, model granularity and computation granularity are explained in more detail respectively.

Definition of model and computation granularities

In the phenomena of heat conduction, the behavior is strongly affected by the strength and location of heat sources. Similarly, in thermal simulation, it is important to model heat sources appropriately in order to simulate the temperature behavior with accuracy. We classify model granularity into spatial and temporal model granularities from the spatio-temporal point of view.

In spatial model granularity, we assume that a logic gate, which is regarded as a cell in a standard cell design method, is the finest spatial model granularity as a basic heat source. We call the model granularity cell level. Also, the chip die is partitioned into functional blocks according to microarchitecture functionality and each functional block is considered as one heat source. In this case, the spatial model granularity is referred to as functional-block level. Considering a functional block is composed of a lot of cells, the functional-block level is coarser than the cell level. Likewise, we can assume sub-functional block level which has some number of cells arbitrarily. Accordingly, there can be some successive levels between the cell level and the functional-block level in spatial model granularity. In this paper, because we presume logic cells are basic heat sources, the relation of power between cell level and functional-block level is expressed as follows.

P C = N i=1 P Fi ( 1
)
where P C is the power of a coarser heat source and P F i is that of a logic cell which is included in the coarser heat source. Fig. 2 illustrates the relation and shows the definition of the model granularities.

Similarly to the spatial model granularity, for the temporal model granularity we assume a basic time interval. Each logic cell generates heat/power depending on its type of logic and the switching activity. In fact, the power distribution is not only dependent on the cell connection topology but also the input vector at every clock cycle. Therefore, we regard one clock cycle interval as a basic time interval, which is the finest temporal model granularity in this paper. We can arbitrarily control the length of a coarser time window(T W C ) based on the basic T W F (= 1 clock cycle). The power of a heat source in a coarser temporal granularity can be described in the following. where P avg is the power of a coarser temporal heat source, P cell x is the power in a finer time window of Cell x , M is the length of a coarser time window and α i is the switching activity in i clock cycles. Fig. 3 shows the relation visually.

P avg = M i=1 P cellx × α i T W C (2)
Likewise, computation granularity has two components. One is mesh resolution as spatial granularity and the other is time interval as temporal granularity. These granularities are defined specifically in numerical computation conditions. In mesh resolution, every heat source that overlaps the area of a grid point serves as a power source feeding into that grid, and the grid point has the corresponding power value which is calculated based on the ratio of the heat source area to the total area of the heat source. For illustration of mesh resolution, we show three levels of mesh resolution in Fig. 4.

In time interval resolution, a time interval represents the length of one time step of a numerical iter- ation. Due to the correspondence of the total power between a coarser and a finer time window as shown in eq.( 2), temporal model granularity have to be the same as the time interval resolution. Therefore, the temporal model granularity is inevitably affected by the time resolution(interval) resolution. Fig. 5 shows the difference of time interval resolutions in numerical computation with using two different time intervals.

Note that changing these computation granularities directly affects forming temperature profiles in terms of computational truncation error.

ADAPTIVE-GRAIN THERMAL

SIMULATION

In this paper, based on our previous work [START_REF] Ito | SIMULATING FINE-GRAIN THER-MAL BEHAVIORS ON VLSIS[END_REF], we extend the functionality of the thermal simulation method in terms of spatio-temporal analysis granularity. The former simulator only focused on the cell level and clock-cycle level model granularity, which was referred to as "fine-grain" thermal simulation. The fine-grain thermal simulator requires two input data; cell level geometrical information and clockcycle level switching information, which are obtained in temporal phase and spatial phase along a simulation flow respectively, as shown in Fig. 6. In Fig. 7, we illustratively show the relation between the fine-grain thermal simulator and two input data. Exploiting the cell level and clock-cycle level model information as the finest model granularity, we can deal with arbitrary model granularity. We call the extended simulation method "adaptive-grain" thermal simulation method. As a result, the extended thermal simulator has advantages of flexibly varying spatio-temporal analysis granularity. Specifically, the following sections provide the policy to realize the adaptability exploited by the proposed simulation.

Adaptability of model and computation granularities

The adaptability of heat source model with respect to model granularity is realized as follows; in spatial granularity, the heating value per unit area of a coarser heat source is to be the area-average of heating values of several finer heat sources covered with the coarser one; similarly, in temporal granularity, a time window is defined. The time window means that a heat source generates uniform power during the given period. In a coarser-grain time window, the heating value per unit time of a heat source is regarded as the time-average of the sum of activating heating values of the heat source in finer-grain time window within the coarser-grain one.

Similarly to the model granularity adaptability, computation granularity has mesh and time resolution granularities. Both the mesh and time resolution granularity are explicitly determined by a numerical computation condition, i.e., the degree of spatial and temporal discretization.

The proposed adaptive characteristics are apparently very simple but enable us to realize high adaptability in different design stages. Due to the hierarchical characteristics which can model and comprehend complexity of specifying heat sources across design stages, accordingly, the proposed method has capability to freely change the granularities adaptively along design stages.

Thermal modeling

In order to estimate the impact of changing analysis granularity on forming temperature profiles, firstly, we focus on the finest analysis granularity, i.e., celllevel and clock cycle-level. Additionally, we assume that a target chip is as a thin plate almost composed of silicon base on the assumption that silicon is a relatively poor heat conductor and cannot spread heat efficiently compared with some other metal materials such as aluminum.

We simulate a chip using the following mixed 2-D/1-D strategies: (1) 2-D simulation is performed for the chip substrate, considering the fine granularity of the proposed method, and (2) packages and heat sinks are modeled as 1-D thermal resistances based on a well-known duality between heat transfer and electrical phenomena in order to reduce the computational complexity [START_REF] Cheng | ILLIADS-T: An Electrothermal Timing Simulator for Temperature-Sensitive Reliability Diagnosis of CMOS VLSI Chips[END_REF].

Numerical approaches

Focusing on our thermal model, the general 2-D heat conduction equation is transformed as follows:

∂T (x, y, t) ∂t = κ " ∂ 2 T (x, y, t) ∂x 2 + ∂ 2 T (x, y, t) ∂y 2 « (3) + Q(x, y, t) ρC p - h ρC p (T (x, y, t) -T amb )
where T (x, y, t) is the time dependent temperature at any point, κ = λ ρCp is thermal diffusivity, ρ is the density of the material, C p is the specific heat, λ is the thermal conductivity, Q(x, y, t) is the heat energy generation rate, h is the constant derived from the effective heat transfer coefficient.

The equation is subjected to the following boundary conditions: the four sides and the top are set to be in the insulated condition(Neumann condition), i.e., ∂T ∂x = ∂T ∂y = 0, and the bottom is convective to room temperature with a heat transfer coefficient(Robin condition). The last term represents it, what we call Newton's law of cooling. Throughout our simulation, we assume ambient temperature is 298K(25 • C).

We use the alternating-direction-implicit(ADI) method [START_REF] Cheng | ILLIADS-T: An Electrothermal Timing Simulator for Temperature-Sensitive Reliability Diagnosis of CMOS VLSI Chips[END_REF][10] to solve the differential equations. Basically, the ADI method is a process to reduce the 2or 3-dimensional problems to a succession of 2 or 3 1-D problems. Then eq.( 4) and the subjected boundary conditions discretized by the ADI method are effectively solved by an algorithm with linear time complexity.

EXPERIMENTAL RESULTS AND

DISCUSSION

As mentioned above, to facilitate more practical temperature-aware design at each design stage and then make DTM techniques effective, it is significant for designers to have comprehensive knowledge about the effects of variation of analysis granularity on temperature profiles. Therefore, in the beginning, we investigate and evaluate the effects for some circuits with using our proposed thermal simulation method which has the ability to freely change spatio-temporal analysis granularity, and then try to find the appropriate spatio-temporal analysis granularity.

Simulation conditions

First, we need the switching and geometrical information to identify when and where heat sources are activated in the chip. In this simulation, we use standard cell design method for target chips. Therefore we can simply regard cells, which are provided as standard cells by CAD vendors, as logic gates. Then switching information is obtained in the phase of logical simulation, and geometrical information in the phase of placement & routing(P&R) respectively during implementing a target chip.

During the logical simulation, we make the toggle counting file for a given input vectors. The clock cycle-level switching information dependent on input vectors is derived from the difference between the files which depict the number of toggle counts on each cell by each clock cycle. The switching information file also has the power of each cell obtained by the CAD tool. After a placement and routing phase, we obtain the places and surface areas of heat sources.

We use two combinational logic circuits, an 8bit ripple-carry adder(RCA) and an 8-bit carry look-ahead adder(CLA), and a 16-bit microprocessor [START_REF] Shibamura | Design and Implementation of An Educational Microprocessor Using Field Programmable Gate Arrays[END_REF] in order to make it clear that the proposed method has potentiality for investigating the impact of dynamical power distribution and cell-level layout changes from the spatio-temporal viewpoint. The target circuits are written in VHDL. In the logic synthesis, using Design Compiler from Synopsys, Inc., 1 we make their netlists together with the EXD's cell library subject to ROHM's 0.35µm CMOS technology, and then we obtain their circuit's layout information by using Milkyway and Apollo as a placement and routing tool.

KITE[11]

Fig. 8 shows the positions and area of every cell for two types of simple layouts: an RCA and a CLA. Fig. 8(a) is an 8-bit RCA, and Fig. 8(b) is an 8-bit CLA with the same area utilization percentage. Fig. 9 presents a layout of 16-bit microprocessor KITE. In Fig. 9(a) indicates the functional block level layout and cell level layout is shown in Fig. 9(b).

We assume both of these circuits have the capability of operating at a frequency of 100MHz at a supply voltage of 3.3V and the simulation time interval ∆t was one clock cycle time, or 10 nsec. Table 1 summarizes several properties of each target circuit. While 8-bit adders execute additions of 33000 random input vectors, KITE's execution program is the "Tower of Hanoi", which requires 33000 clock cycles to complete.

Table 1: Properties of target circuits.

Comparison of thermal behaviors between the finest model granularity and the coarsest model granularity

In order to clearly demonstrate the influence of variation of model granularity, we compare temperature profiles simulated under different model granularities. On the one hand, we fixed the computation granularity. Here, the spatial computation granularity is 100 × 100 and the temporal one is 1 clock cycle time step. Specifically, each layout of 8-bit adders is included in the chip area or computational area of 200µm×200µm, where the area is divided into a 100 × 100 square mesh and, therefore, has 10000 grid points in itself. In addition, KITE is in the chip area of 1000µm×1000µm. Similarly, the area is meshed by 100 × 100 square grid.

We focus on the effect on the maximum temperature in terms of the difference between the cell level and clock cycle level, and the functionalblock level and steady state model granularities. We call these model granularities "finest-grain" and "coarsest-grain" heat source model respectively. As a typical value, Table 2 shows each temperature difference between the two model granularities and errors due to coarser model granularity at 20000 clock cycles. Table 2 indicates that the error of KITE is more than twice as large as that of CLA, more than seven times larger than RCA. On the other hand, in 8-bit adders, the difference of maximum temperatures did not appear significantly because they had no remarkable difference between their power density maps made by different model granularities. This significant difference among these circuits suggests that the temperature difference induced by different model granularity was strongly affected by the chip area and the power density distribution.

In Fig. 10, the transition of maximum temperature on the processor KITE is shown in terms of the finestgrain and the coarsest-grain heat source model. The upper curve T(cell,clk) was obtained with the finest model granularity and the lower curve T(fnc,std) were obtained with the coarsest model granularity. The difference between each max temperature was about 0.12 • C and clearly observed as the effect of the spatial model granularity rather than temporal model granularity because T(cell,clk) showed little fluctuation caused by variation of power generation in the clock cycle level. Furthermore, as shown in Fig. 11, two maximum temperature points at 20000 clock cycles and each temperature and power density distribution along xand y-axis are illustrated. These results present that the heat source with highest power density does not always make the maximum temperature point within itself, and the displacement is strongly affected by chip configuration and the power density distribution. From the following simulation, we focus on KITE since only KITE provides us with more diversified analysis granularities than the other target circuits.

Evaluation of complications between accuracy and cost-effectiveness

Evaluation here has two categories: accuracy, or error, and cost-effectiveness, or computational cost. In other words, "accuracy" indicates the degree of computational resolution, i.e., computation granularity. "effectiveness" indicates the degree of heat source modeling, i.e., model granularity.

In effectiveness evaluation, first, we inspect the effect induced by the variation of the spatio-temporal model granularity on temperature profiles, consider- ing the change of maximum temperature. In this evaluation, cell level and clock-cycle level model granularity of a heat source model is regarded as the base line of the evaluation of effectiveness. Second, in accuracy evaluation, we estimate the effects of changing the degree of mesh/time resolution in numerical simulation on on-chip temperature profiles, revealing the sufficient mesh resolution to observe on-chip temperature behaviors.

Complications dependent on model granularity

In this simulation, we fixed computation granularity and considered that its mesh resolution was 100×100 and unit time interval was clock cycle level. On the contrary, in model granularity, we used our proposed simulator for KITE under the conditions of two types of spatial model granularity and six types of temporal one: cell and functional-block level in terms of the spatial granularity, and 1, 10, 100, 1000 and 10000 clock-cycle time window and time average(steadystate) in terms of the temporal one, respectively. As a the baseline of accuracy, the model granularity of cell level and 1 clock-cycle time window was chosen. We used relative error as the criterion to quantitatively compare the baseline model granularity with that of rough model granularity. The relative error is defined in terms of:

E r = |T f ine -T coarse | T f ine × 100(%) (4)
Also, we think of cost-effectiveness as the length of execution time. The simulator was implemented with C++ language and executed on a PC with a 3.4-GHz Pentium 4 processor and 3 GB of memory. The simulation results with respect to accuracy and costeffectiveness were plotted in Fig. 12. In addition, the evaluation was performed in three temperature profiles of 10000, 20000 and 30000 clock cycles, respectively. As Fig. 12 clearly shows, the finer temporal model granularity becomes, the better accuracy is obtained. Although the coarser temporal model granularity reduces computation cost, the increase of error would nullify the merit. The finest granularity provides high accuracy while the computation cost dramatically increased. These results suggest that there is an appropriate model granularity which offers reasonable accuracy and effectiveness at the same time. Note that the three error plots of functional-block level and time average were omitted since these values of error were around 0.07% and the value was much larger than others even the computation cost was about almost same.

Complications dependent on computation granularity

In contrast to the previous simulation, the model granularity were fixed at cell and clock cycle level, i.e., the finest granularity. On the other hand, in computation granularity, we executed our thermal simulation under the conditions of five types of spatial computation granularity and five types of temporal computation granularity: 10×10, 25×25, 50×50, 100×100 and 200×200 mesh resolution, and 1, 10, 100, 1000 and 10000 clock cycle time interval. As a base line, the computation granularity had 200×200 mesh and 1 clock cycle time interval. Similarly to the previous error evaluation, here we used relative error. But, in this time, coarser grid mesh does not always have a corresponding grid point of finer grid mesh. Therefore, in coarser grid, all gird points corresponding to finer grid were obtained to be interpolated by use of linear Lagrangian interpolation scheme. Also, together with accuracy evaluation, we determined the execution time which indicates cost-effectiveness. As performed in the previous evaluation, based on three thermal profiles of 10000, 20000 and 30000 clock cy- cles, we evaluated each profile. These results are shown in Fig. 13, where we can see that over 100 clock cycle time interval the value of error suddenly rose. However, little change of error was along mesh axis in every time interval. The almost same phenomena happened to each temperature profile. On the one hand, the distribution of computation cost shows a similar relation to Fig. 12 with regard to uprush of computation cost in finest computation granularity. These results suggest that time resolution has a much larger impact on error than mesh resolution although this phenomena might be strongly influenced by a dispersion of power density distribution and a chip area size.

CONCLUSIONS

In this paper, we have defined and classified analysis granularity, which should be considered in thermal simulation along circuit design stages. Then, considering our previously proposed fine-grain thermal simulator, we have presented the extended adaptivegrain thermal simulation method, which is able to handle not only the cell level and the cycle level granularity but also functional-block level and steady state granularity.

To have extensive knowledge about the effects of variation of analysis granularity in terms of accuracy and cost-effectiveness, we performed the proposed simulation for several target circuits and investigated the complication quantitatively. Consequently, the results suggest that the variation of analysis granularity strongly affects the error and the computation cost. Almost same tendency was observed through our simulation in view of model and computation granularity. In temporal analysis granularity, to some extent, time window or time resolution could be set roughly, but over a threshold, error dramatically increases. Meanwhile, in view of spatial analysis granularity, the effects induced by the variation of spatial granularity could not be observed clearly. But, so far, we have investigated the complication under only a little number of target circuits. In the future, we will carry out our thermal simulation for several circuits in order to realize the effective and accurate thermal simulation method for temperature-aware design methodology.

Figure 2 :

 2 Figure 2: Illustration of the definition of spacial model adaptability.

Figure 3 :

 3 Figure 3: Illustration of the definition of temporal model adaptability.

Figure 4 :

 4 Figure 4: Mesh resolution granularity.

Figure 5 :

 5 Figure 5: Time resolution granularity.

Figure 6 :

 6 Figure 6: Simulation flow obtaining two main input data for the fine-grain themal simulation.

Figure 7 :

 7 Figure 7: The relation between the fine-grain themal simulator and the two input data.

Figure 8 :

 8 Figure 8: Layouts of an RCA and a CLA.

Figure 9 :

 9 Figure 9: KITE layout.

Figure 10 :

 10 Figure 10: Comparison between max. temperatures of the finest-and coarsest-grain heat source models.

Figure 11 :

 11 Figure 11: Comparison of temperature and power density distributions after 20000 clock cycles.

Figure 12 :

 12 Figure 12: Complications dependent on model granularity.

Figure 13 :

 13 Figure 13: Complications dependent on computation granularity.

Table 2 :

 2 Comparison of transition of max. temperature on each circuit.

 TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4

"This work is supported by VLSI Design and Education Center(VDEC), The University of Tokyo with the collaboration with Synopsys Corporation."  TIMA EDITIONS /

THERMINIC 2005 ISBN 2-916187-01-4