In 2015, crude oil represents 32% of the global energy resources, which in fact is the first source of energy for the whole planet. 1,2 In 2016, the world production of oil (crude oil, shale oil, oil sands and natural gas liquids) was about 92150 thousand barrels (4382 million tonnes) daily and the consumption about 96558 thousand barrels (4418 million tonnes) daily. 3 The petroleum refining processes are used in petroleum refineries (or oil refineries) to transform crude oil into useful products such as liquefied petroleum gas (LPG), gasoline, jet fuel (kerosene is a jet fuel), diesel oil and fuel oils. Catalytic reforming is one of the main processes in the refining industry aiming at the transformation of petroleum fractions with a low research Octane Number into a high octane reformate, a major blending fuel for gasoline motors and an important source of aromatic hydrocarbons, while valuable co-product is hydrogen. [4][5][6] The aromatic hydrocarbons produced are of interest for petrochemicals. Mainly, targeted reactions in catalytic reforming are dehydrogenation, dehydrocyclization and alkane isomerizations. [7][8][9] During the 1950s and 1960s, platinum on chlorinated or non-chlorinated alumina catalysts were employed almost exclusively in commercial reforming units. 8,10 The outstanding performance of these catalysts led to the wide applications of catalytic reforming in petroleum refineries. This kind of catalyst operates in a bi-functional way. The superior activation properties of platinum for C-H bond and low activity for C-C bond cleavage also makes the platinum based catalyst on g-alumina a popular choice for the non-oxidative dehydrogenation of light olefins. 11 Alumina proves to be the most suitable acid support required for cyclisation and isomerization reactions, where chlorine changes the acidity of the support. 5,[12][13][14] Early study of Parera et al. 12 suggested that a 0.8-0.9% chlorinated alumina shows a good selectivity and activity for n-

Heptane reforming. Platinum catalyzes the dehydrogenation-hydrogenation reactions. The dehydrogenation of hydrocarbons by platinum is generally considered to be structure sensitive, which means that the control of the size and shape of platinum particles is of high importance in reforming. 8,15,16 In industrial catalysts, the size of the platinum nanoparticles is thus close or even smaller than 1 nanometer 7,[17][18][19] with a very high dispersion close to 100%. From the late 1960s to the present the platinum on alumina catalysts have largely been replaced in commercial practice by catalysts containing platinum and a second metallic element, such as tin or rhenium, to improve the selectivity to aromatics and reduce deactivation of catalysts by coke formation.

Due to the high level of complexity inherent to the reaction networks involved in naphta reforming, model reactions have to be chosen for a better understanding of the catalytic properties. [20][21][22][23][24][25] A very popular one is the reforming of n-heptane, which already give rise to many reactions and products, as isomerization, dehydrogenation, dehydrocyclization but also alkane cracking, hydrogenolysis and coking may concomitantly occur. 4,7,20 We will focus on the mechanism of a more simple but essential reaction: dehydrogenation of methyl-cyclohexane to toluene. Thus, this reaction aims at probing predominantly the catalytic properties of the metallic active phase with respect to its dehydrogenation function in absence of any secondary reactions such as hydrogenolysis or cracking. It has also been the subject of numerous experimental kinetic investigations on mono-or bi-metallic platinum based catalysts, 16,[25][26][27][28][29][30][31][32][33][34][35] sometimes together with kinetic modeling. 27,[29][30][31] However, dome debates remains about the relevant mechanism, rate determining step and corresponding kinetic parameters.

Detailed knowledge on the mechanisms taking place during methylcyclohexane dehydrogenation on supported platinum particles is required to obtain a high degree of control for reactivity and selectivity, which by the way is known to depend a lot on operating conditions (temperature, pressure of H 2 and hydrocarbons 23 ). We propose here to investigate the reactivity of those nanoparticles, in a first step mono-metallic platinum nano-aggregates, by quantum simulations based on the density functional theory (DFT). In the literature, regarding DFT modeling aspect, model Pt (111) surfaces at low hydrogen coverage have been extensively used for the modeling of the hydrogenation/dehydrogenation reaction [36][37][38][39][40][41][42][43][44][45][46][47] involving small alkene molecules (ethylene or propene) 15,36,44,[48][49][50][51] and aromatics (such as benzene). [40][41][42][52][53][54] Aiming at a more innovative and realistic approach, we propose here to simulate the catalytic system using models developed in the past at IFP Energies nouvelles for subnanometric particles supported on γ-alumina. [55][56][57][58][59] The influence of the partial pressure of hydrogen will be taken into account.

Comparison with the Pt (111) surface will be performed. A promising approach for the validation of the mechanisms and rate constants obtained ab initio is multi-scale modeling, performed by integration of the data calculated ab initio in higher-scale models. 60 Comparison with careful experiments is fruitful to get unedited information about the reaction mechanisms at the atomic scale. This combined experimental and multi-scale modeling methodology was applied recently to several kinds of catalytic systems, 53,61,62 and will be the object of some trials in the present work.

Chapter I proposes a literature analysis of the current state of knowledge for the catalytic systems under investigation and reactions of interest, and also an overview on the relevant modeling achievement of the catalyst properties. A methodology part follows in Chapter II, setting the theoretical background employed, as well as the experimental details for the catalytic tests performed. In Chapter III, we report the results obtained in the DFT simulations of methylcyclohexane dehydrogenation, on a Pt 13 /γ-Al 2 O 3 (100) model developed previously. 14,[55][56][57]63 In Chapter IV, we report a combined experimental and simulation kinetic study of 4 methylcyclohexane dehydrogenation. We establish kinetic models of Langmuir-Hinshelwood (LH) type, fully parameterized by ab initio kinetic constants of the mechanistic model, in comparison with kinetic experimental data obtained currently at IFPEN on a relevant nonchlorinated platinum based catalyst. These models were examined for the validation in aspect of several kinetic descriptors: the evolution of reaction rates as a function of operational conditions at the initial reaction state or during the reaction course, and also the apparent reaction activation energy. These achievements open perspectives in terms of variation of the hydrogen content on the particle, the improvements on the mechanistic model and also the discussions on the containment of employed LH models, while the micro-kinetic modeling is fully expected to be pursued in the future, as will be presented in the last section of the manuscript. Targeted reactions leading to the formation of aromatic hydrocarbons involve dehydrogenation, cyclization (dehydrocyclization), isomerization, whereas unwished reactions are hydrogenolysis and coking. [1][2][3][4][5][6] They are illustrated in the following on the example of n-heptane and toluene molecules as reacta,ts.

CHAPTER II -STATE OF THE ART AND STRATEGY OF THE THESIS

Targeted reaction:

(1) Dehydrogenation

(2) Isomerization (3) Aromatization (cyclization and dehydrogenation, so called dehydrocyclization)

Unwished reaction:

(4) Hydrogenolysis:

(5) coking:

The reforming catalyst is a bifunctional catalyst 4 with a metal function for hydrogenation and dehydrogenation reactions and an acid function for hydrocarbon rearrangements. Both the metal and acid sites are dispersed on the surface of the support. The two catalyst functions interact with olefins, which are key intermediates in the reaction network.

The first three reactions (1)-(3) lead to higher octane number products whereas the last two reactions (4) and ( 5) are undesirable since they decrease the yield of gasoline. In fact, under reforming conditions, the bi-functional acid catalyzed cyclization pathway is dominant. [7][8][9][10] In the 1930s, the early thinking materialized as the Twigg mechanism 11 which implies that cyclization leads to an adsorbed cyclohexane, which means the dehydrogenation to form the aromatic occurred after ring formation. Many of the early mechanistic studies were based on kinetic measurements, which will be presented in the following part. It should however be realized that the reaction network is in fact much more complex, with a large number of reactants that may lead to over 100 reaction products.

In this thesis work, as we mentioned in the general introduction part, we will basically focus on the dehydrogenation of methyl-cyclohexane to toluene, which is one of the key reaction in catalytic reforming.

Thermodynamics of the reactions

The petroleum naphtha fractions consist of hydrocarbons having boiling points within the approximate range of 60-180°C. Reaction temperatures of 425-525°C and pressures of 10-35 atm are employed in the process. Paraffin dehydrogenation is strongly endothermic while hydrocracking and hydrogenolysis are exothermic (Table II-1). Thus, in practice, the employed temperature is around 500°C in the reactors. The dehydrogenation and dehydrocyclization reactions produce hydrogen during the process, which makes a low hydrogen partial pressure beneficial to thermodynamics. However, at high temperatures and low hydrogen partial pressure, formation of coke on the surface of the catalyst occurs, which leads to a decrease of the catalyst activity. This is the usual explanation given for maximum curves such as the one shown in Figure II-2, 12 for n-heptane dehydrocyclization rate versus hydrogen pressure. Similar patterns were obtained by Rohrer et al. et Bond et al.. [13][14][15][16][17][18] Figure II-2 Rate of dehydrocyclization versus hydrogen pressure for various hydrocarbon pressures 12 For the investigations dealing with the effect of the hydrogen partial pressure on the activity in dehydrogenation of methyl-cyclohexane to toluene, the total pressure and the hydrogen partial pressure for this reaction remains really variable. 4,13,[19][20][21][22][23] The total pressure varies from 1.5 to 30 bar; hydrogen partial pressure varies between 1.1 and 20 bar; the P(H 2 )/P(HC) ratio ranges from 1.5 to 30. And these pressure values highly depend on the nature of the catalyst. The mono-or bimetallicity of the catalyst and also the composition of the alloy can change a lot on the choice of the reaction pressure as well. 1,2,4 The optimal operating conditions in this work by using Pt supported on non-chlorinated gamma alumina for the dehydrogenation of methyl-cyclohexane to toluene employ a temperature range of 320-380°C, a total pressure of 12 bar and a P(H 2 )/P(HC) of 15, the reason of this condition choice will be explained in next chapter.

Catalyst

The reforming catalyst as we presented is a bifunctional catalyst, which consists of γ-alumina support for its acidic function and metal component for the dehydrogenation (or hydrogenation) function. This metal is usually chosen among the noble metals as platinum. Nowadays, bimetallic catalyst are made by platinum combined with a second noble metal such as rhenium 20,24- 26 , iridium 27,28 or tin 7,[29][30][31] to provide a better stability and selectivity. 2,4

The catalyst support

Figure II-3 Transformation of boehmite into γ -alumina nanoparticles with the corresponding surface orientations 32 γ-Al 2 O 3 is obtained from boehmite by calcination in air or vacuum. [33][34][35] The γ-Al 2 O 3 particle morphology is directly inherited from the equilibrium morphology of boehmite particles (Figure II-3). The most common shape of a boehmite nanoparticle is rhombohedral: the predominant (010) surface is referred to as the basal surface, while three types of edge surfaces (100), (001), and (101) may be exposed. Once the topotactic transformation is done, the crystallographic orientation using a spinel-type indexation, the topology of γ -alumina surfaces can be classified according to the oxygen atom sublattice: the (100) surface exhibits a square oxygen atom sublattice, the (110) a rectangular one and the (111) a hexagonal one. The (110) surface corresponds to the predominant area between 70 and 83% 36,37 . The (100) surface is less abundant and accounts for 17%, according to Ref. 36 . The (111) surface can be exposed, too, but its importance depends on the synthesis conditions 37 .

In order to enhance its acidity and activate the catalyst, the γ-Al 2 O 3 is chlorinated 38 .

However, it's important to choose a balanced acidity with chlorine, in order to enhance the desirable reforming reaction like isomerization and also to hinder the non-desirable reaction such as hydrocracking 39 . Gates et al. 40 revealed that by increasing the acidity of the support with a high chlorine content will give rise to excessive undesired hydrocracking, while a low content leads to low activity for isomerization and dehydrocyclization. So, an optimal chlorine concentration must be chosen. Generally, a dose of 0.8-0.9% chlorine is proposed to present a good selectivity and activity of catalyst and incites a minimum coke formation during the reforming. 41 In addition, it is also observed experimentally that chlorine may prevent the sintering of Pt nano-clusters 39,42,43 . In the recent DFT theoretical study of Mager-Maury et al. 44 , this peculiar effect of the chlorination was explained as limiting the sintering of metallic phase by acting as a surface ligand and helping stabilizing its optimal dispersion.

The Pt/γ-Al 2 O 3 based catalysts

Platinum (Pt) supported on γ-alumina is the most used reforming catalyst. 4,5,13,14,38,[45][46][47] It is favored for Pt to be the active phase of the catalyst because of its high activity and good selectivity for dehydrogenation, compared to the other noble metals. Table II-2, extracted from ref. 2 , compares the activity of different catalyst supported on alumina, silica or silica-alumina for dehydrogenation of cyclohexane to benzene. Compared to the other mono-metallic catalyst such as palladium (Pd), iridium (Ir) and rhodium (Rh), Pt catalyst presents obviously a superior activity level. However, platinum on alumina catalysts have largely been replaced in commercial practice by catalysts containing platinum and a second metallic element. Among them all, three of such bimetallic catalyst systems that have been employed extensively in commercial reformers are platinum-rhenium, 20,[24][25][26]48 platinum-iridium 27,28 and platinum-tin. 7,[29][30][31] The application of these bi-metallic catalysts in reforming has resulted in major improvements of the selectivity of the major products like aromatic hydrocarbons, and also in the reduction of deactivation of catalysts by coke formation. 25,[28][29][30] . For instance, Pt-Sn bimetallic catalyst exhibits an increase on the catalyst selectivity and stability and a decrease on hydrogenolysis. 30,31,[49][50][51][52][53][54][55] To explain these phenomena, some studies show that an electronic effect has been provoked from Sn to Pt, which makes Pt inhibit part of its activity and become more stable during the reaction. 30,48,[52][53][54][55] While others consider a geometric effect that either the Sn atoms help to divide the Pt particles into smaller clusters, or the existence of these Pt-Sn alloy dilutes and blocks Pt atoms, thus changes its activity. [49][50][51] Meanwhile, a combination effect of the electronic and geometric effect has also been proposed. 56 The mono metallic Pt catalyst is ultra-dispersed on the porous alumina support, possibly atomically deposited due to its high cost. In industrial catalysts, the size of the platinum nanoparticles is thus close or even smaller than 1 nanometer with a very high dispersion close to 100%. High activity and high dispersion require only small amounts of platinum and the current commercial catalysts typically contain in the order of 0.2-0.4 wt% of platinum and the metal particle size can vary in the range 0.8 to 2.5 nm. 16,27,57,58 Figure II-4(a) 27 shows selected STEM (scanning transmission electron microscopy) images of reduced monometallic Pt/γ-Al 2 O 3 -Cl (0.3 wt% Pt; 0.98 wt% Cl). The monometallic catalysts show a narrow particle size distribution between 0.6 and 2.5 nm, which is about 10-20 atoms per particle. The bimetallic particles size range on the reduced catalysts between 0.7 nm and 3.5 nm. The average particle size is determined at 1.5 nm.

Kinetic studies on dehydrogenation of methyl-cyclohexane into toluene 3.1 Overview of experimental kinetic studies

Focusing on the mechanism and kinetics of dehydrogenation of methyl-cyclohexane on toluene, different studies by using experimental or kinetic fitting modeling methods have been reported. Sinfelt et al. 13 studied the reaction kinetics over a 0.3 w% platinum-on-alumina catalyst in the 315 to 372°C temperature range, at methyl-cyclohexane partial pressures ranging from 0.07 to 2.2 atmospheres and hydrogen pressures ranging from 1.1 to 4.1 atmospheres. The reaction was found to be nearly zero order with respect to methyl-cyclohexane (MCH) and hydrogen (H 2 ) over the range of conditions studied. The apparent activation energy for the reaction was found to be 138 kJ/mol. The near zero order behavior of the reaction suggests that the active catalyst sites are heavily covered with adsorbed molecules or radicals at reaction conditions. Bournonville et al. 12 used the catalyst 0.35 wt% Pt-0.20 wt% Sn on γ-Al 2 O 3 to investigate the reaction kinetics, over the temperature range 300-450°C, at methyl-cyclohexane partial pressures ranging from 0.02 to 0.2 atmospheres and hydrogen pressures ranging from 0.8 to 0.98 atmospheres. They found the same reaction orders near zero for both MCH and H 2 and an apparent activation energy of 116 kJ/mol, which is very closed to the value Touzani et al. 59 obtained. These two studies are based on a simple kinetic scheme without considering the intermediate steps. Alhumaidan et al. 22 obtained the partial reaction orders to methyl-cyclohexane and hydrogen equal -0.05 and -0.41, respectively by fitting the experimental data on a Power-law kinetic model. Van Trimpont et al. 20 applied a single site surface reaction mechanism by applying the Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism and fitting modeling. They proposed the reaction rate-determining step is the dehydrogenation of methyl-cyclohexadiene into toluene. The activation energy obtained by kinetic fitting is 180 kJ/mol. Usman et al. 23 performed the same single site LHHW mechanism and they found the dehydrogenation of the first hydrogen molecule as the rate-determining step and an activation energy of 39.3 kJ/mol.

Finally, Verstraete 60 in his thesis by using the same kind of mechanism as van Trimpont, also compared the fitting results with experimental results and found a good match, in the case of platinum, platinum-tin and platinum-rhenium catalysts.

Focus on the kinetic model of Van Trimpont et al. and Verstraete

Hougen Watson reaction rate equations

As suggested by Langmuir in 1921 and further developed by Hinshelwood in 1926, the Langmuir Hinshelwood Hougen Watson (LHHW) model [61][62][63] provides a mechanistic analysis that describes the elementary steps of surface catalytic reactions. It is one of the most commonly used approach to solve the reaction kinetics, by assuming that the reactant diffusion on the catalyst surface can be neglected. If so, the reaction rates depend on the chemisorption/desorption steps (obeying Langmuir formalism) and on the surface reaction steps. Furthermore, the derivation of rate equations assumes the existence of a rate-determining step, whereas the other elementary steps are in pseudo-equilibrium . In addition, the total concentration of surface active sites, which is the sum of the concentration of all surface species including the adsorbed reactants, products, and vacant sites, is assumed to be constant (thanks the equation of sites conservation). This LHHW model allows us to describe the surface catalytic process and the rate equations derived from the mechanistic model, more or less adequately according to the relevance of the approximations.

In the reference work of Van Trimpont 20 et al. in 1986, the reaction mechanism of the dehydrogenation of methyl-cyclohexane on toluene was investigated by a LHHW kinetic method and kinetic parameters were proposed, fitted on experimental data obtained on alumina supported sulfided platinum catalyst. One decade later in 1997, these mechanisms and kinetic parameters were revisited and extended by Verstraete 60 who determined about 20 reaction rates including the earlier model of Van Trimpont in order to apply it on alumina supported platinum-tin catalyst as a function of reaction conditions (hydrogen partial pressure in particular). One intriguing result of the thesis of Verstraete is that a maximum of the rate as a function of the hydrogen partial pressure, can be obtained from a model without including any equation related to coke formation at low hydrogen partial pressure. This trend agrees with the one observed during the experiments.

It must be underlined that such a trend exhibiting a maximum was reported by numerous experimental kinetic studies involving either dehydrogenation, dehydrocyclisation, hydrogenolysis reactions. [14][15][16][17][18] At this stage, it is surprising that by only using mathematic fitting results and kinetic model without including coke formation in his mechanistic model, this experimental phenomenon seems to be explicitly arisen. However, in both works, 20,60 the chemical origins of such a maximum, which cannot be reproduced by a power law rate equation as shown previously, have never been developed in details.

As a preliminary analysis to our work, and in order to better understand this mechanism and the possible kinetic models of methyl-cylohexane dehydrogenation, we propose to review in what follows the works by Van Trimpont 20 . Three kinds of models were proposed by the authors, leading to successive simplifications: (I) a dual-site sequence, with generation of surface hydrogen atoms on another site (although similar in nature) than the dehydrogenated species, (II) a dual-site sequence, with generation of adsorbed molecular dihydrogen in single steps, (III) a single-site sequence, with formation of gaseous H 2 in single steps. After the analysis of all the possibilities in terms of sequence and rate limiting step, the authors concluded that the most relevant scheme is the dual-site reactions sequence, with generation of adsorbed H 2 , where step (4) is the rate limiting step, which is presented here :

MCH + s D MCH•s (1) MCH•s + s D MCHe•s + H 2 •s (2) MCHe•s + s D MCHde•s + H 2 •s (3) MCHde•s + s D Tol•s + H 2 •s (4)
Tol•s D Tol + s (5)

H 2 •s D H 2 + s (6)
With MCH = methyl-cyclohexane in gas phase; s = active site; MCH•s = methylcyclohexane surface species on the active site; MCHe•s = methyl-cyclohexene surface species on the active site; MCHde•s = methyl-cyclohexadiene surface species on the active site; Tol•s = toluene surface species on the active site; Tol = toluene in gas phase; H 2 •s = dihydrogen surface species on the active site; H 2 = dihydrogen in gas phase.

The rate-determining step of the reaction on the surface is indicated as the elementary step (4). All LHHW rate equations are thus re-established here in this work, in order to achieve the final reaction rate expression mentioned in their work, by understanding each of the hypotheses they made.

The reaction rate is expressed according to the rate-determining step (ES: elementary step) :

ES (4) : [ ][ ] [ ][ ] s H s Tol k s s MCHde k r × × - × = - 2 4 4

Equation (II-1)

The equation of sites conservation is the following :

SS-1: [ ] [ ] [ ] [ ] [ ] [ ] 1 2 = + × + × + × + × + × s s H s Tol s MCHde s MCHe s MCH Equation (II-2)
The reaction equilibrium constants are established for each elementary step (ES) except for the rate determining step (4) :

ES (1) : [ ] [ ] [ ] [ ] s P K s MCH s P s MCH K MCH MCH 1 1 = × Þ × × = Equation (II-3)
ES (6) : Combining equations ES (1), ( 2), (3), ( 5), (6)

[ ] [ ] [ ] [ ] 6 2 2 6 2 2 K s P s H s H s P K H H = × Þ × × = Equation (II-4) ES (2) : [ ][ ] [ ][ ] Þ × × × = s s MCH s H s MCHe K 2 2 [ ] [ ][ ] [ ] [ ] 2 6 2 1 2 2 H MCH P s P K K K s H s s MCH K s MCHe = × × = × Equation (II-5) ES (3) : [ ][ ] [ ][ ] Þ × × × = s s MCHe s H s MCHde K 2 3 [ ] [ ][ ] [ ] [ ]
+ + + + + - = Þ - Equation (II-9)
In Equation (II-9), assuming that the desorption of hydrogen and toluene are very fast and quantitative elementary steps, both terms is also omitted in the final expression of rate equation given by Van Trimpont et al.. Somehow, this simplification is given no explanation in their work. However, in the work of Verstraete, it is found that on the same fitting model for the dehydrogenation reaction on Pt-Sn/Al 2 O 3 , during the first discrimination step for the parameter estimations, the parameters K 5 and K 6 are significantly negative. Therefore, for the second discrimination step, these parameters that could not be relevantly determined were set to zero (or neglected) and the remaining parameters were re-estimated. That could probably explain the fact that the term where K MCHde will be considered as the reaction equilibrium constant for the formation of the adsorbed methyl-cyclohexadiene intermediate.

In addition, at reaction equilibrium,

4 4 4 - = k k K
, so the term

= × =
. For the dehydrogenation reaction in gas phase at equilibrium, we define : RDS-2 :

MCH H Tol Tol MCH P P P K 3 2 = ® Tol MCH MCHde K K k K K k ® - = Þ
2 2 2 3 2 2 2 3 4 ) 1 ( ) ( ) 1 ( ) (
P P K k r + + - = + + - = ® ® ® ® Equation (II-12)
where

Tol MCH MCHde k K k ® = 4
. Equation (II-12) is precisely the rate equation reported by Van Trimpont et al. We are now aware of the assumptions behind this model.

Kinetic fitting parameters and reaction rate evolution as a function of hydrogen partial pressure

In the work of Van Trimpont, the pre-exponential factors, reaction enthalpies and activation energies involved in the Equation (II-12) have been determined to best fit the experimental data at a reaction temperature of 623 K. The fitting data are presented in terms of pre-factors and activation energies for each term in Equation (II-12), via the Arrhenius equation (Table II-3). (2) The values in blue were recalculated in this work from the corresponding parameters given by Table V and VII for the rate equation II (4) in Ref. 20.

Therefore, the initial reaction rate (P Tol = 0 bar) depending on hydrogen partial pressure at constant methyl-cyclohexane partial pressure of 0.5 bar and temperature of 623 K can be easily plotted by employing the Equation (II-12) with constants given in Table II-3, as shown in Figure II-5.

Kinetic Paramters Rate equation II-4

A MCH→Tol , kmol bar n /(kg of cat.h) Moreover, for P Tol = 0 bar as considered here, and starting from equation (ES4), the rate equation can be rewritten as:

[ ][ ] s s MCHde k r × = 4
From this expression, it is clear that high amounts of both adsorbed MCHde•s and s are required to obtain significant rate values. Comparing figures II-5 and II-6, it turns out that in the framework of this model, the rate is null at zero P(H 2 ) due to the absence of free sites s, needed for the dehydrogenation reaction, those sites being saturated by MCHde in these conditions. At reverse, at high partial pressure of hydrogen, the fact that the rate tends to zero is due to the vanishing of [MCHde•s], with a predominance of free sites. This is however not explained by a competition of MCHde with adsorbed H 2 in this model, at [H 2 ] is neglected in any case. This is rather due to thermodynamic aspects, the equilibrium for the formation of MCHde However, at this stage, the chemical relevance of the set of hypotheses made to reach this result have to be discussed. Assuming that [H 2 ] is negligible may not hold true in the high P(H 2 ) regime, in particular in the absence of any other adsorbed hydrocarbon compound in significant amount. Moreover, considering its high level of unsaturation, assuming that [Tol•s] is negligible too might be a strong assumption. Finally, the hypothesis according to which [MCHe•s] can be neglected needs to be justified.

Models of reforming catalysts and related reactivity from DFT calculations

The understanding at the atomic scale (in a range of 0.8-1 nm) of catalytic properties of mono-and bi-metallic nano-aggregates highly-dispersed on γ-alumina is needed for controlling reactivity and selectivity in catalytic reforming. Quantum molecular modeling (ab initio calculations) has become very successful to understand the properties of platinum metallic nanoaggregates supported by gamma-alumina. A growing number of studies is reported on quantum modeling of these metallic systems by applying density function theory (DFT), which have dealt with alkene dehydrogenation and hydrogenolysis mechanisms occurring either on infinite surface of platinum [START_REF] Zhao | [END_REF][65][66][67] or Pt clusters. 46,68 In Figure II-9, the shape and position of the envelope (blue-red-green) varies from large width (blue) to narrow width (green) reveals that the stability of the different intermediates decreases when increasing P(H 2 ). For a given reaction step, the selectivity of the system can be thermodynamically switched from the formation of one adsorbed intermediate to another one just by increasing/decreasing the P(H 2 ). At low J values, the olefin intermediates (e.g. ethylene) are more thermodynamically favored. From a more general point of view, the hydrogen coverage impacts significantly not only the surface morphology, but also for the choice of reaction pathways. As a consequence, DFT study quantified the interval of process conditions to be used for favoring moderate dehydrogenation of alkanes into olefins. It also gives a rational explanation of the thermodynamic optima in hydrogen pressure for maximizing either dehydrogenation or hydrogenolysis and avoiding coke formation catalyzed by platinum clusters highly dispersed on γ-alumina.

So far, no investigation was ever performed by DFT calculations, regarding the dehydrogenation of methyl-cyclohexane into toluene on supported platinum clusters. Extending the literature search to investigations performed on the Pt(111) surface, it appears that to the best of our knowledge, this reaction was not investigated either. A related reverse reaction, namely the hydrogenation of benzene into cyclohexane, was however the object of several studies, which can be a rich source of information for our own study.

DFT investigations of the hydrogenation of benzene into cyclohexane on Pt(111)

The catalytic hydrogenation of benzene to cyclohexane is an important relevant reaction to many critical steps in petroleum industry. Nevertheless, the dominant reaction path for benzene proposed.

hydrogenation
The adsorption energy of the relevant intermediates for these four studies are compared and shown in 3 the energies presented here are also calculated by using the same equation in 1 and the results in ref. 86 for the rest adsorption energy of intermediates cannot be recalculated due to the lack of data.

Open questions and strategy of the thesis

So far, the importance of investigating the selectivity and activity of this metallic nanoaggregate under the reforming condition has been emphasized. The lack of knowledge for describing the complex reactions during the catalytic reforming and elucidating the reaction mechanism from thermodynamic and kinetic points of view, encourages us (i) to focus on a model reaction, namely dehydrogenation of methylcyclohexane into toluene, (ii) to use modern quantum chemistry approaches, such as ab initio DFT methods for our investigation, in combination with experiments and multi-scale modeling approaches.

By using ab initio DFT methods, many questions have been regarding the nature of the model catalyst Pt/γ-Al 2 O 3 , which gives a robust basic starting point for our reactivity investigation. Based on these achievements, the dehydrogenation reaction path for some small molecules like ethane adsorbed on the cluster were investigated, by establishing the thermodynamic profile under the condition of the reforming and considering the effect of hydrogen pressure on this reaction. According to these works, a biplanar morphology cluster consisted of 13 platinum atoms and 6 hydrogen atoms is chosen to be the model cluster (Pt 13 H 6 /γ-Al 2 O 3 ) to undertake our study, this choice will be explained later in this work. Meanwhile, the relevant theoretical studies of benzene hydrogenation over metal slab model surface Pt (111) using ab initio DFT methods provided the reaction mechanism regarding the kinetics of the reaction pathway. All this being considered, there is a lack of knowledge about the elementary steps for methyl-cyclohexane dehydrogenation on supported platinum, which is the goal of the present work.

Besides, existing studies now for the kinetics of dehydrogenation reaction are limited to the fitting of experimental results and have not yet used ab initio methods to investigate the kinetics of these reaction mechanisms. Further, there still exists a disagreement on the determination of the rate-limiting step by using these modeling fitting approaches. We propose here to build a kinetic model from ab initio calculations to give a robust atomistic basis to the model.

However, the dehydrogenation of methyl-cyclohexane to toluene involves numerous possibilities for the reaction network and thus numerous intermediates appear. It is unrealistic to study all of them one by one. To overcome that, our strategy is to focus on some relevant intermediates starting from the C 7 H 12 over Pt 13 H 6 /γ-Al 2 O 3 system. Firstly, we will compare their stability, in order to identify the most stable configurations. All this work and hypothesis in this part aims at providing a final logic and a complete reaction pathway. Then all Gibbs free energy of absorbed intermediates and transition states and the activation energy for the elementary steps along this reaction pathway will be calculated. A similar study has been also consistently adopted on the ideal Pt (111) surface, for the sake of the comparison between these two model systems and in order to deduce the peculiar behaviors of our supported nano-cluster system.

Then, based on these thermodynamic and kinetic ab initio results, a kinetic model on the reaction path will be established. The ab initio kinetic rate constants will be incorporated into the Langmuir-Hinshelwood (LH) mechanism based kinetic models, relying on the stepwise dehydrogenation mechanistic models. Several LH kinetic models will be compared by assuming different rate-determining steps regarding the corresponding mechanistic model. Several relevant features will be thus defined at this stage: the initial reaction rates and surface species coverage as a function of reaction conditions, particularly hydrogen partial pressures and methyl-cyclohexane partial pressure; the reaction rates and surface species coverage as a function of methylcyclohexane conversion to toluene; the apparent reaction activation enthalpy.

Meanwhile, we will perform experimental catalytic tests of methyl-cyclohexane dehydrogenation on a model catalyst Pt/Al 2 O 3 without chlorine to allow us to measure the catalytic activity over a large range of space time and reaction conditions (hydrogen or methylcyclohexane partial pressures), as well as activation enthalpies and entropies that can be compared to the ab initio kinetic model. The comparison between the modeling results and experimental results will allow us to have a better understanding on the reactivity of this catalyst for the reaction under study, which is the objective of this thesis, and justify some refinements to be brought to the ab initio mechanistic investigation.

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CHAPTER III -COMPUTATIONAL AND EXPERIMENTAL METHODOLOGY

This chapter aims at introducing all the methods that we used during ab initio calculations and the catalytic experiments. We start by a brief introduction of the method we used for all the calculation in this thesis (periodic density functional theory (DFT)). Then, we present different hypothesis and parameters chosen for DFT calculations and the code employed. In addition, we explain how we can achieve the calculation of thermodynamic calculations and also a benchmarking test for the vibrational frequency calculations. In the second part, regarding catalytic experiments on dehydrogenation of methyl-cyclohexane into toluene, we focus on presenting the experimental set-up and protocol, followed by the reaction conditions employed in the catalytic tests and then the method of post-treatment of the experimental results.

Ab initio molecular modeling

We aim at solving the Schrödinger equation. The basic assumptions employed are presented Appendix-III. In the following, we focus on the method chosen here, namely Density Functional Theory.

Density functional theory (DFT)

The methods based on the density functional theory (DFT) are very convenient and efficient for quantum calculations of large chemical systems, as a very good compromise between the calculation time and the required accuracy.

This part will concentrate on how density functional theory (DFT) of ab initio method can help to solve the Schrödinger equation 1 by working with the electron density of the system as the basic variable. In the case of DFT, we do not work on possible forms of the wave function, like in the Hatree-Fock method, 2 using slater determinant 3 to build the wave function. DFT is about to use an approximation on the Hamiltonian part.

The Hohenberg-Kohn theorems

The density functional theory is mainly based on two theorems established by Hohenberg et Kohn 4 . The first theorem states that for an N-electrons system, the external potential υ(r) that defines the whole nuclear frame for a molecule completely fixes the Hamiltonian; thus N and υ(r) determine all properties for the ground state (Non-degenerate ground states). And this external potential υ(r) is determined by the electron density ρ(r) and we have ρ(r) expressed by:

ρ(r) = N ... ∫ Ψ(r,r 2 ,...,r N ) ∫ 2 dr 2 ...dr N Equation (III-1)
Since ρ determines the number of electrons, it follows that ρ(r) also determines the groundstate electronic wave function Ψ and all other electronic properties of the system. Then we have:

[ ] [ ] [ ] [ ] [ ] ( ) ( ) r r r r r r = + + = + ò ne e ee HK E V T V r v r dr F Equation (III-2)
Where T e ρ is the kinetic energy of the electrons, V ne ρ the nuclei-electron attraction and

V ee ρ the electron-electron repulsion and v(r) the external potential. The Hohenberg-Kohn functional F HK ρ is a universal functional of ρ, i.e. system independent, as it does not depend on the nuclei coordinates or the nuclear charges,

F HK ρ ! " # $ = T e ρ ! " # $ +V ee ρ ! " # $ Equation (III-3)
We may write

[ ] [ ]+ = r r J V ee exchange-correlation energy Equation (III-4)
Where J ρ is the classical repulsion. The second term (non-classical term) is a very elusive, very important quantity; it is the major part of the "exchange-correlation energy". However, there exists no exact form of F HK ρ and one has to use approximations.

The second Hohenberg-Kohn theorem provides the energy variational principle. 5 According to the variation principle the energy of an assumed trial density 𝜌 "#$%& is always a higher value than the exact ground state energy E 0 that can only be obtained if the exact ground state density is inserted in Equation (III-5).

[

] [ ] [ ] 0 r r r £ = + trial HK trial ee trial E E F V Equation (III-5)
It means that it's possible to use the variational principle to determine the energy of a molecular structure.

The Kohn-Sham equations

The idea developed by Kohn and Sham 6 consists of considering a fictitious system formed by an uniform non-interacting electron gas and having the same electron density as the real gas. The exact wave function of this fictitious system can be described by a Slater determinant and Kohn and Sham proposed to express the density ρ(r) by the following equation:

å = = Nelec i i r r 1 2 ) ( ) ( j r

Equation (III-6)

Where φ i stands for the space part of the spin-orbital χ i .

From this approach, Kohn and Sham proved that the electronic energy, E, from the ground state of a real system can be expressed by this equation:

[ ] [ ] å ò òò å ò = = + - - - + Ñ - = Nelec i Nnuclei I XC i i i i r E dr r r R Z dr dr r r r r dr r r r E 1 1 2 1 2 1 2 1 2 1 2 ) ( ) ( ) ( ) ( ) ( ) 2 )( ( ) ( r r r r j j r

Equation (III-7)

Where r 1 and r 2 represent the coordinates of two interacting electrons. In equation (III-7), the first term on right represent the kinetic energy of the electrons in the fictitious system. The second term relates to the Coulombian energy of the repulsion between a pair of electrons. The third term stands for the energy due to the nucleus-electrons attractions. E XC [ρ(r)] is called the exchangecorrelation energy and collects all the non-classic electronic interactions, which contains:

[ ] [ ] [ ] ) ( ) ( ) ( ) ( r r r r J E T T r E ee s XC - + - = Equation (III-8)
Where T(ρ) is the exact kinetic energy of the real system, T s (ρ) is the kinetic energy of the fictitious system. E ee is the total energy related to the electronic repulsions and J(ρ) represents the classical Colombian energy of the electron-electron repulsion.

If we apply the variational principle to the functions φ i (spin-orbitals space part), we will have the Kohn-Sham equation that is similar to the principal Hartree-Fock equations:

i i i Nnoyaux I XC i i r r V r R Z dr r r r j e j r = ú ú û ù ê ê ë é + - - - + Ñ - ò å = ) ( ) ( ) ( 2 1 1 1 1 2 2 1 2 2 1 Equation (III-9)
V XC is called the exchange-correlation potential functional and defined by:

[ ] ) ( ) ( r r E V XC XC dr r d = Equation (III-10)
The Kohn-Sham equations are resolved by using an approach of the self-consistent field (SCF). The test function is used in the Equation (III-10) from which a new orbitals function is obtained and then re-used again in the Kohn-Sham equations. This iterative process is done till an energy convergence is reached. The new φ i orbitals are used to build a Slater determinant. They are developed over a basis sets where the coefficients are obtained by a similar way to Hartree-Fock theory. 2 The density functional theory (DFT) method is an exact theory, but the functional allowing to obtain E XC is unknown. The DFT methods varies thus by the chosen approximations to get an acceptable estimation of E XC .

Exchange-correlation functionals

Several types of exchange-correlation functional (E XC ) have been proposed in the literature. 7,8 There are three main families of functionals.

The first one is called local-density approximation (LDA). It applies the uniform-electrongas results to infinitesimal portions of the non-uniform-electron distribution for the system of an atom or molecule or solid. The LDA is applicable to systems with slowly-varying densities but cannot be formally justified for highly inhomogeneous systems such as atoms and molecules.

Thus a second functional generation was developed and based principally on the idea to take into account not only the electronic density ρ(r), but also the gradient Δρ(r), which is called the generalized gradient approximation (GGA). Finally, the third functional generation is the hybrid functionals.

-

Local-density approximation (LDA)

Here we introduce the equation for LDA,

( ) ò = dr r E xc LDA XC ) ( ) ( r e r r

Equation (III-11)

If the electron density for the electrons with different spins, i.e. α-spin and β-spin is not identical, the LDA approach is replaced by the Local spin density approximation (LSDA). In this case, the total electron density can be written as the sum of the electron densities with α-spin (ρ α ) and β-spin (ρ β ):

( ) ò = dr r E xc LSDA XC ) , ( ) ( b a r r e r r
Equation (III-12) However, the LDA and LSDA are identical for closed-shell systems. Although the exchangecorrelation functional of the LSDA is based on a strong approximation, it is of major importance for DFT, since it is the only functional where the form of the exchange-correlation energy is exactly known. Unfortunately, due to the rapidly varying electron densities in molecules, the LSDA approach cannot be employed for many chemical problems like for thermochemical data, electron correlation is overestimated and electron exchange is underestimated. That is why LSDA overestimates bonding energies. Somehow, often with the compensations of errors, LDA, LDSA can still offer an average performance which is accurate enough for some calculations.

-Generalized gradient approximation (GGA)

A way to improve on the LDA or LSDA is to allow the exchange-correlation energy per particle to depend not only the density at the point r, but also on the density gradients. Then we have: A large diversity of GGA functionals have been developed. In this thesis, we use the exchange-correlation functional GGA-PBE, developed by Pedrew, Burke and Enzerhof in 1996 for our calculations. 9,10 However, all GGA functionals lack in describing long-range electronic correlation effects, responsible for Van der Waals forces (in particular dispersion), playing an important role for many chemical problems (e.g. orientation of molecules on surfaces). Therefore, finding DFT functionals including dispersion forces have become an active field of research over the last years.

dr r E xc GGA XC ) , , , ( ) ( )
However, in GGA functionals, the van der Waals (vdW) dispersion forces is not properly accounted for, which will cause a significant impact when doing the calculations of molecular adsorption on surface. These vdW dispersion forces, however can be integrated into the classic PBE functional according to several ways. One of them is called Opt-PBE, 11 a non-local functional that incorporate a non-local description of the correlation functional, such as vdW-DF method. 12 Another approach consists in adding a correction term to the GGA one, this is for example done in the PBE-dDsC functional. 13,14 This functional adds a vdW term E disp in the GGA functional, by using the atom pair correction parameters to calculate the vdW interactions. The dispersion term depends on dispersion coefficients (calculated from atomic ionization potentials and static dipole polarizabilities), the distance between atomic pairs and the sum of atomic van der Waals radii. In PBE-dDsC, the atom pair specific parameters (dispersion coefficients and short range damping strength) are determined from the electron density.

In this work, we applied both the functional PBE as implemented in VASP 5.3.5 and the PBE-dDsC functional as implemented in VASP 5.4.1. 15 A comparison between the results of these two methods and will be presented in Chapter IV, section 5.

Molecular modeling

This part of methodology is inspired by ref. 16,1,[17][18][19][20] .

Plane waves and periodic boundary conditions

A crystal consists in three-dimensional periodic array of atoms. The three-dimensional integration scheme allows for great freedom in choosing a suitable basis for representing the KS orbitals. We will thus perform periodic boundary calculations. It is necessary to have a basis set which is capable of reasonably spanning the orbital function space when cut to the minimum. The basis set allows to a fast-converging series when more and more functions are allowed. 16 A suitable approach for periodic calculations is the expansion of the basis set by plane waves. Since the crystal is a periodic entity and via the Bloch Theorem 21 which is the general solution for the stationary Schrödinger equation for a periodic potential V r+L =V(r) the eigenfunction can be written in the form:

( ) ( ) y = ikr i i k r e u r Equation (III-16)
where u ik (r) is a periodic function that has the period of the crystal lattice with u ik r =u ik (r+R) and R is a translational vector of the lattice. The Bloch theorem changes the problem of computing an infinite number of electronic wave functions to calculate a finite number of wave functions at an infinite number of k-points in the first Brillouin zone (to each kvector a k-point in the reciprocal lattice is attributed starting from the Г-point, which is the origin of the reciprocal lattice 22 ). The Born-von-Karman approximation says that a wave function must be periodic if a super cell is build up by a primitive cell.

( ) ( )

y y + = i i r N R r Equation (III-17)
N i being an integer and R i are primitive vectors of the lattice. Combining both theorems allows to write the wave functions as a sum of plane waves :

( ) ( ) 3 1 2 , 1 2 3
... where G is a reciprocal lattice vector, C G are the coefficients, k is a vector in the reciprocal lattice and r is a position vector. In principle there is an infinite number of plane waves but in practice only those reciprocal lattice vectors are kept in the expansion that fulfill the following condition :

y + = + + + = å i k G r iG r iG r iG r n k G G
2 2 cut k G E + < Equation (III-19)
while the remaining coefficients are set to zero. Hence, the cut-off energy, E cut determines the energy and the number of plane waves that are kept in the expansion. From this, it is obvious that the higher the cut-off energy, the more plane waves are included in the expansion and thus the better the description of the electronic system. However, a higher number of plane waves is computationally more expensive.

Pseudo-potentials and PAW method

The fact that core electrons have a low kinetic energy, i.e. a short wave length, means that they have to be treated with a higher spatial resolution. Pseudo-potentials 23 serve to replace the atomic all-electron potential in such a way, that the electronic core states are no longer treated explicitly. They are treated as frozen cores. In quantum mechanics, all wave functions describing electronic states need to be orthogonal to each other. Hence, the valence electron wave function has to be orthogonal to the core electron wave function which is difficult to describe numerically, due to the high oscillation of the wave function near the core. Thus, it is more justifiable to replace the real wave function by an ionic component describing the cores by a nodeless, smoother wave function (frozen core approximation) which describe the electrons properties in the bonding region and nearly zero probability for the valence electrons in the core region (i.e. no oscillation of the wave function, see Figure III-1). Hence, the wave function of the pseudopotentials has the same scattering properties of the all electron wave function outside the scattering region (defined by a cut-off radius r c ) and a smoother behavior inside the core region. 24 The method used for this approach is called pseudo-potentials of the projector augmented wave (PAW) 25 method. The main idea is to replace the real valence electron wave function 𝜑 ) *+ into three terms:

j j y y = - + å å AE PS PS AE V V i i i i i i c c Equation (III-20)
where φ V PS is a valence electron pseudo-wave function which reproduces the behavior of the all electron wave function (in the augmentation region) expected in the core region, ψ i AE is exact in the augmentation region (incorporating the node structure of the exact wave function)

and smoothly decays to zero in the outside and a net part ψ i PS which is also smooth. The latter two are local functions defined in the augmentation spheres where i comprises the quantum numbers n, l and m.

Geometry optimization

Once the electronic energy of the fundamental state is calculated at the desired level, geometry relaxation can be performed, aiming at minimizing forces on each atom. All residual forces applied on the cores are calculated by the Hellman-Feynman theorem. 26,27 Then, a conjugate gradient algorithm is performed until the convergence criterion is fulfilled.

The force due to the movement of the atom A in the direction of α is conventionally the derivative of energy compared to this movement 19 :

A A E F a a ¶ ¶ - = , Equation (III-21)
Where ∂α represents an infinitesimal movement. It is calculated with the Hellmann-Feynman theorem which stand for the derivative of a steady state energy with respect to a parameter P, equal to the mean value of the partial derivative of the Hamiltonian on this steady state. So we have here:

Equation (III-22)
The step to move the atoms on function of forces in order to minimize the energy has been done in the present work by two different methods. The Quasi-Newton algorithm 28 proposes a geometric convergence depending only on forces acting in the system. With the conjugate gradient algorithm, 29 the convergence is provided both by the electron energy and the forces. The first method is used in my thesis when doing the geometry optimization for the transition state, aiming to obtain a better description of minimum energy, while the second one used generally for all the discussed optimized structures of local minima such as intermediates.

In the present work, all calculations were performed using the ab initio plane-wave pseudopotential method as implemented in VASP Package (5.3.5 and 5.4.1). 30,31 The PBE 9,10 and PBE-dDsC 13,14 functionals were applied. The projected augmented wave (PAW) method 25,32 was used to describe the core-electron interactions and the electron wave functions are developed on a set of plane waves with a cut-off energy of 400 eV. The electronic convergence criterion is 10 -6 eV and the convergence criterion on forces for nuclei is 0.01 eV/Å for geometry optimizations.

The Pt 13 /γ-Al 2 O 3 (100) (Figure III-2) system considered in the present study consists of a

F A,α = - ∂E ∂α A = -ψ ( ! r i , ! R I ) ∂H ∂α A ψ ( ! r i , ! R I ) triperiodic cell,

Ab initio Molecular Dynamics

Ab initio molecular dynamics allows to simulate the atoms' evolution of a system over time. This method varies from the conjugate gradient method for the evolution of atom positions that molecular dynamic doesn't look for minimizing the system energy from a certain geometry, but to leave it evolve under the influence of residual forces. This permits the system to exceed the lowest energy barriers and thus to explore different potential wells. To do that, the residual forces are calculated by the Hellmann-Feynman theorem 26 and then the Newton movement equations are integrated by the Verlet algorithm. 33 The trajectories and speeds of each atoms are also defined. Several types of molecular dynamics are described in the literature and basically distinguished by their speed control and thus the temperature during the calculations. The choice we made for our work is a type "velocity scaled", which means that at each step of the dynamics, the temperature is calculated from the atom speeds and a same multiplicative factor is applied for each speed in order to obtain the required temperature. The parameters adjusted are the dynamic step and also the temperature.

The increase of the temperature can improve the migration of atoms and the space of explored configurations. However, the step should stay below the lowest period of interatomic vibration.

Otherwise, a bad description of the interaction will cause an uncorrected evolution of the system.

In our calculations, velocity scaled molecular dynamics (MD) was performed to explore the configurations of the cluster, in relation with its intrinsic fluctionality, dependent on the adsorbed molecules. We set a time step of 5 fs and regulated the hydrogen mass as 10 g/mol instead of 1.

Three distinct temperatures of 500K, 800K and 1200K have been employed in order to improve the migration of atoms and the number of explored configurations. Same relaxed atoms as for the geometry optimization are concerned for the molecular dynamics. In addition, the molecular dynamics with all platinum frozen has also been tested for the temperature of 1200K. For selected low energy configurations identified along MD, a subsequent "quenching" step of geometry optimization at 0K is applied after each MD in order to calculate the energy of the quenched system in a similar manner as the original system, for the sake of comparison.

Nudged Elastic Band Method

The Nudged Elastic Band (NEB) method [34][35][36] is one popular method used to find saddle points and minimum energy paths (MEP) between two stable intermediates (known reactants and products) being local minima on the potential energy surface (Figure III-3). The method works by optimizing a number of intermediate images along the reaction path. Each image finds the lowest energy possible while maintaining equal spacing to neighboring images. On the NEB, this constrained optimization is done by adding spring forces along the band between images and by projecting out the component of the force due to the potential perpendicular to the band and any point on the path is an energetic minimum in all directions perpendicular to the path. The geometric structure belonging the first order saddle-point is called transition state. The difference between the energy of the initial state and the transition state is the corresponding electronic activation energy of a given reaction. To start a NEB calculation, typically a linear interpolation between the initial and final geometries is needed, whereas for more complex reactions, e.g. rotation motions, an interpolation in internal coordinates might be a more suitable approach. 35 Thus, the images nominated by R 0 , R 1 , R 2 , ... R N , where R 0 is the reactant and R N is the final product, N-1 intermediates along the guessed reaction path have to be optimized (N =9 normally during our investigations). So, the forces function is noted as F, can be expressed as :

F (R 1 ,..., R N ) = E(R i ) + i=1 N -1 ∑ k 2 (R i -R i-1 ) 2 i=1 N ∑ Equation (III-22)
Where k is the spring constant, a force projection is introduced, referring to as "nudging".

Since the corner-cutting results from the component of the spring force perpendicular to the path and the reason for the down-sliding comes from the parallel component from the interaction between the atoms in the system, the structures along the NEB path are relaxed to the MEP by a force projection scheme. Here, potential forces are perpendicular to the band and the spring forces act parallel to the band. Hence, this leads to a NEB force on image i containing two components:

F i NEB = F i ⊥ + F i S|| Equation (III-23)
with :

F i ⊥ = -∇(R i ) + ∇(R i ) τi τi Equation (III-24)
being the force component due to the potential perpendicular to the band and :

F i S|| = k( R i+1 -R i -R i -R i-1 ) τi Equation (III-25)
as the spring force parallel to the band.

Note, τi = R i+1 -R i-1 R i+1 -R i-1 Equation (III-26)
is the unit vector at an image i estimated from two adjacent images, R i+1 and R i-1 , along the path.

The most common strategies for finding a saddle point between the initial and final states are first to roughly optimize the NEB path, followed by performing a quasi-Newton structure optimization on the image with the highest energy. Another approach, which is similar to the NEB method and called climbing-image NEB (CI-NEB 37 ) can be used to more efficiently determine the saddle point. In the CI-NEB method, the images with the highest energy, is not subjected to a spring force coming from adjacent images and thus climbs to the saddle point.

In this thesis work, we combined these two methods. To start with, an interpolation scheme involving both Cartesian and internal coordinates is used (Opt'n-Path developed by Paul Fleurat-Lessard). 38 we performed firstly a NEB path between the initial and final states, as implemented in the VASP Transition State Theory (VTST) module, 39 then picked up the points near the "suspect" saddle point among the results and performed a climbing-image NEB path this time.

The supposed transition state is then relaxed using a quasi-Newtonian algorithm 28 (E cutoff = 400 eV) until convergence criteria are reached (electrons: 10 -6 eV; nuclei: 0.01 eV•Å -1 ).

Thermodynamic calculations

In order to evaluate free energies, equilibrium and rate constants, we apply ab initio thermodynamic calculations derived from the vibrational frequency calculations, the latter being performed with VASP.

Expression of enthalpic and entropic terms according to statistical thermodynamics

The thermodynamic potential for transformation at constant pressure and temperature, as in the case of the reactions taking place under the reaction conditions, is the Gibbs free energy G. It is expressed as a function of the enthalpy H and entropy S of the system:

S T H G - = Equation (III-27)
We consider in practice the intensive molar quantities (rated X m in the following). They all depend explicitly on the temperature. The molar enthalpy of a system is expressed as follows:

m m rot m trans m vib m elec m PV U U U U H + + + + = , , , ,

Equation (III-28)

Where U elec,m , U vib,m , U trans,m , U rot,m , V m are respectively the electronic energy, vibrational energy, translational energy and the molar volume. The molar volume term PV m can be considered for an ideal gas system and for condensed phase systems, the term will be assimilate H m and U m in this case. The first term electronic energy is obtained by the result of DFT calculations, other energy terms can be calculated using the results from statistical thermodynamics.

Vibrational energy is obtained by knowing all of the vibrational frequencies of the system using the formula:

ú ú ú û ù ê ê ê ë é - + = å å - - i i T k h T k h i i A m vib B i B i e e h h N T U n n n n 1 2 1 ) ( , Equation (III-29)
where h is Planck's constant, k B is the Boltzmann constant and T the absolute temperature.

The first term of U vib,m corresponding to the vibrational energy of the system at 0K and is called "Zero Point Energy".

Relational and translational components of the internal energy have an analytical expression in the case of ideal gas:

T k N T U T U B A m rot m trans 2 3 ) ( ) ( , , = =
For a linear molecule:

T k N T U B A m rot = ) ( , Equation (III-30)
Different from the case of a molecule adsorbed on a surface, the translational and rotational energies can only be defined in the same manner when it comes to an ideal gas. The surface diffusion phenomena, which is difficult for molecular modeling, can take place, for example. As a first approximation, it is assumed in the following that the translation and rotation modes are converted into vibration modes, and thus the associated enthalpy (as well as those of the entropy) are included in the vibrational energy.

Similarly, the molar entropy energy of system can be written as follows:

m rot m trans m vib m S S S S , , , + + = Equation (III-31)
Where S vib,m , S trans,m and S rot,m are respectively the molar vibrational, translational and rotational entropy. From the vibrational frequencies we can calculate the vibrational entropy:

ú ú ú ú ú û ù ê ê ê ê ê ë é - - - = å å - - - i i T k h T k h T k h B i B A m vib B i B i B i e e e T k h k N T S ) 1 ln( 1 ) ( , n n n n Equation (III-32)
For rotational and translational components in the case of an ideal gas, the following formula are used:

ú ú û ù ê ê ë é + = 3 , 2 3 ) 2 ( ln 2 5 ) ( h N V T Mk k N k N T S A B B A B A m trans p Equation (III-33)
where P is the partial pressure of the gas, M is molar mass (formula Sackur-Tetrode) [40][41][42] where A e , B e and C e are the rotational constants of the molecule, and σ is the symmetry number.

Again, for an adsorbed molecule, it is considered that rotation and translation modes are converted into the vibration modes by only using the vibrational component to describe the molar entropy of a system. So far, for an absorbed molecule phase, thus we have :

elec vib U U H + = , vib S S = vib elec vib S T U U G - + = Equation (III-35)
So, in our case, the dehydrogenation reaction of MCH (g) leading to an adsorbed intermediate i and to the release of dihydrogen in gas phase (Equation (III-36)) is characterized by the dehydrogenation Gibbs free energy D r G dehyd,MCH (g) (i) , defined by Equation (III-37):

{ } { } 3 , 2 , 1 , / / ) ( 2 3 2 13 3 2 13 14 7 = + - - ® - + n nH O Al Pt i O Al Pt H C g g g Equation (III-36) 3 , 2 , 1 , ) ( 3 2 13 ) ( ) ( 2 ) ( / , = - - + = D - n G G nG G i G O Al Pt MCH H i MCH dehyd r g g g g Equation (III-37)
Notably, the electronic reaction energy variation and reaction enthalpy for the same dehydrogenation reaction, are defined similarly as D r E dehyd,MCH (g) (i) and D r H dehyd,MCH (g) (i) respectively.

Thus, for two neighboring intermediates along reaction path, the dehydrogenation reaction Gibbs free energy from i to j j i r G ® D will be given by Equation (III-38) :

) ( ) ( ) ( ) ( , , i G j G G g g MCH dehyd r MCH dehyd r j i r D - D = D ® Equation (III-38)
Similarly, the activation Gibbs free energy

i TS i r G ® D ‡
from reactant i to the corresponding transition state (TS i ) will be calculated by Equation III-(39) :

) ( ) ( ) ( ) ( , , ‡ i G TS G G g g i MCH dehyd r i MCH dehyd r TS i r D - D = D ® Equation (III-39)
With the help of the vibrational frequencies described in the following paragraph, the partition function calculations are performed in order to deduce enthalpy, entropy and Gibbs free energies of each system and these thermodynamic data are evaluated as a function of the temperature varying from 0 K to 1000 K, at standard condition of 1 bar pressure.

Vibrational frequencies calculations

Harmonic vibrational frequency calculations were determined, with a displacement of ±0.02 Å around the equilibrium atomic positions. All vibrational analysis has been done primarily at the PBE level. If after doing the geometry optimization at the PBE-dDsC level, the structure does not change, we considered that the PBE-dDsC have barely no influence on vibrational frequencies of each structure (for the sake of limited calculation time). So we mainly modified the electronic energies and kept the same vibrational contribution (in enthalpy, entropy and zero point energy terms). Some exceptions are observed however, in particular for the radical intermediate methylcyclohexyl adsorbed on the cluster, which will be presented later in the results. So in this case, the vibrational frequencies have been recalculated at PBE-dDsC level for the new methylcyclohexyl configuration.

These calculations allow us to determine reaction enthalpies, entropies and Gibbs free energies. These harmonic vibrational frequency calculations are also performed to evaluate the reliability of the identified transition states (according to the previously described method), whereas one and only one imaginary frequency appears in the frequency calculation corresponding to the reaction coordinate, since it belongs to a first order saddle point. However, in some cases, some low vibrational imaginary frequencies might arise, relating to the soft modes. 43 We assessed that this apparition of low imaginary frequencies is related to the chosen criterion for the geometry optimization convergence. Piccini et al. 44,45 explained that since soft vibrations can couple with the surface modes, the vibrational structure of the whole crystal framework changes consistently with the presence of the adsorbate. This means that the crystal adapts its structure to accommodate the molecule weakening the strength of some bonded interactions, which gives rise to a highly entropic adsorbed state. This vibration of the crystal framework forms the structure adaption was also observed when we visualized the soft modes of our cluster system.

In order to eliminate these soft modes in form of imaginary frequencies, we firstly attempted different parameters combination "packages" in terms of cut-off energy (400, 500, 600 eV), precision flag in VASP (normal, accurate, high), electronic convergence criterion (10 -5 , 10 -6 , 10 -8 eV) and forces convergence criterion (0.01, 0.02 eV/Å) to optimize the methyl-cyclohexene adsorbed system for a benchmarketing test (reaction presented in Equation III-( 40)), since that this is one of the crucial reaction intermediate considered in our mechanism later. These tests were done to probe if there is a potential connection between the extinction of these parasite imaginary frequencies and the calculation parameters. Among all the parameters choices applied on the methyl-cyclohexene adsorbed system, it turns out only five parameter "packages" managed to eliminate these imaginary frequencies: (1) cut-off energy = 400 eV; normal precision; electronic convergence criterion = 10 -5 eV; forces convergence criterion = 0.02 eV/Å;

(2) cut-off energy = 400 eV; normal precision; electronic convergence criterion = 10 -5 eV; forces convergence criterion = 0.01 eV/Å; (3) cut-off energy = 500 eV; normal precision; electronic convergence criterion = 10 -5 eV; forces convergence criterion = 0.01 eV/Å; (4) cut-off energy = 400 eV; normal precision; electronic convergence criterion = 10 -8 eV; forces convergence criterion = 0.005 eV/Å; (5) cut-off energy = 400 eV; accurate precision; electronic convergence criterion = 10 -8 eV; forces convergence criterion = 0.005 eV/Å. Sometimes, with more severe optimization parameters (ex. high cut-off energy and precision, 600 eV), the extinction of parasite imaginary frequencies are not guaranteed. However, the cut-off energy = 400 eV at normal precision are constantly efficient. In addition, high electronic and forces convergence criterions are also recommended by our tests for the extinction of these parasite imaginary frequencies (tests ( 4) and ( 5)). Nevertheless, these high criterions demand relatively long calculation time.

{ } { } ) ( 2 3 2 13 12 7 3 2 13 14 7 / / g H O Al Pt H C O Al Pt H C + - - ® - + g g Equation (III-40)
On the other hand, the contribution of these small parasite imaginary frequencies, which are converted from negative eigenvalue to positive by DFT at the end of calculation, can be tremendous and uncertain to the vibrational entropy term if no proper countermeasures are adopted. This can be seen by the expression of vibrational entropy term in Equation (III-41), When ν i → 0, we have

T k h T k h B i B i B i e e T k h n n n - - - 1 → 1 and ) 1 ln( T k h B i e n - - → -∞, so S vib,i → +∞. ú ú ú ú ú û ù ê ê ê ê ê ë é - - - = - - - ) 1 ln( 1 , T k h T k h T k h B i B A i vib B i B i B i e e e T k h k N S n n n n Equation (III-41)
An analysis of the vibrational frequencies was thus done to evaluate the entropy deviation induced by the soft modes and imaginary frequencies obtained by different calculation parameters for methyl-cyclohexene system at reforming temperature T = 800 K. The last five vibrational frequencies coming out from the DFT calculations are listed in Table III-1, which includes soft modes and imaginary frequencies (underlined value) that are converted from negative eigenvalue to positive by DFT at the end of calculation. Here in Table III-1, three parameter "packages" (with same electronic convergence criterion = 10 -5 eV and forces convergence criterion = 0.02 eV/Å, for the sake of calculation time) were chosen to make a comparison: (a) cut-off energy = 400 eV; normal precision; (b) cut-off energy = 400 eV; High precision; (c) cut-off energy = 500 eV; normal precision. These three cases were representative among all because the case (a) have no parasite imaginary frequencies, while the cases (b) and (c) reveals the most (±) deviation on total vibrational entropy at 800 K compared to (a) during our analysis, due to the apparition of parasites imaginary frequencies. The vibrational entropy corresponding to each frequency is calculated by using Equation (III-41). It indicates thereby from Table III-1 that the apparition of these soft modes or imaginary frequencies contributes -20 ~ +3 kJ/mol to the vibrational entropies term TS vib at 800 K.

Table III-1 Frequency analysis for the contributions of last five soft modes and imaginary frequencies to the vibrational entropies at T=800 K calculated on PBE level (The underlined values correspond to imaginary frequencies)

In addition, a recommended method for treating residual imaginary frequencies has been proposed by Sabbe et al. 46 , which is to replace the frequencies lower than a given frequency cutoff by a common value. In line with this previous work, we replaced all frequencies lower than 50 cm -1 and all spurious imaginary frequencies (if any) by 50 cm -1 before thermodynamic calculations. For transition states, the imaginary frequency corresponding to the reaction coordinate and to a first order saddle point has to be eliminated before the Gibbs free energy calculation. The reaction enthalpy and Gibbs free energy for the dehydrogenation of methylcyclohexane (taken in gas phase) to adsorbed methyl-cyclohexene and one molecule H 2 released in gas phase has been calculated here in Figure III-4. We investigated the effect of the energy cutoff (400, 500, 600 eV) and the precision (normal, accurate, high) of the calculation, at same electronic convergence criterion = 10 -5 eV and forces convergence criterion = 0.02 eV/Å. It can be noticed in Figure III-4 that the parameter choices (energy cutoff and precision) used for the calculation strongly impacts the Gibbs free energy values, even though after replacing all frequencies lower than 50 cm -1 and all spurious imaginary frequencies (if any) by 50 cm -1 . It can be seen that the deviation on the reaction enthalpy is very small, taking the reforming temperature 800 K for a comparison, the deviation is close to 1 kJ/mol, which can be neglected on the final result. However, the deviation on the Gibbs free energy is higher (21 kJ/mol at 800 K). This makes this kind of calculation very sensitive to the chosen parameters in the reforming conditions. This important deviation on the Gibbs free energy is thus due to the vibrational entropic terms, since enthalpies varied very little in our case.

Since the "standard" calculation (cut off energy of 400 eV, normal precision) leads to Gibbs energy values in the center of this fluctuation interval with a reasonable computational time and without any spurious imaginary frequency, we chose it as the best compromise for further calculations and with a slightly higher electronic convergence criterion = 10 -6 eV and forces convergence criterion = 0.01 eV/Å.

Catalytic experiment

This second part of the chapter aims at presenting the catalytic tests based on the methylcyclohexane dehydrogenation reaction in our work. In the literature, different catalyst tests have been done under different reaction conditions, with variable platinum contents in catalyst. [47][48][49][50][51][52] As it can be observed in Table III-2, a large range of reaction conditions is used on purpose to provide specific experimental data for dedicated kinetic studies. In our work, the adapted reaction conditions and catalyst will be also chosen to provide these experimental data, in order to enable the later confrontation with the kinetic model parameterized by the ab initio calculations. So in this chapter, the protocols of catalyst preparation will be presented first, followed by the catalyst characterizations. The employed experimental conditions and protocols for the tests will then be described in detail. At last, the test results will be interpreted in comparison with the available literature, depending on the reaction conditions employed, such as temperature, reaction space time, hydrogen partial pressure and methyl-cyclohexane partial pressure.

Methodology and experimental techniques 2.1.1 Catalyst preparation and characterization

The catalytic reforming catalysts are prepared by depositing platinum (0.3 wt%) on a γalumina support (beads shape). Due to the use of chlorinated platinum precursor, 0.12 wt% chlorine remains on the catalyst, which can be considered as a nearly non-chlorinated catalyst during our catalytic tests, in order to compare with the ab initio calculation model chosen.

Indeed, industrial reforming catalysts are far more chlorinated (about 1% wt) resulting from a specific chlorination treatment. The employed catalysts were synthesized and then characterized in the Catalysis and Separation Division, by Carine Guégan. The protocols of catalyst synthesis and characterization are now presented :

Preparation and acidification of alumina support :

The support (boehmite type) is firstly calcined for 2 h at 520 °C (Heating rate: 5 °C/min), under a dry air flow rate of 1 L.h -1 .g -1 of support, in order to transform the boehmite into γalumina. Pre-calcination of the support can remove hydroxyl groups from the alumina. This results in the presence of highly reactive sites where the metal will preferentially attach. To avoid a heterogeneous distribution, the alumina is therefore rehydrated progressively by adding water drop by drop. This step also makes it possible to avoid excessive exothermicity and bursting of the beads during the introduction of the support into the fluidized bed in the presence of a large quantity of water. The support is then placed in the fluidized bed, the alumina is contacted with a sufficient amount of hydrochloric acid (HCl) at 35% concentration. The hydrochloric acid (HCl) is injected with a syringe during 45 minutes. After a total acidification time of 2 h, then the liquid is withdrawn from the alumina support.

Impregnation of Pt :

The impregnation of the platinum is carried out by ion exchange in a solution using an adsorption competitor (Cl -), in order to allow a quick migration of the platinum into the catalyst grain. To do this, the hexachloroplatinic acid (H 2 PtCl 6 ) + hydrochloric acid (HCl) is then added (in the form of [PtCl 6 ] 2-in an acid phase). The H 2 PtCl 6 solution is prepared by dissolving the contents of a flask of 25 g of hexachloroplatinic acid (concentration of 38-40% by weight of Pt) in 300 g of water. The solution (H 2 PtCl 6 + HCl) is then injected into the addition pot which contains the alumina support with a syringe during 45 minutes (same method as the acidification). The quantity of H 2 PtCl 6 injected is calculated by aiming at 0.35 wt% Pt that will be impregnated at last instead of 0.3 wt%. This quantity of metal precursor introduced is slightly greater than the target quantity and empirically determined. The quantity of HCl injected is calculated as reference of 0.5 wt% Cl of the support. An adsorption equilibrium then takes place rapidly between the Cl -and PtCl 6 2-ions at the surface of the support. The fluidization lasts a total of 4 h and then the liquid is withdrawn.

Drying and calcination :

The catalyst is dried overnight in an oven at 120 °C and then is calcined for 2 h at 520 °C, (heating rate: 5 ° C/min.), with a dry air flow rate of 1 L.h -1 .g -1 of the catalyst.

Dechlorination :

The catalyst obtained after the drying and calcination is a catalyst contains 1.35 wt% Cl (chlorine, analyzed by X-ray fluorescence), which is not our desired Cl content. Therefore, our employed catalyst for the catalytic reaction tests requires a chlorine elimination to reach a non or low-chlorinated state. A step of dechlorination has to be done in this case. The dechlorination consists in principle in injecting a quantity of water at high temperature in a given time.

In a quartz reactor, the catalyst is put inside to be dechlorinated, an inert buffer made by quartz and carborundum (SiC) are charged (» 200 g for a reactor of diameter » 60 mm et » 500 g for the diameter » 80 mm) to prevent the catalysts from blowing away by water and air during the dechlorination process. The reactor is placed in a vertical tubular furnace and processed under a stream of dry air of 1 L.h -1 g cata -1 . The heating rate of the furnace is set at 5 °C/min from room temperature to 520 °C. At this temperature of 520 °C, 8000 ppm of water are then injected into the gas pendant 80 h. At last, the catalyst is cooled in dry air (11 L.h -1 g cata -1 ) and discharged at room temperature. Thus, the catalyst is about to be determined by X-ray fluorescence for the new chlorine content and also the platinum content.

X-ray fluorescence:

The elemental mass loadings are determined by X-ray fluorescence (XRF). The analysis of the wavelength dispersive X-ray fluorescence spectrum allows to get the information on identification of the nature of the simple elements by the energetic distribution of the characteristic rays on the spectrum and at same time, the intensity of each characteristic radiation is directly related to the amount of each element in the material. 53 Therefore, the chlorine (Cl) content (wt%) analyzed by XRF is 0.121 and the platinum (Pt) content (wt%) is 0.295 for the catalyst synthesized. Accuracy is respectively ± 0.006 and 0.007%.

Electron microprobe :

The metal and chlorine distributions inside the catalyst beads are determined by electron microprobe. The electron microprobe is an analytic technique to characterize the composition of chemical components within a material by analyzed the characteristic wavelength of the emitted X-ray to the sample elements when they are bombarded by a focused incident electron beam (or electron probe), without destroying the sample. 54 The electron microprobe produces twodimensional images of elemental distributions that gives us a quantitative analysis in order to determine the mass concentration of the sample elements. 54

H 2 -O 2 titration :

The H 2 -O 2 titration is a common technique used to quantify the platinum dispersion. The pretreatment protocol includes a decrease in temperature between the calcination (550°C under dry air) and the reduction, and a rise in temperature under hydrogen for the reduction (550 °C).

Once the catalyst is reduced, the first titration of O 2 occurs. The catalyst is treated in contact with the oxygen pulses; the hydrogen atom on the platinum atom is thus oxidized into water and progressively replaced by adsorbed molecular oxygen. The reaction of this titration step can be written as:

(1) Pt-H + 3/4 O 2 à Pt-O + 1/2 H 2 O
The remaining oxygen flow rate is detected and the detection ends when the inlet oxygen flow rate is equal to the outlet oxygen flow rate. Then the catalyst goes through a second reduction at room temperature this time. The reaction of this reduction step can be expressed as :

(

2) Pt-O + 3/2 H 2 à Pt-H + H 2 O
Then, second titration starts after this reduction step undergoing exactly the same reaction as the first titration. The metal dispersion can be thus calculated by the first titration : By using this H 2 -O 2 titration analysis, the dispersion of platinum in our catalyst is determined at 90 %.

Disp % = V 1 22400•T a 273 • 3 4 • wt% Pt 100•M Pt With V 1 = chemisorbed

Transmission Electron Microscopy :

The So far, the platinum dispersion of the catalyst is determined to be about 90%. However, it is crucial to control the catalyst granulometry to avoid internal transport gradients between the catalyst body surface and the catalyst body center, in order to get reliable results. So, for this purpose, the beads have been grinded and sieved to 200 -355 µm before catalytic tests, a choice that we made after comparing the test results of different granulometries (See in Appendix-III).

The catalyst weight for each test is 0.56 g.

Catalytic test set-up

The simplified reaction set-up scheme is presented in

Inlet zone

The adjustable and controllable parameters for the reaction conditions are the reaction temperature, the inlet gas flow rate for H 2 gas, the inlet methyl-cyclohexane charge flow rate and the total pressure during the reaction. The reaction temperature is set up by a heating system connected with the reaction oven (RO) that surrounds the reactor and is surveyed by three thermocouples extending into the reactor (R). The H 2 gas is directly injected into the reactor from the gas flow line and one can measure its flow rate from the gas flow controller. The methylcyclohexane liquid charge (Sigma-Aldrich, 99% reagent grade, 0.77 density, 2.5 L/bottle) is stored in the feedstock tank (FT) of 3 liters, and is pressurized by a line of low nitrogen pressure.

The liquid charge is pumped from the feedstock tank to the reactor inlet at reaction pressure by the pump (P). This liquid charge flow is regulated by the pump and is measured by a manually burette upstream of the reactor.

Reaction zone

The catalytic tests for the methyl-cyclohexane dehydrogenation reaction are carried out in a vertical fixed bed reactor with an internal diameter of 19 mm and a length of 585 mm.

Outlet zone

At the outlet of the reactor, the reaction products in gaseous phase at high reaction pressure are blown into the first high pressure separator (HPS), in order to cool down and to condense the "heavy" compounds into liquid phase and separate them from H 2 . At the output of the high pressure separator (HPS), an automatic pressure swing valve (PSV) can be found to control the pressure in the reactor. Once the desired liquid level (4 % of the HPS total volume in this work) is set up, this level in the separator is full-time controlled and adjusted by the help of a plug-in detector in the separator. The automatic pressure swing valve (PSV) is connected with this detector in order to be turned on/off depending on the liquid level. That allows us to have a continuous product feed flow from the high pressure separator (HPS) to the low pressure separator (LPS), instead of being accumulated in the high pressure separator (HPS). Before the liquid flow goes into the low pressure separator (LPS), we force a part of the product feed to pass into an automatic sampler (AS), which can be programmed to recover the product liquid feed hourly and can analyze 80 samples at maximum for each test.

Then the samples are analyzed by a gas chromatograph (GC) analyzer equipped with a flame ionization detector (FID) in order to determine the product yield in the liquid portion. The liquid sample is vaporized into gas at the moment of being injected into the gas chromatograph (GC). In gas chromatograph (GC), the sample comes through in a carried gas stream as a mobile phase (helium), interacted with the liquid stationary phase inside a capillary column. The The output gas flow from the low pressure separator (LPS) is firstly flowing through a 100 mL ampoule that contains glass balls, which role is stirring the mixed gas and also calibrating the gaseous volume in the ampoule to 100 mL. After about 15 minutes, we close the two valves of the ampoule and then inject 250 µL of pure cis-2-butene as reference gas. With the help of the glass balls inside, we mix the gas and then retrieve 250 µL mixed gas and analyze it by gas chromatograph (GC). By this way, we identify and quantify the different gaseous components outlet of the reaction zone. The detail quantifications and calculations will be presented in next section.

Reaction conditions

The operating conditions are different from those generally applied in the industrial reforming processes [56][57][58] . The dehydrogenation reaction of alkyl cyclohexanes into aromatics is a highly endothermic reaction and reported to have a reaction heat of about 215 kJ/mol for all carbon numbers. 59 At the same time, these reactions present also a very high equilibrium constants which have an order of magnitude of 10 6 . 59 The reaction is very favored with high temperatures and can reach a very high conversion at reaction equilibrium. Moreover, the reaction rate of dehydrogenation of alkyl cyclohexanes is very fast compared to other reforming reactions : about 6 times faster than that of isomerization of paraffins and naphthenes and 25 times faster than those of dehydrocyclisation of paraffins and hydrocracking. 59 Another important reaction that should be considered is the coke formation, which is the slowest process in catalytic reforming (1000 times slower than the dehydrogenation reaction 59 ). However, this reaction is sensitive to the hydrogen partial pressure and the hydrogen to hydrocarbon ratio. 59,60 The coking rate increases by decreasing the hydrogen to hydrocarbon ratio at constant total pressure. 60 It is thus important to employ the optimal operating conditions to ensure the catalyst stability from metal sintering, to achieve a large conversion range and also to guarantee no thermal effects or diffusional limitations. The high temperature may favor the conversion but in our study, we would like to achieve conversion levels in a relative large range, in order to study the reaction kinetics. So, lower temperatures compared to the industrial catalytic reforming temperatures were employed. On the other hand, the lower temperature can eliminate the other reforming reactions as hydrocracking and hydrogenolysis. In order to avoid catalyst deactivation by coke formation, the total partial pressure was maintained at 13 bar and the hydrogen to hydrocarbon ratio was set at 15 for most catalytic tests, excepted for those which are aim at studying the partial pressure impact. For those purposes and by previous catalytic tests done at IFPEN, 55 the choice of reaction conditions for the methyl-cyclohexane dehydrogenation reaction is presented in Table III-4. focus on the impact of methyl-cyclohexane partial pressure at constant hydrogen partial pressure.

Van Trimpont at al. 50 already performed a similar approach in order to estimate the partial reaction orders for each reactant, but for different reaction conditions and different catalysts.

They used a sulfur-pretreated (100 ppm of sulfur) Pt/Al 2 O 3 catalyst containing 0.59 wt% of platinum and the hydrogen partial pressure (P H 2 ) varied from 5 to 20 bar at constant methylcyclohexane partial pressure (P MCH ) of 0.5 bar. The temperature employed was set at 350 °C and the weight hourly space velocity was around 30 (g MCH .h -1 .g cata -1 ). The detailed comparison of these results will be presented later.

Notably, due to limitations of the set-up (both in terms of flows and minimal mass of catalyst), the WHSV was limited to 150 g MCH .h -1 .g cata -1 , corresponding to a minimal space time of 24 s.g cata .g MCH -1 . Indeed, if we increase the charge flow rate, the hydrogen flow rate has to be increased as well with regard to keep the H 2 /HC ratio constant. The maximum hydrogen flow rate for our laboratory set up is 300 L/h. Test-5 reaches this limit. Moreover, the minimal methylcyclohexane flow rate is 29 mL/h to ensure a stable flow rate.

Experimental protocol of catalytic tests 2.2.1 Catalyst activation

Before contacting the charge with the catalyst, the latter was activated in two in situ steps :

drying and reduction. The drying process is undertaken by heating the catalyst to 150 °C at the heating rate of 5°C/min under a N 2 gas flow rate of 10 L/h, during 1 h. Then the temperature increases from 150 °C to 500 °C by same heating rate for around 1.2 h to thus undergo the reduction process performed at 500 °C for 5 h, under a H 2 gas flow rate of 30 L/h. These activation steps should be redone as long as the catalyst is unloaded and a new one is reloaded into the reactor during the test sequences.

Thermal profile inside the reactor

The catalytic tests are supposed to be undertaken under an isothermal condition. Nevertheless, the dehydrogenation reaction is very endothermic and when the reactant feed flow reaches the catalytic zone (Figure III-8) into the reactor, it passes firstly by the thermocouple T 2c , the one on the top. The whole catalytic zone measures 32.5 mm for the feed to flow through and when the feed flow arrives at T 2a , the endothermic reaction completes and the product forms. That explains the fact that the temperature from T 2c to T 2a decreases, the latter being at the lowest temperature compared to the other two thermocouples. with respect to the recorded temperature is however about 3-4 °C, lower than in a previous study (10 °C). 55 We can thus conclude that the isothermicity is reasonable during the reaction. the product feed at the output of reactor, which makes 8 conversion points for each temperature.

Reactant conversion and mass balance calculations

Product yield in liquid phase

The automatic sampler allows us to analyze the liquid products collected hourly from the outlet of the reactor and to calculate the product yield obtained in the liquid effluent. From the chromatography spectrum, the only observed components are toluene and methyl-cyclohexane (more than 99% in total). Toluene only was detected as the product of the reaction, also in the gas effluent analyzed by gas chromatogram, which suggests that there are no obvious nor relevant side reactions happening beside the dehydrogenation reaction. Therefore, only methylcyclohexane and toluene were considered for further calculations. Note that this result also justifies why in the ab initio kinetic modeling we neglect the desorption of partially dehydrogenated molecules.

RF MCH = aM MCH n carbon ×M carbon =1.08 Equation (III-45)
Where a is a correction factor that is given for correcting the molecular mass in the response factor expression of the gas chromatograph, the value of a equals 0.923; M i is the molecular mass for each molecule i; n carbon is the number of carbon atoms of the molecules (7 in both cases). The toluene yield in weight in liquid phase y Tol(l) is then calculated by Equation (III-

46)

.

y Tol l = RF Tol A Tol RF Tol A Tol +RF MCH A MCH

Equation (III-46)

A i represents the peak area surface of each component in the chromatograph. These areas are normalized by the response factor RF i .

Product yield in gaseous phase

The quantity of each component, methyl-cyclohexane and toluene in gaseous phase is determined by ampoule sampler system already explained in

n MCH (g) =n 0,MCH (g) × V measured V 0 Equation (III-50) n Tol (g) =n 0,Tol (g) × V measured V 0 Equation (III-51) n H 2 = V measured V m -n MCH (g) -n Tol (g) Equation (III-52)
With V m the molar volume of an ideal gas at 1 atmosphere of pressure and at room temperature (25 °C) equals 24.4 L/mol. So the toluene yield in outlet Y Tol % by considering both the liquid and gaseous phases can be calculated according to Equation (III-53).

Y Tol %= m Tol (g) +m Tol (l)

m Inlet ×100%

Equation (III-53)

Table III-5 Mass balance between inlet and outlet for each catalytic test

The tolerance on the loss or gain on this mass balance is around 5 % -10 % maximum, because of the uncertainty on the calculation by the unavoidable manipulation errors or facility defects. As we can observe in Table III-6, most of our tests have respected this tolerance.

However, the loss or gain on the mass balance could indeed have some impacts on the toluene conversions and eventually underestimate the product yield. To correct this dependence caused by mass balance on our conversion, we adopted a normalization method on our conversion calculations.

Table III-6 Mass balance calculated for each catalytic test along with their reaction conditions

The normalization can be done on either outlet mass or inlet mass, by simply applying the ratio between total inlet mass and total outlet mass (

m Inlet m Outlet
). Here it is given an example on normalized outlet mass appeared in Equation (III-53), specifically calculated for the normalized total liquid mass in outlet m' Outlet (l) and the gaseous toluene mass in outlet m' Tol (g) :

m' Outlet (l) = m Outlet (l) × m Inlet m Outlet Equation (III-54) m' Tol (g) = m Tol (g) × m Inlet m Outlet Equation (III-55)
Hence, the new normalized toluene yield in weight redefined from Equation (III-53) can be expressed as :

Y' Tol %= m' Tol (g) +Y Tol (l) ×m' Outlet (l)
m Inlet ×100%

Equation (III-56)

Reaction kinetics calculations

Arrhenius plot

Once the conversion is determined, the apparent activation energy can be obtained by assuming the reaction behaves as an irreversible first order reaction to the reactant (methylcyclohexane). Thus, the reaction rate can be written by power-law rate equation :

r = kP MCH = - dP MCH dt ⟺ ln P MCH P 0,MCH = -kt ⟺ k = 1 t ln 1 1-X MCH→Tol Equation (III-57)
Where r is the overall reaction rate, k is the apparent reaction rate constant, t is the space time and X MCH à Tol is the equivalent toluene yield in concentration (mol/mol), which can be deduced from Y Tol by Equation (III-58).

Y Tol = m Tol m Inlet = n Tol M Tol n MCH,0 M MCH ⇒ X MCH→Tol = n MCH,0 -n MCH n MCH,0 = n Tol n MCH,0 = Y Tol M MCH M Tol Equation (III-58)
Meanwhile, according to the Arrhenius equation :

k = Ae -E a RT ⇔ ln k = ln A - E a RT Equation (III-59)
Combing Equation (III-57) and Equation (III-59), we obtain Equation (III-60) which describes the relation between the reaction temperatures T and reaction constant k, provided that the space time is kept constant :

ln ln 1 1-X MCH→Tol =- E a RT +const.
Equation (III-60)

For a temperature remaining within a small interval, we assume that the slope of this linear relation of ln ln

Eyring plot

Henry Eyring developed the transition state theory in 1935 and Equation (III-61) gives the corresponding Eyring equation 61 in the case of an order 1 elementary step.

k= k B T h e -∆ r G ‡ RT = k B T h e -∆ r H ‡ RT e ∆ r S ‡ R Equation (III-61)
where k is the reaction rate constant, k B is the Boltzmann constant, h is the Planck constant. This equation defines the relationship between the activation Gibbs free energy Δ r G ‡ , the activation enthalpy Δ r H ‡ , the activation entropy Δ r S ‡ and the reaction rate constant.

Once more, if we combine Equation (III-57) and Equation (III-61), we will then have :

ln k T = ln ln 1 1-X MCH→Tol T =- ∆ r H ‡ R ⋅ 1 T +const. Equation (III-62) With const. = ln( k B h )+ ∆ r S ‡ R .
For a temperature remaining within a small interval, we assume that the slope of this linear relation of ln

ln 1 1-X MCH→Tol T as a function of 1 T
is constant, and we can thus calculate the apparent activation enthalpy of the reaction for the targeted temperature. Simultaneously, the Eyring plot allows also an access to the pre-factor term depending on the activation entropy.

Experimental reaction rate

During the experiments, the methyl-cyclohexane conversions to toluene were obtained by Equation (III-56) and (III-58), for each experimental space time. Normally, if the studied conversion plotting curve is continuous as a function of space time, on can calculate the reaction rate at one specified experimental point by simply deriving the slope of the curve on this point. However, the curve is discontinuous in our case, due to a limited sampling of conversion with respect to space time. So, in this case, we use the points before and after to estimate the slope of the middle point, as presented in So, for a flow system at steady-state conditions, the reaction rate of the point i at a given space time (or conversion) can be calculated by using the experimental data of t i-1 , X i-1 , t i+ 1 and X i+1 . Then, we have :

r i = ∆X MCH→Tol M MCH ∆t Equation (III-63)
Where ∆X MCH à To𝑙 is the variation of the molar conversion of methyl-cyclohexane to toluene (= X i+1 -X i-1) at a given space time for a space time variation, ∆t (=t i+ 1 -t i-1 ).M MCH stands for the molar mass of methyl-cyclohexane. Any problem in the electronic structure of the matter is covered by Schrödinger's equation including time dependency. In most cases studied here, however, one is concerned with atoms and molecules without time-dependent interactions. Hence, in order to obtain the energy of a polyatomic system, one must solve the following simplified Schrödinger equation 1 :

Equation (III-64)
Where E is the electronic energy, Ψ is the wave function, and 𝐻 is the Hamiltonian operator. The product Ψ with its conjugate complex ΨΨ * (or often noted as Ψ : ) is known as probability distribution function of the particle, in the sense to express the probability of finding the system with position coordinates. In the case of a molecular system (with several electrons and nuclei), Ψ is a function of the coordinates of electrons and nucleus of the molecule that we define here by, respectively, 𝑟 and 𝑅. The different solutions if the Equation (III-65) correspond to different steady states of the molecular system. The state with the lowest energy is called ground state of the system. For a molecular system, Hamiltonian consists of terms of kinetic energy and potential energy of nucleus and electrons:

Ĥ Ψ ! r 1 , ! r 2 ,..., ! r N , ! R 1 , ! R 2 ,..., ! R M ( ) = E Ψ ! r 1 , ! r 2 ,..., ! r N , ! R 1 , ! R 2 ,..., ! R M ( ) Equation (III-65) With , ,
, , Equation (III-66)

The operator for the electrons kinetic energy 𝑇 e , for the kinetic energy of the nuclei 𝑇 n , the one for describing the electrostatic electron-electron interaction 𝑉 ee , the electrostatic nucleusnucleus interaction 𝑉 nn and the electrostatic nucleus-electron interaction 𝑉 ne . They are all given in atomic units. In the above shown equations 𝑀 * and 𝑍 * stand for the mass and charge of a nucleus, respectively.

-The Born Oppenheimer approximation

As the Schrödinger equation of a many-body system can neither analytically be solved, one has to make approximations. The Born Oppenheimer (B.O) 17 approximation is considered as the first approximation used for simplifying the resolution of Schrödinger equation. The idea in this approach lays in the separation of electron and nucleus motion by using the fact that nucleus, due to their higher mass (several 10 3 times heavier), move much slower than electrons. So we can consider that electrons react instantaneously to any position change of nuclei. This approximation makes the assumption that the kinetic energy and electrostatic repulsion term of the nuclei in the total Hamiltonian can be considered as constant and independent of the time, hence resulting in

ˆˆˆˆˆ= + + + + e n e e n n n e H T T V V V 2 1 1 ˆ2 = = - Ñ å N e i i T 2 1 ˆ2 = Ñ = -å M A n A A T M 1 1 ˆ= > = - åå N N ee i i j i j V r r 1 ˆ= > = - å å M M A B nn A B A A B Z Z V R R 1 1 ˆ= = = - - åå N M A ne i A i A Z V r R
an electronic Hamiltonian describing the motion of N electrons in an external field of M fixed point charges:

Equation (III-67)
Where the solution to this electronic Hamiltonian is the electronic wave function

) , , , ; , , , ( 2 1 2 1 A i el el R R R r r r ! ! Y = Y Equation (III-68)
It describes the electron motion explicitly and the nuclear coordinates parametrically, i.e. for a given nuclei configuration Ψ el is a different function of the electron coordinates. Hence, the total energy E tot is then the sum of electronic energy E elec and the constant term for the nuclear repulsion E nn . Thus, Equation (III-69) and Equation (III-70)

The BO approximation allows us to build an equation of electronic Hamiltonian which ignores the term kinetic energy of nucleus (T n ).

å å å å å å å > < + + - Ñ - = el i el i n I el i el i j n I n I J J I J I j i iI I i el R Z Z r r Z H ) ( ) 1 ( ) ( , , 2 2 1
Equation (III-71)

-Variational principle for the ground state

When a system is in the state Ψ, which may or may not satisfy the Schrödinger equation, the average of many measurements of the energy is given by the formula: 1 to define a procedure for giving from N and ν(r) to the ground-state wave function Ψ. Note that in this statement there is no mention of the kinetic-energy or electron-repulsion parts of 𝐻, because these are universal so that they are determined by N. We say that E is a functional of N and ν(r).

E Ψ " # $ % = Ψ Ĥ Ψ Ψ Ψ Ψ Ĥ Ψ = Ψ * Ĥ Ψ dx ∫ E Ψ [ ] ≥ E 0 E 0 = min Ψ E Ψ [ ] δ Ψ Ĥ Ψ -E Ψ Ψ # $ % & = 0

Granulometry study for the employed catalyst

Introduction

This chapter is devoted to the DFT calculations of the free energy profiles of the dehydrogenation steps of methyl-cyclohexane into toluene on Pt 13 /g-alumina systems. We will proceed as follows: We will first start by recalling the atomistic model used in section 1.. Due to the complexity of the reaction network, we will first identify one representative pathway involving 4-methylcyclohexene based on a preliminary analysis of the stability of C 7 H 12 intermediates (section 2.) at PBE level. The adsorbed configuration of 4-methylcyclohexene will be then refined as a function of Pt sites and by molecular dynamics in section 3.. Such a study will be generalized to other intermediates involved along the dehydrogenation pathway relating to 4-methylcyclohexene (section 4.). A comparison with the Pt(111) surface will be also given in section 3. and 4.. To analyze the effect of dispersion corrections, a systematic comparison of the structure and energetics of these intermediates will be then analyzed with the PBE and PBE-dDsC functionals in section 5.. The complete Gibbs free energy profiles will then be established at PBE and PBE-dDsC levels in sections 6. and 7., whereas a direct comparison of this profile with the case of the (111) surface will be provided in the final sections (section 8. and 9.).

Atomistic model of the catalyst

As we mentioned in the introduction, a previously established Pt 13 /γ-Al 2 O 3 model of catalyst will be used to undertake a kinetic investigation. We focus here on the dehydrated and dechlorinated (100) g-alumina surface as determined in previous DFT works 1,2 using the bulk model of g-alumina as solved by Krokidis et al. 3 Indeed, in catalytic reforming conditions, this alumina facet is shown to be mostly dehydrated and dechlorinated. 4 On this facet, a rather strong interaction exists between the metal cluster and the alumina support, [5][6][7] which stabilizes a Pt 13 cluster with a bi-planar (BP) structure interacting with the g-alumina surface through 7 platinum atoms (S1 to S7 in Figure IV-1). 6 The morphology and electronic properties of the platinum cluster were shown to be very sensitive to the hydrogen pressure such as applied in the reforming conditions. 6 By increasing the hydrogen coverage on the surface of these nano-particles, a reconstruction takes place, from the BP structure at low hydrogen coverage (θ H ) to a cuboctahedron (CUB) at H/Pt ratio higher than 1.5. This structural reconstruction is associated with a large change of the electronic properties of the platinum sites, from a metallic to a partially oxidized state. This phenomenon has been confirmed experimentally by X-ray absorption nearedge structure (XANES) and extended X-ray-absorption fine-structure (EXAFS) measurements on γ-Al 2 O 3 supported Pt nano-particles. 8,9 The hydrogen coverage at 25°C was found to increase from 1.9 to 2.5 H/Pt with an increase of pressure from 1 to 21 bars, revealed by XANES. 9 The EXAFS revealed a structure change from 2D to 3D, evidenced by increasing Pt-Pt coordination numbers and decreasing Pt-O coordination numbers. 10 By applying the results obtained in the DFT calculation of Mager-Maury et al. 6 , under catalytic reforming conditions (temperature of 800 K and a hydrogen partial pressure close to 10 bar), an interval of 6 to 18 hydrogen atoms per cluster is found to be the most stable situation.

111

Considering the bulkiness of the methyl-cyclohexane reactant and toluene product, the accessibility of both molecules is strongly hindered for H/Pt ratio greater than 1 (e.g. H coverage above 13). In addition, we also noticed that DFT calculations might slightly overestimate the H coverage when compared to XANES experiments, 8,9 so we decided to undertake our study with 6

hydrogen atoms covering the Pt 13 cluster, as shown in Figure IV-1.

For 6 H atoms, the BP morphology of the platinum particle is only slightly modified with respect to the bare cluster, thus this allows us to define the layer interacting with the alumina surface as the atoms holding the letter "S", and the layer contacting with vacuum space by using the letter "V" (see Figure IV-1). Likewise, we define all the hydrogen atoms by using letter "H".

We will start our mechanistic investigations by considering all those different adsorption sites, with migration of hydrogen atoms on the metal particles when needed (for example, to access the V6 site).

Preliminary investigation on the stability of C 7 H 12 intermediates

The proposed mechanism for the dehydrogenation of methyl-cyclohexane (MCH) into toluene (Tol) involves firstly two key intermediates invoked in numerous studies: [11][12][13][14][15][16][17][18][19][20] order to analyze a complete reaction pathway, our strategy is to focus on some relevant intermediates formed with respect to the literature.

Respective stability of C 7 H 12 radical and non-radical intermediates

Firstly, we study the dehydrogenation of methyl-cyclohexane (C

{ } { } 3 2 6 13 14 7 ) ( 2 3 2 6 13 12 7 , / ) ( ) ( / ) ( O Al H Pt E H C E H E O Al H Pt H C E E g MCH dehyd r g - - - + - - = D g g Equation (IV-1) Table IV-

Analysis of the adsorption modes of 4-methyl-cyclohexene with respect to ethylene, comparison with Pt(111)

We also found that the dissociative-adsorption di-σ mode is less favorable than π mode for all olefinic intermediates. Raybaud et al. 21 reported for the dissociative-adsorption of ethane on Pt 13 H 6 /γ-Al 2 O 3 (100) that the di-σ mode for ethylene was preferred when the two hydrogen atoms removed from ethane are maintained on the cluster. A complementary study has been performed to identify the most stable adsorption modes related to the effect of hydrogen coverage (θ H ), as the cluster is richer in hydrogen (θ H = 8) in Raybaud et al., and the intrinsic nature of the molecules (Appendix-IV-1), so as to understand the discrepancy between the preferred adsorption modes of ethylene and MCHe. From these calculations, this can be assigned both to an effect of hydrogen coverage and nature of the adsorbed molecule.

117

The different adsorption modes of alkenes on the Pt(111) surface are reported in the literature from experimental methods. It is found for the case of ethylene, for temperature below 52 K, that the π mode is the most stable; when temperature is over 52 K and up to 220 K, di-σ bonded ethylene become dominant on the Pt (111) surface. [22][23][24] While it is also reported that at the temperature 50 K, base pressure 3 × 10 -11 Torr, a conversion occurs freely between the di-σ and π bonded ethylene, and the two surface species co-exist. 25 It is also pointed that the π mode is the precursor and primary intermediate for undergoing the ethylene hydrogenation reaction. 26 In our work, these two different adsorption modes of 4-methyl-cyclohexene were examined on Pt (111) surface, same as on the cluster. As a matter of fact, the same conclusion can be drawn that the di-σ mode is more favorable at low coverage condition (here θ H = 0 ML). Otherwise, as for the supported cluster, the radical intermediate (c) in Table IV-2 is much less stable than the olefinic intermediates (a) and (b) by at least 16-32 kJ/mol. For this reason, we did not calculate all the possible radical intermediates, which exhibit di-σ dissociative-adsorption modes. The result is similar to the DFT study of Sabbe et al. 27 of cyclohexene on Pt(111). They found that the benzene hydrogenation reaction favored the path via 1,3-cyclohexadiene and cyclohexene, compared to the path via the 118 1,2,3,5-or 1,2,4,5-tetrahydrobenzene radicals, as also reported experimentally by Bera et al. 28 . In contrast, the study of Saeys et al. 29,30 reported a path via 1,3,5-trihydrobenzene and 1,2,3,5tetrahydrobenzene as predominant. Campbell et al. 19 found that the experimentally observed pathway for cyclohexane dehydrogenation on Pt(111) proceeds via adsorbed cyclohexene, again consistent with an ortho pathway as Sabbe et al. proposed. It is shown that the most stable adsorption mode for 4-methyl-cyclohexene is always the π mode on site V3 (32 kJ/mol), which exhibits a minimum dehydrogenation energy. That is probably due to the fact that the V3 site has less hydrogen atoms surrounded and causes a lower steric hindrance for the adsorption of molecule. As already discussed in the previous paragraph, it is also observed that the π mode is generally more favored than di-σ mode for a given site. For example, D r E dehyd,MCH is equal to 32 and 55 kJ/mol at V3 and V5 for the π mode, respectively.

Adsorption of 4-methylcyclohexene on Pt

Compared to the di-σ mode on both sites, D r E dehyd,MCH increases up to 74 kJ/mol.

The C3-C4 average distance for the π mode (1.42 Å) is much shorter than for the di-σ mode (1.48 Å). The C3-C4 (double bond) distance for the isolated methyl-cyclohexene molecule in gaseous phase measures 1.34 Å. This implies that the energy cost induced by the deformation of the molecule is likely higher in the di-σ mode. Meanwhile, the carbon-metal average distances for the di-σ mode (2.15 Å) is shorter than for the π mode (2.19 Å), which suggests that the di-σ bonded molecule exhibits higher interaction strength than π-bonded molecule. However, the compensation of these two forces between carbon-carbon bonds and carbon-metal bonds makes the π mode generally more favored than di-σ mode.

Static conformation analysis for the adsorption of 4-MCHe on the V3 site

It should also be noticed that for a given adsorption site and for the given π mode, several local energy minima of the system are found according to the orientation of the molecule.

Considering the most stable adsorption π mode for 4-methyl-cyclohexene on the V3 site, the energy variations for different conformations are presented respectively in Table IV-4 and Figure 121 IV-4. It should be emphasized that these conformations were obtained by merely rotating the molecule from their initial positions. It can be shown that in this case, the variation remains within an interval of 16 kJ/mol, which means that temperature effect may allow the molecule to explore these various metastable states on this given site. While the molecule rotates around the axe perpendicular to the π-bond, the energy is minimized when the carbon-metal distances are also minimized and well symmetric (2.17 and 2.19 Å, for V3-6 and V3-2 respectively). For the less stable conformation V3-5, the difference between these two distances reaches 0.14 Å. In addition, for the most stable cases (V3-6 and V3-2), the methyl group of the molecule remains the furthest from the cluster and from the support surface, which may thus minimize the steric hindrance.

Molecular Dynamics conformational analysis of the adsorption of 4-MCHe on the V3 site

To further refine the adsorption geometry on the V3 site, we also used ab initio molecular dynamics (AIMD), in order to explore more systematically the various possible conformations of 4-methyl-cyclohexene on Pt 13 H 6 /γ-Al 2 O 3 (100) at a given temperature, which enables to overcome the lowest energy barriers and thus to explore different potential minima.

The molecular dynamics approach explained in the Chapter III: Methodology, section 125

Depending on temperature, the potential energy fluctuates in a more or less large interval.

For T=500 K, energy range is about 400 kJ/mol; for T=800 K, energy range is about 800 kJ/mol and for T=1200 K, energy range exceeds 1200 kJ/mol. Moreover, the system at higher temperature becomes unstable and the system is rapidly destroyed (at t > 500 fs). This explains why we extract less points to be quenched on the profile at T=1200 K than at T=500 K. the dehydrogenation energies obtained after quenching the systems from the MD at 500 K reach lower energy values compared to 800 and 1200 K. In particular, two new configurations are found at 500 K and exhibit lower energies than the starting configuration (obtained from the static approach). The configuration (P-2) leads to a dehydrogenation energy of methylcyclohexane(g) to 4-methyl-cyclohexene equal to 28 kJ/mol and will be considered as the most stable system for the further study. The temperatures 800 K and 1200 K are probably too high and induce a progressive destabilization of the molecule (even after quench), which slightly desorbed from the cluster as illustrated by the insets in Figure IV-6.

Therefore, it is concluded that at T= 500 K, the whole AIMD calculations plus quench method enables to reach lower energy configurations. Consequently, for the other intermediates presented later, MD calculations are undertaken at T=500 K systematically. The energy and structural data for this optimized system before and after AIMD are compared in Table IV-5.

Table IV-5

Most relevant geometrical parameters for the system before and after MD at the PBE level 127 * : Atom Al 87 stands for the aluminum atom marked by green cycle on the structure images, the one which is linked with the Pt (S6) before and after MD.

Firstly, it can be noticed that the shape of the metal cluster differs significantly. The distances between Pt(V6-S4) atoms are obviously increased by an order of 0.26 Å and simultaneously the distances between the metal cluster and the support are also changed, as it can be particularly observed that Pt(S6)-Al(87) has been raised because of the increase of Pt(V6-S4) distance. Meanwhile a migration of hydrogen (H6) atom from site V6 to V4 happened.

Nevertheless, the molecule remains almost in a similar position becoming slightly closer to the metallic cluster (slightly shorter M-C distances).

On purpose of figuring out the effect of this deformation on the energy, the decomposition of the energy into various components has been performed. The dehydrogenation energy was decomposed to several parts, including the metal cluster deformation, the support deformation, the interaction of the metal cluster with adsorbed molecule, the interaction of the support with the metal cluster. The detailed analysis is reported in Appendix-IV-2. In summary, the separation of the metal cluster and the support is highly endothermic and requires + 980 kJ/mol. MD calculations weakened the interaction (decrease about 131 kJ/mol) between the metal cluster and the support. But these positive energies are mostly compensated by the final recombination energies of the metal cluster and the support. Whereas the deformation energy of the support is modest, the deformation of the metal cluster after MD reveals a gain on electronic energy of 81 kJ/mol. From this analysis, it can be concluded that MD calculations give access to the deformation of the metal cluster in the presence of the adsorbed intermediate, which can stabilize the system and needs to be considered during the simulation of other intermediates. *For the radical species, the cluster keeps one more hydrogen atom transferred from the molecule (7 hydrogen atoms in total on the cluster in these cases). It must be noticed that the π mode adsorption becomes the predominant adsorption mode for methyl-cyclohexadiene and toluene. Ma et al. 31 and Morin et al. 32,33 found for 1,3-cyclohexadiene 131 and benzene adsorbed on Pt (111) surface, that the most stable adsorption modes are 1,4-di-σ-2,3π and bri 2π2σ, respectively. This result may again highlight the specific behavior of the cluster.

Stability of other intermediates along the dehydrogenation pathway, comparison with Pt(111) surface

Moreover a reconstruction of the cluster takes place in the course of the dehydrogenation reaction, as we can see from Figure IV-8. These reconstructions come up with several hydrogen migrations on the cluster, and with local structural reconstruction of the cluster itself, which aims at stabilizing the system by adapting its morphology and H locations as a function of the adsorption modes of the molecules. At this point, three cluster morphologies are observed, which implies that these reconstruction steps and hydrogen migration steps along with C-H cleavage steps must be considered for studying the reaction mechanism.

To enrich our understanding, we simultaneously achieved a complementary study of Table IV-7 shows that adsorption configurations of the relevant intermediates on Pt (111)

significantly differ from those obtained on the cluster. The results on the (111) surface agree with published studies. 32,33,31 The di-σ mode of methyl-cyclohexene is more favorable on the Pt (111)

surface. Meanwhile, a conjugated σ-π adsorption mode has been found for both methylcyclohexadiene and toluene, compared to the π mode on the cluster. One can explain this phenomenon related to the hydrogen coverage in the case that we investigate here for Pt (111), a θ H = 0 ML favors inherently the σ mode. The average bond length decreases indicating the formation of a double bond on the molecule. Moreover, the distance between the molecule and 133 the metal surface decreases in the course of the dehydrogenation, suggesting a stronger and stronger interaction between the molecule and the metal. At last, we find that the dehydrogenation energies for the most stable intermediates on cluster (Table IV-5) are less positive than those on Pt (111) at the PBE level, which suggests that our cluster model stabilizes better the intermediates, referring to the conventional Pt (111) ideal surface at the PBE level.

Effect of the functional : PBE vs. PBE-dDsC

The most relevant reaction pathway (with intermediates (b), (c), (d), (g), (h) and (k) in A similar work was performed for the MCH physisorption on the Pt (111) surface with two configurations: vertical and parallel (Table IV-9). The gain on stability is once again underlined by applying PBE-dDsC functional and the parallel configuration is again more enhanced than the vertical one. Nevertheless, the decrease of energy on Pt (111) surface for the parallel or vertical configurations (93 and 50 kJ/mol) is much stronger than those on the cluster (62 and 20 kJ/mol). This suggests that the platinum surface has a stronger stabilizing effect on intermolecular interactions than the γ-Al 2 O 3 support.

{ } { } 3 2 13 3 2 13 ) ( / / O Al Pt MCH O Al Pt MCH g - - ® - + g g 3 2 13 ) ( 3 2 13 ) ( / / , O Al Pt MCH O Al Pt MCH MCH ads r E E E E g g - - - - - = D g g Equation (IV-2) 134

Effect of the functional on the MCH physisorption step

{ } { } Pt MCH Pt MCH - ® + Pt MCH Pt MCH MCH ads r E E E E g g - - = D - ) ( ) ( ,

Equation (IV-3)

Table IV- support. Moreover, this tremendous decrease on the Pt (111) surface results in similar stabilities for intermediates on both surface and cluster systems with the PBE-dDsC functional, which was not the case with the PBE functional. The enhanced stabilities of the intermediates on the supported cluster previously found with the PBE functional is thus not confirmed by the PBE-dDsC level.

138

Table IV-11 Adsorption modes, sites and dehydrogenation electronic energies for key intermediates adsorbed on the Pt(111) surface along the dehydrogenation path at the PBE-dDsC level, with energies calculated with the PBE functional in parenthesis.

Considering the important role of dispersion correctionsin the energetics of the dehydrogenation reaction, in the following section the whole reaction path will be first analyzed by using PBE-dDsC. At the end of this contribution (section IV.9.), we will come back to the comparison between the two energy profiles obtained with PBE and PBE-dDsC functionals.

Detailed reaction mechanism and free energy profiles of methyl-cyclohexane dehydrogenation over Pt 13 H 6 /γ-Al 2 O 3 (100) with the PBE-dDsC functional

In what follows, we will estimate electronic energy, enthalpy, entropy and Gibbs free energy for each intermediate and transition state, with the PBE-dDsC functional. The ultimate 139 goal is to deduce forward and backward rate constants for each elementary step. For that purpose, we will consider firstly a temperature of 625 K, since this temperature is used in kinetic experiments reported in the literature 11,12,34 and also later for our catalytic tests. In addition, since the reforming process is generally performed at a higher temperature close to 800K, we will also consider it as a complementary analysis. This may also allow us to check the sensitivity of our model with respect to this reaction condition. Note that in practice, if the geometries and energies were determined at the PBE-dDsC level, the vibrational analysis required for the estimation of enthalpies and entropies was most of the time performed at the PBE level, except when some significant geometry changes were observed between both functionals. Specifically, the five first

structures

General feature on temperature influence

The general view of the electronic energy profile at 0 K and the free energy profiles for two temperatures are illustrated in Figure IV-10, while Table IV-12 reports the corresponding name of the intermediates and elementary steps identified along the reaction pathway. 625K and 800K with the electronic energy profile at 0 K, a crossing point at intermediate methyl-cyclohexenyl+H (F) is observed for the three profiles which reflect an inversion in the relative stabilities of the intermediates formed. Before (F), the increase of temperature destabilizes all intermediates, whereas beyond (F) it stabilizes the profile. This trend is not related to the enthalpy terms (including vibrational, rotational and translational contributions), which variation is very small (3 kJ/mol) for these two temperatures 625 K and 800 K. On the other hand, it is mainly due to the entropy term (TΔS). Hence, before the formation of intermediate (F), in particular for the first MCH physisorption step, the intermediate dehydrogenation reactions are generally exothermic at 0 K and become more and more endergonic when temperature increases. After the formation of intermediate (F), this thermodynamic trend shifts. As three molecules of H 2 are formed and released in gas phase sequentially, the entropy of the system increases and as a consequence the Gibbs free dehydrogenation energy decreases both at 625 K and 800 K, compared to the opposite profile at 0 K. Notably, for the H 2 desorption steps (CàD, HàI, MàN) and toluene molecule (N) desorption step, the temperature effect is significantly crucial.

Table IV-12 Various intermediates and nature of elementary steps along the dehydrogenation of methyl-cyclohexane over

These steps become less endergonic when the temperature goes from 0 K to 800 K, related to the entropic effects. Especially for the last toluene desorption steps, the Gibbs free energy decrease of this desorption step from 0 K to 800 K is about 170 kJ/mol. This information can be used to explain why the industrial reforming process employs preferentially this temperature at 800 K, not only because the overall reaction is endothermic, but also because toluene desorption becomes much easier above 800 K. A similar analysis can be made for the three H 2 desorption steps, which become less endergonic at high temperature due to the same entropic effects. In other word, the increase of temperature favors the desorption steps but of course disfavors the 143 MCH adsorption step for entropic reasons. At last, this temperature impact has little effect on the other elementary steps (C-H bond cleavage, cluster reconstruction and H atom migration steps).

In order to make a detailed analysis of the complex reaction mechanism, all the elementary steps will be discussed in what follows according to the 5 different families highlighted in Table IV Gibbs free energies (Δ r G, Δ r G ‡ ) will be commented for each steps at 625 K, using as a reference the reactant of the given step.

Methyl-cyclohexane adsorption and toluene desorption

The methyl-cyclohexane adsorption occurs through a physisorption step, which is a precursor state before the first C-H bond cleavage. This step is exothermic (Δ r H = -40 kJ/mol) and endergonic (Δ r G = 51 kJ/mol). The large difference between enthalpy and free energy is due to the complete loss of rotational and translational entropies for this physisorption step, which corresponds to a decrease of 91 kJ/mol from the gas phase to the adsorbed state. Note that we make the assumption that methyl-cyclohexane is an immobile complex on the catalytic surface.

However, this entropy loss is at the origin of the positive Gibbs free energy and causes a high free energy barrier for the system. This barrier depends on the temperature (Figure IV-10): the higher the temperature, the higher the barrier. Note: (i) Before intermediate (A) (during step (1)), there is one extra step, where we consider a preliminary cluster reconstruction from the original structure to the deformed one. This step will not be presented in the following reaction energy profiles and is assumed as merged within a single step (1). An analysis has been done for this step, Reconstruction A in section 6.4.

(ii) The same occurs for the deformed cluster after the last toluene desorption step, from the deformed cluster of (N) alone to the original cluster alone, a Reconstruction N 1,2 happens at the end of reaction path. The analysis of this step is also reported in the section 6.4.

By contrast, the toluene desorption step is endothermic and endergonic with a large gain of entropy due to the release of toluene from the adsorbed state to gas phase. The free energy variation of this step is also strongly temperature dependent (Figure IV-10): the higher the temperature, the lower the Gibbs free energy barrier for toluene desorption. Notably, the 3π adsorption mode of toluene on the cluster makes it rather complicated to study the transition state of the desorption step to gas phase.

As indicated in the note of Table IV-13, one should underline that the energies reported here include also the cluster reconstruction step as illustrated in Figure IV-10. It is however interesting to decoupled this two steps from a thermodynamic point of view: this will be done in section 6.4. 145 on free activation energy between these two steps is very small (8 kJ/mol) and their activation free energy is much higher than the other four C-H bond cleavage steps. So far, it is hard to make conclusion on the rate-determining step because these two are very competitive. Moreover, the activation data among these six steps are widespread over large enthalpy and free energy intervals (19-98 kJ/mol for enthalpies and 33-95 kJ/mol for free energies) which allows us to check if a Brønsted-Evans-Polanyi (BEP) linear relationship [35][36][37] exists here. This 147 relation aims to rationalize possible correlations between the reaction activation energy (Δ r E ‡ ) and the reaction energy (Δ r E) within a given nature of elementary steps. This method was already employed to reduce computational burden of complex system for the bond breakings of C-O, C-H and C-C of different reaction type, by using these linear relationships. 31,[38][39][40][41] It is described by the following equation :

C-H bond cleavage Table IV-14 Thermodynamic and kinetic data for the C-H bond cleavage elementary steps involved in the methylcyclohexane dehydrogenation mechanism over

Δ r E Δ r H TΔ r S Δ r G Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ A à B TS a -
Δ r E ‡ = αΔ r E + β Equation (IV-4)
We explored if the Brønsted-Evans-Polanyi (BEP) linear relationship holds for the six C-

H cleavage steps (forward reactions, reported in Table IV-15 and Figure IV-12). As shown in

Table IV-15, the electronic activation energy and enthalpy exhibit a relatively better linear correlation with similar coefficients α and β, compared to Gibbs free energy. The Gibbs free energy does not follow such a relationship, which is related to entropy effects. For a cluster system with a high fluctionality character (as we will see below), the enthalpy and entropy can hardly be expected to vary linearly when it is not simply related to the dissociation of a bond (C-H) but also depending on the cluster morphology. This linear relationship is also investigated on the Pt (111) surface, presented in the same Table IV-12. A very good linearity is found for E, H and G. This BEP comparison between the two systems once again emphasizes that the cluster system cannot be described simply as the Pt (111) surface because of its peculiar fluctionality, inducing some complexity. If we now look at Figure IV-12, the BEP linear relationship that we obtained for the reaction free energies and activation free energies seems to enable to have a better linear behavior without two exceptional points, the points corresponding to first C-H bond cleavage step and the last one. It suggests that our calculations may perhaps underestimate the first C-H bond cleavage activation free energy and overestimate the last one. These two steps 148 involved intermediates fully interacting with the support, or fully interacting with the platinum surface, which may be at the origin of various impacts of the PBE-dDsC functional. If we look at the backward reaction, activation enthalpies and free energies exhibit much smaller variation intervals from one step to another than those for forward reactions (around 30 kJ/mol of gap). Particularly, the backward activation enthalpies are all higher than the forward ones, which makes the corresponding transition states rather "early". As for free energy, by the 149 influence of entropies, most of them are "early" states except for the third C-H cleavage (D à E) which shows an "intermediate" transition states (the activation Gibbs free energies in both directions are barely the same). Furthermore, theoretically, these "early" states are supposed to be structurally similar to initial states because they are energetically closer to initial states. But in our case, due to the complexity of the system and reaction elementary step, the structural resemblance of the transition state falls in between the reactant and product structures, where it reflects the partial similarities of both, presented in At this stage, it should be also underlined that during the transition states search for C-H bond cleavage involving methyl-cyclohexenyl (G), methyl-cyclohexadiene (J), and methylcyclohexadienyl (L), several metastable precursor states (E, F, J and K) have been found so that the NEB approach can be successfully achieved to locate a relevant saddle point. This is often due to steric hindrances induced by the methyl group and/or hydrogen atoms on the cluster that implies either cluster reconstruction or H migration. Thus, in the two following sections, we analyze the elementary steps involved in cluster reconstruction and H migration, which are often pre-required step for the C-H bond cleavages.

Cluster reconstruction

As we pointed out before and in a previous theoretical study, 6 the reaction environment induces a morphology change of the Pt 13 cluster. In the present case, we find that four main cluster reconstructions occur and lead to three morphologies distinct from the initial structure along the dehydrogenation path (including adsorption A and desorption N steps). These deformed clusters obtained by molecular dynamics stabilize the adsorbed intermediates in the course of dehydrogenation reaction, which reflects the fluctionality of the supported cluster contrasting with the ideal Pt(111) surface.

Table IV-16 Thermodynamic and kinetic data for the cluster reconstruction steps at the PBE-dDsC level

It should be first noticed that the initial cluster (with only 6 H atoms adsorbed on it) does not remain as the most stable when the reactant, methyl-cyclohexyl, methyl-cyclohexene and toluene are adsorbed on it. So at the very beginning of the reaction, the cluster slightly reconstructs before methyl-cyclohexyl is formed (green cluster in Figure IV -10). In that case, a preliminary reconstruction step may occur between the grey cluster and the green cluster (Figure step occurs before methyl-cyclohexane adsorption (cluster reconstruction from grey to green without adsorbed molecule), the electronic energy cost is very similar: Δ r E= +37 kJ/mol, which means that the methylcyclohexane physisorption does not impact strongly the cluster reconstruction. At the same time, the adsorption energies of methyl-cyclohexane (Δ r E= -82 before the reconstruction vs -80 kJ/mol after the reconstruction) does not depend strongly whether the cluster is reconstructed or not. So, the reconstruction might occur either before or after methylcyclohexane physisorption.

Δ r E Δ r H TΔ r S Δ r G Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ Recons. A 35 32 7 25 -- -- F à G TS f - 18
Regarding the last step, the toluene molecule is proved to be more stable on the deformed cluster (blue cluster in Figure IV-10) than on the initial cluster found by AIMD. However, once toluene is desorbed from the blue cluster, there is actually a supplementary step to restore the morphology of the initial cluster (grey cluster in These steps (Figure IV-15) were investigated either to stabilize the intermediates formed on the cluster (K à L), or to release one occupied Pt site required for the next step (E à F). In this latter case, this reveals that increasing the hydrogen coverage can hinder the dehydrogenation reaction. By the fact that we chose a non-zero but rather low initial hydrogen coverage as a modeling point, the reaction pathway may be affected if higher hydrogen coverage would be varied. For these reasons, these two elementary steps have quite different reaction energies (Table IV-17): E à F is endothermic while K à L is exothermic. They are both exergonic. However, despite these slight differences, forward activation enthalpies and activation free energies are rather similar. The Gibbs free activation energies at 41-42 kJ/mol are generally smaller than those of C-H bond cleavages but equal or higher than those of cluster reconstructions. In order to keep the hydrogen coverage constant (θ H = 6 hydrogen atoms) on the cluster, we remove the two extra hydrogen atoms (from the system exhibiting 8 adsorbed hydrogen atoms) after their dissociation from each intermediate, releasing H 2 in the gas phase. These three H 2 molecule desorption steps are all endothermic and endergonic (Table IV -18), despite a gain of rotational and translational entropy (as already mentioned for toluene desorption step). The reaction Gibbs free energy of these steps varies consequentially depending on the reaction temperature: the higher the temperature, the lower the barrier. The search of the transition state for the first H 2 desorption has been made and is presented in Appendix-IV-5. In summary, the energy of transition state is very close to the final state. It also means if one look at the backward reaction of this desorption step, the adsorption of H 2 molecule onto the cluster, this adsorption step is not activated. It was also already reported on the Pt surface, the adsorption step of hydrogen reveals no activation energy. 43,44 As a result, the activation free energies for the H 2 molecule desorption steps are considered identical to their reaction free energy in forward steps and non-activated (Δ r G ‡ = 0) for backward steps. 156

Δ r E Δ r H TΔ r S Δ r G Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ E à F TS e 5 6

Effect of the functional on the Gibbs free energy profile over Pt 13 H 6 /γ-Al 2 O 3 (100): PBE vs PBE-dDsC

In order to take into account the dispersion forces into account, the whole reaction pathway has been calculated so far by performing PBE-dDsC functional. However, it may be interesting to highlight the cases (if any) where the PBE-dDsC functional is critical to be applied with respect to PBE. To conclude, the choice of the exchange correlation functional affects both the free energy profile and part of the reaction mechanism. The most demanding step is still the same but overall, the choice of the functional may affect the results of further kinetic modeling. In order to enrich the discussion of the results obtained on the supported cluster, we report here a parallel study on the ideal Pt(111) surface. Thus, we investigate a similar sequential C-H bond cleavage reaction mechanism of methyl-cyclohexane over this ideal surface. One key 160 difference is the absence of strong reconstruction phenomenon. Moreover, results for the hydrogenation reaction of benzene and dehydrogenation reaction of cyclohexane previously reported in the literature 30,33,18,27 In particular, for the hydrogenation of benzene another reaction pathway («ortho» Path 33 ) has been proposed in the literature. Instead of forming the methyl-cyclohexene molecule adsorbed on Pt (111), the two carbon atoms which form di-σ bonds with platinum atoms should be on the meta position and then go through an ipso adsorption configuration (Table IV -20).

Detailed reaction mechanism and free energy profile of methyl

These intermediate configurations have been also investigated in our case. However, they are found to be relatively less stable in terms of electronic energies when compared to the intermediates D', E' and F' at the PBE level (Table IV -20). In addition, the ipso adsorption configuration cannot be stabilized during the geometry optimization and turned to pass directly to the configuration of C 7 H 10 + 2H. For that reason Table IV The enthalpy of intermediates does not vary very much when the temperature goes from 625 to 800 K (around 5 kJ/mol increase on enthalpy), similar to that on the cluster. Once again, the free energies are more strongly affected by the temperature change, which is linked to the sensibility of entropy term depending on the temperature, especially for the MCH adsorption step (MCH (g) à A'), the toluene desorption step (J' à Tol (g) ) and the H 2 desorption steps (C' à D', F' à I' and I' à J'). At 0 K, the first physisorption step of methyl-cyclohexane molecule is exothermic, while increasing the temperature, the free energy of this step increases because of the increase of entropy loss (TΔ r S<0). On the contrary for the molecule desorption steps, these steps present a gain of entropy (TΔ r S>0). In particular, the H 2 and toluene desorption free energies at 163 toluene desorption involves a significantly huge drop in the profile form 0 K to 800 K because of this entropy effect. Last but not least, the same shift on free energy also occurs after the second H 2 desorption, similar to what we observed on the cluster in Figure IV-10. This phenomenon depends on the temperature but not on the type of catalyst surface or reaction mechanism. It can be used to explain the fact that at high temperature, the molecule adsorption step can be difficult to achieve but once the molecule adsorbs on the surface, the reaction can be more easily performed at high temperature to give the product. Note that we did not investigate here the effect of hydrogen coverage on the Pt (111) surface, which may also affect the free energy profiles.

Table IV-21 reports the thermodynamic and kinetic data for all the elementary steps at 625 K calculated at the PBE-dDsC level. The temperature is chosen at 625 K in order to make a comparison with the investigation performed on the cluster. The H 2 desorption steps are all endothermic and endergonic at the temperature of 625 K, as well as the desorption step of toluene at the last of reaction. The reaction free energy of these steps are also temperature-dependent because of the gain of entropy. The hydrogen atoms obtained by dissociation of the H 2 molecule are co-adsorbed temporally on Pt (111) in a threefold hollow site, which has been already proved to be the most stable adsorption mode on this metal face 45 . The activation energy of hydrogen desorption has been estimated experimentally at about 40 kJ/mol 46 . From a previous theoretical DFT work, the hydrogen desorption electronic activation energy was determined as 53 kJ/mol at high hydrogen coverage (7/6 of a ML) in a small unit cell 47 . The values we calculate (Table 18) are generally higher than these two previously mentioned values, which can likely be assigned to the presence of the hydrocarbon intermediates co-adsorbed with the 2 hydrogen atoms at the surface. (Appendix-IV-8) but this stabilization is eliminated at the PBE-dDsC level. In a general manner, it is hard to conclude about the system which will catalyze the reaction most efficiently, from the free energy diagrams only. The profiles are very close at the beginning of the reaction but the cluster still stabilizes more strongly the intermediates (and most transition states) starting from H (methyl-cyclohexadiene). This could be in favor of the supported cluster but the very strong stabilization of adsorbed toluene could also be a drawback, rendering the desorption of the product limiting in certain conditions. Kinetic modeling is required to conclude on the respective reactivities of the two catalytic systems.

Δ r E Δ r H TΔ r S Δ r G Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ Δ r E ‡ Δ r H ‡ TΔ r S ‡ Δ r G ‡ MCH (g) à A' -- -105 -104 -105 1 -- -- -- -- -- -- -- -- A' à B' TS a' 9 - 3
I' à J' + H 2 -- 77 82 75 7 -- -- -- -- -- -- -- -- J' à Tol (g) -- 192
So far, the importance of applying the PBE-dDsC functional is thus emphasized both on the cluster and the surface. For next step to integrate our ab initio results into kinetic models, the parameters obtained by PBE-dDsC will be used.

171

(3) Depending on the geometries obtained by DFT calculations for each intermediate, the cluster exhibits an obvious fluctionality along the reaction path, which tends to stabilize the whole system.

(4) The temperature effect is related to entropy, which mostly affects the molecule (methyl-cyclohexane, H 2 and toluene) adsorption/desorption steps on both systems.

( 172

The following step of the study will be dedicated to establishing a kinetic model from the present mechanism, where the calculation of rate constants related to each activation energy and corresponding to each elementary step will be proceeded from the present ab initio calculations.

The kinetic rate constants determined by ab initio will be incorporated in a Langmuir-Hinshelwood (LH) kinetic model, based on the stepwise dehydrogenation mechanism: rate equations will be integrated and lead to a quantification of the expected rate of formation of the product, sensitive steps and reaction apparent activation energy and enthalpy. Such a modeling approach, from elementary steps studied ab initio to the calculation of macroscopic data, allow us to compare with the conventional kinetic fitting modeling approaches which have already been reported in the literature. 12,15 As the objectives of the next chapter, we will undertake catalytic tests to compare with the ab initio kinetic modeling.

Appendix-IV 1. Comparison on different adsorption modes of MCHe and ethylene, and effect of hydrogen coverage

Raybaud et al. 21 reported that for ethylene on Pt 13 H 6 /γ-Al 2 O 3 (100) the di-σ mode was preferred.

Two intricate effects are suspected to be the cause of the different behavior observed with the 4-Methyl-cyclohexene:

1) the effect of hydrogen coverage on the metal surface and the substituent effect (the 2 hydrogen atoms were maintained on the cluster in the case of the study of Raybaud et al.).

2) the intrinsic nature of the molecules.

For that purpose, ethylene and 4-methyl-cyclohexene have been adsorbed on Pt 13 H 6 /γ-Al 2 O 3 (100) and Pt 13 /γ-Al 2 O 3 (100) (Equation IV-5 with A = MCHe, ethylene).

{ } { } 6 , 0 / / 3 2 13 3 2 13 ) ( = - - ® - + n O Al H Pt A O Al H Pt A n n g g g Equation (IV-5)
The adsorption energy of these two molecules on the metal face has been calculated as E ads,A :

Adsorption energy : Note: for the adsorption, the di-σ is on the site V3-V5 and the π mode is on V3.

{ } { } 6 , 0 ) ( / / ) ( 3 2 13 3 2 13 , ) ( = - - - - - = n A E O Al H Pt E O Al H Pt A E E g n n A ads g g g Equation (IV-6)
The calculated adsorption energies of these two molecules in both di-σ and π modes are reported in Table 21. It can be observed that for both molecules ethylene and 4-MCHe, with 6 coadsorbed hydrogen atoms, the π mode is well favored. For n=0, the di-σ mode turns out to be more stable for ethylene, while for 4-MCHe the two modes remain energetically competitive.

This result proves that the hydrogen coverage impacts the adsorption energies and modes of the two molecules. When there is less hydrogen atom on the metal surface, the molecule seems to prefer to sit on two metal sites. However, it should be underlined that for 4-MCHe, the di-σ mode is intrinsically significantly less favored in general compared to ethylene (39 kJ/mol for the difference on electronic energy for n =6 and 36 kJ/mol for n =0). The two adsorption energies are very close, while for ethylene, the difference of energy for these two adsorption modes at both hydrogen coverage is more pronounced. At the same time, this means that ethylene is more sensible for the hydrogen coverage on the metal surface than 4-MCHe. The former result by Raybaud et al. shows that the di-σ mode can also be possible even at higher H coverage which may reveal also an impact of the position of hydrogen atoms on the adsorption mode. Figure 22 shows the most stable geometry of each system calculated. Step (0) is the transformation from the reference catalytic system to the deformed catalyst (induced by MCHe after MD), which correspond to +40 kJ/mol, confirming that the reference catalyst model is the most stable one. For step (1), the energy to 179 separate the metal cluster and the support is highly endothermic and requires +980 kJ/mol. If we compare this value to the one for step (1'), it is found that the MD calculations weakened the interaction (+849 kJ/mol) between the metal cluster and the support. These endothermic energies are mostly compensated by the final recombination energies at step ( 6) and (6'). Steps (2") and

(3") correspond to the deformation energy of the support and the cluster (in gas phase). Whereas the deformation energy of the support is modest, the cluster after MD tends to be more stable (negative deformation energy of -81 kJ/mol). After that, the dehydrogenation of MCH (g) to 4-MCHe is presented by step ( 4) and (4') , respectively on the cluster before and after MD: both exhibit modest energy change. However, as for step (3''), step ( 5) is exothermic by -94 kJ/mol: the difference of stability of the metal cluster is still the dominant reason to explain that deformed system is more stable. But once the system is recombined, the difference on the stability stays very small, presented by step (7) = -4 kJ/mol. So by now, it can be concluded that the MD calculations stabilize mainly the metallic cluster in the presence of the molecule and seem to reduce the interaction between the metal and the support. ). There are also a difference on the energy term between these two systems concerning the three H 2 desorption steps and the toluene desorption step. Those steps are found to be endergonic on the cluster while they turn to be slightly exergonic on the (111) surface. The thermochemistry of these steps is directly connected to the reaction conditions (hydrogen coverage and temperature) as already studied by Mager-Maury et al. 6 . So the endergonicity of these steps may depend on our initial choice of hydrogen coverage. Especially, our cluster system has a higher hydrogen coverage compared to the Pt (111) surface (zero initial hydrogen coverage). On the one hand, the same number of initial hydrogen atom on the cluster (θ H = 6) cannot be easily adopted for the surface system in reforming conditions. 6 On the other hand, we have already tried some investigation on zero-hydrogen-coverage cluster system to compare with the non-hydrogenated Pt(111), but the cluster structure turned to be completely deformed, even dislocated, by performing a Molecular Dynamic study at 500 K, which rendered the strict comparison impossible. Moreover, it should also take into account once again the impact of dispersion forces while calculating the energy for those steps. The first part of this chapter is devoted to the experimental investigation of the kinetics of the reaction, to obtain reliable and reference data to be compared with ab initio based kinetic modeling, which comes in second part of the chapter. In this second kinetic modeling part, a preliminary Power-law kinetic study widely applied in many works, will be depicted firstly. Then here follows an extended Langmuir Hinshelwood (LH) kinetic study by using the DFT mechanistic model parameterized by ab initio reaction constants, acquired in Chapter IV, in order to unravel the reaction kinetics by considering the various possible rate-determining steps. All the kinetic models will be compared with our experiments, in terms of reaction rates values, reaction rates dependence upon hydrogen partial pressure, methyl-cyclohexane partial pressure, and conversion. The apparent reaction activation enthalpy will also be the object of a comparison between experiments and models. The surface species coverage will also be analysed in some cases.

Catalytic experiment

The experiments are performed in the conditions reported in Chapter III: Computational and Experimental Methodology, section 2..

Temperature effect

Four reaction temperatures (320, 340, 360 and 380°C) were investigated by Test-1.

Meanwhile the variable temperature range is also crucial for establishing the Arrhenius and Eyring plots. 191

Very satisfactory linear relationships are obtained (both with R 2 =0.997, nearly 1). From the two slopes and by using the Equation (III-60) and (III-62) in Chapter III : Computational and Experimental Methodology, section 2.2.4, we deduce that the apparent activation energy E a is equal to 200 kJ/mol, and the apparent activation enthalpy Δ r H ‡ is equal to 195 kJ/mol with an apparent activation entropy of 0.056 kJ/(mol.K), calculated from Erying plot by determining the constant in Equation (III-62), which can be expressed as const. = ln(

k B h )+ ∆ r S ‡ R .
These apparent activation enthalpies will be compared with the values determined by using the ab initio kinetic models described in the next chapter. At this stage, it is however interesting to recall the values obtained in the literature corresponding to the conditions reported in Table 1. Sinfelt et al. 1 found experimentally an activation energy of 138 kJ/mol for 0.3 wt% platinum-on-alumina catalyst, at reaction temperatures enclosed between 315 and 372 °C with the methyl-cyclohexane partial pressures 0.36 bar and hydrogen pressure 1.1 bar. Maria et al. 2 found an activation energy of 220 kJ/mol for sulfided platinum on alumina reforming catalyst at reaction temperatures of 282-309 °C, with a hydrogen to methyl-cyclohexane ratio of 2.5-10, total pressure 7 atm and the space time of (1) 61; (2) 82; (3) 123; (4) 246 (g cata .s/g MCH ).

Alhumaidan et al. 3 From Test-1 to Test-6 in the Table III- commented: compared to the normalized toluene yield containing the gaseous phase, the one calculated only in liquid phase is overestimated while the non-normalized one containing the gaseous phase is underestimated. This means that the toluene yield in gaseous phase is lower than that in liquid phase and without the normalization, the non-normalized conversions are thus underestimated by compensating the gaseous phase part with the yield in liquid phase, if this impact depending on mass balance is not eliminated. The conversion increases rapidly till space time reaches 40 g cata .s/g MCH . It increases more slowly for space time greater than 50 g cata .s/g MCH .

Notably, the reaction kinetics at the very beginning (t < 25 g cata .s/g MCH ) are not studied because of the constraints of limit operating reaction conditions due to the set-up. Nevertheless, we still managed to fit a simple Power-law type reaction rate fitting model by using these data as described later in this chapter, section 2.1,. In the following, normalized values of methylcyclohexane conversion to toluene will be reported.

Figure V-4 Methyl-cyclohexane conversion to toluene by the evolution of space time

The methyl-cyclohexane conversions to toluene as a function of the reaction space time obtained from Tests 1 to 6 are thus compared with the literature, 5,4 in Figure V-4. First of all, it can be noticed that a high reactant conversion is reached in a much smaller (by a factor of 10 5 ) space time in the study of Usman et al., 4 whereas conversion levels remain lower in the work of Van Trimpont et al.. 5 That could be probably explained by the different reaction conditions employed in these three works summarized in Table V-1. In particular, Usman et al. 4 used a higher platinum content in the catalyst and a higher temperature. Moreover, the low hydrogen partial pressure can also lead to higher reaction rates (see next section). If comparing the conversions at steady state, it can be concluded that higher temperature leads to higher conversion to toluene. The work of Van Trimpont et al. 5 was performed on a sulfided catalyst, which can largely reduce the reactivity of the catalyst. That would explain the conversion The impact of the partial pressure of methyl-cyclohexane and hydrogen is crucial to be investigated. It was already discussed in the literature 6,5,7 . So, we addressed those effects thanks to the conditions of Test-7 to Test-10 combined with Test-1. Figure V-5(a) depicts the evolution of the conversion to toluene as a function of the hydrogen partial pressure at a constant methylcyclohexane partial pressure of 0.8 bar. Conventionally, the conversion curve should reach a maximum level at one critical hydrogen pressure. 7,8 A possible explanation is that above this critical hydrogen partial pressure, the conversion decreases by increasing hydrogen pressure because of the reverse reaction and hydrogen "poisoning" of the catalyst. 8 The low H 2 pressure regime is more difficult to understand. It can be due to deactivation phenomenon induced by coking when H 2 pressure becomes too low. However, a fitting model carried out by Verstraete 6 by reproducing the kinetic model of Van Trimpont 5 provided us a similar conversion curve regarding hydrogen pressure, without taking the coke formation into account. The origin of this phenomenon will be discussed in detail in section 2.. here after. This can be probably explained by the saturation of active sites on the catalyst when the reactant surface concentration becomes too high.

MCH and H2 partial pressures effects

This phenomenon has been observed during our test by

198

We then calculated initial reaction rates by applying Equation (III-63), using these relatively high conversions illustrated in Figure V-5 to estimate approximately the conversion curve slope at the initial reaction time (t=0). Note that with such a method, we likely underestimate somehow the initial reaction rate. Sinfelt 1 and Van Trimpont et al. 5 performed similar studies, on the investigation of the impact of methyl-cyclohexane and hydrogen partial pressure on the reaction rate. Hence, we make a comparison of these studies with ours. The different catalyst types and reaction conditions and studied space time are recalled in Table V-2. (a), we notice that our initial reaction rates are about 5 to 10 times higher than those of Sinfelt and Van Trimpont. As previously explained, this is probably because that Van Trimpont et al.

used catalyst that was presulfided and the reactivity of which was reduced with respect to our catalyst. For Sinfelt, the catalyst seems to be the same as ours but the reaction temperature is lower and especially, the methyl-cyclohexane partial pressure chosen for the study of the effect of the hydrogen partial pressure is twice lower than ours. Moreover, these two previous studies, also less exhaustive in terms of interval of hydrogen partial pressure than ours in

Conclusions and Perspectives

So far, the catalytic tests on methyl-cyclohexane dehydrogenation reaction were achieved in a fixed bed reactor, with the following catalyst : 0.3 wt% platinum and 0.12 wt% chlorine on γ-Al 2 O 3 support. The temperature effect has been discussed at four different levels (320, 340, 360, 380 °C) and by applying Arrhenius plot and Eyring plot, we managed to determine the reaction activation energy and activation enthalpy, E a = 200 kJ/mol and Δ r H ‡ = 195 kJ/mol, respectively.

These experimental activation energy and enthalpy will be confronted with the values obtained by the kinetic model parameterized by ab initio kinetic constants in the next section.

Then, the weight hourly space velocity was set up for a value range from 40 -150 g MCH .h - 1 .g cata -1 , in order to deduce the reactant conversion as a function of reaction space time. This evolution permits to describe the reaction kinetics in terms of reaction space time.

The impacts of hydrogen and methyl-cyclohexane partial pressures on conversion and initial reaction rates were unravelled. The comparison with previous works in the literature showed a qualitative agreement in terms of the curve shape. However, regarding reaction rates, the different reaction conditions, especially the pressure ranges and the different type of catalysts (either pre-sulfided or not) made it different quantitatively.

For the next steps of our study, these experimental data will be used firstly to help us to established a power-law type reaction rate fitting model. Secondly, the Langmuir-Hinshelwood (LH) type kinetic model will be built by using the ab initio calculation results and finally the discussion will be focused on the confrontation between these experimental results and the LH modelling results, in order to validate our mechanistic investigation on the dehydrogenation of methyl-cyclohexane carried out by DFT calculations. in that section. A power-law rate reaction is thus rewritten by taking into account the reaction order in MCH, called n, at the corresponding reaction conditions (total pressure of 13 bar, a H 2 /HC molar ratio equals 15.3 and temperature at 360 K). However, this new approach does not provide any information about the reaction mechanism but does correlate the effect of the reactant concentration on the experimental reaction rate. We have then:

r = - dP MCH dt = kP MCH n ⟺ dP MCH P MCH n = -kdt t 0 P MCH P MCH,0 ⟹ P MCH = P MCH,0 1-n -1-n kt 1 1-n ⟹ P MCH,0 -P MCH P MCH,0 = X MCH→Tol = 1-1- 1-n kt P MCH,0 1-n 1 1-n Equation (V-1) CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 202
With t the space time (g cata .s.g MCH -1 ) and P MCH , 0 the initial partial pressure of methylcyclohexane (bar). This relation between the conversion and reaction space time allow us to fit the experimental data. The kinetic parameters such as apparent reaction rate constant k (mol MCH .g cata -1 .h -1 .bar -n ) and reaction order n are solved by optimizing and minimizing the sum of squared residuals (SSR).

The reaction rate r(t) (mol MCH .g cata -1 .h -1 ) can then be deduced from this fitting curve by using the expression in Equation (V-2), where M MCH is the molar mass of methyl-cyclohexane (98 g.mol -1 ) :

r(t)= X MCH→Tol (t+∆t) -X MCH→Tol (t) M MCH ∆t Equation (V-2)
Note that for the current fitting, we assume that the H 2 pressure will not significantly change as a function of the space time, due to its high initial value compared to that of methylcyclohexane, so that its contribution to the power law rate expression is merged in the effective rate constant k. The fitted rate constant k and reaction order n (for methyl-cyclohexane) are reported in Table V-3. Despite the very satisfying fitting SSR and also a good match with experimental points in Figure V-7, the reaction order for the reactant methyl-cyclohexane is about 3 from the fitting model, which is surprizing from a chemical point of view. In the literature, there also exists several studies by using the power-law kinetic fitting model (to provide information and clues for a next step on mechanistic model, before leading to a more formal kinetic model), summarized in Table V-4. The partial reaction order of methyl-cyclohexane is found to be between 0-1, generally. As for the rate constants, the one found in our work seems higher than those in the literature 5,3,4,6 , by two to three orders of magnitude. Besides the fact that Van -n ), while the rate constant estimated by DFT (s -1 ) correspond to one catalytic site at standard pressure for mono-molecular transformation of methyl-cyclohexane. So, it is quite hard to compare here directly these two factors. Meanwhile, we cannot simply induce the fitting activation energy from the fitting rate constant without having the value of the pre-factor A, due to the fact that the fitting is done for one temperature condition. Thereby, it emphasizes the difficulty of power-law kinetic model to compare with our DFT results and great interest to build a more formal and compatible mechanistic model at this point.

With fitting parameters reported in

Impact of MCH and H 2 partial pressures

The same kind of fitting procedures were also done for the influence of hydrogen and methyl-cyclohexane partial pressures on the experimental methyl-cyclohexane conversion to toluene. However, in the literature (Table V-4), the authors often fit the partial pressure of methyl-cyclohexane and hydrogen at the same time. In the present work, in order to simplify this preliminary fitting study and also because of the limited amount of experimental data that could be used for the fitting model, these two parameters P MCH and P H 2 were discussed separately (giving rise to the PL-II and PL-III models), by assuming that only one partial pressure governs the reaction at a time while the other remains constant, and thus is merged with the rate constant term. The equations used for these fitting models, written in the following, are established similarly as Equation (V-1) for the first power-law model (PL-I):

⟹ X MCH→Tol = 1-1- 1-n a k a t P MCH,0 1-n a 1 1-n a Equation (V-3) r = k b P H 2 n b ⟹ X MCH→Tol = 1-1- 1-n b k b t P H 2 ,0 1-n b 1 1-n b Equation (V-4)
Moreover, the experimental data set used for this fitting is obtained at constant WHSV (40 g MCH .h -1 .g cata -1 ) which corresponds to a constant space time t (90 g cata .s.g MCH -1 ), with variable initial pressures of methyl-cyclohexane or hydrogen (P MCH,0 or P H 2 ,0 ). For the determination of n a , the hydrogen partial pressure is kept constant (12.2 bar, Test-1,11,12) and for determination of n b , the methyl-cyclohexane partial pressure remains constant at 0.8 bar (Test-1,7,8,9,10). Let us recall that experimentally, at P H 2 = 2 bar and P MCH = 0.8 bar (Test-10), maximal conversion is obtained when one considers the effect of P(H 2 ). However, the power-law model does not achieve to fit the deactivation part at low hydrogen partial pressure. So the fitting is started from the decreasing part (the red point in From the SSR in Table V-5, the fitting results for PL-II and PL-III are worse than that of PL-I (Table V-3), especially regarding the dependence of the conversion with respect to hydrogen partial pressure (PL-III), which emphasizes the complexity of the impact of hydrogen partial pressure on the reaction kinetics. On the other hand, the reaction orders were found to be 0.3 (close to 0) with respect to hydrogen and 1.5 with respect to methyl-cyclohexane. The MCH reaction order obtained by this last fitting is not compatible with the fitting results of PL-I. Comparing this to the results reported in the literature (Table V-4), the MCH reaction order found by PL-II close to 1 is still higher. The H 2 reaction order determined by PL-III is nearly 0, which seems more coherent with the orders reported in Table 2. Whereas the authors reported this order negatively tends to 0, opposite to the positive order obtained by PL-III. Meanwhile, two extra studies 1,9 reporting the reaction orders in the literature without applying power-law fitting method are also found. Sinfelt 1 found the reaction to be nearly zero order with respect to methyl-cyclohexane and hydrogen, upon observation of the evolution of the reaction rate as a function of the methyl-cyclohexane and hydrogen partial pressures. As mentioned previously in this chapter, section 1.3, this may be explained by the much narrower interval of operating conditions described in the study of Sinfelt.

Jossens and Petersen 9 found the reaction to be positive order in MCH for a very low methylcyclohexane concentration (0.03 bar), whereas at higher concentration the order approached zero.

210

To conclude, we show in the present section that applying power law rate expressions is possible by that unreliable results are obtained from one fit to the other. This suggests that more detailed atomistic models are required to assess the numerous elementary steps involved in the mechanism as described in the previous Chapter. These conclusions are in agreement with previous works from the literature. 5,3,4,6 2.2 Langmuir Hinshelwood mechanistic models

Individual steps and rate constants from DFT

The mechanism considered for the methyl-cyclohexane dehydrogenation reaction and studied by the DFT calculations reported in the previous chapter are much more complex than those considered in the earlier work of Van Trimpont. In particular, it involves 15 elementary steps and includes also the atomic hydrogen migration and cluster reconstruction steps, as we have already explained in the previous chapter. We recall the elementary steps in Table V-6.

Rate limiting steps

From the data reported in Table 6 and looking only at the feature of individual steps, step

(5) appears to be a limiting process. In the forward direction, the D à E step indeed exhibits the highest activation Gibbs free energy (95 kJ.mol -1 ). It is closely followed by step (13), with Δ r G ‡ = 87 kJ.mol -1 . Consequently, in sections 2.3 and 2.4, we will establish two types of kinetic models assuming that either (5) or step (13) is the rate limiting step. hydrogen and dehydrogenated MCH molecules will not be considered.

The second family of models (called RDS (IV)-(VI), see later section 2.4) makes the distinction between each adsorbed species and the cluster sites as it is the case in a standard LH model. However, in order to take into account H-migration and clusters reconstructions, these steps will be considered as if they were generating specific intermediate molecular species adsorbed on the cluster. In that case, the competitive adsorption between hydrogen and dehydrogenated MCH molecules will be considered.

TOF-determining intermediates (TDI) and transition states (TDTS)

It is suggested 10 that the method to determine the reaction kinetics with isolated and stable intermediates in one single reaction step may result in overlooking other intermediates that may also play un crucial role in the catalytic reaction and may even induce changes of rate determining step. If we now look at the full Gibbs free energy profiles reported in Figure V-9, we can see that the kinetics may not simply be related to the individual steps ( 5) and (13). Relying on 10,11 the rate shall be limited by some elementary step sequences relating TOF-determining intermediates (TDI) and transition states (TDTS). So in this spirit to define the "resting states" (TDI) and "the rate-limiting TS" (TDTS), in order to calculate the apparent activation energy of the catalytic cycle, we herein found three reaction sequences that involves several sequential intermediates or transitions states to form new energy barriers that may affect the assumption of isolated rate-determining step (5) or (13). We can see that with the exception of the first sequence (C D D à E), such considerations do not lead to the same steps to focus on as the previous RDS approach. We tried to develop Langmuir-Hinshelwood models considering those sequences as globally limiting, however we failed in writing rate expressions independent of surface species concentrations due to the merging in single steps of several elementary steps, which prevents to deduce simple expressions for the concentrations of surface species enclosed within the sequence. To find an analytical solution, we then chose to build the models as if the last step of the sequence (in practice more often: the most demanding one of the sequence) was the RDS, with pre-equilibria. This leads to three new models as summarized in Table V- (11) and (15) are considered as rate limiting steps. These three models will be integrated into the standard LH mechanistic formalism with the explicit consideration of adsorption competition with adsorbed atomic hydrogen.

RDS-(I)

Single rate determining elementary step

Step (5) No No

RDS-(II)

Step ( 5) Yes No

RDS-(III)

Step ( 13) Yes No

RDS-(IV)

Step ( 5) No Yes

RDS-(V)

Step ( 5) Yes Yes

RDS-(VI)

Step ( 13) Yes Yes

TDTS-(I) ó RDS-(V) Single {TDI

; TDTS} couple

Step (5), {C;TS d } Yes Yes

TDTS-(II)

Step (11), {H;TS j } Yes Yes

TDTS-(III)

Step (15), {M;Tol (g) +L 0 } Yes Yes [ ]

D k r 5 =
All other steps are assumed to be at quasi-equilibrium, which leads to the following reaction equilibrium constants : These rates correspond to the monomolecular reaction rates on one catalytic site. So they cannot be directly compared to those obtained experimentally (mol MCH .g cata -1 .h -1 ). It can be observed that the reaction rate decreases and tends to zero when the hydrogen pressure increases, whereas it increases and tends to 51.6 (s -1 ) by increasing methyl-cyclohexane partial pressure.

ES (1) : [ ] [ ] [ ] [ ] 0 1 0 1 L P K A L P A K MCH MCH = Þ = ES (2) : [ ] [ ] [ ] [ ] [ ] 0 2 1 2 2 L P K K A K B A B K MCH = = Þ = CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 217 ES (3) : [ ] [ ] [ ] [ ] [ ] 0 3 1 3 3 L P K B K C B C K MCH i i Õ = = = Þ = ES (4) : [ ] [ ] [ ] [ ] [ ]
In order to make these results and experiments comparable, we introduce the catalyst dispersion and metal content impacts, by assuming that 13 platinum atoms is actually one reaction site with respect to the DFT model. The dispersion for the catalyst used in our experiment is Pt dispersion = 0.90 and the platinum content is 0.3% (Pt content = 0.003), as mentioned in

K K

Once again, if we focus on the initial reaction rate at P Tol = 0 bar, the initial overall reaction rate equation remains identical to the one of the RDS-(I) model. However, at non-zero conversion, the toluene partial pressure will increase and affect the reaction rate which may give a different evolution of the rate between these two models. In order to illustrate these evolutions along the reaction course, we will compare the reaction rates as a function of reaction conversion at constant hydrogen partial pressure of 12.2 bar at 625 K. The conversion is fixed by the change of the partial pressures of MCH and Toluene (constraining P MCH and P Tol at 0.8 bar).

RDS-(III) model: reversible rate-determining step (13)

As the elementary step ( 13) exhibits an free energy of activation (87 kJ/mol) which is very close (according to the DFT accuracy) to the one of step (5) (92 kJ/mol), we also built a model with elementary step (13) as a reversible rate-determining step (RDS-(III)). In this case the overall reaction rate is given by: ES

[

] [ ] M k L k r 13 13 - - =
The expressions of equilibrium constants from K 5 is different from RDS-(I) and RDS-(II) models as step (5) in no longer the rate determining step.

ES (5) :

[

] [ ] [ ] [ ] [ ] 2 0 5 1 5 5 H MCH i i P L P K D K E D E K Õ = = = Þ = ES (6) : [ ] [ ] [ ] [ ] [ ] 2 0 6 1 6 6 H MCH i i P L P K E K F E F K Õ = = = Þ = ES (7) : [ ] [ ] [ ] [ ] [ ] 2 0 7 1 7 7 H MCH i i P L P K F K G F G K Õ = = = Þ = ES (8) : [ ] [ ] [ ] [ ] [ ] 2 0 8 1 8 8 H MCH i i P L P K G K H G H K Õ = = = Þ = CHAPTER V -REACTION
Õ = = = Þ = ES (10) : [ ] [ ] [ ] [ ] [ ] 2 0 10 1 10 10 2 H P L P K I K J I J K MCH i i Õ = = = Þ = ES (11) : [ ] [ ] [ ] [ ] [ ] 2 0 11 1 11 11 2 H P L P K J K K J K K MCH i i Õ = = = Þ = ES (12) : [ ] [ ] [ ] [ ] [ ] 2 0 12 1 12 12 2 H P L P K K K L K L K MCH i i Õ = = = Þ = Whereas we still have : ES (15) : [ ] [ ] [ ] [ ] 15 0 0 15 K L P N N L P K Tol Tol = Þ = ES (14) : [ ] [ ] [ ] [ ] [ ] 15
= = Þ =
After deducing [L 0 ] in the same way as we did in model (I), we obtain :

Tol E Tol H H MCH I G H MCH J MCH A P K P P K P P K K P P K P K L H + + + + + + = - 2 2 2 2 1 0 ) ( 1 Equation (V-18) with åÕ = = = 8 4 1 i i j i J K K , 15 14 1 K K K H = , Õ = = 12 1 i i I K K ,
So the overall reaction rate expressed by reversible rate-determining step (13) can be written as : The initial reaction rate can thus be written as :

K G = K i P MCH P H 2 2 i=1 j ∏ j=9 11 ∑ ú ú û ù ê ê ë é + + + + + + - = - Tol E Tol
ú ú û ù ê ê ë é + + + + = 2 2 13 0 2 2 2 ) ( 1
H H P P K K P P K P K P P K k r MCH I G H MCH J MCH A MCH I Equation (V-20)
The influence of hydrogen partial pressure and methyl-cyclohexane partial pressure on the initial reaction rate for this model is reported in Figure V-13. However, if the increase of the rate with P MCH is well reproduced, once again the maximum of rate by varying the hydrogen partial pressure was not found at P Tol = 0 bar. Moreover, the order of magnitude of the initial rates in this RDS-(III) model is worse as compared to RDS-(I) and (II), with respect to experiments (between 3 and 4 orders of magnitude of overestimation by the model).

If we compare our rate expression with the one of van Trimpont (Equation (II-4) in Chapter II, section 4.2.1), in our mechanistic model, the discrepancy is probably due to the fact that so far we did not consider the competitive adsorption between hydrogen, dehydrogenated MCH molecules and free active sites, whereas this is taken into account by Van Trimpont et al. We also investigate the reaction rates as a function of the conversion at constant hydrogen partial pressure of 12.2 bar at 625 K, as we did for the two previous models. RDS-(I), (II) and

(III) models are compared in Figure V-14, which reveals that the three models lead to very different rates also at non-zero conversion, in terms of order of magnitude (ratio of 10 8 ).

However, the RDS-(III) model (assuming step (13) as reversible rate-determining) shows a very good agreement with experimental data for non-zero conversion, while the irreversible/reversible rate determining step (5) models failed on the these, in spite of the satisfaction of the initial rates.

Furthermore, the two reversible rate-determining step models RDS-(II) (step ( 5)) and RDS-(III) (step ( 13)) indicate a similar conversion to toluene at the steady state (0.65 conversion). So far, we can conclude that these extended LH kinetic models based on a single RDS are not fully satisfying models for all the investigated features (order of magnitude of the rate, at zero and non-zero conversion, as a function of P H 2 and P MCH ). A tentative conclusion could be that at low conversion, the rate-determining step is rather step (5) as the good order of magnitude are found on for initial reaction rates in models RDS-(I) and (II). However, when reaction goes on and toluene starts to be produced, the rate-determining step is moving towards step (13), considering the better performance of model RDS-(III). However, these models may be too simple to conclude. The next source of possible improvement investigated in the following is the DFT calculations provide us thermodynamic and kinetic data that include reaction free energy and activation free energy as a function of the temperature (from 0 to 1000 K). It allows us to parameterize our kinetic model at different temperatures with corresponding reaction rate constants and equilibrium constants as reported in Table V-9. Similarly, as we did for the catalytic test, we study the reaction rates by varying the reaction temperature (600, 625, 650 and 675 K), to derive the apparent kinetic parameters to be compared with experimental temperatures.

The initial reaction rates at these four temperatures were calculated by the three Langmuir We rewrote the mechanism following a similar model as the one of Van Trimpont et al. 5 , consideringadsorbed hydrogen explicitly . However, we have to include the H atom migration and cluster reconstruction steps. We chose to consider these steps as a generation of specific intermediate molecular species adsorbed on the same cluster. Moreover, all the three molecular hydrogen desorption steps are defined successively in our model, from three distinct types type of atomic hydrogen, which is different from the model of Van Trimpont. 5 This new reaction scheme including explicit site competition between atomic hydrogen and dehydrogenation intermediates is presented in Table V-11.

Table V-11 Dual site dehydrogenation mechanisms, including explicit site competition between atomic hydrogen and MCH dehydrogenation intermediates, giving rise to the RDS-(IV), RDS-(V) and RDS-(VI) models

Elementary step Reaction type

(1) 5) and (13).

MCH (g) + L D MCH-L methyl-cyclohexane adsorption (2) MCH-L + L D A 1 -L + H a -L C-H bond cleavage (3) A 1 -L + L D MCHe-L + H a -L C-H bond cleavage (4) 2 H a -L D 2 L + H 2(g) H 2 desorption (5) MCHe-L + L D A 2 -L + H b -L C-H bond cleavage (6) A 2 -L D A 2(d) -L H atom migration (7) A 2(d) -L D A 2(r) -L cluster reconstruction (8) A 2(r) -L + L D MCHde-L + H b -L C-H bond cleavage (9) 2 H b -L D 2 L + H 2(g) H 2 desorption (

RDS-(IV) model: rate-determining step (5)

As same as for the extended LH kinetic model, we firstly consider the elementary step (5) as rate determining and as being irreversible. The overall reaction rate can be thus expressed as follows :

ES (5) : [ ][ ] L L MCHe k r - = 5 Equation (V-21)
All the steps (1) to ( 4) are assumed to be at quasi-equilibrium and the steps after (5) are omitted in this simplified case because of the irreversibility of step (5). We will indeed consider initial rates at this stage. At P Tol = 0 bar we have

[A 2 -L] = [A 2(d) -L] = [A 2(r) -L] = [MCHde-L] = [MCHde (r) -L] = [A 3 -L] = [A 3(d) -L] = [Tol-L] = [H b -L] = [H c -L] = 0,
[ ] [ ] [ ] [ ] L P K L MCH L P L MCH K MCH MCH 1 1 = - Þ - = ES (4) : [ ] [ ] [ ] [ ] 5 . 0 4 5 . 0 2 2 4 2 2 K L P L H L H L P K H a a H = - Þ - = ES (2) : [ ][ ] [ ][ ] [ ] [ ][ ] [ ] [ ] 5 . 0 5 . 0 4 2 1 2 1 1 2 2 H MCH a a P L P K K K L H L L MCH K L A L L MCH L H L A K = - - = - Þ - - - = ES (3) : [ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ] 2 4 3 2 1 1 3 1 3 H MCH a a P L P K K K K L H L L A K L MCHe L L A L H L MCHe K = - - = - Þ - - - =
Then the summation of all the coverage of active sites by surface species from above ES (1) to (4) and the vacant sites :

[ ] [ ] [ ] [ ] [ ] 1 1 = - + - + - + - + L H L MCHe L A L MCH L a [ ] 5 . 0 ' ' 5 . 0 ' ' 1 2 2 2 1 H a H P K P P K P P K P K L H H MCH C MCH B MCH A + + + + = Û - Equation (V-22)
With the new constants defined as :

1 ' K K A = , 5 . 0 4 2 1 ' K K K K B = , 4 3 2 1 ' K K K K K C = , 5 . 0 4 ' - = K K a H Equation (V-23)
The new constants K ' A and K ' H can be regarded as the adsorption constants for the methylcyclohexane and H 2 (per hydrogen atom and giving H a atoms, L + ½ H 2 ↔ H a -L), respectively.

The other constants refer to the combination product of several elementary steps. Equation (V-21), which gives the initial rate, can then be rewritten as :

Equation (V-24)

As this was done previously, the predicted initial rates (already converted in mol MCH .g cata - 1 .h -1 ) are compared with the experimental ones, as a function of P(H 2 ) and P(MCH) (Figure 12). . This analysis suggests that there is a maximum reaction rate (relatively of huge order of magnitude) at some point of hydrogen pressure between P H 2 = 0-1 bar. The position of this maximum is not in agreement with our experimental observations, but its existence suggests that the explicit inclusion of adsorption competition with atomic hydrogen is a relevant approach. In Figure V-17(b), the rate monotonously increases with P MCH instead of reaching a plateau. This is a strong limitation for the validity of the RDS-(IV) model.

RDS-(V) model: reversible rate-determining step (5)

In this next case, the overall reaction rate can be expressed as follows :

ES (5) : [ ][ ] [ ][ ] L H L A k L L MCHe k r b - - - - = - 2 5 5

Equation (V-25)

The steps (1) to (4) are identical to those in the irreversible case. The elementary steps from (6) to (15) are developed for taking into account all the intermediate surface species at quasiequilibrium state in the model :

ES (15) : [ ] [ ] [ ] [ ] 15 15 K L P L Tol L Tol L P K Tol Tol = - Þ - = ES (14) : [ ] [ ] [ ] [ ] 5 . 0 14
5 . 0 2 2 14 2 2 K L P L H L H L P K H c c H = - Þ - = ES (13) : [ ][ ] [ ] [ ] [ ] [ ][ ] [ ] [ ] 15 5 . 0 13 5 . 0 13 ) ( 3 ) ( 3 13 14 2 K K K L P P L K L H L Tol L A L L A L H L Tol K H Tol c d d c = - - = - Þ - - - = CHAPTER V -REACTION
K K K K L P P K L A L A L A L A K H Tol d d = - = - Þ - - = ES (11) : [ ][ ] [ ][ ] [ ] [ ][ ] [ ] [ ] Õ = = - - = - Þ - - - = 15 11 11 3 ) ( ) ( 3 11 2 i i H Tol c r r c K L P P L K L H L A L MCHde L L MCHde L H L A K ES (10) : [ ] [ ] [ ] [ ] [ ] Õ = = - = - Þ - - = 15 10 10 ) ( ) ( 10
2 i i H Tol r r K L P P K L MCHde L MCHde L MCHde L MCHde K ES (9) : [ ] [ ] [ ] [ ] 5 . 0 9 5 . 0 2 2 9 2 2 K L P L H L H L P K H b b H = - Þ - = ES (8) : [ ][ ] [ ] [ ] [ ] [ ][ ] [ ] [ ] Õ = = - - = - Þ - - - = 15 10 5 . 0 9 8 5 . 1 8 ) ( 2 ) ( 2
8 2 i i Tol b r r b K K K L P P L K L H L MCHde L A L L A L H L MCHde K H ES (7) : [ ] [ ] [ ] [ ] [ ] Õ = = - = - Þ - - = 15 10 5 . 0 9 8 7 5 . 1 7 ) ( 2 ) ( 2 ) ( 2
) ( 2 7 2 i i Tol r d d r K K K K L P P K L A L A L A L A K H ES (6) : [ ] [ ] [ ] [ ] [ ] Õ = = - = - Þ - - = 15 10 5 . 0 9 8 7 6 5 . 1 6 ) ( 2 2 2 ) ( 2 6 2 i i Tol d d K K K K K L P P K L A L A L A L A K H
Then the summation of all the coverage of active sites by surface species from above ES (1) to (15) and the vacant sites :

[ ] [ ] [ ] [ ] [ ] 1 1 = - + + - + - + - + L Tol L MCHe L A L MCH L ! 238 [ ]
1 i i D K K K K K K K K K , Õ = + = 15 10 10 ' 1 i i E K K K , 15 5 . 0 14 13 12 12 ' 1 K K K K K K F + = , 15 ' 1 K K G = , 5 . 0 14 5 . 0 9 5 . 0 4 ' 1 1 1 K K K K H + + = Equation (V-27) ~ (V-31)
The new constants K ' G , K ' H can be regarded as the adsorption constants for toluene and all the atomic hydrogen from H 2 gaseous phase, respectively. K ' D , K ' E , K ' F can be treated as the combination product of several elementary steps. So if we replace the term [L] in Equation (V-27) and the term [MCHe-L] into Equation (V-26), the rate-determining step can be written as :

+ + + + + + + + - = - Equation (V-32) With Õ = = 15 6 ' i i I K K Equation (V-33)
In this case, the initial reaction rate (P Tol = 0 bar) can be expressed as : The difference between the Equation (V-24) and (V-34) is simply the adsorption of hydrogen term K ' H a and K ' H . Despite in the Equation (V-35), the initial reaction rate is limited by step (5), the steps ( 9) and ( 14) which occur after RDS are still explicitly implicated in the initial rate expression. This can be explained by the fact that we considered the rate-determining step is reversible and all the surface intermediates which are not relevant to the product toluene (P Tol = 0) are still contributing to the reaction rate. In this case, the respective influences of hydrogen partial pressure and methyl-cyclohexane partial pressure on the initial reaction rate have the same With the new constants defined as : -L] into Equation (V-36), the rate can be written as : In this case, the initial reaction rate (P Tol = 0) can be expressed as : bar. This is so far the best kinetic model that is achieved by our study to meet this kinetic phenomenon, by assuming step (13) as the rate-determining step. Nevertheless, this maximum reaction rate is found at 10 bar, against the experimental value found near 5 bar and the rate at the maximum is smaller than the experimental one. This point deserves a complementary analysis on the sensibility to each parameter in order to enhance the agreement with experiments, which will be done in detail in next section. In In order to identify the key parameters playing on the position of the maximum as a function of the hydrogen pressure, the rate expression in Equation (V-43) is analysed in case of P H 2 → 0 and P H 2 → ∞ to be able to parameterize the curve shape from the two sides. Then we have: It appears that the constants k 13 , K' N , K' M , K' H play a role on these two limit behaviours.

The rate constant k 13 , which is related to the activation free energy, is not varied in the following analysis. The strategy is to focus on the other constants K' N , K' M , K' H that are calculated from

Conclusion and perspectives

In section 2., the experimental results we reported in section 1 are firstly fitted by a powerlaw kinetic model. We found the apparent reaction order for methyl-cyclohexane to be about 3 by fitting the reaction rates as a function of space time; the reaction orders were found to be 0.3 order (near 0) with respect to hydrogen and 1.5 with respect to methyl-cyclohexane by fitting the reaction rates as a function of methyl-cyclohexane partial pressure and hydrogen partial pressure.

The fitting results suggest that more detailed models are required to assess the complexity of the mechanism.

Before building several types of Langmuir-Hinshelwood (LH) kinetic models from our ab initio calculations, the latter being used to set up the reaction scheme, choose relevant ratedetermining steps and calculate each rate and equilibrium constant was needed in the integration of the model. It leads firstly to three "extended" Langmuir Hinshelwood kinetic models, for which each intermediate is a system embedding the cluster and the adsorbed species without considering competitive adsorption between hydrogen and dehydrogenated MCH molecules.

Secondly, a complex mechanistic model including explicit site competition between atomic hydrogen and dehydrogenation intermediates was proposed and three new Langmuir Hinshelwood kinetic models were thus proposed. Finally, two extra LH models inspired by the energetic span concept, considering reaction step sequences as globally limiting step, were also studied by using the same formalism including explicit site competition with atomic hydrogen.

The results can be summarized in Table V-14.

Table V-14 Summary agreement between each kinetic model compared to experiments (T = reasonable agreement ; F = non-reasonable agreement), for various kinetic parameters.

We can conclude that it is very difficult to have one LH model that validates all these kinetic descriptors compared to experimental results at the same time. All these criteria are strongly related to the reaction mechanism that we assume. However, among all the imperfections, models RDS-(II), RDS-(VI) and TDTS-(II) behave reasonably and these three models also happen to have three different nature of RDS, step (5), ( 13) and (11), respectively. This suggests that the real complete reaction kinetics may be a combination of all these 3 steps, a simple RDS cannot simply achieve all the expectations.

As consequence, a micro-kinetic model parameterized by ab initio constants is strongly required in the future. At this point, according to our current results, the hydrogen coverage is a crucial parameter to take into account.

towards calculation parameters. The investigation of this sensibility allowed us to choose our calculation parameters with a compromise on the calculation time. The importance of dispersion interactions was also emphasized, as estimated with PBE-dDsC (with respect to PBE), both for Overall, our ab initio calculations reveal the complexity of the reaction pathway for the subnanometric clusters, but give rise to proposals for rate determining steps, which validity can be tentatively estimated thanks to kinetic modeling compared with experiments.

Kinetics for dehydrogenation reaction on γ-alumina supported platinum catalyst

In the second part of our work, the reaction kinetics has been studied by both experimental and kinetic modeling methods.

Catalytic methylcyclohexane dehydrogenation experiments were performed on a Pt/γ-Al 2 O 3 catalyst which characteristics are as close as possible to the ab initio system: high dispersion of monometallic platinum particles, dechlorinated support. The operating conditions were chosen to guarantee the absence of diffusion limitations and the access to intrinsic kinetics.

The influence of parameters such as space time, temperature, partial pressure of hydrogen and methylcyclohexane, was investigated systematically. Notably, a maximum in rate was observed as a function of P(H 2 ), while it monotonously increases with P(MCH). The apparent activation energy and enthalpy were determined (200 and 195 kJ/mol, respectively).

These data were then used to confront with kinetic models that we built. A Power-law kinetic model was preliminarily constructed by solely fitting the experimental results in order to receive the information on reaction constant and reactions orders. However, considering the inconsistencies between reaction orders found, these fitting results suggested that more detailed models are required to assess the complexity of the mechanism.

model based on the third C-H bond cleavage step (from methyl-cyclohexene to methylcyclohexenyl + H) as rate-determining step without explicit consideration of adsorption competition with adsorbed atomic hydrogen. These results suggest that the real complete reaction kinetics may be a combination of all these 3 steps, a simple RDS cannot simply achieve all the expectations with current LH kinetic approach.

Perspectives

The results reported in this thesis open perspectives for the better understanding of the catalytic system, of the reaction mechanism and more generally for the understanding and control of the behavior of the catalyst in catalytic reforming. Relevant parameters to investigate un the future are the following, in particular by ab initio calculations:

-The influence of the hydrogen partial pressure on the hydrogen coverage. Indeed, so far, a constant hydrogen coverage was considered as the starting point, whereas experimentally it may vary. For this, the various models established in the past by C.

Mager-Maury 3 will be useful starting points.

-Also, the influence of the facet of gamma-alumina. So far, the cluster considered is located on the (100) surface of alumina, whereas the (110) is the most abundant. The latter surface is partially hydrated in reforming-like conditions, which is expected to influence the electronic and reactive properties of the aggregates. The models established by A. Gorczyca 4 describe the interaction of hydrogen with Pt 13 clusters with the hydroxylated (110) surface, which would be of interest to consider for further reactivity investigations.

-The effect of chlorine on rate constants, present on the real catalytic systems, could also be of interest. Mager-Maury et al. 7 prepared models of platinum clusters supported on chlorinated alumina. The effect of chlorine on the affinity of the clusters for hydrogen would be a required preliminary step before engaging a reactivity study.

-In a more long-term research, it is also of great interest to investigate the behavior of bi-metallic nano-aggregates, particularly Pt x Sn y /Al 2 O 3 . Models for this bi-metallic catalyst have been using ab initio calculations combined with experimental work at IFPEN by A. Gorczyca. 5 and Jahel et al.. 6 The atomic scale mechanism and kinetics of dehydrogenation of methyl-cyclohexane to toluene on such systems still need to be investigated.

-Finally, other reactions of interest in catalytic reforming, such as cyclisation, isomerization and hydrogenolysis should be undertaken.

Regarding kinetic modeling, a micro-kinetic model parameterized by ab initio constants is substantially required in the future, in order to give us a clear vision on the more detailed kinetics, such as rate-determining step and the reaction order and apparent constant. The advantage of such an approach with respect to the LH models proposed here is to avoid any assumption on RDS, considering explicitly all forward and backward rate constants for the integration of the rate equations. At this point, according to our current results, the hydrogen coverage is a crucial parameter to take into account. It will be also strongly necessary to have a micro-kinetic model on the case of Pt (111) system, in order to compare the reaction kinetics with cluster system.

Finally, all the perspectives mentioned above for ab initio calculations could lead to dedicated kinetic modeling works.

1. Reactions taking place in catalytic reforming 1 . 1

 11 Nature of the reactionsCatalytic reforming involves the transformation of low-octane hydrocarbons boiling in the gasoline range into more valuable high-octane gasoline components, such as aromatics and highly branched paraffins, without significantly changing their carbon numbers (FigureII-1).

Figure II- 1

 1 Figure II-1 Research Octane Number of different hydrocarbons (paraffins, olefins, naphtenes and aromatics) and different reforming reactions (adapted from 1 )

  Figure II-4(b) 27 depicts the STEM image of reduced bimetallic PtSn/γ-Al 2 O 3 -Cl (0.3 wt% Pt; 0.32 wt% Sn; 0.98 wt% Cl).

  Figure II-4 Selected STEM images of reduced catalysts: (a) Pt/Al 2 O 3 -Cl (b) PtSn/Al 2 O 3 -Cl

  can be neglected with respect to 1. Note that this approximation is the one used by Van Trimpont et al. to simplify the number of parameters to be fitted experimentally.

5 K P Tol and 6 2 K 5 K

 525 of being significantly negative. Note that this appears to be in contradiction with the first hypothesis according to which P H are negligible. On the other hand, that could also be considered as the reason that both terms as the equilibrium constant for the sum of Equation (II-3) +(II-4) +(II-5) + 2(II-6), which corresponds to the reaction : MCH + s ⟺ MCHde•s + 2

1 (

 1 equilibrium constant for the formation of the adsorbed MCH intermediate), we express the apparent reaction rate equation from Equation (II-9) as follows :

Figure II- 5

 5 Figure II-5 Influence of hydrogen partial pressure on initial dehydrogenation reaction rate related to the work of VanTrimpont20

  •s being shifted to the left at high partial pressures of H 2 . At intermediate P(H 2 ) values, the [MCHde•s][s] product exhibits positive values, with a maximum close to 5.2 bars.

Figure II- 6

 6 Figure II-6 Coverage of relevant surface species: methyl-cyclohexadiene (blue line), methyl-cyclohexane (red line), free active sites (green line) and the product of methyl-cyclohexadiene and free active sites (purple line), as a function of hydrogen partial pressure related to the work of Van Trimpont 20

4 . 1

 41 Considerable progresses have been made at IFPEN in this important area of research, which has concerned the description of γ-alumina-supported metallic particles in the catalytic reforming context, from 2002. 69-72 The γ-alumina support Digne et al. 32,73 , using Density Functional Theory, built the first realistic models of γ-Al 2 O 3 (110), (100) and (111) surfaces, taking into account of temperature effects on hydroxyl surface coverage. These surface models were derived from the bulk model of Krokidis et al., 74 obtained by simulating dehydration process of boehmite into γ-alumina. The selected models are validated for representing the active surface of γ-alumina catalyst because of the correct surface density and vibrational properties of hydroxyl groups as compared with experiments. 75 The precise nature of the acid surface sites (concentrations and strengths) is also determined. The acid strengths are quantified by simulating the adsorption of relevant probe molecules such as CO and pyridine in correlation with surface electronic properties. The γ-alumina (100) surface with different hydroxyl coverage (0 or 8.8) is shown in Figure II-7.

Figure II- 7 32 4. 2

 7322 Figure II-7 Relaxed configurations of γ -Al 2 O 3 (100) surfaces for different hydroxyl coverages (θ in OH nm -2 ). Al n stands for aluminum atoms surrounded by n oxygen atoms, and HO-µ m for OH groups linked to m aluminum atoms. Black balls, oxygen atoms. Gray balls, aluminum atoms. White balls, hydrogen atoms.32

Figure II- 8 ( 4 . 3

 843 Figure II-8 (a) Thermodynamic diagram depicting the hydrogen coverage on supported Pt 13 clusters as a function of P(H 2 ). Operating conditions considered for the interaction with hydrocarbons are shown and the stable hydrogenated particles depicted in (b) 20 hydrogen atoms, (c) 18 hydrogen atoms, (d) 4 hydrogen atoms. J stands for the P(H 2 )/P(C 2 H 6 ) ratio. The number of H atoms per cluster is reported on each colored region of the diagram. 79,69

Figure II- 9 Δ

 9 Figure II-9 Δ r G of all intermediates involved in dehydrogenation and/or C-C bond scission steps including hydrogenolysis for J = 0.01, 1 and 100, respectively. Envelopes are drawn following the stability of each carbonaceous species: the blue (J = 0.01), pink (J = 1), and green (J = 100) envelopes encompass the carbonaceous species (except desorbed methane) for the corresponding J. Evolution of

  is still not clear in the literature. Considering this reaction is very similar to the reverse reaction of the dehydrogenation of methyl-cyclohexane to toluene, it becomes interesting in our case to be inspired by those existing DFT calculations focused on this similar reverse reaction. However, in the literature, most of those calculations have been done on the Pt (111) surface, instead of the Pt/γ-Al 2 O 3 cluster. So in the present work, a parallel study to investigate the dehydrogenation of methyl-cyclohexane to toluene on Pt (111) surface will be required in order to make a closer comparison with Pt cluster. Saeys et al. 82,83 used a Pt (111) catalyst modeled by a two-layer Pt 22 cluster with 14 atoms in the top layer. By using the Horiuti-Polanyi mechanism 84 that involves the consecutive addition of hydrogen atoms, the authors proposed a dominant reaction path where the hydrogenation happens in a meta position of methylene group by forming 1,2,3,5-tetrahydrobenzene, 1,3,5trihydrobenzene and 1,3-dihydrobenzene as reaction intermediates. Cyclohexadiene and cyclohexene are not found to be formed along this proposed dominant pathway. Morin et al. 85 used an extended slab model of the Pt (111) surface for their calculation on hydrogenation of benzene to cyclohexene. They found that the reaction path through a meta position as Saeys et al. proposed and the one though the cyclohexadiene and cyclohexene, the two are very competitive. It is found that the 1,3-cyclohexadiene is less stable then 1,3dihydrobenzene, while cyclohexene is more stable then 1,3,5-trihydrobenzene on the surface. Ma et al. 86 investigated the dehydrogenation of 1,3-cyclohexadiene to benzene on Pt (111) and they found for the same intermediates configuration with closed adsorption energy as Saeys et al. and Morin et al. found. Sabbe et al. 87 employed microkinetic simulation based on periodic DFT calculations for the full network of benzene hydrogenation on Pt (111) at a hydrogen coverage of 0.44 ML at industrial hydrogenation condition (p B = 0.1-0.6 bar; p H 2 = 0.5-6 bar; T = 400-500 K). They found the ortho pathway, via cyclohexene, 1,2,3-trihydrobenzene and 1,3dihydrobenzene, is identified as dominant path, partially different from what Saeys et al.

4

  Sabbe et al., Morin et al., and Ma et al. used PW91 functional for these calculations; Saeys et al. used BP86.

Figure II- 10

 10 Figure II-10 Electronic barriers for all the possible reaction steps of the hydrogenation of benzene (kJ/mol), with indication of the minimum energy path found by Sabbe et al. 87 (green) and the path identified by Saeys on Pt 22 clusters 82 (red). Energy barrier for forward reaction (black), for reverse reaction (grey).

Figure II- 10

 10 Figure II-10 extracted from the publication of Sabbe et al. 87 shows the electronic

Figure III- 1

 1 Figure III-1 diagram illustrating the replacement of an all-electrons wave function f(r) (with oscillation near the core) and a core potential V(r) by a pseudo-wave function f PS (r) (no oscillation near the core) and a pseudo-potential V PS (r). r c , the cut-off radius24

25 Å 3

 3 cells for all C 7 molecules, and a 20 × 20 × 20 Å 3 cell for H 2 in order to provide a enough large cell to prevent lateral interactions. The calculations was performed on a 1 × 1 × 1 k-point grid. For the Pt(111) system, the surface was modeled by periodic five-layer slabs and (3 × 3) (1/9 ML) super cell, only the three uppermost platinum layers were allowed to relax along with the adsorbed molecule. The nearest distance of the Pt atoms was 2.82 Å on Pt(111) and the height of the super cell is 29.2 Å. The calculations was performed on a 5 × 5 × 1 k-point grid. The cutoff energy, electronic and forces convergence criterions are the same as for the calculations of cluster system.

Figure III- 2

 2 Figure III-2 The periodic Pt 13 /γ-Al 2 O 3 (100) system considered in present work

Figure III- 3

 3 Figure III-3 Schematic representation of the potential energy surface of an arbitrary reaction. The minimum energy path (MEP) and the nudged elastic band path (NEB) are shown as well as the NEB forces acting on image i 20,35

Figure III- 4

 4 Figure III-4 Deviation of dehydrogenation Gibbs energy Δ r G dehyd,MCH(g) and Enthalpy energy Δ r H dehyd,MCH(g) for the dehydrogenation of methyl-cyclohexane to adsorbed methyl-cyclohexene, using different parameters for the DFT calculations parameters. Curve style legend: Line (reaction Gibbs free energy); Dot line (reaction enthalpy). Curve color legend: E cutoff = 500 eV, normal precision (red); E cutoff = 400 eV, normal precision (orange); E cutoff = 500 eV, accurate precision (yellow); E cutoff = 400 eV, accurate precision (green); E cutoff = 500 eV, high precision (bleu); E cutoff = 600 eV, normal precision (purple); E cutoff = 400 eV, high precision (pink).

  Figure III-5 presents the microprobe scanning results for the catalyst by calculated the average value of five scanning results. It can be noticed from the figure that the three elements aluminum, platinum and chlorine are all homogeneously distributed. The three elements content is generally constant as an evolution of scanning distance. The global concentration determined by the electron microprobe analysis is 0.289 wt%, which is agreed with the FX results.

Figure III- 5

 5 Figure III-5 Electron microprobe scanning results for 0.3%Pt-0.12%Cl/γ-Al 2 O 3 (average microprobe calculated from five individual microprobe scanning results)

  volume at the first titration (mL/g) expressed at conditions T a = reference temperature (25°C) and P = atmospheric pressure (101325 Pa); M Pt = molar mass of platinum (195.08 g/mol) ; wt% Pt = Pt content obtained by XRF and corrected by the loss of mass at 550 °C.

  Figure III-6. It can be seen that the catalyst sample represents a homogeneous metallic phase

Figure III- 6

 6 Figure III-6 Transmission electron microscopy (TEM) results for the catalyst sample of 0.3%Pt-0.12%Cl/γ-Al 2 O 3 at two different magnifications

Figure III- 7 ,

 7 which consists of 3 parts : inlet zone (feedstock tank, pump and different gas flow lines), reaction zone (reactor and reactor oven) and outlet zone (high/low pressure separator, sampler, chromatogram analyzer and gas counter).

Figure III- 7

 7 Figure III-7 Simplified reaction set-up scheme of the catalytic test set-up 55

  However, the reaction area measures only 470 mm. The catalyst (0.56 g) is loaded in the middle of the reactor, where the catalytic stuffing zone measures about 32.5 mm. The reactor oven (RO) is made up of three hot shells. Each shell measures 150 mm height and the middle shell mainly heats the catalytic zone of reactor, as described in Figure III-8. There are three thermocouples T 2c , T 2b and T 2a , extending into the reactor at T2 shell level and reaching different levels in the catalytic zone : top, middle and bottom levels, respectively. The distance between T 2c and T 2a is about 50 mm. The two extreme thermocouples T 2c and T 2a are positioned outside of the catalytic zone, in order to measure the temperatures of the influent entering/exiting the catalytic zone, while the T 2b measures the exact reaction temperature in the catalytic bed. During the tests, these three thermocouples send back the temperature from the three levels on catalytic zone instantaneously and allow us to survey and adjust the reaction temperatures timely. The catalytic zone is filled up with a total volume of 10 cm 3 of the following mixture: 1 cm 3 of catalyst (corresponding to 0.56 g) and 9 cm 3 of silicon carbide (SiC) equivalent of 13.68 g, to reach a dilution ratio of 1/10. This mixture is loaded in the catalytic zone by dividing the load into three identical portions, in order to guarantee a good homogeneity on the distribution of particles within the catalyst layers in this isothermal zone. The total layer length of the catalytic zone in the reactor is about 32.5 mm, located in the middle of the reactor. The rest of the reactor is filled up with inert silicon carbide (SiC). Quartz wool covers the bottom of the reactor. Between each layer, the reactor should by tapped delicately to insure that the catalytic zone remains immobile in the middle of the reactor during the test, where the three thermocouples are accurately placed and report the reactor temperature before, during and after the charge admission into the catalytic zone.

Figure III- 8

 8 Figure III-8 Reactor zone for catalytic reaction (fixed bed reactor). The yellow zone corresponds to the catalytic bed.

  different compounds in the sample move in the column with different rates depending on their properties. As the sample exits the end of column, they are detected and identified electronically by the flame ionization detector (FID). The flame ionization detector (FID) combusts the organic compounds in the sample into ions by a hydrogen flame and the generation of these ions is proportional to the concentration of the organic compounds in the sample. The concentration is described by the response factors related to the number of the carbon atoms in the molecule. The rest of the product getting out of the high pressure separator (HPS), without being analyzed by gas chromatograph (GC), are contained in the low pressure separator (LPS). This is also where we can weigh the product mass to set the mass balance of the reaction. At the end, the gas flow released from the low pressure separator (LPS) goes through the gas counter to measure the flow rate. An ampoule sampler is used to analyze and determine the quantity of product in the gaseous phase escaped from the separator. This part of product is thus considered into the calculation of product yield and to correct the final mass balance of the reaction. The system of the ampoule sampler to trap the product in the output gas is presented in FigureIII-9.

Figure III- 9

 9 Figure III-9 Ampoule sampler system to quantify the product on gaseous phase

Figure III- 10

 10 Figure III-10 Thermal profile detected by three thermocouples during Test-1

  Figure III-10 corresponds to a complete and model Test-1 performed in our work. For each temperature studied, the reaction is left to execute during 8 h, in order to guarantee the reaction equilibrium before shifting to the next temperature. The automatic sampler (AS) (Figure III-7) collects hourly

Figure III- 11

 11 Figure III-11 Liquid effluent chromatograph for Test -8

  Figure III-9. Especially for high flow rate (Test-3 to Test-5) and high reaction temperatures (T = 360, 380 °C), the charge and product feed parts became non-negligible in the outlet gaseous flow. Firstly we determined the quantity of each component in the 100 mL ampoule by using the reference of 250 µL cis-butene gas and also the analysis of the chromatograph on the 250 µL gas sample shown in the Figure III-12 as example.

Figure III- 12

 12 Figure III-12 Gaseous effluent chromatograph for Test-7

1 1-X MCH→Tol as a function of 1 T

 11 (called Arrhenius plot) is nearly constant, and we can deduce the apparent activation energy of the reaction for the targeted temperature.

  Figure III-13.

Figure III- 13

 13 Figure III-13 Scheme depicting the determination of experimental reaction rate of point i (red point) on the conversion plot scheme as a function of space time

  Ĥelec = Te + Vee + Vne , each particular measurement of the energy gives one of the eigenvalues of 𝐻, we immediately have Equation (III-74)The energy calculated from a given Ψ is beyond to the true ground-state energy E 0 . Full minimization of the functional 𝐸 Ψ B = 𝐸 B ; that is, Equation (III-75) For a system of N electrons and given nuclear potential ν(r), we use Equation (III-76)

Figure III- 14

 14 Figure III-14 Comparison of toluene yields on different granulometries (200-355 µm vs 355-500 µm)

Figure IV- 1

 1 Figure IV-1 Molecular structure of the starting model of Pt 13 /γ-Al 2 O 3 (100) with 6 adsorbed hydrogen atoms. The labels of each Pt site and H atom is reported as explained in the main text. Left: side view ; Right: top view.

  methylcyclohexene (MCHe) and methyl-cyclohexadiene (MCHde). Nevertheless, if one analyzes the complete reaction network by considering all possible elementary steps, there is a large number of other possible surface intermediates (Figure IV-2). In particular, assuming subsequent monodehydrogenation steps, we can readily imagine the various radical intermediates formed after the C-H bond breaking from the initial molecule, before the formation of one new double-bond.

Figure IV- 2

 2 Figure IV-2 Simplified and non-exhaustive reaction network of dehydrogenation of methyl-cyclohexane to toluene by sequential C-H bond cleavage at each step. (black dot means radical component formed on the metal surface)

1 Figure IV- 3 1 .

 131 Figure IV-3 Various dissociative adsorption modes during dehydrogenation of MCH to C 7 H 12 intermediates on the Pt cluster : (a) 1-Methyl-cyclohexene, (b) 3-Methyl-cyclohexene, (c) 4-Methyl-cyclohexene, (d) Methylenecyclohexane (e) C 3 ,C 5 -radical, (f) C 1 ,C 4 -radical, (g) C 2 ,C 4 -radical. Corresponding energies are given at the PBE level in Table IV-1.

1

 1 Stability of the adsorbed intermediate on Pt 13 H 6 /γ-Al 2 O 3 as a function of the adsorption site In the previous paragraph, we calculated the dehydrogenation energy of methylcyclohexane(g) to 4-methyl-cyclohexene on the V3 platinum site. It is however important to check the sensitivity to the sites for this dissociative adsorption process. Meanwhile, the different possible adsorption conformations of 4-methyl-cyclohexene should also be carefully investigated as a function of the molecule orientation with respect to the cluster. Thus, a systematic geometry optimization investigation was performed, considering 20 adsorption sites and combination of sites and 57 conformations. The feature of the most stable conformations for each site are gathered in Table IV-3.

*:

  The conformation involves the displacement of atom H6 from a top position on V6 to a bridge position between V4 and S6 **: The conformation involves the displacement of atom H6 from a top position on V6 to a bridge position between V6 and S6 (Figure IV-1) 120

Figure IV- 4

 4 Figure IV-4 Different conformations for the adsorbed 4-MCHe with the π mode on the V3 site (PBE level). The corresponding energy data are given at the PBE level in Table IV-4.

1. 2 . 4

 24 has been performed at 3 distinct temperatures (500K, 800K and 1200K) for the 4-MCHe-Pt 13 H 6 /γ-Al 2 O 3 (100) on the V3 site, starting from the most stable configuration (V3-6 in Figure IV-4). Figure IV-5 reports the profile of potential energy during molecular dynamics at these three temperatures.

Figure IV- 5

 5 Figure IV-5 Potential energy as a function of time steps during AIMD for 4-MCHe-Pt 13 H 6 /γ-Al 2 O 3 (100) system on the V3 site : (a) 500 K; (b) 800K; (c) 1200K. ( PBE level) (the structures correspond to the chosen points that correspond to local minimum on the energy curve shown by circles, labeled by "P-n")

Figure IV- 6

 6 Figure IV-6 Calculated dehydrogenation electronic energy after quenching the relevant points of AIMD at temperature 500, 800 and 1200 K (P-0 : initial system before MD calculation). The structures correspond to the optimized geometry after quench at the PBE level

Following

  the previous detailed study of the 4-methyl-cyclohexene key intermediate, we now investigate the other intermediates involved in the simplified reaction network of Figure IV-7.We consider here a mechanism composed of sequential C-H breaking reactions, assuming that the molecule undergoes a mono-dehydrogenation steps and that one hydrogen atom is removed from the molecule to cluster, which can be described by a dissociative adsorption step of atomic hydrogen. This hypothesis induces 6 C-H cleavage steps, which produce 3 radical intermediates: methyl-cyclohexyl, methyl-cyclohexenyl, and methyl-cyclohexadienyl. Since at each step, one extra hydrogen is added to the cluster, we remove every two steps the two extra hydrogen atoms by releasing one H 2 molecule, which can be described as an associative desorption of molecular hydrogen, in order to keep the hydrogen coverage almost constant (6 or 7 hydrogen atoms) along the reaction pathway.

Figure IV- 7

 7 Figure IV-7 Simplified network for the dehydrogenation of MCH into toluene via 4-methyl-cyclohexene

Figure IV- 8

 8 Figure IV-8 Stable adsorption modes of each intermediate on Pt 13 H 6 /γ-Al 2 O 3 (100) at the PBE level : (a) Methylcyclohexyl C3-σ, (b) Methyl-cyclohexyl C4-σ; (c) Methyl-cyclohexenyl πσ (conjugated) (d) Methyl-cyclohexenyl πσ; (e) Methyl-cyclohexadiene 1,4-di-σ-2,3-π (f) Methyl-cyclohexadiene 2π; (g) Methyl-cyclohexadienyl C5-σππ (h) Methylcyclohexadienyl C6-σππ;(i) Toluene bri-2π2σ (j) Toluene 3π

Table IV- 7

 7 Adsorption modes, sites and dehydrogenation electronic energies for key intermediates adsorbed on Pt (111) along the dehydrogenation path at the PBE level. *For the radical species, the surface keeps one more hydrogen atom transferred from the molecule. ** d C-C : average C-C bond length *** d Pt-C : the vertical distance between the C6 ring center and the first metal surface layer.

Figure IV- 8 )

 8 Figure IV-8) was thus chosen to pursue investigations at the PBE-dDsC level between the various

  the cluster: configuration (a) is directly related to the geometry of methyl-cyclohexyl (the first intermediate of the reaction, Figure IV-8 (b)), whereas configuration (b) takes into account the possible interaction with the alumina support with a flat adsorption configuration parallel to the surface of the support. Adsorptions are significantly more favorable with the PBE-dDsC functional (up to 62 kJ/mol). Whereas with the PBE functional, no significant difference between configurations (a) and (b) is observed, the latter is strongly preferred with the PBE-dDsC functional.

9 PBE

 9 Electronic physisorption energy, Δ r E ads,MCH (g) (in kJ/mol), for methyl-cyclohexane calculated with PBE and -dDsC impact on adsorption configuration for the dehydrogenated intermediates Despite that PBE-dDsC functional generally induces only minor structure change for most of the intermediates after re-optimizing the systems obtained at the PBE level, we observed among all one particular intermediate that exhibits a major structural difference: methylcyclohexyl adsorbed on the cluster with one more hydrogen atom dissociated from the molecule to the cluster. The molecule cannot maintain its initial configuration and rotated slightly around the equatorial Pt-C bond while performing the geometry optimization with the PBE-dDsC functional (FigureIV-9). This configuration change can be likely explained by the fact that the dispersion forces between the molecule and the support are strong enough to induce such a the Pt (111) surface, the adsorption configurations of all intermediates stay closely consistent between PBE and PBE-dDsC.

Figure IV- 9 137 *

 9137 Figure IV-9 The unmaintained methyl-cyclohexyl configuration optimized with the PBE-dDsC functional

Pt 13 H 6 /

 136 Figure IV-10 Free energy profile for methyl-cyclohexane dehydrogenation over Pt 13 H 6 /γ-Al 2 O 3 at 625 K and 800 K along with the corresponding electronic energy profiles at 0 K at the PBE-dDsC level. The various colors for clusters in the schemes correspond to different cluster morphologies induced by major cluster reconstructions.

  Pt 13 H 6 /γ-Al 2 O 3 (100) at the PBE-dDsC level The C-H bond cleavage steps are suspected to be the most important ones related to the reactivity and selectivity of the catalysts. The relevant intermediates and transition structures for these steps are shown in Figure IV-11, while their thermodynamic and kinetic feature are reported in TableIV-14. These steps are all exothermic and mostly exergonic except that the third C-H bond cleavage from methyl-cyclohexene to methyl-cyclohexenyl + H (D à E) which is slightly endergonic. This step exhibits very low reaction electronic energy and enthalpy, but the biggest loss in entropy compared to other five C-H cleavage steps. Moreover, when it comes to activation data, the third C-H bond cleavage step (TS d ) gives the higher barrier in the forward direction in terms of electronic energy, enthalpy and free energy. This is probably due to the rotation and translation of the MCHe molecule (D) towards the cluster during the breaking of this

Figure IV- 11

 11 Figure IV-11 Configurations of all transition states of C-H bond cleavage steps for methyl-cyclohexane dehydrogenation reaction mechanism over Pt 13 H 6 /γ-Al 2 O 3 (100) at the PBE-dDsC level

Figure IV- 12

 12 Figure IV-12 Brønsted-Evans-Polanyi (BEP) linear relationships for Gibbs free energy profile for C-H bond cleavage steps in methyl-cyclohexane dehydrogenation reaction over Pt 13 H 6 /γ-Al 2 O 3 (100) at the PBE-dDsC level

Figure IV- 11 (

 11 See the other BEP figures inAppendix-IV-5).

Figure IV- 11

 11 Figure IV-11 illustrates the structures of these six transition states, with similar features:

Figure IV- 13

 13 Figure IV-13 Three centers configuration on the transition state TS d (the third C-H bond cleavage TS)

IV- 10 )

 10 , as soon as the methyl-cyclohexane is physisorbed on the cluster. If we assume that methyl-cyclohexane is adsorbed on the initial non reconstructed cluster (grey), the corresponding electronic energy variation Δ r E (reconstruction A in FigureIV-14) is +35 kJ/mol while the free energy variation Δ r G is about +25 kJ/mol in TableIV-16. If we assume that the reconstruction

  Figure IV-10). From a thermodynamic point of view (Table IV-16, Figure IV-14), the toluene desorption exhibits an electronic energy Δ r E of +220 kJ/mol, corresponding to Δ r G of 89 kJ/mol, while the subsequent cluster reconstruction into the initial one involves Δ r E= -41 kJ/mol and Δ r G= -25 kJ/mol presented in Table IV-16 as Recons. N 1 . If one assumes that the reconstruction occurs first in presence of adsorbed toluene and then the desorption occurs, the energy variation sequences are Δ r E= +52 kJ/mol (Δ r G= +70 kJ/mol, presented in Table-16, Figure IV-14 as Recons. N 2 ) and Δ r E= +127 kJ/mol (Δ r G= -5kJ/mol). Contrary to the methyl-cyclohexane adsorption step, the energy variations involved depend strongly on the order of the steps. According to this thermodynamic analysis, we suspect that the toluene desorption may occur preferentially after the cluster reconstruction.As shown in Table IV-16, the F à G reconstruction (with methyl-cyclohexenyl) is exothermic and exergonic,. Conversely, the I à J reconstruction (with methyl-cyclohexadiene) is endothermic and endergonic. The forward activation Gibbs free energies for the two 153 reconstruction steps during the reaction (F à G and I à J) are significantly smaller(40 and 20 kJ/mol at 625 K) than the highest ones calculated for the C-H bond cleavages. It can also be noticed that in the course of the I à J reconstruction several H atom migrations occur simultaneously. It should also be remarked that these cluster reconstruction steps remain moderate when compared to the morphological reconstructions invoked by the hydrogen coverage and temperature changes mentioned in the introduction, discovered by the previous study of Mager-Maury et al.6 That could explain the fact that the Gibbs free activation energies of these steps are smaller than those of the C-H cleavage steps.

Figure IV- 14

 14 Figure IV-14 Geometries (side views) of the reactant, transition state and product for the cluster reconstruction steps at the PBE-dDsC level

Figure IV- 15

 15 Figure IV-15 Transition states for H migration steps at the PBE-dDsC level

Figure IV- 16

 16 Figure IV-16 Gibbs free energy profiles for methyl-cyclohexane dehydrogenation reaction mechanism over Pt 13 H 6 /γ-Al 2 O 3 calculated with the PBE (blue line) and the PBE-dDsC (red line) functionals at 625 K

Figure IV- 16

 16 Figure IV-16 highlights that the dispersion forces have significantly impacted the adsorption

Figure IV- 17

 17 Figure IV-17 First five reaction intermediates and transition states discovered by PBE-dDsC functional during the geometry optimization calculation compared with those implied in reaction pathway with the PBE functional

1

 1 Reaction mechanisms of methyl-cyclohexane dehydrogenation over the Pt(111) surface at the PBE-dDsC level Table IV-19 Various intermediates and nature of elementary steps along the dehydrogenation of methyl-cyclohexane over the Pt(111) surface

Figure IV- 18

 18 Figure IV-18 Free energy profile for methyl-cyclohexane dehydrogenation reaction mechanism over the Pt(111) surface at 625 K and 800 K along with the corresponding electronic energy profiles at 0 K at the PBE-dDsC level.

  intermediates and transition states involved in C-H bond breaking steps are shown in Figure IV-19.The methyl-cyclohexane molecule adsorption reaction is an slightly endergonic step with nearly zero reaction free energy at 625 K.The C-H bond cleavage steps are all exothermic and exergonic. The ranges on these activation enthalpies and activation free energies are both about 50 kJ/mol. Nevertheless, BEP linear relationship on these C-H bond cleavage steps (TableIV-15 and Appendix-IV-4) were found both for enthalpy and free energy, better than on the cluster. This time, the most demanding step in terms of free activation energy is the second C-H bond cleavage step (B' à C' via TS b' ), in competition with the first one (A' à B' via TS a' ), which is not in an agreement with what we have found on the cluster model (third C-H bond cleavage was limiting whereas on Pt(111) it requires relatively low free activation energy).

Figure IV- 19 8 . 3

 1983 Figure IV-19 Configurations of all transition states of C-H bond cleavage steps for methyl-cyclohexane dehydrogenation over Pt(111) calculated with the PBE-dDsC functional

9 .

 9 Figure IV-21 Comparison of free energy profiles for methyl-cyclohexane dehydrogenation reaction mechanism on Pt 13 H 6 /γ-Al 2 O 3 and Pt (111) at 625 K calculated with the PBE-dDsC functional

)( 7 )

 7 The highest energy barrier found so far on Pt 13 H 6 /γ-Al 2 O 3 (100) corresponds to the third C-H cleavage step of methyl-cyclohexene into methyl-cyclohexenyl + H with a free activation energy of 95 kJ/mol at the PBE-dDsC level. However, the free activation energies for several steps are competitive (ex. The last C-H cleavage step of methyl-cyclohexadienyl +H to toluene + 2H with an free activation energy of 87 kJ/mol at the PBE-dDsC level), it is thus difficult to draw at this stage an unambiguous conclusion about the nature of the rate limiting step. Furthermore, on the Pt(111) surface, the second C-H cleavage step of methyl-cyclohexyl +H to methyl-cyclohexene + 2 H is found to be the most demanding step with a free activation energy of 79 kJ/mol, which is very close to that of first C-H cleavage step with an free activation energy of 78 kJ/mol at the PBE-dDsC level.(6) BEP linear relationship for these C-H cleavage steps was determined for both systems and have a better linear behavior on the surface than on the cluster. It is probably because of the complexity of the cluster system, with morphology change from one C-H bond breaking step to another. The cluster reconstruction steps and hydrogen atom migration steps are generally less activated than the C-H cleavage steps.

Figure IV- 22

 22 Figure IV-22 Most stable adsorption geometry for ethylene and 4-methyl-cyclohexene on the Pt 13 H 6 /γ-Al 2 O 3 (100) and Pt 13 /γ-Al 2 O 3 (100) surfaces : (a) ethylene π on Pt 13 H 6 /γ-Al 2 O 3 (100) ; (b) ethylene di-σ on Pt 13 /γ-Al 2 O 3 (100) ; (c) 4-MCHe π on Pt 13 H 6 /γ-Al 2 O 3 (100) ; (d) 4-MCHe di-σ on Pt 13 /γ-Al 2 O 3 (100)

Figure IV- 23

 23 Figure IV-23 Decomposition of the dehydrogenation energy (in kJ/mol) for adsorbed 4-methyl-cyclohexene before and after MD (Color legend: blue : reference system ; green : system before MD; orange : system after MD calculations.)

180 3 . 6 . 7 . 8 .

 3678 Figure IV-24 Thermodynamics table for reaction path on Pt 13 H 6 /γ-Al 2 O 3 (100) cluster at different temperatures at the PBE-dDsC level

  CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 188 CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A Pt/Al 2 O 3 CATALYST

Figure V- 1

 1 Figure V-1 Toluene yield in weight in the liquid outlet feed analyzed by gas chromatograph as a function of time for Test-1. The color code indicates the temperatures recorded by thermocouple T 2b ; The arrow interval marks the conversion points at steady state that are used to calculate the yield average value.

Figure V- 2

 2 Figure V-2 (a) Arrhenius plot (Equation III-60) (b) Eyring plot (Equation III-62) deduced from Test 1 at P(H 2 ) = 12.2 bar, P(MCH) = 0.8 bar and space time of 90 g cata .s.g MCH -1 .

Figure V- 3

 3 Figure V-3 Methyl-cyclohexane conversion to toluene as a function of space time at 360 °C and H 2 /HC = 15, with P(H 2 ) = 12.2 bar and P(MCH) = 0.8 bar. Both normalized and non-normalized conversions contain the liquid and gaseous phases. The non-normalized conversion is calculated by Equation (III-53) and normalized conversion is calculated by Equation (III-56) in Chapter : Computational and Experimental Methodology, section 2.2.

  4 in Chapter III, section 2.1.3, methyl-cyclohexane conversions into toluene were obtained at various weight hourly space velocities (WHSV). By applying Equation (III-43) we deduced the space time from WHSV. Figure V-3 plots the results obtained from three methods to calculate the toluene yield described in Chapter III, section 2.2.3 : the toluene yield in liquid phase, the non-normalized toluene yield containing the liquid and gaseous phase and the normalized toluene yield containing the liquid and gaseous phase. The error bars on each point represent about ± 7% conversion. Within this margin of errors, all methods lead to rather similar conversion levels. Some systematic deviations can however be CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 194

  CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 196 difference between our work and the one of Van Trimpont, despite the similarity on the reaction conditions and a higher platinum content in Van Trimpont's study.

Figure V- 5

 5 Figure V-5 Methyl-cyclohexane conversion to toluene as a function of (a) hydrogen partial pressure, at a constant methylcyclohexane partial pressure of 0.8 bar; (b) methyl-cyclohexane partial pressure, at a constant hydrogen partial pressure of 12.2 bar. All tests were at temperature T=360 °C and space time t= 90 g cata .s.g MCH

  Figure V-5(a), even though this maximum curve shape is not very pronounced in our case and the minimal hydrogen pressure we employed (P(H 2 ) = 2 bar) still provides a relatively high conversion point. The maximum is close to P(H 2 ) = 3 bar. According to the fitting modelling study carried out by Verstraete 6 on the kinetic data of Van Trimpont, a maximum at around P(H 2 ) = 5 bar at 350 °C was found, with different reaction conditions mentioned in Table V-1. In Figure V-5(b), at 360 °C and P(H 2 ) = 12.2 bar, it is shown how the conversion increases with increasing the methyl-cyclohexane up to P(MCH) = 0.5 bar and reaches a plateau

Figure V- 6

 6 Figure V-6 displays initial reaction rates measured for these three studies. In Figure V-6

Figure V- 6 (

 6 we observe: Van Trimpont et al. recovered only the decreasing trend in the high hydrogen partial pressure range whereas Sinfelt reported the increasing part at low hydrogen partial pressure. The same difference on reaction rate is also observed in Figure V-6(b), depicting the effect of P(MCH) at constant P(H 2 ). Nevertheless, we observe similar evolutions of reaction rate as a function of methyl-cyclohexane partial pressure for all three studies.

Figure V- 6

 6 Figure V-6 Initial reaction rate of methyl-cyclohexane dehydrogenation to toluene as a function of (a) hydrogen partial pressure (b) methyl-cyclohexane partial pressure

2 . Kinetic modelling investigation 2 . 1 Power-law kinetic model 2 . 1 . 1

 221211 CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 201 Variations of the reaction rate as a function of space time In order to define the effective reaction rate constant and reaction order more precisely at high conversion as in our case, we proposed a first power-law kinetic model (PL-I) rendering the evolution of the conversion as a function of the reaction space time. The reaction space time is defined as a function of the weight hourly space velocity (WHSV) previously by Equation (III-42) and (III-43) in Chapter III, section 2.1.3, which is varied from Test-1 to Test-6 in Table III-4

  Figure V-7 illustrates the Power-law fitting conversions and reaction rates (lines)obtained by Equation (V-1) and (V-2), compared with the experimental results (dots).

Figure V- 7

 7 Figure V-7 Power-law kinetic fitting model (PL-I) for the conversion to toluene and reaction rate as a function of spacetime fitted by the experimental data.

Reaction rate r 3

 3 MCHàTol ( mol MCH .g cata -1 h -1 ) Power-law kinetic fitting parameters (PL-I) for conversion as a function of space time (SSR: sum of squared residuals)

Figure V- 8 1 Table V- 5

 815 Figure V-8 Power-law fitting of the conversion, as a function of (a) methyl-cyclohexane partial pressure (PL-II) at constant hydrogen partial pressure of 12.2 bar (b) hydrogen partial pressure (PL-III) at constant methyl-cyclohexane partial pressure of 0.8 bar ; both at a temperature of 360 °C and WHSV of 40 gMCH.h -1 .g cata -1

  CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON APLATINUM/ALUMINA CATALYST 209

Table V- 6

 6 Single site surface reaction mechanisms with generation of molecular hydrogen as obtained by DFT calculationswith L 0 = active site. From A to N are all surface intermediates with active sites intrinsically included.The enthalpy and Gibbs free energy of the reaction as well as the enthalpy and free energy of activation for each elementary step are calculated from DFT (PBE-dDsC functional, see previous chapter) and are used to determine the reaction rate constant for both forward and backward reactions and equilibrium constant at T=625 K (Table V-7), according to the following equations :

Figure V- 9

 9 Figure V-9 Free energy profile calculated ab initio with the PBE-dDsC functional at 625 K, with mention of the three reaction sequences appearing to be the most relevant considering TDI and TDTS couples.

8 .

 8 The first one (TDTS-(I)) is equivalent to the RDS-(V) model. The two other ones (TDTS-(II) and (III)) are different in nature, as steps

2. 3 LH kinetic models based on a single rate determining elementary step without explicit consideration of adsorption competition with adsorbed atomic hydrogen 2 . 3 . 1 5 )

 32315 RDS-(I) model: irreversible rate-determining step (In this first LH kinetic model, we consider the elementary step (5) as rate determining and as being irreversible. The overall reaction rate can be thus expressed as follows : ES (5) :

H

  In order to recover the expression of the surface concentration of all subsequent intermediates to step(6), the equilibrium constant expressions have to be written from the last ES (Then the conservation of the number of sites provides:Equation (V-9) ~ (V-13) CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 219 So if we replace the term [L 0 ] in Equation (V-8) into ES (5) and ES (4), the rate can be written as : now, we derived the overall rate equation from our mechanistic model where all rate constants and equilibrium constants are calculated at the DFT level (Table V-7). Hence, no further assumption on these constants is required to study the evolution of the rate as a function of the partial pressures H 2 , MCH and Tol.If we first consider the early stage of the reaction (P Tol = 0 bar), the initial reaction rate can be expressed as: initial reaction rate equation presented by Equation (V-15) can be regarded as a simplified mechanistic model where only the first five elementary steps are involved in reaction kinetics. As a matter of fact, it is logical in this condition that the rate-determining step is irreversible and presents a relatively high energy barrier that "blocks" the next elementary steps.The respective influences of hydrogen and methyl-cyclohexane partial pressures on the initial reaction rate (in s -1 ) is reported in Figure V-10.

Figure V- 10

 10 Figure V-10 Initial reaction rates (P Tol =0 bar) calculated by model RDS-(I) (irreversible step (5) as RDS) as a function of (a) H 2 partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar (b) Methyl-cyclohexane partial pressure at constant H 2 partial pressure of 12.2 bar

r PH 2 à∞ à 0 r

 0 Chapter III: Computational and Experimental Methodology, section 2.1.1. So the new reaction rate r 0 (mol MCH .g cata -1 .h -1 ) obtained by model RDS-(I) can be calculated by Equation (V-16) : PMCHà∞ à 51.6 CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 221 The new reaction rates are thus compared with the experimental results in the Figure V-11. The order of magnitude on both sets of reaction rates (kinetic model versus experiments) is very satisfactory.

Figure V- 11 5 )

 115 Figure V-11 Initial reaction rates (P Tol =0) calculated by model RDS-(I) (irreversible step (5) as RDS) in comparison with experimental results (633 K), as a function of (a) H 2 partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar (b) Methyl-cyclohexane partial pressure at constant H 2 partial pressure of 12.2 bar at 625 K

Figure V- 12

 12 Figure V-12 Reaction rates as a function of methyl-cyclohexane conversion to toluene for RDS-(I) and RDS-(II) models (irreversible step (5) as RDS), at 625 K and at P 0 (H 2 ) = 12.2 bar and P 0 (MCH) = 0.8 bar, as a comparison with PL-(I) model and experimental results

5

 5

Figure V- 13

 13 Figure V-13 Initial reaction rate (P Tol =0) calculated by the RDS-(III) model (reversible step (13) as RDS) as a function of (a) H 2 partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar (b) Methyl-cyclohexane partial pressure at constant H 2 partial pressure of 12.2 bar

Figure V- 14

 14 Figure V-14 Reaction rates as a function of methyl-cyclohexane conversion to toluene for RDS-(I), (II) and (III) models at 625 K, as a comparison with experimental results and PL-(I) model at initial hydrogen pressure of 12.2 bar and initial methyl-cyclohexane pressure of 0.8 bar

2 . 3 . 4

 234 REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 229 explicit consideration of the site competition between atomic hydrogen and methyl-cyclohexane dehydrogenation intermediates, which is the object of the section 2.4. Arrhenius plot and Eyring plot for models RDS-(I), (II) and (III)

2 . 4

 24 Figure V-15 Arrhenius plot and Eyring plot for the RDS-(I) and (II) models

  10) MCHde-L D MCHde (r) -L cluster reconstruction (11) MCHde (r) -L + L D A 3 -L + H c -L C-H bond cleavage (12) A 3 -L D A 3(d) -L H atom migration (13) A 3(d) -L + L D Tol-L + H c -L C-H bond cleavage CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUMD Tol (g) + L toluene desorption with L = free active site, MCH = Methyl-cyclohexane; A 1 = Methyl-cyclohexyl; MCHe = Methyl-cyclohexene; A 2 = Methyl-cyclohexenyl; MCHde = Methyl-cyclohexadiene; A 3 = Methyl-cyclohexadienyl; Tol = Toluene; H a , H b , H c = three types of atomic hydrogen; subscript (d) = intermediate molecular species from the hydrogen atom migration step; subscript (r) = intermediate molecular species from the cluster reconstruction step; subscript (g) = gas phase.The free energy and reaction constants for each numbered elementary step remain the same as in

Figure V- 17

 17 Figure V-17 Initial reaction rates (P Tol =0 bar) calculated by the RDS-(IV) model (irreversible step (5) as RDS) in comparison with experimental results (633 K), as a function of (a) H 2 partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar (b) Methyl-cyclohexane partial pressure at constant H 2 partial pressure of 12.2 bar at 625 K

  REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 239

  shape as in Figure V-17. Instead, the rate scale calculated by Equation (V-34) is 10 5 times smaller than the experimental results, due to the term K ' H instead of K ' H a . Nonetheless, the evolution of the surface species concentrations at the very beginning of the reaction (P Tol = 0 bar), as a function of variable hydrogen pressure at same condition for a constant methyl-cyclohexane partial pressure, can probably provide us a clue on the explanation of the maximum rate discovered by the two models locating in a very narrow hydrogen pressure interval (P H 2 < 0.1 bar). This analysis is presented in the Figure V-18.

Figure V- 18

 18 Figure V-18 Evolution of the coverages of surface species methyl-cyclohexene (MCHe), hydrogen (Ha or H) and active sites (L) as a function of hydrogen partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar at 625 K for (a) RDS -(IV) model; (b) RDS -(V) model

Figure V- 19

 19 Figure V-19 Reaction rates as a function of methyl-cyclohexane conversion to toluene for RDS-(V) model at 625 K and at P 0 (H 2 ) = 12.2 bar and P 0 (MCH) = 0.8 bar in comparison with PL-(I) model and experiments

Figure V- 20 13 )

 2013 Figure V-20 Evolution of the concentrations of relevant surface species Toluene (Tol), methyl-cyclohexadienyl (A 3(d) ), Methyl-cyclohexene (MCHe), hydrogen (H) and active sites (L) as a function of methyl-cyclohexane conversion to toluene for the RDS-(V) model at 625 K and at P 0 (H 2 ) = 12.2 bar and P 0 (MCH) = 0.8 bar

  37) ~ (V-39)The other constants remain identical as for model RDS-(V).So if we replace the term [L] in Equation (V-36) and the terms [A 3(d) -L], [Tol -L] and [H c

  REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A PLATINUM/ALUMINA CATALYST 246 Therefore, the impacts of hydrogen and methyl-cyclohexane partial pressure on the initial reaction rate are also studied for RDS-(VI) (Figure V-21).

Figure V- 21

 21 Figure V-21 Initial reaction rates (P Tol =0 bar) calculated by RDS-(VI) in comparison with experimental results (633 K), as a function of (a) H 2 partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar (b) Methyl-cyclohexane partial pressure at constant H 2 partial pressure of 12.2 bar at 625 K

  Figure V-21(b), the model fits very well with the experiments as the rates stop increasing rapidly at around 0.5 bar of methyl-cyclohexane.

Figure V- 22

 22 Figure V-22 Evolution of the coverage of surface species methyl-cyclohexadienyl (A 3(d) ), hydrogen and active sites as a function of (a) hydrogen partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar and of (b) methylcyclohexane partial pressure at constant hydrogen partial pressure of 12.2 bar, for the RDS-(VI) model at 625 K

Figure V- 23

 23 Figure V-23 Reaction rates as a function of methyl-cyclohexane conversion to toluene for the RDS-(VI) model at 625 K and at P 0 (H 2 ) = 12.2 bar and P 0 (MCH) = 0.8 bar

Figure V- 29 Figure V- 30

 2930 Figure V-29 Converted initial reaction rates (P Tol =0 bar) calculated by the TDTS-(III) model (reversible step (15) as RDS) in comparison with experimental results (633 K), as a function of (a) H 2 partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar (b) Methyl-cyclohexane partial pressure at constant H 2 partial pressure of 12.2 bar at 625 K

Figure V- 31 2 . 4 . 6

 31246 Figure V-31 Reaction rates as a function of methyl-cyclohexane conversion to toluene for the TDTS-(III) model (reversible step (15) as RDS) at 625 K and at P 0 (H 2 ) = 12.2 bar and P 0 (MCH) = 0.8 bar

Figure V- 33 2 . 4 . 7

 33247 Figure V-33 Evolution of the calculated rates in t sensibility analysis for model RDS-(VI) compared to the experimental results: (a) initial reaction rate as a function of hydrogen partial pressure at constant methyl-cyclohexane partial pressure of 0.8 bar (b) initial reaction rate as a function of methyl-cyclohexane partial pressure at constant hydrogen partial pressure of 12.2 bar (c) reaction rate as a function of methyl-cyclohexane conversion to toluene at P 0 (H 2 ) = 12.2 bar and P 0 (MCH) = 0.8 bar

Pt 13 H

 13 6 /γ-Al 2 O 3 (100) and Pt(111) systems. The dispersion corrections have significantly decreased the free energy profiles and also impact some adsorption structures, especially prominent for the first methyl-cyclohexane physisorption step of and methyl-cyclohexyl chemisorption. These dispersion forces are stronger on the Pt(111) surface than on Pt 13 H 6 /γ-Al 2 O 3 (100), with a free energy lowering of 80 kJ/mol on Pt(111) against 30 kJ/mol on Pt 13 H 6 /γ-Al 2 O 3 (100).On Pt 13 H 6 /γ-Al 2 O 3 (100), the fluctionality of the cluster induces several steps of cluster reconstruction and hydrogen atom migration coming along with the sequential C-H bond cleavage steps. The highest energy barrier found so far on Pt 13 H 6 /γ-Al 2 O 3 (100) corresponds to the third C-H cleavage step of methyl-cyclohexene into methyl-cyclohexenyl + H with a free activation energy of 95 kJ/mol at the PBE-dDsC level. However, the free activation energies for several steps are close:for instance, The last C-H cleavage step of methyl-cyclohexadienyl +H to toluene + 2H exhibits a free activation energy of 87 kJ/mol at the PBE-dDsC level. The cluster reconstruction steps and hydrogen atom migration steps are generally less activated than the C-H cleavage steps. Meanwhile, on the Pt (111) surface, the second C-H cleavage step of methylcyclohexyl +H to methyl-cyclohexene + 2 H is found to be the most demanding step with a free activation energy of 79 kJ/mol, which is very close to that of the first C-H cleavage step with an free activation energy of 78 kJ/mol at the PBE-dDsC level.

Table II -1 Thermodynamic data, at 500°C, of typical reforming reactions with C6 and C7 hydrocarbons 2 Reaction type Reaction Δ r H°(kJ/mol)

 II

	Dehydrogenation	Methylcyclohexane D Toluene + 3 H 2	216
	Dehydrocyclization n-Heptane DToluene +4 H 2	252
	Hydrocracking	n-Heptane + H 2 D Propane + n-butane	-52
	Hydrogenolysis	n-Heptane + H 2 D Methane + n-hexane	-62

Table II -2 Cyclohexane dehydrogenation activities of supported metal and metal oxide catalysts 2 Catalyst, wt% Dehydrogenation activity (µmoles benzene/g catalyst/s) 34% Cr 2 O 3 cogelled with Al 2 O 3 0.5 10% MoO 3 coprecipitated with Al 2 O 3 3 5% Ni on Al 2 O 3 or SiO 2 -Al 2 O 3 13 5% Co on Al 2 O 3 13 0.5% Ir on Al 2 O 3 190 1% Pd on Al 2 O 3 200 5% Ni on SiO 2 320 1% Rh on Al 2 O 3 890 0.5% Pt on Al 2 O 3 or SiO 2 -Al 2 O 3

 II

1400-4000 *differential flow reactor at 427°C, 6.8 atm, H 2 /HC=6 (mole ratio), activity determined after 30 min on stream, pretreated with H 2 at reaction conditions.

Table II -3 Kinetic rate and equilibrium constants fitted for the LHHW dual site surface reaction mechanism at 623 K in the work of Van Trimpont 20

 II

Note :

(1)

The values in black were taken from the Table V and VII for the rate equation II (4) in Ref.

20;

Table II -4 Comparison of the adsorption energies obtained by four DFT studies for benzene hydrogenation on Pt (111) or Pt 22 cluster. 82,85,87,86 Species ΔE ads (kJ/mol) 1,4

 II

  all the values are calculated by equation : ΔE ads (BH n,ads ) = E el (BH n,ads ) -E el,Benzene,g -E el,cat 2 the energies presented here are recalculated by Sabbe et al. using the same equation in1 and the results in ref.82

					$ %	E H 2 ,g -
		-68(fcc 3π)	-65(fcc 3π)	-71(fcc 3π)	-45(fcc 3π)
	Benzene
		---	-87(bri 2π2σ)	-102(bri 2π2σ)	-77(bri 2π2σ)
	monohydrobenzene	-100	-99	-125	---
	1,3-cyclohexadiene	-135	-133	-151	---
	1,3-dihydrobenzene	-140	-140	-167	---
	1,4-cyclohexadiene	-122	-120	-141	---
		-169(σπ)	-173(σπ)	-210(σπ)	---
	1,2,3-trihydrobenzene
		-177(σσσ)	-179(σσσ)	---	---
	1,2,4-trihydrobenzene	-161	-165	-194	---
	1,3,5-trihydrobenzene	-164	-168	-199	---
	cyclohexene	-204	-200	-228	---
	1,2,3,5-	-189	-191	-216	---
	tetrahydrobenzene
	1,2,4,5-	-172	---	-180	---
	tetrahydrobenzene
	cyclohexyl	-240	---	-257	---
	cyclohexane	-295	---	-323	---

Sabbe et al. Morin et al. Saeys et al. 2 Ma et al.

3

1

  the size of which is 16.7 × 16.8 × 25.8 Å 3 , occupied by 7.2 Å thick γ-alumina slabs (normal to the z axis) separated by a 18.6 Å vacuum layer. During geometry optimization, only the two uppermost alumina layers, the platinum cluster and the adsorbed molecule were allowed to relax. The properties of free gas phase molecules were calculated thanks to 25 × 25 ×

Table III -2 Summary of the methyl-cyclohexane dehydrogenation reaction conditions used for alumina supported platinum catalysts in the literatures 47-52 First author wt% Pt Pressur e (bar) Temperatur e (°C) H 2 /HC (mol/mol) WHSV (g MCH .h - 1 .g cata -1 ) Space time (g cata .s.g MCH -1 )

 III

	Alhumaidan 47	1.0	0-9	340 -450	0 -9	2.9 -11.5	313 -1241
	Rochefort 48	0.06 -0.82	1.01	300	5	580 -2300	1.6 -6.2
	Sinfelt 49	0.3	1.4 -6.3	315 -372	2 -20	50 -100	36 -72
	Van Trimpont 50	0.5 (0.67-Cl; sulfided)	4.5 -20	309 -410	9 -100	8 -200	18 -450
	Usman 51	1.0	1 -9	340 -380	0 -8.4	3 -12	300 -1200
	Maria 52	Sulfided	6 -16	289 -309	2.5 -10	14 -60	60 -257

Table III -4 Reaction conditions for the methyl-cyclohexane dehydrogenation catalytic test over Pt/γ-Al 2 O 3 catalyst

 III

	Equations (III-42) and (III-43):
	WHSV	g MCH h.g cata	=	Mass flow rate of MCH Catalyst mass	=	F m,MCH m cata
							Equation (III-42)
	Space time	h.g cata g MCH	=	1 WHSV	=	m cata F m,MCH
							Equation (III-43)

* : WHSV = weight hourly space velocity MCH = methyl-cyclohexane H 2 /HC = hydrogen to hydrocarbon ratio

The tests are parameterized according to four investigation purposes. Test-1 is a complete and model test with 4 different temperatures from 320 to 380°C and one repeated temperature (360°C) at the end to confirm that the catalyst is not deactivated. The pressure and the weight hourly space velocity (WHSV) are chosen to achieve different conversion ranges for each temperature while minimizing coking or sintering the catalyst. The catalyst is considered as nondeactivated if the conversion at the repeated temperature 360 °C at the end of the test is found identical to the one at the same temperature 360 °C before. For the other tests, are varied each time one operating condition to make comparison with the others at one temperature of 360°C, which was found to give access to the wider conversion range by changing the reaction conditions. Test-1 to Test-5 aim at varying the weight hourly space velocity (WHSV) parameter in order to unravel the conversion and reaction rate as a function of space time, by using Test-7 to Test-10 aim at quantifying the impact of hydrogen partial pressure as compared to Test-1, keeping the methyl-cyclohexane partial pressure constant; while Test-1, 11 and 12

  ). represents the number of mole of each component i found in the sample volume V

			Equation (III-47)
	n 0,Tol (g) =n 0,butene (g) ×	A Tol RF' Tol A butene RF' butene
			Equation (III-48)
	RF i ' =	1 n carbon
			Equation (III-49)
	n 0,i
	n 0,MCH (g) =n 0,butene (g) ×	A MCH RF' MCH A butene RF' butene

0 = 100 mL, RF' is the new response factor employed, which is simply related to the number of carbon atoms counted in the molecule. Assuming that the amount of each component in our outlet gas feed volume V measured is proportional to that in ampoule volume V 0 , we thus have:

  7 H 14 ) into methyl-cyclohexene (C 7 H 12 ) or related compounds on Pt 13 H 6 /γ-Al 2 O 3 (100), the H 2 molecule being released in gas phase, as we would like to keep the hydrogen coverage constant. We start by a systematic exploration of the stability of the various possible C 7 H 12 intermediates adsorbed on Pt 13 H

6 /γ-Al 2 O 3 (100) involving thus numerous isomers for methyl-cyclohexene (MCHe) and also radical intermediates as reported in Table IV-1 and Figure IV-3 for the two sites V3 and V5, which are chosen due to their availability for the molecule from a steric point of view (non-occupied by H atoms). The corresponding dehydrogenation electronic energies of methyl-cyclohexane (g) into these different intermediate isomers (and dihydrogen in gas phase) have been evaluated and compared in Table IV-1. The dehydrogenation electronic energy of methyl-cyclohexane can be calculated in the same way of the free energy notion mentioned in Chapter III: Methodology, section 1.3.1 with Equation (III-36) and (III-37) , then we have :

Table IV -2 Dehydrogenation energy of relevant C 7 H 12 adsorbed on Pt (111) surface at the PBE level

 IV

Table IV -3 Calculated feature (dehydrogenation energy, distances) for different 4-MCHe adsorption modes at different adsorption sites at the PBE level

 IV

	Adsorption	Most stable	Number of adsorption	D r E dehyd,MCH(g)
					d C3-C4 (Å) d C3-M (Å) d C4-M (Å)
	Site(s)	adsorption mode	conformations calculated	(kJ/mol)
	V1	π	6	51	1.41	2.23	2.22
	V2	π	6	84	1.42	2.17	2.22
	V3	π	6	32	1.42	2.17	2.17
	V4	π	1	71	1.43	2.18	2.14
	V5	π	5	55	1.41	2.24	2.24
	V6 *	π	2	99	1.43	2.17	2.17
	S2	π	3	63	1.43	2.12	2.13
	S6	π	2	88	1.43	2.13	2.11
	S7	π	2	130	1.40	2.27	2.33
	V1-V2	di-σ	2	97	1.50	2.10	2.10
	V2-V3	di-σ	2	72	1.48	2.14	2.13
	V2-V5	di-σ	2	110	1.44	2.26	2.27
	V3-V5	di-σ	2	74	1.46	2.12	2.17
	V5-V6 **	di-σ	2	73	1.50	2.13	2.10
	V1-V4	di-σ	2	62	1.48	2.20	2.13
	V4-V6	di-σ	2	127	1.50	2.12	2.12
	V4-V5	di-σ	3	136	1.46	2.21	2.25
	V2-V4	di-σ	2	129	1.50	2.17	2.15
	V3-S2	di-σ	3	72	1.49	2.10	2.10
	V2-S2	di-σ	2	69	1.48	2.10	2.10

Table IV -4 Dehydrogenation energies and bond lengths for the adsorbed 4-MCHe with the π mode on the V3 site for various conformations at the PBE level. The corresponding molecular structures are given at the PBE level in Figure IV- 4.

 IV

			D r E dehyd,MCH(g)
	Adsorption Site	Adsorption mode		d C3-C4 (Å) d C3-M (Å) d C4-M (Å)
			(kJ/mol)
	V3-1	π	43	1.42	2.18	2.20
	V3-2	π	36	1.41	2.19	2.19
	V3-3	π	48	1.43	2.18	2.14
	V3-4	π	44	1.41	2.25	2.17
	V3-5	π	48	1.41	2.30	2.16
	V3-6	π	32	1.42	2.17	2.17

Table IV -

 IV 6 and Figure IV-8 present the features of the most stable geometries calculated for each intermediate at the PBE level. For non radical species, two relevant species are depicted.

Table IV -8 Electronic physisorption energy, Δ r E ads,MCH (g) (in kJ/mol), for methyl-cyclohexane calculated with PBE and PBE-dDsC functionals over Pt 13 H 6 /γ-Al 2 O 3 (100) cluster

 IV

	Functional
	PBE	21	17
	PBE-dDsC	1	-45

Table IV -

 IV

8 reports the stability of two physisorption modes for methyl-cyclohexane on

Table IV -

 IV 10 shows the dehydrogenation energies of the chosen intermediates for the reaction pathway, at the PBE-dDsC level. Compared to the energies calculated with PBE, we observe that the energy decrease is around 20 kJ/mol for each intermediate, except for the

methyl-cyclohexyl radical for which it is reduced of about 40 kJ/mol, the latter decrease being even stronger than for MCH physisorption (Table

IV-8

). The configurations of physisorbed MCH and methyl-cyclohexyl are quite similar, both parallel with an interaction with the alumina support. Starting from methyl-cyclohexene, the intermediates tend to rotate toward the cluster and move away from alumina till the formation of toluene, which is adsorbed flat on the cluster and shows nearly no contact with alumina for this configuration ((j) in Figure

IV-8

). The dehydrogenation energies for each intermediate on the Pt (111) surface is also calculated at the PBE-dDsC level (Table

IV

-11)

. Once again, on the surface, the gain of stability (50-90 kJ/mol) for intermediates from PBE to PBE-dDsC is much more remarkable than that on the cluster. The platinum metal surface once again induces stronger intermolecular interactions than the γ-Al 2 O 3

  -12: methyl-cyclohexane adsorption and toluene desorption, C-H bond cleavage, cluster reconstruction, H atom migration, H 2 desorption. Reaction, possibly activation when determined, energies (Δ r E, Δ r E ‡ ), enthalpies (Δ r H, Δ r H ‡ ), entropic terms (TΔ r S, TΔ r S ‡ ) and

Table IV -13 Thermodynamic data for the methyl-cyclohexane adsorption and toluene desorption elementary steps involved in the methyl-cyclohexane dehydrogenation mechanism on Pt 13 H 6 /γ-Al 2 O 3 at the PBE-dDsC level Elementary step Reaction energy, enthalpy, entropy term and Gibbs free energy at 625 K (kJ/mol)

 IV

		Δ r E	Δ r H	TΔ r S	Δ r G
	MCH (g) à A	-45	-40	-91	51
	N à Tol (g)	179	174	130	44

  Figure IV-11). The second most energy demanding step in forward reaction (electronic energy, enthalpy and free energy) is the last C-H bond cleavage step (TS l ) on methylcyclohexadienyl + H to form the most stable intermediate toluene + 2H (L à M). The difference

	C-H bond (
					42	-48	-7	-41	31	19	-14	33	73	67	-7	74
	B à C	TS	b	-18	-27	3	-31	88	74	4	70	106	101	1	101
	D à E	TS	d	6	-6	-12	6	113	98	3	95	107	104	15	89
	G à H	TS	g	-70	-78	-4	-74	47	33	0	33	118	111	4	107
	J à K	TS	j	-41	-52	6	-58	45	34	-10	44	86	86	-17	103
	L à M	TS	l	-23	-30	16	-46	107	94	7	87	130	124	-8	132
																146

Table IV -15 Brønsted-Evans-Polanyi (BEP) linear relations for C-H bond cleavage steps on Pt 13 H 6 /γ-Al 2 O 3 (100) cluster and Pt (111) surface on electronic energy (Δ r E), enthalpy (Δ r H) and Gibbs free energy (Δ r G)

 IV

		Pt 13 H 6 /γ-Al 2 O 3 (100)		Pt (111)
		Δ r E	Δ r H	Δ r G	Δ r E	Δ r H	Δ r G
	α	1.10	1.13	0.75 1.20 1.33	1.31
	β (kJ/mol)	106	104	91	81	83	84
	R 2	0.66	0.67	0.56 0.90 0.95	0.81

Table IV -18 Thermodynamic data of H 2 desorption steps at the PBE-dDsC level Elementary step Reaction energy, enthalpy, entropy term and Gibbs free energy at 625 K (kJ/mol)

 IV

		Δ r E	Δ r H	TΔ r S	Δ r G
	C à D + H 2	108	103	74	29
	H à I + H 2	147	141	81	60
	M à N + H 2	127	124	59	65

  on such a surface model also provide references for this part of work, in terms of molecular structures and adsorption energies. The various intermediates involved in the reaction mechanism of methyl-cyclohexane dehydrogenation over Pt(111) are presented in Table IV-19. Compared to the mechanism taking place over Pt 13 H 6 /γ-Al 2 O 3 (100), the reaction mechanism simply implies the C-H bond cleavage and the molecule adsorption/desorption steps.

  -20 does not report any electronic energy for the ipso intermediate (C 7 H 11 +H) at the PBE level. This significant discrepancy with the case of benzene hydrogenation is certainly due to the steric hindrance of the methyl-group on the carbon atom bearing one radical and thus the ipso intermediate is not as "flat" as in absence of methyl group.

	162

Table IV -21 Thermodynamics and kinetic data for all elementary steps involved in methyl-cyclohexane dehydrogenation over Pt (111) at 625 K calculated with the PBE-dDsC functional Elementary step Transition States Reaction energy, enthalpy, entropy term and Gibbs free energy at 625 K (kJ/mol) Activation energy, enthalpy, entropy term and Gibbs free energy (forward) at 625 K (kJ/mol) Activation energy, enthalpy, entropy term and Gibbs free energy (backward) at 625 K (kJ/mol)

 IV

Table IV -22 Adsorption energy for ethylene and 4-methyl-cyclohexene on the Pt 13 H 6 /γ-Al 2 O 3 (100) and Pt 13 /γ-Al 2 O 3 (100) surface at the PBE level Pt 13 H n /γ- Al 2 O 3 (100) E ads , Ethylene (kJ/mol) E ads , 4-MCHe (kJ/mol)

 IV

		di-σ	π	di-σ	π
	n = 6	-107	-122	-68	-111
	n = 0	-166	-140	-130	-127

Table V -1 Different reaction conditions employed for each curve in Figure V-4

 V

Table V -2 Different catalysts and reaction conditions employed in this work and in the literature for studying the impact of MCH and H 2 partial pressure on the reaction rate

 V

  Table V-3, the agreement between experiments and the power rate law is satisfactory, except for the very first points of rate values, due to the lack of experimental points at very low contact time, rendering the estimation of the slope rather imprecise from experimental data. Although, the fitting result is quite satisfactory with a SSR of 11.

  Trimpont et al. use sulphided catalysts, likely to be less reactive, and Usman et al. work with higher loadings in platinum (1 %) than we do, with suspected impact on the dispersion, this difference may be as consequence of the hydrogen pressure term, which is implicitly included in our rate constant. However, if we use the partial reaction orders of hydrogen in Table V-4 and take into account our employed hydrogen pressure 12.2 bars, we can thus deduce the new rate form of the employed power-law rate equations and also the reaction order, regarding the unit that contains the term bar -n . For this reason, the rate constants found by Usman et al.4 is 100 times smaller than that found by Verstraete6 and for the new constants, Van Trimpont et al. and Alhumaidan et al. have a good agreement on value but not unit. Moreover, with the same power-law rate equation for the study of Alhumaidan 3 and Verstraete6 , the methylcyclohexane order is different as well as rate constants. All this suggests that a power-law rate model is much too simplified for the present case, and is not sufficient to reflect the real mechanistic complexity. A more precise model for each reaction elementary step has to be established if we are looking forward to finding a logical explanation on the reaction kinetics.

	CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A
	PLATINUM/ALUMINA CATALYST
	depending on the
	constants of each study in literature, implicitly including the hydrogen pressure term in the rate
	constant as ours. We found that the new constants: 0.033 mol MCH .g cata	-1 h -1 bar -0.68 for Van
	Trimpont et al.; 0.036 mol MCH .g cata	-1 h -1 for Alhumaidan et al.; 0.12 mol MCH .g cata	-1 h -1 bar -0.68 for
	Verstraete et al.. Still, it appears to exist an incoherence. Likewise, the rate constant varies
				205

Table V -4 Summary of the different Power-law kinetic fitting models for the methyl-cyclohexane dehydrogenation reaction in the literature 4,5,3,6

 V Note: all the employed catalysts in these works are Pt-based catalyst. However, Usman and Alhumaidan used same 1.0 wt% Pt catalyst; while Van Trimpont and Verstraete were on sulphided 0.5 wt% Pt catalyst.

	CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A
															PLATINUM/ALUMINA CATALYST
	Moreover, this apparent reaction rate constant that we obtained by fitting experimental
	data describes the reactivity by catalyst mass and the pressure (k is expressed in mol MCH .g cata	-1 .h -
	1 .bar
	First Author					Usman									Van Trimpont		Alhumaidan			Verstraete
	Rate equation	r	=	k	(	MCH P	-	Tol P	K P	3	H	2	)	n	r	=	MCH kP	n	MCH	H 2 n H P	2	Tol P	Tol n	r =	MCH kP	n	MCH	2 H n H P	2	r =	MCH kP	MCH n	2 H n H P	2
	k	0.053 (mol MCH .g cata -1 .h -1 .bar -0.5 )	0.81 (mol MCH .g cata -1 .h -1 .bar 0.6 )	0.10 (mol MCH .g cata -1 .h -1 .bar 0.4 )	1.34 (mol MCH .g cata -1 .h -1 .bar 0.3 )
	T (°C)					344										350					344				375
	n MCH																0.71					-0.05				0.64
	n H 2					0.52									-1.28					-0.41				-0.98
	n Tol																		0						--						0
																																		206

*

  The reaction rate constants are, however, closer to the values reported in the literature than the one found by PL-I. As we determined the H 2 reaction order by PL-III, we can now deduce the intrinsic rate constant contained in the reaction rate determined by PL-I on space time, on the purpose of rendering this rate constant, obtained by the best fitting model among the three,

	comparable with the values reported in the literature. The component P H 2	n b is thus divided from
	the k in Table V-3 (P H 2 = 12.2 bar; n b = 0.3; k = 81.8 mol MCH .g cata	-1 .h -1 .bar -3.3 ) and the real rate
	constant k r determined by PL-I and PL-III equals 38.6 mol MCH .g cata	-1 .h -1 .bar -3.6 . This is still higher
	than the values reported in Table V-4.

Table V -7 Thermodynamic and kinetic data calculated by DFT (PBE-dDsC functional) for single site dehydrogenation reaction mechanisms at 625 K Elementary step Reaction enthalpy, Gibbs free energy and equilibrium constant (T = 625 K)

 V

												Forword activation enthalpy, Gibbs	Backward activation enthalpy, Gibbs
												free energy and rate constant	free energy and rate constant ()
													(T = 625 K)	(T = 625 K)
									ΔrH (kJ/mol)	ΔrG (kJ/mol)	Keq	ΔrH ‡ (kJ/mol)	ΔrG ‡ (kJ/mol)	kr+ (s	-1	)	ΔrH ‡ (kJ/mol)	ΔrG ‡ (kJ/mol)	kr-(s	-1	)
	(1) MCH	(g) + L	0 D A	-40	51	6.01E-05	-40	51	7.83E+08	0	0	1.30E+13
	(2) A D B							-48	-41	2.85E+03	19	33	2.31E+10	67	74	8.13E+06
	(3) B D C							-27	-31	3.63E+02	74	70	1.86E+07	101	101	5.13E+04
	(4) C D D + H	2			103	29	4.05E-03	103	29	5.27E+10	0	0	1.30E+13
	(5) D D E							-6	6	3.33E-01	98	95	1.56E+05	104	89	4.69E+05
	(6) E D F							6	-2	1.54E+00	53	41	5.11E+09	47	43	3.31E+09
	(7) F D G							-17	-32	4.58E+02	61	40	6.21E+09	78	72	1.36E+07
	(8) G D H							-78	-74	1.49E+06	33	33	2.35E+10	111	107	1.58E+04
	(9) H D I + H	2					141	60	1.02E-05	141	60	1.33E+08	0	0	1.30E+13
	(10) I D J							1	11	1.24E-01	20	20	2.60E+11	19	10	2.09E+12
	(11) J D K							-52	-58	7.35E+04	34	44	2.56E+09	86	103	3.48E+04
	(12) K D L							-30	-23	8.04E+01	48	42	3.97E+09	78	65	4.94E+07
	(13) L D M							-30	-46	6.36E+03	94	87	7.62E+05	124	132	1.20E+02
	(14) M D N + H	2		124	65	3.67E-06	124	65	4.78E+07	0	0	1.30E+13
	(15) N D Tol	(g) + L	0	174	44	2.30E-04	174	44	3.00E+09	0	0	1.30E+13

  The first family of models (called RDS (I)-(III), see later section 2.3) will use a so-called "extended LH model" (presented in Table V-6) for which each intermediate will be a system embedding the cluster and the adsorbed species. The advantage of this hypothesis is to facilitate the treatment of the H-migration and cluster reconstruction that are considered to generate new intermediates. So, this model does not distinguish the hydrogen atoms from the dehydrogenated MCH molecules but considers all the species adsorbed on the cluster and the reconstructed cluster itself as a global intermediate. Hence, this first family of models will not allow to simulate the coverage of the cluster by the various species instead of the distribution of each global extended intermediate [cluster + adsorbed species]. In particular, competitive adsorption between

	CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A
	PLATINUM/ALUMINA CATALYST
	213

Table V -8 Terminology and main characteristics of the various LH models built. Name of the model Approach Nature of the RDS and {TDI ; TDTS} couple when it applies

 V

	Consideration of the	Explicit consideration of
	backward (reversible) or not (irreversible) for the	adsorption competition with
	RDS / limiting sequence	adsorbed atomic hydrogen

Table V -9 Kinetic parameters derived from DFT calculated energy profile (PBE-dDsC functional) for different temperatures

 V

  Table V-7 and Table V-9. The LHHW rate equations are however re-written by what is following in cases of rate-determining step (

  so we have :

	CHAPTER V -REACTION KINETICS FOR THE DEHYDROGENATION OF METHYLCYCLOHEXANE INTO TOLUENE ON A
	PLATINUM/ALUMINA CATALYST
	ES (1) :
	234

With m Tol (g) the mass of toluene in gaseous phase, m Tol (l) the mass of toluene in liquid phase from the manual sampler (MS in Figure III -7), which can be obtained by the toluene yield in Equation (III-53). m Inlet the inlet mass of methyl-cyclohexane liquid feed flow introduced into the set-up, which can be calculated from the inlet methyl-cyclohexane (MCH) volumetric rate flow (Table III-4) and density.

Mass balance

It is crucial to establish the mass balance between the inlet and the outlet, for the sake of the reliability of the calculated conversion. This mass balance could be affected by several factors, such as facility leaks, secondary reactions, manipulation uncertainties, etc. The mass balance can be established by comparing the total mass at the inlet and that at the outlet. The calculation is summarized in Table III-

Conclusions and perspectives

This chapter aimed at the investigation of the reactivity of metallic nano-aggregates, composed of platinum supported on γ-alumina, as models of catalytic reforming catalysts. We addressed so far the simulation of the dehydrogenation reaction of methyl-cyclohexane into toluene over Pt 13 clusters supported on γ-Al 2 O 3 , by periodic Density Functional Theory (DFT) calculations at the PBE-dDsC and PBE levels. Our present modeling results obtained on the Pt 13 H 6 /γ-Al 2 O 3 (100) and Pt (111) systems are based on the assumption that the reaction pathway consists of important intermediates such as methyl-cyclohexyl radical, methyl-cyclohexene, methyl-cyclohexenyl radical, methyl-cyclohexadiene and methyl-cyclohexadienyl radical, formed subsequently by dissociation of C-H bonds on the cluster or the surface. On Pt 13 H 6 /γ-Al 2 O 3 (100), the fluctionality of the cluster induces also several steps of cluster reconstruction and hydrogen atom migration. A combination of ab initio molecular dynamics, transition states search and vibrational properties determination allowed to make the following conclusions :

(1) Accurate estimation of Gibbs free energies including vibrational contributions for condensed phases and adsorbed molecules was undertaken and showed a high sensitivity towards calculation parameters. Taking into account these contributions is however of paramount importance for the future quantification of rate constants.

(2) The importance of dispersion interactions was emphasized, as estimated with PBE-dDsC (with respect to PBE), both for Pt (11) as rate determining step can be written as :

As before, we can deduce the concentration of the surface active sites [L] :

Then we have the reaction rate expression:

With:

, Equation (V-47), (V-48)

In this case, the initial reaction rate can be written as : Its evolution as a function of H 2 and methyl-cyclohexane partial pressures is depicted in + K H ' P H 2 0.5 ) 259 reaction free energy. These constants are the functions of several equilibrium constants for elementary steps (Equation (V-31), (V-39) and (V-41)). Moreover, the equilibrium constants in common of K' N , K' M , K' H are K 4 , K 9 and K 14 , which are the desorption constants of hydrogen from its various surface forms (H a , H b and H c ). So the free energy of elementary steps (4), ( 9) and ( 14) are operated as shown in Table V-12 by five most representative analysis after several trials. The tolerance for the deviation on these ab initio calculations are ± 10kJ/mol.

Table V-12 Relevant parameters operated for the sensibility analysis on the case of RDS-(VI) model (reversible rate determining step (13))

Table V-12 indicates the five analysis (parameters (a) to (e)) to examine the sensibility of the relevant parameters on the evolution of reaction kinetics, via simply modifying Δ r G (4) , Δ r G (9) and Δ r G (14) , standing for the reaction free energy of elementary steps (4), ( 9) and ( 14). The recalculated constants K' N , K' M , K' H are also given, as a comparison to the original ab initio values. The evolution on the reaction kinetics of these five analyses is given in Figure V-33. properly the three types of data at same time. When increasing Δ r G (4) , Δ r G (9) and Δ r G (14) individually (parameters (a), (b) and (c)), the intermediate hydrogen partial pressure corresponding to the maximum rate moves towards that observed experimentally in Figure V-33 (a). This can be explained by the fact that increasing these reaction free energies corresponds to preventing the desorption of H 2 , thus increasing the poisoning effect by adsorbed atomic hydrogen, e.g. making it appear at lower hydrogen pressure. However, the shape of the curve in the decreasing part is not satisfying. Moreover, these adjustments make the trends worse when considering the evolution of the rate as a function of P MCH and of the conversion

and (c)). This again can be understood as the poisoning effect by hydrogen being stronger, the rate increases much more slowly than expected by increasing P MCH . The set of parameters (d)

gives the best compromise. It corresponds to the strong weakening of constants K' N and K' M , like all other parameters (a) to (e) do. However, the parameters (d) is the only one that achieves to weaken K' H by increasing Δ r G (4) and reducing Δ r G (14) . This means that the desorption of H c has to be promoted, whereas the desorption of H a has to be inhibited as compared to our original DFT calculations. Note however that 10 kJ.mol -1 is typical of errors made in the DFT calculation of free energies (Chapter III: section 1.3.2), so that the main conclusion we can reach here is that the model is very sensitive.

CHAPTER VI -CONCLUSIONS AND PERSPECTIVES

Conclusions

The present work dealt with the reactivity of γ-alumina supported platinum subnanometric clusters, focusing on the mechanism of methyl-cyclohexane dehydrogenation to toluene as a model reaction for catalytic reforming. The goal was to unravel the reaction mechanisms, combining ab initio calculations, kinetic experiments and modeling, to provide guides for the control of catalytic properties and reaction conditions. Molecular aspects are indeed lacking in the literature to unravel these questions of high practical relevance.

Ab initio dehydrogenation mechanisms of methyl-cyclohexane over

Pt13H6/γ-Al2O3 (100) cluster and Pt (111) surface

Firstly, by periodic Density Functional Theory (DFT) calculations at the PBE-dDsC and PBE levels, we chose the Pt 13 H 6 /γ-Al 2 O 3 (100) system as a relevant model for the catalyst, and considered the Pt (111) surface as a reference system. We assumed that the reaction proceeds via sequential C-H bond cleavages and H 2 desorption steps, but in the case of the supported clusters with co-adsorbed hydrogen, reconstruction and H migration steps appeared to be necessary to consider. The overall Gibbs free energy profile was determined, with all the intermediates and transition states involved in the proposed reaction pathway.

From a technical point of view, accurate estimation of Gibbs free energies including vibrational contributions for condensed phases and adsorbed molecules showed a high sensitivity undertaken here, consisting in the feeding of kinetic models with ab initio data. They will also be important for bridging the gap between model approaches often undertaken in computational chemistry, and the real catalyst, with complex chemical composition, and the real process, involving a large set of reactants, products and reaction conditions.

Abstract: Catalytic reforming aims at transforming naphta into high octane aromatics and producing simultaneously dihydrogen. The catalyst used is composed of platinum-based sub-nanometric clusters highly dispersed on a gammaalumina support which behavior under reaction conditions is the subject of numerous questions. We investigate experimentally and theoretically one model reaction probing the metal sites, the dehydrogenation of methylcyclohexane into toluene. A detailed atomic scale understanding of the mechanisms involved, and their related kinetic parameters, is required. We undertook DFT calculations with PBE and PBE-dDsC functionals on a relevant Pt 13 /γ-alumina model, in order to determine the intermediates, transition states and their free energies. The reaction mechanism was explored by assuming sequential C-H breaking steps. Reconstructions of the cluster and hydrogen migrations occur along the reaction pathway, highlighting its high fluctionality (also confirmed by molecular dynamics). Free energies of activation for C-H bond breaking, H migration and cluster's reconstruction were systematically determined at T=625 K.