Jean-Marc Schweitzer
email: jean-marc.schweitzer@ifpen.fr

Marion Servel

Fabien Salvatori

Aurélie

Marine Minière

Jean-François Joly

Quentin Gaubert

Fabrice R A Onofri
email: fabrice.onofri@univ-amu.fr

Spray drying of colloidal suspensions: coupling of particle drying and transport models with 2 experimental validations

Keywords: Spray drying, drying kinetics, colloidal suspensions, crust 26 formation, particle yield, computational fluid dynamics, acoustic levitation

A numerically effective approach was developed for the modeling of spray-drying of colloidal suspensions. This approach was based on the 14 integration of two models. The first is a phenomenological and radially symmetric model accounting for the drying of single-droplets, while the 16 second employs computational fluid dynamics (CFD) simulations to account for the gas flows conditions and atomization in a spray dryer.

18

Experiments were also conducted on single suspension droplets trapped in an acoustic field as well as on droplets in a mini-spray dryer. The 20 predictions of the models were found to be in reasonable agreement with the experimental data, in terms of droplet shrinking and buckling, 22 particle yield, and spatial distribution in the spray dryer mockup.

Introduction

Spray drying technology is commonly used in numerous process 30 industries. It is extensively used for food processing, as well as in polymer, pharmaceutical, and porous material engineering, to obtain 32 powders composed of solid particles with well-defined characteristics, such as particle morphology, size distribution, porosity, and density 34 [START_REF] Bonazzi | Quality Changes in Food Materials as 918 Influenced by Drying Processes[END_REF][START_REF] Cheow | Spray drying formulation of 928 hollow spherical aggregates of silica nanoparticles by experimental design[END_REF][START_REF] Cotabarren | Modelling of the spray drying process for particle design[END_REF][START_REF] Fu | Shrinkage 946 behaviour of skim milk droplets during air drying[END_REF][START_REF] Langrish | New Engineered Particles from Spray Dryers: 970 Research Needs in Spray Drying[END_REF][START_REF] Langrish | Prospects for the Modelling and 972 Design of Spray Dryers in the 21st Century[END_REF] 36 [START_REF] Lintingre | Control of 990 particle morphology in the spray drying of colloidal suspensions[END_REF][START_REF] Sen | Buckling-driven morphological 1050 transformation of droplets of a mixed colloidal suspension during evaporation-induced self-assembly by spray drying[END_REF][START_REF] Singh | Spray drying formulation of 1054 amorphous solid dispersions[END_REF][START_REF] Sosnik | Advantages and challenges of the 1064 spray-drying technology for the production of pure drug particles and drug-loaded polymeric carriers[END_REF][START_REF] Sperling | Droplets, Evaporation and a 1068 Superhydrophobic Surface: Simple Tools for Guiding Colloidal Particles into Complex Materials[END_REF] 38 [START_REF] Walton | The Morphology of Spray-Dried Particles: The Effect of Process Variables upon the Morphology of 1080 Spray-Dried Particles[END_REF]. Among the many droplet-to-particle drying patterns, three typical behaviours can be distinguished (Lefebvre 40 and McDonell, 2017;[START_REF] Walton | The Morphology of Spray-Dried Particles: The Effect of Process Variables upon the Morphology of 1080 Spray-Dried Particles[END_REF]. In the first one, the sprayed droplets tend to form a "skin" at their surface (which is 42 generally the case with polymers); in the second, the droplets are susceptible to crystallization (if there are dissolved components); and in 44 the third, the droplets show an agglomerative tendency (which is the case with colloidal suspensions). This study was focused on the third 46 behaviour.

48

Figure 1 (a-d): Scanning electron and (f) transmission electron images of particles formed by: the drying of (a, b, d) suspension

droplets of quasi-monodisperse silica nanoparticles (zoomed in (e)), (c) a suspension droplet of boehmite nanoparticles (zoomed in (f)).

In the spray drying process of colloidal suspensions, the solid nanoparticles, suspended in an aqueous solvent, are sprayed with an 54 assisted nozzle into a chamber, which is supplied with an additional hot gas flow. The droplets are transported by the gas, while getting dried.

56

The nanoparticle agglomerates (henceforth referred to as just "particles") and are essentially collected at the bottom of the spray 58 chamber when the solvent within the droplets is fully vaporized (see Figure 1). The control of both unit operability and outlet particle 60 properties requires a thorough understanding (possibly through modeling) of various complex phenomena, which include: (i) interaction 62 of the gas and solid flows in the chamber; (ii) drying mechanism at the particle scale; (iii) particle-particle collisions; and (iv) particle adhesion 64 on the walls. In the next paragraphs, we briefly review and understand how these phenomena are fundamental.

66

The interaction of gas and solid flows in a spray chamber (i) is intrinsically linked to the spray chamber geometry, gas injection, and 68 the suspension injection nozzles. All these parameters have significant effects on the particle residence time. The modeling of particle transport 70 in a gas flow requires extensive computational fluid dynamics (CFD) calculations, based either on the Euler-Euler or Euler-Lagrangian 72 methods, e.g., [START_REF] Poozesh | On the particle formation in 1032 spray drying process for bio-pharmaceutical applications: Interrogating a new model via computational fluid dynamics[END_REF]. [START_REF] Mezhericher | Theoretical Models of Single Droplet Drying Kinetics: A Review[END_REF] overviewed the various approaches for 74 modeling of droplet drying kinetics. The identified models were suitable for droplets with insoluble solids, dissolved solids or both types of solid 76 content. They classified these approaches into four different categories: semi-empirical models, utilizing the concept of characteristic drying 78 curve; deterministic drying models describing the processes within the droplet with momentum, energy, and specie conservation; deterministic 80 models coupling distribution of solid component described by population balance; and, finally, reaction engineering methods. During 82 the first stage, the nanoparticles in the suspension agglomerate as the droplets shrink, until they form a crust on the droplet surface, e.g., [START_REF] Cheow | Spray drying formulation of 928 hollow spherical aggregates of silica nanoparticles by experimental design[END_REF][START_REF] Fu | Shrinkage 946 behaviour of skim milk droplets during air drying[END_REF][START_REF] Lauga | Evaporation-Driven Assembly of Colloidal Particles[END_REF][START_REF] Onofri | Sizing highly-ordered buckyball-shaped aggregates of colloidal 1018 nanoparticles by light extinction spectroscopy[END_REF][START_REF] Style | Crust formation in drying colloidal suspensions[END_REF][START_REF] Yarin | Drying of acoustically levitated droplets of liquid-solid suspensions: 1092 Evaporation and crust formation[END_REF]. In the second 86 stage, depending on the rigidity of the crust, the particles (i.e., solid shells with a liquid core) remain spherical, but continue to dry at a 88 constant volume. Alternatively, their shape can start to deviate from being spherical owing to the deformation (buckling) of their crust 90 [START_REF] Lintingre | Controlling the buckling instability of drying droplets of suspensions through colloidal interactions[END_REF][START_REF] Lintingre | Control of 990 particle morphology in the spray drying of colloidal suspensions[END_REF][START_REF] Pauchard | Invagination during the collapse of an inhomogeneous spheroidal shell[END_REF][START_REF] Sen | Formation of hollow spherical and doughnut microcapsules by evaporation 1046 induced self-assembly of nanoparticles: effects of particle size and polydispersity[END_REF][START_REF] Tirumkudulu | Buckling of a drying colloidal drop[END_REF]; see Figure 2. Walker et al.

92

(1999) discuss the effect of inter-particle forces on the buckling phenomenon. According to their model, strong repulsive forces between 94 colloids will tend to a bifurcation between droplet shrinking and buckling phenomena. Conversely, attractive inter-particle forces will 96 help to conserve the droplet spherical shape along the complete drying process. The shrinking and buckling processes have a significant 98 influence on the gas-solid friction forces, flow conditions, and particle yield of the spray drying unit [START_REF] Jubaer | 964 On the importance of droplet shrinkage in CFD-modeling of spray drying[END_REF]. The particle-particle 100 collision effects are usually considered minimal, compared to the particle-wall bouncing (iii), and specifically, the particle sticking and 102 droplet wetting effects (iv), e.g., [START_REF] Ali | CFD Simulation of a Counter-current Spray 912 Drying Tower with Stochastic Treatment of Particle-wall Collision[END_REF]. In fact, the dropletdroplet and particle-particle collisions have a lower probability for the 104 divergent sprays used in spray dryers. However, the quality of the spray created by the nozzle(s) and the fouling of the walls are considered as 106 key parameters, governing the yield of industrial spray dryers, e.g., [START_REF] Sirignano | Fluid Dynamics and Transport of Droplets and Sprays[END_REF].

108

A literature review of spray dryer models for practical relevance to operating problems reveals a great variability of complexity. Full spray 110 dryer models were classified according to their complexity by Oakley [START_REF] Oakley | Spray Dryer Modeling in Theory and Practice[END_REF] and ranked models into four levels ranging from simple 112 heat and mass balances (level 0), Heat and Mass Balances with solidvapor equilibrium (level 1), Rate-based with simplifying assumptions 114 about particle motion Level 2A and Rate-based with simulation of gas flow and particle motion obtained from CFD (Level 2B). Despite the 116 recent developments in the CFD modeling of spray dryers, e.g., [START_REF] Cotabarren | Modelling of the spray drying process for particle design[END_REF][START_REF] Pinto | Development of an axisymmetric population balance model for spray 1028 drying and validation against experimental data and CFD simulations[END_REF][START_REF] Poozesh | On the particle formation in 1032 spray drying process for bio-pharmaceutical applications: Interrogating a new model via computational fluid dynamics[END_REF], the operating conditions required to obtain powders with well specified properties, such as morphology and specific area, e.g. [START_REF] Walton | The morphology of spray-dried particles a qualitative view[END_REF] 120 are still essentially established through an empirical approach (i.e., trial and error). Such an approach is not only time consuming, but also often 122 inadequate for scaling up the process systems and pilot plants, and for extensive parametric studies. Thus, any affordable and efficient 124 modelling approach that takes into account the basic particle drying mechanisms and the hydrodynamics in the spray chamber is highly 126 desirable.

With this perspective, the present work proposes an efficient numerical 128 model that accounts for the drying process at the droplet scale, and the interactions and transport phenomena at the scale of the spray dryer unit.

130

The numerical results and discussions were supported by experiments carried out on boehmite and silica colloidal suspensions using a mini

Single droplet in an acoustic trap 162

To study the drying of a single droplet, a droplet levitation method was 164 chosen over the other methods, e.g., [START_REF] Daubersies | Séchage de fluides complexes en géométrie 936 confinée[END_REF][START_REF] Hu | Evaporation of a Sessile Droplet on a Substrate[END_REF][START_REF] Lauga | Evaporation-Driven Assembly of Colloidal Particles[END_REF], to limit the effects (e.g., surface 166 contamination and triple line) that are not relevant for spray drying studies. Among the different methods for levitating a single particle 168 (acoustic, hydrodynamic, electrostatic, magnetic, and optical) [START_REF] Brenn | Evaporation of 922 acoustically levitated multi-component liquid droplets[END_REF][START_REF] Jakubczyk | Combining weighting and scatterometry: Application to a levitated 958[END_REF][START_REF] Maconi | Non-994 destructive controlled single-particle light scattering measurement[END_REF]Onofri et al., 170 1995;[START_REF] Onofri | Experimental validation of the vectorial complex ray model on the 1022 inter-caustics scattering of oblate droplets[END_REF][START_REF] Saha | Experimental analysis of thermo-physical processes in acoustically levitated heated 1042 droplets[END_REF][START_REF] Sperling | Droplets, Evaporation and a 1068 Superhydrophobic Surface: Simple Tools for Guiding Colloidal Particles into Complex Materials[END_REF][START_REF] Yarin | On the acoustic 1094 levitation of droplets[END_REF][START_REF] Yu | Optical caustics associated with the 1096 primary rainbow of oblate droplets: simulation and application in non-sphericity measurement[END_REF], the acoustic levitation was However, this method also suffers from some drawbacks, such as acoustic streaming effects(i.e induced recirculations, [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF] 186 [START_REF] Yarin | Evaporation of acoustically levitated droplets[END_REF], which need to be corrected or minimized. The experimental facility, specially developed for this study, is shown in 188 Figure 3. It was built around an ultrasonic levitator (1-2), operating at 100 kHz (i.e., a wavelength of 3.2 mm). The levitator is enclosed in an 190 evaporation chamber (3). A suspension droplet (4) is trapped slightly below a pressure node of the acoustic field. In fact, this standing 192 acoustic field is the superimposition of a travelling wave produced by the acoustic transducer (1) and a counter travelling wave reflected by the 194 parabolic reflector (2). This reflector (with a convergent internal profile) was designed with a metal 3D printer [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF].

196

Prior to starting the experiments, the temperature (T) and relative humidity (RH) within the chamber are set with a controlled evaporation 198 and mixing (CEM) system (not shown in the Figure) [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF]. This CEM allows, via the inlet (5) and a circular hole in the reflector 200 (6), the generation of a vertical laminar jet of dry steam (7), which is blown on the droplet. This jet subsequently exits at the top of the 202 chamber (8). It is worth noting that this acoustic trap is operated upside down, compared to the usual acoustic levitators. This configuration 204 helps stabilize the droplet position by a distance of a few hundred micrometers, when the drag force induced by the jet increases. Thus, the 206 droplet can stay in equilibrium under the action of three major external forces, namely gravity, drag, and acoustics (from the incident and 208 reflected acoustic waves). The evaporation chamber, with a double wall water heating system (9) and thermocouples (10) distributed vertically, is also equipped with eight optical windows (11). The latter allows the introduction of a relative humidity sensor (not shown) into the chamber, 212 as well as the introduction of the droplet in the trap. It also facilitates the optical diagnostics. For the present study, two optical diagnostic systems 214 are setup, a particle image velocimetry (PIV, 12-13) system to characterize the gas velocity field around the droplet, and a 216 shadowgraph (13-14) for imaging the backlighted droplet. The shadowgraph measures the size of the droplet or the particle with a 218 subpixel resolution [START_REF] Fdida | Drop size distribution measured by 938 imaging: determination of the measurement volume by the calibration of the point spread function[END_REF][START_REF] Onofri | Chapter II: Optical particle 1008 characterization[END_REF], provided it is a spherical or spheroidal object (Onofri et al., 220 2015). The PIV results [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF], obtained by seeding the gas jet by smoke from incense [START_REF] Melling | Tracer particles and seeding for particle image velocimetry[END_REF], have shown that the jet is 222 laminar, in a first approximation, with a nearly flat velocity profile at the position and scale of the droplet. The initial droplet Reynolds number 224 (Re) investigated was in the range of 106 -230, corresponding to a local gas velocity of 1.66 -3.6 m/s. Note that for a droplet Re greater than 226 106, the jet would cause the advection of the eddies generated by the acoustic streaming, e.g., [START_REF] Al Zaitone | Evaporation of pure liquid 908 droplets: Comparison of droplet evaporation in an acoustic field versus glass-filament[END_REF]Yarin et al., 228 1999). Owing to the limitations of the transducer electronics, the temperature range within the chamber is limited to 20 -65 °C.

230

Depending on the temperature, its relative humidity can be adjusted between 2.5% and 95%. In this study [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF], experiments were 232 conducted with two types of aqueous suspensions -one containing colloidal silica beads (Klebosol™, from AZ Electronic Materials), and 234 the second, irregularly shaped boehmite particle (Pural SB3, an aluminum oxide hydroxide prepared in-house) in different 236 concentrations. These colloids differed especially, in their nanoparticle shapes and particle size distribution (PSD), see Figure 1 (e-f). The silica 238 beads were almost perfectly spherical and quasi-monodisperse with a radius 𝑟 𝑠𝑜𝑙 (±𝜎) = 25 ± 3 𝑛𝑚 [START_REF] Onofri | Sizing highly-ordered buckyball-shaped aggregates of colloidal 1018 nanoparticles by light extinction spectroscopy[END_REF], while the boehmite 240 nanoparticles were mostly irregularly shaped and elongated with 𝑟 𝑠𝑜𝑙 (±𝜎) = 9 ± 6 𝑛𝑚 [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF].

Spray in a mini spray dryer 244

The mini spray drying experiment was built around a mini spray dryer B-290, commercialized by BÜCHI Labortechnik AG. Figure 4 shows 246 the key components of this laboratory mock-up, extensively studied and documented in the literature, e.g., [START_REF] Cheow | Spray drying formulation of 928 hollow spherical aggregates of silica nanoparticles by experimental design[END_REF]Cotabarren et al., 248 2018;[START_REF] Pinto | Development of an axisymmetric population balance model for spray 1028 drying and validation against experimental data and CFD simulations[END_REF]. It allows producing droplets, of a few tens of micrometers in diameter, which are composed of aqueous or non-250 aqueous suspensions. This system was operated in an open mode, i.e., the atmospheric air was heated up and transported to the drying chamber 252 and then vented back into the atmosphere. This device allows adjusting the gas temperature up to 220 C for a maximum air flow of 35 m 3 /h.

254

The nozzle was assisted with nitrogen up to 0.4 m 3 /h at 5.5 bar. As the residence is very limited in this device (close to 1 s), we will assume 256 constant temperature and humidity based on logarithmic average between the inlet and the outlet. buckling. On the other hand, more complex particle drying models ware developed taking into account the droplet shrinking, the crust formation 276 and the prediction of buckling phenomena. In the case of crystallization phenomena, several authors have coupled those complex models with a 278 population balance in order to predict the nucleation and the growth of solid particles (Handscomb et al., 2009a;Handscomb et al., 2009b). The We consider a single droplet, initially spherical and homogeneous. The experimental conditions are uniform (i.e no gradients in temperature and 290 species concentrations). In the drying process of this droplet, the first observation is a shrinking, characterized by an isotropic reduction of its 292 radius (see Figure 2). In most practical situations of interest, the hypothesis of homogeneity of the properties of the droplet is not valid.

Materials: (A) additional gas injection; (B) nozzle gas supply; (C) suspension supply; and (D) collected powder. Technical parts include

(1) peristaltic pump; (2) assisted nozzle; (3) gas heater; (4) drying chamber; (5) outlet; (6) collection pot of the drying chamber; (7)

294

In fact, the evaporation of the water at the droplet surface induces a solid concentration profile within the droplet. This is particularly the 296 case when the Peclet number (Pe) of the droplet exceeds unity,

𝑃𝑒 = 1 𝐷 𝑠𝑜𝑙 𝑅𝜕𝑅 𝜕𝑡 > 1, 298 (1)
where R is the radius of the droplet and D sol is the diffusion coefficient 300 of the solids (i.e., nanoparticles), within the suspension forming the droplet, calculated using a modified Stokes-Einstein equation in order 302 to account for the solid concentration effect (Sobac et al.,2020). To calculate the solid concentration profile within the droplet, we discretize the droplet along the droplet radius in concentric layers of equal thickness. The radial transport of solids into the droplet is expressed 306 through Fick's diffusion law, which reduces, for a spherically symmetric object [START_REF] Crank | The mathematics of diffusion[END_REF], to:

308 dn sol dt = 4πD sol ∂ ∂r (r 2 ∂C sol ∂r )
(2)

310
where n sol is the local number of moles of solid in a layer of thickness dr at a radial coordinate r; C sol is the local molar concentration of solid;.

312

Eq. ( 2) is accompanied by two boundary conditions for the solids, namely no diffusion at the center (𝑟 = 0) and outside (𝑟 = 𝑅) of the 314 droplet; that is,

𝐷 𝑠𝑜𝑙 • 𝜕𝐶 𝑠𝑜𝑙 𝜕𝑟 | 𝑟=0 = 0 316 𝐷 𝑠𝑜𝑙 • 𝜕𝐶 𝑠𝑜𝑙 𝜕𝑟 | 𝑟=𝑅 = 0 318 (3)
This equation is numerically solved using a finite difference approach.

320

The effect of internal circulation on evaporation of fluid droplets containing nano-sized particles caused by viscous effects at the liquid-322 gas interface in the convective environment is not investigated in this work. The internal circulation is expected to increase the effective 324 particle diffusion and leads to the concept of effective Peclet number [START_REF] Wei | Effects of internal circulation and particle mobility during nanofluiddroplet evaporation[END_REF]. In this work, the contribution of internal circulation Water emerges as vapor from the droplet outer layer. At this 344 interface, the water vapor in the external gas mixture is assumed to be in thermodynamic equilibrium with its condensed state. The water vapor 346 pressure is deduced from the vapor pressure of free water P wat vap,free , and the activity coefficient of water aw: P wat vap,sat = P wat vap,free a w [START_REF] Fu | 942 Reaction Engineering Approach (REA) to model the drying kinetics of droplets with different initial sizes-experiments and analyses[END_REF]. During drying, the droplet rapidly heats to the wet-bulb temperature 358 (Td), and its temperature remains constant whilst the surface remains saturated with moisture [START_REF] Handscomb | A new model for the 952 drying of droplets containing suspended solids[END_REF]. A second drying 360 period begins when moisture can no longer be supplied to the surface at a rate sufficient to maintain saturated conditions. The transition between 362 these two regimes occurs at the critical moisture content and may also coincide with the beginning of crust formation [START_REF] Cheong | A receding interface model for the drying of slurry droplets[END_REF]. In this work, we will not account for that change of temperature after the crust formation phase.

366

The molar water balance in the outer layer is : where D wat vap is the diffusion coefficient of water vapor in the surrounding atmosphere and α gs is an additional correcting factor that is adjusted 388 experimentally in the acoustic trap experiment [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF].

In this work, a numerical discretization was used considering that all 390 layers are of equal and constant thickness, except the outer one. The thickness of this layer must vary with the evaporation of water. This implicit time dependency of the outer layer thickness is written as follows:

394

dr| r=R = V wat + V sol 4πR 2 (9) 396
where V wat and V sol are the volumes of the liquid water and solids contained in this layer. The new radius of the droplet (at time t) is 398 obtained by summing up all thicknesses as R = ∫ dr R 0

. At this stage, there is only solids and liquid water in the droplet; therefore, the volumes of 400 water and solid in each layer are recalculated from the corresponding number of moles as V wat = (n wat M wat )/ρ wat liq and V sol = (n sol M sol )/ρ sol .

402

For the solid and liquid water concentrations in a layer, we use the relations C sol = n sol /V lay and C wat = n wat /V lay .

404

The condition of formation of the first crust is defined by a limit solid concentration within the suspension, which is C sol ≥ C sol lim . This condition 406 can also be expressed in terms of a limit suspension density, with the dry zone of the crust, can also be introduced (Figure 5). In the previous equation, the term 𝜀(𝐷 𝑤𝑎𝑡 𝑣𝑎𝑝 /𝜏) is the water vapor diffusivity in the dry zone of the crust [START_REF] Reuge | A dimensionless study of the evaporation 1038 and drying stages in spray pyrolysis[END_REF].

452

Finally, the molar flow rates equations ( 2) and ( 5 Step 4 ends when the crust is completely dry and the menisci in the 458 pores reach the liquid core of the particle.

Core reduction and crust thickening (Step 5 and iterations with Steps 3 and 4)

462

Once the crust is dried, the water remaining in the core continues to 464 evaporate. If there is a deformation of the crust, it does not necessarily result in a gas inlet (Step 3). However, if the droplet shape evolution is 466 mechanically blocked by the rigidity of the crust, the water released by the liquid core must be compensated for by some gas inlet from the 468 surrounding atmosphere. In the latter case, three phases (water, solid, and gas) are present at the same time in the core, and an iteration 470 between Steps 3 and 5 needs to be performed. To account for this effect on the core (i.e. all layers of index l such that 𝐿 𝑙 ≤ 𝑅 𝑐𝑜𝑟 ), Eq. ( 2) must be 472 corrected by a gas holdup ε gas for the gas in the core: At this stage, two scenarios (a and b, see Figure 2) are envisaged for the distribution of the gas into the core In scenario (a), the gas is 486 distributed peripherally and the core receives the gas flow, as given by dε gas /dt = (dV gas /dt)/(4πR core 2 dr), when r = Rcore; and dε gas /dt = 0 488 when r < Rcore. In scenario (b), the gas is homogenously dispersed within the core, and the temporal variation of the gas retention is 490 constant along the core radius, as dictated by dε gas /dt = (dV gas /dt)/ (∫ 4πR core 2 dr R core 0 ) 492 for r = [0, Rcore]. Note that the gas retention rate ε gas = V gas /V tor is 494 directly related to the porosity [START_REF] Johnson | Impact of a Porosity-Dependent Retention Function on Simulations of Porous 962 Flow[END_REF].

dn sol dt =
Writing the liquid water balance in the core requires accounting for the 496 counter-diffusion of solids and gas for the two scenarios; for scenario (a): When the concentration of the solids in the outer layer reaches the limit C sol lim , in Step 5, the crust thickens again and the number of layers 508 discretizing the core is reduced by one. This process is repeated until the core completely dries up. 510

Case of particle shape deformation during crust drying 512

In this section, the particular case of particle shape deformation 514 from a sphere to a torus is modeled from a geometrical point of view. In other words, the buckling phenomenon is not predicted but the 516 deformation is simulated depending on a deformation coefficient determined experimentally [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF]. In a further work, this 518 parameter can be correlated to a buckling criterion as proposed in the work of [START_REF] Timoshenko | Theory of Elastic Stability[END_REF]. were spherical to spindle-torus shaped [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF]. When the crust is formed, the flowrate of liquid water leaving the particle (due to In geometry, a torus is a surface of revolution generated by revolving a 548 circle in three-dimensional space about an axis that is coplanar with the circle (see Figure 6). intermediates shapes between a sphere and a ring torus (see Figure 7). The volume of all intermediate particle shapes between a sphere and a torus can be calculated as follow:

560 { R tor + r tor = R cru if R tor ≤ r tor , V tor = 2π [R tor r tor 2 [θ l - sin(2θ l ) 2 ] + 2 3 r t 3 sin 3 (θ l )]
if R tor > r tor , V tor = 2π 2 r tor 2 R tor 562 [START_REF] Brenn | Evaporation of 922 acoustically levitated multi-component liquid droplets[END_REF] with θ l = π -Acos ( R tor r tor ) 564

Given that the system of equations Eq (18) allows to calculate at each 566 time the particle volume Vtor after the first crust formation, one can deduce the temporal evolution of Rtor and rtor solving the system of 568 equations Eq [START_REF] Brenn | Evaporation of 922 acoustically levitated multi-component liquid droplets[END_REF]. free L wat /(R gas T). For example, when T=353.15K and R = 500 µm, we find that with ∆T/T = 0.002 (i.e., approximately 0.1K over 582 353.15K). Thus, the temperature gradient within the particles and droplets is effectively negligible.

584

Spray dryer model 586

As a first step, this model uses an Eulerian approach to determine the gas flow properties within the spray drying chamber. Then, these 588 calculations are combined with the droplet drying model using a

Lagrangian approach, which injects and tracks the suspension droplets, 590 individually and sequentially.

We will consider only the gas flow without any disturbance due to 592 particle motion. This assumption seems acceptable for this lab tool because of the low liquid volume fraction, and a small droplet size 594 distribution. For bigger dryer, it will not the case anymore and it will be necessary to take into account a better coupling for mass and energy. 596

Gas flow 598

The general gas flow field in the chamber is calculated by solving the Navier-Stokes equations with the finite element method (using 600 COMSOL Multiphysics® 5.3a). For the turbulence, the V2-f model is used [START_REF] Laurence | A robust formulation of the v2-f model[END_REF]. Briefly, the latter contains two more [START_REF] Jubaer | 964 On the importance of droplet shrinkage in CFD-modeling of spray drying[END_REF]. Owing to the symmetry of the dryer geometry only half of its geometry is simulated. The global flow

The droplet momentum equation account for the evolution of the mass and dynamics of a single droplet along its trajectory, and their form is as 644 follows: where ϑ slip stands for the particle slip velocity with respect to the surrounding gas and CD is the drag force coefficient.

m(t) dv ⃗ dt = F f ⃗⃗⃗ + m(t) g ⃗ 646

656

Droplet-droplet collisions and spray-induced turbulence are neglected; however, collisions with the cylindrical and conical walls of the dryer 658 are modeled. An elastic rebound (total reflection) is assumed for particles with a crust. A sticking (or more precisely wetting) process is 660 assumed for the liquid droplets. The coupling of the resulting gas flow field with the droplet injection, transport, interaction with the walls, and 662 their drying kinetics, is implemented in Fortran 90 computer language.

Results and discussions

Single droplet and droplet drying model

Experiments on the drying of a single droplet in levitation were 666 conducted on droplets of silica and boehmite suspensions [START_REF] Gaubert | Caractérisation et modélisation des phénomènes gouvernant le séchage par atomisation de suspensions colloïdales 950 Aix-Marseille University[END_REF], for a relative humidity of 2.5% (to limit the harmful streaming effects), a temperature of 29 to 51 °C (see Figure 10), and gas-jet velocities (Vjet) ranging from 1.66 to 3.60 m/s. This range of parameters 670 is well below the drying conditions encountered in the industry, but it is the price to pay for obtaining detailed experimental data.

672

For these conditions, Pe of the initial droplets was approximately 10, while the Re was within the range 106 -230. However, it should be 674 noted that Re increased during the course of the experiment (with a reduction in the droplet size). For the numerical simulations, the initial 676 number of layers was set to 50, as a good trade-off among the computational efforts, resolution, and numerical dispersion. The later 678 comes from the finite difference method and notably the second-order central difference in the diffusion term, with error magnitude (d r 3 ).

680

The other fixed (known a priori) parameters of the simulations were 𝛼 𝑑𝑒𝑓 = 1, estimated from the particle image analysis; and 𝜏 ≈ 2.75 ± 682 0.25, estimated with a classical mercury porosimetry analysis of the collected powder. The diffusivity of the nanoparticles was estimated 684 using the Stokes-Einstein equation.

Figure 8 illustrates a typical evolution, in three parts, for the normalized 686 particle surface area 𝐴(𝑡)/𝐴(𝑡 = 0) versus time. The 4𝜋 coefficient in front of time t is a normalization term used in the well-known 𝐷 2 -𝑙𝑎𝑤 688 evaporation models, e.g., [START_REF] Ranz | Evaporation from Drops[END_REF]. As noted, we first observed a linear decay (with slope 𝛽) of the particle area. It was 690 followed by a transition zone, the start of which indicated crust formation, and the end of which corresponded generally to particle 692 buckling (if present). The third part is similar to a plateau, slightly decreasing in buckling, and corresponding to the particle drying.

particle were not exactly facing the camera, which explains the large blank space in part 3 of Figures 8. Figure 9 presents the experimental estimation of α gs and C sol lim in the case 724 of silica suspensions with various concentrations. Both coefficients were obtained by comparing, with a classical iterating and minimizing 726 method, the experimental data for different temperatures and gas-jet velocities, and the predictions of the droplet drying model. In the present 728 case, i.e., for silica suspensions, the optimal values were found to be α gs (±1𝜎) = 0.95(±0.16) and C sol lim (±1𝜎) = 0.12(±0.02). Revisiting

+

All experiments with the mini spray dryer B-290 were carried-out for a 760 maximum gas flow temperature of 200 °C, a relative humidity of 2.5%, and a gas flowrate (fixed by the manufacturer) of 30 m 3 .h -1 . The gas 762 flow injected simultaneously with the suspension through the nozzle is not considered in the simulations as it is only representing one percent 764 of the total inlet gas flow. Two boehmite suspensions were sprayed with a fixed flowrate of 0.44 L.h -1 . The PSDs of the droplets sprayed were 766 estimated to be of with parameters (30,1.5) and(40, 1 For the simulations, a constant temperature across the spray dryer chamber was assumed, even though a decrease of approximately 30 °C 782 from the atomizer to outlet regions was observed experimentally. In these conditions, the Peclet number of the droplets was approximately 784 10, which corresponded to a diffusion regime. The droplet temperature was almost constant and remained below the ebullition temperature.

786

Figure 12 shows some cross-sectional views illustrating the gas flow structure and particle trajectories within the spray chamber, for three 788 values of the gas flow rate, 2, 10, and 30 m.s -1 (experimental conditions). The asymmetry induced by the outlet was clear. The 790 increase in the gas recirculation and droplet path lengths (and thus, the resident time) with the gas flow rate was also evident. obtain reliable statistics. To this end, Figure 13 shows the numerical estimation of the particle mass fractions (yields), in the atomizer region, 806 spray dryer outlet, and on the walls of the spray dryer chamber, versus the number of droplets sprayed, for a gas flowrate of 30 m 3 /h 808 (corresponding to a mean velocity of nearly 3 m/s) and RR-PSD of (30, 1.5).

816

A good convergence was obtained for 1000 droplets, i.e., a value 818 that was systematically used for all the following simulations. Figure 12 also indicates that nearly 78% by mass of the droplets were stuck to the 820 walls, an amount that is definitely detrimental to the drying process. This was also observed in the experiments; See Figure 14, which shows 822 an image of the B-290 spray drying chamber after a boehmite suspension doped with a small amount of red dye was sprayed. The 824 deposit (pink color) on the internal wall of the chamber could be easily observed. is too important. The B-290 gives only access to the mass fraction of the particle yield at the outlet of the dryer. By collecting different particle samples, this value was estimated to be 0.25 ± 0.05, which was in good 852 agreement with a numerical simulation value of 0.22 ± 0.005, as estimated for the same conditions (gas flowrate of 30 m 3 .h -1 and RR-

Conclusion 868

The predictions of the single-particle drying model, in term of the 870 droplet shrinking process, was found to be in good agreement with predictions on droplet buckling and particle drying processes, based on some information known a priori (mostly, the concentration limit for 874 crust formation and deformation coefficient), were found to be less satisfactory, albeit acceptable. To pursue further on this aspect, it is 876 essential to model the pressure drop and mechanical constraints within the crust. It is also necessary to develop new experimental diagnoses 878 that allow the probing of the internal structure of the droplets, especially the crust formation, in real-time, e.g., [START_REF] Jakubczyk | Combining weighting and scatterometry: Application to a levitated 958[END_REF]Lamadie 880 et al., 2012;[START_REF] Onofri | Size, velocity, and concentration in suspension measurements of 1012 spherical droplets and cylindrical jets[END_REF][START_REF] Onofri | Electromagnetic scattering 1014 from a multilayered sphere located in an arbitrary beam[END_REF]. The latter improvement is already underway. The full spray drying model allows

132Figure 2 :

 2 Figure 2: Schematic diagram of the droplet drying model in five steps:

  172found to be the most flexible to trap and characterize both spherical and non-spherical particles in a gaseous flow, whose sizes typically range 174 from one mm, down to a few tens of micrometers.

Figure 3 :

 3 Figure 3: Experimental setup (not to scale) of drying of a suspension droplet in acoustic levitation: (1) acoustic transducer; (2) acoustic

  184

Figure 4 :

 4 Figure 4: Experimental setup: schematic of the mini spray dryer B-

  particles drying models are described by[START_REF] Poozesh | On the particle formation in 1032 spray drying process for bio-pharmaceutical applications: Interrogating a new model via computational fluid dynamics[END_REF] according to their complexity. Simplest models describe an 270 homogeneous droplet where only average properties are calculated like overall water content. Due to their low computing time, coupling with 272 complex hydrodynamics is facilitated. Those models cannot predict crust formation due to solid concentration radial profile nor particle 274

280

  model developed in this work is close to Handscomb's approach without taking into account the population balance (no crystallization 282 phenomena).

  .1 Droplet shrinking and formation of the first crust (Steps 1 286 and 2) 288

  326 will be encompassed in the maximum solid concentration determining the crust formation, especially since we are working at high Peclet 328 values. At a constant volume, the diffusion of solids induces a counter-diffusion 330 of the liquid water. A volume flow balance must be valid for each layer of volume Vlay:

  348with subscript sat for saturation. The dependency of vapor pressure of free water on temperature can be modeled with the Antoine's equation, 350 P wat vap,free = A -B/T where, for instance, A ≈ 13.7mmHg, and B ≈ 5120 mmHg. °C for T=[20,70]°C. The activity coefficient of water 352 depends moderately on the nature of the solids and their concentration; however it depends exponentially on the temperature through the 354 relation 𝑎 𝑤 = 𝑎 0 exp[-𝐸 𝑏 /(𝑅 𝑔𝑎𝑠 𝑇)] (Blandamer et al., 2005). As an example, for the boehmite suspension used later, the constants a 0 ≈ 356 1850 and E b ≈ 20 kJ. mol -1 were estimated experimentally.

  wat + M sol C sol lim (1 -ρ wat /ρ sol ). When the crust is not yet 408 formed, it is necessary to control the water quantity contained in the outer layer at each calculation step. In practice, when n wat R ≈ 0 the total 410 number of layers is decreased by one, to account for the droplet shrinking. On the other hand, when the crust formation limit conditions 412 are reached in the outer layer, the droplet size reduction is to be blocked (i.e. rigid crust and evaporation at constant volumes). To do so, the 414 number of layers is then simply fixed when the conditions C sol ≥ C sol lim or 𝜌 𝑠𝑢𝑠 ≥ ρ sus lim are first fulfilled. At the end of Step 2, the particle is 416 composed of a liquid core (remaining suspension) surrounded by a hardening mantle (growing crust). 418 3.1.2 Crust drying (Step 3) 420 During this step, the water remaining in the crust is progressively 422 evaporated. As in Steps 1 and 2, the external transfer can be characterized by an external transfer coefficient k gs . In fact, the evaporation of water is now a combination of the internal diffusional transport through the pores of the crust, visible in the Figure 5, and the 426 external mass transfer towards the surrounding atmosphere. The diffusion of water vapor through the dry pores is modeled with an 428 apparent transfer coefficient k gs app , defined as the ratio of the molecular diffusion of water vapor in free space to the product of thickness  and 430 mean tortuosity  of the dry zone of the crust, k gs app = D wat vap /(τδ) (Reuge and Caussat, 2007). Finally, a global transfer coefficient k gs glo that 432 accounts for the decrease of the wetted area A wet of the crust, in contact

  434

Figure 5 :

 5 Figure 5: Liquid core shrinking after crust formation

  460

520

  After Steps 1 and 2, when the crust is still thin, the outlet flow of the liquid water can induce the buckling (Step 3) of the particle and the 522 entry of gas within the liquid core (Step 4). The modeling of the crust deformation is a complex problem[START_REF] Miglani | Sphere to ring morphological 1002 transformation in drying nanofluid droplets in a contact-free environment[END_REF] that is 524 tackled in a simple way in this present work. With our radial model, we can evaluate its influence on the kinetics of the drying by introducing 526 some a priori information from the experiments. The ring-torus-shaped particles (see Figure1and Figure2) are commonly reported in the 528 literature, and were essentially observed in our experiments with silica suspensions. For boehmite suspensions, most of the particles observed 530

  be compensated by gas entering into the particle and / or by a change in particle volume due to its deformation from a 534 spherical to a toric shape. The balance between both phenomena is obtained by introducing a weighted deformation coefficient (def) = [0,1]. Therefore, the variation of particle volume (Vtor) in time and the gas flowrate entering into the particle can be determined as follow:

  Figure 6: Torus geometry

Figure 7 :

 7 Figure 7: Intermediate shapes between a sphere and a torus as a function of Rtor and rtor

  the isothermal of the droplets and the particles during the drying process. To evaluate the validity of this hypothesis, let 574 us consider a particle in a surrounding drying gas at atmospheric pressure, saturated in water vapor. The maximum heat flux for water is k gs P sat,T free L wat /(R gas T), where L wat is the (latent) heat of vaporization of water. The maximum conductive flux inside the particle 578 can be estimated by a linear approximation of the Fourier's law, ∅ con = λ(∆T/R). If all the evaporative heat flux is driven by the droplet, then 580 ∆T/T = k gs P sat,T

602

  equations in addition to the classical -ε model(Launder, 1972). The first equation describes the transport of the turbulent velocity 604 fluctuations normal to streamlines and the second equation accounts for the non-local effects, such as the wall-induced damping of the turbulent 606 kinetic energy

  664

  718

Figure

  Figure 9: Experimental estimation of the gas-liquid mass transfer

730Figure 9

 9 Figure9, it is clear that the value C sol lim = 0.12 allowed retrieving the basic features of the experimental curve, even though the description of

740Figure 10 Figure 10 :

 1010 Figure 10 compares the slopes of the linear part of the evaporation curves obtained experimentally (βexp), with those from the simulations

Figure

  Figure 11: Spray drying of boehmite suspension: comparison of the

  810

Figure 13 :

 13 Figure 13: Convergence plots of the calculations versus the number of

Figure 14 :

 14 Figure 14: Comparison of numerical predictions for the axial

Figure 15 :

 15 Figure 15: Distribution of the particle mass fractions (yields) in the

  on a single-droplet in acoustic levitation. Its 872

882

  accounting for the droplet drying process, in addition to the geometry, gas flows, and atomization conditions in a realistic spray dryer. Its 884 predictions, in terms of particle mass fraction distribution in the dryer and the PSD, agree with the experimental data collected on the mini 886 spray dryer B-290. However, although the B-290 is widely used in the literature, its limited operating flexibility, excessive wall fouling, and a 888 lack of accessible data make it difficult to perform a complete validation of any spray drying model. The correction of the aforementioned 890 experimental limitations is a part of the perspectives gained from this work. Nevertheless, the results and validations reported here already 892 confirm the potential of the modeling approach introduced in the present work, especially in terms of optimizing the spray dryer's performance. the surrounding gas phase mol/m 3 C sol lim limit solid concentration of crust formation mol/m 3

  wat and V sol are the volumes of liquid water (subscript wat ) and solids (subscript sol) in a given layer, respectively; n wat and 𝑛 𝑠𝑜𝑙 are the 336 corresponding number of moles; M wat and M sol are the molecular weight of the liquid water and solid, respectively; and ρ wat , ρ sol are the

							(4)
	338
		corresponding densities. From Eq. (4), the variation in the number of
	340	moles of water in the liquid state within a layer is
	342			dn wat dt	= -	ρ wat ρ sol	M sol M wat	dn sol dt
							(5)
	332
		dV lay dt	= 0 =	d(V wat + V sol ) dt	=	d ( n wat M wat ρ wat	+ n sol M sol /ρ sol ) dt

334

where V

Acknowledgements 902 This work was partially funded by the French National Research Agency (ANR) under grant numbers ANR-13-BS09-0008-02, Labex 904 MEC (ANR-11-LABX-0092), and A*MIDEX (ANR-11-IDEX-0001-0).

behaviour is conserved by imposing symmetrical boundary conditions.

The spray dryer geometry is also decomposed in three parts, the gas 610 flow inlet system (an assister coaxial nozzle) [START_REF] Cotabarren | Modelling of the spray drying process for particle design[END_REF]; the spray dryer chamber itself; and the gas outlet (only partly visible in 612 the bottom right corner of Figure 12). All the dimensions are those of the BÜCHI B-290 mini spray dryer (e.g., spray chamber with a 614 cylindrical (cyl) body with a height Hcyl = 0.42 m and diameter Dcyl = 0.14 m; bottom cone (con) with a height hcon = 0.05 m; and a gas outlet 616 with a cylindrical T-junction located 0.04 m above the conical part). In the same way, the gas inlet has a classical coaxial and annular shape 618 with inner and outer radiuses R1 = 0.015 mm and R2 = 0.035 mm, respectively (see Figure 4).

Spray simulation 622

Atomization is a complex process [START_REF] Lebas | Numerical simulation of primary break-up and atomization: DNS and modelling study[END_REF] and is not modeled in the present work. Instead, the droplets are injected at the top

702

These behaviours, including the transition from spherical to ring-torus shape (𝛼 𝑑𝑒𝑓 = 1), were systematically observed for all silica suspensions 704 (i.e., all investigated temperatures, gas-jet velocities, and initial volume fraction in silica beads, C sol vol = 0.0032 to 0.16). For boehmite 706 suspensions and the same conditions (except that C sol vol = 0.0082 to 0.04), the evaporation curves were found to be similar; however, the final 708 particle remained almost spherical (𝛼 𝑑𝑒𝑓 ≈ 1) when Re < 106, and they adopted a horn torus shape (with 𝛼 𝑑𝑒𝑓 ≈ 0.8) when Re > 106 (Gaubert, 710 2017). Note that, in the acoustic trap, non-spherical particles tended to rotate on their own vertical axis (as depicted in Figure 8). We believe 712 that this slow rotation (approximately 1 -2 Hz) had a negligible influence of the evaporation process. However, this rotation was a 714 concern for optical diagnoses. In fact, with the shadowgraph system, the

parameters of the torus-shaped particle could not be measured, when the to evaluate the number of droplets that need to be tracked numerically to


Martin Jakoobi

Vincent Dardun

Clément Camp

Chloé Thieuleux

catalyst for the synthesis of functionalized polymethylhydrosiloxane oils and unconventional cross-linked materials

Co2(CO)8 as an efficient catalyst for the synthesis of functionalized polymethylhydrosiloxane oils and unconventional cross-linked materials

Introduction

Polyorganosiloxanes, commonly known as silicones, are semiinorganic polymers, which have found a wide use in many applications (for example elastomers, coatings, sealants etc.) due to their unique physical and chemical properties. To date, platinum-based complexes are the most widely used catalysts in siloxane hydrosilylation and cross-linking reactions involved in the preparation of silicone materials. 1,2 Although Pt-catalysts are highly effective at very low ppm levels for the functionalization of polysiloxanes, these processes lead in the end to the large scale loss of valuable precious-metal based catalyst which cannot be recycled. 3 Consequently, from an economical and environmental point of view, the use of platinum and other noble metal catalysts should be avoided in the modern-day synthesis of siloxane materials. ‡ Therefore, the development of environmentally benign catalytic systems should be on the forefront of silicone science. While currently, the dominance of Pt-based catalysts is still undisputed in the functionalization of silicone Si-H bonds, first row transition metal complexes have more and more contested their use. The applicability of the latter complexes in alkene hydrosilylation with small-size molecular silanes has been well covered by recent reviews, [4][5][6] however the functionalization of long-chain polysiloxane oils by non-precious catalysts is still underexplored. 2 To the best of our knowledge, the current types of functionalization of polysiloxane Si-H bonds are limited to the formation of new Si-O-R (R=alkyl, aryl, acyl) and Si-R (R=alkyl) bonds (Scheme 1) in polysiloxane oils. For example, Cu 7 and Zn 8 based catalysts, and tris(pentafluorophenyl)borane (B(C 6 F 5 ) 3 ) 9 are known to catalyze the synthesis of functionalized PMHS (polymethylhydrosiloxane) via dehydrogenative coupling using alcohols or carboxylic acids (Scheme 1a). However, when the formation of new Si-C bond is preferred, there is only one example in the literature where a non-precious metal Ni complex was successfully used to functionalize PMHS with 1hexene or 1-octene (Scheme 1a). 10 Additionally, there are examples from the Nagashima's group where Co and Fe isocyanide complexes have found use in functionalization of terminal SiMe 2 -H groups of polydimethylsiloxanes (PMDS) with α-methylstyrene and styrene with yields up to 99% (Scheme 1b). 11 The current number of examples describing the cross-linking of PMHS (or its ethyl analogues) with non-precious metal catalysts are also limited, as most of them involve the hydrosilylation of polydimethylsiloxanes containing terminal or internal vinyl groups (vPDMS) (Scheme 2a). [11][12][13][14][15][16] It should be noted that only two examples in the literature report the use of non-precious metal catalysts for the cross-linking of PMHS with short alkenes (Scheme 2b). The first one employs a Co catalyst to cross-link PMHS chains with short alkenes (1-octene and dodecene) via dehydrogenative hydrosilylation followed by hydrosilylation. 17 The second example uses a Mn(II) catalyst to hydrosilylate 1,2,4-trivinylcyclohexane with PMHS to form cross-linked polymers. 14 In search for an efficient earth-abundant transition metal catalyst for the hydrosilylation process, our group previously described the preparation and use of simple cobalt nanoparticles (NP) as effective catalysts for the synthesis of silicone oils via alkene hydrosilylation with MD ' M (1,1,1,3,5,5,5heptamethyltrisiloxane). 18 These cobalt NPs were derived from Co 2 (CO) 8 , which has previously been used in alkene hydrosilylation with monomeric silanes, 4 but examples with polymeric silanes are scarce as only one example where crosslinking of polymethylphenylvinylsiloxane with polymethylphenylhydrosiloxane is described using Co 2 (CO) 8 . 19 We therefore investigate here the use of Co 2 (CO) 8 for the synthesis of functionalized PMHS oils and cross-linked materials in attempt to step closer to the goal of using active non-precious metal complexes in the silicone industry.

Si H O n n n R [cat] R X O H or X=CH(Alk), CH 2 or C=O R=Alkyl, Aryl R=n-butyl or n-hexyl [cat]= Cu or Zn catalyst [cat]= Ni catalyst O X R R or a) b) n Si O O Si Si Ph R [cat] H n O Si Si Ph R PMHS subunit PDMS subunit H Ph R Me

Results and discussion

Throughout this study, all the reactions were carried out with Co 2 (CO) 8 (0.1 mol% compared to Si-H units in PMHS) at 60 °C unless stated otherwise and all the products depicted in various Tables and Schemes represent simplified structures of (poly)functionalized siloxane materials which do not correspond to block-polymers. The absence of trace amount of Pt in Co 2 (CO) 8 was verified by ICP-MS (inductively coupled plasma mass-spectrometry) analysis and the Pt content (if any) was below the 0.05 ppm detection limit of the apparatus. Additionally, the yields expressed throughout this work correspond to the 1 H NMR yield of Si-H bonds functionalization.

In Table 1, we represent the scope of alkenes tested for PMHS functionalization under mild conditions (60 °C for 24 h) and with a molar alkene C=C/Si-H ratio of 1:1. Using 1-octene in the functionalization process gave rise to 57% of alkylated PMHS 1a (Table 1, entry 1) and additionally to considerable amount (43%) of internal octene isomers. Switching from this linear substrate to a cyclic analogue, vinylcyclohexane (entry 2), led to an improved yield of 77% of 1b alongside with the formation of internal isomers (23%). Notably, non-isomerizable tert-butyl ethylene (TBE, entry 3) was incorporated into the PMHS chain in 1c with 79% efficiency, while styrene demonstrated quantitative hydrosilylation of Si-H bonds in 1d (entry 4). Using the more sterically hindered heptamethyl-3-vinyltrisiloxane (MD Vi M) (entry 5) gave rise to 65% of functionalized product 1e.

It should be noted that all the products in entries 1-5 were formed exclusively as anti-Markovnikov hydrosilylated products. Additionally, we used 1,3-cyclohexadiene (entry 6) to introduce a C=C bond to the hydrosilylated product, which could offer further reactivity for the functionalized PMHS oil.

The reaction between 1,3-cyclohexadiene and PMHS led to 1,2and 1,4-addition products in approximate ratio of 6:1 (based on 29 Si NMR -see ESI) in 1f, knowing that both isomers are known to occur for dienes in presence of Co 2 (CO) 8 . 20 In all examples in Table 1, 29 Si chemical shifts in the range of -19 to -27 ppm confirm the formation of new Si-C bonds via C=C bond hydrosilylation (see ESI).

To further demonstrate the versatility of this catalytic system, we performed the double functionalization of PMHS with two different alkenes in a one-pot reaction. Treatment of PMHS (1.0 eq) with styrene (0.6 eq) and MD Vi M (0.6 eq) in the Inspired by these results, we turned our interest towards the cross-linking of polymethylhydrosiloxanes with traditional short-chain tethers containing two terminal C=C bonds. For example, the reactions between PMHS (1.0 eq of Si-H) and 0.5 eq. of the dienes (i.e. 1.0 eq of C=C), namely divinyltetramethyldisiloxane (DVTMS) or diethyl diallylmalonate (DEDAM), led to the expected cross-linking of PMHS chains in products 2a and 2b respectively (Scheme 4). The gelation process for both substrates occurred via double alkenyl group hydrosilylation, but not quantitatively as evidenced by the presence of unreacted olefin 1 H and 13 C signals in solid state NMR spectra (See ESI). Somewhat surprisingly, the 29 Si CPMAS spectrum of the reaction product after DEDAM incorporation exhibits one low intensity resonance at -66 ppm, which and PMHS as an effective combination to deoxygenatively reduce amides to corresponding amines without mentioning the formation of gelous materials. 26 Very recently, B(C 6 F 5 ) 3 catalyzed cross-linking of PMHS chains through hydrosilylation of carbonyl groups in α-diketones was demonstrated by Hawker and co-workers. 27 In this latter example, no Si-O-Si bridge formation from C=O group was reported. With this additional and unconventional cross-linking capability in mind, we decided to investigate the use of unsaturated esters as promising tethers for the synthesis of functionalized polysiloxane materials. Entries 1 and 2 in Table 2 demonstrate how simple unsaturated acetates can be used as cross-linkers via the double reactivity of the C=C and C=O functionalities at 60 °C for 3a and 3b. Additionally, entry 3 indicates that the cross-linking procedure is not limited only to alkenyl acetates but can also be extended to alkyl alkenoates as demonstrated in 3c. Furthermore, comparing the curing time for entries 1-3, we see that faster reaction occurred for substrates that have the two hydrosilylable functionalities further apart from each other. For comparison, when the reaction between PMHS and vinyl terminated esters is catalyzed by Pt-based systems, only the vinyl moiety is hydrosilylated without reactivity on the carbonyl group. 28 Moving towards more industrially relevant esters, we tested methyl methacrylate (MMA) and allyl methacrylate (AMA) in the cross- linking reaction. The former is known to polymerize in the presence of Co(OAc) 2 and to react with PMHS to give semiinterpenetrating networks. 29 However, in our case the reaction between PMHS and MMA (entry 4) led to the cross-linked product 3d via the hydrosilylation of both the C=C bond and the ester functionalities (evidenced from solid-state 13 C and 29 Si spectra, see ESI). On a further note, it is known in literature that when Pt-based catalysts are used instead, the reaction between PMHS and other alkyl acrylates leads to the expected alkene hydrosilylation product without the ester group reduction. 30 When AMA (entry 5), which contains an additional allyl group, is used in the presence of Co 2 (CO) 8 and PMHS, the reduction of the ester group was suppressed and cross-linking in 3e occurred via hydrosilylation of the two C=C bonds only (evidenced from solid state 13 C and 29 Si spectra, see ESI). For comparison, allyl (meth)acrylates have previously been incorporated into PMHS chains through the exclusive hydrosilylation of the allyl group, without evidence of cross-linking through the C=C bond in the alkenoate part of the molecule nor via ester group reduction. 31,32 This result from entry 5 suggests that, in the presence of multiple C=C and C=O bonds, the cross-linking is faster via the hydrosilylation of two C=C bonds. While unsaturated esters (entries 1-5) have demonstrated excellent aptitude as unconventional tethers, the question about the reactivity of the carbonyl group remains to be explored further. When the same reaction was carried out with hex-5-ene-2-one (entry 6), which is a less reactive carbonyl compound, the gelation of 3f took <90 min to cross-link PMHS chains via C=C and C=O bond hydrosilylation, and via Si-O-Si bond formation.

R O O R' PMHS ([Si-H] n ) R O O R' [Si][Si-H] n-1 H [Si-H] n Co 2 (CO) 8 (0.1 mol%) R H O R' H [Si-H] n-1 [Si] [Si-H] n-1 [Si]
On a general note, while all the examples in Table 2 show the formation of cross-linked products in <90 min, this did not result in complete hydrosilylation of all active Si-H groups, as evidenced by DRIFT, 1 H and 29 Si solid-state NMR spectra (see ESI). Additionally, the scheme depicting the cross-linked products in Table 2 illustrates that the formation of each new Si-O-Si bridge between the PMHS chains was accompanied by the formation of reduced sidechain after full reduction of the carbonyl group in the incorporated substrate. It should be noted that all the obtained gels were colored (Table 2) and in comparison to known colorless gels formed via non-precious metal catalyzed cross-linking 11,16,31 , our gels did not undergo discoloration under air in 24 h. However, while the gels were colored, they yielded slightly colored or white solids after drying at 60 °C overnight. § § Interestingly, in the case of AMA (entry 5) the product was intense blue hard glassy solid, while all the other products in Table 2 were soft gels that could easily be punctured and sliced. In order to illustrate the potential of Co 2 CO 8 to catalyze the formation of gels, the reaction was carried out with DEDAM and MMA using a lower Co loading of 0.01 mol%. A gel was obtained within 2 h when MMA was used but no gel could be formed with DEDAM even after one day of reaction. These results show that the Co loading could be decreased to prepare a gel on the case-by-case basis depending on the olefinic reagent.

Examples in Table 2 have demonstrated the possibility to use various (un)saturated ester and carbonyl group containing substrates as effective tethers in polymethylhydrosiloxane cross-linking. Considering the end-product's lifetime and its eventual release to the environment, we feel that the environmental impact can be minimized 33 with the use of biosourced tethers, such as fatty acid derivatives. Based on the analogy of the esters used in Table 2, we believe that Si-O-C linkage formed from fatty acid derivatives would offer an ideal target for facile degradation pathway under acid-or basecatalyzed hydrolysis. 34,35 In Scheme 6a, we demonstrated that the reaction between methyl oleate and PMHS led to the gel 3h within 60 min. Similar gel 3i was formed in 90 min with the use of oleic acid (Scheme 6b). As the last example for PMHS cross-linking, we tested olive oil, which contains mostly oleic acid based triglycerides [START_REF] Mariotti | Extra-Virgin Olive Oil Handb[END_REF] and therefore offers high ester group density. As seen on Scheme 6c, 1 mol% of Co 2 (CO) 8 catalyzed the cross-linking reaction in <10 min to yield 3j. Excerpts of 29 Si NMR spectra of all three products (Scheme 6d) confirm the presence of silyl acetal groups (-57 to -62 ppm) and the formation of Si-O-Si bridges (ca.

-66 ppm). However, the similarities between gels 3h-3j end here, as the extent of C=C and C=O group hydrosilylative reduction varies between those samples. For example, methyl oleate gel 3h has undergone full reduction of ester groups to silyl acetal groups (99.3 ppm in 13 C NMR) and the complete hydrosilylation of the C=C bonds (evidenced by the lack of C=C signals in 13 C and formation of new Si-C bonds in 29 Si NMR). The C=C bond hydrosilylation of oleic acid derivatives by Co 2 (CO) 8 is somewhat unexpected, as we demonstrated recently that while cobalt NPs in solution can tandem isomerize-hydrosilylate internal C=C bonds of methyl oleate to the terminal position with MD ' M (monomeric analogue of PMHS), such reactivity was not seen with Co 2 (CO) 8 . 18 On the other hand, the products from PMHS cross-linking using oleic acid and olive oil, 3i and 3j, have mainly reacted via the carboxylic group (formation of Si-O-C and Si-O-Si bonds in 29 Si NMR, Scheme 6d), while leaving the C=C bond mostly untouched (low intensity of the Si-C peak between -21 to -24 ppm in 29 Si NMR, Scheme 6d). We also carried out test reactions with oleic acid derivatives and MD ' M under the same reaction conditions and, in all cases, no C=C, C=O or COOH hydrosilylation was observed. The different behavior of oleic acid and olive oil from that of the methyl oleate may be due to the reactive nature of COOH group in oleic acid and the close proximity of three C=O groups in the olive oil, which leads to preferential C=O group reduction than to new Si-C bond formation after C=C bond hydrosilylation. Additionally, we would like to emphasize that the reaction with olive oil (Scheme 6c) was successfully carried out on a gram-scale, demonstrating the potential of using Co 2 (CO) 8 and possibly other non-precious metal catalysts for the synthesis of biosourced cross-linked siloxanes materials.

Conclusions

In this study, we have demonstrated the use of simple Co 2 (CO) 8 as an excellent non-noble metal catalyst for the synthesis of mono-and bi-functionalized PMHS oils in a one-pot reaction, with catalyst loadings as low as 0.1 mol%. Importantly, this catalytic system offered a unique method for the cross-linking of PMHS with traditional dienes and unconventional organic

  Yong Qin et al. Highly dispersed Pt nanoparticles supported on carbon nanotubes produced by atomic layer deposition for hydrogen generation from hydrolysis of ammonia borane

Scheme 2 .

 2 Scheme 2.Current examples of cross-linking of polysiloxane oils using nonprecious metal catalysts.

O 5 . 4 |

 54 Scheme 5. Plausible mechanism of the formation of Si-O-Si bridges between PMHS chains in presence of carbonyl groups.Catalysis Science & Technology Accepted Manuscript

  Same reaction conditions as in Scheme 3, but on two times larger scale. The numbers on the vials correspond to the entry numbers in Table2. [b] All the gels (except 3c) contain presence of Si-O-Si bridge signals in their29 Si NMR spectrum.

Scheme 6 .

 6 Scheme 6. Functionalization and cross-linking of PMHS with renewable fatty acid derivatives. Same reaction conditions as in Scheme 3. Reaction scale for: a) Methyl oleate (1.17 mmol), PMHS (2.34 mmol [Si-H]), b) Oleic acid (technical grade 90%) (1.17 mmol), PMHS ([Si-H] 2.34 mmol), c) olive oil (1143 uL), PMHS ([Si-H] 7.03 mmol). d) 29 Si SSNMR excerpts (20 to -100 ppm) of 3h-3j. Si-C bond (O), Si-H bond (#), Si-O-R bond (*) and Si-O-Si bridge (&) in cross-linked material.

Table 1 .

 1 Scope of alkenes for the production of functionalized silicone oils from PMHS using Co 2 (CO) 8 .[a] Table 1 entry 4 vs entry 5), we therefore expected a higher level of styrene incorporation into the final product. Surprisingly, the experimental result demonstrates that only 28% of Si-H bonds were functionalized with styrene and 49% with MD Vi M in 1g. § This last result is a rare example of a one-pot double functionalization of a polymethylhydrosiloxane derivative and highlights the versatility and the potential of using simple nonprecious metal catalysts, such as Co 2 (CO) 8 , in this process. Considering the lack of examples in the literature, the results in Table1and in Scheme 3 represent considerable expansion of the alkene scope in the functionalization of PMHS using a nonprecious metal catalyst with up to >99% efficiency.

	R		50	Co 2 (CO) 8 0.1 mol%		a	b
		1:1 ratio of [C=C]:[Si-H]	60 o C, 24 h		R	a+b=50
	#	Label	Alkene	Isom. [b]	Yield [c]	State of the
							art [d]
	1	1a	1-octene		43	57	>99 10
	2	1b	Vinylcyclohexane	23	77	n.r
	3	1c	TBE		-	79	n.r
	4	1d	Styrene		-	>99	n.r
	5	1e	MD Vi M		-	65	n.r
	6	1f	1,3-cyclohexadiene	-	>99	n.r
	[a] Reaction conditions: alkene (0.94 mmol, 1.0 eq), PMHS (0.94 mmol, 1.0 eq of
	Si-H functionalities), Co 2 (CO) 8 (0.1 mol% compared to Si-H functionalities) in
	toluene and mesitylene (as NMR standard). Conversions of starting materials and
	formation of product are based on 1 H NMR. [b] Isomerization (%) corresponds to
	the sum of formed isomers. [c] The yield refers to the % of functionalized [Si-H]
	bonds in the functionalized PMHS. [d] State of the art example corresponds to the

highest functionalization yield of corresponding hydrosilylation product catalyzed by a non-precious metal system reported in literature. n.r -not reported. [e] 1.2 eq. of styrene was used due to formation of small amount of polystyrene at the beginning of the reaction.

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Table 2 .

 2 Cross-linking of PMHS with unconventional C=C and C=O bond containing tethers.[a]

Catalysis Science & Technology Accepted ManuscriptPublished on 29 March 2021. Downloaded by Université Claude Bernard Lyon on 3/29/2021 1:24:49 PM. View Article Online DOI: 10.1039/D1CY00191D

Acknowledgements

We thank Nesrine Oueslati and Christine Lucas for solid-state NMR measurements.

Author Contributions

M. J. and V. D. carried out the experiments. The manuscript was written through the contributions of M. J., C. C. and C. T. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Notes and references ‡ During January 2019-January 2021 platinum price has varied 597-1079 USD per troy ounce, https://www.nasdaq.com/marketactivity/commodities/pl%3Anmx. § At the beginning of the reaction, formation of polystyrene was observed. This parasitic reaction counts to some extent why we observed lower styrene incorporation than expected but does not explain the overall result. § § Such discoloration process is reversible when the dry gels are wetted with toluene. This observation suggests that the coloration is not related to the structure of the gels but to Co catalyst that is embedded in the gel framework.

Catalysis Science & Technology Accepted Manuscript