Souhir Mankai
email: souhirmankai@yahoo.fr

Jamel Madiouli

Jalila Sghaier

Didier Lecomte

Determination of porosity from shrinkage curves during sintering of granular materials

Keywords: Graphical method, model, porosity, shrinkage, sintering none defined

This paper investigates the implementation of an analytical model to determine the porosity of a granular material during reactive and nonreactive sintering. A graphical interpretation of this model is proposed to calculate the porosity by comparing the experimental shrinkage curve with the ideal one. For the nonreactive sintering, some examples have been taken from the literature to illustrate the application of this method for two granular materials (alumina and zircon). In the case of reactive sintering, we have used our experiments to study the sintering behavior of magnesium hydroxide. The shrinkage curve was determined by dilatometer and the porosity was measured by helium pycnometer. The comparison revealed that the porosity calculated from the model is fully consistent with the porosity measurements in the both cases.

Introduction

Sintering can be described as the change of a powder compact in a coherent material under the action of heat. This industrial process is used in several areas such as biomedical material, [START_REF] Guidara | Elaboration and Characterization of Alumina-Fluorapatite Composites[END_REF] fabrication of nuclear combustible, [START_REF] Martin | Contribution à la modélisation du frittage en phase solide[END_REF] catalyst in sensors, [START_REF] Singh | Formation of Nanocrystalline Calcia by the Decomposition of Calcite[END_REF] etc.). It is considered as a very complex phenomenon because the fundamental mechanisms of sintering are still a matter of controversy.

The sintering process usually causes volume and surface change. In fact, atomic diffusion results in joining of the particles (formation of necks between grains, [START_REF] Bouvard | Deformation of Interparticle Necks by Diffusion-Controlled Creep[END_REF] neck growth, rearrangement, grain growth with shrinkage, and deformation) and reduction of the porosity which is the main objective of sintering.

The control of these parameters (deformation, shrinkage, and porosity) is essential, to avoid posttreatment, to optimize, to better understand the sintering process, and therefore to improve the quality of the sintered components.

In many cases, there are chemical reactions of two or more components during sintering [START_REF] Nachiappan | Synthesis and Densification of Monolithic Zirconium Carbide by Reactive Hot Pressing[END_REF][START_REF] Dong | Reaction-Sintered Porous Mineral-Based Mullite Ceramic Membrane Supports Made from Recycled Materials[END_REF][START_REF] Naga | Synthesis and Characterization of Laminated Si/SiC Composites[END_REF][START_REF] Sarbandi | Finite Element Simulation of Ceramic Deformation During Sintering[END_REF][START_REF] Ertugrul | Influence of Zircon Particle Size on Conventional and Microwave Assisted Reaction Sintering of In-Situ Mullite-Zirconia Composites[END_REF] ; in this case, the sintering allows the formation of a new chemical compound and its shrinkage.

For this, various techniques have emerged depending on the way of heating the powder. These techniques include natural sintering also called conventional sintering (using an oven as a heating source) [START_REF] Naga | Synthesis and Characterization of Laminated Si/SiC Composites[END_REF][START_REF] Ertugrul | Influence of Zircon Particle Size on Conventional and Microwave Assisted Reaction Sintering of In-Situ Mullite-Zirconia Composites[END_REF][START_REF] Gonzalez Ocampo | Porous Bodies of Hydroxyapatite Produced by a Combination of the Gel-Casting and Polymer Sponge Methods[END_REF] and nonconventional sintering such as microwave sintering (irradiation by a microwave field), [START_REF] Ertugrul | Influence of Zircon Particle Size on Conventional and Microwave Assisted Reaction Sintering of In-Situ Mullite-Zirconia Composites[END_REF][START_REF] Croquesel | Direct Microwave Sintering of Pure Alumina in a Single Mode Cavity: Grain Size and Phase Transformation Effects[END_REF] sintering under load (compaction hot uniaxial or hot isostatic pressing), [START_REF] Kim | Fabrication and Mechanical Properties of Powder Metallurgy Tantalum Prepared by Hot Isostatic Pressing[END_REF][START_REF] Chrétien | Influence of Hot Isostatic Pressing on Sintering Trajectory and Optical Properties of Transparent Nd: YAG Ceramics[END_REF] flash sintering also called SPS (applying a uniaxial pressure and an electric current), [START_REF] Hilger | Fabrication and Characterization of Oxide Dispersion Strengthened (ODS) 14 Cr Steels Consolidated by Means of Hot Isostatic Pressing, Hot Extrusion and Spark Plasma Sintering[END_REF][START_REF] Huang | Microstructure and Bubble Formation of Al-K-Si Doped Tungsten Prepared by Spark Plasma Sintering[END_REF][START_REF] Huang | Enhanced Energy Storage Density of Ba0.4Sr0.6TiO3-MgO Composite Prepared by Spark Plasma Sintering[END_REF] and laser sintering (scan a powder bed by a laser beam). [START_REF] Khalil | Influence of Energy Density on Flexural Properties of Laser-Sintered UHMWPE[END_REF][START_REF] Mengucci | Effects of Thermal Treatments on Microstructure and Mechanical Properties of a Co-Cr-Mo-W Biomedical Alloy Produced by Laser Sintering[END_REF] In the literature, many works have been presented to determine experimental parameters during sintering. [START_REF] Sanad | Morphological and Dielectric Properties of Sintered Mullite Ceramics at Two Different Heating Rates Prepared from Alkaline Monophasic Salts[END_REF][START_REF] Shang | Densification and Microstructural Evolution of Hierarchically Porous Ceramics During Sintering[END_REF][START_REF] Zou | Development and Optimization of Porosity Measurement Techniques[END_REF] Many products were studied like alumina, [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF][START_REF] Baber | In Situ Measurement of Dimensional Changes and Temperature Fields During Sintering with a Novel Thermooptical Measuring Device[END_REF] zircon, [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] copper oxide, [START_REF] Marinel | In Situ Measurement of the Shrinkage During Microwave Sintering[END_REF][START_REF] Marinel | Sintering of CuO and ZnO in a Single Mode Microwave Cavity with Shrinkage Control[END_REF] ceramics, [START_REF] Sanad | Morphological and Dielectric Properties of Sintered Mullite Ceramics at Two Different Heating Rates Prepared from Alkaline Monophasic Salts[END_REF][START_REF] Shang | Densification and Microstructural Evolution of Hierarchically Porous Ceramics During Sintering[END_REF][START_REF] Zou | Development and Optimization of Porosity Measurement Techniques[END_REF][START_REF] Zymelka | Continuous and Contactless Method of Measuring Shrinkage and Temperature Distribution During Microwave Sintering[END_REF][START_REF] Chemani | Corrélation entre microstructure, processus de division, propriétés physiques dimensionnelles et surfaciques des poudres SnO 2 élaborés par voie chimique en vue de leurs applications dans des domaines diversifiés[END_REF][START_REF] Zymelka | Suivi par méthode optique du frittage micro-ondes d'oxydes céramiques[END_REF] titanium, [START_REF] Chen | An In-Situ Study of Sintering Behavior and Phase Transformation Kinetics in NiTi Using Neutron Diffraction[END_REF] and alloys. [START_REF] Xu | A Comparative Study of Powder Metallurgical (PM) and Wrought Fe-Mn-Si Alloys[END_REF] Parallelly, numerous models have been developed taking into account the different mechanisms induced by sintering (particle size distribution effects, surface diffusion, particle coalescence, phase transformation, evaporation/ condensation, etc.). These models are ranging from macroscopic (phenomenological) models to mesoscopic and microscopic (physical) ones. The microscopic model, also called two spheres model, is the first analysis of sintering and the simplest model. [START_REF] Frenkel | Viscous Flow of Crystalline Bodies Under the Action of Surface Tension[END_REF][START_REF] Herring | Effect of Change of Scale on Sintering Phenomena[END_REF][START_REF] Coble | Diffusion Models for Hot Pressing with Surface Energy and Pressure Effects as Driving Forces[END_REF] The micromechanical model can handle agglomeration, anisotropy, and particle grain size distribution, but it cannot directly model the effect of impurities and doping. Their influence on the microstructural evolution is reflected in the diffusion coefficient and interfacial energies.

The mesoscopic models are based on simple geometries (like two or multisphere model). These models involve the mass transfer mechanisms during sintering and they are used to describe the evolution of microstructure during sintering, [START_REF] Holm | The Computer Simulation of Microstructural Evolution[END_REF] which determine the thermal, mechanical, and electrical properties at macroscopic scale.

The macroscopic models have been developed to simulate the shrinkage and the deformation during the sintering process. With these models, the temperature, mechanical, and densification properties of the sintered compacts can be described by developing a constitutive law based on the continuum mechanics of porous media. [START_REF] Olevsky | Theory of Sintering: From Discrete to Continuum[END_REF][START_REF] Bordia | On Constrained Sintering I, Constitutive Model for a Sintering Body[END_REF][START_REF] Kraft | Numerical Simulation of Solid State Sintering; Model and Application[END_REF] In the literature, some numerical models [START_REF] Sarbandi | Finite Element Simulation of Ceramic Deformation During Sintering[END_REF][START_REF] Ou | Experimental Analysis and Finite Element Simulation of the Co-Sintering of Bi-Material Components[END_REF][START_REF] Maca | Sintering Densification Curve-A Practical Approach for its Construction from Dilatometric Shrinkage Data[END_REF][START_REF] Maizza | Relation between Microstructure, Properties and Spark Plasma Sintering (SPS) Parameters of Pure Ultrafine WC Powder[END_REF][START_REF] Maizza | Moving Finite-Element Mesh Model for Aiding Spark Plasma Sintering in Current Control Mode of Pure Ultrafine WC Powder[END_REF][START_REF] Li | Sintering of Bi-Porous Titanium Dioxide Scaffolds: Experimentation, Modeling and Simulation[END_REF][START_REF] Wei | Spark Plasma Sintering of Commercial Zirconium Carbide Powders: Densification Behavior and Mechanical Properties[END_REF] describing the shrinkage and the porosity change during sintering have been validated by experiments. Ou et al. [START_REF] Ou | Experimental Analysis and Finite Element Simulation of the Co-Sintering of Bi-Material Components[END_REF] studied the sintering behavior of microbimaterial components during a powder injection molding with dilatometry experiments and gravitational beam bending. As a complement to their experimental study, a thermoelastoviscoplastic model was developed and simulated by finite element method. The simulations were based on constitutive equations identified from specific experiments performed for each blend at different sintering heating rates and loadings. Maca et al. [START_REF] Maca | Sintering Densification Curve-A Practical Approach for its Construction from Dilatometric Shrinkage Data[END_REF] developed a new automatic procedure to recalculate dilatometric shrinkage data to plot density as a function of time and temperature. Maizza et al. [START_REF] Maizza | Relation between Microstructure, Properties and Spark Plasma Sintering (SPS) Parameters of Pure Ultrafine WC Powder[END_REF][START_REF] Maizza | Moving Finite-Element Mesh Model for Aiding Spark Plasma Sintering in Current Control Mode of Pure Ultrafine WC Powder[END_REF] have proposed a numerical/experimental methodology. Their experimental part is based on experiments of SPS sintering on pure and ultrafine tungsten carbide powder. The developed model is a thermoelectric model taking into account the shrinkage phenomenon. A comparison between shrinkage curves and the numerical and experimental temperatures was used to test the model developed and to estimate all the unknown variables (density, heat capacity, thermal diffusivity). Li et al. [START_REF] Li | Sintering of Bi-Porous Titanium Dioxide Scaffolds: Experimentation, Modeling and Simulation[END_REF] have determined experimentally the sintering behavior of T i O 2 monomodal porous compacts containing intergranular pores and bimodal porous scaffolds prepared by freeze casting, containing small intergranular pores and large interlamellar pores, then they comared the obtained results with those examined by finite element analysis. Wei et al. [START_REF] Wei | Spark Plasma Sintering of Commercial Zirconium Carbide Powders: Densification Behavior and Mechanical Properties[END_REF] have used a model known as power-law creep of powder to describe the densification mechanism of zirconium carbide (Z r C) powder under SPS. The numerical solution of this model is compared to the obtained experimental data in the inverse regression process to evaluate the power-law creep coefficients of the Z r C powder.

Modeling can help estimate and better optimize the process parameters. In this context, the aim of the present work is to develop a general model based on a graphical interpretation to determine the porosity from the experimental and ideal shrinkage curves during sintering. The graphical interpretation was used in our previous work [START_REF] Madiouli | A Method for Determination of Porosity Change from Shrinkage Curves of Deformable Materials[END_REF] to determine porosity during drying. In the literature, several works, allowing to calculate the porosity from the shrinkage during drying, [START_REF] Qiu | Porosity, Bulk Density, and Volume Reduction During Drying: Review of Measurement Methods and Coefficient Determinations[END_REF][START_REF] Wang | Estimation of Total, Openand Close-pore Porosity of Apple Slices During Drying[END_REF][START_REF] Noor Aidawati | A Model of Drying Kinetics of Acacia mangium Wood at Different Temperatures[END_REF][START_REF] Martynenko | Particle and Bulk Density of Shrinkable Biomaterials: Evaluation from Drying Experiments[END_REF][START_REF] Tsuruta | Study on Shrinkage Deformation of Food in Microwave Vacuum Drying[END_REF] have been presented.

During sintering, the proposed analytical models in the literature [START_REF] Herring | Effect of Change of Scale on Sintering Phenomena[END_REF][START_REF] Coble | Diffusion Models for Hot Pressing with Surface Energy and Pressure Effects as Driving Forces[END_REF] can only treat complex diffusion and transport mechanisms. The prediction of the porosity from shrinkage has been processed numerically. [START_REF] Ou | Experimental Analysis and Finite Element Simulation of the Co-Sintering of Bi-Material Components[END_REF][START_REF] Wei | Spark Plasma Sintering of Commercial Zirconium Carbide Powders: Densification Behavior and Mechanical Properties[END_REF]

Model formulation

A granular material, composed of solid matrix and air, with an initial volume V 0 , initial mass m 0 , initial bulk density q 0 , and initial porosity e 0 , is sintered under controlled conditions.

At time instant t, the volume is V, the density is ρ, the mass is m, and the porosity is ε. We suppose that volumes of solid and air phases are additive and the mass of air phase is negligible with respect to the mass of solid.

We will treat two cases of sintering: the reactive and the nonreactive sintering.

Reactive sintering

We consider that a solid S 1 , undergoing a thermal process, is reacted to give a solid S 2 and gas according to the following chemical reaction:

aS 1 ! bS 2 á cg
where a, b, and c are the stoichiometric coefficients.

Initially (at t à 0), the number of moles of the solid S 1 is n 0 and the mass of the solid m 0 is given by the following expression:

m 0 à n 0 M 0 Ö1Ü
where M 0 is the initial molar mass.

During the thermal process, the chemical reaction occurs, the number of moles of the reactant S 1 decreases to n 0 n. Considering the material balance of the system, the number of moles of S 1 is transformed into several moles b a n of the solid S 2 and c a n of gas. where n is the number of moles decreasing from the solid S 1 at time instant t.

The masses m s1 and m s1 of the solids S 1 and S 2 are, respectively, given by the following equations:

m s1 à n 0 n Ö ÜM s1 Ö2Ü m s2 à b a nM s2 Ö3Ü
where M s1 and M s2 are, respectively, the molar mass of the solid S 1 and S 2 .

The bulk density at the beginning of the chemical reaction is expressed as:

q 0 à m 0 V 0 à m s1 V 0 à m s1 V s1 V s1 V 0 Ö4Ü q 0 à m s1 V s1 V 0 V a Ö Ü V 0 Ö5Ü
Thus:

q 0 à 1 e 0 Ö Üq s1 Ö6Ü
where q s1 is the solid density of the solid S 1 and e 0 is the initial bulk porosity.

During the heating cycle, the bulk density is given by:

q à m V à m s1 á m s2 V s1 á V s2 V s1 á V s2 V Ö7Ü q à m s1 á m s2 Ö Ü q s2 m s1 q s2 á m s2 q s1 1 e Ö Üq s1 Ö8Ü
After development, we obtain the following expression:

q 1 m s2 m q s2 q s1 q s2 ✓ ◆ ✓ ◆ à 1 e Ö Üq s1 Ö9Ü
where q s2 is the solid density of the solid S 2 and ε is the bulk porosity. Knowing that:

q q 0 à m m 0 V 0 V Ö10Ü
And introducing the parameter Δ defined as d à q s2 q s1 q s2 , Eqs. ( 6), ( 9) and ( 10) can be combined to yield:

1 e Ö Ü 1 e 0 Ö Ü V V 0 à K á 1 á K Ö Ü m m 0 Ö11Ü With K à bM 2 d bM 2 aM 1 Ö12Ü
where M s1 and M s2 are, respectively, the molar mass of the solids S 1 and S 2 .

The parameters governing the shrinkage are the solid density, molar mass of the two solids (reactant and product), and the stoichiometric coefficients of the chemical reaction.

From Eq. ( 11), we deduce that the shrinkage 1 e

Ö Ü 1 e 0 Ö Ü V V 0
varies linearly with the reduced mass loss m m 0 . Two basic cases can be examined: Case (a): Ideal shrinkage with initial porosity; e à 0, e 0 6 à 0 In this case, the ideal shrinkage curve y can be written from the Eq. ( 11) in the form:

y à V V 0 à 1 e 0 Ö Ü K á 1 á K Ö Ü m m 0 ✓ ◆ Ö13Ü
Case (b): The general case: Nonideal shrinkage with initial porosity; ε ≠ 0, e 0 6 à 0

In general case, Eq. ( 11) is reduced to:

1 e Ö Üz à 1 e 0 Ö Ü K á 1 á K Ö Ü m m 0 ✓ ◆ Ö14Ü
where z is a dimensionless parameter representing the experimental shrinkage curve for a product. The porosity can be easily deduced from Eqs. ( 13) and ( 14) and given by: e à z y z Ö15Ü

A graphical interpretation of Eq. ( 15) is shown in Fig. 1a where the porosity is equal to the ratio of the

Nonreactive sintering

In the case where sintering is not preceded by a chemical reaction, the shrinkage will be deduced from Eq. ( 11) with m à m 0 and K à 0, thus leading to the following equation:

1 e 1 e 0 à V 0 V Ö17Ü
From Eq. ( 13), the ideal shrinkage coefficient becomes a constant:

y à 1 e 0 Ö18Ü
Two properties measured at the beginning and at the end of the experiment (initial porosity e 0 and initial volume V 0 ) are necessary for the full description of the model.

The porosity change can easily be deduced from Eq. (15).

As the reactive case, the graphical interpretation can be used to determine the porosity (Fig. 1b).

The porosity thus depends on the experimental values of the shrinkage and on set of properties (initial bulk density and solid density).

Materials and methods

High-purity magnesium hydroxide powder (Sigma-Aldrich, 95%) with an average granule size of 2.86 µm (the particle size dimension of the powder was measured by Microtrac S3500) was used in all experiments.

The powder was uniaxially pressed at 10 1 Mpa, for 240 s, into 6 mm diameter cylindrical porous compacts and various thickness. The porosity in the green state (initial porosity), e 0 ⇡ 71%, was calculated from the geometric volume and the true volume, considering the true density measured by the helium pycnometer for Mg(OH) 2 .

The green compact was sintered at various temperatures (from 400 to 1,350°C) using a Nabertherm furnace. The heating and cooling rates were, respectively, 10 and 30°C min 1 with a holding time of 60 min at 400°C.

At 400°C (the decomposition temperature), the samples before and after sintering were weighted and examined by structural analysis with X-ray diffraction (XRD) in a X'PERT Pro MPD PANALYTICAL diffractometer, using a CuKα radiation (k à 1.540060 Å). The crystallite size was determined by XRD through the full width at half-maximum (FWHM) of the (2h) Bragg peak using the formula:

s à dk= G cos h Ö Ü Ö19Ü
where s is the FWHM, k is the X-ray wavelength, G is the crystallite size, h is the diffraction angle, and d is the Scherrer constant to account for the particle shape (close to unity, normally 0.9). The crystalline phases were identified by reference to the International Center for Diffraction Data.

Differential thermal analysis and thermogravimetry were performed using 28.7 mg of powder with a DTA-TG SETARAM SETSYS Evolution-1750. Linear shrinkage was determined by dilatometry (SETARAM SETSYS Evolution-1750) using the same thermal cycle as for DTA.

Apparent and true densities were measured using helium pycnometer (Accu Pyc II 1340, Micromeritics), and the bulk material density of the body was calculated from the weight and geometrical dimensions.

In this study, open, closed, and total porosities are calculated according to the following formulas:

e closed à 1 q app q true Ö20Ü e à 1 q bulk q true Ö21Ü
e open à e e closed Ö22Ü

To track the porosity change, the microstructures of the sintered specimens were observed by scanning electron microscopy (SEM) (JEOL JSM-5400). The presintered and sintered samples were fractured and gold sputtered before examination.

Results and discussion

To calculate porosity, we applied the shrinkage model for two nonreactive materials (alumina and zircon) sintered under free sintering. The data were collected from Falamaki et al. [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] (Table 1). For these materials, two properties were listed: the bulk initial density and the solid density (Table 2).

The experimental works of Falamaki et al. [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] were used for the application of the model for alumina and zircon to calculate porosity changes during sintering.

Fig. 2 shows the experimental data from Falamaki et al. [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] with the experimental values of solid density and initial bulk density; an initial porosity ε 0 was calculated (Table 2) allowing the calculation of the ideal shrinkage. Equation ( 15) allows determining porosity during the whole sintering process.

The calculated porosity curve (Figs. 3 and4) shows the same form as experimental porosity of Falamaki et al. [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] for both cases (alumina and zircon products). We observe that at the initial stage of sintering (for small values of the temperature T < 1,300°C), the calculated porosity obtained from the proposed model is quite different compared to the measured porosity. The difference may be due to the microstructure of the sample and measurement errors. In fact, in general, in the initial stages of sintering, pore growth may occur by different mechanisms such as particle coalescence, particle size distribution effects, surface diffusion. The result is some kind of particle rearrangement in the initial step of sintering. Some groups of relatively small highly compact aggregates shrink on themselves by particle rearrangement with neck growth, resulting in the growth of irregular voids caused by the separation between the shrinking groups.

During this first stage, shrinkage is minimal and porosity deceases only slightly.

A transition zone (at higher sintering temperatures beginning from T à 1,350°C) may be observed in the porosity and in the experimental shrinkage versus temperature curves for alumina and zircon as well.

Within this transition zone, the densification process undergoes acceleration and shrinkage and porosity becomes significant.

The model was tested for a reactive product (the magnesium hydroxide). The XRD patterns of the initial and free sintered powder are given in Fig. 5. The XRD diffraction pattern of the initial powder reveals only peaks of Mg(OH) 2 called brucite. At 400°C, the Mg (OH) 2 was decomposed; the phase composition of the sample sintered at 400°C consists of magnesium oxide (called periclase): the following thermal reaction which takes place is: Free nonreactive sintering of alumina and zircon: ideal shrinkage (calculated using Eq. ( 18)) and experimental shrinkage curves (Falamaki et al. [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] ). 15) by referring to Table 2 and experimental porosity of alumina ( : Falamaki et al. [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] ).

Mg OH Ö Ü 2 ! DT MgO á H 2 O
The study of thermal behavior of the initial and sintered powder has proved to be a powerful way for understanding physical phenomena during sintering. Dilatometric analysis, differential and gravimetric analysis were used. A feature that is interpreted from Fig. 6 is the bulk shrinkage coefficient of compacts. The bulk shrinkage coefficient is related to the linear shrinkage L L 0 L 0 ⇣ ⌘ measured by the dilatometer by the relation:

V V 0 à 1 á L L 0 L 0 ✓ ◆ 3 Ö23Ü
Dilatometric analysis was performed at 1,400°C. If shrinkage behavior is evaluated considering microstructural evaluation, three main stages are observed in the system. 15) by referring to Table 2 and experimental porosity of zircon ( : Falamaki et al. [START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] ). 15) and referring to Table 2 and experimental porosity ( ) of magnesium hydroxide.

In the first stage, volumetric expansion is dominant and the grains grow larger (exaggerated grain growth). In the second stage, the microstructural evaluation is more complicated as sintering shrinkage is more effective because thermal activation is enough to join particles together and develop the neck formation between them. When the transformation is completed (third stage), shrinkage is dominant because sintering takes place for densification.

The decomposition path of Mg(OH) 2 was studied by DTA/TGA analysis (Fig. 7). Two endothermic peaks were observed. The small endothermic peak below 250°C with a weight loss of 1.4% is related to the dehydration process. The second peak (at 400°C) which corresponds to the decomposition reaction was very strong with a weight loss of 10.71%.

The data in Fig. 8 show that the measured porosity is in concordance with that obtained by the proposed method which confirms the validity of the model in case of reactive sintering.

The SEM images of Mg(OH) 2 sintered at various temperatures (30, 400, 1,050, 1,150, 1,250, 1,350°C) are reported in Fig. 9. The surface fractures reveal an apparent change in the sample microstructure. At 30°C, the sample presents an important intergranular porosity which disappears partially when the temperature increases (Fig. 9). We can also notice the absence of intragranular porosity from the beginning, so it can be assumed that powder porosity is opened which was confirmed by the values of porosity measured by pycnometry (Table 3).

Microstructure of the Mg(OH) 2 sintered at 400°C (decomposition reaction) was characterized by the formation of clusters of particles; this agglomeration becomes more important at 1,350°C and, at this temperature, the density increases.

Thus, the results due to the microphotography are consistent with the values of intragranular, intergranular, and total porosities obtained by the model and by the experimental measurements.

Conclusion

In the frame of this study, an analytical model for determining the porosity during reactive and nonreactive sintering using a limited number of parameters identified with specific experiments (shrinkage, initial porosity, and weight loss) was proposed. This model, based on a graphical interpretation of the shrinkage curves to determine the variation of porosity, was applied to experimental data from the literature for the nonreactive sintering and ad hoc experiments for the reactive sintering.

For the case of nonreactive sintering, a transition zone is observed at the initial stage of sintering. Afterward, the densification process dominates and at 1,500°C, a quite dense product is obtained. A difference was observed between the calculated and experimental porosities. This difference is due to the microstructure sample and the error measurements.

For the reactive sintering, a microstructural analysis was performed to evaluate the microstructure of the magnesium hydroxide. The observations of microphotographs are consistent with the porosities obtained from the model and the experimental measurements. A slight difference between experimental and calculated porosities was observed. This difference can be attributed to the experimental device or measurement errors.

It can be concluded that the graphical interpretation which is a continuous and nondestructive method can be an efficient way to compute porosity from mass balances without using porosity measurement.

Nomenclature

Figure 1 .

 1 Figure 1. Determination of porosity using visual interpretation of the shrinkage curves for: (a) nonreactive sintering and (b) reactive sintering.

Figure 2 .

 2 Figure 2.Free nonreactive sintering of alumina and zircon: ideal shrinkage (calculated using Eq. (18)) and experimental shrinkage curves (Falamaki et al.[START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] ).

Figure 3 .

 3 Figure 3. Free nonreactive sintering: comparison of calculated porosity (■) from Eq. (15) by referring to Table2and experimental porosity of alumina ( : Falamaki et al.[START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] ).

Figure 4 .

 4 Figure 4. Free nonreactive sintering: comparison of calculated porosity (■) from Eq. (15) by referring to Table2and experimental porosity of zircon ( : Falamaki et al.[START_REF] Falamaki | Initial Sintering Stage Pore Growth Mechanism Applied to the Manufacture of Ceramic Membrane Supports[END_REF] ).

Figure 5 .

 5 Figure 5. XRD spectrums of Mg(OH) 2 sintered at various temperatures: (a) 30 and (b) 400°C. Note: XRD, X-ray diffraction.

Figure 6 .

 6 Figure 6. Experimental (b) and ideal shrinkage (a) calculated using Eq. (13) as a function of temperature for free reactive sintering (Mg(OH) 2 ).

Figure 7 .

 7 Figure 7. DTA and TGA thermograms of Mg(OH) 2 .

Figure 8 .

 8 Figure 8. Free reactive sintering: comparison of calculated porosity (▬) using Eq. (15) and referring to Table2and experimental porosity ( ) of magnesium hydroxide.

Figure 9 .

 9 Figure 9. SEM micrographs of magnesium hydroxide samples sintered at different temperatures: (a) 30, (b) 400, (c) 1,050, (d) 1,150, (e) 1,250, and (f) 1,350°C. Note: SEM, scanning electron microscopy.

Table 1 .

 1 Sintering conditions and material properties from the reference used in the application of present porosity estimation model (Eq. (17)).

		Techniques and conditions of sintering
			Conditions	Measured	Measured
	Product	Techniques	(heating program)	properties	apparatus	Reference
	Alumina	-Uniaxial pressing (forming pressure 31.2 MPa)	-Heating up to 1,000°C with a heating rate of 20°C min 1	-Porosity	-ASTM C 373-88	Falamaki et al. [22]
		-No binder addition
	Zircon	-Uniaxial pressing (forming	-Heating up to the sintering	-Shrinkage	-Dilatometer Setaram
		pressure 31.2 MPa) -Addition of 4 wt% PVA	temperature with a heating rate of 5°C min 1		16/18
		-Firing in air atmosphere	-1 h soaking time

Table 2 .

 2 Properties of the studied granular materials used in the application of present model.

	Product	Initial bulk density (kg m 3 )	Solid density (kg m 3 )	Initial calculated porosity (%)
	Alumina	2,300	4,000	0.425
	Zircon	2,400	4,800	0.5
	Magnesium hydroxide	795.403	2,360	0.662
	Magnesium oxide	-	3,580	-

Table 3 .

 3 Total and closed porosities of Mg(OH) 2 measured by pycnometry, balance and calipers, and open porosity calculated using Eq. (22) at different temperatures.

	m n M V L T y z G g d	mass (kg) number of moles (mol) molar mass (kg mol 1 ) volume (m 3 ) length (m) temperature (°C) ideal shrinkage coefficient (-) experimental shrinkage coefficient (-) crystallite size (µm) gas the Scherrer constant (-)
	Greek letters ε q	bulk porosity (-) bulk density (kg m 3 )
	s k	Full width at half maximum (-) wavelength (Å)
	h a	diffraction angle (°) stoichiometric coefficient
	b c	stoichiometric coefficient stoichiometric coefficient
	Subscripts 0 s a	initial solid air
	App	apparent


Lilya Boudriche

Rachel Calvet
email: calvet@mines-albi.fr

Boualem Hamdi
email: bhamdi99@yahoo.fr

Henri Balard
email: h.balard@wanadoo.fr

Effect of acid treatment on surface properties evolution of attapulgite clay: An application of inverse gas chromatography

Keywords:

come

Introduction

Acid activation is an usual method employed for improving the surface properties of clay minerals [START_REF] Djoufac-Woumfo | Acid activation and bleaching capacity of some cameroonian smectite soil clays[END_REF][START_REF] Suarez Barrios | Textural and structural modifications of saponite from Cerro del Aguila by acid treatment[END_REF]. This chemical treatment allows to optimize the adsorption capacity of some clays in different fields, like in water pollution [START_REF] Amari | Optimised activation of bentonite for toluene adsorption[END_REF][START_REF] Frini-Srasra | Acid treatment of south Tunisian palygorskite: removal of Cd(II) from aqueous and phosphoric acid solutions[END_REF], and in catalysis by elaboration of porous structures used as catalysts or catalyst supports, on which are adsorbed or deposited active elements [START_REF] Lenarda | Solid acid catalysts from clays: preparation of mesoporous catalysts by chemical activation of metakaolin under acid conditions[END_REF][START_REF] Cabrera | 1,3-Dioxolane formation with a montmorillonite-type clay catalyst[END_REF]. These practical applications are a consequence of the existence of a high physico-chemical activity in the clay surface. In this sense it is important to note that the clay behavior will be conditioned by extent of its surface properties. Such channels may be considerably modified by heat and acid treatment, producing a sensible change not only of its surface geometry (specific surface and porosity) but also in its surface chemistry and surface energy. Indeed, this type of treatment makes it possible to increase specific surface, to create and modify the pores and can even transform structure of material. Moreover, acid treatment of clay will produce changes in the nature and number of the active sites. These acid sites and the extent of the surface area are fundamentally responsible for the physico-chemical activity of the surface of clay.

Consequently, the assessment of the surface properties modification of clay, like chemical, morphological properties and energy surface, is essential to explain and understand the behavior of materials in a given application.

The work reported here is based on the study of an Algerian clay "attapulgite". So, acid treatment was applied on attapulgite at increasing concentration to monitor the physico-chemical properties evolution of the solid, particularly its surface properties. Different methods, such as X-rays diffractometry, Fourier transform infrared, scanning electron microscopy, porosity analysis were used to characterize the evolution of the properties of attapulgite before and after treatment by HCl acid. Inverse gas chromatography (IGC) was also carried out, it is now a well-established technique for the determination of the surface thermodynamic properties, including London (i.e. apolar) and specific (i.e. polar) interactions, at the molecular level. It was proved that this technique is very effective. It was applied extensively for the characterization of the surface thermodynamic energy of various finely divided powders, (mineral fillers, pigments, silicates etc.) [START_REF] Boudriche | An assessment of the surface properties of milled attapulgite using inverse gas chromatography[END_REF][START_REF] Kellou | Surface properties of dimethylsilylated silicas, assessed using IGC at finite concentration[END_REF][START_REF] Hamdi | IGC characterization of surface energy and morphology of two natural fillers: kieselguhr and bentonite[END_REF], composite materials [START_REF] Huang | Investigation on interfacial interaction of flame retarded and glass fiber reinforced PA66 composites by IGC/DSC/SEM[END_REF], organic materials (plastics, textiles, food, pharmacology etc.) [START_REF] Nastasovic | Determination of glass temperature of polymers by inverse gas chromatography[END_REF][START_REF] Swaminathan | Measurement of the surface energy of lubricated pharmaceutical powders by inverse gas chromatography[END_REF][START_REF] Cantergiani | Use of inverse gas chromatography to characterize cotton fabrics and their interactions with fragrance molecules at controlled relative humidity[END_REF].

Theoretical part

Depending on the amount of probe molecules injected into the chromatographic column, two techniques of IGC may be distinguished:

Inverse gas chromatography at infinite dilution (IGC-ID)

This technique reflects the interaction between the isolated probe molecule and the solid surface, it consists on the injection of negligible quantities of probes molecules (vapour) with known properties (polarities, ramification).

Depending on the chemical nature of the probe molecule, inverse gas chromatography at infinite dilution (IGC-ID) provides access to many parameters:

-The dispersive component of the surface energy ( d s ), obtained by injection of linear alkanes. This parameter indicates the ability of the solid surface to have non-specific interactions with probe molecules [START_REF] Dorris | Adsorption spreading pressure and London force interactions of hydrocarbons on cellulose and wood fiber surfaces[END_REF].

-The nanomorphological index I M ( t ), established by injection of branched or cyclic alkanes. This value delivers an information about the roughness of the solid surface at the molecular scale [START_REF] Brendlé | A new topological index for molecular probes used in inverse gas chromatography for the surface nanorugosity evaluation. (1) Method of evaluation[END_REF]. -The specific component of the surface energy (I sp ), determined by injections of polar probes, it gives access to polar interactions, mainly the acid-base interactions [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations[END_REF].

Inverse gas chromatography at finite concentration (IGC-FC)

This technique reflects the interaction of a population of probe molecules with the solid surface by injecting few microliters of liquid probe (1-20 L) into the column containing the solid to be analysed.

Due to the presence of sites of adsorption having high interaction energies, a non-negligible part of the injected probe is not eluted in time corresponding to the return of the signal to the base line. In order to assess the amount of probe irreversibly adsorbed on the surface, the temperature of the chromatograph oven is increased up to 150 • C, the conditioning temperature, leading to the small peak observed on the right side of the inverse gas chromatography at finite concentration (IGC-FC) chromatogram. Then the irreversible part of the adsorption phenomena could be assessed from the ratio of the area of the thermodesorption peak to the total area of the chromatogram, designed as irreversibility index (I irr ) [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF] and computed according to the Eq. ( 1):

I irr = S th (S rv + S th ) (1)
where S rv is the surface of the main chromatographic peak and S th is the surface corresponding to the thermodesorption peak. IGC-FC gives also access to the first isotherm derivative [START_REF] Conder | Physicochemical Measurements by Gas Chromatography[END_REF], which is directly related to the net retention time of each point of diffuse front of the chromatogram by the Eq. ( 2):

∂N ∂P L,tr = 1 RT D c m (tr -t 0 ) ( 2
)
where N is the number of probe molecules adsorbed at one point on the rear descending front of the chromatographic peak, P the partial pressure of the probe at the output of the column, L the column length, t r the retention time of this point, t 0 the retention time of CH 4 , a molecule not retained by the solid surface, D c the corrected flow rate and m the mass of the solid contained in the column, T the oven temperature. Also, the pressure of the probe is directly related to the height of the signal at this point.

Hence, one has easily access to the desorption isotherm of the molecule probe, from a single chromatographic peak [START_REF] Conder | Physicochemical Measurements by Gas Chromatography[END_REF].

Desorption isotherm and its main parameters such as the Henry and the BET constants and the specific surface area were computed using a home-made softaware from the Adscientis society (Wittelsheim, France).

On another hand, the shape analysis of the isotherm leads to the knowledge of distribution functions of the adsorption energy sites (DF), which are related to the surface heterogeneity of the solid contained in the column. The calculation of DF is based on a physical adsorption model, which admits that the global isotherm may be considered as a sum of local isotherms of adsorption on isoenergetic domains (patchwork model) [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF][START_REF] Balard | Estimation of the surface energetic heterogeneity of a solid by inverse gas chromatography[END_REF][START_REF] Rudzinski | Physical adsorption of gases on heterogeneous solid surface: evaluation of the adsorption energy distribution from adsorption isotherms and heats of adsorption[END_REF]. Then, the surface heterogeneity is described by a distribution function corresponding to the relative abundance of each type of domain having the same characteristic energy of interaction (ε c ). DF was computed using the home-made software from the Adscientis Society (Wittelsheim, France).

Comparing the computed DF with the DF corresponding to a homogeneous surface that fit the left descending branch of the experimental DF, towards the lowest interaction energies, [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF] one has access to an index of surface heterogeneity I hete , given by the Eq. ( 3):

I hete = A -A H A (3)
where A is the area under the experimental DF and A H that of the homogeneous DF. This index will permit to compare simply the surface heterogeneity of the studied samples.

Materials and methods

Material

The attapulgite used in this study is from the region of Ghoufi, at the northeast of Algeria. The crude attapulgite was first coarsely crushed and sieved in order to obtain a size fraction below 1 mm, allowing easier analysis, measurements, and treatments at the laboratory-scale processes.

Palygorskite and attapulgite are synonymous terms for the same hydrated magnesium aluminum silicate mineral. The preferred name as specified by the International Nomenclature Committee is palygorskite but the name attapulgite is so well entrenched in trade circles that it continues to be used by many producers and users.

According to Bradley [START_REF] Bradley | The structural scheme of attapulgite[END_REF], the structure of attapulgite belongs to the 2:1 phyllosilicate classification, in which the sheets of silica tetrahedral are periodically inverted with respect to the tetrahedral bases (Fig. 1). As a result of this inversion, the octahedral sheets are periodically interrupted and terminal cations must complete their coordination spheres with water molecules. This structure confers to the material a fibrous morphology.

Acid treatment of attapulgite

The acid treatment of the attapulgite was carried out under reflux system at the boiling point of the HCl solution for 6 h. The experiments were done with different HCl concentrations: 0.5 M, 1 M, 3 M and 5 M.

For each concentration, the obtained solution was filtered and the residue was washed with distilled water several times. The titration of the filtered solution with silver nitrate (AgNO 3 ) Fig. 1. Crystal structure of attapulgite [START_REF] Bradley | The structural scheme of attapulgite[END_REF].

permitted us to ensure that the chloride ions were totally removed from the residue. Then, the obtained sample was dried at 110 • C overnight, before characterizations.

Characterization methods

The particle morphology was investigated using a scanning electron microscope (Philips XL 30 model ESEM-FEG) operating at 3 kV. The X-rays analysis by SEM or energy dispersive spectroscopy (EDS) was conducted to determine the elemental composition of particles. This method is based on the emission of a photon X, knowing that the X-ray photons have an energy characteristic of each element that issued them. These photons are collected and classified according to their energy (EDS detector) to provide information on the chemical composition of the sample.

The density of the obtained solids was determined by an helium pycnometer (Accupyc 1330-Micrometrics).

The specific surface areas, BET constants, and meso and micropore volumes were determined using nitrogen adsorption at liquid nitrogen temperature (ASAP 2010, Micromeritics) by applying the BET, BJH, and t-plot methods, respectively. The samples were out gassed, before analysis, at 105 • C for 24 h at a pressure of 6.6 × 10 -3 mbar.

Phase identification was performed on a Panalytical X'PERT Pro diffractometer (Philips) (CuK radiation) with a step size of 0.017 • for 2Â angles ranging from 5 • to 80 • . The 2Â values were analysed with the X'Pert High Score software and compared with the ICDD (International Centre for Diffraction Data) database.

The IR spectra of activated attapulgite were obtained using a Perkin Elmer 560 Fourier transform infrared (FTIR) spectrophotometer with a resolution of 2 cm -1 and a scan number equal to 64. The spectral study was extended over the range 4000-400 cm -1 . The analysis was done on KBr pellets with 1% of treated sample, using a hydraulic press by applying a pressure of 73.5 kPa.

For the analysis of silicon, samples were mineralized by alkaline fusion with sodium hydroxide. For the analysis of the following elements: Al, Mg, Ca, Fe, samples were mineralized by wet way in acid media. After mineralization, all the elements were then analysed by ICP-AES.

The IGC measurements were performed with two GC devices (Agilent 7890 A and 6890), fitted with sensitive flame ionization detectors (FID). Helium was used as the carrier gas with a flow rate of 30 mL/min measured with an electronic flowmeter (Flow 500-Agilent). The temperatures of the injector and detector were respectively 130 • C and 200 • C. The columns were partially filled with a mass of attapulgite powder varying between 0.3 and 1 g and completed with glass beads. The mass of powder was depending of the pressure drop into the column which had to be lower than 1 bar in order to avoid leaks at the septa and fittings.

The IGC-ID study was done with an oven temperature of 130 • C, using stainless steel columns of 20 cm in length, with 6.35 mm in diameter. The columns were conditioned overnight at 150 • C. The conditioning temperature was taken equal to 150 • C after a study made on the effect of temperature on the surface properties of the attapulgite, this temperature does not alter the surface properties of the solid. The oven temperature for the analysis must be less than the conditioning temperature so it was chosen equal to 130 • C to allow a good separation between the peak of methane and the peak of the probe at this temperature.

The probes used were linear alkanes (hexane C6, heptane C7 and octane C8), two branched alkanes, the 2,3,4-trimethylpentane (2,3,4-TMP) and the 2,5-dimethylhexane (2,5-DMH), a cyclic alkane, the cycloctane (Cycl 8) and polar probes (chloroform CHCl 3 and dichloromethane CH 2 Cl 2 ). These probes had a chromatographic grade (>99%) purity.

For IGC-FC, the chromatographic columns were 10 cm in length with 6.35 mm or 3.18 mm in diameter. The conditioning temperature was 130 • C and analysis temperature depended on the probe used, according to the Conder criterion [START_REF] Conder | Physicochemical Measurements by Gas Chromatography[END_REF] which states that the contribution of probe vapour to the flow of carrier gas does not exceed 5% of the initial flow at the maximum of the chromatographic peak. Three probes were examined in IGC-FC, the octane (C8) at 53 • C, the isopropanol (IP) at 43 • C and the 1,4-dioxan (DX) at 51 • C. We chosed an apolar probe 'octane' to study the surface morphology and two polar probes to study the surface chemistry. These probes had a chromatographic grade (>99%) purity and were placed on a molecular sieve to avoid the water effect.

The injections of each probe are repeated three times and three columns were made with the raw attapulgite for taking into account the heterogeneity of the powder. For each parameter, a media is then calculated from the values resulting from the different injections and from the three columns. The repeatability measured with three columns was only examined with the raw powder because of the duration of the analysis. For the other samples, only the injections on one column were repeated three times.

To be sure that the amount of injected probe corresponds to the ID conditions, different injections are realised varying the amounts of probe vapour. If the retention time at the maximum of the chromatogram is constant, the ID conditions are respected.

To reach the FC conditions, the probe is injected in the liquid form to lead to a highly asymmetric chromatographic peak. Experimentally, some increasing quantities of liquid probes are injected, the diffuse fronts of the chromatographic peaks are recovering themselves in the case of a solid leading to a type II adsorption isotherm. The tops of the peaks appear for retention times lower and lower as the quantity of probes increases until the chromatogram obtained when the monolayer of probe is reached at the surface of the solid.

Results and discussion

Structural and textural characterizations

Scanning electron microscopy

The scanning electron microscopy was used for the determination of the morphology of acid treated attapulgites. Fig. 2 displays two microscopies of the raw attapulgite.

One sees in Fig. 2A that the raw attapulgite exhibits a fibrous morphology with fibers having an average length less than 3 m.

Fig. 2B shows a typical crystalline inclusion present in the raw attapulgite, which are attributed to carbonated impurities according to their X-rays analysis (EDAX): Ca (22.38%), C (18.48%), O (44.76%) and Mg (13.32%), present in calcite CaCO 3 and dolomite CaMg(CO 3 ) 2 .

Fig. 3 shows a SEM micrography of the attapulgite treated with HCl 0.5 M.

If it is observed that the silica keeps its fibrous morphology unchanged comparing with the raw attapulgite, some carbonate impurities had disappeared, leaving holes in the fibrous solid.

Then, the influence of the strongest treatment done with HCl 5 M, on the attapulgite morphology was so examined (Fig. 4).

It is worth to point out that the fibrous morphology is still preserved with this strong acid treatment. Gonzalez et al. had made the same observation after activation with HCl of sepiolite [22] or attapulgite [START_REF] Gonzalez | Structural and textural evolution of Al-and Mg-rich palygorskites, I. Under acid treatment[END_REF]. He explained that the silica generated during the activation process could behave as a protective gel preserving the fibrous morphology of attapulgite.

The loss of material due to the acid treatment of the carbonated impurities will have certainly an influence on the global apparent density of the treated attapulgite as it could be measured using a helium pycnometer.

Density measurements

Table 1 reports the values of the apparent densities of initial and treated attapulgites. It is observed that the apparent density decreases readily with increasing HCl concentration. For the sample treated with 5 M HCl, the apparent density decrease is equal to 15% of the initial one.

This loss of material will certainly have an influence on the surface morphology in terms of specific surface areas and porosity as it could assess through nitrogen adsorption at 77 K.

Specific surface areas and porosity measurements

The values of specific surface areas, micro and mesoporous volumes, obtained by exploiting the adsorption-desorption isotherms of N 2 at 77 K, are gathered in Table 2.

The specific surface areas increase from 125 m 2 /g before treatment to 399 m 2 /g after a treatment with a 3 M HCl concentration. There are good correlations between the density data quoted and specific surface area and with the mesoporous volumes.

The increase of the surface area is due to the creation of new surfaces in activated samples. This creation of porosity is caused, at first, by dissolution of carbonate species, followed by those of the octahedral sheets, and exchangeable cations [START_REF] Suarez Barrios | Acid activation of a palygorskite with HCl: development of physico-chemical, textural and surface properties[END_REF].

But beyond the 3 M HCl concentration, BET surface decreases down to 315 m 2 /g for the 5 M solution, at the same time of the microporous volume decreases. These evolutions could be attributed to the plugging of the active sites created after acid treatment, by the deposition of insoluble impurities. This trend was previously observed by Vincente Rodriguez [START_REF] Vincente Rodriguez | Acid activation of a spanish sepiolite: physico-chemical characterization, free silica content and surface area of the obtained products[END_REF] and Mendiorez et al. [START_REF] Mendiorez | Texture evolution of montmorillonite under progressive acid treatment: change from H3 to H2 type of hysteresis[END_REF], on sepiolite and montmorillonite activated also with HCl. The BET constant is also affected by the acid treatment; it decreases significantly from 436 to 131, reflecting a decrease in the interaction ability of nitrogen with the surface of the activated samples.

All these change in surface morphology have certainly related to a change of the crystalline structure of the attapulgite that could be evidenced by X-ray diffraction and IR spectroscopy.

X-ray diffraction and IR spectroscopy

Diffraction patterns of acid treated attapulgite samples are gathered in Fig. 5.

It is observed that the XRD diffractogram of attapulgite remains unchanged when treated with a 0.5 M HCl concentration. Beyond this value, a progressive reduction in the peaks intensity of dolomite and calcite with the increase of HCl concentration is noticed. Comparing with the raw clay diffractogram, for a 1 M HCl concentration the disappearance of peaks at 29.2, 30.8, 37.5, 39.3, 42.9, 44.8, 47.6, 48.5, and 50.9 (2Â) characteristic of calcite (CaCO 3 ) and dolomite (CaMg(CO 3 ) 2 ) is observed whereas the attapulgite pattern remains unchanged. This observation confirms the loss of the two crystalline forms of carbonates, which was evidenced by SEM.

For a 3 M HCl concentration, the attapulgite peaks become broader, indicating the loss of crystallinity. After 5 M HCl treatment, the diffraction patterns in Fig. 5 shows a broadened band (between 15 and 35 (2Â)) corresponding to the formation of an amorphous silica phase, insoluble in acid medium, generated by the dissolution of octahedral sheet in attapulgite under acid treatment. Suarez Barrios et al. [START_REF] Suarez Barrios | Acid activation of a palygorskite with HCl: development of physico-chemical, textural and surface properties[END_REF] have reported similar results on a Spanish attapulgite, with 7 M HCl. IR spectroscopy could also gives information about the structure of the studied attapulgites.

Fig. 6 represents the evolution of FTIR spectra of attapulgite before and after activation with HCl at different concentrations in the spectral range of 3800-2900 cm -1 .

The band located at 3614 cm -1 is attributed to the stretching vibration of OH associated with Al 3+ cations in dioctahedral coordination (Al 2 OH) and to OH stretching vibration of water coordinated to Mg along the fibers. The second band located at 3546 cm -1 is related to stretching vibrations of OH in (Fe, Mg)-OH and (Al, Mg)-OH [START_REF] Blanco | Differences between one aluminic palygorskite and another magnesic by infrared spectroscopy[END_REF].

The peaks intensities at 3614 cm -1 and 3546 cm -1 remain constant until a 1 M HCl concentration and then are weaker for 3 M solution until their total disappearance for the 5 M concentration, revealing a broad intense band centered around 3440 cm -1 .

Thus, the disappearance of these bands confirms the total dissolution of the octahedral sheets for highest concentrations of acid. This variation agrees with that reported by Suarez Barrios et al. [START_REF] Suarez Barrios | Acid activation of a palygorskite with HCl: development of physico-chemical, textural and surface properties[END_REF] on a Spain attapulgite treated with acid. Fig. 7 shows the evolution of the IR pattern under the effect of acid treatment in the 1500-400 cm -1 region.

The bands characteristic of carbonates, at 1423 cm -1 and 877 cm -1 , disappear from the treatment with 0.5 M HCl, corroborating again the elimination of carbonate impurities at this concentration. At 1 M concentration the characteristic bands of the attapulgite structure remains quite unchanged.

Nevertheless, at this concentration, new bands appear, which will increase with increasing HCl concentration:

-At 800 cm -1 , this band increases in intensity as the concentration of HCl increases. It is attributed to the vibration of Si-O-Si in the formed free silica (SiO 2 ) [START_REF] Gonzalez | Structural and textural evolution of Al-and Mg-rich palygorskites, I. Under acid treatment[END_REF][START_REF] Suarez Barrios | Acid activation of a palygorskite with HCl: development of physico-chemical, textural and surface properties[END_REF]. -At 950 cm -1 , this band is attributed to the silanol groups vibration related to the formed amorphous silica (bending vibration of Si-OH) [START_REF] Gonzalez | Structural and textural evolution of Al-and Mg-rich palygorskites, I. Under acid treatment[END_REF][START_REF] Mendelovici | Infrared study of attapulgite and HCl treated attapulgite[END_REF]. -At 1200 cm -1 , a broad band, characteristic of the silica bulk [START_REF] Gonzalez | Structural and textural evolution of Al-and Mg-rich palygorskites, I. Under acid treatment[END_REF][START_REF] Mendelovici | Infrared study of attapulgite and HCl treated attapulgite[END_REF].

In summary, the different spectroscopic analysis confirms that activation of the attapulgite with HCl is strongly dependent on the acid concentration. Of course, these modifications would be accompanied by some important chemical modification that we have evidenced by elemental chemical analysis.

Chemical composition

The quantification of elemental composition (%Si, %Al, %Mg, %Ca, %Fe, %C) in the solid after treatment will help us to precise the evolution of the structure of attapulgite treated with different acid concentrations.

The evolution of their respective percentage, with the HCl normality, is reported in Table 3:

As expected, the percentage of Si increases with increasing the acid concentration, at the same time as the decrease of Ca, Mg and Al contents. This was attributed to the dissolution of carbonated impurities, calcite and dolomite, and to the partial treatment of the octahedral sheets, containing Al and Mg cations.

The rapid decrease of the carbon content between the initial and 0.5 M HCl solution corroborates the previous results, that say that the carbonate impurities are quite completely eliminated at this concentration whereas the augmentation in aluminum content proves that this treatment permits the purification of the raw attapulgite. Beyond a 1 M HCl concentration, the Al content decreases strongly, emphasizing the modification of the attapulgite structure. As observed with RX and IR, a higher acid concentration is required to affect the attapulgite structure.

For the normality equal and higher to 1 M, a continuous decrease of the cationic species goes on indicating clearly the transformation of the attapulgite into amorphous silica. However, the 5 M HCl solution does not eliminate all the cations and the silicon content remains lower and is equal to about 80% to that corresponding at the pure silica (46.8%).

Surface properties characterization by IGC

The surface properties of the initial and acid treated attapulgites were examined calling on IGC-ID and IGC-FC.

Characterization of samples by IGC-ID

By IGC-ID analysis, the three following parameters were determined, at 130 • C, on raw and acid treated attapulgites:

-The dispersive component of surface energy, d s , using alkanes probes.

-The nanomorphological indexes, I M ( t ), of two branched alkane probes and of one cyclic probe. -The specific interaction parameters (I sp ) of two acid probes.

Their values are reported in Table 4. The values of the dispersive component of the surface energy decrease from 164 mJ/m 2 to 47 mJ/m 2 , as the acid concentration increases. The initial value of 164 mJ/m 2 is typical of a phyllosilicate, this high value is attributed to the insertion of the alkanes probes into the fibrous channels of the attapulgite or into structure defects between fibers [START_REF] Boudriche | An assessment of the surface properties of milled attapulgite using inverse gas chromatography[END_REF], whereas the final value of 47 mJ/m 2 is of the same order of some synthetic silica like the S13 one (Wacker, 40 mJ/m 2 measured at 150 • C) with a specific surface area of 132 m 2 /g [START_REF] Khalfi | Characterization of silylated silicas by inverse gas chromatography: modelization of the poly(dimethylsiloxane) monomer unit/surface interactions using poly(dimethylsiloxane) oligomers as probes[END_REF].

The specific components of the surface energy I sp determined by injecting acid polar probes, chloroform and dichloromethane, decrease slightly as the HCl concentration increases. These decreases can be attributed to the gradual disappearance of basic sites associated with the constituent cations and the appearance of acidic silanol groups, exchanging weaker interactions with these two acid probes.

Moreover, a close relation exists between the evolution of dispersive component ( d s ), the nanomorphology index (I M ( t )) and the chemical composition of attapulgite activated with HCl acid as depicted in Fig. 8.

Indeed, the highest d s parameter value and the lowest I M one corresponds to the lowest Si/Al ratio attributed to the raw attapulgite. Beyond 3 M HCl concentration, the d s reaches very low values while I M values tend to 1, testifying of the disappearance of the surface roughness, as, in the same time, a pronounced increase of the Si/Al ratio is observed corresponding to an increase of percentage of free silica formed from tetrahedral and octahedral sheets of the attapulgite. The same correlation between the silicification phenomenon and the decrease of the dispersive component of the surface energy was already observed [START_REF] Hamdi | IGC characterization of surface energy and morphology of two natural fillers: kieselguhr and bentonite[END_REF] on acid treated minerals fillers like bentonite and kieselguhr, particularly at high concentration (HCl 6 M). These evolutions of IGC-ID parameters demonstrate the HCl treated attapulgite loses its crystalline structure responsible of its surface roughness and acquires at high HCl concentration the surface structure of an amorphous silica and therefore, it corroborates the conclusions of the X-rays and IR spectroscopies.

Following, our work will focus on studying the influence of acid activation not only on the specific surface areas, but also on the surface heterogeneity of attapulgite as it could be assessed by IGC-FC.

4.2.2.

Characterization of samples by IGC-FC 4.2.2.1. (a) Evolution of the isotherm characteristics with the acid treatment. The values of the specific surface areas, BET constants and irreversibility indexes of the samples activated with HCl, determined by IGC-FC and nitrogen adsorption are reported in Table 5.

The specific surface areas with nitrogen are higher than those measured with octane probe, which are themselves higher than those measured with the two selected polar probes (isopropanol and dioxan).

The gap could be due to:

-Uncertainty on the actual molecular areas of organic probes, which were computed from adsorption isotherm data "on nonporous solids" which is not the case of the attapulgite. -Structures of the probes (polarity and steric encumbrances).

-The irreversible adsorption of the probe on the solid surface, because IGC-FC provides the desorption isotherm, leading to an underestimation of the specific surface area.

To overcome this last difficulty, the specific surface area could be corrected by adding to that measured from the desorption isotherm, the contribution corresponding to the irreversible part, which could be assessed calling on the irreversibility index (I irr ) determined from the thermodesorption peak as described above. This index provides an estimate of the proportion of high energy sites. The values of the corrected specific surface areas (a corr ) are reported in Table 6.

Nevertheless, the corrected specific surface areas (a corr ) measured with the organic probes remains lower than those with nitrogen. Irreversible adsorption is not the only factor responsible of the low values of the specific surface areas measured with organic probes but also the uncertainty on the actual molecular of the probes.

The evolution of the specific surface area as a function of the acid concentration is displayed in Fig. 9.

Whatever the probe used -nitrogen or organic molecules -the curves have the same shape, they pass through a maximum for the 3 M HCl concentration.

The increase of the surface observed during the initial concentrations (<3 M) is explained by the creation of new surfaces caused by the removal of carbonates impurities. Beyond the 3 M concentration, the decrease of specific surface areas values could be attributed to the collapse of the channels characteristic of the attapulgite structure and the formation of the amorphous silica deposit. It is also worth to point out that the irreversibility indexes are also sensitive to the acid treatment. Those calculated with octane and isopropanol follow the same trend and go through a maximum for the acid concentrations comprised between 0.5 M and 1 M HCl.

This observation supports again the hypothesis done previously that these acid concentrations permit the purification of the raw attapulgite without affecting notably its crystalline structure between 0.5 M and 1 M HCl, the XRD patterns in Fig. 5 shows the peaks related to the attapulgite are preserved. The disappearance of roughness surface and the destruction of the attapulgite structure, at high acid concentrations, make the surface more uniform.

Dioxan behaves differently because its irreversibility index increases as the acid concentration increases indicating a greater affinity, bound to its strong base character, for the formed silica surface through the acid silanol sites.

In the same way, the isopropanol BET constant increases significantly as the HCl concentration increases until the 5 M HCl concentration, it was attributed to the strong interactions that take place between the isopropanol and the silanol at the surface of the silica formed gradually as the acid concentration increases. Now the evolution of the surface heterogeneity with the increase of the acid concentration, will be assessed through the distribution functions of the adsorption energies of the organic probes.

(b)

Evolution of the surface energetic heterogeneity. The DF of the initial and treated attapulgites were calculated according to the Rudzinski Jagiello method [START_REF] Balard | Estimation of the surface energetic heterogeneity of a solid by inverse gas chromatography[END_REF] and developed by Balard [START_REF] Rudzinski | Physical adsorption of gases on heterogeneous solid surface: evaluation of the adsorption energy distribution from adsorption isotherms and heats of adsorption[END_REF]. The DF allows us to evaluate the surface heterogeneity of our activated samples. It was first evaluated with a non polar probe, n-octane (Fig. 10), which exchanges only dispersive interactions with the surface of the studied samples and therefore is not sensitive to the surface functionality.

The obtained DF obtained with octane are essentially monomodal and almost superposable for all the studied samples. Nevertheless their heterogeneity indexes I hete (Fig. 10) go through a maximum for the 0.5-1 M solutions, testifying that dissolution of carbonate impurities liberates high energetic sites, which are probably insertion sites. For the 5 M concentration, the surface becomes quite homogeneous, a proof that the surface is quite smooth at the molecular level as it was also proved by the fact the nanomorphology index of the cyclooctane was close to one.

On the contrary, by its ability to exchange strong interactions through hydrogen bonding, the isopropanol probe is sensitive to the surface functionality. The DF of isopropanol of the raw and treated attapulgite samples and their corresponding I hete are depicted in Fig. 11.

The DF of the raw attapulgite shows only a tail extending towards the high energies, a proof that the presence of the impurities generates some sites having intermediate interaction energies, leading to a continuum.

The treatment with 0.5 M HCl modifies only a little bit the initial DF shape, no define secondary maximum appears. This observation corroborates the fact that at this concentration, attapulgite structure remains practically unchanged. With increasing the acid concentration, the DF become clearly bimodal, very similar to those acquired for pyrogenic silicas [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations[END_REF][START_REF] Donnet | Influence of specific surface area of pyrogenic silicas on their heat of immersion in water and on their surface properties assessed using inverse gas chromatography[END_REF][START_REF] Papirer | Surface Energetics of silica Investigated by Inverse Gas Chromatography[END_REF], reflecting an evolution toward a silica like structure. According to the literature, the peak towards low energies reflects the hydrogen interactions between the alcohol function of the isopropanol probe and siloxane bridges Si-O-Si on the solid surface, whereas the peak at about 28 kJ/mol is attributed to stronger interactions through hydrogen bound of the probe with the silanol groups on the solid.

The regular growth of the I hete parameter from the raw material up to 5 M HCl treated one, denotes an increase of the surface heterogeneity bound to the change of its chemical functionality. This agrees with the gradual formation of siloxane and silanol sites on free silica surface. DF of dioxan probe and their corresponding I hete parameters are depicted in Fig. 12.

As for the isopropanol probe, the DF of the raw sample and the one treated with 0.5 M HCl exhibit same shape and show no defined structure due to the multiplicity of the adsorption sites on their surface, testifying again that this treatment does not affect notably the structure of the attapulgite despite it permits the elimination of the most part of the carbonated impurities.

For higher acid concentrations, dioxan DF become clearly trimodal. This difference in behavior compared with isopropanol probe should be attributed to the basic character of the dioxan, that can establish strong specific interactions with silanol group. If the main peak centered at 18 kJ/mol can be again attributed to the interaction probe-siloxane groups, two new peaks located at 28 kJ/mol and 36 kJ/mol, should correspond to the interactions of dioxan with different acid sites, some acting as Lewis site, like cations or as Brönsted site like silanol groups.

The dioxan heterogeneity indexes values, I hete , do not evolve strongly, if we except the 5 M treated sample. This could perhaps be bound to the ability of this basic probe to interact with different type of acid sites and to the fact the silanol on the amorphous silica will replace Lewis ones when the acid concentration increases.

Conclusion

The activation of attapulgite with increasing HCl concentrations indicates that:

At low concentrations of HCl (≤1 M), the morphology and the crystal structure of attapulgite are preserved and the elimination of carbonates is mainly observed. Decarbonation causes an increase in surface area and pore volumes, measured with nitrogen and a decrease of the apparent density of the sample.

At higher concentrations of HCl (>3 M), the dissolution of Al and Mg cations from the tetrahedral and octahedral sheets leads to a progressive destruction of the chemical structure leading to the formation of amorphous silica, which keeps the original fibrous morphology.

By IGC-ID, it was observed a decrease of the dispersive component of the surface energy and correlatively an increase of the index of nanomorphology of the cyclooctane corroborating the passage from a clay structure to that of a amorphous silica. Whereas the I sp , determined by injection of polar probes, indicates a change in the surface acidity, the silica being more acidic.

The n-octane DF, which is not sensitive to the surface functionality, leads quite symmetrical DF characteristic of a quite homogeneous surface.

On another hand, the DF of the two polar probes (isopropanol or dioxan) are strongly asymmetrical for the initial attapulgite and bimodal for the isopropanol probe or trimodal for the dioxan probe, because of their high sensitivity to the surface functionality. These probes interact by hydrogen bonds or strong acid/base interactions with the surface functional groups.

Thus, inverse gas chromatography has enabled us to gather many informations about the surface properties of attapulgite activated with HCl.

In conclusion, if one wants to purify an attapulgite and simultaneously to preserve its structure, a one molar HCl solution will be the best, having a high specific surface area, whereas a treatment with a 5 M HCl solution will permit to transform the attapulgite into an amorphous silica, having very different surface properties and also a high specific surface area.

Fig. 2 .

 2 Fig. 2. SEM micrographies of (A) attapulgite fibers and (B) a carbonate inclusion.

Fig. 3 .

 3 Fig. 3. SEM micrography of a hole appearing in attapulgite structure after acid treatment with 0.5 M HCl.

Fig. 4 .

 4 Fig. 4. SEM micrography of attapulgite, after treatment with 5 M HCl.

Fig. 5 .

 5 Fig. 5. XRD diffractograms of attapulgite before and after acid activation at different HCl concentrations (Att = attapulgite, D = dolomite, C = calcite).

Fig. 6 .

 6 Fig.[START_REF] Cabrera | 1,3-Dioxolane formation with a montmorillonite-type clay catalyst[END_REF]. FTIR spectra of attapulgite before and after treatment with HCl, in 3800-2900 cm -1 region.

1 Fig. 7 .

 17 Fig.7. FTIR spectra of attapulgite before and after treatment with HCl, in the 1500-400 cm -1 region.

Fig. 8 .

 8 Fig. 8. Evolution of the dispersive component d s , the nanomorphological index IM( t ), and the Si/Al ratio of attapulgite treated with HCl acid at different concentrations.

Fig. 9 .

 9 Fig.9. Evolution of the specific surface area of attapulgite treated with various concentrations of HCl, measured by nitrogen adsorption ᭹ and IGC-FC with octane , isopropanol , and dioxan .

  χ(ε)(µmol/(kJ/mol))

Fig. 10 .

 10 Fig. 10. Adsorption energy distribution functions of the n-octane probe of the initial and treated attapulgite, measured at 53 • C.

χFig. 11 .

 11 Fig. 11. Adsorption energy distribution functions of the isopropanol probe of the initial and treated attapulgite, measured at 43 • C.

Fig. 12 .

 12 Fig. 12. Adsorption energy distribution functions of the dioxan probe of the initial and treated attapulgite, measured at 51 • C.

Table 1

 1 Density measurements of HCl activated attapulgites.

	Samples	Density (g/cm 3 )
	Raw attapulgite	2.57
	Activated attapulgite with HCl
	0.5 M	2.40
	1 M	2.35
	3 M	2.21
	5 M	2.18

Table 2

 2 Values of the specific surface areas (aBET), BET constants (CBET), meso (Vmeso) and micropores (V micro ) volumes of attapulgite samples before and after HCl treatment at different concentrations, determined by nitrogen adsorption at 77 K.

		aBET (m 2 /g)	CBET	Vmeso (cm 3 /g)	V micro (cm 3 /g)
	Raw attapulgite	125.1	436	0.302	0.018
	Activated attapulgite with HCl
	0.5 M	273.5	468	0.397	0.047
	1 M	336.6	299	0.532	0.058
	3 M	399.0	243	0.662	0.054
	5 M	315.2	131	0.728	0.014

Table 3

 3 Chemical composition of elements in raw and activated attapulgite at different HCl concentrations.

	Element (%)	Elemental analysis
		Raw attapulgite	Activated attapulgite with HCl
			0.5 M	1 M	3 M	5 M
	Si	16.63	24.99	27.68	34.04	38.71
	Mg	6.35	5.10	4.41	1.83	0.24
	Al	4.12	5.36	4.61	2.14	0.28
	Ca	8.62	0.15	0.42	0	0.11
	Fe	2.33	2.26	1.54	0.23	0
	C	5.03	0.30	0.51	1.73	0.52

Table 4

 4 Variation of the d s , IM( t ) and Isp values, determined by IGC-ID at 130 • C, for attapulgite activated at different HCl concentrations.

		d s (mJ/m 2 ) ±4%	IM( t ) 5%			Isp (kJ/mol) ±4%
		C5, C6, C7	2,3,4-TMP	2,5-DMH	Cycl 8	CH2Cl2	CHCl3
	Raw attapulgite	164	0.69	0.67	0.22	17	13
	Activated attapulgite with HCl
	0.5 M	133	0.71	0.69	0.26	14	12
	1 M	99	0.64	0.64	0.31	13	11
	3 M	65	0.70	0.62	0.42	13	11
	5 M	47	1.02	0.83	0.76	*	10

*: Measurement not exploitable.

Table 5

 5 Values of the specific surface areas (aBET), BET constants (CBET) and irreversibility indexes (I irr ) of raw and treated attapulgite with HCl, obtained by nitrogen adsorption and IGC-FC.

		Adsorption N2		IGC-FC
				C8 (53 • C)			IP (43 • C)			DX (51 • C)
		aBET (m 2 /g)	CBET	aBET ±2.8 (m 2 /g)	CBET	I irr ±0.2 (%)	aBET ±4 (m 2 /g)	CBET	I irr ±0.6 (%)	aBET ±3 (m 2 /g)	CBET	I irr ±0.1 (%)
	Raw attapulgite	125.1	437	114.5	9	0.6	71	22	8.3	71	21	7.8
	Activated attapulgite with HCl
	0.5 M	272.6	592	135.4	10	2.1	100	20	10.4	142	13	12.9
	1 M	336.6	299	183.4	9	1.3	201	28	18.1	174	17	19.9
	3 M	399.0	243	239.8	6	0.8	237	32	15.2	251	16	20.5
	5 M	315.2	131	222.6	5	0.2	142	60	9.9	201	19	20.4

Table 6

 6 Corrected values of specific surfaces of attapulgite samples after treatment with HCl solutions.

	acorr (m 2 /g)