Joël Puibasset
email: puibasset@cnrs-orleans.fr

Monte-Carlo Multiscale simulation study of argon adsorption / desorption hysteresis in mesoporous heterogeneous tubular pores like MCM-41 or oxidized porous silicon

Keywords:

In a recent paper [J. Chem. Phys. 127, 154701 (2007)], a multiscale approach was introduced which allowed the calculation of adsorption/desorption hysteresis for fluid confined in a single 2 mesoporous, heterogeneous tubular pore. The main interest in using such an approach is that it allows to reconcile a molecular simulation approach generally limited to the nanometer scale (atomistic description of the confined fluid and pore roughness) with the much larger scale (micrometer) relevant to understand the complexity of adsorption/desorption hysteresis (the numerous metastable states in the hysteresis loop are a consequence of the large scale disorder in the porous material). In this paper, this multiscale approach is used to study adsorption phenomena in mesoporous models made of a collection of disordered, non-interconnected tubular pores, as MCM-41 or porous silicon. A double-distribution is introduced, one to characterize the disorder in a given pore, and the other one to characterize the disorder between the pores. We consider two distribution shapes: Gaussian and uniform truncated, and the two cases of pores open at one or at both ends. These models are expected to cover a wide variety of real materials made of independent pores, as MCM-41 and oxidized porous silicon.

A large variety of hysteresis shapes is obtained, ranging from almost parallel adsorption/desorption branches typical of MCM-41 adsorption, to triangular hysteresis typical of porous silicon. The structure of the metastable states inside the hysteresis (scanning adsorption/desorption curves) is also examined. The results are expected to be useful to experimentalists who want to infer pore structure and level of disorder from experimental adsorption/desorption experiments.

KEYWORDS (Word Style "

INTRODUCTION

An essential feature of porous material is its structure, which is obviously easier to take into account to determine material properties when geometry is simple. This explains the importance of inorganic mesoporous materials of well defined geometry. In particular MCM-41 molecular sieves 1,2 and porous silicon, 3 which exhibit cylinderlike pore shape, and negligible interconnections between pores. These exceptional geometric properties and the fact that they are easy to produce explain they are commonly used for phase separation, catalysis, chemical sensors, and nanotechnologies. But they are also of greatest importance for fundamental studies on adsorption phenomena. [4][5][6][7][8][9] In this paper we focus on such porous materials which are believed to be made of a collection of independent (non-interconnected) pores. The case of perfectly cylindrical pores is quite well understood from a theoretical point of view. 10 However, there is still some disagreement between experimental observations of adsorption/desorption hysteresis and their theoretical prediction, showing that there is still room for improvement of pore structure description.

Despite exceptional geometric qualities, the above mentioned materials most probably contain some disorder, as suggested by the experimental adsorption/desorption hysteresis. For instance, a non-negligible pore size distribution exists (in particular in porous silicon), which can be confirmed by microscopy. Furthermore, the MCM-41 or porous silicon inner surfaces are most probably rough and irregular. 8,[11][12][START_REF] Berenguer-Murcia | About the exclusive mesoporous character of MCM-41[END_REF][START_REF] Fenelonov | [END_REF][15][16] The consequence is a variation of pore size and wall thickness in the sample, which is a source of disorder. 17 The term disorder refers to any spatial variation in the porous material characteristics which has consequences on the thermodynamic properties of the fluid. It was shown elsewhere [18][19][20] that a purely geometric deformation of a pore (keeping the fluid/wall interaction constant) has negligible consequences on the thermodynamic properties of the adsorbed fluid. On the other hand, any modulation of fluid/wall interaction has strong consequences. [21][22][23][24][25][26][27][28] Of course, in a real porous material both geometric and fluid/wall effects cannot be disentangled, since pore size variations have direct consequences on fluid/wall interaction intensity. Important geometric effects are also expected when the structural disorder of the surface is transferred to the adsorbed fluid phase. Such effects are neglected in this study and could constitute points for future improvement. In the present work, it will be considered that the most important sources of disorder are those which affect directly the fluid/wall interaction. The porous substrates considered in this study exhibit three important sources of disorder, associated to three length scales. The shortest wavelength variations in fluid/wall interactions are due to the atomistic roughness of the walls. This affects essentially the first stage of fluid adsorption (from low chemical potential up to the monolayer) by creating favorable sites for adsorption. This is naturally taken into account in our molecular simulation approach, provided a reasonable atomistic pore model is used. Longer wavelength variations also exist. As previously mentioned, for a given pore, one has possible chemical or wall thickness variations along the pore axis which induces modulation of the fluid/wall interactions: the pore is heterogeneous.

The typical scale for such heterogeneities is the nanometer. It corresponds to the size of the elemental domains of the material, as introduced by Everett. 29 This is probably the most important source of disorder to explain the hysteresis, as shown by the work of Kierlik and coworkers [30][31][32] in a mean-field density functional theory of a disordered lattice gas model. It is also the most complex to be modeled because these domains generally cannot be considered as independent. In most cases, one has to take into account the whole chain of domains of a given pore in order to calculate accurately its adsorption properties. This is achieved by the multiscale approach used in this work. It is emphasized that, in this work, the term "pore" should not be confused with "domain": the porous sample is seen as a collection of pores which are themselves made of a chain of domains. The last source of disorder is due to possible variations of global pore characteristics over the whole sample. For instance, inspection of porous silicon surface by microscopy shows a distribution of pore size which is wider than the variations of the size of any given pore along its axis. 33 This source of disorder can easily be taken into account in calculations since the pores are independent in MCM-41 and porous silicon. 7 This requires that the wall thickness is large enough to avoid strong interaction between molecules through the walls. It also requires that the pore structure is rigid enough not to be distorted during adsorption, because this would have non-negligible effects on fluid adsorption in the neighboring pores. These hypotheses are assumed.

The aim of this paper is to calculate the adsorption/desorption hysteresis as well as the first ascending and descending scanning curves for a simple fluid (e.g. argon) adsorbed in mesoporous silica, taking into account the three sources of disorder. Nanometer-scale and large-scale heterogeneities are modeled in a realistic but simplified way so as to be characterized by a single parameter. Two distributions are then introduced, one to characterize the variations between pores, the other one to model the domain heterogeneity in each pore.

By varying the variance of these distributions, one may model either a collection of identical homogeneous pores, or a distribution of various homogeneous pores, or a collection of statistically identical but heterogeneous pores, or a large distribution of heterogeneous pores.

The impact on hysteresis and scanning curves is studied and compared to experiments in order to infer conclusions on MCM-41 or porous silicon structure. The issue of pores open at one or at both ends is also addressed.

The paper is organized as follows: In section 2, the pore model is first introduced, and the two distributions characterizing the pore and domain heterogeneities are defined. The issue of system size effect is then discussed in order to define a reasonable number of pores and domains to avoid finite size artifacts. In section 3 the numerical details and algorithm are introduced, where it is shown how a multiscale approach may be successful to take into account the interconnections between the domains for each pore. The simulations results are given in section 4, followed by discussion and conclusion.

PORE MODEL

As explained in the introduction, a model for mesoporous silica as MCM-41 or oxidized porous silicon should describe the material as an arrangement of parallel and noninterconnected tubular pores with a high aspect ratio (few nanometers in diameter and few microns of length). Besides the atomistic disorder which is naturally taken into account in our molecular approach, some disorder should also be introduced, at two levels: differences between pores (for instance their average diameter may differ), and physico-chemical variations at nanometer scale along the axis of each pore. Note that these variations most probably rise during the fabrication of the material, and could in principle be obtained by numerical reconstructions. 17 With present computer capabilities, it is however impossible to reach the required large scales. A simplification is thus introduced, by considering the fact that the most relevant physico-chemical heterogeneities for fluid adsorption are those which induce a modulation of the fluid/wall interaction intensity (see introduction). As a consequence, the heterogeneities are characterized by a single parameter which varies from pore to pore and along any given pore. A more precise definition for this parameter is given below.

The silica pore diameter is taken to be 3 nm. This is in the range of the smallest MCM-41, but smaller than typical porous silicon pores (10nm or more), and results from a compromise due to computer limitations. The pore length is few micrometer, representative of mesoporous materials like MCM-41 or oxidized porous silicon In order to perform accurate calculations, the system is described at the molecular level, and the mesopores are drilled in an initial substrate made of pure silica of density close to the expected one (mesoporous silica walls are expected to be made of amorphous silica). The fluid/wall interaction intensity is then well reproduced since the density of interacting sites is correct. heterogeneity values between 0.7 and 1.3 may be found in all pores (in various proportions), which has non-negligible consequences and may be unrealistic. This is why we also consider distributions which are equal to zero out of a given interval (support of the distribution strictly included in [0.7,1.3]. In this case, for a given pore with average heterogeneity hpore, h is distributed uniformly (simplest model) over the interval [hpore-domain; hpore +domain], the average value hpore being chosen uniformly over the interval [1-pore; 1+pore] (see Fig. 1).

With such a distribution, all heterogeneity values are not found in all pores. The variance of this distribution is pore 2 /3.

The simulations are performed in the grand canonical ensemble. The chemical potential of argon is imposed and related to the gas pressure in the reservoir using the ideal gas relation since it is a good approximation at the temperature at which the simulations are performed where required). 34 The last point to be discussed is the choice of the number of domains and pores in our calculations. Figure 2 shows the adsorption/desorption isotherms obtained by the multiscale approach (to be described in the next section) for a single pore and various numbers of domains in this pore. As can be seen, for 500 or 1000 domains the curves are almost superimposed, whereas for 100 domains some differences appear. Furthermore, for 100 domains, the adsorption/desorption curve is sensitive to the special choice made for the chain of heterogeneities (not shown), which is not the case for 1000 domains per pore. This last value seems to produce results close to the thermodynamic limit. Note that it corresponds to pore approximately 7 m long. For the same reason, we take 1000 pores in our system. The total number of domains in our model is then 10 6 .

MULTISCALE APPROACH

The fluid adsorption properties in the porous material are calculated by the Grand Canonical Monte Carlo (GCMC) method. [START_REF] Nicholson | Computer Simulation and the Statistical Mechanics of Adsorption[END_REF][START_REF] Allen | Computer Simulation of Liquids[END_REF] Of course, the brute force simulation in a pore of few micrometers is out of computer capabilities. On the other hand, performing the calculations in each domain independently of the others is a crude approximation. It is possible to perform a parallel calculation where each processor treats a single domain, taking into account the fluid configuration in the rest of the pore (information given by the other processors). The number of required processor is however too large. Reasonable approximations are possible. For instance, in most cases, the fluid-fluid interaction is short range. If the domains are large enough, it can be assumed that the fluid properties in a given domain depend essentially on the fluid state in the neighboring domains (two in the simplest case of tubular pores). It is possible to be even more restrictive, since it is actually sufficient to know the fluid state within a distance of the order of the range of the interaction (for instance 2.5 in our case).

These small domains in the immediate vicinity of the central domain under study play the role of boundaries, and are intended to reproduce the influence of the rest of the pore. The second approximation is to consider that if the fluid is far from its critical point, the correlations are short range, and then the relevant property of the fluid in the boundary domains is its density distribution and fluctuations, which depends only on the chemical potential imposed to the system. As a consequence, each domain may be treated independently. The difference with the independent domain theory is however the presence of these boundaries and their effect on The adsorption/desorption curves have now to be determined for any value of the heterogeneity parameter h. They are obtained by linear interpolation of the results obtained for h = 0.7, 0.8, 0.9, 1.0, 1.1, 1.2 and 1.3 in a previous work. 34 Depending on the boundary conditions, the curves are reversible (G-L boundaries) or present a hysteresis (G-G and L-L boundaries). In the case of G-L boundaries, the system always presents a meniscus, which moves forward during adsorption and recedes during desorption (at coexistence). For L-L boundary conditions, two menisci fill the pore during adsorption until they merge (at coexistence). Upon desorption, a bubble has to nucleate somewhere in the pore. This delays the desorption (nucleation barrier), which takes place below coexistence. For G-G boundaries, it is the adsorption which has to proceed via nucleation of a meniscus (above the coexistence), while upon desorption (which occurs at coexistence) two menisci are present due to the gaslike boundaries, which simply recede until they merge. Calculations show that the boundaries do not affect the main adsorption and desorption branches, but only the path followed by the system (positions of the transitions). In other words, the boundaries affect the nucleation barriers, not the grand potential of the fluid. When increasing the heterogeneity parameter h, hysteresis narrows and shifts to lower . The vertical jumps between gaslike and liquidlike branches are considered as discontinuities. The adsorption properties are then described by two continuous surfaces in the (, h) plane, and several lines of discontinuities associated to vertical adsorption or desorption. Interpolation between the various (, h) points calculated by simulation is made in the simplest way (linear) for each of the two surfaces.

The adsorption/desorption isotherms for the whole system are calculated as follows. For low , the adsorption in each domain is single valued, and does not depend on the fluid state in the rest of the pore. The amount adsorbed is simply the sum over all domains. Note that in this case, all domains are in the gaslike state and follow the isotherm with G-G boundaries. The chemical potential is then increased by small amounts until one domain reaches its limit of stability. This domain jumps to the liquidlike branch. This has consequences for the two neighboring domains, which boundaries are now G-L and L-G. Their state has then to be reconsidered according to their dissymmetric G-L isotherms. They may stay in the gaslike state (adsorption limited to the initial domain), or switch to the liquidlike state (propagation of the meniscus created in the initial domain). In this case, the next domains need now to be reconsidered, and so on until the meniscus stops (end of the avalanche). The amount adsorbed is given by the sum over the domains. The chemical potential in then increased again, and the same procedure is applied until saturation is reached. The desorption and scanning isotherms are obtained in a similar way.

SIMULATION RESULTS AND DISCUSSION

The adsorption, desorption and first scanning descending and ascending isotherms are

Gaussian distribution for pores open at both ends

The simplest case concerns a set of identical, perfectly homogeneous pores ( 3, corresponds to a Gaussian distribution of independent, homogeneous pores with various fluid/wall interactions. The adsorption and desorption branches are now continuous and smooth. They remain essentially parallel. Three descending (Fig. 3) and ascending (Fig. 4) scanning curves are shown. They are essentially straight and parallel to the main gaslike and liquidlike branches. Starting from the main adsorption or desorption branches at a given level of filling of the system, they reach the opposite branch straightforwardly (so-called "crossing" ascending and descending scanning curves). As expected, these properties are those given by the independent domain theory.

The introduction of a small width domain The main differences appear in the scanning curves. The initial portions of the ascending and descending scanning curves are essentially parallel to the main gaslike and liquidlike branches, but they deviate at the end. The ascending curves get steeper before they reach the opposite adsorption branch (crossing ascending scanning curves). The effect is stronger for the descending curves which drop parallel to the desorption branch, and reach the lower closure point of the hysteresis (descending converging scanning curves). This is interpreted as follows: upon desorption (scanning descending curves), the less favorable domains which have not been filled during adsorption (gaslike bubbles in the material) significantly favor the complete desorption of the system compared to the main desorption loop (from the saturated system). This is again a consequence of the interconnection between domains. It is emphasized that this difference of behavior between ascending and descending scanning curves (crossing versus converging) is quite remarkable. Despite it has been observed experimentally for N2 adsorption at 77K in SBA-15 samples, [START_REF] Tompsett | [END_REF] few models are able to reproduce it. For instance, the independent domain theory, networks approaches, and meanfield density functional theories applied to lattice gases, generally predict the same behavior (crossing or convergence) for both ascending and descending curves. 31,32,[START_REF] Tompsett | [END_REF][START_REF] Everett | [END_REF][40][41][42] Our approach then allows to reproduce a wider variety of behaviors.

Another interesting case is the combined distribution for pores and domains with equal variances ( pore  = domain  = 0.05, Figs. 34). Here again the main adsorption and desorption branches are continuous, but contrarily to the previous cases, the branches are not parallel anymore: the adsorption is smoother than desorption. The scanning curves exhibit an intermediate behavior between the previous cases: they are not parallel to the gaslike and liquidlike branches, and reach the opposite branch. Note that the introduction of some disorder between pores makes the descending curves more and more crossing-like.

Uniform distribution for pores open at both ends

Figures 78show the adsorption/desorption isotherms and scanning curves for the uniform distributions characterized by domain and pore. As for Gaussian distributions, the introduction of differences between homogeneous pores (domain = 0, pore ≠ 0) makes the adsorption and desorption curves smoother while they remain almost parallel. The scanning adsorption and desorption are parallel to the gaslike and liquidlike branches, and meet the opposite adsorption or desorption branch. On the other hand, for a distribution of statistically identical heterogeneous pores (pore = 0, domain ≠ 0), the introduction of a small distribution of heterogeneities (domain = 0.1) has almost no effect on the main hysteresis loop, while for stronger disorder (domain = 0.2), the adsorption branch becomes smoother while the desorption branch remains vertical. As can be seen, each time the adsorption or desorption branch is vertical, the desorption or adsorption scanning curves do not exist. For pore = 0 and domain = 0.2, the scanning desorption curves are initially almost parallel to the liquidlike branch, but finally decrease rapidly to meet the main desorption branch at the lower closure point of hysteresis.

The introduction of both kinds of heterogeneities exhibit interesting behaviors. For moderate heterogeneities along the pores (domain = 0.1), the pore distribution essentially produces smooth, almost parallel adsorption/desorption branches, with scanning curves parallel to the corresponding gaslike and liquidlike branches, and crossing the hysteresis loop.

In this case, the pore distribution dominates, and the system behaves essentially accordingly to the independent pore model. Interestingly, for a given pore distribution amplitude (pore), the presence of small heterogeneities along each pore (domain = 0.1) makes the adsorption and desorption branches steeper compared to the case domain = 0, and slightly displaced towards lower  due to easier nucleation on the most attractive sites during adsorption, and delayed meniscus recession due to the same attractive sites upon desorption. On the other hand, for larger heterogeneities along the pores (domain = 0.2), the desorption branches are steeper, while the adsorption branches are smoother than for domain = 0.

Comparison between pores open at one or at both ends

The case of pores closed at one end is now considered. All results obtained for Gaussian distributions are identical to the case where pores are open at both ends, and are thus not shown. On the other hand, in the case of uniform distributions, the isotherms exhibit differences when pores are closed at one end (see Fig. 910). The differences appear only for adsorption, which occurs more rapidly for pores closed at one end (easier nucleation of the meniscus). After further increase in chemical potential beyond the point where a meniscus can nucleate in the most attractive domains of the pores, the two adsorption curves merge. The most striking difference is for domain = 0, in which case the isotherms become reversible for pores closed at one end. On the other hand, for wide distributions of heterogeneities along the pores (domain = 0.2) the effect of pore ends is negligible. In other words, the larger the support of the distribution (2domain), the smaller the influence of pore ends.

Why do we observe a difference between closed and open pores for uniform truncated distributions and not for Gaussian distributions? The difference between pores open at one or at both ends is that, in the first case, the closed end immediately provides a fluid meniscus.

However, to produce a difference in adsorption, this meniscus has to be able to propagate at least in some of the pores. This propagation occurs only in pores for which all domains have a fluid/wall heterogeneity parameter higher than a threshold value imposed by . This is possible in the case of the uniform and truncated distributions, which explains that a difference is observed between open and closed pores. On the other hand, in the case of the Gaussian distribution, all pores contain several domains of the lowest fluid/wall parameter (even though the probability might be small), which always impedes the propagation of the meniscus in the hysteresis region (< -8.2). In the thermodynamic limit, the propagation of the meniscus from the closed end is negligible in all pores, and hysteresis loop is identical whatever the pores are closed or open. It is then the extreme values of the disorder in the pores which seems to be relevant to explain the possible difference between pores open at one or at both ends.

CONCLUSION

The adsorption of a simple fluid in a mesoporous silica substrate made of independent heterogeneous tubular pores (as MCM-41 or porous silicon) is addressed by a multiscale approach based on GCMC molecular simulation. This framework allowed calculation of adsorption/desorption hysteresis loop and scanning curves for large scale porous material models (1000 pores, several m long), inaccessible to conventional molecular simulations.

The natural heterogeneity in the porous material is characterized by a single parameter, essentially related to the fluid/wall interaction intensity. This disorder is supposed to follow a double distribution, which characterizes the heterogeneity between pores and within each pore. Two types of distributions are used: Gaussian or uniform and truncated.

The results first show the importance of a large number of various domains (heterogeneities) to produce realistic hysteresis loops presenting a multiplicity of metastable states. The models obtained with extremely sharp distributions produce vertical hysteresis, where scanning curves cannot be drawn. Furthermore, the interconnection between the domains, despite simply chainlike in our case, has proven to be of greatest importance to determine the hysteresis loop shape. This can easily be seen by exchanging the values of pore and domain or pore and domain. For instance, interconnected domains (heterogeneous tubular pore). As a general trend, for a small disorder within the pores, the hysteresis essentially presents parallel adsorption/desorption branches, whatever the level of disorder between pores. The scanning curves are essentially parallel to the gaslike and liquidlike branches (crossing scanning curves). This behavior is reminiscent of MCM-41 adsorption experiments. On the other hand, for stronger disorder within pores, the hysteresis is essentially triangular, with desorption steeper than adsorption, and scanning curves converging to lower or higher closure points of the hysteresis. This behavior is reminiscent of adsorption in porous silicon. This qualitative change in behavior occurs for a disorder variance within pores around 0.3-1.0 percent, whatever the distribution shape. It also shows that the disorder within the pores is more important in determining hysteresis shape than the disorder between pores. This work shows that a tree-dimensional network of interconnections is not required to produce a triangular hysteresis, the main origin being the chemical heterogeneity in the pores. It would however be very interesting to study the effect of possible interconnections or any other "interaction mechanism" 33 between pores to compare with the effect of disorder. Future work will also be devoted to the effect of a true pore size distribution to improve comparison with experiments. It was also shown that, contrary to most of usual calculations, our approach is able to produce hysteresis with ascending and descending scanning curves with mixed behavior, i.e. crossing and converging, which was observed in some experimental systems.

The last important conclusion is that comparison between pores open at one or at both ends only exhibit differences if the heterogeneity distribution in the pores is zero out of an interval which is not too wide. In other words, the disorder distribution in the pores should not have long tails. In this case, the consequence of having one of the pore ends closed is that capillary condensation is slightly favored in the first steps, but finally reaches the adsorption branch for pores open at both ends. The hysteresis is then triangular. For extremely homogeneous pores, the hysteresis is significantly reduced, and eventually suppressed for perfectly homogeneous pores. This observation suggests that if MCM-41 pores are quite homogeneous, then they are most probably open at both ends. Another important conclusion from this work in that no difference is observed upon desorption, whatever the pores are open or closed. How does this compare to experiments, performed essentially in porous silicon? 7,33 The authors observe differences between open/closed pores upon adsorption and desorption, which could not be reproduced by our approach. This might be an argument in favor of the effect of the porous matrix elasticity suggested by the authors 33 (which is not taken into account in our study).

This work being a systematic study of the influence of disorder in mesoporous silica made of independent heterogeneous tubular pores, it is expected to be useful to experimentalists interested in the effect of the level of disorder inside and between the pores to interpret experimental adsorption/desorption experiments in MCM-41, porous silicon, or any material made of non-connected pores. It is however emphasized that this study focused on a special case of disorder (modulation of fluid/wall interaction), and therefore conclusions might be different in the presence of other sources of disorder, like pore size or structural variations. Such effects will be studied in future work.

) and variance 2 pore

 2 The fluid/fluid and fluid/substrate interactions are modeled by the (6-12) Lennard-Jones intermolecular potential cut and shifted at 2.5 , which is accurate enough to catch the main features of simple fluid adsorption. The parameters for argon are Ar-Ar = 0.3405 nm and k / Ar Ar   = 120K where k is Boltzmann constant, and the parameters for argon/silica interactions are k nm (fluid/wall interactions are mainly with O species). For further details concerning the choice for these typical values, see Ref [34]. As previously explained, the physicochemical heterogeneities in the porous substrate are approximated by a modulation over the porous substrate of the fluid/wall interaction intensity of course sampledependent and unknown. However, it is expected to have a typical correlation length (corresponding to the definition of a domain) and a random distribution at larger scale. It is expected that the domain size is few nanometers, and we have arbitrarily chosen the value 7.36 nm for the simulations. It is emphasized that choosing 5 nm or 15 nm would not change the results obtained in this work. A typical pore then contains several hundreds of domains. be constant within each domain, and to take uncorrelated values between two adjacent domains. Its value within a given pore is supposed to follow a Gaussian distribution around its average value pore . See Fig. 1 for a schematic representation. Since h is restricted to the interval [0.7;1.3] the distributions are actually truncated, and normalized accordingly. The Gaussian distribution being strictly positive, all

.

  approximately to 70K). The saturating chemical potential for the pure fluid at this temperature has been calculated by GEMC: 35  sat = -All adsorption/desorption results are given as a function of the reduced chemical potential *=  / Ar Ar   . The relative pressure P/P sat can be easily deduced from - sat . The correspondence is shown in the first figure only (Fig. 2, bottom and top axis). Long simulations are performed in order to reduce the uncertainties down to 7%, taking into account the correlation between successive configurations (10 8 Monte Carlo trials per argon

  fluid adsorption in the domain. Considering the essentially cylindrical shape of the pores, and depending on the value of the chemical potential , the fluid in the neighboring domains may be in one or two states. For low , the fluid is necessarily in the so-called gaslike state (fluid adsorbed at the walls), denoted G. For high  the fluid is necessarily in the liquidlike state (fluid filling the pore), denoted L. For intermediate values of  the fluid may be in either the gaslike or the liquidlike states. As a consequence, the fluid properties in each domain depend on temperature T, , and the fluid state in the two boundaries: G-G, G-L, L-G, and L-L. For further technical details, see Ref [34].

  figures. In all cases, the amount adsorbed is divided by the number of domains(10 6 ), and

  at both ends (lower-left panel in Fig.3). The main hysteresis is identical to the one obtained in a single domain for h = 1. The vertical branches are unphysical because, in the grand canonical ensemble, the system jumps from the gaslike to the liquidlike state without intermediate densities. As a consequence, the exploration of the hysteresis loop in this grand canonical situation is impossible.The introduction of a small disorder between pores ( shown in Fig.



  has different consequences, as shown in Figs 3 and 4 for the case pore  = 0 and domain  = 0.05, corresponding to a collection of statistically identical heterogeneous pores. The main adsorption and desorption branches are continuous and almost parallel, as previously, but they are shifted to lower , and the slopes are significantly steeper. This difference is a direct consequence of the interconnection between the various domains which allows the appearance and propagation of menisci (avalanches).

  completely changes the previous observations (seeFigs. 5-6). For instance, for perfectly cylindrical pores ( of the hysteresis, while the branches remain parallel.The ascending and descending scanning curves remain parallel to the gaslike and liquidlike branches (essentially horizontal), and reach the opposite adsorption or desorption curves. For statistically identical heterogeneous pores ( pore  = 0), increasing the value of domain  makes the hysteresis more and more triangular, with steeper desorption and smoother adsorption. Note the kink in adsorption. It corresponds to the limit of stability of the gaslike branch for the most attractive domains, which induces nucleation and rapid propagation of meniscus in pores. The descending scanning curves are not parallel to the liquidlike branch, and reach the main desorption branch at the lower closure point. The ascending scanning curves are initially parallel to the gaslike branch, but finally increase rapidly to meet the adsorption branch at the upper closure point of the main hysteresis loop. When both distributions are combined ( and desorption branches smoother. On the other hand, when increasing domain  the hysteresis loop tends to converge toward a triangular shape which is almost independent on pore  . In other words, the disorder within the pores has stronger effect than that between the pores. 8 Inspection of hysteresis shows that, for domain  = 0 and 0.05, the hysteresis exhibit parallel branches with essentially crossing scanning curves, while for domain  = 0.1 and 0.2, the hysteresis are essentially triangular, with converging scanning curves. A qualitative change in hysteresis structure then takes place for domain  between 0.05 and 0.1.

1 .

 1 The scanning curves also exhibit drastic change for domain = 0.2, since they have a tendency to reach the upper and lower hysteresis closure point. Inspection of hysteresis shows that, for domain  = 0 and 0.1, the hysteresis exhibit essentially parallel branches with crossing scanning curves, while for domain  = 0.2, the hysteresis are triangular, with essentially converging scanning curves. A qualitative change in hysteresis structure then takes place for domain  between 0.1 and 0.2. Such a behavior was previously noticed for Gaussian distributions, for domain  between 0.05 and 0.1. Since the variance of the flat distribution is domain  2 /3, the qualitative change in hysteresis occurs on the same variance interval of pore heterogeneity for both distributions.

FIGURE CAPTIONS FIG. 1 . 24 FIG. 5 .

 CAPTIONS1245 FIGURE CAPTIONS

FIG. 6 .FIG. 9 .

 69 FIG.6. Same as Fig.5with the first ascending scanning curves.

Figure 1 h

 1 Figure 1

  Figure 3

ACKNOWLEDGMENT It is a pleasure to acknowledge A. Delville, E. Kierlik, P. Porion and G. Tarjus for fruitful discussions. The Institut de Développement des Ressources en Informatique Scientifique (IDRIS-CNRS, Orsay, France) is gratefully acknowledged for providing computer capabilities.


L Barthe

M Hemati

K Philippot

B Chaudret

A Denicourt-Nowicki

A Roucoux

Rhodium colloidal suspension deposition on porous silica particles by dry impregnation: Study of the influence of the reaction conditions on nanoparticles location and dispersion and catalytic reactivity

Rhodium composite nanomaterials were synthesized by an innovating process called dry impregnation in a fluidized bed. It consists in spraying an aqueous colloidal suspension of rhodium on silica porous particles. The use of this precursor solution containing preformed nanoparticles avoids calcination/activation step.

Different composite nanomaterials were prepared displaying various metal loadings. The operating conditions were tuned to modify s , the solvent vapour saturation rate value, in order to influence the deposit location: either uniform on the whole silica particles or at the particles surface like a coating. s is defined as the ratio between solvent content in the bed atmosphere and the maximum solvent content.

The obtained samples were investigated in catalytic hydrogenation of aromatic compounds under very mild conditions. Their catalytic performances were compared to those of the original colloidal suspension in one hand and of a similar catalyst prepared through wet impregnation in another hand. Interesting activity and selectivity were observed.

This illustrates the interest of the dry impregnation method: this way allows an easy control of the metal loading as well as of the metal loading location in the support particles. Moreover, the support particle size and morphology are preserved.

Introduction

The interest in metal nanoparticles for applications in catalysis is now well-known [START_REF] Feldheim | Metal Nanoparticles Synthesis, Characterization and Applications[END_REF][START_REF]Nanoparticles: From Theory to Application[END_REF][START_REF] Gual | [END_REF][START_REF]Nanoparticles and Catalysis[END_REF] and mainly results from their high specific surface area due to their small size giving rise to high active sites numbers. Metal nanoparticles are generally considered as species at the frontier between homogeneous and heterogeneous catalysts. From this particular matter state, catalytic specificities, which are not offered by classical catalysts, could be expected and several systems are now available in the literature illustrating their particular behaviour [START_REF] Jansat | [END_REF][START_REF]The Handbook of Homogeneous Hydrogenation[END_REF][START_REF] Favier | [END_REF].

The preparation of metallic nanospecies in liquid-phase is possible through various chemical syntheses and the reduction of metal salts in aqueous media is one of the most known methods [8]. For example, colloidal suspensions of rhodium can be prepared by chemical reduction of RhCl 3 and stabilized by highly hydrosolu-ble quaternary ammonium salts and they have proved to be active catalysts for hydrogenation of various aromatic compounds [9]. Nevertheless, colloidal suspensions display some disadvantages as their lack of stability at elevated temperatures (agglomeration is often observed at temperature higher than 100 • C) or their recycling with soluble products. It appears then clearly that the deposition of metal nanoparticles onto a support would circumvent these drawbacks and afford the advantages of traditional supported catalysts. The way followed to prepare supported nanocatalysts is generally the wet impregnation method [10]. It consists in the immersion of the chosen support in a colloidal suspension under stirring to favour the diffusion of the nanoparticles inside the support grains. This technique is easy to carry out but can present some weak points such as: loss of precursor, reduction of the support particle size (most of the porous supports, prepared by sol-gel process, disaggregate in solution under stirring) and dependence of the deposit location on the physico-chemical properties of the solution-support couple.

Taking into account these different points, the preparation of supported catalysts following a dry impregnation method appears as an interesting alternative technique. The preparation of composite nanomaterials by dry impregnation in a fluidized bed has been developed by [START_REF] Hemati | Fabrication de catalyseur d'un nouveau type par imprégnation en lit fluidisé[END_REF]. Its principle consists in spraying a solution containing a metal source into a hot fluidized bed of porous fine particles. After the impregnation step, metallic precursor decomposition and/or activation can be performed in the same apparatus. Up to now, this technique has been successfully applied using solutions of metal salts (iron, manganese and copper nitrate) or organometallic complexes (bis(dibenzylidene)palladium, [Pd(dba) 2 ] or palladium allyl chloride [PdCl(allyl)] 2 ) as metal sources. Most particularly, the deposition of metal salts gave rise to interesting composite nanomaterials displaying catalytic properties [START_REF] Barthe | Synthèse et dépôt de nanoparticules métalliques dans un support poreux par imprégnation en voies sèche dans un lit fluidisé : élaboration de catalyseurs supportés[END_REF].

This dry impregnation technique offers several advantages. For example, the whole sprayed metal precursor is deposited and the metal loading is thus controlled by the impregnation time. Moreover the initial size of support grains is conserved. But, its major advantage concerns the deposit location that can be oriented depending on the targeted composite nanomaterials [START_REF] Barthe | Synthèse et dépôt de nanoparticules métalliques dans un support poreux par imprégnation en voies sèche dans un lit fluidisé : élaboration de catalyseurs supportés[END_REF][START_REF] Barthe | [END_REF]. Indeed, previous works with metal complexes showed that a competition between two phenomena, the drying and the capillarity, controls the deposit location. An adequate choice of operating conditions (bed temperature, liquid and fluidization gas flow rate), otherwise the appropriated values of s , the solvent vapour saturation rate, and IM, the impregnation module, permit to predict the deposit location. s is defined as the ration the ratio between solvent content in the bed atmosphere and the maximum solvent content. IM is defined as the ratio between a drying characteristic time, t dry , and a capillary penetration time, t cap .

t cap , the time necessary for liquid penetration in the pores, can be estimated from the following equation taken from the model of the parallel capillary beam [14]:

t cap = 2x 2 LV cos r pore (1)
where is the liquid viscosity, x the pore length equivalent to the radius particle multiplied by the tortuosity factor, LV the interfacial tension, the contact angle and r pore the pore radius. t dry , the time necessary for a particle saturated by pure solvent to be transformed into a dry particle under defined fluidized bed conditions (temperature and humidity). The calculation of this characteristic time is based on the mass and energy balances on a single wetted particle considering that the mass transfer is controlled by external resistance (gas phase). The model's equations described in previous works [START_REF] Barthe | [END_REF][START_REF] Desportes | Imprégnation en voie sèche en lit fluidisé, application à la synthèse de catalyseurs supportés[END_REF] lead to this last equation:

t dry = d p s 6k y (Y i -Ȳ ) (2)
where d p is the particle diameter, the internal support porosity, s the solvent density, k y the overall mass transfer coefficient, Ȳ the average solvent content in the bed atmosphere determined by overall mass balance on the reactor, and Y i the absolute solvent content at the interface (depending on the particle temperature and humidity [START_REF] Barthe | [END_REF]).

According to these two parameters, homogeneous deposit of nanoparticles is located inside or at external surface of the support. For example, in the case of dry impregnation of fine silica particles by an iron nitrate aqueous solution, our experimental results show that soft drying conditions ( s ≥ 0.2 and IM ≥ 30) lead to a homogeneous deposit while under fast drying conditions ( s < 0.2 and IM < 30), the deposit is located at the particle external surface.

After these findings, a new challenge for us consisted in the use of aqueous colloidal solutions containing preformed metal nanoparticles to check the applicability of our process to another metal source. This approach using metallic nanospecies could be promising since it avoids thus the necessary step of decomposition/activation of metal complexes. Nevertheless, this project was ambitious because no deposition of colloidal solution was known in the literature and this could present some technical difficulties.

This paper describes the dry impregnation of fine porous silica particles by a rhodium colloidal suspension. The so-prepared samples were characterised to follow the impregnation kinetics and check the metal deposit location. Finally, the activity of these composite nanomaterials was compared to that of colloidal suspension on one hand and to that of similar catalysts prepared with the same materials (colloidal suspension and support) by classical wet impregnation on the other hand.

Methods and materials

Starting materials 2.1.1. Metal source

Rhodium chloride hydrate was obtained from Strem Chemicals. Sodium borohydride and all aromatic substrates were purchased from Aldrich or Fluka and were used without further purification. Water was distilled twice before use by conventional method. The surfactant HEA-16Cl was prepared as previously described in the literature [START_REF] Schulz | [END_REF].

Solid supports

Fine porous silica particles of two different sizes but with similar physical properties were used as catalysts support (silica gel Merck 60). Their average pore diameter was 5.5 nm. Their other physical and hydrodynamic characteristics are listed in Table 1.

Experimental procedures 2.2.1. Preparation of rhodium colloidal suspensions

The rhodium colloidal aqueous suspensions containing rhodium (0) nanoparticles were prepared as previously described (Fig. 1a) [17]. More precisely, sodium borohydride (36 mg, 9.5 × 10 -4 mol) was added to an aqueous solution of N,N-dimethyl-N-cetyl-N-(2-HydroxyEthyl)Ammonium chloride salts, namely HEA16Cl (95 mL, 7.6 × 10 -3 mol L -1 ). This solution was quickly added under vigorous stirring to an aqueous solution of the precursor RhCl 3 .3H 2 O (100 mg, 3.8 × 10 -4 mol). The initial red solution darkened immediately, proving the formation of the aqueous Rh(0) colloidal suspension. Transmission Electron Microscopy (TEM) images revealed well-dispersed rhodium nanoparticles (Fig. 1b) with a mean size of 2.4 nm (Fig. 1c). It was verified that such colloidal solutions are stable for several months at room temperature.

Preparation of supported nanoparticles by dry impregnation in fluidized bed (Dry Imp catalysts)

The experiments were carried out in a batch fluidized bed, allowing syntheses under controlled atmosphere (inert or reductive) depending on the metal precursor nature. The reactor is a stainless steel conical column with a 30 mm base diameter, a 112 mm top diameter and 300 mm in height (Fig. 2). Its dimensions make it possible to reduce the metal precursor consumption and the impregnation time since it operates at laboratory scale (production of catalyst: 30 to 100 g). The gas distribution at the column base is ensured by a stainless steel perforated plate with a porosity of 0.5% (12 holes of 1 mm, organized according to a triangular mesh of 5 mm). Before entering the bed, the fluidizing gas flow rate is measured by a rotameter and preheated by an electrical heater. The bed temperature is controlled by means of a PID regulator which commands the furnace heating power. At the outlet of the column, the elutriated particles are separated from the gas phase by a cyclone.

The impregnating solutions are placed into two reservoirs, one containing pure solvent for experiment starting, and the second containing the metallic precursor solution. The solution is drawn up by a volumetric pump from a reservoir to a spray nozzle. The atomizer is a downward facing nozzle and is located in the bed. Temperature and pressure drop monitoring is achieved throughout all the impregnation.

The general experimental protocol is as follows:

• The column is initially charged with a given mass of porous silica particles. • The powder is fluidized by a fixed hot gas flow rate.

• The pure solvent (water in the present case) is sprayed within the bed, at the same flow rate as the colloidal suspension. • As soon as the bed temperature is stabilized, the solvent is replaced by the solution containing metallic nanoparticles.

For all the experiments carried out, the solution flow rate (50 g/h) and the support mass (30 g) were maintained constant. The fluidization gas flow rate is adjusted according to the particles diameter (0.8 m 3 /h when d p = 120 m and 0.6 m 3 /h when d p = 80 m). It should be noted that the selected gas flow rate is about 10 times the minimum fluidization velocity at 25 • C. For each experiment, the bed temperature, the final metal loading, s and IM are presented in Table 2.

A study of the impregnation kinetics can be obtained from experiments 1 to 4. The influence of the bed temperature parameter on the rhodium nanoparticles dispersion in the porous silica particles can be studied considering experiments 3 and 5 while the support particle size effect can be determined from experiments 3 and 6.

Catalytic tests: hydrogenation of arenes

Catalytic reactions were carried out under mild conditions (ambient temperature, 1 atm of H 2 ). A 25 mL round bottom flask, charged with silica-supported Rh(0) catalyst (1 g, 10 mL solvent) and the appropriate aromatic substrate ([substrate]/[Rh] = 100), is connected to a gas burette (500 mL) with a flask to balance pressure. Then, the system is filled with hydrogen and the mixture is magnetically stirred at 1500 min -1 . The reaction is monitored by gas chromatography analyses.

Characterization methods

To determine the textural properties of the different samples obtained after impregnation of silica particles with colloidal rhodium suspension, various characterization techniques were -Laser granulometry (particles mean diameter and size distribution), -Helium pycnometry (apparent and real bulk density), -Mercury porosimetry (pore volume), -N 2 adsorption-desorption (BET specific surface and pores size distribution), -Transmission electron microscopy (TEM) (topology of the catalysts and metal nanoparticles size) -Elemental analysis for metal content determination (metal loading).

Results and discussion

We have studied the influence of various parameters on the morphological characteristics and the catalytic properties of solids obtained through dry impregnation.

Morphological characteristics of the samples prepared by dry impregnation (Dry Imp catalysts)

Kinetic study

Experiments 1 to 4 were carried out using different impregnation times and constitute thus a kinetic study.

The first observation concerns the colour of the obtained composite materials which is grey. Since silica particles have a white colour and the colloidal suspension a black one, this grey colour evidences that a metal deposit took place in the support grains. To confirm that the whole sprayed rhodium nanoparticles were deposited within the support, the solid metal loading was determined for all samples. The results are gathered and compared with the theoretical values in Table 3.

The results show that the experimental loadings obtained are very close to the expected theoretical values. It thus appears that all the sprayed colloidal suspension was deposited in the support. There is no metal loss. Therefore, at a given precursor concentration, the spraying time determines the metal loading. Two parameters could be controlled during the catalyst preparation. The impregnation module, IM, is defined as the ratio between a drying time and a capillary penetration time. A solvent vapour saturation rate is also considered, s , defined as the ratio between solvent content in the bed atmosphere and the maximum solvent content. The experimental results show that soft drying conditions ( s ≥ 0.2 and IM ≥ 30) lead to a homogeneous deposit inside the support particles while under fast drying conditions ( s < 0.2 and IM < 30), the deposit is located at the particle external surface.

For experiments 1 to 4, the solvent vapour saturation rate s is equal to 0.77 > 0.2 and the Impregnation Module IM is equal to 400 > 30, favouring an uniform deposit inside the support particles. To check that deposited nanoparticles are well dispersed on all the support grains volume and that they remained individual (no agglomeration), the samples were analyzed by granulometry. It appears that the average diameter of the silica particles remains the same and does not increase during the deposit. This indicates that no agglomeration phenomenon took place. However, the quantity of added metal being rather weak, it may be not detected by granulometry that make it impossible to conclude on the deposit location. It was thus necessary to use other techniques.

The porosity of the four catalysts has then been determined. In spite of the small quantity of deposited rhodium, the results presented in Table 4 show a tendency towards a reduction of the specific surface (from 500 to 485 m 2 /g) and pore volume (from 0.81 to 0.75 cm 3 /g). This leads to think that the metal deposit was carried out in a homogeneous way within the silica grains.

This hypothesis was confirmed by analysing the evolution of the pore size distribution for each rhodium loading (Fig. 3). The pattern is not modified and the curves are very close. The different samples have also been observed by Transmission Electronic Microscopy after ultramicrotomy preparation to check rhodium nanoparticles dispersion. The analysis of various silica particles regions showed rhodium nanoparticles homogeneously dispersed in the support (Fig. 4a). From TEM micrographs we could also determine the rhodium nanoparticles size distribution and their mean diameter by manual counting (Fig. 4b). The size distribution can be represented by a Gaussian model and the rhodium nanoparticles mean size is 5.5 nm (standard deviation 2 nm). After deposition, the rhodium nanoparticles have an average size of around 5.5 nm corresponding to the silica pore average diameter (5.5 nm). It seems thus that the pore diameter controls the nanoparticles maximum size.

Deposit location

The influence of the temperature of the fluidized bed on rhodium nanoparticles dispersion in the porous support was studied from experiments 3 and 5. The same colloidal suspension quantity was sprayed for these two experiments, but during experiment 5 the values of s and IM were reduced to obtain a deposit on the silica particles surface, like a coating. So, the fluidized bed temperature was increased from 45 to 106 • C, which reduces s from 0.77 to 0.01 and IM from 400 to 28 (Table 2).

The samples obtained were analysed by elemental analysis. The experimental rhodium loadings are very close to the expected theoretical values. This confirms the good deposit efficiency.

A granulometry analysis was carried out on the two solids. The average diameter of the silica particles is quite the same for the two samples, the difference being not significant. This result was expected as the deposit thickness at the particle surface would not exceed 1 m.

The porosities of the samples were also determined and compared. The pore size distribution pattern is similar for the two products and also close to the one of the virgin support (Fig. 5). For the two impregnated solids, a very light reduction of the porosity was observed, slightly more pronounced in the case of experiment 5 corresponding to s and IM weak. This is confirmed by the observation of a low reduction in pore volume. In the same way, the specific surface decreases in a more significant way when s and IM are weak.

The different samples were also observed by Transmission Electronic Microscopy after ultramicrotomy preparation to check rhodium nanoparticles dispersion. Sample 3 has been previously described (see kinetic study and Fig. 4) for which a uniform dispersion of the rhodium nanoparticles in the silica support was observed. Concerning Sample 5, at low magnification (×10,000), a dark zone has been observed on all silica particle circumference, Fig. 6a. Thus in this case, the deposit took place on the silica particles surface, forming a coating of approximately 500 nm thickness. This was confirmed at higher magnification (×100,000), Fig. 6b. The nanoparticles detected on the silica particles surface are individual nanoparticles (diameter around 5 nm), or assembled into small agglomerates (size around 30 nm). No rhodium nanoparticles were detected in the core of the silica grains.

Support particles size

The effect of the size of the silica particles can be determined comparing experiments 3 and 6. The same operating conditions were followed in these two experiments, using supports presenting the same characteristics (specific surface, pore volume, pore diameter) but having different particle diameters (respectively 120 and 80 m).

The silica particles being finer, we had to decrease the fluidization gas flow rate to get satisfying fluidization regime. This led to a reduction of heating by the gas used for solvent evaporation. To circumvent this lack, the temperature of the inlet gas and consequently the bed one were increased, to maintain s and IM at the previous value.

The obtained product, Sample 6, was characterized by the same techniques as those previously used. Results were perfectly identical to those obtained for Sample 3:

-All the metal sprayed is deposited. The operation efficiency is about 100%. -The silica particles diameter is not affected significantly by rhodium nanoparticles deposit. -Specific surface and pore volume decrease very slightly compared to virgin support. -The pore size distribution pattern is the same before and after deposit. -The TEM micrograph after ultramicrotomy revealed a good dispersion of the rhodium nanoparticles in the support grains. -The detected rhodium nanoparticle average size is around 5.5 nm.

Taking into account all these results, it appears that the support particle size modification (between 80 and 120 m) does not affect the rhodium nanoparticles deposit.

In conclusion of this part, we can say that the dry impregnation technique is very flexible. First, the metal loading can be fixed by the spraying time. Secondly, the deposit location can be oriented by choosing correctly the operating conditions: the metal deposit can be either only at the surface of the support particles like a coating or homogeneously distributed on the whole particle volume. Finally, the support particle size and morphology are preserved and the silica particles pore diameter controls the nanoparticle maximal size. The choice of the support is thus very important, at least in the case of silica gel.

Investigation in catalytic hydrogenation of aromatic compounds

The rhodium based composite nanomaterials prepared by dry impregnation in a fluidized bed (Dry Imp catalysts) as previously described have been tested in catalysis. The hydrogenation of aromatic compounds has been chosen to evaluate these catalysts in terms of catalytic performances in comparison with the original colloidal suspension [START_REF] Schulz | [END_REF] and with similar catalysts obtained by wet impregnation method [10]. For that purpose, several parameters have been evaluated in the hydrogenation of toluene as model substrate. Then, based on optimized conditions, alkylated, functionalized and disubstituted substrates have been studied to check efficiencies of Dry Imp catalysts.

Comparison of catalytic performances of rhodium colloidal suspension, Wet Imp and Dry Imp catalysts in toluene hydrogenation

The performances of a Dry Imp catalyst have been investigated in toluene hydrogenation reaction in aqueous phase and compared to those of colloidal rhodium suspension [START_REF] Schulz | [END_REF] and a Wet Imp catalyst [10] already known. For this study, the selected catalyst is the solid Dry Imp 3, which presents the same rhodium content as the catalyst prepared by wet impregnation as well as that of the colloidal suspension. The results are reported in Table 5.

This comparison evidences that higher activities are obtained with supported catalysts: a total conversion is obtained in 2.25 h and 2.5 h respectively with Dry Imp and Wet Imp catalysts against b Dry Imp and catalyst s prepared according to dry impregnation approach. Rh-HEA16Cl suspension and Wet Imp catalysts prepared as described previously.

c Determined by GC analysis. d Turnover frequency defined as mol of H2 per mol of rhodium per hour.

3.6 h with the colloidal suspension. In addition, the Dry Imp catalyst is slightly more active than the Wet Imp one. These findings show that the diffusion phenomenon in the solid is not the limitation step in reaction process. Moreover, these results highlight the interest to deposit the rhodium nanoparticles on a support to enhance their catalytic properties. This deposition probably permits to avoid their aggregation. Moreover, the catalyst recuperation is easier in this case.

Investigation of Dry Impregnation catalysts in various reaction conditions and other substrates hydrogenation 3.2.2.1. Effect of the solvent.

The influence of various solvents (water, hexane, dichloromethane) has been investigated in the hydrogenation of toluene. The results obtained with Dry Imp 3 catalyst are summarized in Table 6.

Dry Imp catalyst shows a slow catalytic activity in dichloromethane since only 27-33% conversion is obtained in 5.5 h (Entry 3). However, as already reported in previous works with the Wet Imp, [10], total conversion in water has been achieved with quite interesting Turnover Frequency (TOF) of 167 h -1 (Entry 2). Finally, the best catalytic activity has been reached in hexane with total conversion in methylcyclohexane (TOF of 282 h -1 ) with Dry Imp (Entry 1).

The difference of catalytic activity observed in hexane and water may be explained by a better solubilisation of the substrate in hexane and thus a better diffusion of the substrate to the metallic species inside the support grains. It could be attributed to the surface quality of the catalysts grains and their affinity with hexane.

Catalyst recycling.

We have also investigated the recycling of the silica-supported nanoparticles, which constitutes one of the main advantages of supported catalysts, in toluene hydrogenation in hexane at 20 • C and 1 atm H 2 . The catalyst was easily recovered after each run by simple filtration and dried at 60 • C before another run with a new addition of substrate. The kinetics of the two runs are presented on Fig. 7, using Dry Imp catalyst.

The two runs present the same kinetics curves. However, the reaction is slightly slower in the second run with a complete conversion in methylcyclohexane after 90 min, compared to 80 min for the first run. This slight fall in catalytic activity could be related to a rhodium loss during recycling. However, elemental analysis of Dry Imp catalyst has proved that the metal loading remains the same between the two runs. Another explanation could rely on the filtration step. To justify this hypothesis, we have reloaded the reaction mixture with the same quantity of substrate (toluene) at the end of the first catalytic run. For two consecutive tests performed with Dry Imp catalyst, we have observed the same catalytic activity (complete conversion in 80 min), and thus no loss of activity between the different runs. It is important to notice that this refill protocol is very used in industry.

Effect of the support and of deposit location.

We have first investigated the effect of the support, thus modifying the grains size of catalysts. Two kinds of silica have been evaluated: the classical one, which has been used for all the previous experiments, with a particle diameter of 120 m and a finer one, possessing a diameter of 80 m. The two catalysts have been tested in toluene hydrogenation in hexane, under standard conditions (1 bar H 2 and RT). The results are given in Table 7.

It appears that the grains size of the two tested silica has no significant influence on catalytic performances since TOFs (Turnover Frequency) are quite similar. These results confirm again that the diffusion process is not the limitation factor in our operating conditions.

It should be noted that the catalysts particles desagglomerate in solution during the catalysis. So the support particle size can not really be studied in the application. This size reduction of the support grains could be explained by the silica preparation. It's a material presenting a pellet-grains morphology formed by small particles agglomerates [START_REF] Barby | Characterization of Powder Surfaces[END_REF]. It appears that, in solution and under stirring, the particles desagglomerate due to low cohesion forces.

As previously mentioned, the interest in using dry impregnation method is the possibility to orient the deposit location. In that context, the influence of the rhodium nanoparticles location on toluene hydrogenation has also been studied, comparing the activity of two catalysts having different metal location (Dry Imp 3 and Dry Imp 5). Dry Imp 3 displays an uniform distribution of metal nanoparticles in the support, whereas Dry Imp 5 possesses at the silica particle surface a coat of approximately 500 nm constituted by rhodium nanoparticles. The results are reported in Table 7.

As expected, these tests reveal that the deposit location has a weak influence on the catalytic activity: the results are similar whatever the deposit location is. Whatever the location of metal is, all rhodium becomes accessible. This would explain why the same catalytic activities are obtained.

Effect of the rhodium loading.

Dry Imp catalysts with different rhodium loadings have been prepared and evaluated in toluene hydrogenation in hexane using the standard conditions and a substrate/metal ratio of 100. The results are reported in Table 8.

These experiments highlight that the catalytic activity increases with the increase in rhodium loading. At very low rhodium loadings (Entries 1 and 2), very low conversions between 4 to 39% are obtained in 2.75 h. However, at higher metal loadings (Entries 3 and 4), the toluene is totally converted in methylcyclohexane in less than 1.33 h. We could presume that all the deposited rhodium is active and accessible to the substrate.

Hydrogenation of various aromatic derivatives.

The performances of Dry Imp catalysts have been investigated in the hydrogenation reactions of monofunctionalized and disubstituted arene derivatives, such as toluene, anisole and o-xylene, respectively. All the tests were carried out in hexane under standard conditions (1 bar H 2 , RT). The results are presented in Table 9.

In all cases a complete conversion of the substrate in the totally hydrogenated compound has been observed. Moreover, the hydrogenation of o-xylene (Entry 3) leads to the formation of 1,2-dimethylcyclohexane with a 92/8 cis/trans ratio. This result has already been reported in the literature for aqueous b Dry Imp catalysts according to the dry impregnation method. c Determined by GC analysis.

Table 9

Hydrogenation of various substrates by Dry Impregnation Catalyst a . HEA16Cl-stabilized Rh(0) colloidal suspensions [17] and also for nanoparticles inserted into mesoporous siliceous materials [START_REF] Boutros | [END_REF].

Conclusion

The deposit of a rhodium colloidal suspension on porous silica particles by the dry impregnation technique in a fluidized bed was carried out successfully. The kinetic study of the impregnation revealed that the deposit of the colloidal suspension presents the same behaviour as that of a metal salt: the operation efficiency is about 100%, the impregnation time controls the metal loading and the deposited nanoparticles maximal size is controlled by the matrix pores diameter. The deposit location can be chosen, by fixing the value of s . A value of s < 0.2 led to the silica particles coating by rhodium nanoparticules while a value included between 0.2 and 0.8 permit to obtain a uniform deposit.

The prepared and characterized composite materials were tested in catalysis of aromatic compounds hydrogenation, interesting reaction at the economic as well as environmental levels. We could note that the solids prepared by dry impregnation in a fluidized bed are active under very soft conditions. They present catalytic performances equivalent to those of catalysts prepared in a traditional way but higher than those of the corresponding colloidal suspension. Hydrogenation of compounds such as toluene, anisole and orthoxylene were carried out with good conversions and an interesting selectivity for the last substrate. The various catalytic tests permit to conclude that for these aromatic compounds, hexane is the better solvent and the consecutive refills lead to the same performance. The rhodium loading is a key parameter whereas the deposit location is not very important for these tested reactions as the catalysts particles desagglomerate in solution under stirring.

Indeed, to obtain a dry catalyst this catalyst preparation technique presents several advantages such as: (1) the support particles morphology and size are preserved, (2) no loss of precursor is observed, (3) the metal loading can be fixed and (4) the metal deposit location can be oriented.

Fig. 1 .

 1 Fig. 1. (a) Preparation of surfactant-stabilized Rh(0) nanoparticles, (b) TEM observations of the colloidal suspension and (c) nanoparticles size distribution.

Fig. 2 .

 2 Fig. 2. Experimental set up for rhodium nanoparticles deposition by dry impregnation.

Fig. 3 .

 3 Fig. 3. Pore size distributions obtained for pure silica and Dry Impregnation catalysts 2 to 4.

Fig. 4 .

 4 Fig. 4. (a) TEM micrograph (magnification: 200,000); (b) nanoparticles size distribution for Dry Impregnation catalyst 3.

Fig. 5 .

 5 Fig. 5. Pore size distributions obtained for pure silica and Dry Impregnation catalysts 3 and 5.

Fig. 6 .

 6 Fig. 6. TEM micrographs for Dry Impregnation catalyst 3 (a) magnification 10,000 and (b) magnification 100,000.

Table 5

 5 Toluene hydrogenation in aqueous phase by various catalytic systems (Dry Impregnation Catalyst 3, Wet Impregnation Catalyst and the colloidal suspension) a . Catalyst Rh-SiO2 (1 g, 0.08 wt% Rh), toluene, [S]/[M] = 100, 10 mL H2O, 1 atm H2, RT.

Fig. 7 .

 7 Fig. 7. Recycling of Dry Impregnation catalyst in toluene hydrogenation in hexane.

  Catalyst Rh-SiO2 (1 g, 0.08 wt% Rh), toluene, [S]/[M] = 100, 10 mL hexane, 1 atm H2, RT. b Dry Imp catalysts according to the approach dry impregnation. c Determined by GC analysis. d Turnover frequency defined as mol of H2 per mol of rhodium per hour.

Table 1

 1 Physical and hydrodynamic characteristics of the silica particles used as supports.

	Characteristics	Si 120	Si 80
	Mean diameter dp (m)	120	80
	Pore diameter dpore (nm)	5.5	5.4
	Specific surfaces S bet (m 2 /g)	530	490
	Pore volume Vp (cm 3 /g)	0.81	0.77
	Internal porosity (%)	60	58
	U mf at 25 • C (minimum fluidization velocity) (m/s)	0.0035	0.0022
	Ut at 25 • C (terminal velocity) (m/s)	0.23	0.15

Table 2

 2 Operating conditions used for the preparation of supported rhodium nanoparticles by Dry Impregnation in fluidized bed.

	Dry Impregnation samples	Particle diameter dp (m)	Bed temperature T bed ( • C)	Impregnation time (min)	Final metal loading (%)	s	IM
	Dry Imp 1	120	45	23	0.02	0.77	400
	Dry Imp 2	120	45	43	0.04	0.77	400
	Dry Imp 3	120	45	108	0.08	0.77	400
	Dry Imp 4	120	45	156	0.16	0.77	400
	Dry Imp 5	120	106	108	0.08	0.01	28
	Dry Imp 6	80	51	108	0.08	0.76	400

Table 3

 3 Theoretical and experimental rhodium loadings for Dry Impregnation catalysts 1 to 4.

		Dry Imp 1	Dry Imp 2	Dry Imp 3	Dry Imp 4
	Theoretical rhodium	0.02	0.04	0.08	0.16
	loading (%)
	Experimental rhodium	0.015	0.035	0.08	0.15
	loading (%)
	used such as:

Table 4

 4 Physical properties of the virgin support and Dry Impregnation catalysts 1 to 4.

		Silica	Dry Imp 1	Dry Imp 2	Dry Imp 3	Dry Imp 4
	Experimental rhodium loading (%)	0	0.015	0.035	0.08	0.15
	Specific surface S bet (m 2 /g)	500	498	493	488	485
	Pore volume Vp (cm 3 /g)	0.81	0.80	0.79	0.77	0.75

Table 6

 6 Toluene hydrogenation by Dry Impregnation catalyst 3 in various solvents a .

	Entry Catalyst b	Solvent nature	Time (h) Conversion	TOF d (h -1 )
					rate c (%)
	1	Dry Imp 3 Hexane	1.33	100	282
	2	Dry Imp 3 Water	2.25	100	167
	3	Dry Imp 3 Dichloromethane 5.5	27	18
		a Conditions: Catalyst Rh-SiO2 (1 g, 0.08 wt% Rh), toluene, [S]/[M] = 100, 10 mL
	solvent, 1 atm H2, RT.

b

Dry Imp catalyst prepared according to dry impregnation approach. c Determined by GC analysis. d Turnover frequency defined as mol of H2 per mol of rhodium per hour.

Table 7

 7 Hydrogenation of toluene by catalysts prepared by Dry Impregnation on various sized silica and with various deposit location a .

	Entry	Catalyst b	Silica particle diameter (m)	Deposit location	Time (h)	Conversion c (%)	TOF d (h -1 )
	1	Dry Imp	80	Uniform	1.33	94	265
	2	Dry Imp 3	120	Uniform	1.33	100	282
	3	Dry Imp 5	120	At the surface	1.33	100	282
	a Conditions: Catalyst Rh-SiO2 (1 g, 0.08 wt% Rh), toluene, [S]/[M] = 100, 10 mL hexane, 1 atm H2, RT.
	b Dry Imp catalyst prepared according to dry impregnation approach.
	c Determined by GC analysis.
	d Turnover frequency defined as mol of H2 per mol of rhodium per hour.

Table 8

 8 Influence of rhodium loading of Dry Impregnation Catalysts in toluene hydrogenation a .

	Entry	Catalyst b	Rhodium loading (%)	Time (h)	Conversion c (%)
	1	Dry Imp 1	0.015	2.75	4
	2	Dry Imp 2	0.035	2.75	39
	3	Dry Imp 3	0.08	1.33	100
	4	Dry Imp 4	0.15	1	100

a Conditions: Catalyst Rh-SiO2 (1 g), toluene, [S]/[M] = 100, 10 mL hexane, 1 atm H2, RT.