Rija Nirina Raoelison

Jishuai Li

Thaneshan Sapanathan

Essole Padayodi

Nicolas Buiron

Dany Racine

Zhan Zhang

Daniel Marceau

Mohamed Rachik

A new nature of microporous architecture with hierarchical porosity and membrane template via high strain rate collision

Keywords: porous structure, micro-pores, ballistic collision, cavitation, depressurization

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

Introduction

Porous materials are increasingly become attractive and offer superior functional properties including energy absorption [START_REF] Wang | Nano-deposition on 3-D open-cell aluminum foam materials for improved energy absorption capacity[END_REF], catalytic performances [START_REF] Fan | Preliminary Study of Performance of Dye-Sensitized Solar Cell of Nano-TiO2 Coating Deposited by Vacuum Cold Spraying[END_REF], conduction capabilities [START_REF] Luan | Synthesis of hierarchically macro/meso/microporous carbon spheres and its application in fast rechargeable electric double layer capacitor[END_REF], removal or cleaning functions [START_REF] Lefebvre | Porous Metals and Metallic Foams: Current Status and Recent Developments[END_REF], energy storage capabilities [START_REF] Xia | An unusual method to prepare a highly microporous carbon for hydrogen storage application[END_REF] and osteointegration properties [START_REF] Ryan | Fabrication methods of porous metals for use in orthopaedic applications[END_REF]. Those functional capabilities of metallic porous structures have been widely exploited, while the growing interest is given to the performance of micron and submicron size porous structures. Microporous materials are particularly attractive to fulfil new technological requirements and their elaboration recently received significantly high interest from the industry and scientific community. The available literatures on the processing methods of such microporous materials support various porous architectures resulting from specific processes.

During the manufacturing processes of porous structures, the required microporosity was obtained using various phenomenological principles. These phenomenological principles can be classified into four generic categories such as (1) powder stacking-consolidation [START_REF] Ryan | Fabrication methods of porous metals for use in orthopaedic applications[END_REF], [START_REF] Fan | Preliminary Study of Performance of Dye-Sensitized Solar Cell of Nano-TiO2 Coating Deposited by Vacuum Cold Spraying[END_REF] selective removal process [START_REF] Zhang | Formation and microstructure of nanoporous silver by dealloying rapidly solidified Zn-Ag alloys[END_REF], (3) template-assisted method and [START_REF] Wang | Nano-deposition on 3-D open-cell aluminum foam materials for improved energy absorption capacity[END_REF][START_REF] Ryan | Fabrication methods of porous metals for use in orthopaedic applications[END_REF] (4) in-situ synthesis of porous structure [START_REF] Li | Hydrogen bubble dynamic template synthesis of porous gold for nonenzymatic electrochemical detection of glucose[END_REF][START_REF] Cherevko | Direct electrodeposition of nanoporous gold with controlled multimodal pore size distribution[END_REF]. In a powder stacking-consolidation process, the porosities mainly occur during sintering or thermal spraying deposition of micron size powders, while the compaction of the powder is controlled to promote the formation of micropores between the unbonded surfaces (Fig. 1a). This manufacturing method is rather simple and rapid; however, it has a limitation in terms of reaching very high porous density. For instance, considering a lattice of a simple cubic system, the compactness is stable with the maximum of 50%, highlighting the limitation of the powder stacking-consolidation method. A post chemical corrosion treatment is mostly suggested to increase the porosity after the powder stackingconsolidation process. The chemical corrosion treatment is also known as the selective removal method that can be also applied to fully dense metallic structures. A selective chemical dealloying produces the porosity [START_REF] Kaiser | Selective dissolution of high and low diffusivity alloys-A comparison of kinetical and micromorphological aspects[END_REF][START_REF] Cox | Bulk gold with hierarchical macro-, micro-and nano-porosity[END_REF].. The selective removal methods also use some other dissolution mechanisms such as centrifugation [START_REF] Loryuenyong | The synthesis of microporous and mesoporous titania with high specific surface area using sol-gel method and activated carbon templates[END_REF] or thermally activated disintegration via laser irradiation or combustion or heat treatment [START_REF] Xing | Preparation of hierarchical porous carbon by post activation[END_REF][START_REF] Murzin | Exposure to laser radiation for creation of metal materials nanoporous structures[END_REF][START_REF] Chen | Preparation of hierarchical porous metallic materials via deposition of microporous particles[END_REF]. The use of removal template offers the possibility to obtain a regular porous architecture with a tailored porosity. These capabilities highlight the effectiveness of the selective removal method to produce micro/nano pores with increase in porous density (Fig. 1b). However, this method requires a costly preparation and post-treatment to obtain a clean porous structure. Some other studies suggest a template-assisted method using a solid porous preform produces a primary porous structure, while subsequent adsorption reaction caused by a carbonization process increases the porosity [START_REF] Xing | Preparation of hierarchical porous carbon by post activation[END_REF]. Furthermore, using a skeleton as the pre-porous structure that can also be coated using a chemical vapour deposition or an electrolytic reaction [START_REF] Wang | Nano-deposition on 3-D open-cell aluminum foam materials for improved energy absorption capacity[END_REF][START_REF] Ryan | Fabrication methods of porous metals for use in orthopaedic applications[END_REF], to produce a porous structure composed of a specific material deposit (Fig. 1c andd).

In-situ synthesis of porous structure is based on a cavitation phenomenon. This method is also known by "foaming" and it has been widely considered to produce large pores. Nevertheless, in recent research studies, the cavitation method has also been successfully applied to the synthesis of small pores in micron size. Electrodeposition is another viable method that can generate dynamic hydrogen bubbles while solid phase coalesces from the bubbles wall and grows between the bubbles during an electrolytic reaction (Fig. 1e andf) [START_REF] Li | Hydrogen bubble dynamic template synthesis of porous gold for nonenzymatic electrochemical detection of glucose[END_REF].

However, the increasing demand for the porous materials requires innovative methods to manufacture the porous structure. Recently, it was found that a ballistic collision enables a cavitation phenomenon that can produce a micro/nano-porous metallic structure [START_REF] Raoelison | Magnetic pulse welding: Interface of Al/Cu joint and investigation of intermetallic formation effect on the weld features[END_REF]. Thus, this work focusses to explore the detail of the porous structure formation, at an interface of a high-speed impact (HSI) welded joint. It is identified that HIS process enables to produce high porosity with thin membrane wall pours structure at an Al/Al welded interface. Eulerian numerical simulation considering the thermomechanical phenomena during the process enables to understand the fundamental mechanism of the porous structure formation. Fig. 1. Typical morphologies of porous structures produced by (a) powder stackingconsolidation [START_REF] Ryan | Fabrication methods of porous metals for use in orthopaedic applications[END_REF], (b) selective removal method [START_REF] Zhang | Formation and microstructure of nanoporous silver by dealloying rapidly solidified Zn-Ag alloys[END_REF], (c) template-assisted coating using chemical vapour deposition [START_REF] Ryan | Fabrication methods of porous metals for use in orthopaedic applications[END_REF], (d) template-assisted coating using electrocatalytic reaction [START_REF] Wang | Nano-deposition on 3-D open-cell aluminum foam materials for improved energy absorption capacity[END_REF] and (e, f) in-situ synthesis of porous structures resulting from hydrogen bubbling assisted electrodeposition [START_REF] Li | Hydrogen bubble dynamic template synthesis of porous gold for nonenzymatic electrochemical detection of glucose[END_REF][START_REF] Cherevko | Direct electrodeposition of nanoporous gold with controlled multimodal pore size distribution[END_REF].

Porous structure formation using a ballistic collision

Magnetic pulse welding (MPW) is a high-speed impact welding process, had a growing attention over the past four decades and investigated to fabricate welded joints of various material combinations in different geometrical configurations. During an investigation for identifying the appropriate conditions for producing a welded joint using MPW, we made a serendipitous discovery of porous architecture that exhibits a very unusual feature. The porous structure is generated when a hollow tube of aluminium AA6061-T6 impacts on a motionless inner rod of the same material. The high-speed impact is produced by MPW device that induces Lorentz force due to an impulse magnetic field when an electrical discharge of some kV supplied using total capacitance of 690µF, flows through a 3-turn coil combined with a fieldshaper. A Rogowski probe was used to measure the discharge current which has a frequency of 10kHz. Our previous studies [START_REF] Raoelison | Efficient welding conditions in magnetic pulse welding process[END_REF][START_REF] Raoelison | Study of the elaboration of a practical weldability window in magnetic pulse welding[END_REF][START_REF] Raoelison | Magnetic pulse welding of Al/Al and Al/Cu metal pairs: Consequences of the dissimilar combination on the interfacial behavior during the welding process[END_REF] using various such experimental conditions suggest that the interface is subjected to the ballistic impact and form a bonded joint, but detail analysis of the interface produced under some welding conditions revealed confinement of porous architecture having a singular characteristics, those are investigated in detail in this study.

Characteristics of the porous structure

Scanning electron microscopy (SEM) observation of a post-debonded weld surface obtained for an input voltage of 7.5 kV reveals a porous template that consists of hierarchical microporous structure formed by spherical pores (Fig. 2). The microstructure reveals a random allocation of the pores and a stochastic porosity. The pores are interconnected like an open cells structure, and are larger than the solid membrane space between them, indicating an apparent high specific surface with a low relative density. Such template conceals the potential of HSI process to generate porous structure with specific characteristics compared to those produced by various processes shown in Fig. 1. Another SEM observation in Fig. 3 reveals the porous media wrapped inside a thin wall membrane structure and additional peculiar details of the porous zone. Fig. 3 shows adjacent pores inside the porous media. The pores are organized like a honeycomb structure (Fig. 3) behind a wall. The visualisation of inner pores from outside is possible due to the presence of sufficiently thin outer wall that becomes transparent during the SEM observation. The transparency itself is not an optical property as viewed on (Fig. 3). Rather, this result indicates that the observed transparency is an electron response of the wall under the secondary electron (SE) imaging technique during the SEM observation. Transparency to electrons is widely used in transmission electron microscope (TEM) observation for fine structural characterization. Those TEM samples are generally ultrathin with a thickness of some nm and the analysis is rather focus on the electron transmission across the sample towards an electron detector. Recently, the combination of electron transparency analysis with SEM observation has received an attention for electron microscopy observation of liquid samples [START_REF] De Jonge | Electron microscopy of specimens in liquid[END_REF][START_REF] Stoll | Electron transparent graphene windows for environmental scanning electron microscopy in liquids and dense gases[END_REF]. A liquid specimen enclosed by an ultrathin membrane, less than 100nm thick, was sufficiently thin to act as an electron transparent material. Thus, a similar fact can explain the transparency of the thin wall membrane during the SEM observation (Fig. 3). That is, the outer wall of the porous template may behave like an electron-transparent material while capturing the topographic details under SE mode. There is a variance in thickness between the outer wall and the thickness of the inner structure which appears like honeycomb structure. The outer encapsulating wall is likely thinner than the honeycomb wall which is roughly about a few µm (Fig. 3). Fig. 4 provides further insight on the thickness of the membrane wall that behaves like an electron-transparent material. The porous walls clearly show the front template and exhibit also back pore cell, i.e. from behind. Such pore cell appears as darker zone that can also be viewed through the membrane wall. This electron-transparent zone is not thick enough to be measured. Therefore, an image analysis technique was used to determine the thickness of the membrane and identify that the wall has a thickness of 50nm.

The detail image analysis of membrane thickness is given in Supplementary material. To calculate the surface porosity across the cross section of the porous zone and the pore size distribution, the Fig. 2 is used for further image analysis (see Supplementary material for more details). Using the grey value of each pixel, a porosity rate of 66% x was found. This value does not include the 3D porosity since this is a calculated surface ratio. However, it indicates the typical porosity rate that can be achieved by a hierarchical porous structure produced by HSI.

The pixels of Fig. 2 are also analyzed to assess pores size and distribution. The pore size given by the area is converted into an equivalent diameter. Their distribution is analyzed for the whole image and plotted in Fig. 5a. The results show that the porous structure contains 60% of pores lower than 2µm in diameter. Less than 8% of the pores are greater than 5µm in diameter. Analysis of the fine pores is also performed on the original image (Fig. 2), but the selection of suitable grey range becomes tricky due to the hierarchical template of the pores and the variance of grey they exhibit. That is, the hierarchical pores have grey values close to each other, so that they can be easily merged during the segmentation operation. For the greyscale of the pores, the range of 175-255 best matches with the zone of fine pore and then enables the identification of the fine porosity (Fig. 10) (see Supplementary material for more detail). There are some hierarchical pores also counted in this analysis and they correspond to large pores correspond to a very small proportion as shown in Fig. 10. So, those hierarchical pores do not adversely affect the distribution results of the fine pores. The pores size less than 2µm represents more than 80% over the whole size range, and at least 38% of them are submicron size pores. In summary, these dimensional characterizations reveal that the hierarchical porous architecture has high porosity, membrane structure including ultra-thin wall, and micron sized porosity including a significant proportion of sub-micron pores. The whole features of this porous template represent new findings that could be said unconventional with respect to the current variance of porous architectures as reported in Fig. 1. In terms of the overall morphology, significant differences have been evidenced between this porous structure and those reported in Fig. 1. The mechanisms that develop this new type of porous media is unusual compared to current conventional manufacturing processes. Therefore, the next section focuses on understanding the novelty of the solid interface turns into such porous template. We focus on phenomenological aspects of this transformation while they are supported by the experimental observations and computational simulation.

Formation of the porous cell made of porous membrane

The porous zone arises from the high-speed collision at the interface between two aluminum parts. The interface experiences rapid changes in a confined narrow zone and they are difficult to investigate using in-situ experimental observations. To identify the phenomena that prevail during the collision, we highly depend on the characteristic features of the interface generated during the process. Thus, a thermomechanical finite element computation is used in this study to further understand the governing mechanisms during the formation and development of the porous structure. Fig. 6 shows an optical microscopy observation of the porous zone at the interface, bounded between two aluminum parts. The grain boundaries of the parent material The progression of the impact between the two parts of the weld involves strong shearing at high strain rate. Several macroscopic examinations evidence shear instability phenomena such as wave formation, wake and vortex formation and jetting and emission of particles from the interface [START_REF] Raoelison | Magnetic pulse welding of Al/Al and Al/Cu metal pairs: Consequences of the dissimilar combination on the interfacial behavior during the welding process[END_REF][START_REF] Raoelison | Interfacial kinematics and governing mechanisms under the influence of high strain rate impact conditions: Numerical computations of experimental observations[END_REF][START_REF] Sapanathan | Depiction of interfacial characteristic changes during impact welding using computational methods: Comparison between Arbitrary Lagrangian -Eulerian and Eulerian simulations[END_REF][START_REF] Sapanathan | Magnetic Pulse Welding: An Innovative Joining Technology for Similar and Dissimilar Metal Pairs[END_REF]. It was also observed that the grains adjacent to the bonded interface are highly elongated and flattened to form a shear affected zone (SAZ), at the vicinity of the interface [START_REF] Raoelison | Magnetic pulse welding of Al/Al and Al/Cu metal pairs: Consequences of the dissimilar combination on the interfacial behavior during the welding process[END_REF][START_REF] Sapanathan | Depiction of interfacial characteristic changes during impact welding using computational methods: Comparison between Arbitrary Lagrangian -Eulerian and Eulerian simulations[END_REF]. The plastic deformation and the associated impact phenomena at the interface is significantly high to generate excessive heating of the SAZ beyond the melting point of the parent material. Virtual computations of the collision for Al/Al welding indicate that the local plastic strain reaches up to 600% and temperatures of above the melting point of aluminum within the narrow zone at the interface [START_REF] Raoelison | Interfacial kinematics and governing mechanisms under the influence of high strain rate impact conditions: Numerical computations of experimental observations[END_REF][START_REF] Sapanathan | Depiction of interfacial characteristic changes during impact welding using computational methods: Comparison between Arbitrary Lagrangian -Eulerian and Eulerian simulations[END_REF]. Since the zone outside of the SAZ is very large and remains cold during the high strain rate collision, the melted zone is subjected to a rapid solidification with very high cooling rate that prevents the generation of new grain boundaries by equilibrium grain growth. Thus, non-equilibrium transformations rather prevail in such solidification condition. TEM observation in an IZ across the interface was successfully realized as shown in Fig. 12a. The interaction of the electron beam with the IZ zone at position 1 (Fig. 12a) does not reveals neither periodical spots nor reflections organized into clear rings (Fig. 12b). Instead, the diffraction pattern consists of random-like structure (Fig. 12b), imputes the rapid solidification that rather freezes the atoms in their random position. Thereby, the IZ is likely to be free of grain boundaries (amorphous) or contain nanograin structures or a combination of both due to the presence of following three major phenomena, viz. high strain rate localized shearing, confined melting and fast cooling. SEM observations are further used to analysis the resulting microstructure of the IZ. It shows a development of fine structure that consists of random epitaxial and columnar cells (Fig. 8a).

A few dispersed black spots that emerge from this solidified zone indicates that the IZ is the favorable site for the porous structure formation. The onset of nucleation of new columnar is noticed from these random black spots that could be related to different thermal kinetics at those local regions. Fig. 8b shows a relatively more developed nucleation characterized by more submicron size pores whose shapes are nearly spherical. Observation over a larger zone provides further convincing results (Fig. 8c). The pores clearly arise from the IZ and the random aspect of the nucleation sites as well as the porosity development is still observed.

Nucleation, coalescence and onset of growth into micron pores are evidenced. Moreover, the grain like structures in Fig. 8a-c confirm that they are submicron grains. Fig 8b andc also shows some zone without the absence of the grain like features that could partly being amorphous. Therefore, the complex grain structure with the combination of rapid cooling may resulted from the extremely high cooling rate and this result also support the TEM observation (Fig. 7b). The evolution of the confined melting towards the porous structure is an ultra-transient phenomenon which is difficult to include among equilibrium transformations. This is a new phenomenon that has not received attention in the literature of high-speed impact welding which rather gives interest to process development and control. The mechanism that forms such fine pores at extraordinary reaction speed can be explained by an approach based on thermodynamics of phases change describing the transitions between solid, liquid and gas governed by the changes in pressure and temperature. This thermodynamic notion is more appropriate to identify the ultrafast pores formation from a phenomenological point of view.

A sublimation, i.e. a physical change directly from solid phase into gaseous phase, producing a porous media is unlikely to happen since such change is a sub-atmospheric phenomenon.

Sublimation of aluminum alloy was investigated in some research studies that indicate the sublimation of Al requires very low pressures, in the range of some Pa [START_REF]Vacuum Sublimation of Anhydrous Aluminum Chloride--《Chinese Journal of Vacuum Science and Technology》2009年[END_REF][START_REF] Teghil | A thermodynamic study of the sublimation processes of aluminium and copper acetylacetonates[END_REF]. Such pressures limits are excessively exceeded at the interfacial zone during MPW. The collision is extremely intense to produce impact pressures of some GPa, so the sublimation under low pressure conditions such as a condition suitable for anhydrous aluminum compounds does not prevail. Instead, a phase change from liquid state into gaseous state is more plausible.

Vaporization can also be suggested but there are some aspects which make this consideration unsuitable. That is, the IZ contains more than 80% of Al content according to EDS analysis (see Supplementary material for EDS spectrum) performed during TEM observations (Table 1). Other chemical elements of at the IZ are also very weak. Moreover, the increase in This phenomenological incompatibility between high thermal conductivity and strong confined thermal gradient that generates multiple heat spots precludes the phenomenology based on vaporization for producing the porous structure. Furthermore, the spherical nature of the pores, fine or large, and the hierarchical porosity within membrane template (Fig. 4) suggest a radial growth of pores. A porous coalescence by vaporization should therefore involve occurrence of several sites of strong radial thermal gradients enable for a progressive radial vaporization. However, such phenomenological condition is also physically unrealistic due to the high thermal conductivity of the Al. Instead of an isobaric vaporization, an isothermal transition from intermediate liquid state can explain the formation of porous structure. Following the interfacial melting, nucleation of pores appears in the Al liquid due to a fast change of pressure during the collapse of the high pressure resulting from the collision. We can suggest that the local pressure decreases below the saturated vapor pressure of the Al liquid to generate spherical vapor bubbles. Then, there is a phase change by cavitation phenomenon due to the pressure decrease, and the subsequent micron-sized bubbles create the porous structure during a rapid solidification. The pressure and temperature changes during the high strain rate collision can be characterized by a thermomechanical simulation of the collision. Thus, we can rely on a robust Eulerian method capable for computing interfacial kinetics and governing mechanisms under the influence of high strain rate impact conditions. This method allows to reproduce the interfacial characteristic changes during impact welding [START_REF] Raoelison | Interfacial kinematics and governing mechanisms under the influence of high strain rate impact conditions: Numerical computations of experimental observations[END_REF][START_REF] Sapanathan | Depiction of interfacial characteristic changes during impact welding using computational methods: Comparison between Arbitrary Lagrangian -Eulerian and Eulerian simulations[END_REF][START_REF] Teghil | A thermodynamic study of the sublimation processes of aluminium and copper acetylacetonates[END_REF]. pores size provides some hint for the interpretation of the resulting radial growth and coalescence of vapor bubbles, the governing mechanisms should be further understood.

During MPW, these interfacial processes are extremely fast, last a few microseconds, so identifying experimentally reliable phenomena of bubbles growth and coalescence becomes tricky. However, a comparison between two experimental observations provide some considerable insight in the formation of porous structure. Two MPW tests were conducted using similar colliding workpieces (similar flyer) but under different collision conditions. The porous structure shown in Fig. 11a and b are obtained for the initial air gap (prior to the collision test) of g = 1.5mm with the discharge voltage of U = 6.5kV, and initial air gap of g = 5mm with the discharge voltage of U = 7.5kV, respectively. The intensity of the collision makes the major difference between these two cases. Higher discharge voltage and higher initial gap is conducive to higher impact velocity and resulting with higher collision pressure, higher strain rate, large plastic straining and significantly more heating. Characterization of welded interfaces clearly reveals the consequences of the collision conditions that becomes important with the increase in air gap and discharge voltages [START_REF] Raoelison | Efficient welding conditions in magnetic pulse welding process[END_REF][START_REF] Raoelison | Study of the elaboration of a practical weldability window in magnetic pulse welding[END_REF][START_REF] Raoelison | Magnetic pulse welding of Al/Al and Al/Cu metal pairs: Consequences of the dissimilar combination on the interfacial behavior during the welding process[END_REF]. Regarding the porous structure formation, the parameter set with g = 1.5mm and U = 6.5kV rather creates a dense structure (Fig. 11a) compared to the porous structure obtained with g = 5mm and U = 7.5kV which provides significantly developed pores, i.e. with larger and hierarchical pores, but also membrane architecture (Fig. 11b). The difference of cavitation between these two cases can be attributed to a difference of depressurization. The more intense collision provides the stronger impact pressure, therefore later (g=5mm, U=7.5kV) experiences the higher depressurization gap and increased fluid rupture due to higher inherent fluid tension. At low collision intensity (g=1.5mm, U=6.5kV), the depressurization reaches the conditions to begin the cavitation process while a weak growth and onset of coalescence occur (Fig. 11a). The strong collision (g=5mm, U=7.5kV) provides significantly high depressurization which enables a powerful coalescence that forms the highly porous structure (Fig. 11b) during solidification at high cooling rate.

Conclusions

A new type of porous architecture is produced by high speed collision exhibiting an unusual feature of a porous template that consists of a hierarchical porosity made of nearly spherical pores. Dimensional analysis reveals that the porous structure has high porosity of 66% in the cross-section area, membrane structure including ultra-thin wall of 50 nm, and micron sized porosity including a significant proportion of sub-micron pores. The pores appear within a solidified structure where random nucleation of cavities occur. The spherical shape and the hierarchical organization of the porosity suggest a mechanism during the development of pores due to a cavitation phenomenon. Based on the thermodynamic considerations combined with computational simulation of the high strain rate collision, pores nucleation, growth and coalescence are explained as an ultra-fast isothermal and isochoric transition of a molten phase into a vapor phase. During these phenomena, cavities emerge due to a high rate of depressurization followed by a solidification at rapid cooling rate to produce the porous structure. An experimental comparison between cavitation onset and a fully developed cavitation allows to corelate the degree of cavitation with the depressurization intensity. The highly developed porous structure is favoured by the conditions corresponding to strong collision, i.e. high impact pressure followed by a significant depressurization. Together, those fast-dynamic phenomena represent a potential method for the manufacturing porous structures based on a micro-cavitation mechanism. This new finding merits to be further explored in the future.

Fig. 2 .

 2 Fig. 2. SEM observation of hierarchical and stochastic open porosity produced by HSI process.

Fig. 3 .

 3 Fig. 3. Typical membrane structure of the porous architecture evidenced through the outer membrane wall.

Fig. 4 .

 4 Fig. 4. Membrane structure of the porous zone showing the onset of void genesis at the walls adding additional porosity.

Fig. 5 .

 5 Fig. 5. Global pore sizes range and distribution calculated from the surfaces of segmented regions (a) and (b) pore size and distribution of the fine pores.

(

  AA6061 -T6) are visible outside the porous interface zone, that evidences thereby a formation of a new feature at the welded interface; we refer it as an intermediate zone (IZ) in this work.

Fig. 6 .

 6 Fig. 6. Interface containing an intermediate zone (IZ) where the formation of pores occurs.

Fig. 7 .

 7 Fig. 7. TEM observation revealing the IZ (a) and electron diffraction pattern corresponding to the position 1 (marked in Fig. 7a) showing random-like structure (b).

Fig. 8 .

 8 Fig. 8. SEM observation showing the nucleation of pores within the IZ revealing traces of cooling (random epitaxial and columnar cells) in (a), developed nucleation and growth onset characterized by more submicron pores with nearly spherical shape in (b), and typical heterogenous aspect of the pore formation: heterogeneous nucleation, growth and coalescence into micron pores in (c).

  temperature beyond aluminum vaporization (~2450°C) combined with the high thermal conductivity of aluminum would have produced a large melted zone instead of a confinement of heat affected zone over a very narrow distance of some micrometers (Fig 11). Therefore, assuming a vaporization of the Al is not appropriate to explain a selective nucleation of pores during HSI. The porosity obtained in the previous experimental observations exhibit heterogenous formation of pores in terms of both size and spatial distribution. A selective vaporization, conducive to such nucleation, is inconsistent with the presence of high thermal conductivity of Al which rather involves heat dissipation instead of local heat confinement.

Fig. 9

 9 presents typical characteristic variations of pressure and temperature obtained from Eulerian simulation of HSI. The timedependent temperature profile at the interface evidences a strong transient peak that far exceeds the melting temperature of Al, due to an ultrafast heating induced by the excessive shear deformation at high strain rate. The melting stage lasts about 150ns that includes the increase of temperature from the melting point of Al to the maximum temperature (~1200°C) and then the drop of temperature before or during the solidification. During this very short melting-solidification stage, the local pressure varies simultaneously with a similar trend to the temperature curve. After a rapid increase of local pressure, there is a sudden decrease of pressure with a rate of about 100MPa/ns that creates the depressurization condition necessary for cavitation. Subsequently, solidification occurs at high cooling rate of 10°C/ns that quickly freezes the cavities along with the progress of the depressurization. The continuous process of pore formation from the solid state, through the successive transitions, is described on a schematic representation of thermodynamic pressure-temperature diagram of Al (Fig.10), which specifies the phenomenological changes during HIS and physical parameter variations during the porous structure formation.

Fig. 9 .

 9 Fig. 9. Typical variation of pressure and temperature computed during the HSI using Eulerian simulation, and typical computed molten zone predicting the morphology of IZ corresponds to the porous structure formation (NT11 denotes the temperature in °C).

Fig. 10 .

 10 Fig. 10. Schematic illustration of thermodynamic pressure-temperature diagram explaining the successive transitions during the porous structure formation.

Fig. 11 .

 11 Fig. 11. Difference of cavitation attributed to difference in depressurization. Weak cavitation attributed to a low collision intensity with g = 1.5mm and U = 6.5 kV in (a), and highly developed porous structure attributed to higher impact pressure obtained with g = 5mm and U = 7.5kV in (b).

Table 1 .

 1 Chemical composition of the Al6061 material measured by EDS using TEM

	Weight (%)		Chemical elements
	C	O	Si	Cu	Mg	Al

Acknowledgments

Authors acknowledge the "Région Picardie" and "Le fonds européen de développement économique et régional (FEDER)" for funding of the MSIM project (2010/2012) and COILTIM project (2014/2020). Jishuai Li acknowledges the financial support of China Scholarship Council (CSC) during his PhD candidature at Université de Technologie de Compiègne.


J Yon
email: yon@coria.fr

F Liu

J Morán

A Fuentes

Impact of the Primary Particle Polydisersity on the Radiative Properties of Soot Aggregates

Keywords: Radiative properties of soot aggregates, Polydisperse primary particles, Discrete dipole approximation, Generalized multi-sphere Mie, laser light scattering by soot

Combustion generated soot appears as fractal aggregates formed by polydisperse nearly spherical primary particles. Knowledge of their radiative properties is a prerequisite for laser based diagnostics of soot. In this parametric study, the effect of primary particle polydispersity on soot aggregate absorption and scattering properties is investigated numerically. Two series of fractal aggregates formed by normal and lognormal distributed primary particles of different levels of standard deviation were numerically generated for typical flame soot with a fractal dimension and prefactor fixed to D f = 1.73 and k f ≈ 1.5, respectively. Three aggregate sizes consisting of N p = 15, 50 and 150 monomers per aggregate were investigated. Due to the uncertainty in soot refractive index, radiative properties were calculated by considering two different refractive indices at λ ≈ 532 nm recommended in the literature using the Discrete Dipoles Approximation and the Generalized multi-sphere Mie method. The results are interpreted in terms of correction factors to the Rayleigh-Debye-Gans theory for fractal aggregates (RDG-FA) for the forward scattering cross section A and for the absorption cross section h. It is shown that differential cross section for vertically polarized incident light, total scattering and absorption cross sections are well predicted by the RDG-FA theory for all considered aggregates formed by normally (σ/ dp ≤ 30%) and lognormally (σ geo ≤ 1.6) distributed primary particles. The refractive index is found to be of greater impact than primary particle polydispersity on the importance of multiple scattering. The radiative force per unit laser power experienced by the soot aggregates was found primarily determined by the aggregate volume, regardless of the level of primary particle polydispersity.

Introduction

Accurate knowledge of the optical properties of soot aerosol is essential to interpret the detected signals in terms of soot properties, such as concentration, primary particle (PP) and aggregate sizes, in laser based measurements, to assess the role of soot aerosol in atmospheric chemistry and combustion processes. In this context it is highly desirable to develop relatively simple yet sufficiently accurate models for the radiative properties of fractal-like soot aggregates. The Rayleigh-Debye-Gans theory for fractal aggregates (RDG-FA) is very simple to use but suffers some drawbacks and poor accuracies under certain conditions, mainly due to the neglect of internal coupling or multiple scattering within an aggregate.

Many studies have been performed to evaluate the accuracy of RDG-FA theory [START_REF] Liu | 40th Thermophysics Conf[END_REF][START_REF] Farias | [END_REF]. In addition, a few studies have been carried out to introduce correction factors or to propose some alternatives to the RDG-FA theory to extend its applicability and/or improve its accuracy. In almost all light scattering experiments, the results were interpreted using the RDG-FA theory assuming that soot aggregates are formed by monodisperse PP in point-contact, though in reality these particles are formed by polydisperse PP with a certain degree of overlapping. In consequence, some efforts have been attempted to investigate the effects of different parameters on soot radiative properties, such as PP polydispersity [3][4][5][6], number of PP per aggregate and wavelengths [7], necking and overlapping [8]. Although it has been demonstrated that the PP polydispersity has a significant impact on soot radiative properties [9][10][11], there is currently a lack of adequate quantitative understanding of the consequence of applying the RDG-FA theory to soot aggregates formed by polydisperse PP and only a few relevant studies have been conducted.

Farias et al. [3] used the Iskander-Chen-Penner (ICP) method to compare numerical results of RDG-FA for normal primary particle size distribution (NPPSD). The authors observed that the forward and total scattering cross sections are increased by an amount of 14 and 41%, respectively, for σ/d p = 0.15 and 0.25. They also demonstrated that this effect can be reasonably predicted by RDG-FA if the volume equivalent PP size is considered. However, the assumptions on ICP method limit the validity of their results. Liu et al. [4] used the Multi Sphere T-matrix method to study the radiative properties of aggregates consisting of lognormal primary particle size distribution (LNPPSD) with σ geo ≤ 1.5. They found that RDG-FA is significantly challenged for approximating the scattering and absorp-tion cross sections of the aggregates with polydisperse PP at λ = 650 nm and a complex refractive index m = 1.75 + i0.435. Finally, Wu et al. [5] used the Superposition T-matrix method to calculate the radiative properties of aggregates for LNPPSD (σ geo ≤ 4.0), λ = 550 nm, and m = 1.95 + i0.79 and found only a slight effect (< 10%) on the extinction and absorption cross sections regarding PP polydispersity. Nevertheless, no attempt was made to extend RDG-FA to fractal aggregates formed by polydisperse PP.

Regarding primary particle size distribution (PPSD) of soot, experimental studies have also found that it can be well described by a LNPPSD or a NPPSD [12,13]. Available experimental studies have reported a maximum polydispersity of σ/d p = 30% (the standard deviation) and σ geo = 1.6 (the geometric standard deviation) for NPPSD [START_REF] Wentzel | Intercomparison of Soot Measurement Techniques[END_REF] and LNPPSD [START_REF] Chakrabarty | [END_REF], respectively. Additionally, the effect of PPSD has been the subject of studies for fractal aggregate physical properties other than radiative, for instance structure and mobility [13,16].

In this parametric study, we investigated the effects of PP polydispersity on the radiative properties of soot aggregates at 550 and 532 nm, which are typical wavelengths used in light scattering experiments, following the recent studies of Liu et al. [4] and Wu et al. [5]. This research and previous numerical studies form the indispensable prerequisite to take into account PP polydispersity in the retrieval of soot aggregate properties based on light scattering experiments. The objectives of this study are threefold: [START_REF] Liu | 40th Thermophysics Conf[END_REF] to investigate the effect of PP polydispersity on fractal aggregate radiative properties under conditions relevant to flame soot, (2) to propose and evaluate corrections to the RDG-FA theory for calculations of radiative properties of soot aggregates formed by polydisperse PPs, and (3) to assess the effect of PP polydispersity on the radiative force experienced by soot aggregates due to laser irradiance.

Numerical Methods

Generation of fractal-like aggregates

Fractal aggregates were generated numerically by using the Flage particle-cluster aggregation algorithm described by Skorupski et al. [17]. The morphology of these aggregates is considered to be fractal-like and described as N p = k f R g /R p D f , where N p and R p correspond to the number and average (arithmetic or geometric for NPPSD and LNPPSD, respectively) radius of primary particles, respectively, and R g is the radius of gyration calculated as proposed by Dastanpour et al. [13].

D f and k f stand for the fractal dimension and prefactor, respectively. Because of its simplicity, capability of generating aggregates of prescribed fractal parameters, and efficiency, the tunable algorithms have been widely used to generate fractal aggregates for study of their radiative properties [4,18,19]. In the present study, concerning the specific role played by PP polydispersity, the fractal dimension is retained approximately constant (D f ≈ 1.73) for all levels of PP polydispersity. The fractal dimension is selected to be representative of soot produced from miniCAST [20]. However, the corresponding prefactor, observed to be ≈ 1.9 from TEM image analysis, is slightly reduced because overlapping is not taken into account in the present study [8]. This reduction is based on the extrapolation of the relationship found by Brasil et al. [21] between k f and overlapping, who proposed k f = 1.5 without overlapping. It was also found that for σ geo > 1.6 the prefactor experiences a small decrease (from k f = 1.50) with increasing level of PP polydispersity. As found by Eggersdorfer and Pratsinis [16], for σ geo > 1.6 the structure of fractal aggregates (regardless of the aggregation mechanism) is considerably affected by PP polydispersity. It is recognized that the tunable method used to generate fractal aggregates in this study does not correspond to particle aggregation via any physical or chemical aggregation mechanisms (including for example surface growth) that could link the PP polydispersity to the fractal-like morphology [16]. On the other hand, tunable algorithms offer the advantages to investigate the effect of a single parameter, such as PP polydispersity, while keeping all other parameters constant. The performance of such modeling in general involves tuning of model parameters given the current lack of detailed understanding of the soot surface growth process. Moreover, the studies of Bushell and Amal [9] and Eggersdorfer and Pratsinis [16] showed that the fractal dimension remains largely unchanged, though the prefactor decreases, with increasing the level of PP polydispersity (up to σ geo ≈ 1.5). For these reasons, we chose to adopt the tunable method that permits to isolate the effect of PP polydispersity and we considered a realistic maximum σ geo of 1.6 for the evaluation of the radiative properties. In addition, the strategy chosen in the present study consists in increasing the PP polydispersity while keeping the mean radius (arithmetic or geometric for NPPSD and LNPPSD, respectively) constant. Consequently, the increase of PP polydispersity impacts the aggregate volume. This effect is illustrated in Fig. 1, where a e f f is the radius of the equivalent sphere having the same volume as the aggregate (V agg = 4πa 3 ae f f /3). Figure 1 shows that the aggregates formed by LNPPSD with σ geo > 2 may have larger levels of PP polydispersity than those formed by NPPSD. In consequence, the volume is more affected for aggregates in the LNPPSD series than those in the NPPSD series. Nevertheless, it is noticed that the fairly high levels of PP polydispersity (S T D(R p )/R p > 0.4) are typically not encountered in flame-generated soot aggregates. Aggregates formed by highly polydisperse PPs, with σ geo > 1.6 are only considered for the calculation of the radiative force in the present study. For lower levels of PP polydispersity, relatively small increase of a e f f is observed in comparison to the change in the number of primary particles.

STD(R p )/R p a eff ( m) 10 -2 10 -1 10 0 0.0 0.1 0.2 Normal Lognormal Lognormal (high polydispersity) __ N p =15 N p =50 N p =150 /R p =0.98% /R p =8.90% geo =2.23 geo =2.73 geo =2.96 /R p =29.59%

The discrete dipole approximation

The radiative properties of soot aggregates were calculated by using the Discrete Dipole Approximation (DDA) through the DDSCAT code (version 7.3.2) [22]. This method offers the advantage for dealing with particles of complex shapes or morphologies. The principle of DDA is to discretize the particle into a finite array of polarizable points (dipoles) and to consider their interactions with the local electric field. It is equivalent to the volume integral equation for the electric field. In this study, the dipole density was fixed at 15 (corresponding to 15 dipoles per mass equivalent diameter). The present study concerns the visible domain of the spectrum. Since numerous light scattering experiments have been done with green lasers, λ = 532 nm is selected in the present study.

The considered optical index m 1 = 1.5 + i0.62 was reported by Bescond et al. [20] for miniCAST soot characterized by a low amount of organic compounds (OC/TC= 4.1%) and high degree of graphitization. It was determined by interpreting extinction spectra measurements based on a modified RDG-FA theory by applying some correction factors regarding the multiple scattering effects, using the Drude-Lorentz dispersion law, by considering the size distribution, bulk density and specific morphological properties. It is noticed that the optical index of soot generated under the same conditions was previously reported to be m = 1.66 + i0.76. However, it was obtained with a simpler size distribution, neglect of multiple scattering effect, and without measurement of the bulk density. Nevertheless, the optical index of soot is subject to uncertainties, depending on the flame conditions and the experimental and analysis methods. To evaluate the influence of refractive index, calculations are also conducted with another refractive index m 2 = 1.95 + i0.79 determined by Smith et al. [23] for annealed amorphous carbon films and recommended to be used at similar wavelengths (550 nm) by Bond and Bergstrom [24]. Finally, to determine the aggregate structure factors without multiple scattering additional calculations were performed using m = 1.01 + i0.01. The criterion |m|kd < 0.5 for accurate calculations of the radiative properties using DDA [22] is ensured in this study (|m|kd < 0.12). The radiative properties of aggregates calculated by DDA were averaged over 1000 orientations.

Validation of the DDA results

To validate the results of DDA, calculations were also carried out using the numerically exact Generalized Multi-sphere Mie Solution method (GMM). GMM is an extension of Mie theory for solving exactly the Maxwell's equations for a particle system containing non-overlapping spheres. GMM results were obtained with averaging over more than 15,000 orientations. Ta- ble 1 shows the relative error X = 100 • (X DDA -X GMM )/X GMM of the DDA results benchmarked by those of GMM. The error was calculated for three variables (X): (1) the ratio of polarized angular scattering cross sections C hh /C vv (here C hh denotes the differential scattering cross section for horizontally incident and horizontally scattering polarized light, other quantities are similarly defined), (2) C vh /C vv , and (3) the absorption cross section C abs for the three aggregate sizes with different levels of PP polydispersity. The agreement between DDA and GMM is considered very good with only small deviations ( X < 8% for the two ratios and C abs < 6% for the absorption cross section). It is noticed that when comparing the C hh /C vv and C vh /C vv ratios, the relatively large relative errors only occur for C vh /C vv , but not for C hh /C vv . This is because the former is generally very small. Nevertheless, the DDA results are considered sufficiently accurate for the purposes of this study.

Results and discussion

The structure factor without multiple scattering is presented in Fig. 2 ). Indeed, in the forward scattering the RDG-theory stipulates that the scattered intensity is proportional to V 2 agg . This methodology enables a good determination of the theoretical value of unity in forward scattering at qR g = 0. We can distinguish the Guinier regime of small values of qR g less than unity (exponential decrease, with q = 4πsin(θ/2)/λ) from the power-law regime of large values of qR g (larger than unity). The structure factor of Dobbins and Megaridis for fractal aggregates [25] is reported as black dashed lines with D f = 1.73 initially imposed during the aggregate generation. For both considered series of aggregates, corresponding to primary particles of NPPSD and LNPPSD, the Guinier regime is well observed, though the decrease is enhanced for large σ geo of the LNPPSD series. For qR g > 1.62, based on statistics of a large ensemble of aggregates, a linear behavior is expected with a slope supposed to be -D f . For individual aggregates formed by NPPSD and those formed by LNPPSD of low levels of polydispersity, this behavior is essentially preserved with an apparent individual fractal dimension slightly different from that initially imposed (D f ).

Nevertheless, for the range of PP polydispersity relevant to flame soot (σ geo < 1.6) the fractal behavior can largely be ensured.

Let us consider now the structure factors calculated using the assumed refractive indexes of soot at 532 nm for aggregates of both series. By using m = 1.5 + i0.62, the internal coupling or multiple scattering within aggregates is automatically considered in DDA calculations. To highlight the effect of internal coupling, Figs. 2(c) and 2(d) present the ratio between both the structure factors with and without multiple scattering. This ratio is useful to develop corrections to the RDG-FA theory to improve its accuracy for the calculation of vertical-vertical differential scattering cross section (C vv ) of soot aggregates formed by polydisperse PP. In Figs. 2(c) and 2(d) we can observe that, for the considered wavelength and refractive index, the ratios remain at almost unity for aggregates formed by NPPSD and for those formed by LNPPSD except for backscattering at large qR g , indicating a good prediction by the RDG-FA theory.

The correction factor required to bring the RDG-FA results to those of DDA for the prediction of the forward scattering A corresponds to the ratios of forward scattering shown in Figs. 2(c) and 2(d) at qR g = 0. Its repre-sentation as a function of the standard deviation does not display a clear trend (see supplementary material that also contains results for larger geometric standard deviations). Contrarily, its representation as a function of the equivalent radius a e f f shows a more clear trend, regardless of the aggregate size or the level of PP polydispersity (Fig. 3(a)). This leads to a conclusion that, for a given optical index, the aggregate size or volume has a stronger impact on A than PP polydispersity itself. To identify the sensitivity of A to PP polydispersity, we also investigated the corresponding ratios for aggregates formed by monodisperse PP for N p = 50 by varying the primary particle size (dashed lines in Fig. 3) and by increasing N p at fixed D p (black dotted lines) based on previously published results [7] (obtained with m 3 = 1.61 + i0.74). The comparison of the tree curves indicates that, for a given aggregate volume, the deviation of A from unity is enhanced by the increase of the PP diameter and even more when the polydispersity increases (presence of very large primary spheres in the aggregate). Nevertheless, the optical index seems to play a predominant role (the small difference in wavelength between 532 and 550 nm is not expected to have a large impact on the ratio). The refractive index proposed by Smith et al. [23] induces a stronger multiple scattering effect, due to the larger deviations from unity, even without PP polydispersity (small a e f f ). This effect is mainly due to the larger real part of the optical index as recently shown in [26]. With regard to the scattering function F(m), the value of Smith et al. (F(m 2 ) = 0.39) is 1.7 times that of the refractive index of miniCAST soot (F(m 1 ) = 0.23). Thus, stronger scattering and multiple scattering effects are expected when using the refractive index of Smith et al.

Figure 3(b) presents the corrections to bring the RDG-FA theory to the DDA results for aggregate absorption cross section. Similar trends between corrections to the absorption cross section and the forward scattering cross section can be observed and this point has already been found in previous studies [6-8, 26, 27].

Figures 4(a) and 4(b) report the ratio C hh /C vv , which is theoretically equal to cos 2 (θ) in the RDG-FA theory. A good agreement between the results of DDA and RDG-FA is observed. However, such agreement deteriorates slightly with increasing level of PP polydispersity, especially for LNPPSD around 90 • . Once again, the multiple scattering effect (internal coupling among primary particles) is suspected to cause the deviations. This conjecture is supported by Figs. 4(c) and 4(d) representing the depolarization ratio, i.e., C vh /C vv . This ratio is supposed to be null in the RDG-FA theory and is shown to generally increase with scattering angle [28]. The present study reveals that the depolarization is not strongly affected by the degree of PP polydispersity. The anisotropy coefficient A 13 of each aggregate was calculated based on the eigenvalues of the inertia tensor as proposed by Heison et al. [29] and adapted to polydisperse monomers [30]. The values are reported in the legend of Figure 4(a) and (b). It is noticed that the increase in depolarization in backward scattering directions (scattering angles close to 180 • ) has often been attributed to an increase of the particle anisotropy. In the present case, even at very small levels of polydispersity, a slight increase of the depolarization ratio is observed without increasing the particle anisotropy. Integration of the differential scattering cross section over 4π sr permits to evaluate the effects of PP polydispersity on the total scattering cross section σ agg sca . According to the RDG-FA theory, σ agg sca = N 2 p σ pp sca g, here g

is the aggregate total scattering factor and can be determined from the DDA results. It is interesting to compare such determined g DDA to the widely used factor in the RDG-FA theory g Dobbins [25]. Previous similar investigations concluded that the accordance between the two factors is good if g Dobbins is multiplied by the correction for the forward scattering (cf. Fig. 3(a)). Because g Dobbins has been obtained by integrating the Dobbins and Megaridis expression of the structure factor (plain curves in Fig. 2). This assumption holds as long as structure factor remains essentially the same. In order to see if this finding holds for aggregates formed by polydisperse PP, we report in Fig. 5 the ratio between g DDA (numerically accurate evaluation) and Ag Dobbins , i.e., the corrected RDG-FA expression. The deviations of this ratio from unity indicate the error caused by RDG-FA theory even though part of the multiple scattering effects is taken into account through the correction factor A. The obtained ratios are scattered but remain around unity for the considered range of PP polydispersity and decrease slightly with increasing the PP polydispersity. Nevertheless, it is important to notice that for the range of PP polydispersity typically encountered in flame-generated soot (S T D(R p )/R p < 0.4), it appears that the RDG-FA theory, once corrected by the A factor, is able to predict fairly accurate aggregate total scattering cross sections. This is shown to be true for both optical indices considered. Finally, we report in Fig. 6 the radiative force experienced by a soot aggregate due to laser irradiance per unit energy density (radiative pressure cross section C pr = C ext -gC sca where g represents the asymmetry parameter [22,31]). This quantity can be of interest not only for optical manipulation of soot material [32], but also for other fields of science, such as astrophysics concerns for interstellar grains [31]. It can be used for the evaluation of the photopheretic force caused by a Planck radiation source [33].

It is interesting to observe a nearly power law relationship between that radiative force and the volume equivalent radius. This is also true for larger LN polydisersities (up to σ geo = 3.0), reported in blue boxes in Fig. 6. The exponent of that power-law is about 2.97, suggesting that radiative force is essentially governed by the absorption cross section (proportional to the aggregate volume) and thus weakly affected by the PP polydispersity (except for very large geometric standard deviations). This was confirmed by comparing the radiative cross sections of the LNPPSD series for the largest aggregates (N p = 150) by scaling the aggregates in order to achieve the same volume (a e f f = 0.1µm). It results in a relative standard deviation of C pr of 1%

Conclusions

The impact of primary particle polydispersity on the radiative properties of soot aggregates was numerically investigated using the discrete dipole approximation by considering two different refractive indices at 532 nm recommended in the literature to demonstrate the effect of uncertainty in soot refractive index on soot radiative properties. This study intents to gain better understanding of the importance of primary particle polydispersity. Such knowledge is essential to extend the current capabilities of light scattering experiments to retrieve more realistic soot aggregate morphological parameters by taking into account the polydispersity of primary particles. Calculations were conducted for both normal and lognormal primary particle size distributions. Fractal aggregates formed by polydisperse spherical primary particles in point-contact were generated by using the tunable Flage code with fractal parameters fixed to reported standard flame soot values. It has been shown that the fractal behavior is not significantly affected by PP polydispersities, for the range concerned in flame conditions.

The results are analyzed in terms of the correction factors required to bring the RDG-FA results to agree with those of DDA for forward scattering and absorption cross sections. The main findings of this study are that for primary particle polydispersity levels relevant to flame-generated soot, the RDG-FA theory is adequate when the volume mean primary particle diameter is used. The validity range of corrections proposed is dominated by internal multiple scattering and the magnitude of this effect is mainly influenced by the refractive index, both the aggregate size and primary particle polydispersity are of second order effect. This is true for angular light scattering C vv , C hh , absorption cross section c abs , and total light scattering cross section c sca . Only the depolarization ratio C vh /C vv seems to be slightly increased in the case of lognormal distribution. Finally, the radiative force acting on soot particles is evaluated. For the considered two PPSDs, the radiative force is nearly proportional to the particle volume.

Figure 1 :

 1 Figure 1: Impact of the PP polydispersity on the aggregate volume equivalent radius. The standard deviation is indicated in the horizontal axis, σ geo is shown as legend.

  (a) and (b). It represents the angular dependency of the vertically polarized scattered light by the aggregates relative to the vertically polarized incident light. It corresponds to the Fourier transform of the pair-correlation function and bears the morphological information of the particle. In the present case, it is obtained by dividing the C agg vv calculated by DDA with m = 1.01 + i0.01 by the product of the primary particle C p vv based on Rayleigh theory and N 2 p . For each aggregate, the PP differential scattering cross section C p vv is based on the Rayleigh approximation of a sphere having a volumetric mean radius (a p3 = a e f f • N -1/3 p

Figure 2 :

 2 Figure 2: Figs. (a) and (b) present the aggregate structure factors (without internal coupling) obtained at λ = 532nm with m = 1.01 + i0.01 for NPPSD and LNPPSD. The dashed lines are the structure factor of Dobbins and Megaridis. Figs. (c) and (d) present the ratio between angular light scattering patterns computed with (using m = 1.5 + i0.62) and without multiple scattering for aggregates of NPPSD and LNPPSD series at λ = 532 nm and N p = 150.

2

 2 Scaling of D p (fixed m 1 & N p ) Scaling of D p (fixed m 2 & N p ) Scaling of N p (fixed m 3 & D p )

Figure 3 :

 3 Figure 3: Corrections to bring the RDG-FA theory for the forward scattering and absorption cross sections for all the aggregates considered at m 1 = 1.5 + i0.62 (F(m 1 ) = 0.23), m 2 = 1.95 + i0.79 (F(m 2 ) = 0.39) and m 3 = 1.61+i0.74: (a) the correction A for forward scattering cross section and (b) the correction h for absorption cross section. The dashed lines are for results obtained for scaled aggregates formed by monodisperse PP and the black dotted line corresponds to the variation of N p based on the results by [7].

Figure 4 : 2 __Figure 5 : 2 Figure 6 :

 42526 Figure 4: Impact of the PPSD on the C hh /C vv and C vh /C vv cross sections at λ = 532 nm and m = 1.5+i0.62. A 13 stand for the anisotropy coefficient of each aggregate.

Table 1 :

 1 Comparison between DDA and GMM results. Average relative errors calculated as: X = 100 • (X DDA -X GMM )/X GMM .

	N p	X	LNPPSD λ 532 λ 550	NPPSD λ 532 λ 550
		C hh /C vv -0,039 -0,015 0,007	0,157
	15	C vh /C vv -3,645 -0,874 0,415	3,758
		C abs	1,111	4,678	0,547	4,411
		C hh /C vv -1,261 -2,048 -0,144 -0,145
	50	C vh /C vv -5,480 -4,684 4,294	6,877
		C abs	0,947	4,338	1,232	5,100
		C hh /C vv 1,193	2,631 -0,234 -0,298
	150	C vh /C vv 5,156	7,821	2,584	4,264
		C abs	0,945	4,406	1,111	4,872

Acknowledgments

The authors thank the CRIANN for the computational resources provided by the Haute-Normandie region. A. Fuentes also acknowledges the Chilean CON-ICYT Research program under FONDECYT project 1161453.


Maxime Carbonnier

PhD Zeynep Serinyel
email: zeynep.serinyel@cnrs-orleans.fr

Alan Keromnes

Guillaume Dayma

Benoîte Lefort

Luis Le Moyne

Philippe Dagaut

Alan Kéromnès

Luis Lemoyne

An experimental and modeling study of the oxidation of 3-pentanol at high pressure

Keywords: 3-pentanol, kinetics, jet-stirred reactor, shock tube

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

Main text:

2751 Words References: (26+2) x (2.3 lines/reference) x 7.6 words/lines) = 489 Words Figure 1: (51.0+10mm) x (2.2 words/mm) x 1 column + 14 words in caption = 148 Words

Introduction

Alcohols constitute an important family of potential biofuels that can be synthesized from renewable resources. Recently larger alcohols have been the focus of many studies due to their higher energy density and better solubility in gasoline. Alcohols up to C4 have been extensively studied so far, however fewer studies are available for larger (C ≥ 5) alcohols. As far as amyl alcohols are concerned, 1-pentanol, iso-pentanol and 2-methyl-1-butanol have already been investigated experimentally in the literature in terms of speciation [START_REF] Togbé | Proceedings of the Combustion Institute[END_REF][START_REF] Dayma | [END_REF][3][4], laminar burning velocity [5][6][7] and ignition delay times [7][START_REF] Heufer | Proceedings of the Combustion Institute[END_REF][START_REF] Sarathy | [END_REF][10]. These isomers have different oxidation tendencies depending on their structure.

Secondary C5 alcohols such as 3-pentanol are much less studied. Köhler et al. [11] investigated oxidation of a 1-, 2-and 3-pentanol doped hydrogen flat flame using molecular-beam mass spectrometry. Li et al. [12] measured laminar flame speeds of 1-, 2-and 3-pentanol. The aim of this study is to provide new kinetic data through a detailed product analysis of 3-pentanol in a jet-stirred reactor (JSR) and by measuring ignition delay times behind reflected shock waves, for the first time.

A chemical kinetic mechanism is developed and used to represent the present data.

Experimental

Jet-stirred reactor (Orléans)

The jet-stirred reactor (JSR) used in this work has been described previously [13]. It consists in a fused silica jet-stirred reactor that can be heated up to 1250 K and pressurized at 10 atm, located inside a regulated electrical resistance oven of ≈ 3kW itself surrounded by insulating ceramic wool and a stainless-steel pressure-resistant jacket. The liquid fuel is brought by an HPLC pump to the entrance of a home-made vaporization system where it is atomized by a nitrogen flow (50L/h) and then vaporized in a heated chamber (Tvaporiser = 120°C). The fuel+N2 mixture is carried to the reactor by a quartz capillary. The oxidizing stream (oxygen + nitrogen) is conveyed independently to prevent any reactions prior to the reactor. All gaseous flowrates are regulated by thermal mass flow controllers (Brooks 5850E). The two flows merged right ahead of the reactor, in which they are injected by four nozzles that ensure stirring. The sampling system, which consists of a fused-silica protected S-type thermocouple and a low pressure sonic fused silica probe, can be moved along a vertical axis to check the temperature and the composition homogeneity inside the reactor. Residence time distribution studies have shown that under the conditions of the present study the reactor is operating under macromixing conditions [13]. Samples are analyzed online by means of FTIR and stored at low pressure for offline GC analysis. The fuel (CAS number 584-02-1, 98% purity) was supplied by Sigma Aldrich and high purity gases (oxygen and nitrogen from Air Liquide, oxygen 99.995% pure and nitrogen with <1000 ppm Ar, <100 ppm H2O, <50 ppm O2, <5 ppm H2) were used for this study. The carbon balance was checked after each experiment and was found to be within ±10%. Uncertainties on the species mole fractions is due to several factors described in [START_REF] Serinyel | Proceedings of the Combustion Institute[END_REF], such as reactor temperature (< 10 K), pressure (±0.1 atm), residence time (< 5%), etc., and are very difficult to evaluate precisely, these are estimated to be around ±15%. Intermediate species observed include, 3-pentanone, formaldehyde, acetaldehyde, propanal, ethylene, methane, 2 pentene (cis and trans isomers). Butanone, methylvinylketone, butadiene, methacrolein and ethylvinylketone are quantified as well but to a lesser extent, and some in trace amounts. All experiments were performed at 10 atm operating pressure and between 700 and 1180 K. Also, few experiments were performed down to 500 K for the lean mixture and no low temperature reactivity was observed.

High pressure shock tube (Nevers)

The ignition delay times were measured in a high-pressure shock tube in DRIVE over a temperature range of 1030-1460 K at 20 bar and 40 bar. Mixtures of 3-pentanol (1%) + O2 diluted in argon are tested for equivalence ratios of 0.5, 1 and 2. The tube consists of a stainless-steel tube with an inner diameter of 50 mm and separated into two parts, the driver section (length: 4m) and the driven section (length: 5m) by a double stainless-steel diaphragm [START_REF] Merhubi | [END_REF]. The tested mixtures are prepared into two stainless-steel tanks based on the partial pressure method using high purity gases (greater than 99.995% for Ar, O2 and He) and 3-pentanol with a purity of 98%. To prevent any contamination, the facility includes a vacuum system, a roughing pump and a turbo-molecular pump, which pumps down the tube, the manifold, the stainless-tanks, the manifold and the previously frozen fuel tank below 5 Pa. In order to avoid any condensation of the fuel, the tube, the tanks and the manifold are heated up to 80 °C to allow the partial pressure of the 3-pentanol be at least three times lower than its vapor pressure. The data acquisition system has a frequency of 1 MHz and includes a NI Compact RIO which records the pressure signals from four individual piezoelectric pressure transducers PCB 113B22 in order to calculate the shock velocity and from a Kistler piezoelectric pressure transducer (603B1) located at the end-wall to calculate the ignition delay time and determine post-shock pressure, P5. It is defined as the time interval between the rebound of the shock wave at the end-wall and the onset of combustion, commonly defined by a sudden change in pressure (inflection point), see Figure 1. Postshock temperature, T5, is calculated from the shock wave velocity and the initial conditions based on the 1-D shock relations and the species thermodynamics using the chemical equilibrium software Gaseq [16] with an accuracy of ±1% which corresponds to ±10-15K according to the uncertainty calculation proposed by Petersen et al. [17].

Kinetic modeling

The kinetic model used in the simulations is constructed by introducing a sub-mechanism of 3pentanol into an in-house C0-C4 base (258 species in 1695 reactions). This base is already involved in our recent studies, e.g. [18,19]. The thermochemical parameters of the fuel and related species were evaluated using Thergas [20], which uses the group additivity methods proposed by Benson [START_REF] Benson | Thermochemical Kinetics[END_REF]. All kinetic simulations were performed using Chemkin-II [START_REF] Kee | SAND89-8009[END_REF] using PSR and SENKIN modules (constant V) for the JSR and shock tube simulations, respectively. Fuel reactions include water elimination, H2 elimination, unimolecular dissociations into radicals, and bimolecular initiation reactions with O2, and hydrogen abstraction reactions by radicals. Through these latter reactions, the fuel can yield four distinct radicals three of which are considered in this study. These are named pent3oh-1 (where the radical site is in γ position with respect to the carbon bearing the -OH group), pent3oh-2 (radical site in β position) and pent3oh-3, which is the α-hydroxyalkyl radical. The 3-pentoxy radical is not included given that its formation would not be favorable because of the large bond dissociation energy associated to this C-H bond (~105 kcal/mol). For the H-abstraction reactions by important radicals such as OH, H, CH3 and HO2 yielding the pent3oh-3 radical, rate constants were taken in analogy with sec-butanol from literature [START_REF] Yasunaga | [END_REF][24][START_REF] Carstensen | Development of Detailed Kinetic Models for the Thermal Conversion of Biomass via First Principle Methods and Rate Estimation Rules[END_REF]. As far as the γ and β radicals are concerned, rate constants are Unimolecular fuel reactions are not of importance in the present JSR conditions and have a negligible contribution at high temperature ignition delays. One of the main oxygenated intermediate species observed in 3-pentanol oxidation is 3-pentanone, which is a product of the β-scission of the αhydroxyalkyl radical. Therefore a sub-mechanism involving reactions of 3-pentanone and ethyl vinyl ketone were also considered, partly in analogy with our previous study on butanone oxidation [START_REF] Thion | Proceedings of the Combustion Institute[END_REF],

which itself is also observed as an intermediate species. Figure 8 shows the primary decomposition pathways of 3-pentanol for the stoichiometric mixture at 800 K. A similar figure can be found in supplementary material covering the analysis to ϕ = 0.35 and ϕ = 4 mixtures. Fuel is mainly consumed by the attack of OH radicals (75% of the flux), and H, HO2 as well CH3 radicals to a lesser extent. Although the bond energy for a tertiary C-H bond neighboring the -OH group is weaker than primary and secondary C-H sites available, given the 0.0E+00 Kinetic model predictions are generally in good agreement with experimental results. However, some discrepancies are observed, for example with propene which is under-predicted by a factor of 3, probably because of a missing pathway. Also, for the ϕ = 4 mixture, there is an over-prediction of

Results and discussion

JSR experiments

23% pent3oh pent3oh-1 pent3oh-2 pent3oh-3 O O 69% 31% pent-1-en-3-one HO 2 CH 3 CHCO C 2 H 5 MVK C 2 H 4 + CH 3 CO C 2 H 5 + CH 2 CO CH 3 CHO + C 3 H 5 -s + OH C 4 H 6 +CH 3 63% 29% O C 2 H 5 +CO -C 2 H 4
reactivity in the fuel mole fraction profile between a small temperature window of 880-1000 K. This results in an over-prediction of the CO profile within the same temperature range. Given the shape of water profile correctly predicted, this small discrepancy is probably not a result of H-abstraction reactions by OH consuming the fuel and other abundant intermediates such as propanal, formaldehyde, etc. but rather an under-estimation of a species likely accumulating and decreasing the overall reactivity. Also, experimental profiles of butanone and 3-pentanone do not quite show the same tendency at ϕ = 2 and 4 as opposed to lean and stoichiometric mixtures and the model prediction for butanone in these rich cases is shifted towards lower temperatures. This observation might suggest an unexplored formation path for this ketone rather than a problem with the branching ratio with the decomposition of the pent3oh-3 radical or the consumption pathways. Water profiles are overpredicted by about 20% for the lean and stoichiometric mixtures, probably because of the higher uncertainty in H2O mole fractions measured at high quantities.

A comparison between different isomers of pentanol investigated in our JSR is presented in figure 9, in terms of fuel mole fraction profiles. According to this, on a logarithmic scale, one can easily note the difference in reactivity between 1-pentanol (pent1oh) and iso-pentanol (butoh3m). The reactivity of 3-pentanol lies between these. A major oxygenated intermediate in 1-pentanol oxidation is pentanal [START_REF] Togbé | Proceedings of the Combustion Institute[END_REF], and both produce reactive alkyl radicals during oxidation, on the other hand isopentanol, due to its structure, produces less reactive intermediates, such as iso-butene [START_REF] Dayma | [END_REF]. An interesting feature in 3-pentanol oxidation, which is a secondary alcohol, is that it produces ketone species as well as aldehydes, unlike primary alcohols where the structure does not allow the formation of a ketone with the same carbon number.

Shock tube experiments

Mixtures of 1% 3-pentanol in O2/Ar are tested in a high-pressure shock tube at 20 and 40 bar of pressure and equivalence ratios of 0.5, 1 and 2 between 1000 and 1460 K. No pressure rise was recorded after the reflected shock wave prior to the main ignition event. Kinetic model and experiment comparisons are presented in figure 10. The influence of the experimental conditions (temperature, pressure and equivalence ratio) on ignition delay times is observed to be as expected: the ignition delay times decrease with increasing pressure and temperature as well as increasing oxygen concentration.

The effect of equivalence ratio is more apparent at 20 bar than at 40 bar, experimentally. Kinetic model agrees very well with the data for the mixtures ϕ = 0.5 and 1, however predicts longer ignition delay times regardless of the pressure as far as the ϕ = 2 mixtures are concerned, although the global activation energy is correct. For example at 1250 K, this over-prediction at ϕ = 2 is less than a factor of 2 at 20 bar and a factor of 2 at 40 bar. We can also note that at the lowest temperatures investigated (≈ 1050-1100 K) experimental ignition delays tend to converge while the model predicts a more pronounced dependence on equivalence ratio over all temperature range. Lower panel (c-e) shows the effect of pressure for a given equivalence ratio.

Sensitivity analysis at 1200 K; ϕ = 1 and 40 bar (Figure S3) shows that among the fuel-related reactions, H-abstraction by OH and H producing the primary radical inhibit reactivity while Habstraction by HO2 producing pent3oh-2 (secondary) radical promote reactivity. Beta decomposition of the latter gives ethyl radicals and propanal, which itself yields ethyl radicals, promoting reactivity by supplying H atoms to the system. Part of the pent3oh-2 yields the stable molecule 2-pentene and OH radicals, inhibiting overall reactivity. Branching between these pathways could be one factor affecting the delays, which is based on estimations in this study. Pathways of fuel and fuel radical decomposition under these conditions can also be found in Figure S4.

Conclusion

High pressure oxidation of 3-pentanol is investigated experimentally in a JSR and in a shock tube, for the first time. Mole fraction profiles of the reactants, final products, and stable intermediates are identified and measured by gas chromatography, mass spectrometry, and Fourier transform infrared spectrometry after sonic probe sampling at five equivalence ratios. Ignition delay times are measured for 1% fuel in O2/Ar mixtures at 20 and 40 bar for 3 equivalence ratios. Under the investigated conditions, 3-pentanol did not show any cool flame behavior and is found to produce various aldehydes and ketones as well as the olefin 2-pentene as one of its C5 intermediates. A submechanism for 3-pentanol was developed in order to represent the data with globally good performance, however some discrepancies were observed in species profiles, which suggest further work. Experimental fuel profile is compared with previous oxidation studies of 1-pentanol, isopentanol and 2-methylbutanol under same conditions and the global reactivity of 3-pentanol is found to be between that of 1-pentanol and iso-pentanol. Moreover, laminar burning velocities of 3-pentanol measured by Li et al. [12] were also simulated with the present model (Figure S1) with reasonably good agreement. More data would certainly be useful, such as detailed speciation at lower pressure, pyrolysis, or ignition delay data at lower temperatures of interest in order to unravel more about 3pentanol kinetics and further refine the kinetic mechanism.

Acknowledgements

Authors gratefully acknowledge funding received from Bourgogne council under the PARI2 program

(No 2016-9201AAO048S01891) and Labex Caprysses (convention ANR-11-LABX-0006-01)

Supplementary material

The kinetic mechanism and thermodynamic data in Chemkin format

List of figures

Figure 2 :

 2 (47.9+10mm) x (2.2 words/mm) x 1 column + 19 words in caption = 146 Words Figure 3: (61.0+10mm) x (2.2 words/mm) x 2 columns + 26 words in caption = 338 Words Figure 4: (60.7+10mm) x (2.2 words/mm) x 2 columns + 26 words in caption = 337 Words Figure 5: (59.3+10mm) x (2.2 words/mm) x 2 columns + 26 words in caption = 331 Words Figure 6: (61.6+10mm) x (2.2 words/mm) x 2 columns + 26 words in caption = 341 Words Figure 7: (59.9+10mm) x (2.2 words/mm) x 2 columns + 26 words in caption = 334 Words Figure 8: (66.3+10mm) x (2.2 words/mm) x 2 columns + 12 words in caption = 348 Words Figure 9: (50.9+10mm) x (2.2 words/mm) x 1 column + 39 words in caption = 173 Words Figure 10: (83.6+10mm) x (2.2 words/mm) x 2 columns + 31 words in caption = 443 Words

Figure 1 .

 1 Figure 1. Ignition delay time measurement, initial mixture: 1% fuel, 7.5% O2, balance argon

  primary and secondary C-H, respectively as in alkanes. Both the mechanism and thermochemistry files are provided as supplementary material, with corresponding references therein.

Figure 2

 2 Figure 2 represents fuel mole fraction at different equivalence ratios investigated. Reactivity

Figure 2 .

 2 Figure 2. Fuel mole fraction at all equivalence ratios investigated (P = 10 atm, and τ = 0.7 s).

Figures 3 -

 3 Figures 3-7 represent mole fractions of the major species quantified for mixtures ϕ = 0.35, 0.5,

Figure 3 .Figure 4 .

 34 Figure 3. Species mole fractions as a function of temperature (K) for the ϕ = 0.35 mixture (P = 10 atm, and τ = 0.7 s).

Figure 5 .

 5 Figure 5. Species mole fractions as a function of temperature (K) for the ϕ = 1 mixture (P = 10 atm, and τ = 0.7 s).

Figure 6 .

 6 Figure 6. Species mole fractions as a function of temperature (K) for the ϕ = 2 mixture (P = 10 atm, and τ = 0.7 s).

Figure 7 .

 7 Figure 7. Species mole fractions as a function of temperature (K) for the ϕ = 4 mixture (P = 10 atm, and τ = 0.7 s).

  secondary C-H sites, the pent3oh-2 radical formation is more favored and corresponds to 53% of the flux. This pent3oh-2 radical forms 2-pentene or propanal by β-scission of C-O and C-C bonds, respectively. All 2-pentene observed is formed this way. On the other hand, the pent3oh-1 radical forms mostly ethylene and C2H5CHOH radical via β-scission This radical, in turn, can give vinyl alcohol and propanal by C-C and O-H bond breaks, respectively. However, propanal formation is largely due to the pathway from pent3oh-2 radical, which is more abundant. The ketones (butanone and 3-pentanone) observed in this study are both products of the chemistry following the formation of pent3oh-3 radical, as shown. Butanone is minor compared to 3-pentanone (20% of the flux of pent3oh-3 radical) except at ϕ = 4 where both species are comparable. Methyl vinyl ketone (MVK) was quantified in trace amounts, around 5-6 ppm which can be seen in figures 2-4. On the other hand, 3-pentanone amounts up to around 90 ppm for the lean mixtures, and pent-1-en-3-one is observed in trace amounts.

Figure 8 .

 8 Figure 8. Main fuel decomposition pathways at 70% fuel conversion, ϕ = 1

Figure 9 .

 9 Figure 9. Experimental fuel mole fraction profiles of 3-pentanol, 1-pentanol [1], 3-methyl-1-butanol [2] and 2-methyl-1-butanol [3] at 10 atm, 1000 ppm of initial mole fraction and τ = 0.7s for all

Figure 10 .

 10 Figure 10. Ignition delay times of 1% 3-pentanol/O2/Ar mixtures at (a) 20 bar and (b) 40 bar.

Figure 1 .

 1 Figure 1. Fuel mole fraction at all equivalence ratios investigated (P = 10 atm, and τ = 0.7 s).

Figure 2 .

 2 Figure 2. Species mole fractions as a function of temperature (K) for the ϕ = 0.35 mixture (P = 10 atm, and τ = 0.7 s).

Figure 3 .

 3 Figure 3. Species mole fractions as a function of temperature (K) for the ϕ = 0.5 mixture (P = 10 atm, and τ = 0.7 s).

Figure 4 .

 4 Figure 4. Species mole fractions as a function of temperature (K) for the ϕ = 1 mixture (P = 10 atm, and τ = 0.7 s).

Figure 5 .

 5 Figure 5. Species mole fractions as a function of temperature (K) for the ϕ = 2 mixture (P = 10 atm, and τ = 0.7 s).

Figure 6 .

 6 Figure 6. Species mole fractions as a function of temperature (K) for the ϕ = 4 mixture (P = 10 atm, and τ = 0.7 s).

Figure 7 . 1 Figure 8 .

 718 Figure 7. Main fuel decomposition pathways at 800 K, ϕ = 1

Figure 9 .

 9 Figure 9. Ignition delay times of 1% 3-pentanol/O2/Ar mixtures at (a) 20 bar and (b) 40 bar