Ester Gutierrez-Acebo

Jérôme Rey

Christophe Bouchy

Yves Schuurman

Céline Chizallet
email: celine.chizallet@ifpen.fr

Location of the Active Sites for Ethylcyclohexane Hydroisomerization by Ring Contraction and Expansion in the EUO Zeolitic Framework

Keywords: zeolite, naphtene, Protonated CycloPropane, confinement effect, side pocket, channel, EU-1, ZSM-50

Identifying the location of the active sites in a zeolite is a current challenge, impeding the design of optimal catalysts. In this work, we identify the location of the most active sites of 1-ethylcyclohexene isomerization in the EUO framework (10 MR channels, 12 MR side pockets), thanks to DFT calculations corroborated by experiments. Skeletal isomerization of cycloalkenes is a crucial industrial reaction for the bifunctional isomerization of ethylbenzene.

Ethylcyclohexene is protonated by framework protons into cyclic carbenium ions, which undergo ring contraction-expansion reactions through protonated cyclopropane (PCP) like transition states. Ab initio calculations clearly show that the acid sites located at the intersection between the channel and the pocket stabilize much less the cyclic carbenium ions involved in the reaction than 12 MR pockets and 10 MR channel sites, due to stronger dispersion stabilizing interactions. This computational finding is fully confirmed experimentally by the comparison of the catalytic performances of the H-EU-1 and H-ZSM-50 zeolites in ethylcyclohexane hydroisomerization. Both zeolites possess the EUO structure, but with different location of the acid sites. The ratio in turnover frequencies is quantitatively rendered by the DFT calculated free energy profiles. Diffusion measurements reveal similar ethylcyclohexane diffusion times for the two zeolites, supporting that the difference in activity is primarily driven by the location of the active sites.

INTRODUCTION

Zeolites are very powerful aluminosilicate catalysts for a variety of reactions in refining, petrochemistry, 1 pollution abatement, [START_REF] Deka | Local Environment and Nature of Cu Active Sites in Zeolite-Based Catalysts for the Selective Catalytic Reduction of NOx[END_REF] and also promising candidates for biomass conversion. [START_REF] Jacobs | Will Zeolite-Based Catalysis be as Relevant in Future Biorefineries as in Crude Oil Refineries?[END_REF][START_REF] Ennaert | Potential and Challenges of Zeolite Chemistry in the Catalytic Conversion of Biomass[END_REF] Their crystalline nature and the large variety of structures makes possible the design of catalysts from structural considerations. [START_REF] Li | Selective Introduction of Acid Sites in Different Confined Positions in ZSM-5 and Its Catalytic Implications[END_REF][START_REF] Gallego | Ab initio" Synthesis of Zeolites for Preestablished Catalytic Reactions[END_REF][START_REF] Yarulina | Structure-Performance Descriptors and the Role of Lewis Acidity in the Methanol-to-Propylene Process[END_REF] For acid catalyzed reactions, such as isomerization and cracking, the active sites are protons related to the aluminum atoms. A main challenge however consists in the identification of the precise location of the active sites of a given zeolite, as the local topology may strongly differ from one T site to another. [START_REF] Knott | Consideration of the Aluminum Distribution in Zeolites in Theoretical and Experimental Catalysis Research[END_REF] This is first of all due to the limited number of zeolites with more or less known location of aluminum atoms. [START_REF] Li | Selective Introduction of Acid Sites in Different Confined Positions in ZSM-5 and Its Catalytic Implications[END_REF][START_REF] Pinar | Direct Evidence of the Effect of Synthesis Conditions on Aluminum Siting in Zeolite Ferrierite: A 27 Al MQ MAS NMR Study[END_REF][START_REF] Van Bokhoven | Stepwise Dealumination of Zeolite Βeta at Specific T-Sites Observed with 27 Al MAS and 27 Al MQ MAS NMR[END_REF][START_REF] Vjunov | Quantitatively Probing the Al Distribution in Zeolites[END_REF][START_REF] Brus | Structure of Framework Aluminum Lewis sites and Perturbed Aluminum atoms in Zeolites as Determined by 27 Al{ 1 H} REDOR (3Q) MAS NMR Spectroscopy and DFT/Molecular Mechanics[END_REF][START_REF] Sklenak | Aluminum Siting in Silicon-Rich Zeolite Frameworks: A Combined High-Resolution 27 Al NMR Spectroscopy and Quantum Mechanics/Molecular Mechanics Study of ZSM-5[END_REF][START_REF] Holzinger | Distribution of Aluminum over the Tetrahedral Sites in ZSM-5 Zeolites and Their Evolution after Steam Treatment[END_REF][START_REF] Perea | Determining the Location and Nearest Neighbours of Aluminium in Zeolites with Atom Probe Tomography[END_REF][START_REF] Van Bokhoven | Determining the Aluminium Occupancy on the Active T-Sites in Zeolites using X-Ray Standing Waves[END_REF][START_REF] Agostini | In Situ XAS and XRPD Parametric Rietveld Refinement To Understand Dealumination of Y Zeolite Catalyst[END_REF] Then, even once the location is known, it is generally not unique so that identifying the precise location of the most stable intermediates and transition states is not straightforward. This is however a condition for the design of better catalysts. The case of the EUO framework is illustrative in that respect. This structure is composed of a monodimensional channel pore system (10 MR) with side pockets (12 MR). Two zeolites exhibiting this structure type, EU-1 and ZSM-50, were deeply investigated in particular by neutron diffraction. [START_REF] Souverijns | Molecular Shape Selectivity of EUO Zeolites[END_REF][START_REF] Peral | Structural Comparison of Two EUO-Type Zeolites Investigated by Neutron Diffraction[END_REF] In the case of ZSM-50, the aluminum atoms are located mainly in the intersection between the channel and the pocket whereas in the case of the EU-1, [START_REF] Souverijns | Molecular Shape Selectivity of EUO Zeolites[END_REF][START_REF] Peral | Structural Comparison of Two EUO-Type Zeolites Investigated by Neutron Diffraction[END_REF] they are found either inside the pocket or in the channels. In contrast with EU-1, the synthesis of ZSM-50 at low Si/Al ratio is challenging. [START_REF] Moreau | Ethylbenzene Isomerization over Bifunctional Platinum Alumina-EUO Catalysts: Location of the Active Sites[END_REF] Naphthenes (cycloalkanes) are an important part of the feedstock converted in refineries and therefore, a matter of interest for the petroleum industry. Nevertheless, their reactivity has not been deeply studied contrary to the case of paraffins. Naphthenes have a more complex reactivity than linear paraffins. This fact is due to the possibility of forming tertiary carbons by adding additional alkyl groups, and to the higher number of possible conversion pathways (including dehydrogenation into cycloalkenes, then isomerization, ring opening and cracking). [START_REF] Marcilly | Acido-Basic Catalysis[END_REF] Typically, the most abundant naphthenic components in the hydrocarbons produced from petroleum are 5and 6-carbon rings, [START_REF] Marcilly | Acido-Basic Catalysis[END_REF] due to minimum tension in the ring compared to the 3 and 4 carbons rings.

In petrochemistry, ethylbenzene hydroisomerization is of importance in the paraxylene production. Paraxylene is a highly sought-after product used in the manufacture of the terephtalic acid, employed for nylon production. Traditionally, the ethylbenzene hydroisomerization employs a bifunctional catalyst [START_REF] Cannella | Xylenes and Ethylbenzene[END_REF] composed by a metal compound (responsible of the hydro/dehydrogenation function, HD/DHD) dispersed over an acidic support (isomerization and cracking function). The EU-1 zeolite is industrially used as acidic function for ethylbenzene hydroisomerization. [START_REF] Vermeiren | Impact of Zeolites on the Petroleum and Petrochemical Industry[END_REF] The location of the active sites is an important question for this zeolite family, as the confinement effect is expected to differ significantly between the 10 MR channel, the 12 MR side-pockets and the intersection between the channels and the pockets.

Ethylbenzene hydroisomerization over bifunctional catalysts involves the isomerization of ethylcylcohexenes over the Brønsted acid phase (the zeolite). [START_REF] Guisnet | Ideal" Bifunctional Catalysis over Pt-Acid Zeolites[END_REF] Reactions involving these cycloalkenes are expected to implicate carbocations. These cyclic carbenium ions can be isomerized by hydride shift, methyl shift and ring contraction expansion via protonated cyclopropane (PCP) steps. [START_REF] Guisnet | Ideal" Bifunctional Catalysis over Pt-Acid Zeolites[END_REF][START_REF] Weitkamp | Peculiarities in the Conversion of Naphthenes on Bifunctional Catalysts, Erdoel Kohle, Erdgas[END_REF][START_REF] Weitkamp | Shape Selective Isomerization and Hydrocracking of Naphthenes Over Pt/HZSM-5 Zeolite[END_REF][START_REF] Weitkamp | Comparison Of The Reactions Of Ethylcyclohexane And 2-Methylheptane On Pd/Lay Zeolite[END_REF][START_REF] Mihindou-Koumba | Methylcyclohexane Transformation over HFAU, HBEA, and HMFI Zeolites: II. Deactivation and Coke Formation[END_REF][START_REF] Martens | Single-Event Rate Parameters for the Hydrocracking of Cycloalkanes on Pt/US-Y Zeolites[END_REF][START_REF] Mcvicker | Methylcyclohexane Ring-Contraction: A Sensitive Solid Acidity and Shape Selectivity Probe Reaction[END_REF] The alkylnaphthenes rearrangements have been classified by Weitkamp 26 in two main categories: type A and type B isomerizations. In type A isomerization, the branching degree remains constant whereas in type B isomerization the branching degree is modified. Type A isomerization is considered to be faster than type B isomerization. [START_REF] Marcilly | Acido-Basic Catalysis[END_REF][START_REF] Weitkamp | Comparison Of The Reactions Of Ethylcyclohexane And 2-Methylheptane On Pd/Lay Zeolite[END_REF][START_REF] Weitkamp | Catalytic Hydrocracking-Mechanisms and Versatility of the Process[END_REF][START_REF] Ribeiro | Hydroisomerization of n-Hexane on Platinum Zeolites: I. Kinetic Study of the Reaction on Platinum/Y-Zeolite Catalysts: Influence of the Platinum Content[END_REF][START_REF] G.; R | Tracer Study of the Isomerization of Paraffins on Bifunctional Catalysts[END_REF] Molecular insight is strongly lacking for these reactions, regarding not only the relevant mechanisms if not as well, the intermediate / transition states involved and the quantification of their stability.

In the present work, we propose a Density Functional Theory (DFT) approach to determine these features in the EUO framework. We also aim at identifying the location of the most active sites for these reactions with the same approach, complemented with experimental comparison of the catalytic performances of the H-EU-1 and H-ZSM-50 zeolites. Furthermore, some diffusion measurements have been performed in order to evaluate the possible influence of the diffusion in the catalytic performance.

The chosen reaction is the isomerization of ethylcyclohexene (ECH = , obtained from the dehydrogenation of ethylcyclohexane (ECH), or the hydrogenation of ethylbenzene) into other branched substituted cycloalkenes. We showed experimentally [START_REF] Gutierrez-Acebo | Metal/Acid Bifunctional Catalysis and Intimacy Criterion for Ethylcyclohexane Hydroconversion: When Proximity Does Not Matter[END_REF] that a relevant apparent reaction pathway consists in the transformation of ECH + (ethyl-cyclohexenium) into EMCP + (ethylmethyl-cyclopentenium), then into DMCH + (dimethyl-cylclohexenium) and finally into TMCP + (trimethyl-cyclopentenium). Experimentally, many products are obtained (16 rehydrogenated products, meaning an even higher number of alkene structures), belonging to the three EMCP, DMCH, TMCP families. It prevents the exhaustive computational investigation of the formation of all of them on all the sites of the zeolite. Thus, we decided to make a relevant choice so as to represent the three families of products. The reaction sequence selected here (Figure 1) takes into account members of each of the three families, focusing on tertiary carbenium ions, which are expected to be stable species. For non-cyclic species it is not always clear from experiments whether carbenium ions exists as free or adsorbed species inside the zeolite pores, or if they are covalently bonded to framework oxygen forming alkoxide intermediates (Figure 2). This depends on the zeolite but also on the nature of the olefin and the carbenium (substitution, delocalized nature). [START_REF] Ivanova | Impact of in Situ MAS NMR Techniques to the Understanding of the Mechanisms of Zeolite Catalyzed Reactions[END_REF] From catalytic hydrocraking experiments, carbenium appear as most probable intermediates. [START_REF] Denayer | Evidence for Alkylcarbenium Ion Reaction Intermediates from Intrinsic Reaction Kinetics of C6-C9 n-Alkane Hydroisomerization and Hydrocracking on Pt/H-Y and Pt/USY Zeolites[END_REF][START_REF] Thybaut | Alkylcarbenium Ion Concentrations in Zeolite Pores During Octane Hydrocracking on Pt/H-USY Zeolite[END_REF] Earliest ab initio calculations used small clusters. These calculations indicated that adsorbed carbenium and carbonium ions (active intermediates of acid-catalyzed transformations of small hydrocarbons up to C 4 ) on zeolites were not reaction intermediates. Indeed, they were the transition states of the alkene protonation elementary step, whose products were their corresponding alkoxides, avoiding charge separation. [START_REF] Kazansky | Adsorbed Carbocations as Transition States in Heterogeneous Acid Catalyzed Transformations of Hydrocarbons[END_REF][START_REF] Rigby | Ab Initio Calculations on the Mechanisms of Hydrocarbon Conversion in Zeolites: Skeletal Isomerisation and Olefin Chemisorption[END_REF] The same conclusion was obtained for PCP species, [START_REF] Rigby | Mechanisms of Hydrocarbon Conversion in Zeolites: A Quantum Mechanical Study[END_REF] isolated as transition states only.

However, the steric constraints and electrostatic field provided by the zeolite framework play an important role which cannot be taken into account by very small clusters as the one used in the earliest studies. These factors are better taken into account by periodic approaches or by big clusters simulations. Both factors can affect not only the stability of alkoxides, which is very sensitive to the local site geometry, [START_REF] Boronat | Are Carbenium and Carbonium Ions Reaction Intermediates in Zeolite-Catalyzed Reactions?[END_REF][START_REF] Boronat | Reaction Intermediates in Acid Catalysis by Zeolites: Prediction of the Relative Tendency To Form Alkoxides or Carbocations as a Function of Hydrocarbon Nature and Active Site Structure[END_REF] but also the stability of carbenium ions, sensitive to the electrostatic field intensity. [START_REF] Rozanska | A Periodic DFT Study of Isobutene Chemisorption in Proton-Exchanged Zeolites: Dependence of Reactivity on the Zeolite Framework Structure[END_REF][START_REF] Leydier | Revisiting Carbenium Chemistry on Amorphous Silica-Alumina: Unraveling their Milder Acidity as Compared to Zeolites[END_REF][START_REF] Rey | Ab Initio Simulation of the Acid Sites at the External Surface of Zeolite Beta[END_REF] Depending on the level of theory (DFT-GGA versus DFT-GGA plus dispersion corrections versus hybrid functionals) and on the location of the Brønsted acid site (itself function of the considered zeolite framework), the carbenium species can however still be considered as transition states for the protonation of alkenes to alkoxides, [START_REF] Boronat | Reaction Intermediates in Acid Catalysis by Zeolites: Prediction of the Relative Tendency To Form Alkoxides or Carbocations as a Function of Hydrocarbon Nature and Active Site Structure[END_REF][START_REF] Rozanska | A Periodic DFT Study of Isobutene Chemisorption in Proton-Exchanged Zeolites: Dependence of Reactivity on the Zeolite Framework Structure[END_REF] or as local energy minima, thus reaction intermediates. [START_REF] Boronat | Reaction Intermediates in Acid Catalysis by Zeolites: Prediction of the Relative Tendency To Form Alkoxides or Carbocations as a Function of Hydrocarbon Nature and Active Site Structure[END_REF][START_REF] Leydier | Revisiting Carbenium Chemistry on Amorphous Silica-Alumina: Unraveling their Milder Acidity as Compared to Zeolites[END_REF] Periodic studies of the isomerization through PCP species are very scarce. Demuth et al. [START_REF] Demuth | Catalytic Isomerization of 2-Pentene in H-ZSM-22-A DFT Investigation[END_REF] focused on the isomerisation 2-pentene in H-ZSM-22. Huang et al. recently reported about hex-3-ene isomerization in H-ZSM-5. [START_REF] Huang | Conversion of n-Hexane and n-Dodecane over H-ZSM-5, H-Y and Al-MCM-41 at Supercritical Conditions[END_REF] The PCP was found as a transition structure, alkoxides being the reaction intermediates in both studies.

Higher level calculations, such as the hybrid MP2 calculations performed by Tuma et al. [START_REF] Tuma | The tert-Butyl Cation in H-Zeolites: Deprotonation to Isobutene and Conversion into Surface Alkoxides[END_REF] revealed the tert-butyl carbenium ion as a reaction intermediate, which was not the case at the PBE level. Nonetheless, it was less stable as compared to the π complex and alkoxides. The consideration of thermal effects were also shown to affect the conclusions about the stability of carbenium ions as intermediates. Tuma and Sauer 48 took into account the influence of the temperature in the stability of the reaction intermediates and transition states, starting from periodic static DFT -PBE calculations. The carbenium appeared as the most stable species with respect to alkoxides when the temperature was raised over 120 K. More recently, studies from van Speybroeck et al. [START_REF] Hajek | On the Stability and Nature of Adsorbed Pentene in Brønsted Acid Zeolite H-ZSM-5 at 323K[END_REF][START_REF] Cnudde | Effect of Temperature and Branching on the Nature and Stability of Alkene Cracking Intermediates in H-ZSM-5[END_REF] compared static and molecular dynamic methods for measuring the stability of adsorbed butene and pentene in H-ZSM-5. By ab initio molecular dynamics (AIMD) at 323 K, linear alkoxides, alkene π complex and tertiary carbenium ions were found as the favored intermediates. Nonetheless, at 773 K, secondary and tertiary alkoxides were not stable, contrary to the carbenium ion, which was found as a stable intermediate.

To sum up, in spite of all the performed studies, the answer to the question if carbenium ions are reaction intermediates or transition states remains elusive. Very scarce are the studies devoted to reactions proceeding via PCP species. Moreover, whereas many work has been done about olefins chemisorption on acidic zeolites, [START_REF] Boronat | Are Carbenium and Carbonium Ions Reaction Intermediates in Zeolite-Catalyzed Reactions?[END_REF][START_REF] Boronat | Reaction Intermediates in Acid Catalysis by Zeolites: Prediction of the Relative Tendency To Form Alkoxides or Carbocations as a Function of Hydrocarbon Nature and Active Site Structure[END_REF][START_REF] Rozanska | A Periodic DFT Study of Isobutene Chemisorption in Proton-Exchanged Zeolites: Dependence of Reactivity on the Zeolite Framework Structure[END_REF][START_REF] Leydier | Revisiting Carbenium Chemistry on Amorphous Silica-Alumina: Unraveling their Milder Acidity as Compared to Zeolites[END_REF][START_REF] Demuth | Catalytic Isomerization of 2-Pentene in H-ZSM-22-A DFT Investigation[END_REF][START_REF] Tuma | The tert-Butyl Cation in H-Zeolites: Deprotonation to Isobutene and Conversion into Surface Alkoxides[END_REF][START_REF] Tuma | Protonated Isobutene in Zeolites: tert-Butyl Cation or Alkoxide?[END_REF][START_REF] Hajek | On the Stability and Nature of Adsorbed Pentene in Brønsted Acid Zeolite H-ZSM-5 at 323K[END_REF][START_REF] Cnudde | Effect of Temperature and Branching on the Nature and Stability of Alkene Cracking Intermediates in H-ZSM-5[END_REF][START_REF] Vollmer | Mechanisms of Hydrogen Exchange of Methane with H-Zeolite Y: An ab Initio Embedded Cluster Study[END_REF] the reactivity of naphthenes was only very barely investigated by DFT. Some cyclic cations have been experimentally observed to be important long-lived intermediates in some reactions of hydrocarbons on zeolites. [START_REF] Yang | Formation of Alkenyl Carbenium ions by Adsorption of Cyclic Precursors on Zeolites[END_REF] A DFT study of the cyclohexene interaction in H-ZSM-5 [START_REF] Cuán | DFT-Quantum Chemical Study of the HZSM-5-Cyclohexene Interaction Pathways[END_REF] revealed the formation of carbenium species instead of alkoxides as local energy minima. The bulkiness of cyclic carbenium with respect to non-cyclic ones may indeed be a factor of easier stabilization of cyclic carbenium, preventing the approach to framework oxygen atoms.

Concerning the mechanism of ring contraction and expansion of cyclic olefins, over the acid sites, no DFT work has been published to date, to the best of our knowledge. Ring contractionexpansion reactions are also of interest in the Methanol to Olefin context, and were studied by computational approaches, [START_REF] Mccann | AComplete Catalytic Cycle for Supramolecular Methanol-to-Olefins Conversion by Linking Theory with Experiment[END_REF][START_REF] Van Speybroeck | First principle chemical kinetics in zeolites: the methanol-toolefin process as a case study[END_REF][START_REF] Wang | Theoretical Insight into the Minor Role of Paring Mechanism in the Methanol-to-Olefins Conversion within HSAPO-34 Catalyst[END_REF][START_REF] Sun | New Theoretical Insights into the Contributions of Poly(methylbenzene) and Alkene Cycles to the Methanol to Propene Process in H-FAU Zeolite[END_REF][START_REF] Wang | Polymethylbenzene or Alkene Cycle? Theoretical Study on Their Contribution to the Process of Methanol to Olefins over H-ZSM-5 Zeolite[END_REF] but the nature of the reaction intermediates and transition state differs as in MTO the starting points are protonated aromatics, whereas we start here from protonated cycloalkenes. As mentioned previously, the first periodic study of isomerization reactions through PCP concerned a non-cyclic short molecule, namely 2-pentene, in H-ZSM-22, at the GGA (PW91) level, by Demuth et al. [START_REF] Demuth | Catalytic Isomerization of 2-Pentene in H-ZSM-22-A DFT Investigation[END_REF] Note that the reactants and products were found in the form of alkoxides, and not carbenium ions, which may have had an influence on the reaction profile. The lower-activated (about 100 kJ.mol -1 ) mechanism proposal involved up to three different transition states (among which an edge-protonated PCP) and two intermediates (a secondary carbenium ion and a neutral dimethylcyclopropane DMCP).

Therefore, the objective of this study is to investigate the reactivity of the cycle contractionexpansion in the context of the ethylcyclohexene isomerization (itself obtained from the dehydrogenation of ethylcyclohexane), identifying the location of the most active sites of an EUO type zeolite for this reaction. To do so, first the stability of the different forms of the adsorbed reactant (carbenium, alkoxide and π-complex) have been evaluated, as well as the intermediates and transition states for the mechanism shown in Figure 1. An exhaustive screening of all the possible active sites of an EUO type zeolite has been as well performed (Figure 3). Furthermore, an experimental evaluation of the activity of zeolites H-EU-1 and H-ZSM-50 has been carried out for the ethylcyclohexane hydroconversion, so as to challenge the calculated features in terms of location of the most active sites. To complete this evaluation, Temporal Analysis of Products (TAP) experiments [START_REF] Gleaves | TAP-2: An Interrogative Kinetics Approach[END_REF] of ethylcyclohexane diffusion in both zeolites H-EU-1 and H-ZSM-50 has been performed, to check if diffusional issues can impact the catalytic activity of these two zeolites.

Figure 3. Section of the EUO framework structure showing the different active sites analyzed in this study: pocket -green zone (light green T9, dark pink T2, light pink T3, dark green T7, and dark purple T8), channel -blue zone (dark blue T1, orange T5, and light purple T6) and intersection between the pocket and the channel -red zone (red T10 and light blue T4) [1 0 0]. Adapted with permission from ref. [START_REF] Peral | Structural Comparison of Two EUO-Type Zeolites Investigated by Neutron Diffraction[END_REF] . The oxygen atoms are not included and the silicon atoms are represented as colored circles.

Channel

Pocket

EXPERIMENTS AND METHODS

DFT calculations

Periodic DFT calculations were performed with the PBE (Perdew, Burke and Ernzerhof) exchange-correlation [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] as implemented in VASP 5.3. [START_REF] Kresse | Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium[END_REF][START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors using a Plane-Wave Basis Set[END_REF] The projected augmented wave (PAW) method [START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] was used to describe the core-electron interactions, and the plane wave basis set was limited to a kinetic cutoff energy of 400 eV except for the optimization of the cell dimensions, for which the cutoff was set at 800 eV. Van der Waals corrections as proposed within the D2 Grimme formalism [START_REF] Grimme | Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction[END_REF] were applied. The convergence criterion for the electronic self-consistent field relaxation was fixed to 10 -7 eV. All calculations were performed at the gamma point.

The bulk cell parameters and ionic positions of EU-1 and ZSM-50 (EUO type) were obtained from International Zeolite Association (IZA) database [START_REF] Baerlocher | Database of Zeolite Structures[END_REF] S1) ranges over 44 kJ.mol -1 , consistently with previous observations made on other frameworks. 44 ,68-69 Full geometry optimizations (zeolite plus hydrocarbons) of the reaction intermediates were performed using a conjugate gradient algorithm, with a convergence criterion on forces of 0.005 eV.Å -1 .

The Nudged Elastic Band (NEB) method [START_REF] Henkelman | Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points[END_REF] was used to locate the transition states. The number of images to investigate reaction pathways between the reactant and the product is 8. To start with, an interpolation scheme involving both Cartesian and internal coordinates was used (Opt'n-Path developed by Paul Fleurat-Lessard). 71 We basically perform 50 NEB steps before optimizing the structure of the highest energy image. The optimization consists in a quasi-Newton calculation, [START_REF] Pulay | Convergence Acceleration of Iterative Sequences. The Case of SCf Iteration[END_REF] sometimes followed by a Dimer calculation [START_REF] Henkelman | A Dimer Method for Finding Saddle Points on High Dimensional Potential Surfaces using only First Derivatives[END_REF][START_REF] Heyden | Efficient Methods for Finding Transition States in Chemical Reactions: Comparison of Improved Dimer Method and Partitioned Rational Function Optimization Method[END_REF] if the quasi-Newton had difficulties to converge.

Harmonic frequency calculations were performed on optimized structures (all atoms of the cell moving) with a displacement of ±0.02 Å around the equilibrium atomic positions. The objective of these calculations was double: i) to identify the true local energy minimum / saddle point nature of the optimized intermediates and transition structure, ii) to deduce vibrational free energies.

To achieve objective i), most of the time some refinements of the intermediate and transition structures had to be performed, to get zero (in the case of intermediates) or only one (in the case transition structures) imaginary frequencies, which was scarcely the case right after the Dimer or quasi-Newton optimizations, despite stringent convergence criteria. Line minimization methods were applied, thanks to algorithms developed by Tomáš Bučko (Univ. Bratislava). [START_REF] Bučko | Monomolecular Cracking of Propane over Acidic Chabazite: An Ab Initio Molecular Dynamics and Transition Path Sampling Study[END_REF] The procedure was repeated until the configuration with a correct vibrational spectrum was identified (typically 1 to 6 repeated cycles are needed). An example of such a sequence is given in Supporting Information S1.

For each transition structure, the connection with the expected reactants and products was established thanks to the intrinsic reaction coordinate (IRC) approach. This concept has been introduced by Fukui 76-77 and was successfully applied within VASP in the case of hydrocarbon reactions in zeolites. [START_REF] Bučko | Monomolecular Cracking of Propane over Acidic Chabazite: An Ab Initio Molecular Dynamics and Transition Path Sampling Study[END_REF] The IRC is the steepest descent path, starting from the transition state in the direction of the transition vector (corresponding to the imaginary vibrational frequency determined via vibrational analysis). Examples are given in Supporting Information S2. The algorithm stops if the energy increases over 20 successive steps. Structures identified at the end of the IRC were re-optimized with a convergence criterion on forces of 0.005 eV.Å -1 .

The adsorption energy E ads of all the considered species was calculated, using isolated ethylcyclohexene and the empty zeolite as references. For each of these species, the Gibbs free energy was then calculated according to the equations given in Supporting Information S3 by considering the rotational, translational, and vibrational degrees of freedom for gas-phase ethylcyclohexene and the vibrational degrees of freedom only for the zeolite models. The translational (and rotational) degrees of freedom were again decoupled from the vibrational one before estimating vibration partition functions.

Catalysts preparation

Commercial zeolite EU-1 supplied by Zeolyst was obtained in the protonic form according to the procedure described in reference 33. ZSM-50 was synthesized according to the protocol given in reference 19. ZSM-50 was obtained in the protonic form as follows. The zeolite was first calcined in order to remove the dibenzyldimethylammonium organic template. The calcination was done under an air flow (2 NL h -1 g -1 ) at 150°C (1h), 250°C (1h), 550°C (1h), 650°C (1h), 750°C (1h) and finally at 800°C for 10 h. The zeolite was then exchanged with an ammonium nitrate solution and calcined with the same protocol used for EU-1. [START_REF] Gutierrez-Acebo | Metal/Acid Bifunctional Catalysis and Intimacy Criterion for Ethylcyclohexane Hydroconversion: When Proximity Does Not Matter[END_REF] The H-EU-1 and H-ZSM-50 bifunctional catalysts were obtained by mixing 20% wt. of the corresponding zeolite with 80% wt. of alumina loaded with 1% wt. platinum. The experimental protocol is described elsewhere. [START_REF] Peral | Structural Comparison of Two EUO-Type Zeolites Investigated by Neutron Diffraction[END_REF][START_REF] Gutierrez-Acebo | Metal/Acid Bifunctional Catalysis and Intimacy Criterion for Ethylcyclohexane Hydroconversion: When Proximity Does Not Matter[END_REF] The mechanical mixtures were pelletized with a hydraulic press, crushed, and sieved to obtain a pellet size between 350 and 500 μm before catalytic tests.

Main features of the two bifunctional catalyst are provided Table 1 .

Material characterizations

Zeolites were characterized by X-ray fluorescence to determine the global Si/Al molar ratio.

XRF analyses were performed with a Thermo scientific ARL Perform'X. [START_REF] Mihindou-Koumba | Methylcyclohexane Transformation over HFAU, HBEA, and HMFI Zeolites: II. Deactivation and Coke Formation[END_REF] Al magic angle spinning nuclear magnetic resonance (MAS NMR) was employed to determine the percentage of framework and extra-framework aluminum. NMR experiments were performed using a Bruker Ultrashield 400 MHz spectrometer equipped with a 4 mm CP MAS probe head at room temperature. The MAS rate was 12 kHz for all experiments, the sequence used for Al was a zg sequence and a delay time of 0.5 s. The number of Brønsted acid sites was calculated from these two techniques (number of Al IV considered to be equal to the number of Brønsted sites). For this calculation, Na residual presence, measured by atomic absorption spectroscopy (AAS) has been also considered. Crystallinity was measured by X-ray diffraction (XRD) using a X'Pert Pro diffractometer from Philips Analytical, using a Cu Kα radiation (λ = 1.5406 Å). Diffraction profiles were scanned using the step mode over a 2θ range of 5-40°, in steps of 0.02° for six hours with a step time of 5 s at each point. Nitrogen adsorption measurements were carried out at -200°C on an automatic Micromeritics ASAP 2420 apparatus. Before adsorption, zeolite samples were degassed under vacuum at 500°C for 6 h. The total porous volume (V total ) was calculated from the adsorbed volume of nitrogen at a relative pressure P/P 0 of 0.98 whereas the microporous volume (V micro ) was determined using the t-plot method. The mesoporous volume (V meso ) was obtained by the difference between V total and V micro .

Platinum dispersion on alumina was determined by hydrogen titration of chemisorbed oxygen (H 2 -O 2 titration) in a Gira Xisorb apparatus with a thermal conductivity detector. The samples were first calcined under air at 530°C for 2 h at 5°C min -1 , then cooled down to room temperature and purged with He. The first reduction with H 2 was done at 450°C for 2 h with a flow of 20 NmL min -1 . After cooling down to room temperature and purging with He, 15 pulses with pressures from 0.5 to 60 kPa of oxygen were added until saturation occurred (oxygen titration). Another He purge was done before a second reduction with H 2 at room temperature.

Then 10 pulses with pressures from 0.5 to 60 kPa of hydrogen were added until saturation (hydrogen titration). The number of platinum surface sites was calculated based on the platinum dispersion and the total amount of platinum measured by XRF.

Catalytic tests

Ethylcyclohexane (ECH) hydroconversion tests were performed in a high-throughput catalytic test unit with sixteen fixed-bed downflow reactors. This test was performed at a total pressure of 11 bar absolute. The hydrogen to ethylcyclohexane molar ratio was set to 30, and the weight hourly space velocity (WHSV) was set to 2 grams of ethylcyclohexane per gram of catalyst per hour. The conversion was changed by changing the temperature in the 200-330°C range. For each temperature two gas chromatography (GC) analyses were performed in order to check the catalyst stability. Return points confirmed that catalyst deactivation was negligible during the test. ECH conversion, product selectivities, and turnover frequencies per acid site were calculated according to reference 33. Catalytic tests demonstrated that the chosen amount of platinum was sufficient to properly balance the zeolite. [START_REF] Weisz | Polyfunctional Heterogeneous Catalysis[END_REF]

Diffusion measurements

Temporal Analysis of Products (TAP) experiments were carried out to estimate the characteristic diffusion time of ethyl-cyclohexane inside H-EU-1 and H-ZSM-50 zeolites. [START_REF] Gleaves | TAP-2: An Interrogative Kinetics Approach[END_REF]

RESULTS AND DISCUSSION

The adsorbed cycloalkene species: π-complex versus carbenium versus alkoxide species

A systematic DFT study of the stability of adsorbed cycloalkenes involved in the reaction network was performed at the T10O12 site, located at the intersection between 12 MR pockets and the 10 MR channel of EUO framework structure (Figure 4). The carbenium species (including some chair and boat conformations) depicted in Figure 1 were considered, as well as the corresponding π-complexes. Some of the optimized structures are depicted in Figure 5. In all attempts to stabilize alkoxides, the optimization failed and provided the corresponding πcomplexes. Considering that we were performing static calculations, this conclusion differs strongly from previous investigations performed at similar level of theory for non-cyclic alkoxide species. [START_REF] Leydier | Revisiting Carbenium Chemistry on Amorphous Silica-Alumina: Unraveling their Milder Acidity as Compared to Zeolites[END_REF][START_REF] Rey | Ab Initio Simulation of the Acid Sites at the External Surface of Zeolite Beta[END_REF] This suggests that the rigidity of the cycle with respect to mobile alkyl chains is a factor that hinders species that are the closest to the framework (such as alkoxides).

Performing a detailed AIMD analysis of the reaction network was beyond the scope of the present work, in particular due to the significant size of the cell and number of atoms (nearly 200 per cell). Even though, we can anticipate that the stabilization of the carbenium species with respect to alkoxides will even be enhanced by a refined approach, as this was shown for noncyclic species. [START_REF] Hajek | On the Stability and Nature of Adsorbed Pentene in Brønsted Acid Zeolite H-ZSM-5 at 323K[END_REF][START_REF] Cnudde | Effect of Temperature and Branching on the Nature and Stability of Alkene Cracking Intermediates in H-ZSM-5[END_REF] Some secondary carbocations were as well analyzed and the results showed either a worse stability compared to the tertiary carbocations or the direct transformation into a tertiary carbocation by hydride shift during the geometry optimization. The energy of the carbenium species did not vary much as compared with the one of πcomplexes. In the case of the ECH skeleton, the π-complexes are at least 25 kJ/mol more stable than the carbenium ions regardless the conformation. For the carbenium, two configurations were investigated due to their relevance in further isomerization reactions (see later): chairs and distorted boats. The chair conformation is 10 kJ/mol more stable than the distorted boat conformation. 12-EMCP and 12-DMCH related carbenium and π-complexes are very close in energy. In the case of 12-DMCH + chair and boat conformation energies were almost the same.

Finally, for 123-TMCP, the π-complex is about 10 kJ/mol less stable than the carbenium.

In order to explain such relative energy differences, we performed structural analysis. The stability of the four π-complexes is directly correlated to the distance between the molecule and the zeolite framework: the closer to the framework, the more stable the π-complexes. The latter was quantified by the average distance between the framework proton and the carbons belonging to the C=C double bond (Figure 6 and Table S2). The ECH π -complex was more stable than the corresponding carbocation and also closer to the zeolite. For bulkier structures, such 123-TMCP, the π-complex is slighter higher in energy compared to the corresponding carbenium. The three methyl groups of this molecule are likely at the origin of a steric constraint to approach the framework.

However, such a correlation between stability and distance was not valid for carbenium species. For these species, the O…H distance (O from the framework were the H originates, H transferred to the molecule) is reported in Figure 6. Some correlations between the energy and other distances (Al-C, C being the carbon atoms of the PCP) were also looked at but failed.

Some other correlations with the local electrostatic field were also looked at, but did not reveal clear trends, contrary to previous findings for smaller hydrocarbons. [START_REF] Leydier | Revisiting Carbenium Chemistry on Amorphous Silica-Alumina: Unraveling their Milder Acidity as Compared to Zeolites[END_REF] This suggests that the stability of these charged bulky species is a combination of several factors (likely electrostatics, van der Waals interaction, etc.) making simple descriptors irrelevant for the prediction of the nature of the most stable species at a given site in the zeolite.

E ads (kJ/mol) distance (Å)

Pi-complexes Carbeniums

Isomerization pathway at the T10O12 intersection site

At the T10O12 intersection site between the channel and the pocket, a full study of the ethylcyclohexene isomerization pathway including proton transfer, hydride transfer and cycle contraction-expansions (Figure 1) has been performed. Starting from 1-ethylcyclohexene (ECH=) the different isomers families considered were the ethylmethylcyclopentenium (EMCP+), dimethylcyclohexenium (DMCH+) and trimethylcyclopentenium (TMCP+). They were obtained via type B isomerization, expected to take place via PCP species.

A first proton transfer from the zeolite framework to the ECH = π-complex is needed in order to start the isomerization reaction. This elementary step (via ts1) exhibits an energy barrier (Figure 7) around 15 kJ/mol and leads to a carbenium with a distorted chair conformation. A conformational change from a chair to a boat ECH + has been found as necessary before any cycle contraction step. The energetic barrier corresponding to this conformational change (via ts2) is around 22 kJ/mol (Figure 7).

Then, the cycle contraction from ECH + to the 12-EMCP + happens through a PCP (TS1), by a bond formation between carbons 1 and 2. The latter was obtained as a transition state, being an edge protonated cyclopropyl species (Figure 7 and Figure 8 a), with an energy barrier of 57 kJ/mol. In the course of the isomerization, the proton from carbon 2 moved to carbon 3 while the C1-C3 bond was broken. The skeleton of the transition state resembles that of the ring contraction-expansion intermediates in MTO, [START_REF] Mccann | AComplete Catalytic Cycle for Supramolecular Methanol-to-Olefins Conversion by Linking Theory with Experiment[END_REF][START_REF] Van Speybroeck | First principle chemical kinetics in zeolites: the methanol-toolefin process as a case study[END_REF][START_REF] Wang | Theoretical Insight into the Minor Role of Paring Mechanism in the Methanol-to-Olefins Conversion within HSAPO-34 Catalyst[END_REF][START_REF] Sun | New Theoretical Insights into the Contributions of Poly(methylbenzene) and Alkene Cycles to the Methanol to Propene Process in H-FAU Zeolite[END_REF][START_REF] Wang | Polymethylbenzene or Alkene Cycle? Theoretical Study on Their Contribution to the Process of Methanol to Olefins over H-ZSM-5 Zeolite[END_REF] with a three carbon cycle connected by an edge to a five carbon cycle. However, due to different saturation levels (number of H atoms connected to each C atom on the rings), the spatial arrangement is very different as well as the charge delocalization.

Hydride transfer from the methyl to the ethyl of the 12-EMCP + is then required in order to start the next cycle contraction (via ts3). The energetic barrier of this step was found at around 12 kJ/mol. ts1, ts2 and ts3 structures are depicted in Figure S3. Then, it appears that the cycle contraction step is by far the most energy demanding step, as compared to proton and hydride transfers, and cycle conformation change. Thus for the following steps, transition states for cycle contractions and expansions only were looked at. 2). TS2 is slightly different since the distance between C 2 -H and C 3 -H were inversed compared to the other transition states (see terminology in Figure 8). These similarities in distance, supports the close adsorption energies found for all of them, i.e. independently of the contraction or expansion of the cycle. The TS are so close that the different energy barriers are determined mainly by the energy differences of the intermediates and not by the TS themselves. Moreover, the transition states are not early nor late transition states.

Table 2. Distances between atoms in the PCP for all optimized transition structures for contractionexpansion steps, at the T10O12 intersection active site. The imaginary frequencies for the transition structures are also given (one single imaginary frequency per transition structure).

Distance (Å) approximation by periodic calculations. Their most likely mechanism goes through an edgeprotonated dimethylcyclopentane transition state (PCP type) similar to our TS. The energy barrier reported is 100 kJ/mol, higher than ours. Similarly, Huang et al. [START_REF] Huang | Conversion of n-Hexane and n-Dodecane over H-ZSM-5, H-Y and Al-MCM-41 at Supercritical Conditions[END_REF] report a barrier of 94 kJ mol -1 for hex-3-oxide isomerization into 3-methylpent-2-oxide, also higher than ours. The difference is not unexpected as the reactant and products are considered as alkoxides in both studies, whereas in our case, carbenium ions are intermediates.

C 1 -C 2 C 2 -C 3 C 1 -C 3 C 2 -H C 3 -H f (i cm -1 ) TS1

Comparison between the different active sites within the EUO framework

First, an analysis of the stability of TS2 and of the reactants (21-EMCP + ) and products (12-DMCH + ) connected to it, has been performed over all the possible active sites of the EUO type zeolite (Figure 3). This TS had the particularity that a methyl group was linked to the carbon of the PCP edge that was not a part of the five-member ring. Figure 10 shows the energy profiles obtained for this reaction step. We failed in optimizing the transition state for two sites at the channel, T5 and T6, likely due to the difficulty of the protonated molecule to get close to the deprotonated active site, located in a poorly accessible area.

We first discuss the behavior of the sites located in the 12MR pocket. Significant differences in energy were found from one site to another, despite the structural similarities for the transition state in terms of C-C and C-H bond lengths (supporting information S4). Nevertheless, the position of this TS in the pocket differs from one active site to another (Figure S7). The energy difference could be due to the different accommodation of the TS inside the pocket, i.e. if the PCP is oriented towards the exit of the pocket (channel) or to the bottom of the pocket and if the methyl-bonded to the edge-carbon is oriented or not towards the active site. The species at T3 and T9 have similar low energies and their positions inside the pocket provided a similar local geometry for the accommodation of the TS. The PCP is oriented towards the channel and the methyl -bonded to the edge-carbon oriented in the opposite site of the active site (towards the channel). This is not the case of the other active sites. Regarding the sites located at the intersection, species located at T4 and T10 exhibited close energies, in line with their similar position at the intersection. The distance from the PCP to the active site position is, however, different in both sites as illustrated in Table S6, which seems to have no influence in the adsorption energy of the TS.

The T1 site was found as the single site able to stabilize the PCP in the channel, as explained previously. Comparing the stability of TS2 and the related reactants and products, the pocket exhibits the most stabilizing sites (T3 and T9), followed by the channel (T1), whereas the intersection (T4 and T10) had less favorable interaction with the cationic species. Some other sites of the pocket (such as T7) did not stabilize much the intermediates. Comparing the barriers from one site to the other, they are rather close (varying from 50 to 77 kJ/mol forward and from 61 to 88 kJ/mol backward, table S7). Thus, in most cases the main differences between the different actives sites are the absolute energies of the intermediates and transition states, and not so much the energy barriers of this step. This reflects a strong site-dependent confinement effect, which does not strongly depends on the nature of the carbenium species (reactant, PCP transition state, product) for a given step.

Table 3 reports the dispersion contribution to the adsorption energy for the reactant, transition state and product of this reaction step. This contribution appears to be strongly negative in all cases, but much more at the pocket and channel sites (from -134 to -101 kJ/mol) than at the intersection sites (from -84 to -59 kJ/mol). However, the dispersion term does only slightly vary along the reaction pathway, which means that the strong energy differences between transition states and intermediates are held by non-dispersive term, due to the PCP nature of the TS.

Table 3. Dispersion contribution to the adsorption energy of the 21-EMCP + , TS2 and 12-DMCH + species.

Note that the no transition state was identified at the T5 and T6 sites. Thus, the respective behaviors of the intersection versus the channel and pocket sites are well rendered by the dispersion interaction. For the molecules considered, these disfavor the intersection site with respect to the two other kinds of sites. This is in agreement with the notion of confinement effect, which variation according to the local topology is often considered to be of van der Waals origin, [START_REF] Derouane | Shape Selectivity in Catalysis by Zeolites: The Nest Effect[END_REF] and with previous computational work addressing the comparison of the stabilization of various hydrocarbons in various zeolites. 80 ,81-82 We extended the comparison of various active sites to the whole reaction pathway, taking into account only the cycle contractions and expansions, and selecting one favorable site per location: one in the channel (T1O1), one in the pocket (T9O6), one at the intersection (T10O12, already investigated in section 3.2). The energy profiles are reported in Figure 9. They confirmed the much higher stability of species at the pocket and the channel as compared to the intersection, regardless the reaction intermediates and the transition states. A slight difference in terms of energy for intermediates (2-11 kJ/mol) is observed between the channel and the pocket sites, except the 125-TMCP + which was clearly more stable in the pocket than in the channel (25 kJ/mol). All transition states are lower in energy in the pocket than in the channel (16-24 kJ/mol). Similar as for TS2, the dispersion contribution to the adsorption energy was extracted for the three sites along the whole reaction pathway (Table 4). The same features are revealed, suggesting that the dispersion interactions are favoring the pocket and channel sites versus the intersection site. Note, however, that along a given pathway at a given site, the dispersion contribution is not sufficient to anticipate the stability of the ionic species considered, as shown in section 3.1. This is in agreement with previous findings devoted to the investigation of various non-cyclic carbocations. [START_REF] Rozanska | A Periodic DFT Study of Isobutene Chemisorption in Proton-Exchanged Zeolites: Dependence of Reactivity on the Zeolite Framework Structure[END_REF][START_REF] Leydier | Revisiting Carbenium Chemistry on Amorphous Silica-Alumina: Unraveling their Milder Acidity as Compared to Zeolites[END_REF][START_REF] Rey | Ab Initio Simulation of the Acid Sites at the External Surface of Zeolite Beta[END_REF][START_REF] Vollmer | Mechanisms of Hydrogen Exchange of Methane with H-Zeolite Y: An ab Initio Embedded Cluster Study[END_REF][START_REF] Mansoor | Impact of Long-Range Electrostatic and Dispersive Interactions on Theoretical Predictions of Adsorption and Catalysis in Zeolites[END_REF][START_REF] Fang | Theoretical Investigation of the Effects of the Zeolite Framework on the Stability of Carbenium Ions[END_REF][START_REF] Song | Origin of Zeolite Confinement Revisited by Energy Decomposition Analysis[END_REF][START_REF] De Moor | Physisorption and Chemisorption of Hydrocarbons in H-FAU Using QM-Pot(MP2//B3LYP) Calculations[END_REF] These observations generalize our findings made before in the case of TS2 tested at all the active sites, even if the step corresponding to TS2 is not the rate-determining one for all sites.

Site

Indeed, it appears that the main differences between the three investigated acid sites is not the precise respective energy of TS1, TS2 or TS3, but the absolute energy levels of all the species (close to 50 kJ/mol in difference between the pocket and the intersection site). The origin of this is found to be the dispersion interaction term between the intermediates/transition states and the zeolite. Moreover, the maximal forward barriers are slightly lower for the pocket (57 kJ/mol) as compared to the other sites (73 kJ/mol in the channel and 68 kJ/mol at the intersection).

All these results suggests that the most probable active site for carrying out the reaction is the one located in the pocket. Thanks to an optimal confinement effect, this site stabilizes all intermediates and transition states, affecting only slightly the barriers of each elementary step.

An impact on the macroscopic kinetic feature is thus expected on apparent activation energies, but mainly due to adsorption terms. Note also that we can retrospectively consider that the protonation barriers (such as the one investigated in section 3.2.) will not be very different from one site to another, and will thus stay negligible with respect to the contraction-expansion barriers.

Gibbs free energy profiles

The Gibbs free energy profiles at 277 °C, calculated according to the methods exposed in section 2 and Supporting Information S3, are depicted in Figure 11, for the T10O12, T9O6 and T1O1 sites. This temperature was chosen as it is a central temperature in the present experimental investigation (see later, section 3.4). Whereas most adsorption energies are negative (Figure 10), entropy contributions lead to positive values of free energies for transition structures, as well as for some of the intermediates. The shape of the profiles is also affected: the Gibbs free energy profile reveals again the pocket as the most favorable site whereas the channel exhibits much higher Gibbs free energy barriers.

The intersection remains a noncompetitive site with respect to the pocket and channel sites.

Table S7 includes all the Gibbs energies for all the intermediates and TS. Table S8 gives all the activation data estimated from the DFT calculations.

In the case of the free energy profile at the pocket site, the intrinsic free energy barrier to pass from ECH = to TS1 is 69 kJ/mol (Figure 11). In the case of the intersection site, this barrier is 59 kJ/mol. Thus, the intrinsic activation free energy difference between the two sites is expected to be close to 10 kJ/mol, for the consumption of the reactant. We may also consider the apparent activation free energies for the first step, given by the difference between the activation free energy and the adsorption free energy (thus the absolute free energy of the transition state in Figure 11). At the pocket site, the apparent activation free energy is close to 56 kJ/mol, while at the intersection it is 74 kJ/mol. The difference is then 18 kJ/mol. These values will be discussed latter in comparison with experimental data (section 3.5).

Experimental characterization and catalytic evaluation of the H-EU-1 and H-ZSM-50 zeolites

XRD characterization confirmed that both solids are well crystallized and corresponded to EU-1 and ZSM-50 respectively (Supporting Information S6). The physicochemical properties of the zeolites in the protonic form are provided Table 5. The very low amount of Na compared to the framework Al (less than 4% molar) demonstrates the efficiency of the ammonium exchange. For both zeolites, the percentage of extraframework aluminum was the same, 9%, according to [START_REF] Mihindou-Koumba | Methylcyclohexane Transformation over HFAU, HBEA, and HMFI Zeolites: II. Deactivation and Coke Formation[END_REF] Al NMR. The total amount of Brønsted acid sites per gram is 1.4 time higher for the H-EU-1 zeolite. This is a consequence of the lower Si/Al molar ratio of H-EU-1 compared to H-ZSM-50.

The microporous volumes are comparable. However, the external surface area and the mesoporous volume of the H-EU-1 are substantially higher compared to H-ZSM-50. The high H-EU-1 external surface area and the significant mesoporous volume are induced by the agglomeration of round nano-crystals (30-60 nm) as revealed by SEM analysis (Supporting Information S6). Such phenomenon was reported for other zeolites such as Beta [START_REF] Coutanceau | Dealumination of Zeolites. Part VII. Influence of the Acid Treatment of a HBEA Zeolite on the Framework Composition and on the Porosity[END_REF] or IZM-2. [START_REF] Mota | IZM-2: A Promising New Zeolite for the Selective Hydroisomerization of Long-Chain n-Alkanes[END_REF] H-ZSM-50 particles are much bigger rods (several nm of length and 200 nm of thickness). S ext (m 2 g -1 )

V micro (mL g -1 )

V mes (mL g -1 ) Applying the Eyring's equation, [START_REF] Eyring | The Activated Complex in Chemical Reactions[END_REF] one can deduce the link between the ratio of TOFs At this stage, the higher turnover frequency per acid site observed for H-EU-1 compared to H-ZSM-50 could be explained either by the different location of the active sites for the two zeolites and/or by increased diffusional limitations for H-ZSM-50 induced by its bigger crystallites sizes.

(Si/
Indeed, diffusion limitations were assigned an important role in the hydroconversion of nheptane in H-EU-1. [START_REF] Raybaud | The Origin of the C7-Hydroconversion Selectivities on Y, , ZSM-22, ZSM-23, and EU-1 Zeolites[END_REF] In order to evaluate the existence of possible diffusional limitations, TAP experiments were carried out. Figure S1-S2 compares the experimental and model normalized TAP pulse responses for ethyl-cyclohexane over H-ZSM-50 and H-EU-1 as a function of temperature. An adequate description of the experimental data was obtained by the model. Table S10 lists the parameter estimates from the TAP data. Rather similar adsorption enthalpies were found for both zeolite samples, as expected for zeolites with similar structures. The characteristic diffusion times are, on the other hand, different for the two zeolites. The diffusion of ethyl-cyclohexane inside the micropores of H-ZSM-50 is faster than for H-EU-1 at 175°C. However, when the values are extrapolated to the reaction temperatures applied in this study, the characteristic diffusion times become similar for both zeolites, due to the difference in activation energy for micropore diffusion. The difference in catalytic performance between the two zeolites can thus not be attributed to transport phenomena.

Thus, the location of the active site remains to explain the difference in performance between the two zeolites. It is known from literature that the active sites of the EU-1 are located in the channel and in the pocket whereas in the ZSM-50 are located in the intersection. [START_REF] Souverijns | Molecular Shape Selectivity of EUO Zeolites[END_REF][START_REF] Peral | Structural Comparison of Two EUO-Type Zeolites Investigated by Neutron Diffraction[END_REF] Thus, in full consistence with our ab initio calculations, the zeolite possessing active sites in the channel and in the pocket (H-EU-1) is much more active than the zeolite possessing active sites in the intersection (H-ZSM-50). The free energy difference of -12 kJ/mol between the two zeolites,

given by the ratio of turnover frequencies (eq. 1), is in excellent agreement with the computational estimation of -10 kJ/mol, according to the difference in intrinsic activation free energy for the first step of the reaction (section 3.4). Considering apparent activation free energies (section 3.4), the difference was estimated at -18 kJ/mol, also close to the experimental value of 12 kJ/mol. This makes our conclusions based on DFT calculations even stronger, regarding the difference in activity of both samples, as a tracer of the difference in confinement effect between the side pockets and the channel. Note that the uncertainty of DFT calculations may be higher than 10 kJ/mol, making the estimation of difference in computed activation free energy approximate. However, the fact that the order of magnitude is the same makes us confident in the validity of the conclusion.

Hence, this work suggests DFT calculations of such reaction pathways is a relevant method for determining the location of the active sites. It also provides new insights in the mechanism of cyclic alkene transformations by Brønsted acid catalysts, which was never investigated at the atomic scale in the past.

CONCLUSIONS

In the present contribution, the location of the most active sites (for ethylcyclohexene isomerization, within the ethylcyclohexane hydroconversion bi-functional framework) within a given zeolitic framework (EUO) is elucidated by DFT calculations, and confirmed experimentally by the experimental catalytic evaluation of two zeolites (H-EU-1 and H-ZSM-50)

depicting this framework but with different positions of the Brønsted acid sites. The active sites in the H-EU-1 zeolite are mainly found inside 12 MR side-pockets and in 10 MR channels, whereas in the H-ZSM-50 zeolite they are located at the intersection between the channel and the side-pocket. The DFT evaluation of the stability of intermediates and transition states revealed the intersection between the channel and the pocket as the most unfavorable active site for the reaction. On the contrary the side pocket is found as the preferred place for the reaction to happen. The origin of the differences were found to be mainly the dispersion interactions between the intermediates/transition states and the zeolite. These results were as well confirmed by the calculation of the Gibbs adsorption energy profile. Consistently, in the experimental hydroconversion of ethylcyclohexane H-EU-1 shows a turnover frequency at 270°C fifteen times higher than H-ZSM-50. This difference in turnover frequency could be attributed either to diffusional limitations or to the active site location. However, TAP experiments revealed that the difference in catalytic performance between the two zeolites cannot be attributed to transport phenomena. Hence, the difference of activity can be attributed to the different active sites location. The experimental difference in activation free energy for the two solids very nicely match the value computed by DFT.

This study also provides detailed computational information about the reaction network for the bi-functional isomerization of naphthenes. The transition structures are PCP-like, the cyclopropane being connected edge-to-edge to a cyclopentane unit. A typical feature of the transition states is the presence of an edge proton, migrating along the cycle contractionexpansion step. This work opens the door to the computational design of zeolitic catalysts from ab initio investigations.

ASSOCIATED CONTENT

Figure 1 .

 1 Figure 1. One ethylcyclohexene isomerization reaction pathway, passing through tertiary carbocations. * Hydrogen shifting. The bond to be broken (in the forward direction) is depicted in red and the forming bond in green.

Figure 2 .

 2 Figure 2. Three possible forms for adsorbed 1-ethylcyclohexene at the bridging acid site of a zeolite: a) π-complex; b) carbenium, c) alkoxide.

  and then reoptimized in the purely siliceous form with an increased energy cutoff of 800 eV (initial parameters from IZA: a = 13.3778 Å, b = 13.3778 Å, c = 20.5820 Å, α=β= 90°, γ=62.6° , parameters after optimization: a = 13.2189 Å, b = 13.3266 Å, c = 20.3045 Å, α=90.0°, β= 89.9°, γ=62.8°). The amount of aluminum atoms (together with a proton per Al) in the zeolite framework came from a Si/Al equal to 15, commonly considered experimentally, 33,66-67 and representative of the EU-1 used in the present study. Since the primitive EUO structure cell possesses 112 T sites, the number of aluminum atoms needs to be between 3 and 4. As a matter of simplicity it has been chosen 3. In the beginning of the study two different cells with three different locations of the Al on each were investigated. The sites choice was basically done taking into account the most different locations in the structure: the pocket, the channel, and their intersection. The sites are named from the number (IZA) of the T atom substituted by Al, and the number of the oxygen atom holding the proton. The first cell contains exchanged T10O12, T1O1, and T9O6 sites, whereas the second one contains exchanged T4O12, T1O2 and T9O20 sites. Afterwards, in order to test the other active T sites all the silicon atoms were successively substituted by Al, the proton being put in an accessible position. The relative stability of the alumination configurations considered (Table

  6 mg of the zeolite sample (200 -300 µm) was placed between two layers of quartz particles (200 -300 µm). A thermocouple was placed inside the reactor close to the zeolite layer. The sample was heated to 400°C (10°C/min) under vacuum and kept for 30 minutes to desorb all water.Pulse experiments were then carried out between 150 -250°C. At the end of the temperature cycle an experiment at 175°C was repeated to check if the sample had not changed. A mixture of 50% ethyl-cyclohexane and 50% Ar was used and the m/e of 55 and 40 were monitored. Single pulse experiments were performed with 10 pulses averaged to improve the signal over noise ratio. Data acquisition times amounted to 20 seconds with pulses rates of 0.04 Hz. Before the experiments the Knudsen regime was verified by changing the pulse intensity and normalizing the Ar data. The pulse size was below 5 nmol per pulse. Details on the modeling procedure of the data can be found in the SI section.

Figure 4 .

 4 Figure 4. Adsorption energies for π-complexes and carbenium for the C 8 species considered in the present work, at the T10O12 intersection Brønsted acid site. For C 6 cycles, two conformations were considered: the chair conformation is noted "c" whereas a distorted boat one is noted "b".

Figure 5 .

 5 Figure5. Structures of selected species at the T10O12 site, at the intersection between the channel and the side pocket: a) ECH = π -complex; b) ECH + carbenium; c) 123-TMCP = π-complex; d) 125-TMCP + carbenium. For π-complexes, the distance (Å) between the proton and the carbons belonging to the double bond is given. For carbenium ions, the distance (Å) between the hydrogen which left the zeolite and the corresponding oxygen is given.

Figure 6 .

 6 Figure 6.Correlation between adsorption energy and distance between pi-complex / carbenium ions and the zeolite framework at the intersection channel-pocket site (T10O12).

Figure 7 .Figure 8 .

 78 Figure 7. Energy profile at the T10O12 intersection site for the proton transfer, conformational change, first cycle contraction and hydride transfer reactions. Full lines represent the different intermediates with their corresponding TS whereas the dashed lines connect the same intermediates coming from different TS, i.e. obtained by two different IRCs. * Hydrogen shifting. The bond to be broken (in the forward direction) is depicted in red and the forming bond in green.

Figure 9 (

 9 Figure 9 (red curve for the T10O12 site) depicts the energy barriers associated to the PCP

Figure 9 .

 9 Figure 9. Energy profile for the cycle contraction-expansions through PCPs, at three sites of the EUO framework located at the 10 MR channel, the 12 MR pocket, and at their intersection. * Hydrogen shifting. The bond to be broken (in the forward direction) is depicted in red and the forming bond in green.

Figure 10 .

 10 Figure 10. Energy profile for the expansions through the TS2 PCP at all the sites of the EUO type zeolite represented in Figure 3. Pocket sites: full lines, intersection sites: dashed lines, channel sites: dot lines. * Hydrogen shifting. The bond to be broken (in the forward direction) is depicted in red and the forming bond in green.

Figure 11 .

 11 Figure 11. Adsorption Gibbs free energy profiles at the pocket (green), the channel (blue) and the intersection (red) at 277°C. * Hydrogen shifting. The bond to be broken (in the forward direction) is depicted in red and the forming bond in green.

𝑇𝑂𝐹 𝐻-𝐸𝑈- 1 𝑇𝑂𝐹 50 ≠°

 150 𝐻-𝑍𝑆𝑀-50 and the difference in apparent activation free energy between the two materials ∆ 𝑟 𝐺 𝐻-𝐸𝑈-1 ≠°-∆ 𝑟 𝐺 𝐻-𝑍𝑆𝑀-difference in apparent activation free energy of ∆ 𝑟 𝐺 𝐻-𝐸𝑈-1 ≠°-∆ 𝑟 𝐺 𝐻-𝑍𝑆𝑀-50 ≠°= -12 kJ/mol.

Figure 12 .

 12 Figure 12. Ethylcyclohexane conversion versus temperature for the H-EU-1 and for the H-ZSM-50 bifunctional catalysts.

Table 1 :

 1 Bifunctional catalysts used in this study.

	Metallic	Acidic	Catalyst composition Catalyst name n Pt*	n A**	n Pt /n A
	function	function			(µmol/g)	(µmol/g)
	1.05%wt	H-EU-1	80%wt Pt-Al 2 O 3 /	1%Pt-Al 2 O 3	43	147	0.29
	Pt-Al 2 O 3		20%wt H-EU-1	/H-EU1
	1.05%wt	H-ZSM-	80%wt Pt-Al 2 O 3 /	1%Pt-Al 2 O 3	43	106	0.42
	Pt-Al 2 O 3	50	20%wt H-ZSM-50	/H-ZSM50

* micromoles of platinum surface sites per gram of catalyst, ** micromoles of Brønsted acid sites per gram of catalyst

Table 4 .

 4 Dispersion contribution (kJ/mol) to the adsorption energy of all the species considered in the pathway, for selected sites at the intersection, channel and pocket zone in EUO.

			Site
	Species	T10O12	T1O1	T9O6
		Intersection	Channel	Pocket
	ECH +	-66	-113	-136
	TS1	-61	-118	-141
	21-EMCP +	-75	-127	-117
	TS2	-77	-124	-111
	12-DMCH +	-84	-121	-112
	TS3	-73	-127	-149
	125-TMCP +	-76	-121	-150

Table 5 .

 5 Physicochemical properties of the H-EU-1 and H-ZSM-50 zeolites

	Sample	S BET (m 2 g -1 )

ACKNOWLEDGMENT

The authors acknowledge Tomáš Bučko for providing line minimizations and intrinsic reaction coordinate algorithms, and Pascal Raybaud (IFP Energies nouvelles) for fruitful discussions. This work was performed using HPC resources from GENCI-IDRIS (Grant 2016-x20160816) and the IFPEN ENER110 supercomputer. Christophe James and Véronique Delattre (IFP Energies nouvelles) are acknowledged for their assistance in performing the catalytic testing experiments.

AUTHOR INFORMATION

Corresponding Author

*Email: celine.chizallet@ifpen.fr

Notes

The authors declare no competing financial interest.

Supporting Information.

Additional figures and tables, regarding DFT procedures, equations and results are given in the Supporting Information file as well as some characterization data from experiments. Additional information as noted in the text. This information is available free of charge via the Internet at http://pubs.acs.org.

GRAPHICAL TOC

EUO framework


Aymen Belghith
email: aymen.belghith@telecom-bretagne.eu

Loutfi Nuaymi
email: loutfi.nuaymi@telecom-bretagne.eu

Design and Implementation of a QoS-included WiMAX Module for NS-2 Simulator

Keywords: I.6.5 [Simulation and Modeling]: Model Developmentmodeling methodologies Implementation, QoS classes, scheduling, simulation, WiMAX

Design and implementation of a QoS-included WiMAX module for NS-2 simulator

Aymen Belghith, Loutfi Nuaymi

INTRODUCTION

Worldwide Interoperability for Microwave Access (WiMAX) is based on 802.16-2004 standard [START_REF] Society | Part 16: Air interface for fixed broadband wireless access systems[END_REF] and its amendment 802.16e [START_REF] Society | Part 16: Air interface for fixed and mobile broadband wireless access systems[END_REF]. It is a Broadband Wireless Access (BWA) technology that promises a large coverage and high throughput. Theoretically, the coverage range can reach 30 miles and the throughput can achieve 75 Mbit/s [START_REF]Deploying license-exempt wimax solutions[END_REF]. Yet, in practice the maximum coverage range observed is about 20 km and the data throughput can reach 9 Mbit/s using User Datagram Protocol (UDP) and 5 Mbit/s using File Transfer Protocol (FTP) over Transmission Control Protocol (TCP) [START_REF]Considerations for deploying mobile wimax at various frequencies[END_REF]. The theoretical values do not always fit the reality. The network simulation presents a solution to test the performance of technologies. Network Simulator 2 (NS-2) [START_REF]The network simulator ns-2[END_REF] is a widelyused tool to simulate wireless networks. Until today, this simulator does not implement a definitive WiMAX module. Nevertheless, there are some WiMAX NS-2 modules implemented by National Institute of Standards and Technology (NIST) [START_REF]Seamless and secure mobility[END_REF] and Network and Distributed Systems Laboratory (NDSL) [START_REF]The design and implementation of wimax module for ns-2 simulator[END_REF] and [START_REF] Chen | The design and implementation of wimax module for ns-2 simulator[END_REF]. These modules implement the physical (PHY) and Medium Access Control (MAC) layers of a WiMAX system. The NIST module implements the Orthogonal Frequency Division Multiplexing (OFDM) PHY while the NDSL module implements the Orthogonal Frequency Division Multiple Access (OFDMA) PHY. Both PHY modules use the same duplexing technique: Time Division Duplexing (TDD). The MAC layer of these WiMAX modules contains the management messages. The NIST WiMAX module also supports mobility, fragmentation, and reassembly of frames. The NDSL WiMAX module supports Call Admission Control (CAC).

As we consider the Wireless-OFDM PHY layer, our NS-2 developments are based on the NIST implementation. Our contribution consists of the addition of QoS classes and their requirements, mechanisms specified by the IEEE 802.16 standard, and some scheduling algorithms. These implemented schedulers take into account the QoS classes. We use the Unified Modeling Language (UML) to design our WiMAX module. UML class and sequence diagrams are introduced in the following sections to model our system in a visual manner. Then, we assess our implementation and compare our implemented scheduling algorithms with the Round Robin (RR) scheduler of the existing module. The comparison is based on two parameters: the throughput and mean sojourn time. The throughput is the amount of data that can be sent in the network per one second. The mean sojourn time is the average time a data packet spends from its generation to its delivery at the destination. Simulation results are given for three scenarios in order to compare scheduling algorithms for three different QoS classes.

This paper is organized as follows. In Section II, we present an overview of the WiMAX technology. In Section III, we describe our NS-2 module as well as a brief presentation of the existing WiMAX module. In Section IV, we present the simulation model and some simulation results. We conclude in Section V.

OVERVIEW OF WIMAX

The IEEE 802.16 standard defines four QoS classes: Unsolicited Grant Service (UGS), real-time Polling Service (rtPS), non-real-time Polling Service (nrtPS), and Best Effort (BE). The IEEE 802.16e amendment added a fifth QoS class, called extended real-time Polling Service (ertPS). The five defined QoS classes are descried as follows.

UGS supports real-time service flows that have fixed-size data packets on a periodic basis. The BS provides grants in unsolicited manner. The UGS subscribers are prohibited from using contention request opportunities.

rtPS supports real-time service flows that have variable size data packets on a periodic basis. The BS periodically provides unicast request opportunities in order to allow the SS to specify the desired bandwidth allocation. The SS is prohibited from using contention request opportunities.

ertPS supports real-time service flows. It is built on the efficiency of both UGS and rtPS. The BS provides unicast grants in an unsolicited manner like UGS. Whereas the UGS allocations are fixed in size, the ertPS allocations are dynamic. Then, the SS can request to change the size of grants by sending bandwidth change request.

nrtPS is designed to support non real-time service flows that have variable size data packets on a periodic basis. The SS can use contention request opportunities to send a bandwidth request with contention. The SS can also provide unicast request opportunities.

BE is used for best effort traffic where no throughput or delay guarantees are provided. The SS can use unicast request opportunities as well as contention request opportunities.

When the BS or the SS creates a connection, it associates the connection with a service. A service flow provides unidirectional transport of packets either to uplink packets that are transmitted by the Subscriber Station (SS) or to downlink packets that are transmitted by the Base Station (BS). It is characterized by a set of parameters as a Service Flow identifier (SFID), service class name (UGS, rtPS, ertPS, nrtPS, or BE), and QoS parameters (such as Maximum sustained traffic rate, minimum reserved traffic rate, and maximum latency).

There are three kinds of dynamic service management messages. Dynamic Service Addition (DSA) for the addition of a new service flow, Dynamic Service Change (DSC) for the modification of service flow parameters, and Dynamic Service Delete (DSD) for the deletion of an existing flow service.

There are three DSA management messages: Dynamic Service Addition Request (DSA-REQ), Dynamic Service Addition Response (DSA-RSP), and Dynamic Service Addition Acknowledgment (DSA-ACK). These messages are used in order to create a new service flow between an SS and a BS, respectively. The addition of a new service flow can be initialized by the SS or the BS (see Figure 1). Once a service flow is created, some or all of its parameters can be changed by the SS or the BS across DSC management messages: Dynamic Service Change Request (DSC-REQ), Dynamic Service Change Response (DSC-RSP) and Dynamic Service Change Acknowledgment (DSC-ACK). A service flow can also be deleted across the exchange of two DSD management messages: Dynamic Service Delete Request (DSD-REQ), Dynamic Service Delete Response (DSD-RSP). The acknowledgment of DSD-RSP is not required. As mentioned, the IEEE 802.16 MAC layer defines the different QoS classes and its requirements, QoS parameters, and management messages. However, it keeps scheduling algorithm(s) to be used as an open issue. Some well-known schedulers were proposed for WiMAX such as the RR scheduler in [START_REF] Ball | Perfermance evaluation of ieee802.16 wimax with fixed and mobile subscribers in tight reuse[END_REF], the Earliest Deadline First (EDF), Weighted Round Robin (WRR), and RR schedulers in [START_REF] Chen | An integrated qos control architecture for ieee 802.16 broadband wireless access systems[END_REF], and the RR and maximum Signal-to-Interference Ratio (mSIR) scheduler in [START_REF] Ball | Performance analysis of temporary removal scheduling applied to mobile wimax scenarios in tight frequency reuse[END_REF]. There are also some schedulers specifically proposed for WiMAX such as Temporary Removal Scheduler (TRS) [START_REF] Ball | Performance analysis of temporary removal scheduling applied to mobile wimax scenarios in tight frequency reuse[END_REF], Opportunistic Deficit Round Robin (O-DRR) [START_REF] Rath | An opportunistic drr (o-drr) uplink scheduling scheme for ieee 802.16-based broadband wireless networks[END_REF], adaptive bandwidth request mechanism [START_REF] Mukul | An adaptive bandwidth request mechanism for qos enhancement in wimax real time communication[END_REF], and packet scheduling using the token bucket [START_REF] Tsai | Cac and packet scheduling using token bucket for ieee 802.16 networks[END_REF].

The IEEE 802.16 PHY layer defines two modes of transmission: the point-to-multipoint (PMP) and Mesh modes. In the PMP mode, the traffic occurs only between BS and SSs. In the Mesh mode, traffic can also occur between SSs. In this work, we consider the PMP mode. The PHY layer supports two duplexing techniques TDD and Frequency Division Duplexing (FDD). In the TDD mode, the uplink and downlink data are transmitted with the same frequency. In the FDD mode, the uplink and downlink data are transmitted in two different frequencies. We consider only the TDD mode.

The IEEE 802.16 standard also defines the Modulation Coding Schemes (MCS) that can be used. This allows the BS and SS a large choice of the suitable MCS used. The MCS used depends on the channel quality. When the BS performs the link adaptation, it compares the Signal-to-Noise Ratio (SNR) value of the subscriber with thresholds in order to select the Modulation and Coding Scheme (MCS) used. There are two kinds of thresholds:

• The minimum entry threshold: represents the minimum SNR required to start using an MCS that is more efficient.

• The mandatory exit threshold: represents the SNR below which the current MCS can no longer be used and it has to start using an MCS that is more robust.

WIMAX NS-2 MODULE

We have implemented a new NS-2 WiMAX module. The version of NS-2 is 2.29 and the programming language is C++. Our module is based on the WiMAX NIST module [START_REF]Seamless and secure mobility[END_REF]. The existing module implements the OFDM PHY and TDD MAC layers. The PHY layer has some configurable parameters such as transmission power, cyclic prefix, The MAC layer contains some MAC management messages such as Downlink Channel Descriptor (DCD), Uplink Channel Descriptor (UCD), Downlink MAP (DL-MAP), Uplink MAP (UL-MAP), ranging request, ranging response, registration request, and registration response. One downlink and one uplink data connection can be added per subscriber. The BS performs the RR scheduler to allocate radio resources for the uplink connections. The existing implementation supports the mobility. The scanning and handover operations are implemented.

Our contribution consists of the addition of some QoS parameters to the service flow, the link adaptation, and some scheduling algorithms for three QoS classes: UGS, rtPS, and BE. We also implement the unicast and contention request opportunities mechanisms as specified in the IEEE 802.16 standard. The IEEE 802.16 MAC class diagram is shown in Figure 2. We are interested in the 802.16 MAC class since our contribution is applied to the MAC layer.

The Mac802.16 class represents the MAC layer. It represents the main class and has relations with other classes: ServiceFlowHandler, peerNode, and WimaxScheduler. Ser-viceFlowHandler is responsible for the management of the downlink and uplink connections. Each connection has an association with a service flow that contains the QoS parameters. The QoS parameters of a service flow are set basing on the connection requirements. peerNode contains information about the SS or the BS. WimaxScheduler is responsible for the ranging and registration and performs scheduling algorithms. It includes two schedulers: one for the BS (BSScheduler ) and one for the SS (SSscheduler ).

Link Adaptation

In the existing implementation, all the subscribers use the same MCS. The MCS used is set from NS-2 Tool Command Language (TCL) script and does not change during the simulation. We provide the possibility of using different MCS in the same scenario. Moreover, an MCS can be changed

Dynamic Service Management

The existing implementation contains a class, called Ser-viceFlow, which identifies the service requirements of the associated connection. This class contains only the Service Flow Identifier (SFID) and Service Flow Scheduling Type (UGS, rtPS, ertPS, nrtPS, or BE) parameters. There is no differentiation between the QoS classes. We add the following parameters:

• CID: represents the identifier of the connection.

• Traffic Priority: defines the priority assigned to the service flow.

• Maximum sustained Traffic Rate: defines the peak information rate of the service flow.

• Minimum Reserved Traffic Rate: defines the minimum reserved rate of the service flow.

• Tolerated Jitter: defines the maximum delay variation of the connection.

• Maximum Latency: specifies the maximum latency between the reception of a packet and the forwarding of this packet.

Once the service flow parameters are initialized, the addition of a new service flow can be performed. This needs an exchange of DSA packets. These packets are defined in the IEEE 802.16 standard and already implemented in the existing NS2 module. These packets do not contain the service flow parameters as scheduling algorithm does not take into account the QoS class requirements. We modify the DSA packets and add some instructions:

• When a DSA-REQ packet is sent, the flow service parameter is added to this packet as defined in the IEEE 802.16 standard.

• When a DSA-REQ packet is received, the service flow and QoS parameters of the created data connection are filled up from the service flow parameter of the received DSA-REQ packet. Then, a value of the CID parameter of the service flow is generated and assigned.

• When a DSA-RSP packet is sent, the service flow parameter is added to this packet.

• When a DSA-RSP packet is received, the service flow and QoS parameters of the created data connection are filled up from the service flow parameter of the received DSA-RSP packet.

The different steps of the creation of a new service flow, in our new module, are depicted in Figure 3. All those modifications are performed in a class, called ServiceFlowHandler. This class handles the list of the downlink and uplink connections and manages the creation of new connections.

Request Opportunities

Unicast request opportunities

We implement the unicast request opportunities mechanism in the existing implementation (see Figure 4). The provision of unicast request opportunities is done as follows. First, the BS determines the unicast polling list. A subscriber belongs to the unicast polling list when the current frame corresponds to its period of unicast request polling. Then, the BS allocates uplink bursts with an Uplink Interval Usage Code (UIUC) equal to the REQ Region Focused value. When an SS receives a burst for unicast request polling, it sends a bandwidth request. The bandwidth request contains the length of its uplink data connection queue. We assume that the subscribers are disciplined and they use the bursts of unicast request polling to only send bandwidth requests.

Contention request opportunities

The existing implementation provides contention request opportunities (see Figure 5). The BS allocates symbols for contention request opportunities at the beginning of each uplink subframe. Every frame, all SSs, having uplink data, send bandwidth requests with contention. We modify the existing implementation in order to prohibit UGS and rtPS SSs from using the contention request opportunities. Moreover, an SS sends a bandwidth request periodically and not every frame. The contention period is set by the TCL script. An SS can send a bandwidth request every frame when the contention period is equal to 1.

Scheduling

The existing implementation does not differentiate between the different QoS classes. The scheduling algorithm of the existing implementation is described as follows. First, the BS sends its downlink packets in the downlink subframe. Then, it reserves all the remaining symbols for a single station using the Round Robin (RR) scheduler. Hence, at each frame, at most one subscriber can send its packets independently of the service classes. The implemented scheduling algorithm has to be changed in order to differentiate between the service classes and take into account the QoS parameters. In this paper, we consider three QoS classes: UGS, rtPS, and BE. We briefly describe some of scheduling mechanisms. The RR scheduler equitably distributes channel resources to all the SSs. The mSIR scheduler allocates radio resources to SSs that have the highest SNR. The WRR scheduler is an extension of the RR scheduler and it is based on static weights. The TRS scheduler [START_REF] Ball | Performance analysis of temporary removal scheduling applied to mobile wimax scenarios in tight frequency reuse[END_REF] temporarily blocks SSs having SNR smaller than a defined threshold. We combine the TRS scheduler with the RR and mSIR schedulers (called TRS+RR and TRS+mSIR, respectively). The TRS+RR scheduler reserves 1/k of the whole radio resources if there are k SSs to schedule. While the TRS+mSIR reserves all radio resources for SSs that have the highest SNR.

Unsolicited Grant Service QoS class scheduling

The proposed UGS scheduling is described as follows (see Figure 6). The BS determines all the SSs that have UGS connections. The connection, that the BS will start serving first, is randomly picked. Since an SS is served periodically, an assignment of a period to each station is recommended. The period, called UGS scheduling period can be set using the TCL script. Otherwise, it is equal to a predefined default value. From the period of scheduling, the BS determines if an SS is served in the current frame. For each UGS connection that will be served, the BS determines the transmission time using the Maximum Sustained Traffic Rate parameter of the connection. Then, the BS determines the number of symbols to be reserved for this UGS connection from the determined transmission time and MCS used. The available symbols must be sufficient to serve all UGS connections. Once the number of reserved symbols is determined, the BS updates the uplink map (UL-MAP) and allocates an uplink burst. The UGS scheduling algorithm is performed at the beginning of each frame.

Real-time Polling QoS class scheduling

The proposed rtPS scheduling is described as follows (see Figure 7). The BS determines all SSs that have rtPS connections. The choice of the next connection to serve depends on the rtPS scheduling algorithm. The implemented scheduling algorithms for the rtPS connections are the Round Robin (RR), maximum Signal to Interference Ratio (mSIR), Weighted Round Robin (WRR), and Temporary Removal Scheduler (TRS) schedulers. If the SS has not a bandwidth request to satisfy, the BS determines the next SS to serve. Otherwise, the BS determines the transmission time and then the number of symbols to be reserved for this rtPS connection. If there are not sufficient symbols, the BS allocates all the remaining symbols. If the BS can satisfy the entire bandwidth request, it removes this request. Else, the BS updates the bandwidth to be allocated in the following frames. Once this SS is served, the BS determines the next SS to be served if there are yet remaining symbols (see Figure 7).

Best Effort QoS class scheduling

The proposed BE scheduling is described as follows (see Figure 8). First, the BS determines all the SSs that have BE connections. The connection, to start with, is determined using the RR scheduler. If the SS has not a bandwidth request, the BS checks the next SS. Otherwise; the BS determines the transmission time and the number of symbols to reserve. If there are not enough available symbols, the BS allocates all the remaining symbols. If the BS can satisfy the entire bandwidth request, it removes this request. Otherwise, the BS updates the bandwidth to be allocated in the following frames. Once this SS is served, the BS determines the next SS to be served if there are yet remaining symbols.

SIMULATION RESULTS

Simulation Model

We have integrated into the existing implementation of WiMAX QoS parameters, QoS classes, unicast and contention request opportunities, five rtPS schedulers, and simple UGS and BE schedulers. The main parameters of the simulation model are represented in Table 2. We consider five UGS, nine rtPS, and two BE subscribers. The subscribers can use the QPSK 1/2, QPSK 3/4, 16-QAM 1/2, 16-QAM 3/4, 64-QAM 2/3, and 64-QAM 3/4 MCSs.

Performance of rtPS scheduling

In this section, we study the behavior of the rtPS schedulers. We consider the scheduler of the existing module (Existing RR) as well as our implemented schedulers: RR, mSIR, WRR, TRS+RR, and TRS+mSIR. We have five UGS subscribers. Each UGS SS generates Constant Bit Rate (CBR) traffic with a rate of 160 Kbit/s s. We have also two BE SSs that generate FTP traffic.

Figure 9 shows the throughput of the rtPS connections as a function of the rtPS traffic load submitted in the net- work. This figure shows the low efficiency of the Existing RR scheduler. Such a scheduler, in the quest of the simplifying of the scheduling steps, throttles the network traffic. Indeed, this scheduler allocates all the symbols to one SS even if it has not data to send. We note that the the rtPS throughput of the Existing RR scheduler is nearly nine times worse than that of our implemented rtPS schedulers. We observe that the mSIR and TRS+mSIR schedulers nicely outperform the other schedulers with a maximum throughput of 9 Mbit/s. These two schedulers favor SSs having the highest SNR values and then the most efficient MCSs.

We also observe that the RR scheduler provides rtPS throughput less than that of the TRS+RR and WRR schedulers. This is due to the fact that the channel quality of the different SSs in not taken into consideration.

Figure 10 shows the mean sojourn time of the rtPS connections as a function of the rtPS traffic load submitted in the network. The mean sojourn time is a vital parameter for the real-time applications. We note that the Existing RR scheduler requires a large average delay to deliver a data packet. This is because this scheduler does not provide sufficient symbols to the SSs. It periodically allocates all the remaining symbols of an uplink subframe to one rtPS SS. This period is equal to the frame duration multiplied by the number of all the SSs. We also note that the mSIR and TRS+mSIR schedulers have a mean sojourn worse than that of the Existing RR scheduler at high traffic load. This is due to the freezing of the traffic of the SSs having small SNR values. On the other hand, the Existing RR scheduler does not block any SS.

We observe that the RR, WRR, and TRS+RR schedulers exhibit a much better sojourn time. These schedulers take into account the bandwidth requests of the rtPS SSs. Moreover, they do not block any SS.

UGS scheduling

In this section, we study the behavior of our UGS scheduler. We have nine rtPS subscribers that generate a mean traffic rate equal to 80 Kbit/s s. We have also two BE SSs that generates FTP traffic.

Figure 11 represents the throughput of the UGS connections as a function of the UGS traffic load submitted in the network. For a very low traffic load, our UGS scheduler and Existing RR provide the same UGS throughput since all the SSs are entirely served. We observe that the Existing RR scheduler throttles the network traffic and the throughput can not exceed 500 Kbit/s. Indeed, the Existing RR scheduler does not differentiate between the QoS classes. Since there are sixteen SSs and five of them uses UGS connections, the Existing RR scheduler always allocates five uplink subframes for each period of sixteen frames. Our UGS scheduler works as defined in the standard. All the UGS subscribers must be entirely served. The curve of our UGS scheduler is linear and the coefficient is equal to 1.

The curves of our UGS scheduler and Existing RR are represented only for an offered UGS traffic load less than 3.5 Mbit/s. This is because we add an admission control. The admission control is such that all the UGS connections can be entirely satisfied.

Figure 12 shows the mean sojourn time of the UGS connections as a function of the UGS traffic load submitted in the network. Our UGS scheduler provides a very low mean sojourn time because it periodically allocates sufficient symbols to all the UGS SSs. Moreover, a new UGS connection is added only when it can be satisfied.

BE scheduling

In this section, we study the behavior of our BE scheduler. Since we have rtPS and UGS schedulers, we can vary the UGS or rtPS traffic load. We choose to study the relationship between the BE and UGS schedulers. In this scenario, we have nine rtPS subscribers that generate a mean traffic rate equal to 80 Kbit/s s. We have also two BE SSs that generates FTP traffic.

Figure 13 represents the throughput of the BE connections as a function of the UGS traffic load submitted in the network. This figure shows that the Existing RR scheduler provides the same BE throughput independently of the offered traffic load. This is because the Existing RR scheduler is applied of all the QoS classes. In our case, it periodically allocates two uplink subframes and the period is equal to the duration of sixteen frames.

The higher the offered traffic load, the lower is the BE throughput. This is because our scheduling implementation serves the UGS, then rtPS, and finally BE connections. So, the higher the remaining symbols, the higher is the BE throughput. This behavior fits with the standard specification as the BE connections has no QoS requirements.

CONCLUSIONS

In this paper, we investigate the behavior of WiMAX scheduling algorithms. We consider some UGS, rtPS, and BE schedulers. We are based on the network simulation. So, we have implemented a new WiMAX module that takes into account the QoS classes and its requirements. Our module supports unicast and contention request opportunities and involves some UGS, rtPS, and BE schedulers. Extensive simulations are conducted to show that the behavior of our UGS, rtPS, and BE schedulers fits with the QoS specifications of the IEEE 802.16 standard. We show through simu-

Figure 1 :

 1 Figure 1: Addition of a new service flow.

Figure 2 :

 2 Figure 2: MAC 802.16 class diagram [14].

Figure 3 :

 3 Figure 3: Steps of the creation of a new service flow.

Figure 4 :

 4 Figure 4: Unicast request opportunities.

Figure 5 :

 5 Figure 5: Contention request opportunities.

Figure 6 :

 6 Figure 6: UGS scheduling.

Figure 7 :

 7 Figure 7: rtPS scheduling.

Figure 8 :

 8 Figure 8: BE scheduling.

Figure 9 :

 9 Figure 9: rtPS throughput versus offered rtPS traffic load.

Figure 10 :

 10 Figure 10: Mean sojourn time of rtPS SSs versus offered rtPS traffic load.

Figure 11 :

 11 Figure 11: UGS throughput versus offered UGS traffic load.

Figure 12 :

 12 Figure 12: Mean sojourn time of UGS SSs versus offered UGS traffic load.

Figure 13 :

 13 Figure 13: BE throughput versus offered UGS traffic load.

Table 1 :

 1 Receiver SNR assumptions (values of the IEEE 802.16e standard) on the SNR values. We then modify the PeerNode class which contains the different characteristics of a station (SS or BS). We also modify the BSscheduler class which manages the changes of the SNR values and we determine the suitable MCS used basing on the SNR parameter of the PeerNode class and the SNR thresholds. These thresholds are taken from the SNR assumptions values that are proposed inTable 266 of the IEEE 802.16e amendment of the standard (reproduced in Table 1).

	Modulation Channel coding rate Receiver SNR (dB)
	BPSK	1/2	3.0
	QPSK	1/2	6.0
		3/4	8.5
	16-QAM	1/2	11.5
		3/4	15.0
	64-QAM	2/3	19.0
		3/4	21.0
	and this depends

Table 2 :

 2 Main parameters of the simulation model

	Parameter	Value
	Frequency band	5 MHz
	Propagation model	Two Ray Ground
	Antenna model	Omni antenna
	Antenna height	1.5 m
	Transmit antenna gain	1
	Receive antenna gain	1
	System loss factor	1
	Transmit power	0.25
	Receive power threshold	205e-12
	Carrier sense power threshold	184.5e-12
	Link adaptation	enabled
	Frame duration	20 ms
	Cyclic prefix (CP)	0.25
	Packet length	1024 bytes
	Simulation duration	100 s