Gilmar

Nogueira

Thierry Gervais

Véronique Peres

Estelle Marc

Christophe L Martin

Using Discrete Simulations Of Compaction And Sintering To Predict Final Part Geometry

Keywords: powder compaction, ejection, sintering, Discrete Element Method, density gradient, friction coefficient

A DEM (Discrete Element Method) model is used to simulate the compaction and sintering of ceramic oxides. The process kinematics are decomposed into loading (double action compaction), unloading, and ejection of the pellet. Interactions between particles and between particles and the die are considered elastoplastic by implementing a model able to tackle large densities. A simplified approach is used in the sintering stage, which focuses on the final part geometry rather than kinetics.

The results are in good agreement with experimental data and FEM simulations from the literature regarding density gradient, elastic spring-back, and final geometry. The simulations show that the friction coefficient between the agglomerates and the die is the primary factor for the density gradient in the pellet. This density gradient induces non-homogeneous sintering, which results in a final geometry with a so-called diabolo effect. It is the first time that DEM reproduces this effect with the advantage of taking explicitly into account the particulate nature of the powder.

Introduction

The finite element method (FEM) has received considerable attention for simulating powder compaction and sintering [START_REF]Proceedings of 2004 Powder Metallurgy World Congress, on CD-ROM[END_REF]. FEM is a numerical tool that allows solving the partial differential equations of the mechanics of a continuous media. Applied to powder forming processes, such as compaction and sintering, FEM uses elastoplastic or elastoviscoplastic models [START_REF] Bathe | Finite Element Method[END_REF] as constitutive equations. These simulations can consider the geometry and boundary conditions, such as pressing conditions and friction between the powder and dies. However, the models implemented in the FEM are derived from the mechanics of continuous media. They do not consider the particulate character of powders directly (i.e., the microstructure of powders and their composition is not considered explicitly). They cannot easily describe fracture phenomena of green compacts because they do not describe rearrangement, fracture of particles, or debonding [START_REF] Bathe | Finite Element Method[END_REF][START_REF] Foo | An experimental and numerical study of the compaction of alumina agglomerates[END_REF]. The complex particulate nature of the powder is generally taken into account by calibrating phenomenological models to experimental data. Therefore, each new powder needs to be characterized, which requires complex instrumented matrix tests performed at different compaction pressures and stress states.

The discrete element method (DEM) is an alternative simulation method that can be used to take into account powders' granular microstructure directly. Initially introduced by Cundall & Strack [START_REF] Burman | A discrete numerical model for granular assemblies[END_REF] for geomaterials, the DEM consists in simulating a granular medium by taking into account each particle, generally represented by a sphere (Figure 1 -a). Contact laws with a normal and a tangential component define the interaction between particles that indent each other (Figure 1 -b). The particle's motion is calculated to satisfy force and moment equilibrium. This method has been used mainly to simulate metallic [START_REF] Shima | A Study of Constitutive Behaviour of Powder Assembly by Particulate Modeling[END_REF][START_REF] Heyliger | Cold plastic compaction of powders by a network model[END_REF][START_REF] Martin | Study of particle rearrangement during powder compaction by the Discrete Element Method[END_REF] , ceramic [START_REF] Pizette | Compaction of aggregated ceramic powders: From contact laws to fracture and yield surfaces[END_REF] and composite powders [START_REF] Skrinjar | Cold compaction of composite powders with size ratio[END_REF][START_REF] Martin | Study of the cold compaction of composite powders by the discrete element method[END_REF]. With DEM, it is possible to simulate the rearrangement and the plastic deformations during cold isostatic and closed die compaction of powders [START_REF] Heyliger | Cold plastic compaction of powders by a network model[END_REF][START_REF] Fleck | On the cold compaction of powders[END_REF], as well as the fracture of agglomerates [START_REF] Moreno-Atanasio | Mechanistic analysis and computer simulation of impact breakage of agglomerates: Effect of surface energy[END_REF].

DEM has also been used to model sintering, taking into account diffusion as well as coalescence [START_REF] Paredes-Goyes | Grain growth in sintering: A discrete element model on large packings[END_REF]. Thus, the DEM is a powerful method to simulate the entire process from compaction to sintering.

Although up to hundreds of thousands of particles can be simulated, the dimensions are too small to represent an industrial part. This explains why most DEM studies focus on a small volume of material and why finite element approaches have been adopted in the last twenty years to model real parts. Some methods propose a micromacro coupling from microscopic DEM simulations to derive macroscopic constitutive relations [START_REF] Vermeer | Continuous and Discontinuous Modelling of Cohesive-Frictional Materials[END_REF].

The computation time can be significantly reduced by using GPU parallelization [START_REF] Radeke | Large-scale powder mixer simulations using massively parallel GPUarchitectures[END_REF]. The computation time can also be reduced by simulating fewer particles that are larger than the size of the real particles. In that context, the present study reports on a method for DEM to simulate a macroscopic compact by considering particle agglomerates instead of crystallites or unit particles. Interactions between the particles are considered elastoplastic. We use this method to simulate the compaction and sintering of uranium oxide powder at a macroscopic scale. A double-action dry pressing has been implemented for the compaction stage, and its process kinematics are decomposed into loading, unloading, and ejection of the pellet. After the compaction, the pellet is sintered at a temperature of 1700°C.

The present study couples with the DEM the simulations of compaction, ejection and sintering to deliver the final shape of an industrial part. This methodology has been employed previously with FEM [xx]. To our best knowledge, this is the first time it is attempted with DEM. The advantage of DEM is that it brings a wealth of information that FEM cannot provide and that it uses constitutive contact laws that explicitly take the granular nature of the powder into account.

Model description

A typical ceramic microstructure is composed of crystallites, aggregates, and agglomerates. The size of these entities depends on the ceramic powder, but typically, crystallite size is in the range of hundreds of nanometers. Porous aggregates made of strongly bonded crystallites are micronic, while agglomerates made of weakly bonded aggregates have a broader range, varying from a few to hundreds of microns (Figure 2). P. Pizette et al. [START_REF] Pizette | Green strength of binder-free ceramics[END_REF] have studied crystallite and aggregate length scales with DEM.

An entire system can be simulated by using the agglomerate length scale without requiring billions of unit particles (as required by the simulation at the crystallites or aggregates scale). In that case, one agglomerate is considered as one single porous particle for DEM. This approach may represent particle deformation and rearrangement well, but it cannot represent agglomerates fracture explicitly. Figure 2 summarizes this approach, which is implemented in dp3D, an in-house code mainly used for material science applications.

In DEM, a contact force law is required for computing the total force applied on each particle. It gives the normal force N as a function of the mutual indentation δ between the two particles (Figure 1b, Figure 3). Forces are shown positive when repulsive. During the loading of a contact, no elastic domain is considered, owing to the weak nature of agglomerates. The plastic loading, is adapted from the high-density model proposed in [START_REF] Harthong | Modeling of high-density compaction of granular materials by the Discrete Element Method[END_REF]. Consider a material characteristic of the agglomerate which uniaxial stress response writes:

𝜎𝜎 = 𝜎𝜎 * 𝜀𝜀 𝑚𝑚 (1)
where 𝜎𝜎 * is a plastic parameter, 𝜀𝜀 the axial strain and m a hardening parameter. The normal repulsive force (𝑁𝑁 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ) for two particles, i and j, at time 𝑡𝑡 + 𝑑𝑑𝑡𝑡 is:

𝑁𝑁 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (𝑡𝑡 + 𝑑𝑑𝑡𝑡) = 𝑁𝑁 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (𝑡𝑡) + 2𝑆𝑆 𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑𝑑𝑑 (2)
where 𝑆𝑆 𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 is the contact stiffness, which is a sum of two terms, 𝑆𝑆 1 and 𝑆𝑆 2 :

𝑆𝑆 𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 2𝜎𝜎 * 𝑅𝑅 * (𝑆𝑆 1 + 𝑆𝑆 2 ) (3)
where 𝑅𝑅 * is the equivalent radius for particles i and j:

𝑅𝑅 * = � 1 𝑅𝑅 i + 1 𝑅𝑅 j � -1 (4)
The hardening parameter � 1 𝑚𝑚 �, and the plastic parameter 𝜎𝜎 * , are material parameters that have to be fitted with the experimental density-stress curve: the hardening parameter changes the curvature of the loading curve in Figure 3, and the stress parameter changes its amplitude. When considering a contact between two different materials with plastic parameters 𝜎𝜎 𝑖𝑖 and 𝜎𝜎 𝑖𝑖 , 𝜎𝜎 * writes:

𝜎𝜎 * = 2 1 𝑚𝑚 �𝜎𝜎 𝑖𝑖 -𝑚𝑚 + 𝜎𝜎 𝑖𝑖 -𝑚𝑚 � - 1 𝑚𝑚 (5)
The stiffness term 𝑆𝑆 1 in Eq. ( 3) is preserved from [START_REF] Harthong | Modeling of high-density compaction of granular materials by the Discrete Element Method[END_REF], and depends on the indentation 𝑑𝑑 at the contact. The term 𝑆𝑆 2 depends on the local relative density, and is adapted to consider porous agglomerates:

𝑆𝑆 2 = 𝛼𝛼 2 (𝑚𝑚) �𝑚𝑚𝑝𝑝𝑚𝑚�0,𝜌𝜌 𝑖𝑖,𝑗𝑗 -𝜌𝜌 0𝑖𝑖,𝑗𝑗 �� 2 (1-𝜌𝜌 𝑖𝑖,𝑗𝑗 ) 𝛽𝛽 2 (6)
where 𝛼𝛼 2 (𝑚𝑚) is a function of the hardening parameter m [START_REF] Harthong | Modeling of high-density compaction of granular materials by the Discrete Element Method[END_REF], 𝛽𝛽 2 is a parameter that depends on the porosity of the agglomerates, 𝜌𝜌 𝑖𝑖,𝑖𝑖 is the local density around the particles, and 𝜌𝜌 0𝑖𝑖,𝑖𝑖 is the initial local density (before plastic indentation). Note that when 𝜌𝜌 𝑖𝑖,𝑖𝑖 tends to unity, 𝑆𝑆 2 tends to infinity to model incompressibility. The local density 𝜌𝜌 𝑖𝑖,𝑖𝑖 is computed using Voronoi tessellations with the Voro++ package [START_REF] Rycroft | VORO++: A three-dimensional Voronoi cell library in C++[END_REF]. Eq. ( 6) allows some hardening of the particulate material to be taken into account due to the local densification. This is in contrast with standard DEM schemes that only consider the mutual indentation between particles.

Elastic unloading is written by considering an elastic stiffness 𝑆𝑆 𝑖𝑖𝑖𝑖 𝑢𝑢𝑢𝑢𝑝𝑝 :

𝑁𝑁 𝑢𝑢𝑢𝑢𝑝𝑝 = 𝑁𝑁 1 -𝑆𝑆 𝑖𝑖𝑖𝑖 𝑢𝑢𝑢𝑢𝑝𝑝 𝑑𝑑 𝑢𝑢𝑢𝑢𝑝𝑝 (7)
where 𝑁𝑁 1 is the force at the maximum plastic indentation 𝑑𝑑 1 and 𝑑𝑑 𝑢𝑢𝑢𝑢𝑝𝑝 is the amount of indentation retrieved elastically (𝑑𝑑 𝑢𝑢𝑢𝑢𝑝𝑝 = 𝑑𝑑 1 -𝑑𝑑, Figure 3). The elastic stiffness is modelled by considering that a bond has been formed between the two particles during plastic loading and using the model of Jefferson et al. [START_REF] Pizette | Green strength of binder-free ceramics[END_REF][START_REF] Jefferson | The elastic response of a cohesive aggregate -A discrete element model with coupled particle interaction[END_REF] :

𝑆𝑆 𝑖𝑖𝑖𝑖 𝑢𝑢𝑢𝑢𝑝𝑝 = 𝐸𝐸 1-𝜈𝜈 2 𝑓𝑓 𝑁𝑁 � 𝑝𝑝 𝑏𝑏 𝑅𝑅 * , 𝜈𝜈� 𝑎𝑎 𝑏𝑏 ( 8
)
where 𝐸𝐸 is the Young's Modulus, 𝜈𝜈 the Poisson's ratio, and 𝑎𝑎 𝑏𝑏 the radius of the bond formed during the plastic loading (𝑎𝑎 𝑏𝑏 2 = 2𝑅𝑅 * 𝑑𝑑 1 ).

The elastic unloading thus depends on the elastic parameters of the agglomerates and on the size 𝑎𝑎 𝑏𝑏 of the bond. In other words, the elastic stiffness of an unloading contact depends on its plastic history. The function 𝑓𝑓 𝑁𝑁 has been derived by Jefferson et al. [START_REF] Jefferson | The elastic response of a cohesive aggregate -A discrete element model with coupled particle interaction[END_REF] and typically increases from 1 to 1.3 as the relative size 𝑝𝑝 𝑏𝑏 𝑅𝑅 * increases. The plastic loading stiffness is capped by the unloading stiffness �𝑆𝑆 𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = min�𝑆𝑆 𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 , 𝑆𝑆 𝑖𝑖𝑖𝑖 𝑢𝑢𝑢𝑢𝑝𝑝 �� to ensure that the plastic response is never stiffer than the elastic one.

The bond formed during plastic loading may sustain tensile forces as sketched in Figure 3. The force necessary to break this bond, 𝑁𝑁 𝑚𝑚𝑝𝑝𝑚𝑚 , depends on how much the agglomerates indented each other:

𝑁𝑁 𝑚𝑚𝑝𝑝𝑚𝑚 = 𝜎𝜎 𝑁𝑁 𝜋𝜋𝑎𝑎 𝑏𝑏 2 (9)
where 𝜎𝜎 𝑁𝑁 is the tensile strength, to be fitted with experimental data. For the time being, no shear strength is introduced in this model. Bonds only fracture in tension. When the tensile force 𝑁𝑁 reaches 𝑁𝑁 𝑚𝑚𝑝𝑝𝑚𝑚 the bond breaks and no force is transmitted anymore. If the contact resumes, it will only transmit repulsive force when 𝑑𝑑 𝑢𝑢𝑢𝑢𝑝𝑝 = 𝑑𝑑 1 -𝑑𝑑 < 𝑑𝑑 𝑝𝑝𝑢𝑢𝑝𝑝𝑝𝑝 , with 𝑑𝑑 𝑝𝑝𝑢𝑢𝑝𝑝𝑝𝑝 given by:

𝑑𝑑 𝑝𝑝𝑢𝑢𝑝𝑝𝑝𝑝 = 𝑁𝑁 1 𝑆𝑆 𝑖𝑖𝑗𝑗 𝑢𝑢𝑢𝑢𝑢𝑢 (10)
Once 𝑑𝑑 𝑝𝑝𝑢𝑢𝑝𝑝𝑝𝑝 is reached during reloading, the contact reloads elastically following the 𝑁𝑁 𝑢𝑢𝑢𝑢𝑝𝑝 branch in Figure 3, until the indentation increases above 𝑑𝑑 1 and the contact re-plastifies.

The tangential force model is composed by a sticking mode and a sliding mode.

The sticking mode uses the Hertz-Mindlin model while during the sliding mode, the tangential force is limited by Coulomb friction. Two friction coefficients are used: the friction between agglomerates (𝜇𝜇 𝑝𝑝𝑎𝑎𝑎𝑎𝑝𝑝. ) and the friction between the agglomerates and the die (𝜇𝜇 die ). The DEM literature has already studied the effects of these friction coefficient on the powder response [xx,yy]. In particular, their role on the fluidity (the ratio between the radial and axial stresses) and on the density gradient in the compact have been reported.

The Bouvard Pan model [START_REF] Bouvard | Deformation of interparticle necks by diffusioncontrolled creep[END_REF][START_REF] Pan | A model for the sintering of spherical particles of different sizes by solid state diffusion[END_REF] is used for the sintering stage. This model takes into account grain boundary and surface diffusion but does not consider grain growth.

The details of the DEM model implementation of the sintering model can be found in [START_REF] Martin | The effect of a substrate on the sintering of constrained films[END_REF]. In short, the model introduces a normal force 𝑁𝑁 𝑝𝑝 :

𝑁𝑁 𝑝𝑝 = 𝜋𝜋𝑝𝑝 𝑠𝑠 4 8Δ 𝑏𝑏 𝑑𝑑𝑑𝑑 𝑑𝑑𝑝𝑝 - 9 4 𝜋𝜋𝑅𝑅 * 𝛾𝛾 𝑝𝑝 (11)
where 𝑎𝑎 𝑝𝑝 is the contact radius, Δ 𝑏𝑏 is a diffusion parameter (grain boundary limited) and 𝛾𝛾 𝑝𝑝 is the surface energy. The first term on the RHS of eqn [START_REF] Martin | Study of the cold compaction of composite powders by the discrete element method[END_REF] is the viscous response of the contact while the second term is always tensile and accounts for the sintering shrinkage.

Here, because we model sintering at the scale of agglomerates that are much larger than the actual grains, the kinetics of sintering are not correct (we use alumina material parameters that can be found in [START_REF] Paredes-Goyes | Grain growth in sintering: A discrete element model on large packings[END_REF]). However, the relative densification kinetics (regions of large relative density shrink slower than regions of small relative density) should be correctly rendered. Thus, the final geometry of the sintered compact should be appropriately modelled.

Process kinematics

A uranium oxide powder was chosen to simulate the compaction and sintering process.

The geometric relative density in the simulation (as if indented spherical discrete elements were dense) is multiplied by a factor 0.45 to obtain the relative density of the compact, thus considering the porosity of agglomerates. The 0.45 value is close to the value (0.41) of density measured by mercury porosimetry by Ablitzer [xx]. It has also the advantage of leading to an initial geometrical density (0.4) with a realistic coordination number ().

The ceramic powder with an initial relative density of 0.18 and 40 000 particles representing agglomerates is introduced into a cylinder die of approximately 10 mm in diameter and 40 mm in height. Figure 4 summarizes the process kinematics. The powder is pressed by two flat punches (double-action dry pressing, same force on the upper and lower punch) up to an axial stress of 600 MPa [START_REF]Proceedings of 2004 Powder Metallurgy World Congress, on CD-ROM[END_REF]. The upper punch is then unloaded until the axial stress reaches 50 MPa (2). This accompanying stress is maintained during ejection, during which the cylinder slides out of the die (3). Finally, the upper punch is completely unloaded (4).

Results and discussion

Compaction

A very stiff material is considered for the die (typically tungsten carbide) with a very large value for σ 𝑑𝑑𝑖𝑖𝑑𝑑 to ensure that contact forces between agglomerates and the die are dictated by the soft agglomerates (Eq. ( 5)). The Young's modulus of the die is set to 550 GPa, which is typical of tungsten carbide. Table 1 shows the material properties used for the compaction of uranium oxide. Each material parameter can be fitted using a given stage of the compaction process. The 𝑚𝑚 and σ 𝑝𝑝𝑎𝑎𝑎𝑎𝑝𝑝. parameters (eqn ( 1)) are fitted using the compaction curve as they essentially control the axial stress response. The 𝛽𝛽 2 parameter (eqn ( 6)) controls the asymptotic increase of the stress when the powder approaches full density. It is also fitted using the axial stress response. 𝐸𝐸 𝑝𝑝𝑎𝑎𝑎𝑎𝑝𝑝. and σ 𝑁𝑁 (eqns ( 8) and ( 9)) are fitted using the experimentally measured axial spring-back of the compact after ejection. The friction coefficients are fitted using the ratio between the radial and axial stresses during compaction (experimentally measured) and using the density gradient in the compact (obtained from FEM simulations [START_REF] Alvain | modélisation et simulation numérique de la mise en forme de pièces par compression et frittage de poudres dures[END_REF]), as detailed below.

After compaction, σ 𝑁𝑁 evolves and a very large value is adopted to better fit with experimental data.

The axial and radial stress evolution are shown in Figure 5 for the loading stage.

The experimental data originates from [START_REF] Pizette | Compaction of aggregated ceramic powders: From contact laws to fracture and yield surfaces[END_REF]. A good fit is obtained with the values of m, 𝛽𝛽 2 and σ 𝑝𝑝𝑎𝑎𝑎𝑎𝑝𝑝. of table 1. Because we have access to both the axial and radial responses of the powder, we are able to fit the friction coefficient in the powder (μ_(aggl.)). Although less good, the fit for the radial stress is reasonable. The powder fluidity (the ratio between radial and axial stresses) is of approximately 0.5, which is typical of ceramic powders.

The friction coefficient in the powder (𝜇𝜇 𝑝𝑝𝑎𝑎𝑎𝑎𝑝𝑝. ) is the main parameter that controls fluidity.

Figure 6 shows that a larger friction coefficient is associated with a smaller fluidity. This may indirectly model the performance of an internal lubricant or of the roughness of agglomerate surface.

DEM simulations give access to the density gradient after the loading stage. For double action pressing, no experimental data is available. Thus, the density gradient of the pellet cross-section is compared with FEM simulations [START_REF] Alvain | modélisation et simulation numérique de la mise en forme de pièces par compression et frittage de poudres dures[END_REF] in Figure 7. Although DEM simulations give a 3D information, we present a 2D map to compare with axisymmetric FEM simulations. DEM simulation shows a good qualitative agreement with FEM simulation. For both methods, a larger density is predicted in the corners of the cylindrical pellet and a smaller density at the radial extremity at mid-height. This gradient is mainly dictated by the friction between the powder and the cylinder die. Figure 8 indicates that increasing 𝜇𝜇 die leads to a more pronounced density gradient. The value of 𝜇𝜇 die is a measure of the performance of the die lubrication. We have observed that after loading, the density gradient continues to evolve slightly during unloading and ejection.

Elastic energy has been stored in the pellet during compaction. The DEM elastic unloading model (Figure 3, Eqs. (7-8)) allows the axial and radial spring-back to be simulated. The amount of spring-back is essentially affected by process kinematics (axial compaction stress) and material parameters (𝐸𝐸 𝑝𝑝𝑎𝑎𝑎𝑎𝑝𝑝. and σ 𝑁𝑁 in table 1). We have observed that after pellet ejection, axial and radial elastic spring-backs are 4% and 1%, respectively.

These results are in good agreement with experimental data. The DEM simulation shows also that the pellet diameter varies slightly with the pellet height and that this variation is directly linked with the density gradient of the pellet. Experimental data could not detect or confirm this slight variation of 25 microns. Note that this diameter variation is in qualitative agreement with FEM.

Sintering

The green compact obtained from DEM is sintered up to a relative density close to unity. The final sintered geometry strongly depends on the density gradient. The sintering is slower in the regions where the local density is high and is faster in the regions where the local density is low, as the driving force for sintering scales with the remaining porosity. It generates an inhomogeneous final geometry in the pellet, the so-called diabolo effect: it densifies more in the middle of the pellet than in the top and bottom. This diabolo effect's amplitude is 40 µm for the DEM simulation and 35 µm for the experimental data.

Even though alumina thermal properties were used for the sintering process, the DEM simulation presents satisfactory results regarding the final pellet geometry. After sintering, DEM simulation indicates that a slight density gradient is still present in the pellet. This result could not be corroborated with experimental data.

Conclusion

A new DEM model was used to simulate the compaction and sintering of ceramic powders at the scale of a whole part. DEM has been chosen because it can directly take into account the powder's granular microstructure, simulating the rearrangement and the plastic deformation of agglomerates. The model chosen considers an agglomerate as a single discrete element, reducing the total number of particles to be simulated and decreasing the computational cost. Results demonstrate that an entire system can be simulated using only agglomerates without requiring billions of particles. A good agreement with experimental data and FEM simulations regarding stress-density curve, density gradient, elastic spring-back, and final geometry is obtained. As classically observed experimentally [START_REF] Lou | The Effects of Lubrication on the Density Gradient of Titanium Powder Compacts[END_REF][START_REF] Lemieux | Benefits of die wall lubrication for powder compaction[END_REF], the DEM simulations show that the friction coefficient between the powder and the die is the primary factor for the density gradient in the pellet.

DEM simulations indicate the presence of a diabolo-effect right after ejection, and it occurs due to a non-homogenous spring-back caused by the density gradient. During the sintering process, this density gradient induces non-homogeneous densification, which results in a final geometry with a so-called diabolo effect.

This work is a proof of concept for DEM to simulate correctly the evolution of a ceramic powder from the compaction stage up to the sintered stage at the length scale of an industrial part. The advantage of DEM is that a more realistic representation of the powder is modelled. In particular, DEM could be used to model composites, to investigate the effects of the initial density (before compaction) or of size distribution. Still, it should be clear that the material parameters used in the simulations need some fitting and that an experimental characterization is still necessary.

Disclosure statement

No potential conflict of interest was reported by the authors Tables Table 1. Material properties fitted for the compaction process.

𝛽𝛽 2 1 FiguresFigure 1

 11 Figures

Figure 2 -

 2 Figure 2 -a) Crystallite, aggregate, and agglomerate length scales for DEM simulations (P. Pizette [16]). b) An agglomerate represented by a single DEM sphere used here.

Figure 3 -

 3 Figure 3 -Evolution of a contact between two agglomerates using an elastoplastic model. A contact may be plastic if the overlap increases through time and is irreversible or elastic if unloading arises. A contact may snap if this overlap decreases further than a critical value. Note how the unloading stiffness increases as the plastic indentation increases.

Figure 4 -

 4 Figure 4 -a) Process kinematics of the compaction process implemented for DEM simulations, b) DEM compact before compaction, after compaction and after sintering.

Figure 5 -

 5 Figure 5 -Axial and radial stress during load for experimental data [8] and DEM simulation of powder A.

Figure 6 -

 6 Figure 6 -Influence of agglomerates' friction coefficient µaggl.. Increasing the value of this material parameter results in a less fluid powder.

Figure 7 -

 7 Figure7-Density gradient of the pellet cross-section after loading for FEM (adapted from[START_REF] Alvain | modélisation et simulation numérique de la mise en forme de pièces par compression et frittage de poudres dures[END_REF]) and DEM simulations.

Figure 8 -

 8 Figure 8 -2D density gradient of a 3D compact: influence of the friction coefficient between agglomerates and the cylinder die µdie.


François Courvoisier

Valeria Viviana Belloni

Mostafa Hassan

Maxime Pinaud

Luca Furfaro

Luc Froehly

Remo Giust

Jiafeng Lu

Matthieu Lancry

Advanced Beam Shaping for Ultrafast Laser Materials Processing

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Advanced Beam Shaping for Ultrafast Laser Materials Processing

The relentless pursuit of novel materials and nano-structures to cater to the needs of next-generation technologies necessitates innovative processing strategies to overcome current limitations. To this end, the use of complex and structured light, modulated in phase, amplitude, and polarization, has emerged as a promising approach to control laser-matter interactions. The unique capabilities of ultrafast laser pulses in generating extreme states of matter at nanometric scales are further enhanced through the shaping of ultrafast laser pulses, thereby creating new avenues for material processing. Here, we will present recent findings highlighting three distinct areas where advanced beam shaping techniques enable access to novel regimes of laser-matter interactions.

Firstly, we will focus on the manipulation of the polarization states of a Bessel beam along its propagation path. By employing laser-produced spatially-variant waveplates, we successfully generated ultrafast Bessel beams exhibiting a polarization rotation up to 90° over the beam length. This approach enabled us to demonstrate laserwritten nano gratings with chiral activity [START_REF] Lu | 3D structured Bessel beam polarization and its application to imprint chiral optical properties in silica[END_REF]. The acquired knowledge in this area will serve as a foundation for designing new optically active optical components and flat optics.

Secondly, we will present the latest results concerning the single-shot production of vertically-standing nanopillars using higher-order Bessel beams of very high angles [START_REF] Valeria V Belloni | Generation of extremely high-angle Bessel beams[END_REF]. These advancements in nanopillar fabrication contribute to the development of new high aspect ratio nanostructures. It opens a new pathway for generating positive nanostructures from materials bulk. The ease of fabrication and single-shot regime opens a number of potential applications for photonics, metamaterial or phononics components.

Lastly, we will address the ablation process in the GHz regime. The extremely high repetition rate of this regime allows for a very efficient vaporization of materials. But the areas irradiated by the laser that are below the vaporization threshold leads to excessive burr. It originates from the melting around the ablation crater, adversely affecting the process quality. To overcome this limitation, we demonstrate the effectiveness of high-precision flattop beam shaping in reducing the amount of molten material and achieving quasi-perfect ablation of silicon with very high ablation rate.

In conclusion, our findings showcase the significance of advanced beam shaping techniques for ultrafast laser materials processing, offering innovative solutions to challenges posed by traditional processing methods. These developments hold immense promise for ushering in new materials and nanostructures, facilitating the realization of cutting-edge technologies.

F 1 -

 1 FEMTO-ST Institute, CNRS, University of Franche-Comté, Besançon 25030, France 2-Institut de Chimie Moléculaire et des Matériaux d'Orsay, Université Paris Saclay, Orsay 91405, France francois.courvoisier@femto-st.fr


Kazem Ardaneh

Mostafa Hassan

Benoit Morel

Luca Furfaro

Luc Froehly

Remo Giust

François Courvoisier

Insights into the microphysics of ultrafast Bessel beam interaction with dielectrics

teaching and research institutions in France or abroad, or from public or private research centers.

Insights into the microphysics of ultrafast Bessel beam interaction with dielectrics

The creation of dense plasmas inside solids by ultrafast lasers is crucial for applications such as EUV radiation, warm dense matter study or laser materials processing. It is conventionally difficult to create large volumes of dense plasmas inside the bulk of dielectrics to benefit from pressure confinement. Here, we demonstrate that femtosecond Bessel beams generate overdense plasmas in single pulse over a very long, sub-wavelength rod. We report here on experimental and numerical investigations on the rich physics at play, that leads to extreme energy density deposition inside the solid, formation of plasma double layer, second harmonic and terahertz generation.

Conventionally, the filamentation of Gaussian beams leads to largely sub-critical densities. In contrast, using Bessel beams, the ionization dynamics triggers several specific mechanisms occurring during the interaction that leads to the extreme regime of ionization inside the bulk. The comparison between several experimental diagnostics and particle-in-cell numerical simulations allowed us demonstrating that overdense plasma can be created during a 100 fs pulse illumination of sapphire, in single shot regime. The generated plasma rod has a typical diameter of 200 nm, while its length can be scaled from tens of micrometers to centimeters. In particular, resonance absorption, which we characterized for the first time in the bulk, accounts for most of the energy deposition. Importantly, this mechanism is extremely efficient [1].

Fig. 1 (a) Electric field parallel to the polarization axis across the plasma rod. We show a trajectory of an accelerated particle that is trapped between the two double layers; (b) Experimental far-field measurement of second harmonic generation (thin ring); (c) Simulation of the radiated spectrum of the particle shown in (a), in the THz range. The blue spectrum corresponds to the particle trajectory between blue dots: it only scatters the pump. In contrast, when the particle is trapped between the double layers, THz emission appears (red curve).

Figure 1(a) shows a numerical simulation of the temporal evolution of the electric field of the Bessel beam impinging on the overcritical plasma. A high resonance is observable at the critical surface, which is the place where particles can be highly accelerated. We also observe the formation of a static electric field after the pulse, that reveals the formation of a plasma double layer on either side of the plasma rod. We have analyzed the radiation pattern emitted by the electrons. It reveals that second harmonic generation is produced during the laser-plasma interaction, which was confirmed experimentally (Fig 1b) [START_REF] Ardaneh | Femtosecond laser-induced sub-wavelength plasma inside dielectrics. II. Second-harmonic generation[END_REF]. In addition, our numerical simulations predict that the trapping of electrons within the double layer is prone to generate THz radiation [START_REF] Ardaneh | Femtosecond laser-induced sub-wavelength plasma inside dielectrics. III. Terahertz radiation emission[END_REF]. These results open up new opportunities for high energy density physics inside transparent solids, enabling unconventional states of matter in confined geometries and high plasma densities for tailored interactions.

Ardaneh, Mostafa Hassan, Benoit Morel, Luca Furfaro, Luc Froehly, Remo Giust, and François Courvoisier

	FEMTO-ST Institute, Univ. Franche-Comté, CNRS, UMR6174,
	15B avenue des Montboucons, 25030 Besançon, France

This research has been supported by H2020 European Research Council (682032-PULSAR), RENATECH CNRS, PRACE HPC resources (PRA19_4980, RA5614), HPC resource at TGCC, CEA (A0090511001, A0130511001), and Mésocentre de Calcul de Franche-Comté.


Waisudin Badri
email: waisudin.badri@univ-lyon1.fr

Mohamad Tarhini

Zineb Lgourna

Noureddine Lebaz

Hassan Saadaoui

Nadia Zine

Abdelhamid Errachid

Abdelhamid Elaissari

Preparation and Characterization of Glued Corn Flakes-Like Protein-Based Magnetic Particles

Keywords: Hybrid particles, Protein, Crosslinking, Magnetic nanoparticles, Particle size, Size distribution 

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Introduction

Based on new estimations, 10% (more than US$40 billion/ year) or over 100 approved peptide-based therapeutics of the pharmaceutical market are peptide and protein drugs. Peptides and proteins (i.e., enzymes and antibodies) are highly selective thanks to their multiple target contacts in compare to the typical small drug molecules, which form 4 UMR 5280, Institut Des Sciences Analytiques, University of Lyon, CNRS, University Claude Bernard Lyon 1, 5 Rue de la Doua, 69100 Villeurbanne, France the large part of the pharmaceutical market [START_REF] Bruno | Basics and recent advances in peptide and protein drug delivery[END_REF]. Different types of proteins were employed like building blocks in the delivery of small molecules that attract much attention thanks to their unique properties including biocompatibility, biofunctionality, and biodegradability. Indeed, proteins such as gelatin, albumin, gliadin, zein could transport drugs over the blood brain barrier [START_REF] Tarhini | Human serum albumin nanoparticles as nanovector carriers for proteins: application to the antibacterial proteins "neutrophil elastase" and "secretory leukocyte protease inhibitor[END_REF]. Nanoparticles are one of the largest groups of nanocarriers, have an important role in diagnostics and therapy [START_REF] Denkbaş | In: Grumezescu AM (Grumezescu A) Magnetically based nanocarriers in drug delivery[END_REF]. Adequate characterization of nanoparticles (NPs) is very important in order to design well-defined nanoformulations of therapeutic relevance. Indeed, nanoparticle physicochemical properties contribute towards their behavior in the biological environment [START_REF] Bhattacharjee | DLS and zeta potential-what they are and what they are not?[END_REF].

These nanoparticles are responsive to the magnetic field from the external environment and may be oriented and stimulated magnetically [START_REF] Denkbaş | In: Grumezescu AM (Grumezescu A) Magnetically based nanocarriers in drug delivery[END_REF]. Magnetic particles have been used in numerous applications and especially in the biomedical area [START_REF] Jamshaid | Preparation and characterization of submicron hybrid magnetic latex particles[END_REF]. In biomedical diagnostics, magnetic particles are used as biomolecules carriers [START_REF] Wu | Recent progress on magnetic iron oxide nanoparticles: synthesis, surface functional strategies and biomedical applications[END_REF]. The first application of magnetic particles was in immunoassays in order to replace the heaviness of the centrifugation step when latexes are Vol.:(0123456789) Waisudin Badri used. Then, various applications have been reported such as controlled drug delivery (cancer, gene, and cardiovascular therapies), hyperthermia, tissue engineering, in specific affinity separation, cells isolation and sorting, biomolecules purification, nucleic acid extraction, purification and concentration, specific capture of DNA and RNA and also as contrast agents in Magnetic Resonance Imaging (MRI) [START_REF] Denkbaş | In: Grumezescu AM (Grumezescu A) Magnetically based nanocarriers in drug delivery[END_REF][START_REF] Mandrand | In colloidal biomolecules, biomaterials, and biomedical applications (Elaïssari A, Marcel D) biomedical application for magnetic latexes[END_REF][START_REF] Cardoso | Advances in magnetic nanoparticles for biomedical applications[END_REF]. These applications have been investigated using various manufactured colloidal magnetic particles. In addition, magnetic nanoparticles can be modified trough ligands that are specific to the target organ or tissues receptor sites [START_REF] Denkbaş | In: Grumezescu AM (Grumezescu A) Magnetically based nanocarriers in drug delivery[END_REF]. It is still crucial but challenging to prepare magnetic particles with the specifications imposed by the targeted application such as quality with well controlled size, a good size distribution and a high saturation magnetization [START_REF] Xianyu | Magnetic particles-enabled biosensors for point-of-care testing[END_REF]. Generally, the obtained particles are polydisperse in nature and in some cases, the presence of both magnetic and non-magnetic particles was not excluded.

Various academic research works devoted to the preparation of hybrid magnetic particles have been also reported. In this direction, special attention was dedicated to the preparation of multi stimuli-responsive particles such as thermally sensitive hybrid magnetic. The first work in this field has been reported by Kondo et al. [10]. This work is focused on the preparation of poly(styrene/N isopropylacrylamide/ methacrylic acid) magnetic particles. The obtained hybrid particles are found to be polydisperse with low magnetic content.

Polystyrene core with magnetic shell hybrid particles have been prepared via heterocoagulation process as first reported by Furusawa et al. [START_REF] Sauzedde | Hydrophilic magnetic polymer latexes. 1. Adsorption of magnetic iron oxide nanoparticles onto various cationic latexes[END_REF]. The encapsulation of electrostatically adsorbed iron oxide nanoparticles onto polystyrene seed was performed using various recipes based on emulsion polymerization of styrene in order to avoid the release of iron oxide. Unfortunately, the final hybrid particles release iron oxide nanoparticles during storage. This original process has been extended by Sauzedde et al. [START_REF] Sauzedde | Hydrophilic magnetic polymer latexes. 2. Encapsulation of adsorbed iron oxide nanoparticles[END_REF] through performing the adsorption of iron oxide nanoparticles onto the oppositely charged polystyrene-core/crosslinked poly(Nisopropylacrylamide)-core-shell followed by the encapsulation process via seed radical polymerization [START_REF] Hunter | The calculation of zeta potential[END_REF].

In order to prepare biocompatible magnetic hybrid particles and to avoid multi-steps preparation processes, special attention has been dedicated to the use of natural polymers in the formulation processes [START_REF] Denkbaş | In: Grumezescu AM (Grumezescu A) Magnetically based nanocarriers in drug delivery[END_REF]. Natural polymers are used in recent years as coating matrices since they are capable of increasing the stability and the biocompatibility of magnetic nanoparticles. Xie et al. [START_REF] Xie | Human serum albumin coated iron oxide nanoparticles for efficient cell labeling[END_REF] developed a dopamineplus-HSA (human serum albumin) approach to modify iron oxide nanoparticles for the labeling of various cell types in a nonspecific manner. Their efficiency was demonstrated by in-vivo magnetic resonance imaging on xenograft and focal cerebral ischemia models. More recently, Nosrati et al. prepared bovine serum albumin (BSA)-coated magnetic nanoparticles as curcumin carriers through desolvation and chemical co-precipitation process [START_REF] Nosrati | Bovine serum albumin (BSA) coated iron oxide magnetic nanoparticles as biocompatible carriers for curcumin-anticancer drug[END_REF]. The structural, colloidal and magnetic properties of the BSA-coated Fe3O4 nanoparticles loaded with curcumin were characterized and their cytotoxicity against breast cancer cells was investigated. Instead of using BSA, Chang et al. employed human-like collagen (HLC) protein as a coating material and explored the size and surface effects of the HLC-coated magnetic nanoparticles on the magnetic hyperthermia heating characteristics [START_REF] Chang | The efficiency of magnetic hyperthermia and in vivo histocompatibility for human-like collagen protein-coated magnetic nanoparticles[END_REF]. It has been shown that HLC coating enhanced the specific absorption rate (SAR) of the HLCnanoparticles significantly and improved the biocompatibility of the nanoparticles. Khramtsov et al. functionalized the nanoclusters of carbon-coated iron nanoparticles with four different proteins including BSA, casein and two types of gelatins for application in biosensing [START_REF] Khramtsov | Magnetic nanoclusters coated with albumin, casein, and gelatin: size tuning, relaxivity, stability, protein corona, and application in nuclear magnetic resonance immunoassay[END_REF]. They demonstrated that the protein-coated magnetic nanoparticles maintain their size in complex media such as juice, milk, serum and plasma and at elevated temperatures. This facilitates their application in homogeneous assays of biomarkers and foodborne pathogens and their applicability may be extended to in-vivo diagnostics and numerous medical applications as reported by Bealer et al. [START_REF] Bealer | Protein and polysaccharide-based magnetic composite materials for medical applications[END_REF].

It is worth mentioning that the colloidal properties of particles (organic, inorganic and composite, etc.) are a crucial challenge facing especially users of magnetic colloids in biomedical applications. In fact, only the colloidal characterization of a given dispersion could help the preparation process, the optimization of biological assays and the particles integration in biological processes (i.e. nanotechnologies-based microsystems, in-vivo circulation of particles, etc.). In addition, the complete colloidal characterization of a prepared dispersion reveals the preparation quality and in some cases the synthesis mechanism. Then, before any application of colloidal particles, the dispersion and the particles require to be characterized in terms of size and size distribution, surface charge density, surface polarity, morphology, electrokinetic properties and colloidal stability. To some extent, all these properties are part of a systematic investigation in colloids science in which particles are generally used as a model colloid, a solid support for biomolecules, and/or a label for revealing the capture of targeted biomolecules.

In this work, to tackle this challenge, we focused on the complete characterization of the prepared BSA-iron oxide colloidal particles concerning particle size and size distribution, morphology, chemical composition, electrokinetic properties, magnetic properties (i.e. magnetic content and saturation magnetization) and colloidal stability.

Experimental

Materials

Ferrous chloride (FeCl2), ferric chloride (FeCl3), hydrochloric acid, ammonia, BSA protein and phosphate buffer were supplied by Sigma-Aldrich (Germany). Deionized Milli-Q water was used in all experiments as the dispersion medium.

Preparation of BSA-Based Iron Oxide Colloidal Particles

BSA-based iron oxide colloidal particles were prepared according to the well-known precipitation-crosslinking process. The precipitation was due to the reaction of FeCl2 and FeCl3 in highly basic medium and the crosslinking and the coating were induced by BSA at the preparation temperature (i.e. 70 °C). The crude magnetic dispersion was sorted (via sedimentation and magnetic separation) in order to obtain narrow size distributed magnetic particles. The synthesis of ferrofluid was carried out at 20 °C in a thermostatically controlled reactor of 500 mL (without cover) equipped with a mechanical stirring system composed from an anchor with three branches. FeCl2 and FeCl3 were firstly dissolved in hydrochloric acid (1 M).

Once the dissolution of iron salts has completed (orangecolored homogeneous solution), concentrated ammonia (20%) was rapidly added into the reactor under strong agitation (1000 round per minute). The immediate appearance of a black precipitate corresponds to the ferrous oxide formation. The coprecipitation reaction was continued in the ammoniacal medium during one hour (the pH of reaction media was consequently near to 9). The particles were washed after decantation and finally redispersed in water to obtain a stable ferrofluid.

Prepared BSA in a 10 -2 M phosphate buffer was consecutively added directly in the reactor. One hour after, the reaction media was heated up to 70 °C. Then the mixture was placed on the magnetic agitation plate for two hours. The covered iron oxide nanoparticles by the dispersed BSA in the aqueous phase were collected after first sedimentation process, by the application of a permanent magnetic field using strong magnet and the precipitate was removed.

Characterization

Hydrodynamic Particle Size Analysis

Hydrodynamic particle size was measured by Quasi-Elastic Light Scattering (QELS) using the Zetasizer 3000HS from Malvern Instrument (Malvern, UK). The hydrodynamic diameter of a highly diluted magnetic dispersion in 1 mM NaCl was measured. The colloidal stability was investigated by measuring the particle size as a function of salt concentration after 10 min incubation. The samples were prepared using deionized Milli-Q water. The mean hydrodynamic diameter Dh was then calculated from the diffusion coefficient measurement using the Stokes-Einstein equation:

where D is the diffusion coefficient, k the Boltzmann constant, T the absolute temperature, and η the dynamic viscosity of the medium. The particle size and size distribution were determined using Contin analysis mode.

Transmission Electron Microscopy

Transmission electron microscopy (TEM) was carried out using a Hitachi electron microscope (Hitachi S 800, CME-ABG at Claude Bernard University Lyon 1, France). The particles morphology was examined deposing one droplet of magnetic dispersion on TEM grid and then dried before analysis.

Electrophoretic Mobility Measurement

The electrophoretic mobility of the prepared dispersions was measured using the ZetaSizer 3000HS, from Malvern Instruments. The experiments were carried out using highly diluted dispersions in aqueous 1 mM NaCl solution or in 1 mM phosphate buffer solution at pH = 6. The electrophoretic mobility was determined as a function of pH (at a constant ionic strength) and as a function of salt concentration at a stable pH (1 mM phosphate buffer, pH 6). In this study, the electrophoretic mobility (µe) values were converted to the zeta potential (ζ) using the classical Smoluchowski's Eq. ( 2)

Where 0 and r are the permittivity of vacuum and relative permittivity of the medium respectively.

All the measurements were at least the average of triplicate values and performed at 25 °C.

Thermogravimetric Analysis (TGA)

To determine chemical composition, thermogravimetric analysis was used. An Atomic Emission Spectrometer equipped with the Plasma and inductive coupling or Inductively Coupled Plasma (ICP), was used to determine the amount of organic and inorganic materials forming the prepared BSA-based magnetic particles. Measurements were 1 3 performed under nitrogen atmosphere for about 10 mg of samples in a dried state between 25 °C and 550 °C at a heating rate of 10 °C/min (TGA from AT Instruments).

Magnetic Properties (Saturation Magnetization)

The saturation magnetization (Ms) and magnetic behavior of the dried BSA-magnetic particles were investigated using a vibrating sample magnetometer. This study was carried out on the Automatic Bench of magnetic measurements, CNRS-IRC Lyon. Magnetization of dried particles was investigated by increasing the magnetic field (H) from zero to + 21,000 Oersted at room temperature.

Results and Discussion

Composition

The organic content of the magnetic material was deduced by thermogravimetric (TGA) measurements performed under nitrogen with a heating rate of 10 °C/min until 550 °C. Weight loss occurring under 550 °C can be attributed to the BSA fixed at the particles surface. Then, the non-calcinated material can be considered as residual inorganic material and corresponds to iron oxide. The amount of inorganic material was found to be about 73% w/w as deduced from the weight loss as a function of temperature illustrated in Fig. 1. It is worth mentioning that the analysis was performed on BSAbased iron oxide dispersion after total removal of both BSA molecules and primary magnetic nanoparticles.

Particle Size and Size Distribution

The size and size distribution of magnetic particles are critical, especially in the case of medical applications. For instance, Wang et al. pointed out the impact of superparamagnetic nanoparticle size on the performance of lateral flow immunoassay [START_REF] Wang | Study of superparamagnetic nanoparticles as labels in the quantitative lateral flow immunoassay[END_REF]. Hence, to tune the size of BSAcoated nanoclusters, variations in pH could be applied [START_REF] Khramtsov | Conjugation of carbon coated-iron nanoparticles with biomolecules for NMR-based assay[END_REF]. Protein-coated nanoparticles are sensitive to sonication. This parameter may be used for nanoparticle size manipulation as reported by Sangeetha and Philip [START_REF] Sangeetha | The interaction, stability and response to an external stimulus of iron oxide nanoparticle-casein nanocomplexes[END_REF] and Khramstov et al. [START_REF] Khramtsov | Magnetic nanoclusters coated with albumin, casein, and gelatin: size tuning, relaxivity, stability, protein corona, and application in nuclear magnetic resonance immunoassay[END_REF].

In the case of our study, hydrodynamic particle size and size distribution of highly diluted dispersions were examined using dynamic light scattering. The average hydrodynamic diameter was found to be around 140 nm ± 20 nm, with a narrow size distribution ranging from 100 to 175 nm as reported in Fig. 2. Since the hydrodynamic particles size is below 900 nm, no sedimentation was observed even after few days' storage.

As clearly shown from light scattering analysis, the obtained hydrodynamic particle size is larger than the size of individual primary iron oxide magnetic particles which is in between 8 and 12 nm [START_REF] Montagne | Preparation and characterization of narrow sized (o/w) magnetic emulsion[END_REF]. This result explains basically the formation of submicron clusters. If individual particles of iron oxide are coated by adsorbed BSA, the particles size should be not far from the hydrodynamic size of individual particles except in the presence of some aggregated particles as reported by Nosrati et al. [START_REF] Nosrati | Bovine Serum Albumin (BSA) coated iron oxide magnetic nanoparticles as biocompatible carriers for curcumin-anticancer drug[END_REF]. In fact, by using BSA for individual iron oxide magnetic nanoparticles coating, they obtained particles of around 56 ± 11 nm. However, this mean size is calculated by image processing based on TEM [START_REF] Nosrati | Bovine serum albumin (BSA) coated iron oxide magnetic nanoparticles as biocompatible carriers for curcumin-anticancer drug[END_REF]. Functionalized nanoclusters of carbon-coated iron magnetic nanoparticles with BSA were prepared following the protocol described by Mikhalev et al. [START_REF] Khramtsov | Magnetic nanoclusters coated with albumin, casein, and gelatin: size tuning, relaxivity, stability, protein corona, and application in nuclear magnetic resonance immunoassay[END_REF][START_REF] Mikhalev | Magnetic state and phase composition of carbon-encapsulated Co@C nanoparticles according to 59Co, 13C NMR data and Raman spectroscopy[END_REF]. They obtained nanoclusters whose mean sizes is ranging from 114 to 233 nm in the different tested cases. These results are via adsorption at room temperature and not via BSA crosslinking process at high temperature. Consequently, even if the reported sizes are in agreement with the mean diameter obtained in our study which is around 145 nm, the preparation processes conditions are different [START_REF] Khramtsov | Conjugation of carbon coated-iron nanoparticles with biomolecules for NMR-based assay[END_REF].

Electrokinetic Study

Surface charge affects the stability of the protein-based magnetic particles and their behavior when dispersed in a given biological fluid such as blood for example. The interactions between the particles themselves and between the particles and biological entities (cells, proteins, etc.) will be affected by the nature of the surface charge of the particles, the particles surface charge density and the surface polarity [START_REF] Clement | Differential interaction of magnetic nanoparticles with tumor cells and peripheral blood cells[END_REF]. It is then crucial to determine the electrokinetic properties of the magnetic nanoparticles in different conditions of pH and salinity, which mimic the properties of the intended application media.

The electrophoretic mobility (µe) of the prepared BSAbased magnetic particles was first measured as a function of pH in a 1 mM NaCl buffer at 25 °C. The obtained values were converted into zeta potential using Eq. ( 2). The zeta potential values of highly diluted BSA-based magnetic particles as a function of pH and at a constant ionic strength (1 mM NaCl) are presented in Fig. 3. The zeta potential values are found to be positive at acidic pH until pH 6 and then negative above pH 6. The positive zeta potential can be attributed to the protonation of amine groups and the Fig. 3 Zeta potential of the BSA-coated magnetic particles versus pH in 1 mM NaCl, at 25 °C negative one can be attributed to the dissociation of carboxylic group. Such zeta potential profile was induced by the BSA molecules rather than the surface charges on primary iron oxide nanoparticles. In fact, BSA molecules are highly charged above and below pH 6.5. This isoelectrical pH (pH 6.5) of the formulated particles was found to be the same as for BSA molecules [START_REF] Bukackova | Mathematical methods in the calculation of the zeta potential of BSA[END_REF].

The high zeta potential values at acidic or basic pH should confer to prepared particles appreciable colloidal stability in the pH domain bellow pH 5 and above pH 7. The measured zeta potential at pH 6 reflects the low surface charge density. It is interesting to notice that no aggregation phenomenon was observed. The observed colloidal stability can be attributed to hydration forces induced by the protein shell [START_REF] Valle-Delgado | Evidence of hydration forces between proteins[END_REF].

Nosrati et al. obtained a zeta potential of -10.1 mV by analysing their BSA-coated magnetic particles loaded with curcumin in phosphate buffered (10 mM, pH 7.4) [START_REF] Nosrati | Bovine serum albumin (BSA) coated iron oxide magnetic nanoparticles as biocompatible carriers for curcumin-anticancer drug[END_REF]. The observed difference in zeta potential can be attributed to the difference in salinity of the measurement medium and also to the non-crosslinking of BSA-coated magnetic particles reported by Nosrati et al. [START_REF] Nosrati | Bovine Serum Albumin (BSA) coated iron oxide magnetic nanoparticles as biocompatible carriers for curcumin-anticancer drug[END_REF].

The zeta potential was also investigated as a function of salinity at a constant pH of 4.5 and the obtained results are reported in Fig. 4. The average zeta potential decreases as the ionic strength increases; this trend is theoretically expected. This is due to the changes in the slipping plan corresponding to the zeta potential induced by decreasing κ-1 (the Debye length) [START_REF] Hunter | The calculation of zeta potential[END_REF].

Colloidal Stability

Colloidal stability of any colloidal dispersion to be used for both in-vivo and in-vitro biomedical application is of 1 3 Fig. 4 Zeta potential of the prepared BSA-based magnetic particles versus NaCl concentration at pH 4.5 and at 25 °C Fig. 5 Hydrodynamic particle size versus NaCl concentration in solution of pH 4.37, at 25 °C paramount importance. Colloidal stability was examined by measuring the hydrodynamic particle size as a function of salt concentration at a constant pH of 4.37 and after 1 h storage. As clearly seen from Fig. 5, the aggregation phenomenon of magnetic particles appears above 10 mM salt concentration, which is encouraging principally for the majority of biomedical applications. The observed aggregation can be attributed to the screening of the repulsive electrostatic interactions between particles. Using such static colloidal stability methodology, the critical coagulation concentration, the Hamaker constant and the surface potential are not reachable experimentally as generally reported for this new colloidal dispersion [START_REF] Montagne | Colloidal and physicochemical characterization of highly magnetic o/w magnetic emulsions[END_REF][START_REF] Nabzar | Electrokinetic properties and colloidal stability of cationic amino-containing N-isopropylacrylamide-styrene copolymer particles bearing different shell structures[END_REF]. In fact, the aggregation kinetic study should be considered.

The colloidal stability of such crosslinked protein-based magnetic particles has never been investigated. Whilst, the colloidal stability of polymer particles bearing adsorbed BSA has been investigated as reported by Molina-Bolivar et al. [START_REF] Molina-Bolívar | Colloidal stability of protein-polymer systems: a possible explanation by hydration forces[END_REF]. The reported results show that the hydration forces ensure the colloidal stability of the particles. This difference can be attributed to the nature of interfacial BSA molecules; in one case they are totally denaturated and crosslinked and the reported case, the BSA molecules are not folded and denaturated.

Surface Charge Density

The surface charge density of such particles cannot be determined using classical conductometry and pH titrations [START_REF] Elaïssari | Colloidal biomolecules, biomaterials, and biomedical applications (Elaïssari A, Marcel D) colloidal polymers[END_REF]. This is due to the possible titration of buried of comment chemical compounds such as carboxylic, amine, and hydroxyl groups. If we assume that the particles are perfectly coated with BSA molecules, the surface charge density is a combination of both amine and carboxylic groups. Consequently, the surface charge density can be estimated from the conversion of zeta potential to surface potential and then to surface charge density as reported for similar complex systems [START_REF] Montagne | Colloidal and physicochemical characterization of highly magnetic o/w magnetic emulsions[END_REF]. This gives in the case of our prepared crosslinked BSA-based magnetic particles a surface charge density in between -6.6 and -7.5 µC/cm2 in a highly basic conditions (pH between 10 and 12). In this pH range, the amine groups are totally deprotonated and the measured zeta potential can be attributed to the dissociation of carboxylic groups only. Then the density of carboxylic groups on the formulated particles can be estimated to be above -6.6 µC/ cm2. Whereas, the surface charge density deduced from zeta potential determined below pH 4.0 can be attributed to the protonated amine only and was found to be around + 7. 0 µC/cm2.

Morphology Analysis

The particles morphology was examined using various microscopic techniques such as transmission electron microscopy (TEM) and atomic force microscopy (AFM) in order to study the shape and the surface texture of the particles.

The particles shape was first examined using TEM and the obtained micrograph is presented in Fig. 6. Using such technique, to some extent, the particles can be considered spherically shaped as showed in a study performed by Talha et al. [START_REF] Jamshaid | Tailoring of carboxyl-decorated magnetic latex particles using seeded emulsion polymerization[END_REF]. It is interesting to notice that using TEM to examine such small complex nanoparticles is problematic. To confirm the light scattering measurement, TEM was carried out. Surprisingly, the particles cannot be individually Fig. 6 Transmission electron micrograph of clustered magnetic nanoparticles observed under appreciable resolution in order to determine the particle size as illustrated in the TEM micrograph. In addition, the sharpness of the viewed particles cannot be exactly defined. This observed behavior can be attributed to (i) low particle size of such particles and (ii) the presence of a protein shell around not only primary iron oxide nanoparticles but also the formed clusters. We can only deduce from the presented micrographs that the formulated BSA-based iron oxide particle size can't be considered as homogeneously size distributed (monodisperse) and cannot be considered as spherical particles. The observed separate clusters mean size is close to the one determined by light scattering. It is interesting to mention that BSA can be seen by TEM even under crosslinking state. In addition, possible flatness and fragmentation of the cluster and sample preparation of such clusters is questionable.

Atomic force measurements (AFM) were also performed in contact mode. The appearance of blobs smooth surface explains the presence of a homogeneous protein shell around the associated iron oxide nanoparticles, but the surface morphology of the cluster is not spherical and not smooth too. The BSA-based magnetic particles can be considered as an association of at least 10 blobs of 40 nm size as clearly evidenced by TEM (Fig. 6) and the particle size deduced from AFM (Z average, Fig. 7) is found to be in between 136 and 165 nm.

Magnetic Properties

Magnetic properties of BSA-based magnetic nanoparticles were examined using a classical magnetization method. The magnetization of nanoparticles was recorded in an applied magnetic field of H(Oe) ≤ 21,000 at room temperature. Indeed, TGA and magnetization measurements are complementary approaches to characterize the magnetic hybrid colloidal particles [START_REF] Tenório-Neto | TGA and magnetization measurements for determination of composition and polymer conversion of magnetic hybrid particles[END_REF].

Firstly, the magnetization curve (Fig. 8) follows the Langevin function with no remanence (residual magnetization), which proves the superparamagnetic behavior of the magnetic material, which is an interesting property in various applications and principally in the biomedical Fig. 8 Magnetization curve of the BSA-coated magnetic nanoparticles as a function of the applied field 1 3 field. The maximum magnetization deduced from the plateau value revealed the non-negligible magnetic properties of the particles since the magnetization at saturation is around 40 emu/g. Then, by assuming that such particles are principally from Fe2O3-based (79.6 emu/g) and by using the magnetization at the plateau value of BSA-based magnetic particles (40 emu/g), the amount of iron oxide material is found to be around 50% w/w. This value is lower than the chemical composition determined by TGA study (i.e. 73% w/w) as above discussed. This difference can be attributed to: (i) the presence of non-magnetic inorganic material such ferric and ferrous hydroxides and (ii) low magnetic Fe3O4 or gamma-Fe2O3 content in the composite particles. In fact, TGA is based on calcination of organic material and magnetization is based on the magnetic property of the used material (i.e. maghemite and magnetite).

Note that the maximum magnetization in our case is the same as that obtained by Nosrati et al. [START_REF] Nosrati | Bovine Serum Albumin (BSA) coated iron oxide magnetic nanoparticles as biocompatible carriers for curcumin-anticancer drug[END_REF] for BSA-coated iron nanoparticles which was around 35 emu/g at a magnetic applied field of 104 Oe [START_REF] Nosrati | Bovine serum albumin (BSA) coated iron oxide magnetic nanoparticles as biocompatible carriers for curcumin-anticancer drug[END_REF]. In the last study, the nanoparticles were loaded with curcumin which reduced further their magnetization. The reduction of the nanoparticles magnetization when coated with BSA is due to protein layer as explained by Maboudi et al. [START_REF] Maboudi | Synthesis and characterization of multilayered nanobiohybrid magnetic particles for biomedical applications[END_REF].

Conclusion

Structural, colloidal and magnetic properties of the formulated BSA protein-based iron oxide nanoparticles were characterized in this study after few fractionations. The particle size was found to be submicronic with a mean hydrodynamic diameter of around 145 nm. The particles morphology was investigated via TEM and AFM and found to be non-spherical but glued corn flakes-like morphology, which reflects the non-controllable heterocoagulation mechanism involved in the formation of the final particles. The colloidal stability of the prepared BSA-based particles prepared at high temperature is low compared to particles coated with BSA via adsorption at room temperature. This has been attributed to the protein crosslinked nature and denaturation in the case of high temperature. Regarding chemical composition, a high difference has been observed between TGA and magnetization results. In fact, TGA analysis revealed that the BSA-based iron oxide nanoparticles contain about 70% w/w iron oxide, whereas only 50% w/w was determined by magnetization. In addition, the prepared BSA-based iron oxide particles exhibited superparamagnetism, even if some of the magnetic properties are lost. Nevertheless, the residual magnetization is sufficient to be used in biomedical separation and drug targeting applications.

Fig. 1 Fig. 2

 12 Fig. 1 Thermogram of dried BSA-based magnetic particles obtained by TGA analysis

Fig. 7

 7 Fig. 7 Atomic Force Microscopy (AFM) images of BSA-based magnetic particles before (left) and after (right) image processing

Acknowledgements

The authors acknowledge Mr. Hassan Saadaoui from CRPP Bordeaux for his contribution in AFM analysis of this study.

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.