Yrieix

E Guesnet

B Bénane

D Jauffrès

C L Martin

G P Baeza

G Foray

S Meille

C Olagnon

B Yrieix

Why fumed and precipitated silica have different mechanical behavior: Contribution of discrete element simulations

Keywords: Discrete Element Method, Vacuum Insulation Panels, powder compaction, nanostructured silica, fractal aggregates

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

Introduction

Energy consumption to heat or cool buildings is an important contributor to greenhouse gas emission and leads to other environmental damages.

Efficient insulation can largely contribute to reduce the amount of energy required. While in many countries new constructions are low-energy ones thanks to regulations imposing efficient insulation, old buildings are often badly insulated and need to be retrofitted. Thermal retrofitting of housing is an important lever for the reduction of greenhouse gas emissions.

A wide range of retrofitting materials and techniques exists on the market, the most commons being mineral wool and expanded polystyrene foam. Their thermal conductivity varies between λ = 30 to 35 mW/(m.K) for a cost of 10 to 15e/m 2 (for a thermal resistance R T = 3 m 2 K/W). For the same insulation performance, a larger thickness is required for materials with higher thermal conductivity. While having a thick layer is generally not too detrimental for insulation from the outside, insulation from the inside is often required (outside space shortage, conservation of the original historical facade) and thick insulation layer is in this case a barrier to thermal retrofitting.

Thin panel for insulation from the inside can only be achieved with super-insulation materials (λ < 25 mW/(m.K)). The most mature super-insulation technology, Vacuum Insulation Panels (VIP), consists of a highly porous nanostructured silica core wrapped under vacuum (pressure ≤ 5 mbar) inside a sealed envelope [START_REF] Kalnaes | Vacuum insulation panel products: A state-ofthe-art review and future research pathways[END_REF][START_REF] Simmler | HiPTI -High Performance Thermal Insulation IEA/ECBCS Annex 39[END_REF][START_REF] Fricke | Vacuum insulation panels From research to market[END_REF]. VIP cost is high (> 100e/m 2 [START_REF] Alam | Energy and economic analysis of Vacuum Insulation Panels (VIPs) used in non-domestic buildings[END_REF]), mainly because of the nanostructured silica core, but thermal conductivities as low as 5 mW/(m.K) are reached. Even if a cost analysis including the saved floor area makes VIP an economically viable choice in high housing price areas [START_REF] Alam | Energy and economic analysis of Vacuum Insulation Panels (VIPs) used in non-domestic buildings[END_REF][START_REF] Johansson | Building Retrofit using Vacuum Insulation Panels[END_REF], their high initial cost is detrimental for their wider use. The nanostructured nature of the silica core is essential in VIP as it allows the reduction of thermal conductivity by the Knudsen effect [START_REF] Zeng | Transport properties of gas in silica aerogel[END_REF][START_REF] Yrieix | VIP service life assessment: Interactions between barrier laminates and core material, and significance of silica core ageing[END_REF], which leads to significantly longer service life than non-nanostructured materials such as glass fibers [START_REF] Alam | Energy and economic analysis of Vacuum Insulation Panels (VIPs) used in non-domestic buildings[END_REF]. The use of precipitated silica (PS) in place of fumed (also called pyrogenic) silica (FS) as nanostructured core material would significantly reduce the cost of VIP [START_REF] Simmler | HiPTI -High Performance Thermal Insulation IEA/ECBCS Annex 39[END_REF]. Precipitated silica is indeed a widely available material, in particular because of its use as a filler in the tire industry [START_REF] Baeza | Multiscale filler structure in simplified industrial nanocomposite silica/SBR systems studied by SAXS and TEM[END_REF]. Also, because of its production by a low temperature process, PS may help to decrease the embodied energy of VIP [START_REF] Karami | A comparative study of the environmental impact of Swedish residential buildings with vacuum insulation panels[END_REF]. Indeed, FS is obtained from an energy consuming high temperature (> 1200 • C) pyrolysis of silicon tetrachloride. Primary particles of 7 to 50 nm in diameter form in flame and coalesce in stable aggregates [START_REF] Ulrich | Flame synthesis of fine particles[END_REF]. Polydispersity in primary particle size arises from temperature gradients in flame and has been observed within a single aggregate by Transmission Electron Microscopy (TEM) [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF]. The aggregates have a fractal morphology [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF][START_REF] Wengeler | Characterizing dispersion and fragmentation of fractal, pyrogenic silica nanoagglomerates by small-angle X-ray scattering[END_REF] with a fractal dimension that may vary depending on the flame temperature and other process parameters. Aggregates also exhibit a polydispersity in size as shown by Small Angle X-ray Scattering (SAXS) [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF]. The silica surface is made of both silanol groups (Si-OH) and siloxane bridges (Si-O-Si) leading to an intermediate hydrophilic character [START_REF] Chal | Nanostructured silica used in super-insulation materials (SIM), hygrothermal ageing followed by sorption characterizations[END_REF]. PS are obtained via acid or base precipitation in an aqueous solution of silicates, resulting in a more hydrophilic surface with a high density of silanol groups. The primary particle size is slightly larger than for FS [START_REF] Roiban | Advanced three dimensional characterization of silica-based ultraporous materials[END_REF] and the fractal dimension is also generally larger than for FS [START_REF] Baeza | Multiscale filler structure in simplified industrial nanocomposite silica/SBR systems studied by SAXS and TEM[END_REF][START_REF] Schaefer | Structure optimization in colloidal reinforcing fillers: precipitated silica[END_REF]. Aggregates of FS and PS form at a larger scale agglomerates (few hundred nanometers) and then powder grains at the macroscale (few microns). However, the mechanical properties of VIP core made of precipitated silica appear very limited. It has been shown for example that to reach a compressive strength of 100 kPa (considered as a minimum required for handling and vacuuming), PS has to be compacted to at least 220 kg/m 3 versus 160 kg/m 3 for FS [START_REF] Simmler | HiPTI -High Performance Thermal Insulation IEA/ECBCS Annex 39[END_REF]. A recent study by instrumented indentation confirms the lower mechanical properties of PS compacts with indentation modulus half as low for PS as for FS for a similar apparent density [START_REF] Benane | Instrumented Indentation of Super-Insulating Silica Compacts[END_REF]. Thermal conductivity greatly depends on the core material density hence the need of a larger compaction density, or the addition of reinforcing fibers, for PS core degrades strongly thermal properties. In short, the thermal/mechanical compromise is presently not optimal to allow the replacement of FS by PS.

Fumed and precipitated silica are nonetheless very similar materials and the origin of the observed differences in mechanical behavior is not clear. It has been suggested that the aspect ratio of the aggregates and their capacity to entangle influence the mechanical behavior [START_REF] Benane | Instrumented Indentation of Super-Insulating Silica Compacts[END_REF]. Differences in surface chemistry and primary particle size also play a role [START_REF] Wang | Fluidization and agglomerate structure of SiO2 nanoparticles[END_REF]. Last, the influence of ageing should also be considered. While the influence of ageing on the ther-mal properties and the service life time has been studied [START_REF] Yrieix | VIP service life assessment: Interactions between barrier laminates and core material, and significance of silica core ageing[END_REF][START_REF] Chal | Nanostructured silica used in super-insulation materials (SIM), hygrothermal ageing followed by sorption characterizations[END_REF], the effect of ageing on mechanical properties has been less investigated. A better understanding of the mechanical behavior in relation with aggregate morphology and surface chemistry would be highly valuable to improve the mechanical properties of precipitated silica. Conversely to FS and PS compacts, the mechanical behavior of silica aerogels have been extensively studied through both experiments and modeling [START_REF] Wong | Mechanical properties of monolithic silica aerogels made from polyethoxydisiloxanes[END_REF][START_REF] Woignier | Mechanical Properties and Brittle Behavior of Silica Aerogels[END_REF][START_REF] Liu | Simulation of the tensile properties of silica aerogels: the effects of cluster structure and primary particle size[END_REF][START_REF] Ferreiro-Rangel | Investigation of the bulk modulus of silica aerogel using molecular dynamics simulations of a coarse-grained model[END_REF][START_REF] Gonçalves | Elasticity and strength of silica aerogels: a Molecular Dynamics study on large volumes[END_REF][START_REF] Gonçalves | Nanocompression of secondary particles of silica aerogel[END_REF][START_REF] Patil | Mechanics of nanostructured porous silica aerogel resulting from molecular dynamics simulations[END_REF]. In particular, the necklace structure of primary particles have motivated mesoscale modeling using the Discrete Element Method (DEM) [START_REF] Liu | Simulation of the tensile properties of silica aerogels: the effects of cluster structure and primary particle size[END_REF] and coarse-grained molecular dynamics [START_REF] Ferreiro-Rangel | Investigation of the bulk modulus of silica aerogel using molecular dynamics simulations of a coarse-grained model[END_REF]. Also, the significant impact of surface energy on mechanics in these nanostructured highly porous materials has been demonstrated by molecular dynamics [START_REF] Gonçalves | Elasticity and strength of silica aerogels: a Molecular Dynamics study on large volumes[END_REF].

In this work, a better understanding of the peculiar contrasted mechanical behavior of FS and PS is sought based on macroscale experimental mechanical characterization and mesoscale DEM modeling. In particular, the use of DEM allows independent assessment of the influence of various morphological or material parameters such as fractal dimension, primary particle size, aggregate size, neck size and surface energy. The paper is organized as follows.

First, the mechanical behaviour of FS and PS is investigated experimentally during oedometric compaction to confirm and measure the differences between both silica. Experiments will also be used for comparison with modeling. The modeling approach and the contact laws are detailed in section 3. The generation of realistic numerical samples, based on recent morphological characterization of the nanostructured silica [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF][START_REF] Benane | Mécanique des lits de silices granulaires pour l'optimisation des coeurs de panneaux isolants sous vide (PIV)[END_REF], is described in section 4. Results are presented in section 5 and discussed in section 6.

Experimental characterization

Materials and methods

A commercial FS (Konasil 200, OCI, Korea) and two commercial PS (Tixosil 365 & Tixosil 43, Solvay, France) have been investigated. While the FS silica has a hydrophobic character (1 to 2.5 OH/nm 2 [START_REF] Zhuravlev | The surface chemistry of amorphous silica. Zhuravlev model[END_REF][START_REF] Hair | Adsorption on hydroxylated silica surfaces[END_REF]28]), the PS silicas are highly hydrophilic (4 to 16 OH/nm 2 [START_REF] Hair | Adsorption on hydroxylated silica surfaces[END_REF][START_REF] Legrand | The surface properties of silicas[END_REF]). The intrinsic (skeletal) densities reported by the manufacturers are 2200 kg/m 3 for the FS and 2100 kg/m 3 for the PS. Oedometric compression tests were performed with a 20 mm diameter cylindrical die using a sapphire pellet in contact with the powder to ensure a flat surface. The same initial mass of powder was used for the three silicas. A conventional testing machine (Zwick-Roell, Germany) was used and the displacement of the punch was recorded with a LVDT sensor. The crosshead speed was 10 mm/min during loading and 5 mm/min during unloading. The same maximum force (400 N, leading to a maximum pressure of 1.27 MPa) was used for all powders. This value was chosen to obtain final pellets with a density close to what is required for the final application (i.e. 200 kg/m 3 for FS [START_REF] Fricke | Vacuum insulation panels From research to market[END_REF]). It must also be mentioned that the silica powder compaction behavior is highly sensitive to humidity and temperature during the test. The conditions of the tests were similar in terms of relative humidity (35% to 45%) and temperature (20 • C to 24 • C) between the three silicas.

Results

The initial relative densities (volume fractions of solid) after pouring the powder in the die were ca. 3% for Konasil 200, and 7.5% for T365 and T43 silica powders. This simple observation already demonstrates significant differences between FS and PS, the former having a significantly lower initial relative density. The compaction curves (average over several tests) are displayed in Fig. 1. A significant difference in compaction behavior of FS and PS is observed, with the FS being significantly harder to compact. The final densities reached after a 1.27 MPa compaction are ca. 290 kg/m 3 (≈ 13%) for PS compacts versus ca. 210 kg/m 3 (≈ 10%) for FS compacts. The oedometric elastic modulus has also been assessed during the first 10% of unloading:

22.4 ± 0.5 MPa, 17.5 ± 1.0 MPa and 18.7 ± 1.0 MPa for Konasil 200, Tixosil 43 and Tixosil 365 respectively. These values are not directly comparable as the difference in density at 1.27 MPa is large between FS and PS. Still, it is remarkable that even at a significantly lower density the FS compact is stiffer than the PS one. Directly comparable data was obtained from iso-density compaction of the three powders to ca. 10%. Compaction pressure and oedometric modulus at 10% density are reported in Table 1 and confirm that FS compacts are significantly stiffer than PS ones. These results are consistent with a recent instrumented indentation study showing that, for a similar density of compacts ca. 10%, FS is twice stiffer than PS [START_REF] Benane | Instrumented Indentation of Super-Insulating Silica Compacts[END_REF]. The measurement of tensile strength of the compacted silica pellets is a challenging task. Still, preliminary biaxial flexural test have shown that for a density of 200 kg/m 3 PS exhibits extremely low strength (< 0.1 MPa), 3 to 5 times lower than FS (ca. 0.3 MPa) at the same density .These results confirm the contrasting behavior between the two types of nanostructured silica. The classical DEM approach [START_REF] Cundall | A discrete numerical model for granular assemblies[END_REF] is used with Hertzian and bonded contacts [START_REF] Potyondy | A bonded-particle model for rock[END_REF]. In DEM the dynamic motion of discrete entities (generally spherical particles) is computed by an explicit time integration of the second law of Newton. Each particle transmit forces to its neighbors through their con-

tacts. The open source version of LIGGGHTS R [START_REF] Kloss | Models , algorithms and validation for opensource DEM and CFD-DEM[END_REF] was used with our own implementation of bonded contacts and numerical damping. For postprocessing and visualization OVITO [START_REF] Stukowski | Visualization and analysis of atomistic simulation data with OVITO the Open Visualization Tool Visualization and analysis of atomistic simulation data with OVITO the Open Visualization Tool[END_REF] was used. In short, at each time step, the DEM algorithm is as follows:

• for each particle a neighbor (or contact) list is established;

• for each contact, forces (and resisting moments) are computed according to contact laws;

• forces (and moments) are summed for each particle;

• Newton's second law and time integration (Velocity-Verlet) are used to get the new particle position.

The mechanical loading is performed by changing the size of the simulation box in one or more directions according to a prescribed strain rate. All particles are moved according to the corresponding affine displacement at the beginning of the timestep. In the present work a quasi-static approach is sought by using low enough strain rates. The quasi-static strain rate is reached once further decrease in strain rate does not affect significantly the results. In order to dissipate the kinetic energy in the system and damp oscillations, viscous forces and moments are added. They oppose the contact normal displacements and rotations. Following the work of Agnolin and Roux [START_REF] Agnolin | Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks[END_REF], the damping coefficient was chosen as a fraction β = 0.1 of the critical damping coefficient. A non-viscous damping force, that opposes the particle velocity and proportional (with a coefficient α = 0.7) to the total force acting on the particle, is also applied to each particle [START_REF] Cundall | A discrete numerical model for granular assemblies[END_REF]. The macroscopic stress tensor on the simulation box of volume V is computed as follows [START_REF] Christoffersen | A Micromechanical Description of Granular Material Behavior[END_REF]:

σ ij = 1 V contacs F i l j (1)
where F i is the i th component of the contact force vector, and l j is the j th component of the branch vector connecting the centers of the two particles in contact. The reader will find more details on the DEM method in the following works: [START_REF] Cundall | A discrete numerical model for granular assemblies[END_REF][START_REF] Potyondy | A bonded-particle model for rock[END_REF][START_REF] Kloss | Models , algorithms and validation for opensource DEM and CFD-DEM[END_REF][START_REF] Agnolin | Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks[END_REF][START_REF] Martin | Study of particle rearrangement during powder compaction by the Discrete Element Method[END_REF][START_REF] Martin | Influence of adhesion and friction on the geometry of packings of spherical particles[END_REF]. Here we will only focus on the description of the contact laws.

Contact laws

Two types of contacts are distinguished: bonded contacts that can transmit normal and tangential forces and resisting moments [START_REF] Potyondy | A bonded-particle model for rock[END_REF], and Hertzian contacts with Derjaguin-Muller-Toporov (DMT) adhesion [START_REF] Derjaguin | Effect of contact deformations on the adhesion of particles[END_REF]. Initially, all intra-aggregates contacts are bonded. New contacts appearing during the simulation are then considered as Hertzian. The latter are mainly interaggregate contacts but Hertzian contacts may also appear within an aggregate during its compaction if initially close (but not bonded) particles of an aggregate contact each other.

The contact law proposed 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 Jauffres et al. [START_REF] Jauffrès | Simulation of the 40 elastic properties of porous ceramics with realistic microstructure[END_REF],

to model the elastic behavior of a solid neck between two sintered particles, is used for bonded contacts. This model has been successfully used for silica aerogels by Liu et al. [START_REF] Liu | Simulation of the tensile properties of silica aerogels: the effects of cluster structure and primary particle size[END_REF]. It is given here for a monomodal set of particles of radius R but has been also developed for particles with different radii [START_REF] Jauffrès | Simulation of the 40 elastic properties of porous ceramics with realistic microstructure[END_REF].

Normal force F N , tangential force F T , resisting bending M T and twisting moments M N (Fig. 2) are given as a function of the contact size a and the elastic properties of the particles, i.e., the Young's Modulus E and the Poisson's ratio ν:

F N = k N δh N , k N = E 1 -ν 2 f N a (2)
F T = k T δh T , k T = 2E (2 -ν)(1 + ν) f T a (3)
M N = k M N α N , k M N = a 2 k T 2 (4)
M T = k M T α T , k M T = a 2 k N 4 ( 5
)
where k N , k T , k M N and k M T are stiffnesses; δh N and δh T are the normal relative displacement and tangent accumulated displacement; α N and α T are the accumulated relative rotations. The coefficients f N and f T have been obtained from finite element simulations at the scale of one sintered neck by

McMeeking et al. [START_REF] Mcmeeking | Elastic and Viscoelastic response of finite particle junctions in granular materials[END_REF]:

f N = 1 + a * π 6 (1 -ν 2 )(1 + 2a * ) -a * 1 -(a * ) 2 -c 0 +4c 1 π a * + (a * ) 2 π 6 (1 -ν 2 )(1 + 2a * ) -a * (6)
f T = 1 + (a * ) 2 π 6 (1 -ν 2 )(1 + 2a * ) -a * 1 -(a * ) 2 (7)
with

a * = a R (8)
c 0 = 0.5650 + 0.04864ν 2 + 1.036ν 4 (9)
c 1 = 0.1396 -0.03061ν + 0.3395ν 2 (10)
Typical elastic properties of dense amorphous silica were used: E = 70 GPa and ν = 0.2. Equations ( 4) and ( 5) are derived from beam theory [START_REF] Potyondy | A bonded-particle model for rock[END_REF]. Practically, the linear stiffness coefficients k N , k T , k M N and k M T are computed according to a given contact size a in a pre-processing step. The same contact size a is used for all bonded contacts. For the sake of simplicity, and also because aggregates are generally considered as unbreakables, no explicit fracture criteria is used. Still, if the normal force is such that the distance between two particles become larger than twice their radius the bond will disappear leading to a geometric breakage of the bond. To limit this artificial behavior an initial overlap h N 0 (Fig. 2) is used between the particles as detailed in section 4.1.1.

Newly formed contacts during simulation are of Hertzian type with Coulomb friction and DMT adhesion [START_REF] Derjaguin | Effect of contact deformations on the adhesion of particles[END_REF]:

F N = √ 2R 3 E 1 -ν 2 (δh N ) 1.5 (11)
F T = min( E √ 2R (2 -ν)(1 + ν) δh N δh T , µF N ) ( 12
)
F DM T = -2γ S πR (13)
with µ the friction coefficient, γ S the surface energy (J/m 2 ). F DM T is an attractive force normal to the contact that adds up to the repulsive Hertzian force F N . A simple dimensional analysis on Eq. ( 1) shows that the only force that introduces a size effect is the DMT adhesion (Eq. ( 13)) as it introduces a term with an inverse size dependence (1/R) in the macroscopic stress σ ij . It is also worth noting that while during synthesis or ageing surface energy and particle size are correlated, these two parameters can be set independently in the DEM simulations.

Simulation methods

4.1. Numerical preparation of initial silica powder bed

Initial gas with controlled aggregate morphology

The porous Eden growth model [START_REF] Guesnet | A growth model for the generation of particle aggregates with tunable fractal dimension[END_REF] was used to generate aggregates, i.e. random assemblies of spherical primary particles in contact. The porous Eden model allows the generation of aggregates with a controlled morphology through two parameters: the number of particles N and the inactivation probability P . The random inactivation of particles with the probability P allows the local blocking of the growth to create porous structures. Aggregates are successively generated inside a periodic (in all three directions) simulation box to form an initial gas of aggregates. When attempting to place a new particle, the non-overlapping condition applies within the growing aggregate and with the other aggregates already in the simulation box.

Experimentally observed initial density (3% for FS and 7.5% for PS) are sufficiently low to ensure that no significant bias exists in the generation of aggregates due to this globally applied non-overlapping condition. In addition, the particle radii are multiplied by a factor ξ to create overlapping contacts (required to limit the geometric breakages) which introduces a third generation parameter. It is important to underline the model nature of the gas of aggregates numerically generated: perfect spheres are used, large scale organization (agglomerate, powder particle) is not considered and no dispersion is used on the particle radius. The fractal dimension and gyration radius are not generation parameters: they are computed after the aggregate generation as described in [START_REF] Guesnet | A growth model for the generation of particle aggregates with tunable fractal dimension[END_REF]. Briefly, the gyration radius is computed us-

ing the classical definition R g = 1 N N i,j>i (r ij ) 2
, where r ij is the distance between particles i and j, and the fractal dimension is obtained through the slope of the structure factor versus q (modulus of the scattering vector) plot.

Consequently there is a small dispersion on these two aggregate characteristics, inherent to the random nature of the generation procedure. As the two selected PS (Tixosil 43 & 365) have a quite similar mechanical response under oedometric compaction, only Konasil 200 and Tixosil 365 silica were studied numerically. Their fractal dimension d f , aggregate gyration radius R g and primary particle radius R were obtained from SAXS [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF][START_REF] Benane | Mécanique des lits de silices granulaires pour l'optimisation des coeurs de panneaux isolants sous vide (PIV)[END_REF]. Their SAXS [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF][START_REF] Benane | Mécanique des lits de silices granulaires pour l'optimisation des coeurs de panneaux isolants sous vide (PIV)[END_REF] Numerical [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF], the d f value used for PS may be overestimated due to aggregate interaction [START_REF] Benane | Mécanique des lits de silices granulaires pour l'optimisation des coeurs de panneaux isolants sous vide (PIV)[END_REF].

d f R g R d f R g R N P ξ
numerical counterparts were generated using an optimization algorithm as described in [START_REF] Guesnet | A growth model for the generation of particle aggregates with tunable fractal dimension[END_REF]. Morphological properties used as inputs and the numerical parameters resulting from the optimization are reported in Table 2. Images of typical aggregates are provided in Fig. 3 (see also supplementary videos).

In total, 30,000 particles, leading to a gas of at least 200 aggregates and a simulation box of ≈ 1 µm 3 (vs. a few mm 3 for the experiment), were used to ensure a good reproducibility during the subsequent mechanical simulations.

Sample preparation by compression-tension cycling

Performing directly a compression of the low density gas of aggregate to simulate the experimental odeometric compaction is not realistic. Indeed, starting with an initial gas, by definition with no inter-aggregates contacts, do not correspond to the experimental initial aggregate packing for which silica aggregates exhibit contacts. We noted several anomalies during the compaction of a gas of aggregates that might be related to this unrealistic initial state:

• large amount of geometric bond breakages (5%),

• still increasing number of Hertzian contacts during tensile loading,

• underestimation of the stresses (ca. 0.3 MPa vs 1.2 MPa in experiment).

A procedure to create more realistic initial packings has been developed based on compression-tension cycling at low density. Packing by gravitation might be a possible alternative but with the drawback of breaking the periodic boundary condition in at least one direction. From a given initial gas, 8

uniaxial compression-tension cycles of amplitude 0.025 (i.e. from 3% to 5.5%

for FS) are performed to create Hertzian inter-aggregate contacts. Creation of new contacts due to adhesive forces and rearrangement occurs during the cycling, leading to a more realistic initial state. The number of cycle has been limited to 8 as more cycles lead to a large amount of unwanted geometrical bond breakages. 8 cycles also corresponds to the threshold from which the number of Hertzian contacts start decreasing during the tensile loading stage (Fig. 4). Fig. 5 shows that after cycling, although a fully continuous network is not achieved, large structures of several aggregates linked by adhesion are formed. To maximize the rearrangements and creation of Hertzian contacts, the friction coefficient has been set to 0 and surface energy to 1.2 J/m 2 for this preparation stage. The other contact law parameters are the same than in the subsequent simulation of compaction and tensile tests. It should be noted that to keep reasonable CPU time, the strain rate has been increased by a factor 10 above the quasi-static strain rate for the preparation stage. This is not problematic considering the fact that the preparation procedure is purely numerical and does not seek to reproduce the material behavior. 4.2. Compaction of a silica powder bed to VIP core density followed by tensile test First, a uniaxial compaction is performed up to a given nominal density and then a uniaxial tensile loading is imposed in the same direction. Five simulations on different initial gas of aggregates were run for each set of parameters to provide an error bar. A typical stress-density curve is reported in Fig. 6. For the sake of clarity the compressive and tensile parts will be reported in two separate graphs. The state of the initial assembly of aggregates (in particular the number of Hertzian contacts) affects the result but primarily the beginning of the compaction and only moderately the maxi- mum stress and tension stage. In the extreme case of no hertzian contacts (no cycling during the preparation stage) the maximum compressive stress is ca. 25 % lower than for 8 cycles during the preparation stage (1 Hertzian contact per particle). The oedometric modulus E o is computed during the first 0.5% of unloading. During the tensile loading, a maximum tensile stress σ f is reached and will be defined as the material strength. The fracture is progressive and does not exhibit any sudden drop in stress. We identified two main reasons for this non-brittle behavior. First and as observed in MD [START_REF] Patil | Mechanics of nanostructured porous silica aerogel resulting from molecular dynamics simulations[END_REF][START_REF] Gonçalves | Elasticity and strength of silica aerogels: a Molecular Dynamics study on large volumes[END_REF] or DEM simulations [START_REF] Liu | Simulation of the tensile properties of silica aerogels: the effects of cluster structure and primary particle size[END_REF], surface energy plays a predominant role in the mechanics of these materials with large surface to volume ratio and nano-metric particles. The adhesive forces (modelled here with the DMT model, Eq. ( 13)) that appear when aggregates resume contact do not allow for a brittle failure. Second, when dealing with small scale simulation, no large defect of micron size that may lead to a catastrophic failure at the macro scale is included in the modeling. The strength values may thus be overestimated for this reason but are still relevant for relative comparison of various silica types. It is also worth noting that in this system, the adhesive DMT forces have a significant influence on the compressive behavior. For example, even during compaction, the Hertzian contacts maintain an attractive character (F N + F DM T < 0) and thus contribute negatively to the macroscopic compressive stress.

Results

Influence of contact law parameters

The stiffness of the bonded contacts between two particles in the aggregates depends, apart from the Young's modulus of the particle, on the contact size a (Eq. ( 11)), a parameter difficult to assess, even with TEM images [START_REF] Roiban | Advanced three dimensional characterization of silica-based ultraporous materials[END_REF].

Liu et al. have assessed the ratio a R in a silica aerogel by considering, during gelation, neck formation by Johnson-Kendall-Roberts (JKR) adhesion [START_REF] Johnson | Surface energy and the contact of elastic solids[END_REF].

This approach would also be applicable for PS and interestingly leads to a R = 0.26 for a primary particle of radius 13 nm (value reported for PS, Table 2). It is also worth noting that a R is expected to increase with ageing of the material [START_REF] Yrieix | VIP service life assessment: Interactions between barrier laminates and core material, and significance of silica core ageing[END_REF][START_REF] Chal | Nanostructured silica used in super-insulation materials (SIM), hygrothermal ageing followed by sorption characterizations[END_REF]. In this work we used a R = 0.3 as a rough estimate and performed a parametric study around this value for FS aggregates (morphological parameters in Table 2 with surface energy γ s = 1.2 J/m 2 and friction coefficient µ = 0.3). The compaction stress-density curves and tensile stress-strain curves are reported in Fig. 7. As expected increasing a R leads to a stiffer aggregate packing due to an increase of the stiffness of the aggregates. The behavior is highly non-linear with a relatively low increase of the maximum compressive stress between a R = 0.15 and a R = 0. Moreover, the behavior of Hertzian contacts is largely dependant on the value of surface energy γ s . 1 J/m 2 is generally considered as a good estimate for oxides [START_REF] Nikolopoulos | A method for the calculation of interfacial energies in AI203 and ZrO2/liquid-metal and liquidalloy systems[END_REF]. A surface energy of approximately 1 J/m 2 has been calculated by MD simulations for pure Silica [START_REF] Gonçalves | Molecular dynamics simulations of amorphous silica surface properties with truncated Coulomb interactions[END_REF]. However, in the case of silica, the chemical nature of the surface (density of silanol groups and physically adsorbed water), that depends on the processing route (pyrogenic or in aqueous solution), the degree of ageing and the relative humidity [START_REF] Yrieix | VIP service life assessment: Interactions between barrier laminates and core material, and significance of silica core ageing[END_REF][START_REF] Chal | Nanostructured silica used in super-insulation materials (SIM), hygrothermal ageing followed by sorption characterizations[END_REF][START_REF] Morel | Pyrogenic silica ageing under humid atmosphere[END_REF],

plays an important role. Indeed, chemically or physically adsorbed water can screen Van der Waals and electrostatics interactions in favor of capillary forces leading to a lower surface energy [START_REF] Wan | Fracture and Contact Adhesion Energies of Mica-Mica, Silica-Silica, and Mica-Silica Interfaces in dry and moist atmospheres[END_REF]. In consequence silica surface energy varies from 5 J/m 2 in ultradry conditions [START_REF] Michalske | Closure and Repropagation of Healed Cracks in Silicate Glass[END_REF] to 0.1 J/m 2 for pure capillary interaction [START_REF] Wan | Fracture and Contact Adhesion Energies of Mica-Mica, Silica-Silica, and Mica-Silica Interfaces in dry and moist atmospheres[END_REF]. To assess the influence of surface energy, a parametric study on γ s was performed for FS aggregates with a R = 0.3 and µ = 0.3. The results in Fig. 8 show that γ s has a relatively low impact on the compaction behavior but a significant influence on the strength and oedometric modulus (E 0 = 2.5, 6.7 and 8.8 MPa for γ s = 0, 0.4 and 1.2 J/m 2 , respectively). Values larger than 1.2 J/m 2 are not reported as the amount of unrealistic geometrical bond breakages become non-negligible and may impact the macroscopic result.

22

No statistically significant influence of the friction coefficient varying from µ = 0.1 to 0.9 has been noted, but simulations with µ = 0 exhibit significantly lower compaction stresses. The negligible effect of µ might sounds surprising but is a consequence of very adhesive hertzian contacts. Indeed, the indentation is very large (δh N /R ≈ 0.1) because of the adhesive forces and consequently F T is, even with µ = 0.1, very rarely capped by µF N (F N ∝ δh N 1.5 and F T ∝ δh N 0.5 see equations 11 and 12), which explains the very limited influence of µ.

Influence of aggregate morphology

The influence of the morphological parameters of aggregates has been studied with the following values for the contact law parameters: γ s = 1.2 J/m 2 , a R = 0.3 and µ = 0.3. The parametric study has been performed around the values of FS aggregates (Table 2). In such a nano-sized system, adhesive interaction are of outmost importance and are directly linked to the size of particles (equation ( 13)). Keeping other parameters identical and enlarging only the primary particle radius up to a value typical of PS has nearly no influence on the compaction behavior but decreases the strength (Fig. 9). This is consistent with the parametric study on γ s : varying the primary particle or the surface energy affects similarly the DMT adhesion forces (Eq. ( 13)).

FS aggregates are generally more branched and elongated than PS, which is quantified by a smaller fractal dimension d f [START_REF] Baeza | Multiscale filler structure in simplified industrial nanocomposite silica/SBR systems studied by SAXS and TEM[END_REF][START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF][START_REF] Guesnet | A growth model for the generation of particle aggregates with tunable fractal dimension[END_REF] (Fig. 10). When the initial density (set by the compression-tension preparation stage) and the gyration radius are kept constant, the fractal dimension of the aggregates shows only a limited effect on the compaction behavior, oedometric modulus and strength for d f varying from 1.7 to 2.8 (Fig. 11). It is worth noting that the Lastly, the influence of the gyration radius is investigated. Fig. 12 displays typical aggregates with increasing radius of gyration used in the simulation. d f is kept constant but because of the increasing number of particles the aggregates are more elongated with large R g for the porous Eden growth model [START_REF] Guesnet | A growth model for the generation of particle aggregates with tunable fractal dimension[END_REF]. It is observed in Fig. 13 that the compaction is more difficult for large R g values. The oedometric modulus follows the same trend than the compaction stress and increases with R g (E 0 = 6.3, 8.8 and 9.1 MPa for R g = 30, 64 and 128 nm, respectively). Strength is nearly unaffected by R g (Fig. 13).

Comparison with experiment

For the sake of comparison with the experimental study reported in section 2, compaction and tensile behavior of numerically generated FS and PS were simulated. In the absence of reliable assessments of the surface energy and the neck size, the same values were used for FS and PS (γ s = 1.2 J/m 2 and a R = 0.3). The experimentally observed initial relative densities were targeted during the initial sample preparation by compression-tension cycling. To follow the experiment, the final density of PS was set to a larger value than the FS one. Compaction curves and tensile stress-strain curves are reported in Fig. 14. Qualitatively the initial part of the compaction curves is very steep, which is not observed experimentally. However, we believe this is an artifact due to the non quasi-staticity of the compression-tension cycling, that may lead to a system slightly out of equilibrium at the beginning of the compaction. Quantitatively, the simulation compressive stresses are lower than the experimentally observed ones but the order of magnitude is correct. This is satisfactory considering the fact that no parameter has been fitted and that neck size, which has a tremendous effect on the stress (Fig. 7), has only been very roughly estimated and fixed constant for all the particles.

The fact that the simulations underestimate the compressive stresses suggests however that the actual neck size maybe larger than the one estimated from JKR model. The simulation odeometric moduli (8.8 MPa for FS at 13 % and 14.5 MPa for PS at 17 %) are lower than the experimentally measured values at lower densities (22.4 MPa for FS at 11 % and 18.7 MPa for PS at 15 %) but the correct order of magnitude is also obtained. For the fracture behavior, only a rough experimental estimation of the strength is known, and again the order of magnitude is correct, at least for FS (ca. 0.3 MPa at a density of 9 % experimentally versus 0.75 MPa but at a density of 13 % numerically). As for PS, the difference in density (9 % experimentally versus 17 % numerically) makes the comparison difficult. The fact that PS has a larger oedometric modulus and strength than FS is difficult to interpret due also to the large difference in density of the two compacts.

Scaling law for oedometric modulus

In order to compare the two silica over similar density range, unloading steps during the compaction were used to evaluate the oedometric modulus of the packing versus its density. The results are reported in log-log plot in Fig. 15, showing that at similar density FS is stiffer than PS but only by a small amount, ca. 20%. The data follow a scaling law of the form E 0 ∝ d κ .

The computed exponents of the scaling have intermediate values between

what is expected for an open foam structure (κ = 2.0 [START_REF] Gibson | Cellular solids. Structure and properties 2nd Ed[END_REF]) and a silica hydrophobized aerogel (κ = 3.8 [START_REF] Gonçalves | Elasticity and strength of silica aerogels: a Molecular Dynamics study on large volumes[END_REF]).

Discussion

The parameters governing the mechanical behavior in compaction of nanostructured silica powders in the simulations are, by increasing order of significance:

• neck size between bonded primary particles

• gyration radius of the aggregate

• surface energy (or primary particle radius)

The fact that the fractal dimension has very limited influence appears surprising as more elongated and branched aggregates have been suggested as a possible explanation for the observed stronger mechanical behavior under compaction and indentation of FS powders [START_REF] Benane | Instrumented Indentation of Super-Insulating Silica Compacts[END_REF]. First, the elongation, formally defined as the square root of the ratio of the minimum and maximum eigenvalues of the inertia matrix, is not just related to its fractal dimension but also to its number of particles N : for the same d f the elongation increases with N or R g for the porous Eden growth model [START_REF] Guesnet | A growth model for the generation of particle aggregates with tunable fractal dimension[END_REF] (Fig. 12). Secondly, decreasing d f will also affect the number of bonded contacts within the aggregates as a larger amount of new bonded contacts are formed when increasing the particle radius during the preparation stage (see 4. • Because of a more elongated and branched structure, more Hertzian contacts are formed which hinders the reorganizations and tends to increase the compaction stress.

• Aggregates are less stiff because of a lower number of bonded contacts per particles, which tends to decrease the compaction stress.

These two competing effect may compensate each other, and finally lead to the apparent very limited influence of d f on compaction noted on Fig.

11. On the contrary, increasing R g does not affect the initial number of bonded contacts and the compaction stress is governed only by the amount of Hertzian contacts which increases with R g leading to the expected behavior: more elongated aggregates are more difficult to compact.

The observed relatively weak influence of γ s on the compaction behavior is not consistent with recent experimental results. Indeed, moderate ageing of FS has a significant effect on the compaction behavior [START_REF] Benane | Mécanique des lits de silices granulaires pour l'optimisation des coeurs de panneaux isolants sous vide (PIV)[END_REF] that is attributed to a decrease of surface energy (gain of hydrophilicity [START_REF] Chal | Nanostructured silica used in super-insulation materials (SIM), hygrothermal ageing followed by sorption characterizations[END_REF]). The simulations have two possible bias that might explain the inconsistency with experiments:

• increasing amount of geometrical bond breakages with increasing surface energy may lead to an artificially too soft compaction behavior;

• preparation by compression-tension cycling was done with γ s = 1.2 J/m 2 for all samples, which may lead to an unrealistically large number of Hertzian contacts, at the beginning of the compaction, for low γ s and hinder the reorganization.

When focusing on tensile behavior, the effect of surface energy predominates. The oedometric modulus and tensile strength are influenced, in our simulation, by order of significance, by:

• surface energy (or primary particle radius)

• neck size between bonded primary particles

• the aggregate morphology (R g for E 0 and d f for σ f )

The parametric study shows that contact law parameters (neck size a and surface energy γ s ) impact more the mechanical behavior (compaction and post-compaction) than the morphology of the aggregates (fractal dimension d f and gyration radius R g ). However the transposition of this result to real silica powder systems is delicate because of the model nature of the numerical aggregates, the omission of larger scale structures (agglomerate and powder grain) and the absence of reliable values for surface energy and neck size.

Still, higher surface energy is expected for FS because of its less hydrophilic surface, and neck size might be influenced by the process. The possibly large influence of these last two parameters on the mechanical behavior of silica powders could thus significantly contribute to the stronger mechanical behavior of FS. More insight is provided by the comparison of FS and PS numerically generated according to morphological parameters extracted from SAXS data [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF][START_REF] Benane | Mécanique des lits de silices granulaires pour l'optimisation des coeurs de panneaux isolants sous vide (PIV)[END_REF]. It is observed in Fig. 14 that the compaction and tensile behavior of FS and PS are close if only morphological differences are considered (in absence of reliable values, the neck size and surface energy are kept similar for both silicas in the simulations). Morphological differences, i.e. larger aggregate radius of gyration, lower fractal dimension and smaller primary particles of FS, taken alone do not explain completely the experimentally observed large differences in mechanical behavior between FS and PS. In terms of stiffness for example, Fig. 15 shows that morphological differences account for a FS slightly stiffer than PS but experimental instrumented indentation data around 10% density have shown that FS is actually twice stiffer than PS [START_REF] Benane | Instrumented Indentation of Super-Insulating Silica Compacts[END_REF]. The stronger behavior of FS in compaction and the higher strength of its compact are thus attributed to a combined effect of morphology of the aggregate, smaller primary particle size, higher surface energy and possibly larger necks between particles. However, the assessment of the significance of each parameter is difficult due to the limitations of the model and lack of data on surface energies and neck sizes.

In light of these findings, the effect of ageing on the mechanical behavior can be discussed. Hygrothermal ageing has two main effects on nanostructured silica: the decrease of the surface energy through water uptake followed by the growth of the necks between primary particles [START_REF] Chal | Nanostructured silica used in super-insulation materials (SIM), hygrothermal ageing followed by sorption characterizations[END_REF]. It has been clearly

shown that these effects are detrimental for thermal insulation [START_REF] Yrieix | VIP service life assessment: Interactions between barrier laminates and core material, and significance of silica core ageing[END_REF]. For mechanical behavior, the decrease of surface energy associated with moderate ageing leads to easier powder compaction (formation of less Hertzian contacts leading to easier reorganization). On the contrary, for more severe ageing, the increase of neck size may lead to the reverse. As for the tensile behavior, ageing is expected to decrease the strength as the surface energy is the main factor governing the strength of the compacts.

Conclusion

The difference in compaction behavior and post-compaction mechanical properties of a fumed and a precipitated nanostructured silica have been investigated through DEM simulations. A parametric study on a set of morphological parameters (R, d f and R g ) and simulations on realistic aggregates numerically generated based on SAXS measurements have shown that differences in morphology alone may not explain the experimentally observed large differences in mechanical behavior between FS and PS. The study of the influence of neck size and surface energy have shown that these two properties have more effect than the aggregate morphology in the simulations. While the compaction behavior is largely influenced by the neck size, the surface energy is the first governing parameter for strength. The extension of these results to real systems should however be treated with caution because of the lack of reliable surface energy and neck size values, and the questionable realistic character of the numerical silica (omission of particle size dispersion and large scale structures). In particular, particle size dispersion may not have a negligible influence on mechanical behavior, as is the case for scattering behavior [START_REF] Genix | Determination of the local density of polydisperse nanoparticle assemblies[END_REF]. Even with these limitations in mind, it is believed that the stronger mechanical behavior of FS as compared to PS is, at least partially, a consequence of larger neck sizes and surface energy. While it is clear that FS have a larger surface energy than PS, it has never been proposed, to our knowledge, that FS may have larger necks. In practice, it may thus be efficient to increase surface energy of PS to improve their mechanical behavior.

Increasing the neck size may also improve the mechanical properties but is detrimental for thermal properties [START_REF] Yrieix | VIP service life assessment: Interactions between barrier laminates and core material, and significance of silica core ageing[END_REF]. Future research on PS should thus focus not only on adjusting the morphology (e.g. by attempting to decrease their fractal dimension) but also on surface modifications to decrease the hydrophilicity and increase the surface energy as it should be highly beneficial for mechanical properties. An experimental investigation of the effect adsorbed water on surface energy and mechanical behavior of silica powders would be of high interest and may help to decouple the morphological and surface energy effects. The proposed modeling approach could also be improved, for example a more realistic model would include primary particle size dispersion (observed by Benane et al. on FS [START_REF] Benane | Multiscale structure of super insulation nano-fumed silicas studied by SAXS , tomography and porosimetry[END_REF]). Small dispersion on d f and R g exists in the present approach but could be enhanced and tuned.

The bonded contact law could allow plastic deformation. Indeed, this would solve the issue related to geometrical breakages by relaxing unrealistically large contact forces. It has been shown that silica glass actually exhibits plasticity when tested at small scales [START_REF] Lacroix | Plastic deformation and residual stresses in amorphous silica pillars under uniaxial loading[END_REF][START_REF] Luo | Size-Dependent Brittle-to-Ductile Transition in Silica Glass Nanofibers[END_REF].

Figure 1 :

 1 Figure 1: Compaction behavior of fumed (Konasil 200) and precipitated (Tixosil 365 & Tixosil 43) silica. The relative density has been computed based on an intrinsic density of 2200 kg/m 3

Figure 2 :

 2 Figure 2: Contact laws. (a) bonded contact. (b) Hertzian contact

Figure 3 :

 3 Figure 3: Typical aggregates numerically generated based on SAXS morphological characterization. Left: Konasil 200 (FS), primary particle radius R = 8.3 nm. Right: Tixosil 365 (PS), primary particle radius R = 12 nm. Note that the enlargement of the particles by the factor ξ has created overlaps

Figure 4 :

 4 Figure 4: Evolution of the Hertzian coordination number (i.e. the average number of Hertzian contacts per particle) with compression-tension cycling during sample preparation. The compression stages are indicated in red. The Hertzian coordination increases both during compression and tension, until the last cycle where it decreases during tension (red arrow).

Figure 5 :

 5 Figure 5: Influence of cycling. (top) No cycling, a different color is assigned to each aggregate indicating that each aggregate is isolated. (bottom) After 8 cycles, colors show the class of equivalence of contacting aggregates indicating a large number of inter-aggregate contacts. The relative density is 3% for both and only a slice of the simulation box is shown.

Figure 6 :

 6 Figure 6: Typical simulation: compaction of a silica powder bed to VIP core density followed by a tensile test. Odoemetric modulus E 0 and strength σ f are extracted from the simulation to characterize the mechanical behavior of the silica core produced by the compaction stage.

  3 and a much larger one between a R = 0.3 and a R = 0.6. This comment also holds for the oedometric modulus that takes the values E 0 = 5.8, 8.8 and 21.0 MPa for a R = 0.15, 0.3 and 0.6, respectively. The tensile strength also increases with the contact size as the aggregates becomes stiffer, even if the number of newly formed Hertzian contacts is lower (rearrangement of stiff aggregates is more difficult).

Figure 7 :

 7 Figure 7: Influence of contact size on the compaction behavior (left) and the tensile behavior (right). FS aggregates with γ s = 1.2 J/m 2 and µ = 0.3. Averaging is done over 5 timesteps and 5 simulations, relative standard deviation ≤ 10%.

Figure 8 :

 8 Figure 8: Influence of surface energy on the compaction behavior (left) and the tensile behavior (right). FS aggregates with a R = 0.3 and µ = 0.3. Averaging is done over 5 timesteps and 5 simulations, relative standard deviation ≤ 10%.

Figure 9 :

 9 Figure 9: Influence of primary particle radius on the compaction behavior (left) and the tensile behavior (right). γ s = 1.2 J/m 2 , a R = 0.3, µ = 0.3. Averaging is done over 5 timesteps and 5 simulations, relative standard deviation ≤ 10%.

Figure 10 :

 10 Figure 10: Aggregates with increasing fractal dimension d f at constant radius of gyration R g = 64 nm . From left to right d f = 1.7, d f = 2.0 and d f = 2.8. Aggregates with larger d f have a larger number of primary particles to keep R g constant [42].

Figure 11 :

 11 Figure 11: Influence of aggregate fractal dimension on the compaction behavior (left) and the tensile behavior (right). γ s = 1.2 J/m 2 , a R = 0.3, µ = 0.3. Averaging is done over 5 timesteps and 5 simulations, relative standard deviation ≤ 15%.

Figure 12 :

 12 Figure 12: Aggregates with increasing radius of gyration R g at constant d f = 2.0. From left to right R g = 30 nm, R g = 64 nm and R g = 128 nm. Aggregates with larger R g are more elongated [42].

Figure 13 :

 13 Figure 13: Influence of aggregate radius of gyration on the compaction behavior (left) and the tensile behavior (right). γ s = 1.2 J/m 2 , a R = 0.3, µ = 0.3. Averaging is done over 5 timesteps and 5 simulations, relative standard deviation ≤ 21%, 5% and 13% for R g = 30, 64 and 128 nm respectively.

Figure 14 :

 14 Figure 14: Comparison of the compaction behavior (left) and the tensile behavior (right) of fumed (K200) and precipitated (T365) silica powders. Averaging is done over 5 timesteps and 5 simulations, relative standard deviation ≤ 10%.

Figure 15 :

 15 Figure 15: Scaling law between oedometric modulus E 0 and relative density d for PS and FS.

  1.1). The initial coordination number (only bonded contacts, i.e. before tension-compression cycling) goes from 2.7 for d f = 1.7 to 3.5 for d f = 2.8. On the contrary, for d f = 2.0 increasing R g will not significantly change the initial coordination number. The influence of lowering d f is thus twofold:

Table 2 :

 2 Morphological properties (fractal dimension d f and radius of gyration R g ) and generation parameters (particle radius R, number of particles per aggregate N , inactivation probability P and radius increase factor ξ) of numerically generated aggregates. The radius R reported is after enlargement by the factor ξ. R g and R are in nanometers. Morphological properties from SAXS experiment used as input to the optimization algorithm are also reported. While a meticulous extraction of d f from aggregates dispersed in a very low volume fraction suspension was possible for FS

Acknowledgments

This work was performed within the framework of the Center of Excellence of Multifunctional Architectured Materials, CEMAM AN-10-LABX-44-01 funded by the "Investments for the Future" Program. EDF, French Ministry for Research (CIFRE grant 2014-0903) and MATeB (joint MATEIS EDF RD laboratory) are also acknowledged for their financial support.


Manon C M Hess
email: hess@tourduvalat.org

Elise Buisson

François Mesléard

Soil compaction enhances the impact of microwave heating on seedling emergence

Keywords: invasive species control, seed-bank, microwave heating

An innovative microwave-based process to control invasive species in the field is currently under development. We investigated the effect of soil compaction levels under three microwave treatment pairings of power and duration (2kW4min, 2kW8min and 4kW4min), on seedling emergence of a diverse seed bank and three major invasive species in Europe (bohemian knotweed, giant goldenrod and jimsonweed). When soil was compacted, the number of seedling emergences of dicotyledons was significantly reduced by the 2kW4min treatment. Furthermore, while some dicotyledon and giant goldenrod's seedling emergences were observed respectively in plain soil in the 4kW4min and 2kW4min treatments, no seedling was recorded in compacted soil for the same treatments. Our results suggest that compacting soil increases the efficiency of microwave heating on seeds. Soil compaction level should therefore be considered in the design of the final microwave-based process.

1

Introduction

Successful eradication of an invasive species requires an effective depletion of the seeds and vegetative propagules, e.g. rhizomes [START_REF] Myers | Eradication and pest management[END_REF][START_REF] Regan | Optimal eradication: when to stop looking for an invasive plant[END_REF][START_REF] Saito | Response of riparian vegetation to the removal of the invasive forb, Solidago gigantea, and its litter layer[END_REF]. Complete destruction of invasive seed banks is rarely achieved by herbicide application [START_REF] Christoffoleti | Conservation of natural resources in Brazilian agriculture: implications on weed biology and management[END_REF], thus alternative methods have been developed. Biological control using natural enemies can be effective in reducing seed production or accumulation in the soil [START_REF] Adair | The biology of Dasineura dielsi Rübsaamen (Diptera: Cecidomyiidae) in relation to the biological control of Acacia cyclops (Mimosaceae) in South Africa[END_REF][START_REF] Impson | Biological control of an alien tree, Acacia cyclops, in South Africa: impact and dispersal of a seed-feeding weevil, Melanterius servulus[END_REF][START_REF] Zimmermann | Biological control in the management of invasive alien plants in South Africa, and the role of the Working for Water Programme: working for water[END_REF], but the release of exotic biological agents has been shown to raise ecological issues like negative impacts on native biota [START_REF] Strong | Biological control of invading species-risk and reform[END_REF]. Heating methods are of interest since they provide chemical-residue-free weed control. The use of fire is appropriate to reduce upper seed banks in fire-adapted ecosystems [START_REF] Holmes | Effects of different clearing treatments on the seed-bank dynamics of an invasive Australian shrub, Acacia cyclops, in the southwestern Cape, South Africa[END_REF][START_REF] Richardson | Seed banks of invasive Australian Acacia species in South Africa: role in invasiveness and options for management[END_REF], but is not suitable for some ecosystems (i.e. wetlands and dunes) and can sterilize soil for years [START_REF] Campbell | Development of integrated control strategies for wattle. II. Control of unwanted wattle[END_REF]. Soil solarization, based on solar heating of soil by mulching it with plastic sheets during the hot seasons, raises temperatures usually up to 40 to 55°C in the upper 5 cm of the soil [START_REF] Cohen | Reducing persistent seedbanks of invasive plants by soil solarization -the case of Acacia saligna[END_REF], enabling the reduction of invasive species seed banks [START_REF] Cohen | Controlling the seed bank of the invasive plant Acacia saligna: comparison of the efficacy of prescribed burning, soil solarization, and their combination[END_REF]. This method however showed certain limitations, such as length of treatment (i.e. several months), climate-dependency, and variable effectiveness [START_REF] Cohen | Soil solarization and weed management[END_REF]. Microwave soil heating has been considered for weed control for several decades [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF][START_REF] Davis | Ultrahighfrequency electromagnetic fields for weed control: Phytotoxicity and selectivity[END_REF][START_REF] Sartorato | Observations on the potential of microwaves for weed control[END_REF]. Microwave radiation induces dielectric heating of moist materials, enabling soil to reach temperatures required for seed viability loss (i.e. 60°C-90°C; [START_REF] Brodie | Microwave technologies as part of an integrated weed management strategy: A review[END_REF][START_REF] Sahin | Effects of microwaves on the germination of weed seeds[END_REF][START_REF] Thompson | The effect of temperature on viability of imbibed weed seeds[END_REF]. Exposure to high temperatures can impact seed mortality directly via thermal killing, or indirectly via increased susceptibility to toxic compounds and microorganisms, i.e. "weakening effects" [START_REF] Katan | The integrated management concept in the context of soilborne pathogens and soil disinfestation[END_REF]. In some cases, heat can break dormancy and stimulate germination (i.e. seeds displaying physical dormancy; [START_REF] Baskin | A comparative study of seed dormancy and germination in an annual and a perennial species of Senna (Fabaceae)[END_REF][START_REF] Herranz | Influence of heat on seed germination of seven Mediterranean Leguminosae species[END_REF][START_REF] Tieu | The interaction of heat and smoke in the release of seed dormancy in seven species from southwestern Western Australia[END_REF]. Several studies revealed however a great potential for microwave heating to control germination of many weed species [START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R. Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatrophagos sypiifolia L.)[END_REF]Brodie et al., 2009;Nelson, 1996 ;[START_REF] Sahin | Effects of microwaves on the germination of weed seeds[END_REF], but the microwave technology used at the time was not developed enough to draw a cost effective and marketable application [START_REF] Brodie | Microwave technologies as part of an integrated weed management strategy: A review[END_REF]. This study is part of a set of studies undertaken to help determine the technical characteristics of a continuous conveying tunnel with microwave equipment, designed for the treatment of soil infested by a wide range of invasive species (seeds and adult stages) collected in situ. Infested soil, once passed through the microwave oven on a conveyor belt, can be put back in place. First studies hold promising results for seedling emergence reduction, with high effectiveness when soil temperature reached 85°C [START_REF] De Wilde | Using microwave soil heating to inhibit invasive species seed germination[END_REF][START_REF] Hess | Microwave soil heating reduces seedling emergence of a wide range of species including invasives[END_REF]. Before this process can be implemented full scale, however, more information is needed on the parameters influencing the effectiveness of microwave treatments. Soil characteristics that mostly alter the dielectric properties of soil, such as initial temperature, texture and moisture content, have been shown to strongly influence the temperature achieved after microwave exposure [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF][START_REF] Brodie | Microwave heating in moist materials[END_REF][START_REF] Brodie | Microwave technologies as part of an integrated weed management strategy: A review[END_REF][START_REF] Davis | Ultrahighfrequency electromagnetic fields for weed control: Phytotoxicity and selectivity[END_REF][START_REF] Davis | Phytotoxicity of a UHF field[END_REF][START_REF] De Wilde | Using microwave soil heating to inhibit invasive species seed germination[END_REF]. Soil compaction has so far been neglected, although compaction directly influences the dielectric properties of the soil [START_REF] De Vries | Thermal conductivity of soil[END_REF]. Increasing soil compaction leads to higher bulk density and lower porosity, thereby enhancing thermal conductivity [START_REF] Abu-Hamdeh | Soil thermal conductivity effects of density, moisture, salt concentration, and organic matter[END_REF][START_REF] Yadav | Effect of compaction and moisture content on specific heat and thermal capacity of soils[END_REF]. Soil compaction may consequently impact the effectiveness of microwave heating in inhibiting seedling emergence.

We investigated the influence of soil compaction on microwave heating effectiveness in inhibiting seedling emergence by comparing the seedling emergence response in plain or compacted soil during exposure to three microwave treatment pairings of power and duration.

We chose to investigate the seedling emergence response of a grassland seed bank extracted in situ not for its invasion status (non-invaded), but because it contained a great diversity of species. We also monitored the seedling emergence response of three emblematic invasive species in Europe (i.e. Datura stramonium L., Reynoutria × bohemica Chrtek and Chrtková and Solidago gigantea Aiton) already used in previous studies [START_REF] De Wilde | Using microwave soil heating to inhibit invasive species seed germination[END_REF][START_REF] Hess | Microwave soil heating reduces seedling emergence of a wide range of species including invasives[END_REF] by placing a fixed number of seeds in the soil before treatments were applied.

Reported as highly aggressive in some European countries [START_REF] Kleunen | Reproductive assurance through selffertilization does not vary with population size in the alien invasive plant Datura stramonium[END_REF]Weber, 2003;[START_REF] Weber | Biological flora of central Europe: Solidago gigantea Aiton[END_REF]), these species were selected because they reproduce by seeds [START_REF] Gillies | Knotweed (Fallopia spp.) invasion of North America utilizes hybridization, epigenetics, seed dispersal (unexpectedly), and an arsenal of physiological tactics[END_REF][START_REF] Saayman | Influence of intraspecific competition on seed production of Datura stramonium L[END_REF][START_REF] Weber | Biological flora of central Europe: Solidago gigantea Aiton[END_REF]) and more importantly because their seeds differ in shape and size. Indeed, these characteristics are known to strongly influence seed sensitivity to microwave heating [START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R. Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatrophagos sypiifolia L.)[END_REF][START_REF] Brodie | Microwave technologies as part of an integrated weed management strategy: A review[END_REF].

Furthermore, none of the three species' seeds displays physical dormancy [START_REF] Bochenek | Do the seeds of Solidago gigantea Aiton have physiological determinants of invasiveness?[END_REF][START_REF] Engler | Seed characteristics and germination limitations in the highly invasive Fallopia japonica sl (Polygonaceae)[END_REF][START_REF] Loddo | Estimation and comparison of base temperatures for germination of European populations of velvetleaf (Abutilon theophrasti) and jimsonweed (Datura stramonium)[END_REF].

Material and methods

The experiment was designed to test the impact of soil compaction ('plain' vs 'compacted') during three microwave treatment pairings of power and duration (2kW4min, 2kW8min and 4kW4min) on seedling emergence of three invasive species in Europe (Datura stramonium, Reynoutria × bohemica and Solidago gigantea) and a seed bank contained in soil extracted in situ.

Soil sampling

Topsoil, characterized as a silty loam (60% silt, 15% clay), was collected from uncultivated species-rich grassland on an abandoned organic hemp growing field (production halted in 2013) located near two rivers, La Cèze and La Tave (Laudun-L'Ardoise, France).

The 25 soil samples collected (1.35m ± 0.15m length × 0.5m ± 0.1m width × 0.1m depth) were mixed to ensure relative homogeneity of soil and seed bank. Blended soil cleared of stones and organic residues was distributed in 1kg batches just before microwave treatments were applied.

Seed sampling of the three invasive species

Achenes of Reynoutria × bohemica and Solidago gigantea were collected in March 2016 along the Isère River in Savoie (France). Seeds of Datura stramonium were collected in October 2014 from stands growing along the Rhône River in Drôme (France). The achenes and seeds were collected randomly from ten ramets of the same population (to reduce variability) and then pooled. They were stored under dry conditions at room temperature until used for experiments.

Microwave system

An AMW200 batch microwave system (SAIREM SAS, Neyron, France) was used in this study. The 304 L microwave stainless steel chamber can contain a block of 0.6m × 0.4m × 0.25m maximum size and 30kg maximum weight. The microwave system has a polyethylene sliding table with a usable surface of 0.84m × 0.62m and a pneumatically driven sliding door, both making block loading/unloading easier. The microwave system operates at 915MHz, which allows greater penetration and treatment of thicker materials (up to 0.25m) than the frequently used 2450MHz microwave frequency (approximately a threefold increase).

Coupling microwave heating from above and below and rotating the turntable enhance heating homogeneity. The output power of 10kW maximum is produced by 2 × 5kW generators (magnetron), adjustable from 1kW to 10kW. The system is water-cooled.

Experimental design

We applied three microwave treatments using the following power and duration pairings: 2kW4min, 2kW8min and 4kW4min. The effectiveness of these treatments was tested in previous experiments [START_REF] De Wilde | Using microwave soil heating to inhibit invasive species seed germination[END_REF][START_REF] Hess | Microwave soil heating reduces seedling emergence of a wide range of species including invasives[END_REF]. Microwave treatments were performed on the premises of SAIREM (Neyron, France), each treatment being applied on 1kg soil replicates placed in 0.22m high × 0.09m diameter glass cylinders. Because the presence of water in soil is essential to creating heat by microwave exposure [START_REF] Metaxas | Industrial microwave heating[END_REF], soil samples were not dried before compaction. Bulk density (i.e. mass of dry soil / volume of bulk soil), which is a common measure of compaction, could therefore not be calculated. Soil humidity before treatment was 7.3%±1.2 (mean ± SD).

For each microwave treatment, two compaction levels were tested: 'plain soil' consisted of 1kg soil filling a volume of 725±19cm 3 and 'compacted soil' consisted of soil compacted directly in the cylinder using a metal weight until soil height was reduced by 15±2% (616±15cm 3 ) compared with plain soil. For each treatment (microwave treatment × compaction level), we used six replicates of soil containing (1) only the natural seed bank, (2) ten seeds of each tested invasive species. Controls without microwave treatment were replicates of plain soil containing (1) only the natural seed bank, and (2) ten seeds of each tested invasive species. After microwave treatments, soil temperature was immediately measured in each replicate, using mercury thermometers inserted in the center and at the periphery of the cylinder (2cm below soil surface). Before treatment, soil temperature was 18.6±0.6°C (mean ± SD). After treatment, compacted soil samples were decompacted and all samples (control and treated soil) were stored for 10 days at 30°C. After microwave treatment, each sample was spread in a 1 to 1.5cm thick layer over a 19cm diameter perforated plastic saucer containing from bottom to top: (1) a 21cm diameter Diatex filter (500-600µm mesh size to prevent loss of coarse sand), (2) 1.5cm of sterilized and desalted sand and (3) a 23cm diameter Diatex filter (50-70µm mesh size to avoid loss of silt and seeds). The plastic saucers were randomly placed in containers where a 1cm water layer was constantly adjusted so as to maintain soil moisture at a level conducive to germination and prevent submersion. The experiment was conducted in an outdoor, pollen-free greenhouse reducing the risk of granivory and contamination by seeds coming from the outside (Institute Tour du Valat, Arles, France). Seedling emergences were recorded weekly for 6 weeks from June 23 to July 28, 2016. Identified individuals were regularly removed to reduce competition.

Statistical Analyses.

We analyzed variations in soil temperature depending on the explanatory variable 'microwave treatment' ('control': absence of microwave treatment and three power and duration microwave treatment pairings: '2kW4min', '2kW8min' and '4kW4min') crosschecked against the explanatory variables 'compaction level' ('plain' or 'compacted) and 'measurement position' ('center' or 'periphery), using permutation tests. The p-values for the multiple comparison tests were adjusted with the BH adjustment [START_REF] Benjamini | Controlling the false discovery rate: a practical and powerful approach to multiple testing[END_REF]. The tests were performed using the 'coin' R package [START_REF] Hothorn | Implementing a class of permutation tests: the coin package[END_REF][START_REF] Core | R A language and environment for statistical computing[END_REF].

We analyzed variations in the number of seedling emergences of monocotyledons and dicotyledons (seed bank) depending on the explanatory variable 'microwave treatment' in interaction with 'compaction level' using generalized linear models (GLM) with Poisson error distribution [START_REF] Crawley | Generalized linear models[END_REF]. Tests were performed with function 'glm' in R ( [START_REF] Core | R A language and environment for statistical computing[END_REF]. We also analyzed variations in the percentage of seedling emergences of Datura stramonium, Reynoutria × bohemica and Solidago gigantea depending on the explanatory variable 'microwave treatment' cross-checked against the variable 'compaction level' using Kruskal-Wallis or Wilcoxon rank sum tests.

All statistical tests were performed using R.3.3.2 software [START_REF] Core | R A language and environment for statistical computing[END_REF]. P-values lower than 0.05 were considered as statistically significant.

Results and discussion

The three tested microwave treatments significantly raised soil temperature (close to 90°C in the 2kW8min and 4kW4min treatments and above 60°C in the 2kW4min treatment; Figure 1) and decreased seedling emergence of species from the seed bank and the invasive species tested (Figure 2 and 3; p<0.05). These results are consistent with the notion that soil microwave treatment affects seed viability via heat diffusion from surrounding soil [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF]Nelson, 1996). The 2kW4min treatment led to a ca. 50% decrease in seedling emergence from the seed bank (Figure 2a,b) and an absence of differences in seedling emergence of D. stramonium and R. × bohemica compared with the control, which is consistent with previous studies (Figure 3a,b;[START_REF] De Wilde | Using microwave soil heating to inhibit invasive species seed germination[END_REF]. This low effectiveness may have been reinforced by the 20°C soil temperature differences occurring between the center and the periphery of the cylinder (Figure 1). Indeed, microwave heating commonly results in uneven temperature distribution patterns [START_REF] Brodie | The influence of load geometry on temperature distribution during microwave heating[END_REF][START_REF] Vadivambal | Non-uniform temperature distribution during microwave heating of food materials-A review[END_REF], with more intensive heating around the central axis and evaporative cooling at the surface of a small cylinder [START_REF] Remmen | Microwave heating distributions in slabs, spheres and cylinders with relation to food processing[END_REF][START_REF] Hess | Microwave soil heating reduces seedling emergence of a wide range of species including invasives[END_REF]. Seeds located at the periphery may have therefore been exposed to substantially lower temperature, which could explain the low effectiveness of the treatment as well as the high variability between replicates.

Seeds of S. gigantea, however, appeared vulnerable to soil microwave heating, with seedling emergence reducing almost five-fold in the 2kW4min treatment (plain soil) compared with the control (Figure 3c). This sensitivity, already revealed in previous experiments [START_REF] De Wilde | Using microwave soil heating to inhibit invasive species seed germination[END_REF][START_REF] Hess | Microwave soil heating reduces seedling emergence of a wide range of species including invasives[END_REF], could be linked to S. gigantea's small seed size [START_REF] Diprose | The effect of externally applied electrostatic fields, microwave radiation and electric currents on plants and other organisms, with special reference to weed control[END_REF]. Testing the influence of seed size on a higher number of samples and species, but also on seeds from one species having different sizes, would be useful to assess the role of seed size in the sensitivity to microwave heating. The thickness of seeds tegument, dormancy type, or the nature of seed reserves could also be impacting.

The two most intensive treatments (i.e. 2kW8min and 4kW4min) resulted in more homogeneous soil temperatures within the cylinders than the 2kW4min treatment (Figure 1), and induced temperatures superior to 90°C, considered as lethal for many types of seeds (>80°C during 30s; [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF], whatever soil compaction level. This enhanced temperature homogeneity could be due to the increased exposure time or, more likely, output power, resulting in changes in temperature spatial distribution by thermal diffusion from the zones where the microwave energy is being absorbed to the rest of the sample [START_REF] Brodie | Microwave heating in moist materials[END_REF].

These more intensive treatments led to the total inhibition of invasive species seedling emergence (Figure 3) and a drastic decrease in seed bank seedling emergence (Figure 2).

With the 2kW8min treatment, seedling emergence still occurred in the seed bank for both levels of soil compaction but was reduced by 97% on average (Figure 1). Microwave heating induces a rapid dehydration of plant tissues, causing plant death in few seconds of microwave treatment [START_REF] Brodie | Microwave technologies as part of an integrated weed management strategy: A review[END_REF]. Above-ground and belowground plant tissues would therefore be easily destroyed by microwave treatments used to control seedling emergence, but their sensitivity will need to be assessed.

Increasing soil compaction appears to enhance microwave treatment effectiveness. In the 2kW4min treatment, the number of seedling emergences of dicotyledons was significantly reduced when soil was compacted (Figure 2b). Furthermore, while some dicotyledons and S. gigantea seedlings emerged in plain soil respectively in the 4kW4min and 2kW4min treatments, no seedling emergence was observed in compacted soil for these treatments (Figure 2b,3c). The higher effectiveness observed in compacted soil is most probably due to the higher bulk density and lower porosity obtained when compacting soil, resulting in higher thermal conductivity during microwave treatment [START_REF] Abu-Hamdeh | Soil thermal conductivity effects of density, moisture, salt concentration, and organic matter[END_REF][START_REF] Yadav | Effect of compaction and moisture content on specific heat and thermal capacity of soils[END_REF]. Such assumption corroborate with our results, showing that soil compaction tended to increase soil temperature (Figure 1).

Our results suggest that soil compaction, at the level tested in our experiment, does not diminish but rather enhances the effectiveness of the microwave-based process (i.e. inhibition of seedling emergence). This implies that microwave heating will be effective at reducing unwanted species emergence in compacted soil, prevalent in agricultural areas [START_REF] Drewry | Pasture yield and soil physical property responses to soil compaction from treading and grazing -a review[END_REF]). However, deliberately compacting soil to enhance microwave effectiveness may be detrimental to crop germination, growth, and water infiltration [START_REF] Bassett | Consequences of soil compaction for seedling establishment: implications for natural regeneration and restoration[END_REF][START_REF] Benvenuti | Soil Physics Involvement in the Germination Ecology of Buried Weed Seeds[END_REF][START_REF] Skinner | The effect of soil compaction on germination and early growth of Eucalyptus albens and an exotic annual grass[END_REF], so that soil might have to be decompacted before sowing. These results also point out that soil compaction should be considered in the design of the final microwave-based process: adjusting power and duration pairings to soil compaction level may help saving energy or increasing treatment effectiveness.

Acknowledgments

  Figures

  Figure 1. Effect of microwave treatment (control: without microwave treatment and three

Figure 2 .

 2 Figure 2. Effect of microwave treatment (control: without microwave treatment and three

Figure 3 .

 3 Figure 3. Effect of microwave treatment (control: without microwave treatment and three