Sébastien Clercq
email: sebastien.clercq@univ-amu.fr

Adil Mouahid

Pèpe Gérard

Elisabeth Badens

Investigation of crystallization mechanisms for polymorphic and habit control from the Supercritical AntiSolvent process

Keywords:

Investigation of crystallization mechanisms for polymorphic and habit control from the Supercritical

AntiSolvent process

Introduction

Crystallization processes involving a supercritical medium are gaining momentum as they are regarded as environmentally friendly processes and allow good control over product properties, especially particle size, Particle Size Distribution (PSD), crystal habit and polymorphic form. This is mainly because crystallization processes using sc-CO 2 often involve only one crystallization step, unlike conventional methods of crystallization in solution. CO 2 being gaseous at ambient conditions of pressure and temperature, the separation of CO 2 from the end-products is spontaneous and does not require successive separation operations. Thus, a single-step process or a process involving a reduced number of steps will lead to the formation of powders with homogeneous characteristics. When a series of steps is involved, the size as well as the habit or the polymorphic nature of the crystals may evolve. The good control of powder characteristics using supercritical fluids is also due to the large number of operating parameters and conditions (pressure, temperature, hydrodynamics and mixing conditions, supersaturation level, etc.) that can extensively be varied, therefore allowing efficient screenings for particle drug design. Amongst the different supercritical processes, the Supercritical AntiSolvent (SAS) process, using supercritical carbon dioxide (sc-CO 2 ) as crystallization antisolvent, brings particular interest for drug reprocessing [START_REF] Yeo | Recrystallization of sulfathiazole and chlorpropamide using the supercritical fluid antisolvent process[END_REF][START_REF] Fages | Particle generation for pharmaceutical applications using supercritical fluid technology[END_REF][START_REF] Chen | Recrystallization and micronization of sulfathiazole by applying the supercritical antisolvent technology[END_REF][START_REF] Rodrigues | Theophylline polymorphs by atomization of supercritical antisolvent induced suspensions[END_REF][START_REF] Badens | Mise en forme de principes actifs pharmaceutiques en phase supercritique[END_REF][START_REF] Fernández-Ponce | Particle design applied to quercetin using supercritical anti-solvent techniques[END_REF][START_REF] Djerafi | Supercritical anti-solvent precipitation of ethyl cellulose[END_REF][START_REF] Guamán-Balcázar | Precipitation of mango leaves antioxidants by supercritical antisolvent process[END_REF][START_REF] García-Casas | Generation of quercetin/cellulose acetate phthalate systems for delivery by supercritical antisolvent process[END_REF], that are often sparingly soluble into sc-CO 2 .

Crystallization during the SAS process is both induced by the sc-CO 2 antisolvent effect and by the organic solvent depletion. When the organic solution containing the solute to recrystallize and sc-CO 2 are put in contact, the organic solvent diffuses into the CO 2 -rich phase while CO 2 diffuses into the organic solution-rich phase, quickly leading to solute supersaturation in the organic solution's expanded phase. Crystal size is often at the micron or sub-micron order of magnitude thanks to the rapid transfer phenomena in supercritical media, which represents one of the most important assets of this technology.

This paper presents an experimental application of drug reprocessing by SAS, using Sulfathiazole (STZ) as the solute to be recrystallized. This compound, a veterinary drug, has a complex drug behavior regarding its ability to crystallize into five known polymorphic forms [START_REF] Hughes | A new polymorph of sulfathiazole[END_REF]. For that criterion, it has been widely described in literature either for crystallographic investigations [START_REF] Kruger | The crystal structures of polymorphs I and III of sulphathiazole[END_REF][START_REF] Blagden | Crystal chemistry and solvent effects in polymorphic systems Sulfathiazole[END_REF][START_REF] Apperley | Sulfathiazole polymorphism studied by magic-angle spinning NMR[END_REF][START_REF] Blagden | Crystal engineering of polymorph appearance: the case of sulphathiazole[END_REF][START_REF] Sovago | Experimental electron density and neutron diffraction studies on the polymorphs of sulfathiazole[END_REF] or for crystallization behavior into both liquid phases [START_REF] Abu Bakar | Investigation of the riddle of sulfathiazole polymorphism[END_REF][START_REF] Su | Recrystallization of phenacetin and sulfathiazole using the sonocrystallization process[END_REF] or supercritical media [START_REF] Kitamura | Crystal size control of sulfathiazole using high pressure carbon dioxide[END_REF][START_REF] Kordikowski | Phase equilibria for the CO2 + methanol + sulfathiazole system at high pressure[END_REF][START_REF] Stefano | Modification of the solid-state nature of sulfathiazole and sulfathiazole sodium by spray drying[END_REF]. It is worth noting that different nomenclatures exist for the five polymorphic forms of Sulfathiazole. In this study, the nomenclature proposed by Apperley et al. has been adopted [START_REF] Apperley | Sulfathiazole polymorphism studied by magic-angle spinning NMR[END_REF]. A brief description of the five crystal cells and their Cambridge Structural Database (CSD) reference are given in Table 1.

Two forms are commonly observed throughout experimentations, namely so-called forms I and IV. At ambient conditions, the relative stability is IV > I. Furthermore, Munroe et al. [START_REF] Munroe | Relative stabilities of the five polymorphs of sulfathiazole[END_REF] investigated the relative stabilities of the five polymorphs of Sulfathiazole depending on the temperature. It appears that, from 283 K up to 323 K at atmospheric pressure, polymorphic form I is the least stable of all five forms, then this order follows: I < II < V < IV < III.

Commonly, process development around drug particle generation consists in optimizing the drug bioavailability by reducing its size, narrowing its size distribution and controlling both crystal habit and polymorphism. As mentioned above, the SAS process can be tuned to target given specific properties of the end-product. Temperature, pressure, solute concentration in the feeding solution and flow rates of both CO 2 and organic solution phases are commonly screened parameters [START_REF] Reverchon | Spherical microparticles production by supercritical antisolvent precipitation: interpretation of results[END_REF]. Erriguible et al. [START_REF] Erriguible | A complete 3D simulation of a crystallization process induced by supercritical CO2 to predict particle size[END_REF] proposed a complete 3D simulation of the SAS process by varying operating conditions in a range of typical target conditions. They have investigated the crystallization of a solution of minococycline-ethanol and predicted a reduction of particle size by decreasing the solid-fluid interfacial tension as well as by increasing the initial concentration in the feeding solution or by increasing the injection jet velocity. Estimation of the interfacial tension has been reported as of major interest to consider the simulation as a predictive tool. Jet dispersion conditions of the organic solution were reported as a significant criterion to control particle characteristics by Petit-Gas et al. [START_REF] Petit-Gas | Role of hydrodynamics in supercritical antisolvent processes[END_REF]. They have studied the crystallization of a solution of STZ-acetone in SCeCO 2 . Finer particles of STZ were obtained for higher jet velocities, but also with larger capillary internal diameter at a constant jet velocity. Furthermore, different morphologies were observed, corresponding to different polymorphic forms of STZ crystals, for different Reynolds number values of the organic solution. Careno et al. [START_REF] Careno | Drug recrystallization using supercritical antisolvent (SAS) process with impinging jets: effect of process parameters[END_REF] and Boutin et al. [START_REF] Boutin | A new system for particle formation using the principle of the SAS process: the Concentric Tube Antisolvent Reactor (CTAR)[END_REF] studied alternative injection technology, namely impinging jets and concentric tubes, to greatly enhance phase mixing and mass transfers, thus reducing crystal size, for STZ-acetone and STZmethanol systems. Other enhanced mass transfer conditions were successfully achieved for the SAS process, by atomizing the liquid jet on a vibrating surface at an ultrasonic frequency [START_REF] Chattopadhyay | Production of griseofulvin nanoparticles using supercritical CO2 antisolvent with enhanced mass transfer[END_REF] (Griseofulvin-dichloromethane and Griseofulvin-tetrahydrofuran systems) or by stirring [START_REF] De Gioannis | Morphology and growth control of griseofulvin recrystallized by compressed carbon dioxide as antisolvent[END_REF] (Griseofulvin-acetone system). As for conventional recrystallization methods in solution, the organic solvent nature has also been reported as one of the most significant factors that control the SAS process and crystal habit. It has been proven that changing the organic solvent [START_REF] Reverchon | Supercritical antisolvent precipitation of micro-and nano-particles[END_REF][START_REF] Lee | Supercritical antisolvent micronization of cyclotrimethylenetrinitramin: influence of the organic solvent[END_REF], or adding a growth inhibitor [START_REF] Caputo | Supercritical fluid crystallization of adipic acid using urea as habit modifier[END_REF], may modify the crystal habit without modifying its crystal structure. A probable explanation is that the growth of one crystal's face may be selectively slowed down in comparison to the others due to solvent-or growth inhibitor-adsorption, which depends on the interaction between the solvent molecules and the solute molecules on crystal faces.

However, predicting and controlling the polymorphic form of the solute crystals has been less extensively studied. Kordikowski et al. [START_REF] Kordikowski | Polymorph control of sulfathiazole in supercritical CO2[END_REF] showed in the case of STZ recrystallized from acetone, that the flow ratio (CO 2 /acetone) has a preponderant role influencing the polymorphic form, whilst temperature has a preponderant role in the case of STZ reprocessed from methanol. The polymorphic form of STZ has therefore been related to the choice of solvent. Bouchard et al. [START_REF] Bouchard | Ways of manipulating the polymorphism of glycine during supercritical fluid crystallisation[END_REF] highlighted a strong dependence of glycine polymorphic form behavior on both the solute concentration into the feed and the ethanol fraction in the CO 2 -rich phase. The form IV is obtained for higher solute concentration and lower ethanol fraction, thus for higher supersaturation values. Later, Rossmann et al. [START_REF] Rossmann | Manipulating the size, the morphology and the polymorphism of acetaminophen using supercritical antisolvent (SAS) precipitation[END_REF] investigated the case of paracetamol, concluding that varying the solvent nature, in this case acetone, ethanol and a mixture of both, can lead to a modification of the crystalline form.

In this work, SAS process experiments were carried out at constant temperature (313 K) and pressure (10 MPa), but organic solution and sc-CO 2 flow rates, STZ concentration and organic solvent nature were varied with the aim of obtaining powders exhibiting only one polymorphic form. Thirteen solvents exhibiting different polarity and proticity properties were tested in a preliminary solubility measurement study at ambient pressure. Among them, four were retained for the SAS experiments according to their solvent power regarding STZ: acetone, acetonitrile, tetrahydrofuran and acetic acid. Solubility measurements of STZ in the four selected organic solvents were performed to evaluate the saturation degree of the initial organic solution used for the SAS process. The powders were characterized by 13 C Nuclear Magnetic Resonance (NMR) to determine the nature of the polymorphic forms obtained pure or in mixture. Pure crystalline powders in terms of polymorphic form were also observed by Scanning Electron Microscopy (SEM). Crystal characteristics were then discussed by considering the varied operating conditions corresponding to different thermodynamic and kinetic conditions. purchased from Sigma-Aldrich, France; Acetonitrile was purchased from VWR; Acetic acid was purchased from Fisher, France. All chemicals were purchased at purity > 98% and were used without further purifications. Carbon dioxide (purity of 99.7%) was purchased from Air Liquide, France.

Materials and methods

Materials

STZ (polymorphic form III), acetone and tetrahydrofuran were

Solubility measurements procedure

STZ and organic solvent are mixed together with a magnetic stir bar in a sealed container with an intentional excess of solute. The container is placed in a temperature bath regulated at 313 K. After several hours, the agitation is stopped and a part of the supernatant is collected with a syringe equipped by a millipore filter (VWR -0.45 μm). This sample is immediately diluted in a weighed quantity of pure solvent to prevent the crystallization from occurring through cooling. The concentration of the diluted solution is given by density measurement, referred to a calibration curve, with a density meter DMA 5000 M Anton (precision of 10 -6 g cm -3 ), at 293 K.

Experimental set-up for SAS process

The experimental apparatus used for this study is detailed in Fig. 1. It includes a 480 mL (internal diameter: 60 mm) double jacket autoclave (TOP INDUSTRIE, France). The maximum allowable pressure is 25 MPa at a temperature of 423 K. It is equipped with pressure and temperature sensors, as well as an 18 MPa rupture disk. The fluids, namely CO 2 and organic solution, are injected at the top of the autoclave thanks to two high pressure liquid piston pumps (SEPAREX, France and GILSON, France, respectively for CO 2 and organic solution). Organic solution feed is injected through a 127 μm internal diameter capillary tube. CO 2 flow is measured thanks to a Coriolis Effect flowmeter (BRONKHORST, France). A frit filter (2 μm) and a glass fiber filter (1.2 μm) are placed at the bottom of the autoclave to retain and easily collect generated particles. A cold solvent trap allows the separation of exiting fluids: CO 2 is evacuated and organic solution is recycled.

Experimental procedure

A first step consists in stabilizing the composition in the autoclave at the target conditions by injecting CO 2 and pure solvent. The target pressure and target temperature have been respectively fixed at 10 MPa and 313 K to ensure monophasic conditions. When the target conditions are reached, exit valves are open and the operating conditions are stabilized. Then, pure solvent feed is replaced by the organic solution, containing the solute to be crystallized. The solute concentration is given as a fraction of the organic solution saturation at 313 K, noted β OS .

From that time on, sc-CO 2 has an antisolvent role. CO 2 and organic solvent reversediffusion occurs due to concentration gradient, causing a rapid and large supersaturation, thus a fast crystallization.

The generated particles are retained at the bottom of the autoclave. At the end of the injection step, the injection line is washed with pure solvent to avoid nozzle clogging, then the organic solvent flow is stopped. The CO 2 flow is kept so as to renew the fluid phase content in the autoclave and dry the crystalline powder, from 3 up to 5 residence time. At the end of these washing steps, the autoclave pressure is dropped to atmospheric pressure and the powder that has been accumulated on the filter is collected.

The experimental conditions tested in this work are listed in Table 3 (see part 3.2). Feed flows of both phases as well as STZ concentration into the organic solution were varied to identify which operating conditions allow the formation of pure powders in term of polymorphic form, for each studied solvent, namely acetone (Acet), acetonitrile (ACN), tetrahydrofuran (THF) and acetic acid (AcAc). CO 2 and organic solution flow rates were varied from 2 up to 21 gmin -1 and from 0.19 up to 6 mL min -1 respectively. Thus, solvent to CO 2 molar ratios (X solv/ CO2 ) were varied from 5 up to 23 mol%. 2.5. Polymorphic form characterization using 13 C NMR Each crystal powder was analyzed to determine the polymorphic form, or the composition of polymorph mixtures, of generated particles. X-Ray Diffraction is a commonly encountered method, but can lack precision when it comes to quantitative analysis. In this work, solidstate Nuclear Magnetic Resonance was chosen for both the qualitative and quantitative analysis of STZ powders, using a BRUKER AVANCE III 400 MHz spectrometer, working at a 13 C resonance frequency of 106 MHz. Characteristic NMR signals for STZ are taken from Apperley et al. [START_REF] Apperley | Sulfathiazole polymorphism studied by magic-angle spinning NMR[END_REF].

Particle observations by SEM

Generated crystals are observed with a Scanning Electron Microscope to determine the crystal habit for each observed sample. Moreover, particle size and the size distributions was determined for the samples exhibiting only one polymorphic form. SEM observations were performed thanks to the JEOL JSM 6320-F device, working with a field emission gun. A metallization step with a gold plasma for 90 s was performed before each observation.

Results and discussions

Solubility of sulfathiazole into organic solvent

STZ solubility was measured into several solvents considered potentially eligible (either for toxicity or solubility in SCeCO 2 ) to be applied to the SAS process for recrystallizing active pharmaceutical ingredients. A list of every tested solvent is given in Table 2. They vary in their intrinsic properties of polarity and proticity and are classified according to their relative permittivity ε. Four solvents were selected, for which the solubility of STZ is included between 0.75 and 10% in weight concentration. Solubility lower than 0.75% w/w. is quite low for a good productivity of the process whereas solubility higher than 10% w/w. may imply drug solubilization in the supercritical phase during the SAS process. These four solvents are acetone, acetonitrile, tetrahydrofuran and acetic acid. Every other tested solvent doesn't solubilize a large enough amount of STZ to be used in this study, except for dimethyl sulfoxide and N-Methyl-2-pyrrolidone, both solubilizing STZ over 10%w/w. Logically, only polar solvents allow a good solubility for STZ, exhibiting a better affinity for aprotic solvents than for protic ones.

Solubility was obtained from calibration curves shown in Fig. 2, giving the density of the organic solution according to the concentration of STZ in it. Density measurements were performed at 293 K.

Influence of operating conditions on polymorphic form

The SAS experimental conditions performed during this work are listed in Table 3. Polymorphic form obtained from solid state NMR are also reported. 13 C NMR spectra are presented in Fig. 3, for powders of pure form I, pure form IV and a mixture of form I and IV.

For each of the three solvents, Acetone, Acetonitrile and Tetrahydrofuran, a dozen experiments mainly led to the formation of powders composed of a mixture of polymorphs (I and IV). Nevertheless, it is worth noting that for each solvent, pure polymorphic forms (I or IV) were obtained for given operating conditions. In addition, experiments with acetic acid led exclusively to the formation of pure polymorphic form I.

CO 2 and organic solution (OS) flow rates as well as STZ concentration in the OS were varied to identify operating conditions allowing the formation of powders that exhibit only one polymorphic form. To interpret the effect of hydrodynamics on the polymorphic nature of obtained particles, Reynolds numbers describing the flows of the organic solution jet (Re jet ) and of the carbon dioxide into the precipitation vessel (Re CO2 ) were calculated as follows:

= Re ρ u d μ jet orga jet nozzle orga (1) = Re ρ u d μ CO CO CO autoclave CO 2 2 2 2 (2)
Where ρ orga and ρ CO2 are measured organic solution and carbon dioxide densities, respectively, u jet is the jet velocity at the exit of the injection nozzle of a diameter d nozzle of 127 μm, u CO2 is the CO 2 velocity throughout the crystallization vessel (considering only CO 2 ) of a diameter of 60 mm, μ orga (measured) and μ CO2 [START_REF] Fenghour | The viscosity of carbon dioxide[END_REF] are organic solution and carbon dioxide viscosities, respectively. The Reynolds numbers associated to both flows correspond to laminar flows (Re < 2500) since they vary from 73 to 2157 for the organic solution flow and from 15 to 155 for the CO 2 flow. These values of Reynolds numbers correspond to different modes of jet dispersion; the highest values corresponding to atomized jet leading to more intense mixing conditions.

Furthermore, the characteristic times associated to the different effects controlling the jet dispersion were calculated [START_REF] Carretier | Hydrodynamics of supercritical antisolvent precipitation: characterization and influence on particle morphology[END_REF]. Inertial, aerodynamic and viscous effects were calculated for each presented experiment. Inertial and aerodynamic effects are preponderant since their associated characteristic times, respectively between 16 up to 508 μs and 17 up to 599 μs, are the lowest in comparison with times associated with the viscous effects (20 up to 37 ms). Inertial effects have a stabilizing effect on the jet during its dispersion while aerodynamic effects are destabilizing ones.

It is evidenced that intense mixing conditions, such as for experiments #3, #18, #31 or #41, lead to the formation of pure form I. In this case, mass transfers are enhanced, and so are the nucleation rates. Besides, less intense mixing conditions such as for experiments #11, #12, #22, #23, #34 or #38, lead to the formation of form IV.

Acetic acid used as solvent represents an interesting case, as it only allows the formation of pure form I, whatever the operating conditions. It is also the only polar protic solvent used in this study. The presence of pure form I is observed at every operating condition, at both intense and moderate mixing conditions. Further investigations are required to fully interpret this observation. Experiments #41, #42 and #43 are therefore not considered in the following interpretation.

For experiments that led to pure polymorphic form, the Re jet and Re CO2 are plotted in Fig. 4. Points obtained from acetic acid were removed.

It shows a clear influence of the Re jet on the obtained form. Amongst the presented experimental conditions, excluding points from acetic acid, every pure powder obtained at Re jet ≤ 508 is pure form IV, while every pure powder obtained at Re jet ≥ 1058 is pure form I. A region where both pure form I and pure form IV were obtained is observed at 661 ≤ Re jet ≤ 726. It can be noticed that the only pure form I present in this region was obtained with a higher STZ concentration in the OS (β OS = 70%, 60% for the other ones). Furthermore, the CO 2 flow rate has no direct influence on the obtained form. Indeed, both pure form I and IV were obtained at either higher or lower Re CO2 values. Therefore, the mixing is more dependent on the organic solution flow rate than on the CO 2 flow rate. Obtaining a pure form IV hence has more chance to occur at lower Re jet , independently of Re CO2 .

The X solv/CO2 values in which pure forms were obtained are ranged between 7.3% up to 20% for form I and 3.4% up to 11% for form IV. There is therefore no evidence that the polymorphic form of a pure powder is directly dependent on this variable. Indeed, X solv/CO2 has a complex influence on the polymorphic form: as it rises, the solute solubility in the continuous fluid phase increases and, consequently, the overall supersaturation decreases and the concentration gradient between the dispersed and the continuous phases decreases. This slows down the nucleation and growth rate and thus may promote the formation of the most stable form. For example, Kordikowski et al. measured the STZ molar solubility in both pure and methanol modified CO 2 . At 10 MPa and 313 K, it rises from 8.1 × 10 -9 in pure CO 2 to 1.56 × 10 -5 in the modified phase containing X methanol/CO2 = 0.1412 [START_REF] Kordikowski | Phase equilibria for the CO2 + methanol + sulfathiazole system at high pressure[END_REF]. However, the highest values of X solv/CO2 are inevitably obtained at high organic solution flow rates, which promotes the formation of the less stable form due to more intense mixing conditions. Solvent nature also has an important influence over the polymorphic form for given flow rates of both phases. Indeed, some key comparisons, for example experiments #4, #19 and #34 together, or experiments #7, #20 and #35 together, show that for a different solvent but with similar flow rates of both phases, the resulting powder is different. Indeed, in the first mentioned set, an organic solution flow rate of 1.9 mL min -1 and a CO 2 flow rate of 21 g min -1 are applied.

When acetone is used (#4), a polymorphic mixture is obtained, whereas when acetonitrile (#19) or tetrahydrofuran (#34) are used, a pure form IV powder is obtained. In the second mentioned set, the organic solution flow rate was set at 1.9 mL min -1 and the CO 2 flow rate was set at 10 g min -1 . In this case, when the organic solvent is acetone (#7), the obtained powder is 100% form IV, while a mixture of both was obtained when acetonitrile (#20) or tetrahydrofuran (#35) are used.

The initial concentration of STZ in the organic solution also has an influence on the polymorphic behavior as it has a direct connection with overall supersaturation. Experiments #18 and #19, using acetonitrile as solvent, show a shift in the polymorphic form of resulting powders from pure form IV to pure form I induced by an increased STZ concentration in the organic solution form β = 0.6 to β = 0.7. This induces a higher supersaturation, thus a faster nucleation and growth rate, at constant X solv/CO2 . Weber Brun et al. [START_REF] Weber Brun | Crystallization of caffeine by supercritical antisolvent (SAS) process: analysis of process parameters and control of polymorphism[END_REF] have reported a contradictory behavior in the case of caffeine crystallized with SAS. A higher proportion of the stable form (at ambient condition of pressure and temperature) has been observed at high initial concentration of solute. However, the proportion of crystalline material (crystalline versus amorphous) decreases by increasing initial concentration of solute. In the case of a solute exhibiting more than one polymorphic form, the obtained form is not only control by the initial concentration of solute but can depend on a variety of process parameters.

Repeatability was measured for some experiments. Two reproduced experiments are given in Table 4, namely #4′ and #4′′ repeating experiments #4, and #12′ repeating experiment #12. In every case, when either a mixture or a pure form is obtained, the repeatability is verified.

SEM observations

Crystalline powders from experiments #3, #7, #18, #19, #31, #34 and #41 (Table 3), pure in one polymorphic form, were observed with SEM. Their habits are presented in SEM photographs for forms IV and I in Fig. 5 and Fig. 6, respectively.

A wide variation of crystals habit can be shown for the form IV of STZ (Fig. 5). When reprocessed by SAS from pure acetone (#7), STZ crystals exhibit large and extremely thin plate-or leaf-like habit. The particle size distribution (PSD) shows two peaks, one around 3 μm and the other around 20 μm. This distribution is classical in the case of fragile crystals. The smaller particles are the result of either attrition during the crystallization/washing steps, leading to the formation of spherical particles (diameter under or close to 1 μm), or mechanical breaking of larger crystals, inside the reactor, during the collecting step or during the SEM sample preparation. When acetonitrile was used as a solvent (#19), crystal habit was equant. The obtained powder has a narrow PSD, at around 2 μm. Lastly, when the solvent used was tetrahydrofuran (#34), crystal habit is of a plate-like type like that of acetone. An important aggregation is however evidenced with the formation of spherical clusters. This behavior prevents attrition and breaking from occurring, the obtained powder therefore has a narrow PSD.

From these pictures, two different crystallization mechanisms have been identified: (a) A nucleation and growth mechanism, leading to particles with a crystal shape, such as those obtained in acetone (Fig. 5, #7) and acetonitrile (Fig. 5, #19). This highlights a gas-like phase composed of all the 3 components in a continuous, mixed phase. Crystal growth occurs by the successive adhesion of crystal units that diffuses through the bulk. In this liquid-like behavior, the growth rate strongly depends on the probability of a crystal unit meeting a grown crystal. Reducing the crystal size can therefore be achieved by decreasing the solute concentration, for example. (b) A droplet drying mechanism, leading to quasi-spherical particles composed of aggregated nanocrystals, such as those obtained in tetrahydrofuran (Fig. 5, #34). In this case, an interface still exists between the CO 2 -rich phase and the organic solution droplet, imposing the spherical shape of generated particles. Crystallization kinetics are therefore highly dependent on the double-diffusivity effect, mostly affected by the affinity between solvent and CO 2 .

STZ crystals of form I (Fig. 6) exhibit two different crystal habits, namely needle-like, and aggregated clusters of plate-like habits, corresponding to the nucleation and growth mechanism and the droplet drying mechanism, respectively. The latter is observable with all tested solvent, while being mainly observed with acetone and acetonitrile (#3 and #18, respectively, 100% of observed particles), but also visible with tetrahydrofuran (#31) and with acetic acid (#41). The nucleation and growth mechanism is only observable when tetrahydrofuran and acetic acid were used, both experimental conditions leading to needlelike crystals. This habit clearly indicates that the growth rate of one or a couple of faces has been slowed down. PSD for an observed sample with both acetone and acetonitrile are narrow around 3 and 2 μm, respectively. However, with both tetrahydrofuran and acetic acid, the PSD is widely distributed. This is due to the combined presence of needle-like crystals and spherical clusters. The smaller particles are observed in the case of acetic acid used as a solvent.

This large habit disparity of crystal habits, for both polymorphic forms IV and I, highlights how important the solvent is for controlling crystal habit. The solvent acts as a growth inhibitor for a given set of crystal faces by adsorbing differently at the surface of every crystal face. The higher the solvent adsorption, the higher the drop of the surface free energy, for a given crystal face. Moreover, it is well established that the different surface free energy of each crystal's face is habit-controlling, and can be modified by solvent adsorption [START_REF] Saska | The theoretical shape of sucrose crystals from energy calculations[END_REF]. Therefore, predicting the crystal habit can be performed by predicting the surface energy as well as solvent adsorption energies thanks to molecular modelling [START_REF] Lin | Prediction of the growth morphology of aminoacid crystals in solution: i. α-Glycine[END_REF]. A current work consisting in the prediction of solvent adsorption energies for STZ is ongoing to validate the method for crystallization in a supercritical medium.

Conclusions

The polymorphic and habit control of sulfathiazole has been studied from the supercritical antisolvent process and with different organic solvents. At moderate mixing conditions and for low supersaturation values, the form IV is obtained, whilst at intense mixing conditions, fast nucleation kinetics lead to formation of form I. Furthermore, crystal habit can be severely influenced by the solvent. Indeed, depending on the solvent nature, polymorphic form IV crystals of sulfathiazole can exhibit a thin plate-like habit or an equant habit. The same behavior occurs for the polymorphic form I crystals of sulfathiazole, exhibiting either a plate-like habit or a needle-like habit. More importantly, two crystallization mechanisms have been identified and are affected by the nature of solvent. These two mechanisms are liquid-like nucleation and growth mechanism and droplet drying mechanism, and depend on hydrodynamic conditions as well as on the affinity between organic solvent and CO 2 . These two behaviors further point out how important and complex the choice of a solvent is for particle generation with the supercritical anti-solvent process.

The strong dependence of crystal habit on the solvent used, in the case of nucleation and growth mechanism, can be imputed to the solvent's ability (or inability) to perform strong intermolecular interactions with a given set of crystal faces. These intermolecular interactions can be regarded as solvent molecules adsorbed at the surface of a crystal, which may be the cause of the crystal habit changes. Adsorption energies can be calculated through molecular modelling to predict and control the crystal habit, for example in a drug producing perspective.

Fig. 1 .

 1 Fig.1. Apparatus for crystallization using the SAS process. E1 to E3: heat exchangers; V1: valve; V2 and V3: 3-ways valves; V4 and V5: depressurizing valves; P1 and P2: high pressure liquid piston pumps; D1 and D2: rupture discs, F1: solvent frit filter; F2: glass fiber filter; S1: cold solvent trap; R1: CO2 pressurized bottle; R2: organic solution tank; R3: pure solvent tank; R4: crystallization autoclave.

Fig. 2 .

 2 Fig. 2. Density calibration curves at 293 K for (a) acetone, (b) acetonitrile, (c) tetrahydrofuran, (d) acetic acid.

Fig. 3 .Fig. 4 .

 34 Fig. 3. NMR spectra for the identification and quantification of form I, form IV and a mixture of form I and IV of STZ. a lines: characteristic picks of form IV at 118.6 ppm and 120.2 ppm; b lines: characteristic picks of form I at 114.2 ppm and 115.7 ppm.

Fig. 5 .

 5 Fig. 5. SEM observations and PSD of form IV of sulfathiazole, obtained with exp. #7 (acetone), exp. #19 (acetonitrile) and exp. #34 (tetrahydrofuran).

Fig. 6 .

 6 Fig. 6. SEM observations and PSD of form I of sulfathiazole, obtained with exp. #3 (acetone), exp. #18 (acetonitrile), exp. #31 (tetrahydrofuran) and exp. #41 (acetic acid).

Table 1

 1 Crystal lattice for the five polymorphic forms of Sulfathiazole.

	Polymorphic form	I	II	III	IV	V
	CSD Ref. Code	SUTHAZ01	SUTHAZ05	SUTHAZ02	SUTHAZ	SUTHAZ04
	a (Å)	10.554	10.399	17.570	8.235	10.867
	b (Å)	13.220	15.132	8.570	8.550	8.543
	c (Å)	17.050	14.280	15.583	15.580	11.456
	β (deg)	108.06	91.21	112.93	93.67	88.13

Table 2

 2 List of solvents used for the solubility measurements at ambient pressure. PA = polar aprotic; PP = polar protic; NP = non-polar.

	Solvent	Origin	#CAS	ε [35] Nature C s at 313 K
						(%w/w)
	Ethanol	Sigma-	64-17-5	25.30	PP	≈0.75
		Aldrich
	Propanol-1	Carlo-Erba	71-23-8	20.80		< 0.75
	Propanol-2	Carlo-Erba	67-63-0	20.18		< 0.75
	Acetic acid	Fisher	64-19-7	6.20		0.83
	Dimethyl sulfoxide	SDS	67-68-5	47.24	PA	> 10
	Acetonitrile	VWR	75-05-8	36.64		1.42
	N-Methyl-2-	Sigma-	872-50-	32.55		> 10
	pyrrolidone	Aldrich
	Acetone	Sigma-	67-64-1	21.01		3.11
		Aldrich
	Tetrahydrofuran	Sigma-	109-99-9 7.52		1.15
		Aldrich
	Ethyl acetate	Carlo-Erba	141-78-6 6.08		< 0.75
	Chloroform	Carlo-Erba	67-66-3	4.81	NP	< 0.75
	Diethyl ether	SDS	60-29-7	4.27		< 0.75
	Limonene	Prolabo	138-86-3 2.37		< 0.75

Table 3

 3 Experimental conditions. Acet = Acetone, ACN = acetonitrile, THF = tetrahydrofuran, AcAc = acetic acid.

	# Exp.	Solvent	OS flow rate (mL min -1 )	C O 2 flow rate (g min -1 )	R e jet	Re CO2	β OS (%)	X solv/CO2 (mol%)	Polymorph
	1	Acet	4	21	1529	155	60	11	Mixture (I + IV)
	2		3.5	21	1338	155		9.6	Mixture (I + IV)
	3		3	21	1147	155		8.2	I
	4		1.9	21	726	155		5.2	Mixture (I + IV)
	5		1.9	21	726	155	40	5.3	Mixture (I + IV)
	6		1.9	21	726	155	20	5.3	Mixture (I + IV)
	7		1.9	10	726	74	60	11	IV
	8		1.9	5	726	37		22	Mixture (I + IV)
	9		1.38	15	528	111		5.3	Mixture (I + IV)
	10		0.91	10	348	74		5.3	Mixture (I + IV)
	11		0.42	5	161	37		4.8	IV
	12		0.19	2	73	15		5.5	IV
	13	ACN	6	21	2157	155	60	23	Mixture (I + IV)
	14		5	21	1797	155		19	Mixture (I + IV)
	15		3	21	1078	155	70	11	Mixture (I + IV)
	16		2.5	10	899	74	60	20	Mixture (I + IV)
	17		2	8	719	59		20	Mixture (I + IV)
	18		1.9	21	683	155	70	7.3	I
	19		1.9	21	683	155	60	7.3	IV
	20		1.9	10	683	74		15	Mixture (I + IV)
	21		1.5	8	539	59		15	Mixture (I + IV)
	22		1.35	21	485	155	70	5.2	IV
	23		1.35	21	485	155	60	5.2	IV
	24		1.25	5	449	37		20	Mixture (I + IV)
	25		1	8	359	59		10	Mixture (I + IV)
	26		0.94	5	338	37		15	Mixture (I + IV)
	27		0.63	5	226	37		10	Mixture (I + IV)
	28	THF	6	21	2088	155	60	15	Mixture (III + IV)
	29		5	21	1797	155		13	Mixture (I + IV)
	30		3.8	10	1322	74		20	Mixture (III + IV)
	31		3.04	8	1058	59		20	I
	32		2.7	10	940	74		14	Mixture (I + IV)
	33		2.16	8	752	59		14	Mixture (I + IV)
	34		1.9	21	661	155		4.8	IV
	35		1.9	10	661	74		10	Mixture (I + IV)
	36		1.9	5	661	37		20	Mixture (I + IV)
	37		1.52	8	529	59		10	Mixture (I + IV)
	38		1.35	21	470	155		3.4	IV
	39		1.35	5	470	37		14	Mixture (I + IV)
	40		0.95	8	331	59		10	Mixture (I + IV)
	41	AcAc	1.9	12	401	89	60	12	I
	42		1.17	15	247	111		5.9	I
	43		0.31	5	65	37		4.7	I

Table 4

 4 Repeatability measurement.

Acknowledgments

The authors gratefully thank Fabio ZIARELLI for characterization by RMN spectrometry and helpful discussions.


Thomas Thiebault
email: thomas.thiebault@ephe.psl.eu

Mohammed Boussafir
email: mohammed.boussafir@univ-orleans.fr

Adsorption mechanisms of psychoactive drugs onto montmorillonite

Keywords: Psychoactive drugs, clay minerals, adsorption, cation exchange, intercalation

The adsorption of psychoactive drugs (PADs) onto sodium-exchanged montmorillonite (Na-Mt) was investigated under two pH conditions. At pH=2.5, the adsorption was performed through cation exchange and the three PADs were intercalated within the Na-Mt layers.

However, the adsorption capacity was lower than the theoretical cation exchange capacity of Na-Mt due to the impact of the acidic conditions on the adsorbent. At pH=7.5, only Codeine was protonated and its adsorption through cation exchange resulted in the highest amount adsorbed among the tested PADs. Diazepam was adsorbed through weak electrostatic interactions, whereas Oxazepam appeared to be intercalated within Na-Mt layers despite its neutral charge. Consequently, the variation in pH strongly impacts the affinity of PADs for Na-Mt. These initial results highlight the impact of raw clay on the fate of these contaminants within environmental compartments and could pave the way for a green solution to the removal of PADs from wastewater effluents.

Psychoactive Drugs (PADs) are among the most concentrated and frequently detected pharmaceutical products in numerous environmental compartments such as wastewaters [START_REF] Thiebault | Temporal dynamics of humanexcreted pollutants in wastewater treatment plant influents: Toward a better knowledge of mass load fluctuations[END_REF],

surface waters [START_REF] Calisto | Psychiatric pharmaceuticals in the environment[END_REF] and sedimentary archives [START_REF] Thiebault | Record of pharmaceutical products in river sediments: A powerful tool to assess the environmental impact of urban management?[END_REF], due to their incomplete removal in wastewater treatment plants (WWTPs) [START_REF] Thiebault | Occurrence and removal efficiency of pharmaceuticals in an urban wastewater treatment plant: mass balance, fate and consumption assessment[END_REF]. Their persistence within the environment raises serious issues due to their impact on the biota, such as for example their altering effect on the behavior of fish [START_REF] Brodin | Ecological effects of pharmaceuticals in aquatic systems-impacts through behavioural alterations[END_REF]. Therefore, it appears necessary to assess the potential of new solutions to improve the removal of PADs from WWTP effluents. Adsorption could be considered as an appropriate way for the removal of organic pollutants [START_REF] Ali | Low cost adsorbents for the removal of organic pollutants from wastewater[END_REF], if the selected adsorbent is low-cost and displays a high adsorption capacity and selectivity [START_REF] Gil | Removal of caffeine and diclofenac from aqueous solution by adsorption on multiwalled carbon nanotubes[END_REF][START_REF] Oliveira | Adsorption of diclofenac onto organoclays: Effects of surfactant and environmental (pH and temperature) conditions[END_REF]. Raw clay minerals such as bentonites exhibit outstanding adsorption properties for some organic compounds, especially cationic ones [START_REF] Thiebault | Competitive adsorption of a pool of pharmaceuticals onto a raw clay mineral[END_REF][START_REF] Thiebault | Adsorption mechanisms of emerging micropollutants with a clay mineral: Case of tramadol and doxepine pharmaceutical products[END_REF][START_REF] Lambert | 7 -Organic pollutant adsorption on clay minerals[END_REF]. However, the affinity of PADs with clay minerals has been poorly investigated, even though it could provide useful information about both the potential of a clay-based solution for the removal of PADs from WWTP effluents [START_REF] Thiebault | Clayey-sand filter for the removal of pharmaceuticals from wastewater effluent: percolation experiments[END_REF], and the fate of these compounds within environmental compartments [START_REF] Stein | Analysis and sorption of psychoactive drugs onto sediment[END_REF]. Moreover, some clay minerals such as montmorillonite are also considered as biocompatible: they are used as active substances to cure enteritis or gastritis [START_REF] Ghadiri | Biomedical applications of cationic clay minerals[END_REF][START_REF] Carretero | Clay minerals and their beneficial effects upon human health. A review[END_REF], and are suggested to act as a carrier for the controlled release of active substances on therapeutic targets [START_REF] Ruiz-Hitzky | Hybrid materials based on clays for environmental and biomedical applications[END_REF]. Investigating the adsorption mechanisms of PADs onto raw clay minerals by varying experimental conditions such as pH value would therefore make it possible to explore the potential of this type of adsorbent to represent an alternative solution for the removal of these contaminants and to control their fate within aquatic environments and/or their possible controlled release for medicinal purposes.

Hence, the aim of this study was to investigate (i) the potential of slightly modified smectite for the removal of three PADs, and (ii) the impact of a pH variation on adsorption mechanisms. To our knowledge, it is the first study to deal with such fundamental interaction mechanisms between PADs and clay minerals.

The selected adsorbent was a Wyoming sodium smectite SWy-2 (Mt), obtained from the Source Clay Minerals Repository, University of Missouri (Columbia, MO). Its structural formula is (Ca0.12Na0.32K0.05)[Al3.01Fe(III)0.41Mn0.01Mg0.54Ti0.02] [Si7,98Al0.02] O20(OH)4. The Mt clay was fractionated to < 2 µm by gravity sedimentation, purified and Na exchanged by well-established procedures [START_REF] Forestier | Textural and hydration properties of a synthetic montmorillonite compared with a natural Na-exchanged clay analogue[END_REF]. The resulting Na exchanged Mt clay mineral (Na-Mt) shows a cation exchange capacity (CEC) of 80 meq per 100 g of clay [START_REF] Thiebault | Adsorption mechanisms of emerging micropollutants with a clay mineral: Case of tramadol and doxepine pharmaceutical products[END_REF][START_REF] Forestier | Textural and hydration properties of a synthetic montmorillonite compared with a natural Na-exchanged clay analogue[END_REF]. The PADs, Codeine (COD), Diazepam (DIA) and Oxazepam (OXA), were purchased from Sigma-Aldrich Chemical, assuming a purity grade > 98% and were used without any further purification. The main properties and characteristics of the selected PADs are presented Table 1. Chemical reagents such as HCl, NaOH were supplied by Sigma-Aldrich and used without further purification. Two pH values were tested, pH = 2.5 and pH = 7.5, respectively. The pH values were adjusted by adding HCl and NaOH. Samples were shaken on a rotary shaker at 250 rpm for 16h at room temperature in order to achieve the equilibrium of adsorption. The kinetics of the adsorption (not shown here) followed a similar trend for all three PADs [START_REF] Thiebault | Competitive adsorption of a pool of pharmaceuticals onto a raw clay mineral[END_REF]: the amount of PADs adsorbed increased as the initial concentration in solution increased while the values tended to be constant after a very short time, as previously observed for other organic compounds onto Na-Mt [START_REF] Thiebault | Competitive adsorption of a pool of pharmaceuticals onto a raw clay mineral[END_REF][START_REF] Chang | Mechanism of amitriptyline adsorption on Ca-montmorillonite (SAz-2)[END_REF].

We therefore assumed that an equilibrium was reached after 150-300 min for all the selected PADs, allowing us to determine the adsorption isotherms which are fundamental for the description of the behavior between adsorbent and adsorbate. Both supernatant and adsorbent were separated by centrifugation (30 min, 8,000 rpm). The concentration of organic carbon in solution was measured using an elemental analyzer (Shimadzu TOC 5050 /SSM 5000-A) and the adsorbed amount was determined by elemental analysis (Carbon, Nitrogen) on dry (100°C during 24 hours) powdered samples using a Thermo Scientific Flash 2000 organic analyzer.

Blank experiments were performed to control the carbon content of distilled water and Na-Mt.

Before their characterization, the entire resulting layered composites (Mt-PADs) after adsorption of PADs were dried at 100°C for 24 hours to eliminate any hydration or adsorption of water of the samples. The d001 spacings of the starting Mt clay mineral and after being in contact with organic pollutants were determined by the first 00l reflection from the X-ray patterns recorded in a conventional θ-θ Bragg-Brentano configuration using a Thermo Electron ARL'XTRA diffractometer equipped with a Cu anode (CuKα1,2 = 1.5418 Å) coupled with a Si(Li) solid detector. The diffractograms on dry powdered samples were performed between 2 and 20° (2θ) with an angular and time steps of 0.04° and 10s respectively. The adsorption isotherms of the three selected PADs onto the Na-Mt are presented in Figure 1.

In the concentration range used in this work, a non-proportional evolution between equilibrium concentration and adsorbed concentration can be observed. The adsorption isotherms display two distinct regimes with the first indicating a gradual increase in the amount of PADs adsorbed with an equilibrium PAD concentration while the second displays a saturation level for the highest starting concentrations. Only the adsorption of COD at pH = 7 did not show any plateau, with a continuous increase of the adsorbed amount with the increase of the starting concentration. The impact of the variation in pH value on the adsorption of each PAD is different. Under acidic pH conditions (i.e. pH = 2.5) the adsorption capacity of COD is lower than at pH = 7.5, whereas the opposite pattern is observed for DIA and OXA (Figure 1). In general, the highest adsorption capacity is observed for COD at pH = 7.5 (i.e. 0.25 mmol.g -1 )

and the lowest adsorption capacity for DIA at pH = 7.5 (i.e. 0.036 mmol.g -1 ).

Experimental data were fitted with three adsorption equations, Langmuir, Freundlich and Dubinin-Radushkevich (D-R), as the affinity of PADs with Na-Mt can be estimated with the model parameters. The Langmuir model is expressed by the following equation [START_REF] Thiebault | Adsorption mechanisms of emerging micropollutants with a clay mineral: Case of tramadol and doxepine pharmaceutical products[END_REF]:

𝑞 𝑒 = 𝑞 𝑚𝑎𝑥 𝐾 𝐿 𝐶 𝑒 1 + 𝐾 𝐿 𝐶 𝑒
where 𝑞 𝑒 is the amount of PAD adsorbed onto Na-Mt (mmol.g -1 ), Ce the equilibrium PAD concentration in the supernatant (mmol.L -1 ), qmax the maximum adsorption capacity of the sorbents (mmol.g -1 ) and KL the Langmuir adsorption constant (L.mmol -1 ) which is related to the free energy (G°) of adsorption. The Freundlich equation can be expressed in its linear form as follows [START_REF] Thiebault | Competitive adsorption of a pool of pharmaceuticals onto a raw clay mineral[END_REF][START_REF] Stein | Analysis and sorption of psychoactive drugs onto sediment[END_REF]:

𝑙𝑛𝑞 𝑒 = 𝑙𝑛𝐾 𝐹 + 1 𝑛 𝑙𝑛𝐶 𝑒
with KF the Freundlich affinity coefficient (in L.g -1 ), n a linearity parameter and Ce the equilibrium concentration in mol.L -1 . The linear form of the D-R model is written as [START_REF] Oliveira | Adsorption of diclofenac onto organoclays: Effects of surfactant and environmental (pH and temperature) conditions[END_REF]:

𝑙𝑛𝑞 𝑒 = 𝑙𝑛𝑞 𝑚 + 𝛽𝜀 2
with qm the calculated maximum adsorption capacity of the material in mol.g -1 , β a constant in mol².J -2 and ε the Polanyi potential expressed in J².mol -2 and calculated as follows [START_REF] Oliveira | Adsorption of diclofenac onto organoclays: Effects of surfactant and environmental (pH and temperature) conditions[END_REF]:

𝜀 = 𝑅𝑇𝑙𝑛 (1 + 1 𝐶𝑒 )
with R the gas constant in J.mol -1 .K -1 and T the absolute temperature in K.

β is related to the mean free energy E (in kJ.mol -1 ) by the following equation:

𝐸 = (2𝛽) -1/2
The magnitude of E gives information about whether the adsorption is chemisorption such as ion exchange (8 < E < 16 kJ.mol -1 ) or physical adsorption (E < 8 kJ.mol -1 ) [START_REF] Oliveira | Adsorption of diclofenac onto organoclays: Effects of surfactant and environmental (pH and temperature) conditions[END_REF][START_REF] Sdiri | Evaluating the adsorptive capacity of montmorillonitic and calcareous clays on the removal of several heavy metals in aqueous systems[END_REF].

Briefly, the Langmuir equation is based on the assumption of a monolayer adsorption onto a homogeneous adsorbent (i.e. adsorption sites display identical energy), whereas the Freundlich and D-R equations assume a heterogeneous adsorbent surface, and variability in the adsorption potential. Adsorption isotherms correctly fitted the experimental data with r² values between 0.92 and 0.99. The quality of the fit obtained meant that work could then be carried out on the resulting parameters (Table 2).

As previously mentioned, the only adsorption isotherm without any saturation level is at pH = 7.5 for COD (Figure 1). Under these pH conditions, COD is protonated (Figure S1) and could be adsorbed through cation exchange onto Mt [START_REF] Thiebault | Adsorption mechanisms of emerging micropollutants with a clay mineral: Case of tramadol and doxepine pharmaceutical products[END_REF][START_REF] Aristilde | Enhanced interlayer trapping of a tetracycline antibiotic within montmorillonite layers in the presence of Ca and Mg[END_REF]. This possible adsorption mechanism is emphasized by the E value derived from the D-R model which is > 8 kJ.mol -1 , indicative of chemisorption. In general, one of the most important limiting factors for the adsorption of cationic compounds onto clay minerals is the CEC, which is 0.8 mmol.g -1 for Na-Mt [START_REF] Forestier | Textural and hydration properties of a synthetic montmorillonite compared with a natural Na-exchanged clay analogue[END_REF]. In the concentration range used in this study, the highest adsorption capacity is 0.25 mmol.g -1 representing ~ 30 % of the CEC of Na-Mt. The maximum adsorption capacities derived from Langmuir and DR model are 0.38 and 0.55 mmol.g -1 , respectively, corresponding to 47 and 67 % of the CEC respectively (Table 2). At pH = 7.5, OXA and DIA are neutral (Figure S1) and their adsorption isotherms display a less favorable adsorption behavior than that of COD.

Hence, the adsorption capacity is lower (i.e. 0.035 and 0.095 mmol.g -1 for DIA and OXA according to Langmuir equation parameters, respectively) and the saturation level is quickly attained. This result highlights the quick saturation of the adsorption sites of Na-Mt for these neutral compounds. At this pH, the three models properly fitted the experimental data (Table 2).

However, under acidic pH conditions (i.e. pH = 2.5) the Langmuir equation fits the experimental data better than the Freundlich equation. Indeed, this latter equation does not reflect any saturation level. Based on the assumptions of the Langmuir equation, this indicates that the adsorption is limited to a monolayer with equal adsorption energy for each adsorption site. Therefore, under these pH conditions, COD and DIA are both protonated and OXA is only partially protonated (~ 20 %, Figure S1). The adsorption capacity of each PAD is similar at pH = 2.5, indicating that the acidification of the solution impacts the behavior of both the adsorbates and the adsorbent. Acidification is favorable for the adsorption of OXA and DIA whereas it can be considered as unfavorable for the adsorption of COD. The adsorbed amount of the three PADs reaches an equilibrium between 0.14 and 0.17 mmol.g -1 according to Langmuir equation which represents ~20 % of the CEC of Na-Mt. The E values, derived from the D-R equation, are systematically higher than 8 kJ.mol -1 , indicating chemisorption (Table 2). The modification of the pH value also impacts the adsorbent. Na-Mt presents two types of charge, with (i) the permanent negative charges generated by the isomorphic substitutions in the layer (e.g. Al -Fe) and (ii) the amphoteric charges on the edge-sites of clay minerals [START_REF] Tombácz | Surface charge heterogeneity of kaolinite in aqueous suspension in comparison with montmorillonite[END_REF].

The variation in the pH conditions reinforces the charge on the edge-sites of Na-Mt. With a pHznpc (zero net proton charge) around 6.5 [START_REF] Tombácz | Colloidal behavior of aqueous montmorillonite suspensions: the specific role of pH in the presence of indifferent electrolytes[END_REF], the edge-sites of Na-Mt are protonated for pH < pHznpc whereas they are deprotonated at pH > pHznpc. That is why acidification of the solution avoids the participation of edge-sites in the CEC of the whole clay minerals. Moreover, acidification of the solution also destabilizes the clay mineral [START_REF] Gautier | Interactions of ammonium smectite with low-molecular-weight carboxylic acids[END_REF], and increases the concentration of H + in the solution. However, H + in excess could be preferentially adsorbed in comparison to other cations such as PADs [START_REF] Tombácz | Colloidal behavior of aqueous montmorillonite suspensions: the specific role of pH in the presence of indifferent electrolytes[END_REF]. According to the results, the CEC of Na-Mt seems to be considerably reduced at pH = 2.5, with an approximate value of 0.15 mmol.g -1 , representing 20% of the CEC at pH = 7.5 (Figure 1).

In Under acidic pH conditions (pH = 2.5) the basal spacing of Na-Mt after interaction with the PADs displays a gradual increase (Figure 3) from 10.4 Å to 12.2, 12.5 and 13.6 Å after interaction with the highest starting concentration of DIA, OXA and COD respectively (Figure 3). All the PADs are intercalated within the layers of Na-Mt at this pH value.

However, the increase in the basal spacing is lower at pH = 2.5 than at pH = 7.5 (except for DIA-NaMt, for which no increase in basal spacing is observed at pH = 7.5). This agrees with the lower adsorption capacity of COD at pH = 2.5 in comparison with pH = 7.5. Conversely, the increase in the basal spacing for OXA is higher at pH = 7.5, although the adsorption capacity is higher at pH = 2.5. This indicates that the impact of the pH modification on the adsorbent impacts the conformation of the resulting PAD-Na-Mt composite after adsorption. Therefore, in the tested conditions, the adsorption of COD is realized through cation exchange whatever the pH conditions. COD is in cationic form in the two pH conditions tested, and its favorable adsorption behavior is attested by the E values (i.e. > 8 kJ.mol -1 ) and by the good fits with the Langmuir equation due to Na + cation exchange mechanisms. Conversely, DIA is adsorbed through weak electrostatic interactions at pH = 7.5 due to its neutral charge [START_REF] Zhang | Sorption and desorption of carbamazepine from water by smectite clays[END_REF],

according to the unfavorable adsorption behavior and the lack of shift in the d001 values (Figure 2). However, at pH = 2.5, since pH < pKa, DIA is adsorbed through cation exchange and is intercalated within Na-Mt layers [START_REF] Parolo | Tetracycline adsorption on montmorillonite: pH and ionic strength effects[END_REF]. For OXA, the adsorption mechanism seems to be more tricky. According to its theoretical speciation, OXA should be neutral at pH = 7.5 (Figure S1); however, an intercalation is observed (Figure 2). Moreover, the adsorption isotherms were wellfitted by the Langmuir equation in this pH condition and the E value was > 8 kJ.mol -1 (Table 2). As a result, it is possible that a significant proportion of OXA is protonated under these pH conditions, contrary to chemical database information, or more probably that neutral OXA was intercalated through ion-dipole interaction or some other mechanism [START_REF] Guégan | Structure and dynamics of nonionic surfactant aggregates in layered materials[END_REF]. At pH = 2.5, a significant part of OXA is protonated, resulting in the possible intercalation within Na-Mt layers through cation exchange.

It should be mentioned here that acidification of the solution modifies the conformation of PADs intercalated within Na-Mt. Hence, at pH = 2.5, the increase in the basal spacing is lower than at pH = 7.5, probably due to the adsorption as a monolayer in acidic conditions whereas another conformation (e.g. bilayer) may be assumed at pH = 7.5. Moreover, the greater increase in the basal spacing of PAD-Na-Mt composites after adsorption of COD in comparison with DIA and OXA can be explained by the larger size of the COD molecules (Table 1).

In this work, it has been shown that the extent to which PADs are adsorbed onto Na-Mt is mainly controlled by the pH value. Acidification of the solution modifies both the adsorption mechanisms of DIA and OXA and also impacts the adsorption capacity of the adsorbent. Hence, cation exchange is the main adsorption mechanism under acidic conditions whereas weak electrostatic interactions can be significant at pH = 7.5 depending on the pKa of the PADs. From this work, it appears that clay minerals could represent a green solution for the removal of PADs

Figure 1 :

 1 Figure 1: Adsorption isotherms of Codeine (circles), Diazepam (squares) and Oxazepam (triangles) onto Na-Mt at pH 2.5 (black symbols) and 7.5 (gray symbols), black lines represent the Freundlich fits, and dashed lines represent the Langmuir fits.

  order to highlight the sorption mechanisms of PADs onto clays, XRD analyses were conducted to investigate possible shifts in the basal spacing of the adsorbents (derived from d001 angular values) accompanying an increase in the amount of PAD adsorbed. The diffractograms of adsorbent after interaction at pH = 7.5 are presented in Figure2. The basal spacings of Na-Mt after interaction with DIA did not show any shift, whatever the starting concentration of DIA. Conversely, the basal spacing of Na-Mt after interaction with both COD and OXA increased for the highest starting concentrations, from 10.4 Å to 14.5 and 13.3 Å for COD and OXA respectively. As a result, it can be assumed that an intercalation occurs for COD and OXA within the Na-Mt layers, whereas DIA is only adsorbed on the external surface at pH = 7.5.

Figure 2 :

 2 Figure 2: X-Ray diffraction patterns of a PAD-Na-Mt layered composite as a function of the starting PAD concentration at pH = 7.5

Figure 3 :

 3 Figure 3: Evolution of the d001 basal spacing determined by the 00l reflection obtained from X-Ray Diffraction patterns of PAD-Na-Mt composites as a function of the starting PAD concentration at pH = 2.5

Table 1 :

 1 Characteristics and properties of the selected PADs, with M the molecular weight in g.mol -1 and Solw the solubility in water at 25°C in mg.L -1 , data from[START_REF] Thiebault | Clayey-sand filter for the removal of pharmaceuticals from wastewater effluent: percolation experiments[END_REF]18]

	Name	Codeine	Diazepam	Oxazepam
	Structure
	Formula	C18H21NO3	C16H13ClN2O	C15H11ClN2O2
	CAS Number	76-57-3	439-14-5	604-75-1
	M	299.36	284.74	286.71
	pKa	8.2	3.4	1.7, 11.6
	Log Kow	1.2	2.82	2.31
	Solw	7,900	50	179
	Batch sorption isotherms were conducted in duplicate using at least 9 initial aqueous
	concentrations ranging from 50 µg.L -1 to 50 mg.L -1 . The prepared aqueous solutions of the

Table 2 .

 2 Equilibrium adsorption isotherm constants determined with the Langmuir, Freundlich, and Dubinin-Radushkevich model fits for the adsorption of Diazepam, Oxazepam, and Codeine onto an Naexchanged smectite clay mineral.

	PP	pH	Langmuir				Freundlich		Dubinin-Radushkevich (D-R)
			qmax (mmol.g -	KL (L.mmol -	∆G° (kJ.mol -	r 2	n	KF (L.g -	r 2	qm (mmol.g -	E (kJ.mol -	r²
			1 )	1 )	1 )			1 )		1 )	1 )
	Codeine	2.5 7.5	0.141 0.381	123.85 19.68	-11.75 -7.26	0.981 0.950	3.95 1.54	0.22 1.24	0.973 0.930	0.137 0.553	11.18 9.33	0,964 0,949
	Diazepam	2.5 7.5	0.174 0.035	48.53 48.80	-9.46 -9.48	0.999 0.923	2.08 2.61	0.43 0.07	0.965 0.929	0.260 0.035	10.43 6.32	0,975 0,915
	Oxazepam	2.5 7.5	0.164 0.095	114.73 129.82	-11.56 -11.86	0.988 0.957	3.30 4.43	0.28 0.13	0.878 0.946	0.209 0.077	11.11 8.16	0,937 0,903

Acknowledgments

The work received financial support from the HArPE Project (2012-00073536) funded by the Région Centre Val de Loire. The authors would also like to thank Marielle Hatton for carbon elemental analysis.

from wastewater effluents and can constitute a key natural material controlling the fate of these contaminants within environmental compartments.


Mokrane Bala

Rachid Zentar

Pascal Boustingorry

Parameter analysis of the compressible packing model for concrete application

. Among its constituents, the aggregates occupy up to 80% of the volume. The remaining volume is occupied by a cement paste. This generates colossal quantities of cement and a heavy carbon footprint. Packing density optimization for the granular mixtures allows not only minimizes the quantity of cement incorporated in the concrete but also enhances its performance and durability. Our work aims to determine the parameters of the compressible packing model (CPM) to predict the maximum compactness of a granular mixture from the characteristics of its constituents. The work will be undertaken on two typologies of grains: crushed and rolled aggregates. 1

Introduction

In the field of civil engineering, concrete is an indispensable raw material which often offering the best technical and economic choice for the construction of buildings and infrastructures. Aggregates in concrete come in different sizes and shapes. They reach up to 80% of the total volume and can arise from natural, artificial (manufactured, industrial by-product,…) or recycled. After the invention of reinforced concrete in the 19th century, concrete formulators found themselves faced with new challenges regarding the composition of the most compact granular mixtures. In conventional concrete formulation methods, granular mixtures are determined empirically, often from particle size curves (ideal distribution curves), as for the works of Fuller & Thompson (1907) d'Andreasen & Andersen (1929) and Dreux (1970). These methods do not make it possible to predict the packing density and may require several series of experiments for the optimization of the granular mix.

With the emergence of modern concretes and special concretes in the 20th century, such as High Performance Concretes (BHP) and Self Compacting Concrete (SCC), concrete mixtures by "ideal" particle size curves proved to be difficult or unsuccessful, as we quickly arrived at five grain scales that are: ultrafine (mineral additions, silica fumes, etc ...), fines (quarry sands, fine limestones, ...), sands, small gravel and coarse gravel.

In order to appear to these difficulties, several models have been developed to predict the compactness of a granular mixture. The demonstration of the interaction effects between grains of different sizes, in particular by the work of Caquot (1937), which shows the major influence of the wall effect on granular mixtures, has prompted researchers to study granular classes in pairs. Inspired by the Mooney viscosity model (1950), Stovall [START_REF] Stovall | Linear Packing Density Model of Grain Mixtures[END_REF] studied binary mixtures with and without interaction. He has developed the linear packing model for granular mixtures with multiple classes, taking into account both the wall effects and the loosening effect between the granular classes of different sizes. The linear model was refined to build the virtual packing model that predicted virtual packing density, including mixtures of grains of the same size but of different shapes. It involves the volume proportions of each of the granular classes (yi), their packing density when they are arranged separately (βi), the wall effect coefficient (bji) and the loosening effect coefficient (aij).

The virtual packing density for a mixture of "n" granular fractions where the class (i) is dominant, is given by the following formula [START_REF] De Larrard | Structures Granulaires et Formulation Des Bétons[END_REF]:

𝛾 = 𝛾 𝑖 = 𝛽 𝑖 1 -∑ 𝑦 𝑗 (1 -𝛽 𝑖 + 𝛽 𝑖 𝑏 𝑖𝑗 (1 - 1 𝛽 𝑖 )) 𝑖-1 𝑗=1 -∑ 𝑦 𝑗 (1 -𝑎 𝑖𝑗 𝛽 𝑖 𝛽 𝑗 ) 𝑛 𝑗=𝑖+1 (1)
2

Advanced materials

The granular interaction coefficients were calibrated on binary mixtures [START_REF]Planetoscope -Statistiques : Production Mondiale de Béton N.d. Site web[END_REF]. The coefficient of loosening effect a12, exerted by the fine particles (2) in a dominant large grain population [START_REF]Planetoscope -Statistiques : Production Mondiale de Béton N.d. Site web[END_REF], and the wall effect b21 exerted by coarse grains on the preponderant fine grains population are given by [START_REF] Stovall | Linear Packing Density Model of Grain Mixtures[END_REF]:

𝑎 12 = 𝛽 2 (| 𝜕𝑒 𝜕𝑦 2 | 𝑦 2 =0 + 1 𝛽 1 ) (2)
And:

𝑏 21 = 1 𝛽 2 -1 -| 𝜕𝑒 𝜕𝑦 2 | 𝑦 2 =1 1 𝛽 1 -1 (3)
"e" is the void ratio of the granular mixture.

After calibration of the coefficients a and b on a series of experiments, de Larrard [START_REF] Stovall | Linear Packing Density Model of Grain Mixtures[END_REF] proposed simplified formulas of the granular interaction coefficients in the following form:

𝑎 𝑖,𝑗 = √1 -(1 - 𝑑 𝑗 𝑑 𝑖 ) 1,02 (4)
And:

𝑏 𝑖,𝑗 = 1 -(1 - 𝑑 𝑖 𝑑 𝑗 ) 1,5 (5)
A first attempt to predict the packing density by the Solid Suspension Model was limited by two defects related to the notion of reference viscosity (considered as a description of the degree of compaction of the system) and the interaction functions that were not satisfactory in their mathematical form [START_REF] Sedran | Une Nouvelle Approche de La Formulation Des Betons[END_REF].

The Compressible Packing Model [START_REF] De Larrard | Structures Granulaires et Formulation Des Bétons[END_REF] represents the latest generation of models developed at "Laboratoire Central des Ponts et Chaussées" (LCPC) in France. This model makes it possible to predict the real packing density of a mixture of several granular classes from the knowledge of the compactness of each one-dimensional class and the energy of the setting up.

We find in the CPM the notion of virtual packing density and real packing density which are respectively the optimal packing density that can be achieved by placing the grains one by one to get a minimal void, and the real packing density of the mixture in which the granular arrangement is naturally disordered.

The real packing density depends on the compaction energy. This energy is introduced into the CPM by the concept of the compaction index "K". The real packing density "C" of a mixture of aggregates is connected to "K" by the expression:

𝐾 = ∑ 𝐾 𝑖 𝑛 𝑖=1 = ∑ 𝑦 𝑖 𝛽 𝑖 ⁄ 1 𝐶 - 1 𝛾 𝑖 𝑛 𝑖=1 (6)
Otherwise, a procedure called LCP No. 61 is associated with the CPM to measure the real packing density experimentally. Several methods existed to determine the real packing density which differs by the packing process: picketing, vibration, ... etc. The compaction table procedure according to the LPC method No. 61 [START_REF] Ledee | Essai de Compacité Des Fractions Granulaires à La Table à Secousses: Mode Opératoire[END_REF] has the advantage that the compaction energy is constant and proportional to the number of shocks applied to the sample.

The experimental packing density can be calculated from the final height of the sample after compaction (h) and its dry density (ρrd) through the following relation:

𝐶 = 𝜌 𝑎 𝜌 𝑟𝑑 (7)
𝜌 𝑎 = 𝑀 𝑉 ⁄ : is the density of the compacted sample. "M" is the weight of the compacted sample and "V" its volume. The calibration of the CPM parameters (granular interaction coefficients and compaction index) on binary mixtures of aggregates of different types (crushed and rolled) has shown that the error does not exceed 0.77% for rolled aggregates and 1.71% for crushed aggregates [START_REF] Stovall | Linear Packing Density Model of Grain Mixtures[END_REF], this taking a value equal to 9 for the compaction index "K".

The analysis of the CPM parameters (interaction coefficients and compaction index) can be lead through the following flowchart (Fig. 1).

Fig. 1

Flowchart of the calibration of the CPM [START_REF] De Larrard | Structures Granulaires et Formulation Des Bétons[END_REF].

The CPM is a very important tool for optimizing and evaluating the compactness of granular mixtures for concrete. In this work, we are interested in determining the packing density of binary mixtures of aggregates in order to identify the different parameters that control this property as well as their degree of influence on the results of the CPM. This step is necessary before starting a study of concrete formulation by a "compactness" approach. Our study was conducted on aggregates of different sizes and shapes from the north and central region of France. First, we will apply the CPM as developed by de Larrard in order to qualify the prediction of the model and determine the most influential parameters. Subsequently, we will lead a phase of optimization of the parameters of the CPM on our granular mixtures.

Materials and methods

Materials

In the Table 1 are listed the aggregates of the present study. The size, shape and roughness of the grains are the three main parameters that affect the packing density that has influenced our choice. Rolled aggregates come from Chevrières quarry (Hauts-de-France region) and Decize quarry (Bourgogne-Franche-Comté region). The crushed aggregates come from the quarries of Boulonnais (Nord Pas-de-Calais). The granular fractions adopted for this study range from sand (0/4 mm) to gravel (10/20 mm).

Equipment

The compaction table for carrying out the compactness measurement test is shown in Fig. 2.

Fig. 2 Compaction table: Bottom part (left) and top part (right) [START_REF] De Larrard | Structures Granulaires et Formulation Des Bétons[END_REF].

A mass (M = 7 kg) of the sample is placed in a cylindrical mould in three equivalent layers. Each layer is subjected to a series of shocks in the compaction table before putting the next layer. The sample will then undergo 40 additional shakes under a pressure of 10 kPa (an equivalent weight of 20 kg was used).

The energy transmitted by shocks to the grains allows them to rearrange in a denser configuration, which improves the packing density of the sample. The process is characterized by a compaction index K = 9 [START_REF] De Larrard | Concrete Mixture Proportioning: A Scientific Approach[END_REF].

Experimental program

The compacities were measured on "Crushed-Crushed" and "Rolled-Rolled" mixtures to determine the optimal packing density that can be achieved with each type of aggregates on binary mixtures. A combination of sand and coarse gravel was analyzed. As shown in Table 2, considering the maximum nominal diameter of each class, the size ratio was fixed and the effect of grain shape on the packing density was experienced. Other combinations of binary mixtures between sand and gravel with an intermediate class (4/10 gravel) were tested. Trends in these mixtures will be given in conclusions. Otherwise, the variation of the proportions of a granular class in the binary mixture equal to 5% in the extreme parts of the curve of the packing density of the mixture and to 10% in the center of the curve. This is to measure the impact of the granular interaction effects we have seen previously (coefficient of wall effect and loosening effect). The main properties of the aggregates of the study are listed in Table 3. The absolute density was measured according to the European standard NF EN 1097-6 and the particle size analysis was carried out according to the European standard NF EN 933-1.

The particle size distribution of the different fractions are shown in Fig. 3.

Particle size analysis showed a high fines content of crushed sand (6% of grains smaller than 63 microns). Mixing curves are continuous and spread except for a small discontinuity for rolled aggregates between 10 and 12 mm sieves due to non-overlapping of granular classes 4/10 and 11/22. Packing densities measurement tests were carried out by the compaction table according to LPC procedure No. 61 on binary mixtures of crushed and rolled aggregates. However, as the fines content is different from one granular fraction to another (especially crushed sand and rolled sand), it was decided to use the materials in their raw state (ie without sieving at 63 microns as recommended by LCP Procedure No. 61). Moreover, for each test, two different measurements of compactness were made. In each case, the average packing density and the possible differences are noted. It has been observed through the experimental program that the repeatability of the tests is ensured (maximum standard deviation of 0.015 for crushed aggregates and 0.004 for rolled aggregates). The evolution curves of the packing density measured by the compaction table as a function of the introduction of small grains in a coarse grain population are shown in Figure 3. The small grains will be introduced into the intergranular voids of large grains if their size allows them to enter in those voids (otherwise, we will see a loosening effect). From the curves in Figure 3, it is observed a rapid increase of the packing density in the area of large grains dominant due to the ratio of large sizes (d1 / d2 = 5) which minimizes the loosening effects. Subsequently, the packing density reaches an optimum before decreasing when entering the area where the small grains are dominant. Wall effects occur in this area.

The high fines content (high particle content <63 microns, minimum d50) of the crushed aggregates (Fig. 4. left) allows achieving high levels of packing density, particularly in the area of small grains dominant. In this case, shape effects were less visible for crushed aggregates. However, despite their low fines content, the rolled aggregates (Fig. 4. right) allowed us to reach the highest packing density. From these results, it is deduced that the maximum packing density that can be achieved on binary mixtures is influenced by the combination of the following parameters: the packing density of the elementary granular classes, the shape and roughness of the grains as well as the fines content. Packing density measured by the compaction table of binary mixtures of crushed aggregates (left) and rolled aggregates (right).

After having made the evolution curves of the experimental packing density for our two binary mixtures (crushed and rolled), we proceed to the modeling phase of these packing densities by the CPM in which we will analyze the different parameters of the model which are: the coefficients of granular interactions (a and b) and the compaction index (K).

Modeling packing density by CPM

In order to determine the packing densities by the CPM, the virtual packing densities are first calculated using Equation [START_REF]Planetoscope -Statistiques : Production Mondiale de Béton N.d. Site web[END_REF]. For this, we need to determine the coefficient of loosening effect (aij) and wall effect (bij). These parameters will be calculated initially using the simplified formulas (Equations ( 4) and ( 5)).

The real packing density of the mixtures is subsequently calculated through the compaction index which is taken as 9 because of this value is associated with the operating mode by the compaction table.

Finally, we will proceed to a calibration of the coefficients a, b and K on our crushed and rolled aggregates.

Coefficients a and b calculated by the simplified formulas (K = 9)

The simplified equations of the granular interaction coefficients were developed following series of experiments on aggregates of different natures (crushed and rolled). In order to verify the agreement of the experimental and theoretical results using these formulas, we have made a modelling of the experimental compactness by the CPM using the Equations ( 4) et [START_REF] Sedran | Une Nouvelle Approche de La Formulation Des Betons[END_REF] for the coefficients a and b. The results are shown in Figure 5. Based on the simplified formulas of the interaction coefficients, the CPM allowed us to predict experimental packing densities with an average error of 2.8% for crushed aggregates and 2.1% for rolled aggregates. We note through the curves in Fig. 5 that the largest differences are found in the area of optimal packing density. In this zone, the packing density is overestimated by the MEC for crushed aggregate mixtures and underestimated in the case of rolled aggregate mixtures. This leads us to say that the efficiency of the compaction mode (by the compaction table) is influenced by the parameters of particle size [START_REF] Sadok | Genetic Programming for Granular Compactness Modelling[END_REF] and shape. The parameters a, b and K taked in this first modelling are given in Table 4. However, the experimental and theoretical data analyzed by de Larrard (de Larrard 2000) revealed an average error of 1.71% for crushed aggregates and 0.77% for rolled aggregates. In order to optimize the results of the modelling, we decided to calibrate the granular interaction coefficients a and b on our binary granular mixtures using Formulas (2) and (3).

4.2

Coefficients a and b calibrated on our aggregates (K = 9)

In the work of de Larrard, the coefficients a and b were determined at the limits of the curves of the void ratio as a function of the proportions of the small grains. Following this path and based on the equations ( 2) and ( 3) that we saw previously, we proceed to the calibration of coefficients a and b on our aggregates through Fig. 6. For some granular mixtures on void ratio curves, we observe dispersions and trends (positive or negative slope) are difficult to determine. This indicates the sensitivity of this method compared to the experimental tests. In fact, carrying out compactness tests between two adjacent points (5% fine-grained interval) can give similar results. The values of the coefficients a and b that could be calculated are given in Table 4 and the results of the modelling in Fig. 7. After determining the interaction coefficients, we can minimize the difference between the model and the experiment at 1.2% for crushed aggregates and 0.6% for rolled aggregates.

Conclusions

In this paper, we studied the packing density of binary mixtures of crushed and rolled aggregates. The results of the modeling by the CPM have shown that the computation of the granular interaction coefficients by the simplified formulas is insufficient to have a good prediction. At the end of this study, we can draw the following conclusions:  The simplified formulas of a and b take into account only the size parameters (maximum diameter of the granular classes "D") without the shape parameters (one law for the two types of aggregates).



After calibration of the interaction coefficients, we can minimize the difference between the model and the experiment at: 1.60% for crushed and 0.90% for rolled aggregates.



The accuracy of the model is influenced by the sensitivity of the coefficients a, b and K:  The pre-established formulas for the granular interaction coefficients (a and b) in CPM do not coincide in all cases with the values calculated on the experimental curves of the binary mixtures.  The compaction index (K) may vary from one mixture to another (especially for crushed aggregates).



For packing density measurements at the compaction table made with the fine fraction (<63 microns), the repeatability of the tests is ensured (maximum standard deviation of 0.015 between two tests). The segregation effects of fine particles can be neglected.



Optimum packing density is influenced by the combination of the following three parameters:  The ratio of size of particles;  The shape and roughness of the grains;  The fines content.



The model has a good accuracy in determining the optimum of binary granular mixtures. The perspectives of the present study are the optimization of the packing density of the ternary granular mixtures for the concrete as well as the study of the parameters of form and fines content of the aggregates. The use of predictive algorithms of artificial intelligence may allow re-establishing new formulas for calculating model parameters, especially the granular interaction coefficients.

Fig. 3

 3 Fig. 3 Particle size distribution of crushed aggregates (left) and rolled aggregates (right).

Fig. 4

 4 Fig. 4Packing density measured by the compaction table of binary mixtures of crushed aggregates (left) and rolled aggregates (right).

Fig. 5

 5 Fig. 5 Measured and modeled packing density of crushed (left) and rolled (right) binary Mixtures -Interaction Coefficients through the CPM Simplified Formulas.

Fig. 6

 6 Fig. 6 Determination of the granular interaction coefficients a and b for crushed (left) and rolled (right) aggregates.

Fig. 7

 7 Fig. 7Measured and modeled packing density of crushed (a) and rolled (b) binary mixtures -Calibrated interaction coefficients on our mixtures.

Table 1

 1 Origin and nature of the studied aggregates.

	Type of aggregates	Origin	Granular class d/D	Density [t/m 3 ]
			Sand 0/4	2.69
	Crushed	Boulonnais	Gravel 4/10	2.67
			Gravel 10/20	2.67
	Rolled	Chevrières	Sand 0/4 Gravel 4/10	2.55 2.43
		Decize	Gravel 10/20	2.54

The nature and state characteristics of the materials were identified according to standard tests. 4 Advanced materials

Table 2

 2 Experimental program of binary mixtures.

		Type of aggregates	Granular class d/D	Binary mixtures	D1/D2 ratio
		Crushed	Sand 0/4 Gravel 12/20	SC 0/4 + GC 12/20	5
		Rolled	Sand 0/4 Gravel 11/22	SR 0/4 + GR 11/22	5
	3	Experimental results

Table 3

 3 Characteristics of the aggregates of the study.

		Crushed aggregates		Rolled aggregates
	d/D	0/4 (Sand)	4/10 (Gravel)	12/20 (Gravel)	0/4 (Sand)	4/10 (Gravel)	11/22 (Gravel)
	Fine content < 63 μm [%]	6.2	1.0	0.8	1.3	1.7	0.1
	d50 [mm]	0.7	7.2	15.2	0.4	7.0	16.0
	Finesse module (for sands)	3.2	-	-	3.4	-	-
	Absolute den-sity [g/cm 3 ]	2.726	2.735	2.711	2.626	2.648	2.626
	Water absorp-tion [%]	0.43	0.59	0.49	1.18	3.06	1.79
	Shape and	Angular aggregates, flat and rough sur-	Rounded shape, flat or elongated ag-
	roughness		face		gregates, smooth surface

Table 4

 4 Parameters of the modeling by simplified and calibrated formulas of a and b (K = 9).

			SC 0/4 + GC 12/20					SR 0/4 + GR 11/22
			C exp.	C théo. (a&b modélisés)			C exp.	C théo. (a&b modélisés)
	Packing density	0.500 0.600 0.700 0.800	0	50	100	Packing density	0.500 0.700	0	50	100
			% fine particules (y2)					% fine particules (y2)
			Parameters		Crushed aggregates	Rolled aggregates
		a (simplified formula)	0.451				0.430
		a (calibrated on our mixtures)	0.633				0.333
		b (simplified formula)	0.284				0.260
		b (calibrated on our mixtures)	0.344				0.039

Acknowledgements

I would like to express my deepest appreciation to IMT Lille-Douai, Research Center and Engineer School in the north of France. A special gratitude I give to CHRYSO France, the French leader for admixtures for construction materials, for their technical and financial support for this modest work.