G Seisson

G Prudhomme

P.-A Frugier

D Hébert

E Lescoute

A Sollier

L Videau

P Mercier

M Boustie

L Berthe

Dynamic fragmentation of graphite under laser-driven shocks: Identification of four damage regimes

Keywords:

This study presents the results of a large experimental campaign conducted on the Luli2000 laser facility. Thin targets of a commercial grade of porous graphite were submitted to high-power laser-driven shocks leading to their fragmentation. Many diagnostics were used such as high-speed time-and spaceresolved imaging systems (shadowgraphy and photography), laser velocimetry (PDV and VISAR), debris collection and post-mortem X-ray tomography. They provided the loading levels into the targets, the spall strength of the material, the shape and size of debris and the localization of the subsurface cracks. The crossed data reduction of all the records showed their reliability and allowed to get a better insight into the damage phenomena at play in graphite. Thereby, four damage regimes, ranked according to their severity and loading level, were identified. It confirms that laser shocks are very complementary to classical impact tests (plates and spheres) since they ally two-dimensional loadings to the possibility of using both, in-situ and post-mortem diagnostics. Finally, the campaign shall be able to provide large and consistent data to develop and adjust reliable models for shock wave propagation and damage into porous graphite.

Introduction

From the beginning of their development, high-power laser facilities have always been considered as potential calibrated-shock generators [START_REF] Demichelis | Laser interaction with solids -a bibliographical review[END_REF]. Indeed, the interaction between the laser and the front face of a solid target generates a plasma whose expansion creates a shock wave into the matter that may lead to its failure. Thus, similarities with plate impact experiments [START_REF] Veeser | Studies of laser-driven shock waves in aluminum[END_REF][START_REF] Ng | Hugoniot measurements for laser-generated shock waves in aluminum[END_REF][START_REF] Eliezer | Laser-induced spall in metals: experiment and simulation[END_REF][START_REF] Boustie | Experimental and numerical study of laser induced spallation into aluminum and copper targets[END_REF] or hypervelocity impacts [START_REF] Pirri | Theory for laser simulation of hypervelocity impact[END_REF][START_REF] Nebolsine | Laser simulation of hypervelocity impact[END_REF] have been pointed out. Many efforts have been done to understand and predict the mechanical effects of the laser-matter interaction through the development of empirical laws [START_REF] Phipps | Impulse coupling to targets in vacuum by KrF, HF, and CO2 single-pulse lasers[END_REF][START_REF] Grün | Characteristics of ablation plasma from planar, laser-driven targets[END_REF][START_REF] Fabbro | Physical study of laserproduced plasma in confined geometry[END_REF][START_REF] Berthe | Shock waves from a waterconfined laser-generated plasma[END_REF] and specific hydrocodes [START_REF] Buresi | Laser program development at CEL-V: overview of recent experimental results[END_REF][START_REF] Ramis | MULTI2D -a computer code for two-dimensional radiation hydrodynamics[END_REF]. As a consequence, high-power lasers are now commonly used in a large scope of shock studies [START_REF] Batani | Hugoniot data for carbon at megabar pressures[END_REF][START_REF] Laporte | Analyse de la réponse d'assemblages collés sous des sollicitations en dynamique rapide[END_REF][START_REF] Loison | Skew photonic Doppler velocimetry to investigate the expansion of a cloud of droplets created by micro-spalling of laser shock-melted metal foils[END_REF][START_REF] Bolis | Étude numérique et expérimentale de la séparation par chocs brefs d'interface de revêtements multicouches[END_REF][START_REF] Ecault | A study of composite material damage induced by laser shock waves[END_REF][START_REF] Jp | Étude du comportement dynamique de matériaux sous choc laser sub-picoseconde[END_REF][START_REF] Holmquist | Laser-induced spall in silicon carbide[END_REF][START_REF] Holmquist | The internal tensile strength of a borosilicate glass determined from laser shock experiments and computational analysis[END_REF].

The present authors have recently studied the dynamic behavior of porous graphite under high or hypervelocity impacts of metallic plates and spheres [START_REF] Hébert | Plate impact experiments and simulation on porous graphite[END_REF][START_REF] Hébert | Simulations of hypervelocity impacts into graphite[END_REF][START_REF] Seisson | Dynamic behavior of a porous brittle material: experiments and modeling[END_REF][START_REF] Seisson | Dynamic cratering of graphite: experimental results and simulations[END_REF][START_REF] Seisson | Penetration and cratering experiments of graphite by 0.5-mm diameter steel spheres at various impact velocities[END_REF][START_REF] Jodar | Enhancement of a dynamic porous model considering compression-release hysteresis behavior: application to graphite[END_REF]. On the one hand, for plate impact experiments, all the phenomena are one-dimensional. Data, exclusively particle velocities (free-surface or interface), are collected during the experiment and samples cannot be recovered for further postmortem analysis. On the other hand, hypervelocity impacts of spheres generate two-dimensional phenomena and allow sample recovering for fine post-mortem analysis such as micrography and tomography. However, in-situ dynamic observations are less reachable because of time and space uncertainties about the impact.

Hence, the purpose of this paper is to show how a better insight into the two-dimensional damage phenomena of porous graphite can be obtained with well-calibrated and repeatable laser-driven shocks using crossed data reduction from various in-situ and postmortem diagnostics. In Section 2, we present the experimental setup. Then, in Section 3, we discuss the free-surface velocity records in order to estimate the loading levels and the spall strength of our graphite. And finally, in Section 4, we confront, correlate and discuss all the experimental results in order to better understand the damage mechanisms, leading to the identification of four different damage regimes.

Experimental set-up

Shock experiments have been conducted with a high-power laser facility onto thin graphite targets leading to their fragmentation and/ or perforation. Various diagnostics have been used in order to measure the laser spot and pulse, to capture time-and spaceresolved images of the fragmentation and to record the particle velocities. In the same time, reference shots have been done onto well-known materials such as aluminum and tantalum.

Facility and diagnostics

Luli2000 is a high-power laser facility of the Laboratoire pour l'Utilisation des Lasers Intenses (LULI) based at the École Polytechnique (Palaiseau, France) [START_REF] Luli | <www.luli[END_REF]. This laser generates square temporal pulses tunable from 0.5 to 5 ns and can reach energies up to 1 kJ at the wavelength of 1064 ns.

Fig. 1 gives a simplified scheme of the experimental set-up. During this campaign, the laser was used at the wavelength of 532 ns with energies between 35 and 700 J, of which about 90% were delivered in 5 ns as shown in Fig. 2(a). The targets were placed at the center of the experimental chamber under high-vacuum where two different beams (called SB and NB, i.e. South beam and North beam) were alternatively focused. They formed a negligible angle of 5.5 degrees with the horizontal x-axis. They shared the same laser source but had their own amplification chain which allowed larger quantity of shots per day. The focal spot of each beam was spatially shaped just before the experiment chamber by means of phase plates that made the beams axisymmetrical and pseudo-Gaussian (see Fig. 2(b) and 2(c)).

The particle velocities of the rear face of the targets were measured by VISAR [START_REF] Barker | Laser interferometer for measuring high velocities of any reflecting surface[END_REF] which has a good temporal resolution. However, its need of a strong return signal can be an issue when the measured surface gets highly deformed and loses its reflectivity. Hence, we also used photonic Doppler velocimetry (PDV) [START_REF] Strand | Compact system for high-speed velocimetry using heterodyne techniques[END_REF][START_REF] Mercier | PDV measurements of ns and fs laser driven shock experiments on solid targets[END_REF][START_REF] Hébert | A KDP equation of state for laser-induced damage applications[END_REF] that has a lower temporal resolution but is capable to record multiple velocities despite weak return signals (around a few percents of the original one). Two PDV probes with 1-mm-diameter beams were placed in the x-y plan, each forming an angle with the x-axis (α 1 and α2 respectively). They were pointed to the back face of the targets measuring its velocity and then the velocity of the ejected fragments.

For some shots, VISAR was replaced by an open cube filled with varagel, a gel derivated from paraffin with a density close to the water one. Placed at a few centimeters from the back face, this collector captured debris without damaging them in order to measure and analyze them by means of tomography [START_REF] Loison | Ballistic properties of debris produced by laser shock-induced micro-spallation of tin samples[END_REF].

The time-and space-resolved laser shadowgraphy recorded fragments ejected from the targets back face [START_REF] Lescoute | Transverse shadowgraphy and new recovery technique to investigate dynamic fragmentation of laser shock-loaded metals[END_REF]. A 527-nm continuous laser enlightened two amplified cameras that took pictures of the shadow of the ejecta according to the x-z plan. Each camera made two images at different times with an exposure time of 5 ns. The exact instant of the capture was known thanks to a synchronization system between the laser facility and all the diagnostics.

High-speed photography was obtained by pulsed-laser illumination [START_REF] Frugier | Quantification 3D d'une surface dynamique par lumière laser structurée en impulsion nanoseconde[END_REF]: two 10-ns pulses of second harmonic YAG laser lightened the scene, hence freezing the movement of the rear surface. The apparatus delivered two high-resolution frames, even when fragment velocities exceeded several hundreds of meters per second. Light was fed through bundles of multimode optical fibers providing flexibility in its positioning and, as a side effect, operating a significant smoothing of both objective and subjective speckles. Its residual contrast was estimated at only 14%. Each frame was captured by a CCD camera with sampling 2048 × 2048 pixels and 500 ns framing for spurious light rejection; an interferometric filter could also be implemented to further reject unwanted light signals (plasma, PDV probes, etc.).

Targets and shot configurations

The shots of the campaign are summarized in Table 1 giving the characteristics of the targets as well as the laser and diagnostic parameters. As mentioned above, reference shots were performed onto 6061-T6 aluminum and tantalum targets whose respective thicknesses were 250 and 125 μm. But most of the shots were done onto 18-mm square plates of EDM3 graphite whose thickness varied from 0.75 to 2.5 mm.

EDM3 is a macroscopically isotropic commercial grade of graphite made by POCO [START_REF] Poco | [END_REF][START_REF] Sheppard | Properties and characteristics of graphite for the EDM industry[END_REF] and has been extensively investigated by the present authors [START_REF] Hébert | Plate impact experiments and simulation on porous graphite[END_REF][START_REF] Seisson | Étude expérimentale et théorique de l'endommagement du graphite sous sollicitation dynamique -Application aux impacts hypervéloces[END_REF] in the context of understanding the dynamic behavior of matrices from carbon-carbon composites. It is about 22% porous with a density of 1.754 g/cm 3 . A binarised optical micrography of a healthy sample of EDM3 (after cutting and polishing) is displayed in Fig. 3. It shows that the side of the cubic Representative Volume Element (RVE) is of the order of 50 μm, i.e. from 15 to 50 times less than the target thickness and around 40 times less than the laser spot diameter. The main features of EDM3 that may be useful to the reader and to the discussions are recalled in Table 2.

Finally, the back face of the targets were covered of a 1-μm aluminum layer in order to better reflect laser diagnostics.

Velocimetry analysis

In this section, we present and analyze the VISAR and the PDV records in order to evaluate the difference between South and North beams, the spall strength of EDM3 and the mechanical loading endured by the targets. Fig. 2. Temporal and spatial characteristics of the laser pulses of South and North beams. For the record, the temporal profile has been measured by a photodiode for every shot. Very stable, the spatial profiles have been gauged at regular intervals with a CCD camera.

Table 1

Summary of the shots on aliminum, tantalum and EDM3 graphite. Only α2 is given since α1 = 13°never changed. The laser energy is the one that has been measured and not the one that has been adjusted by calibration (cf. Section 3.1). The reference time is set to be the arrival time of the high-power laser onto the front face of the target.

Shot number

North beam vs. South beam

Before presenting all the VISAR records, the difference between NB and SB has to be pointed out. The shots conducted on both beams must be considered as two distinct series. This is demonstated by Fig. 4 that presents VISAR signals for three couples of shots with identical thicknesses. For each couple, the energy of NB is slightly higher than the one of the SB but this is not the case of the free surface velocity. For example, the energy of shot #8 is 20% higher than shot #17 but its velocity is 15% lower. For clarity and consistency we specify in the following the laser beam used for each shot adding the letter S or N before the shot number, e.g. S17 and N8.

The most obvious reason of such a discrepancy between NB and SB in spite of similar energies is the shape of their respective focal spots that are rather different. A significant part of the announced energy can be spent in the wings of the Gaussian spot at very low intensities but over a large area. Thus, it is necessary to know the exact amount of energy contained in the useful part of the spot, i.e. the central part where the intensity is high enough to generate a shock wave into the target. Therefore, reference shots onto wellknown materials that are aluminum and tantalum have been performed. A calibration process consisting in computations of lasermatter interaction and shock wave propagation (not presented here) revealed that the useful part of the focal spot contains 45% of the measured energy for NB and 80% for SB which is consistent with the VISAR records plotted in Fig. 4.

Loading levels

P CU m m = 1 2 0 0 ρ (1)
where ρ0 and C0 are the initial density and the bulk sound velocity of the target material and U m is the maximum free surface velocity. The pressure P m of each shot on graphite is given in Table 3, ranging from 0.1 to 1.1 GPa. But this must be considered with caution, because if the acoustic approximation is quite well adapted to dense materials where the sound velocity does not vary so much with the pressure, this is not the case for porous materials such as EDM3 where the sound velocity decreases first and then increases because of the compaction phenomenon. However, it gives good orders of magnitude. It is interesting to compare Pm to the ablation pressure generated on the front face by the plasma expansion. In the case of aluminum, the Grün formula [START_REF] Grün | Characteristics of ablation plasma from planar, laser-driven targets[END_REF] gives good results:

P I ab m = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1440 0 8 10 5 0 8 . . ( 2
)
with P ab the ablation pressure in GPa and Im the maximum laser in- tensity expressed in GW/cm 2 . There is no such empirical law for graphite but we have shown that the Grün formula gives good order of magnitude for graphite at intensities around 1 TW/cm 2 [START_REF] Seisson | Dynamic cratering of graphite: experimental results and simulations[END_REF]. The intensity used here is an equivalent one calculated after the calibration process in the case of a homogeneous top-hat spot whose diameter has been ajusted to conserve the power. Table 3 gives the ablation pressure of each shot deduced from equation 2.

The immense difference (two orders of magnitude) between P ab and Pm must be noticed. It shows a strong attenuation of the shock wave during its propagation through the graphite target. This phenomenon is linked to the target thickness, to the very short laser pulse and to the fact that the velocities of the release waves in porous materials are much higher than the shock wave one.

Spall strength

Fig. 6 shows the back face of shot S27 captured by the laser imaging at 3.4 μs after the laser pulse begining. The Gaussian shape of the beam leads to a strong bulge of the surface degrading its reflectivity. It certainly happened right after the shock break-out instant that can explain the fact that VISAR signal is lost before any pull-back. Thus, VISAR is very useful for recording the shock front but for spall phenomenon, PDV must take over.

Remind that the PDV probes use a collimated beam whose diameter is above 1 mm. It means they record all the velocities over a surface equal to the beam area. As a result, we get a spectrum of velocities whose maximum values are theoritically related to the center of the stressed area. Nevertheless, a correction is needed in order to take into account the angles α i dividing the velocities by the their respective cosine (in the hypothesis of colinearity between the x-axis and the surface and/or debris motion).

The spectrogram of S7-PDV1 plotted in Fig. 7 confirms the maximum free surface velocity of 170 m/s recorded by VISAR, which is the case (± 10%) for every shots with both PDV and VISAR. Then, after 4 μs, it clearly shows a spall flight with a constant velocity signal around 75-80 m/s.

Averaging the velocities before 10 μs gives a unique velocity signal where a pull-back is clearly visible with a ΔU ~70 m/s. One can estimate the spall strength by:

σ ρ sp C U = - 1 2 0 0 Δ (3)
It gives σ sp = -135 MPa a value sensibly higher than the static tensile strength of -70 MPa given in Table 2. However, given the porosity of EDM3, the acoustic approximation must be considered with caution. Anyway, the existence of a planar spall is uncertain because of the Gaussian shape of the focal spot that complexifies the phenomenon. In fact, after 20 μs, the signal lose its intensity and a new trail progressively begins around 20-25 m/s. The joint use of PDV and imaging systems will help to understand this phenomenon.

Correlation of the experimental results

Many in-situ diagnostics have been simultaneously used during the campaign. Each of them gives partial information about the shock propagation into the target or about its fragmentation. They were completed by post-mortem tomographies of the recovered targets and debris, informing about damage. The purpose of the following is to correlate all these results in order to better understand the damage phenomenology of graphite under laser-induced shock.

Representative shots

A first data reduction allowed us to visually identify four different damage regimes to which almost all the shots can be linked to. Each of the four shots discussed in this section is representative of a particular damage regime.

4.1.1. Shot S7 -0.75 mm -0.89 TW/cm 2 Fig. 8 gives the results of the two time-resolved imaging systems used during shot S7. Surprisingly, they evidence two spall levels: the one that is ejected first looks like an Asian conical hat and is constituted of multiple debris; it is followed by a unique spall shaped like a cymbal or a saucer recessed of the first stage of debris. The distance between those two stages is increasing with time which indicates the first one is moving faster.

We drew the position and the size of the PDV1 beam onto the shadowgraphy images. In reality, probes were placed in the x-y plan instead of the x-z plan as suggested here but this is not much inaccurate because of the axisymmetry of the experiment. In this manner, one sees that the Asian hat goes first through the PDV beam. Then, between 16 and 50 μs, the cymbal progressively intercepts the beam. Thus, the velocity signal around 75-80 m/s seen on Fig. 9 should correspond to the first spall level whereas the one around 20-25 m/s should belong to the second stage. It is easily verifiable thanks to the time-and space-resolved shadowgraphy which enables to know the average speed of an object V av between two images, using the simple formula:

V x x t av = - 2 1 Δ (4)
According to Fig. 8(a), it leads to 88 m/s for the first level and 28 m/s for the second one. The order of magnitude is rather good even if a slight discrepancy exists. It probably comes from the fact that the two methods do not consider the velocity of the same points, those possibly varying despite the almost axisymmetry of the experiment.

4.1.2. Shot S15 -0.75 mm -1.89 TW/cm 2 The same analysis is feasible for totally different shots shuch as shot S15, conducted at higher energy and whose results are given in Fig. 9. With shadowgraphy, one identifies three successive debris levels whose velocities are around 250 m/s for the first one (L1), 140 m/s (L2) and 85 m/s (L3). They are represented on the spectrogram of PDV1 by means of three horizontal lines. The identification of the slower level is the easiest because it is the one that stays the longest in the PDV beam (from 10 μs).

Shot S17 -0.75 mm -4 TW/cm 2

Until now, we followed the assumption that the motion of the ejecta was exclusively along the x-axis and thus, the velocity measured by PDV1 could simply be corrected by the cosine of α 1. It was rather accurate for shots S7 and S15. but it is less obvious in the case of shot S17 conducted at even higher energy whose results are outlined in Fig. 10.

Beyond the first instants, one cannot know the exact velocity along the x-axis because the debris cloud takes the shape of an expending sphere, also moving along this axis. Hence, the record is only a projection of the particle velocity along the probe axis. This is an incomplete measure whose bias depends not only on the time but also on the observed particle. When the PDV beam skims over the sphere periphery, it records in the same time particle velocities with strongly different directions. That is why no angle correction has been done on the PDV spectrogram of Fig. 10(a). Nonetheless, at late instants one observes a constant velocity signal around 100 m/s that according to shadowgraphy seems to be the one of the cone following the sphere.

Shot N13 -2 mm -3.11 TW/cm 2

The reading of shot N13 is much more simple as shown in Fig. 11. Except small central debris due to overintensities of the focal spot observable in Fig. 2

Damage regimes

As said previously, shots N13, S7, S15 and S17 were not randomly selected. They are representative of four different damage regimes identified, proceeding from the data reduction of the campaign. Name them D1 to D4 according to their physical aspect and severity: Regime D1: formation of a single conical spall; Regime D2: apparition of a double spall with a multi-fragmented first stage and a one-piece second one; Regime D3: multiple fragmentation of the target into few debris levels; Regime D4: explosion of the target with a sphere-shaped cloud constitued of numerous debris of small size.

Identification and origins

The data reduction of the other shots allows to identify those linked to one or the other regime based on the damage aspect as ranked in Table 4. Because damage necessarily depends on loading conditions, the maximum intensity, the maximum pressure seen by the back face and the maximum free surface velocity are recalled.

Shots S5, N6, S10, S12, S14 and N16 are not ranked, either because there is no apparent damage or because the latter does not look like the one of any other shot. It clearly appears that the belonging of a shot to a regime is not directly related to the laser intensity, i.e. to the ablation pressure. For example, in D2 the laser intensities are varying from simple to double; and the unique intensity of D1 (N13 -3.11 TW/cm 2 ) is higher than the lowest one of D3 (S15 -1.89 TW/cm 2 ). Nevertheless, the back face velocities are very close to each other for shots from a same regime. This phenomenon is illustrated by Fig. 12 that gives an overview of the four regimes for each beam. In the case of NB, the ablation pressure is constant and the target thickness is varying whereas it is the opposite for SB. The only common point between the shots of one regime is the free surface velocity, hence the loading level seen by the sample rear face. Note that the existence of different and identical thicknesses in a same regime (cf. regimes D2, D3 and D4 in Table 4) indicates the statistical homogeneity of all the targets in spite of the fact that the thinnest one represents only 15 times the RVE (see Section 2.2).

We thereby obtained thresholds for the four damage regimes according to the stress endured by the target back face (see Table 4). However, they were estimated by means of the acoustic approximation, which cannot be totally trusted in the case of porous materials, and they should be refined thanks to further reliable simulations.

Other shots analysis

Apparently, six shots do not match with the four-damageregime ranking because their fragmentation does not look like any other. However, some of them have free surfaces velocities close to those of ranked shots. Post-mortem tomographies have been performed in order to detect eventual subsurface damage capable to clarify our analysis.

According to U m, S10 and N16 should belong to D2 but imaging given in Fig. 13 does not show any typical double spall corresponding to this regime. Nevertheless, the tomographic slices on the same figure reveals subsurface cracks that have not completely or not at all reached the back face. Their shape suggests that a second spall was appearing but did not detach itself. Therefore, those two shots are at the threshold between D1 and D2, between a single and a double spall.

Given the velocities of shots S5, N6, S12 and S14, they could be logically linked to regime D1 but no damage was visible with the imaging systems. Fig. 14 presents tomographies of these targets.

The laser shock of shot S5 produced an important crater on the target front face but did not generate cracks nor crack initiations in the direction of the back face as shown in Fig. 14(a). S5 does not belong to any damage regime. Moreover, its free surface velocity is sensibly lower than the observed one for D1, i.e. 51 m/s instead of around 100 m/s.

The tomography of shot S14 evidences a conical crack underlined in yellow in Fig. 14(d). If it had propagated up to the rear face, a conical spall would have been formed and ejected. Hence, S14 is probably at the threshold between no damage and regime D1.

It is harder to interpret shots N6 and S12. In both cases, tomographies reveal conical cracks facing the back surface. There are few hypotheses. First, if cracks had reached the back face, double or triple spall would have occurred and these two shots could not be ranked in regime D1. Second, if only the crack that is the closest to the front face had reached the back face, there would be a single spall. This is likely since it would lead to the perforation of both targets which has been noted for N13 (the unique confirmed shot of D1). Moreover, as the spall of this shot has not been recovered, we cannot know if it held in other crack initiations. In that case, N6 and S12 ranked somewhere between no damage and D2. Third and last, the creation of a large crater on the front face of the two shots may have strongly influenced the crack initiation and propagation in the deeper volumes. Damage regimes would thus not only be linked to the rear surface velocity but also to the target thickness, since large craters are formed onto the thickest ones.

Damage characterization 4.3.1. Targets

Tomographies presented in Figs. 13 and14 show that, when it exists, the subsurface damage into the targets mainly takes the form of long conical cracks. It is the case of all shots up to the regime D2 included. Sadly, for shots of regimes D3 and D4, the belated strong flexions caused by the laser loading broke the targets into unrecovered multiple parts.

Shot S12 is of particular interest as it allows to learn how front face craters are formed thanks to Fig. 14(c). A crack propagates from the depth to the surface apparently leading to the ejection of a not or barely fragmented block of matter despite the fact that the front face endured pressures around 40 GPa.

All these post-mortem observations should be very helpful for a precise adjustment of the thresholds of further numerical failure models.

Finally, note that, even though the graphite-diamond phase transition pressure (18-28 GPa according to the SESAME 7832 table) has been widely exceeded for almost all the shots, no diamond phase has been observed on the tomography.

Debris

For shots N26 (D2) and S27 (D3), debris have been recovered thanks to varagel collectors. Tomographies have been performed in order to analyze their population. Fig. 15 plots for both shots the cumulated debris volume according to the particle volume. The two targets have the same thickness, i.e. 1 mm. To allow the comparison, we neglect the potential shape effect of the laser beam on the ejected particles volume. Unlike we could have anticipated, the volume of the ejected matter during the lowest shot (N26) is almost four times greater than for the highest shot (S27). The difference entirely comes from the cymbal-like debris observed in regime D2 since it accounts for three quarters of total volume of the debris. Once excluded, volumes become equivalent.

Differences in terms of debris population have to be noticed. Particles of volume between 0.0001 and 0.001 mm 3 are more numerous for shot S27 (D3) than for shot N26 (D2) since the slope of the first one is steeper. The slopes are then equivalent for particles between 0.001 and 0.1 mm 3 which indicates a similarity between the debris populations. Finally, beyond 0.1 mm 3 , the slope of shot N26 is the steepest which reveals its debris of this size are more numerous than for S27. These measures are consistent with our visual observations that show the size of debris is decreasing when the loading level increases. According to Grady's theory [START_REF] Grady | Local inertial effects in dynamic fragmentation[END_REF], it confirms that the strain rate is higher in D3 than in D2.

Summary and future work

Previous studies showed the shortcomings of classical impact tests (plates and spheres) in helping to understand the twodimensional damage phenomena of a commercial grade of porous graphite. This paper has demonstrated that a better insight can be obtained using well-calibrated and repeatable laser-driven shocks along with various in-situ and post-mortem diagnostics:

-Spall strength has been estimated thanks to PDV data; -Precise VISAR records allowed to value the stress level seen by the rear face of the targets; -High-speed imaging systems provided a dynamic visualization of damage and fragments and helped to understand unfamiliar long-time PDV spectrograms; -Time-and space-resolved shadowgraphy confirmed velocity measurements; -Fragment analysis and subsurface crack localization became available thanks to post-mortem tomography; -Identification and comprehension of four damage regimes were possible because of a large crossed data reduction.

Given all the collected data, associated numerical works are currently being conducted and will be the subject of a further publication. Free-surface and fragment velocity, back-face deformations, crack localizations and fragment sizes, in conjunction with the space and time characterization of the laser pulse, will help to develop and adjust reliable models for shock wave propagation and damage into graphite. Then, the stress thresholds of the four damage regimes could be refined. Finally, similar experimental and numerical approaches could be conducted for other materials.

Fig. 1 .

 1 Fig. 1. Simplified scheme of the experimental set-up. Two different types of diagnostic have been used: laser velocimetry, and time-resolved laser imaging.

Fig. 5

 5 Fig. 5 gathers the VISAR records obtained for the shots onto EDM3. Note that the time uncertainty is of ± 2 ns. The set of shots covered a large field of loading since the free surface velocities range from 50 to 560 m/s. Using the acoustic approximation, one can roughly evaluate the maximum pressure P m of the shock wave breaking out of the target back face by means of the following expression:

Fig. 3 .

 3 Fig. 3. Binarized optical micrography of a healthy sample of EDM3 after cutting and polishing. Material matrix appears in black whereas voids are in white. The Representative Volume Element (RVE) is about 50 × 50 × 50 μm.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Free surface velocities for three couples of similar shots performed with different beams. It clearly points out the difference between NB and SB. For clarity, noise has been reduced.

Fig. 6 .

 6 Fig. 6. Tilted view of the back face of shot S27, 3.4 μs after the laser pulse. The surface is strongly deformed under the effect of the shock. The black area in the right-handside bottom corner is due to the sensor damage. White trails are a residue of the PDV pumping laser.

7 .

 7 Spectrogram S7-PDV1. The second constant velocity signal around 20 m/s after 20 μs is hardly understandable without the help of the imaging systems. Velocities are corrected by the cosine of α1.

  (b), imaging systems evidence the creation and the flight of a single spall at very low velocity in the order of 15 m/s. This fact is confirmed by the sole constant velocity signal appeared on PDV1. Moreover, one notes that the pull-back observed on the spectrogram (ΔU ~70 m/s) corroborates the one recorded for shot S7 (see Section 3.3).

Fig. 8 .

 8 Fig.8. Shot S7 -0.75 mm -0.89 TW/cm 2 . Results of the laser imaging systems at different instants after the high-power laser pulse.

Fig. 9 .Fig. 10 .

 910 Fig. 9. Shot S15 -0.75 mm -1.89 TW/cm 2 . Laser imaging and shadowgraphy at different instants and debris velocity recorded by PDV.

Fig. 11 .

 11 Fig. 11. Shot N13 -2 mm -3.11 TW/cm 2 . Laser imaging and shadowgraphy at different instants and debris velocity recorded by PDV.

Fig. 12 .

 12 Fig. 12. Evidence of the four damage regimes. The reference time is set to be the arrival time of the high-power laser onto the front face of the target.

Fig. 13 .

 13 Fig. 13. Shots S10 and N16 belong to the threshold between regimes D1 and D2. Imaging systems do not show double spall but post-mortem tomographies reveal a second spall almost formed under the back surface. Left-hand side of tomographies: front face. Right-hand side: rear face. The white dots on tomographies are inclusions of vanadium and titanium from the graphite manufacturing process.

Fig. 14 .

 14 Fig. 14. Tomographies of shots S5, N6, S12, and S14. The target fronts are left. The white dots are inclusions of vanadium and titanium from the graphite manufacturing process. For clarity, crack of S14 has been underlined in yellow.

Fig. 15 .

 15 Fig. 15. Cumulated debris volume according to particle volume. The volume of ejected matter is greater for the lowest damage regime (D2). Particles are smaller for the highest regime (D3).

Table 2

 2 Main characteristics of the EDM3 graphite according to references 22 and 38. The Young modulus was exctracted from tensile and compression tests and confirmed by ultrasonic analysis that also gave the sound velocities.

	Density ρ0 (kg/m 3 )	Porous	1754
		Compact	2265
	Failure stress σr (MPa)	Tension	70
		Compression	140
	Failure strain εr (%)	Tension	1
		Compression	8
	Young modulus E (GPa)		11-12
	Bulk sound velocity C0 (m/s)		2212
	Fracture toughness K

Ic ( MPa ⋅ m ) 0.8-1.2 Porosity γ0 (%) 22

Table 3

 3 The maximum pressure seen by the back face Pm is estimated from the maximum free surface velocity Um and from equation 1. For shots without VISAR (starred numbers), Um is exctracted from PDV signals. The ablation pressure P ab is calculated thanks to the maximum calibrated laser intensity Im and to equation 2.

	Shot number	05	06	07	08	09	10	11	12	13	14	15*	16	17	18	26*	27*
	Laser beam	S	N	S	N	N	S	N	S	N	S	S	N	S	N	N	S
	Thickness (mm)	2.5	2.5	0.75	0.75	1	1	1.5	1.5	2	0.75	0.75	0.75	0.75	1	1	1
	U m (m/s)	51	77	169	511	332	201	163	78	99	97	272	162	564	194	190	320
	P m (MPa)	99	149	327	991	644	390	316	151	192	188	528	314	1094	376	369	621
	Im (TW/cm 2 )	1.57	3.94	0.89	3.59	3.50	1.72	3.35	1.38	3.11	0.26	1.89	0.92	4.00	1.88	2.29	3.42
	P ab (GPa)	43.5	90.6	27.4	84.2	82.5	46.7	79.6	39.2	74.9	10.2	50.4	28.3	91.7	50.2	58.6	80.8

Table 4

 4 Ranking of the shots according to the damage regime they belong to, thanks to imaging systems results. Six shots are not classifiable a priori: S5, N6, S10, S12, S14 and N16.

	Regime	D1	D2				D3			D4
	Shot	N13	S7	N11	N18	N26	N9	S15	S27	N8	S17
	Thick. (mm)	2	0.75	1.5	1	1	1	0.75	1	0.75	0.75
	Im (TW/cm 2 )	3.11	0.89	3.35	1.88	2.29	3.50	1.89	3.42	3.59	4.00
	U m (m/s)	99	169	163	194	190	332	272	320	511	564
	P m (MPa)	192	327	316	376	369	644	528	621	991	1094

Acknowledgments

The authors would like to thank Yannick Pannier (Institut P' -UPR3346) for his help conducting the tomographies and all the LULI staff members for their technical and administrative support during the campaign. The access to the Luli2000 facility was granted by the French Lasers and Plasmas Institute (ILP -FR2707).


Sébastien Roland
email: sebastien.roland@ensam.eu

Guillaume Miquelard-Garnier

Matthieu Gervais

Alain Guinault

Cyrille Sollogoub
email: cyrille.sollogoub@cnam.fr

Controlling the order of triblock copolymer via confinement induced by forced self-assembly

Keywords:

Introduction

Block copolymers have received much interest in the past decades due to their ability to self-assemble with well-defined phase separation at the nanometer scale that leads to domains of the size of few tens of nanometers, which make them very attractive for many applications (e.g., in the field of nanoelectronics, nanolithography, biosensors, optoelectronics, membranes, holographic gratings, etc.) [1][2][3]. These engineering applications demand control over the orientation and the position of the nanodomains. However, during the self-assembling process, nanodomains nucleate randomly and grow as a polygrain texture with a periodical order maintained only over few micrometers. To overcome this lack of order at the macroscale and induce nanodomain orientation and ordering, external stimuli have been successfully used. Several methods, such as solvent or temperature annealing sometimes combined with shearing, are commonly employed efficiently to create long-range ordering in thin films or in the bulk [1,4,5].

Multilayer coextrusion is an attractive technique to produce films made of thousands of alternating layers with individual thickness down to ∼10 nm. In pioneering work, Baer and coworkers used what they have termed a "forced assembly" technique to combine immiscible polymer pairs into unique multilayer structures, leading to remarkable properties such as gas barrier, mechanical, and optical properties [6][7][8][9]. Recently, this forced assembly technique has been used by Korley et al. to confine spherical and cylindrical ABA triblock copolymer [10][11][12]. These studies mainly focus on the relationship between the nanostructure and the mechanical properties of the resulting films, while the extrusion was carried out at a temperature below the order-disorder transition temperature (T ODT ). Flow orientation and confinement induced by multilayer coextrusion creates long-range ordering of cylinders in the extrusion direction. The best ordering has been obtained for the thinnest layers after annealing (performed at a temperature above T g of the major block and below T ODT ).

Because of the three chemically different blocks, ABC triblock terpolymers can lead to a larger set of microstructure morphologies and allows the creation of original patterns [13][START_REF] Abetz | Block Copolymers I[END_REF][START_REF] Hadjichristidis | [END_REF]. Theoretically, ABC copolymers can develop tens of morphologies that are usually studied via computer calculations, by taking into account the parameters between the three blocks [16][17][18]. Experimentally, poly(styrene-b-butadiene-b-methyl methacrylate) (SBM) morphologies were thoroughly studied by Stadler et al.: lamellar, knitting, dotted-cylinders, cylinder-within-cylinders, spheres-onspheres morphologies or other morphologies peculiar to ABC copolymers have been successfully observed [19][20][21][22].

In this paper, we describe a direct and scalable method to produce large quantities of a hierarchical material presenting a double organization of the matter at the nano-and the microscale, by using the coextrusion multilayer process, without additional thermal annealing, to confine and self-assemble SBM. We study the influence of the interfaces on the self-assembling process by using a confining polymer having no particular compatibility with the copolymer blocks. In Korley's work, the impact of the draw ratio on the orientation of the morphology has not been clearly addressed. This contribution helps to demonstrate that processing parameters, especially the draw ratio, which has a direct impact on the confining thickness, are important in the improvement of the ordering mechanism of the SBM triblock copolymer morphology.

Materials and methods

Materials

Polycarbonate 121R (PC) was purchased from Sabic and used as received (confining polymer). Its melt flow index is 17.5 g/10 min (300 C/min and at a strain of 0.1%). Poly(styrene-b-butadiene-b-methyl methacrylate) E20 (SBM, PS-PB-PMMA) triblock copolymer was gratefully supplied by Arkema and used as received without further purification.

Gel permeation chromatography

Polymer molecular weights were determined by GPC at 40 • C using THF as eluent on a Waters apparatus equipped with three Styragel columns HR0.5, HR3 and HR4 and with a Waters 2414 refractive index detector at an elution rate of 1 mL/min. Polystyrene were used as standards. GPC curves show that a large fraction of diblock (SB) remains in the triblock copolymer. Deconvolution of the SBM and SB curves using a Gaussian distribution for both polymers (r 2 = 0.99) leads to M n = 100 kg/mol (PDI = 1.1) for the triblock, and M n = 50 kg/mol (PDI = 1.05) for the diblock. The calculation of their area, assuming the two polymers have the same refractive index, leads to 55 mol% of SBM and 45 mol% of SB in the sample as provided by Arkema (see Fig. SI-1). The PC M w was also measured by GPC, and is 40 kg/mol (PDI = 2.2).

1 H NMR

1 H NMR spectra were recorded with 32 scans on a Bruker apparatus at 300 MHz. Fig. SI-2 displays the chemical shift in ppm from tetramethylsilane with the solvent as an internal indicator (CDCl 3 ; 7.26 ppm), and integration of the main peaks. The calculation of the molar ratio of the three components of the triblock is presented in Supporting information. This gives for the whole sample (SB and SBM) a molar composition of 26% for PS, 47% for PB and 27% for PMMA. In wt%, this leads to 34%, 32% and 34% for PS, PB and PMMA respectively, in very good agreement with the supplier information (33-33-33 wt%). Combining NMR and GPC results, one can conclude that the composition of the triblock with M n = 100 kg/mol is close to 25 kg/mol, 25 kg/mol, and 50 kg/mol for the PS, PB and PMMA blocks respectively while the diblock is 25 kg/mol and 25 kg/mol for PS and PB. In consequence, the composition of triblock itself is actually close to 25-25-50 (wt%).

Rheology

To determine the T ODT and the morphology of the triblock copolymer near the processing temperature, melt rheology was performed on an Anton-Paar rheometer using 25 mm coaxial disks, separated by a 1 mm gap. Complex viscosity (see Fig. SI-3), storage modulus G and loss modulus G were recorded in a frequency range from 10 -2 to 10 2 Hz at various temperatures. The sample was tested isothermally in a nitrogen atmosphere. A strain amplitude of 1% was used to keep the response in the linear domain.

Films preparation

Prior to extrusion, SBM and PC pellets were dried in a SOMOS dry air dryer T 20 eco system, respectively at 80 • C for 3 h and 120 • C for 4 h. The PC grade was chosen so that the viscosity of the two polymers matches at the processing temperature (240 • C) and shear rate (5-20 s -1 ). In this range of shear rates, assumed to be those in the multiplying elements, the viscosity ratio lies between 0.5 and 2, as measured by rheology (Fig. SI-3). Films were prepared using multiplying elements at the end of a classical trilayer coextrusion set-up with SBM at the center of the trilayer flow. The processing route consists of two single screw extruders, a 3-layer coextrusion feedblock (ABA), a series of layer-multiplying die elements, an exit film die, and a thermally regulated chill roll. A 30 mm-diameter Mapre extruder and a 20 mm-diameter Scamex extruder were used for the PC and the SBM, respectively. The amount of each polymer in the film was set to 90% PC for 10% SBM (wt%) by adjusting the screw speeds of each extruder to control the throughput. The triblock was extruded at 240 • C and the PC at 300 • C, the multiplying elements block being set at 240 • C. The theoretical number of the alternating layers (N) in the film is directly determined by the number of elements (n) through the equation N = 2 (n+1) + 1. Depending on the targeted thickness of the confined SBM layer, 7 (257 total layers) or 9 (1025 layers) multiplying elements were used. After the flat die, the films were drawn with a chill roll at 120 • C. Draw ratio (Dr) can be defined as the ratio of the extrusion flow rate at the die over the draw rate of the chill roll and is varied from 1 to 11 (draw rate ranging from 90 cm/min to 1000 cm/min).

Transmission electron microscopy

The morphology of the SBM block copolymer within the extruded films was studied by TEM in the out-of-plane and the transverse directions, so that the electron beam is parallel and perpendicular to the extrusion direction, respectively. TEM micrographs were taken on a Zeiss 912 operated at an accelerated voltage of 80 kV and equipped with a Veleta camera (Olympus). In a first step, pre-faced pieces of the extruded films were cut and immersed in a 1% aqueous OsO 4 solution (Electron Microscopy Sciences) for 48 h. Osmium tetroxide stains preferentially unsaturated carboncarbon double bonds and gives to the PB regions the darkest colors in TEM observations. The PS regions are also stained but the C-C bonds contained in the styrene ring being less reactive than the unsaturated rubber, they appears brighter. Finally, PMMA and PC are the least reactive to OsO 4 . In consequence, they appear transparent, thus brighter in the images. The cross-linking of the PB rubbery phase during the staining causes hardening and allows the ultramicrotomy to be performed at room temperature [23]. The stained films were then ultramicrotomed into slices of approximately 70-80 nm thick, using an LKB Ultrotome V 2088 equipped with a Diatome diamond knife.

Small angle X-ray scattering

SAXS measurements were recorded using a Xerocs X-Ray system. CuK␣ lab source with = 1.54 Å was generated by a tungsten filament operated at 50 kV and 1 mA. The beam was collimated by two pairs of tungsten blades mounted at right angles to each other (beam size of 0.8 × 0.8 mm 2 ) and the sample was placed at 1215 mm from the detector. The scattering vector q, defined as q = 4 sin Â/ (where  is half the scattering angle), ranged from 10 -2 to 0.7 Å -1 and was calibrated using a silver behenate standard sample. Fit-2D analysis software was used to integrate the scattering patterns.

Results and discussion

Fig. 1 presents the dynamic storage G and loss moduli G of the triblock copolymer SBM E20 pellets at different temperatures. Looking at the storage modulus, the relaxation spectrum shows a time-dependent component at low frequency indicating a selfassembling morphology [24][25][26]. Normally, for a disordered state, the slope of the storage modulus should be the same as that of a homopolymer melt in the terminal region (G ∝ ω 2 ) [27,28]. In contrast, the slope for both G and G is close to 0.5 for temperatures between 180 and 240 • C. These slopes were attributed to a lamellar morphology for diblock copolymers [29] as well as for SBM triblock, according to Di Cola et al. [30] It should be noted that G at 260 • C shows an increase compared to the other curves which can be attributed to the degradation of the SBM due to a cross-linking of the PB phase during the analysis, which is not observed at the processing temperature (240 • C). These experiments reveal that, during extrusion, the block copolymer is still self-assembled and does not flow as a homopolymer since the elastic contribution (G ) of the dynamic modulus is higher than the viscous one (G ).

Fig. 2 presents the scheme of the coextrusion process and a typical TEM image cross-section of the multilayered PC/SBM films obtained in this study. Knowing the difficulty to coextrude polymers with mismatched rheological behavior, we may expect interfacial distortion and/or layer breakups when coextruding self-assembled block copolymer below its T ODT (G > G ) with a thermoplastic (G > G ) [31]. However, as can be seen in Fig. 2, the obtained multilayered films of PC and SBM are stable and present continuous layers with slight variations in SBM thicknesses. This stability could be explained by the fact that both storage moduli and viscosities of PC and SBM are actually in the same range at the extrusion shear rate (5-20 s -1 ) (see Fig. SI-3). Thanks to the distribution of the SBM layers thicknesses at a given experimental condition, it is possible to study the effect of the draw ratio on the morphology at a given thickness.

Fig. 3 shows TEM micrographs of the confined SBM layers crosssections as a function of thickness at Dr = 2, Dr = 8, and Dr = 11. It also shows the transverse direction of films made at Dr = 11. The periodical thickness of the block copolymer morphology appears to be around 50 nm, which is quite similar to what has been previously reported in the literature for such material [19,20]. As the confined layer thickness decreases from 200 to 100 nm, the number of block copolymer periods in the confined layer decreases from 4 to 2. At low Dr, the morphology seems to be locally disordered, even though one can guess a global orientation of the morphology along the interfaces. Qualitatively, a better organization of the nanodomains is seen at high Dr, but also for decreasing layer thicknesses.

The morphology of the triblock copolymer is hard to determine with the TEM micrographs. It seems that both lamellae (PS and PB) and cylinders (or nodules, PMMA) are observed in Fig. 3. The presence of SB diblock copolymer in the melt could lead to a mixed and therefore complex morphology. At these compositions, both copolymers (SB and SBM) should have a lamellar morphology [32,33]. However, in a blend, the SB diblock copolymer will be located at the S-B interface, increasing the number of junction points to this interface. To avoid the entropy loss due to the chain stretching, the interfacial area increases compared to the B-M interface. The consequence is the curvature of the S-B interface, which is inexistent for pure lamellar SBM triblock copolymer. Cylinders-in-lamellae, lamellae with fluctuations or double gyroid can then be observed with slight blend composition variations [32,33]. It is noteworthy that the core-shell cylinders and doublegyroid morphologies identified in Ref. [33] by TEM for a 48/52 blend composition of SBM/SB resemble to our TEM observations. The PC-SBM interfaces influence the alignment of the morphology: parallel lamellae clearly appear at the interface due to a preferential wetting towards the polycarbonate layers (see Fig. 3).

Besides, at high draw ratio, the lamellar structure at the interface is more pronounced and within the layer, the arrangement of the morphology appears also more regular even for thicker layers.

When probing the transverse direction, it appears that fewer nodules are observed in this direction and that the morphology is less ordered. It can also be noticed that the interface is less stable, showing some fluctuations that are not seen in the cross-section image, which can be attributed to flow fluctuations during extrusion.

At the interface between the PC layer and the SBM, a black region can be observed and attributed to the PB phase. This black region takes the shape of a well-defined line at high draw ratios, perfectly parallel to the interface. To explain the interface in the case of PC/SBM multilayered films, the solubility parameters were used to calculate the Flory-Huggins parameters (Table 1) of each polymer pairs by using the approach based on Hildebrand solubility parameters:

= V AB RT ı A -ı B 2 (1)
Where V AB is the geometric mean of molar volumes of polymer A and polymer B, R is the universal gas constant (8.314 J/K/mol), T is the processing temperature, ı A and ı B are the solubility parameters of polymer A and polymer B, respectively. a Values of the molar volumes were taken from van Krevelen, the value for PC was calculated using the group contribution according to Fedors tables [START_REF] Van Krevelen | Properties of Polymers Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from Additive Group Contributions[END_REF]. The following values were used: VPC = 174.6 cm 3 /mol; V PMMA = 86.5 cm 3 /mol; VPS = 98 cm 3 /mol ; VPB = 60.7 cm 3 /mol.

b Solubility parameters were taken from the Polymer Handbook [START_REF] Brandrup | Polymer Handbook[END_REF]. The following values were used: ıPC = 19.7 (J/cm 3 ) 1/2 ; ı PMMA = 19.98 (J/cm 3 ) 1/2 ; ıPS = 18.6 (J/cm 3 ) 1/2 ; ıPB = 16.98 (J/cm 3 ) 1/2 .

c Calculated using Eq. ( 1). d Calculated from the interpolation of computed values of at 25 • C and 300 • C [34]. To compare the affinity of the different polymer pairs, we used experimental and calculated values for Flory Huggins and solubility parameters.

From this approach, it appears the PB phase has the smallest affinity with PC (see Table 1). In contrast, PMMA is most likely the block in contact with the PC layer. Even though OsO 4 staining does not allow the contrast between PC and PMMA to be seen, it is then reasonable to assume a PC-PMMA interface. The well-aligned PB layer can then be the consequence of the PMMA "adaptive layer", which accommodate the interface, as observed for block copolymer thin films [START_REF] Tokarev | [END_REF]38].

SAXS experiments were performed on both the normal and the extrusion directions of the films to evaluate more quantitatively the degree of organization of the triblock copolymer morphology under confinement (Fig. 4) and, especially, the effect of the draw ratio (Fig. 5). In Fig. 4, the SAXS patterns of the pure SBM film (unconfined) extruded at Dr = 1 (unstretched) shows three rings in both normal and extrusion directions due to random orientation of the morphology, one of them being slightly transformed into an ellipse (Fig. 4a 1 and 4a 2 ). This is indicative of a slight orientation of the nanodomains in the extrusion direction due to the flow. As for the morphology interpretation with the SAXS patterns, if we make the assumption that the diblock copolymer is fully blended to the triblock copolymer, the blend could give rise to a double gyroid morphology [33]. This kind of morphology can be very difficult to interpret by SAXS, as reported by Hückstadt and coworkers. It is noteworthy that their results observed for a poly(styrene-b-1,2 butadiene-b-vinylpyridine) resemble to what we observe in our case (large peaks with no particular periodicity in the peak position) [39].

For the multilayered films, the extrusion and the normal directions were also studied and SAXS patterns along with azimuthal integrations are shown in Fig. 4. Concerning the confined but unstretched samples (Fig. 4b 1 -b 2 ), a more pronounced ellipsoidal shape is observed in every direction, revealing a more oriented morphology probably due to the confinement induced by the multiple interfaces. The slight shift of the peaks towards higher q values (0.11-0.12 nm -1 , corresponding to scattering domain sizes of 57 nm and 52 nm, respectively, using q* = 2 /d 0 ) indicates a smaller scattering dimension, probably caused by a morphology change at the interface between the PC and SBM layers.

Fig. 5 compares scattering patterns of films drawn at Dr = 1 and Dr = 8 to show the influence of the draw ratio on the organization of the morphology. As the draw ratio is increased, in the normal orientation, the ellipsoidal shape becomes even clearer with its longer axis being more intense along the equator. This can be attributed to the orientation of the morphology induced by stretching during drawing. This behavior resembles to what was observed for cylindrical block copolymer being unidirectionally stretched [40,41]. For curve b 1 , the first peak is also at 0.12 nm -1 , corresponding to a scattering domain size of 52 nm. This value is very close to the block copolymer period observed by TEM. A slight shift is also observed for the extrusion direction (curves b 2 and b 3 ) and can be attributed to a squeeze or a stretching of the morphology (q* = 0.14 nm -1 , d 0 = 44 nm). A scattering pattern along the meridional axis is observed for both the extrusion and the transverse directions and the integration shows q*, 2q*, and 3q* peaks, which is characteristic of a lamellar morphology. At low Dr, the 2nd and 3rd order are not very intense but becomes more intense at higher Dr, which indicates a better alignment of the lamellae in the stretched film and confirms the observations made by TEM. This ordering is then due to a combination of the stretching and the greater influence of the interfaces of the confining layers. For the layered films oriented in the transverse and the extrusion directions, a strong meridional streak can be observed in the scattering patterns. This could arise from the interfaces between the PC and the SBM layers, as it was observed for PP/PS multilayered films [42] Additional annealing experiments were also performed at 145 • C for 5 days (below the T g of PC) to see if the ordering could be improved over time (Fig. SI-4). Contrary to what was observed by Burt et al. [10,12,43], SAXS patterns do not show any significant change, probably due to the lack of mobility of the copolymer at this temperature (T g,PMMA + 15 • C).

Conclusions

Poly(styrene-b-butadiene-b-methyl methacrylate) triblock copolymer has been successfully confined with polycarbonate through multilayer coextrusion. The resulting films have a total thickness between 100 m and 1 mm and are made of hundreds to thousands of alternating layers with the SBM layer thicknesses ranging from a few hundreds to a few tens of nanometers. We showed that despite performing extrusion below T ODT of the SBM, continuous self-assembled structures can be achieved without any further post-treatment such as annealing. We also evidenced, for the first time, long-range ordering for these "as extruded" materials, which, though imperfect, can be improved by increasing the draw ratio after extrusion and decreasing the SBM layer thickness. This industrially scalable and simple technique allows the continuous fabrication of hierarchically organized films that can be of interest for innovative mechanically-reinforced materials or other engineering applications where long-range ordering of the nanodomains is necessary for large quantities of material.

Fig. 1 .

 1 Fig. 1. Dynamic storage G and loss G moduli of SBM E20 pellets as a function of pulsation at different temperatures indicated on the figure.

Fig. 2 .

 2 Fig. 2. Scheme of the multilayer coextrusion process (left). Typical TEM image of the multilayered PC/SBM films obtained (right; 7 elements, Dr = 11; inset: zoom in a SBM layer).

Fig. 3 .

 3 Fig. 3. Bright field transmission electron micrographs of SBM confined layers of different thicknesses at a draw ratio (Dr) of 2, 8 (cross-section) and 11 (cross-section and transverse). Scale bars = 100 nm. The schemes illustrate the film section observation: cross-section (a) and transverse (b).

Fig. 4 .

 4 Fig. 4. Scattering patterns of pure SBM (a) and PC/SBM multilayered (b) films extruded at Dr = 1 in the normal (1) and extrusion directions (2). The schemes show the orientation of the multilayered films relative to the X-Ray beam. The curves are azimuthal integrations of each pattern near the equatorial region (a1, b1) and near the meridional region (a2, b2). Arrows indicate the position of the peaks. Downward and upward arrows indicate the same position.

Fig. 5 .

 5 Fig. 5. SAXS patterns of PC/SBM films drawn at Dr = 1 (a), and Dr = 8 (b) performed in the normal (1), extrusion (2), and transverse directions (3). The schemes show the orientation of the multilayered films relative to the X-Ray beam. Integrations of the SAXS patterns along Phi of PC/SBM films with Dr = 1 (a) and Dr = 8 (b) near the equatorial region (a1, b1) and near the meridian region (a2-3, b2-3) are shown on the graph. Arrows indicate relative position of the peaks. Downward and upward arrows indicate the same position.

  • C/1.2 kg), as provided by Sabic. Its glass transition temperature is 153 • C (measured by Differential Mechanical Thermo-Analysis [Q800, TA Instruments], at a rate of 1

Table 1

 1 Molar volumes, solubility parameters, and parameters of the PC/SBM system.

	Polymer pair	Geometric mean of molar volumes,	V A VB,	Cohesive energy density ı A -ıB	2	, J/cm 3 b	AB using Eq. (1) (240 • C) c	AB using Ref. [34] (240 • C) d
		cm 3 /mol a
	PC/PMMA	122.9		0.08			0.0023	0.016
	PC/PS	130.8		1.00			0.029	0.294
	PC/PB	102.9		7.40			0.213	0.856
	PS/PMMA	92.1		1.64			0.047	0.119
	PS/PB	77.1		2.96			0.085	0.149
	PMMA/PB	72.5		9.00			0.259	0.460

Acknowledgments

This work was funded by the CNAM through the project MAT-ERAM. We would like to acknowledge Arkema for supplying the SBM; Dr M. Barbazanges and the Institut Parisien de Chimie Moléculaire, UMR CNRS 8232 for their help with the NMR characterizations; F. Portail, from Arkema GRL Lacq for her help with the sample preparation for TEM experiments; The Institut de Biologie Paris Seine IBPS/FR 3631 for providing access to its TEM, and G. Toutirais for her guidance with the apparatus; V. Michel for his help with the SAXS experiments; J-S. Montana for the analysis of the GPC curves, and A. Grandmontagne for the coextrusion of the samples. G. Miquelard-Garnier was appointed Editor for Materials Today Communications over the course of the paper submission process but he neither handled the manuscript nor was involved in the final decision.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.mtcomm.2015. 11.003.


Stanislav Miroshnichenko

Dariia Ternova

Isabelle Billard
email: lsabelle.billard@ires.in2p3.fr

Ali Ouadi

Olga Klimchuk

Vitaly Kalchenko

Sabelle Billard

SVNTHESIS OF NEW CALIXARENE-PHOSPHINE OX IDES 2 AND THEIR EXTRACTION PROPERTIES IN IONIC LIQUIDS 3

Keywords: Calixarenes, ionic liquids, phosphine oxides

New calix/4Jare11es flmctio11alized by Alk2P(OJCH2 bi11ding gmups a11d N-8 111e1hyli111idazoli11111 g1v11ps 01 the opposite rims of the macmcyc/ic ske/e1011 have bee11 9 synthesized and characterized. 11,eir extrac1io11 properties 10111011/s of E,, 3+ and Ant 3+ in ionic 10 liquid were i11vestigated.

Synthesis of new calixarene phosphine oxides and their extraction properties in ionic liquids

Isabelle Billard

To cite this version:

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22 RESULTS AND DISCUSSION 23

  We present in this article the synthesis of a series of new cone-shaped calix[4]arenes 24 possessing CH 2 P(O)Alk. 2 metallocomplexing groups at the rnacrocyclic wide and narrow 25 rim and N-methylimidazolium groups at the narrow rim. Extraction properties of the 26 calixarene synthesized and dissolved in ionic liquid were investigated. 27Calix[4]arenes 3-10 functionalized by four or eight Alk 2 P(O)CH 2 binding groups 28 have been synthesized by the Arbuzov reaction of tetrachloromethylcalix[4]arenes 1, 2 with 29 dialkylphosphinites.

Isabelle Billard. Synthesis of new calixarene phosphine oxides and their extraction properties in ionic liquids. Phosphorus, Sulfur, and Silicon and the Related Elements, Taylor Francis, 2011. hal-02271897 12 INTRODUCTION 13

The use of nuclear power has led to the accumulation of great amounts of both high-14 and medium-level activity radioactive wastes, which require efficient methods of separation 15 and safe disposai. The main method for the decontamination of radioactive wastes is 16 liquid-liquid extraction of hazardous radionuclides followed by burial or transmutation. A 17 modern approach in the design of efficient and selective extractants of radioanuclides is 18 based on the functionalization of calixarene platform by several P=O containing fragments, 19 capable of cooperatively binding metal cations. 1 Room temperature ionic liquids (RTIL) 20 are promising solutions for the extraction of the radionuclides from spent nuclear fuel. 2


I Billard

G Marcou

A Ouadi

A Varnek

In silico design of new ionic liquids (ILs) based on QSPR models of ILs viscosity

Keywords: ionic liquids, viscosity, molecular descriptors, QSAR/QSPR

This works is devoted to establishing Quantitative Structure-Property Relationship (QSPR) between chemical structure of Ionic Liquids (ILs) and their viscosity followed by computer-aided design of new IL possessing desirable viscosity. The modeling was performed using back propagation artificial neural networks on a set of 99 ionic liquids at 25°C, covering a large viscosity range from 3 to 800 cP.

The ISIDA fragment descriptors were used to encode molecular structures of ionic liquids. These models were first validated on 23 new ILs from Solvionic company, and then used to predict the viscosity of three new ILs which then have been synthesized and tested. The models display high predictive performance in external 5fold cross validation: determination coefficients R 2 >0.73 and absolute mean absolute errors RMSE<70 cP. For three ILs synthesized and tested in this work, predicted viscosities are in good qualitative agreement with the experimentally measured ones.

Introduction

Owing to their "green properties", Ionic Liquids (ILs) are gaining interest as potential media in replacement of the traditional (volatile) organic solvents currently in use in many fields of industry and research [START_REF] Kirchner | Ionic Liquids[END_REF][START_REF] Wasserscheid | Ionic liquids in synthesis[END_REF] . However, ILs present some drawbacks for industrial applications. Thus, practically all known ILs are relatively viscous, only few of them displaying a viscosity ()

below 20 cP at T = 25 °C, while the most popular ILs (imidazolium and tetraalkylammonium families) have viscosities in the range of 40 -80 cP, which is pretty high compared to  = 0.40 cP for CH 2 Cl 2 or 0.29 cP for hexane [START_REF] Riddick | Organic solvents : physical properties and methods of purification[END_REF] . Nonetheless, it has been emphasized 1,2 that all ILs' physicochemical properties, such as viscosity, density, conductivity or melting point, are tunable, therefore adjustable, through a judicious choice of their cationic and anionic components. As a matter of fact, a subtle variation of ILs' chemical structure, e.g., lengthening of an alkyl chain onto the imidazolium cationic skeleton, may lead to dramatic changes of various ILs' properties [START_REF] Zhou | [END_REF][5][6][7] . In this respect, ILs could formally be considered as "design solvents". However, this tunability is hardly applicable in practice. Indeed, since we do not master the relation between structure and properties of ILs yet, tuning of ILs' properties is merely achieved through a trial/error procedure. Considering the almost infinite number of potential ILs to be tested, the task of conceiving the "best" IL for a given application is more a desirable dream than a user-friendly reality.

The goal of this work is to build predictive QSPR models linking structure and viscosity of ionic liquids. Most of early QSPR studies [8][9][10][11][12][13][14][15][16][17][18] have been performed for ILs melting points for datasets in which the anion was always taken the same . This allowed one to vary the structure of only cationic part of ILs. Carrera et al. 19 performed modeling of melting points on the dataset of guanidinium ILs containing 4 different anions. Descriptors were generated only for the cationic part and for each anion an individual model has been prepared using counter-propagation neural networks.

In this work, we describe an original procedure to generate descriptors vector for the species containing different cation and anion. This approach has been used to build and validate the models for viscosity on the initial set of 99

ILs. The external validation has been performed on 23 new ILs recently produced by Solvonic company. Finally, the developed models have been used

for in silico design of new three ILs, which viscosities have been predicted

before their synthesis and experimental tests. To our knowledge, no QSPR models for ILs viscosity, the property of dramatic importance to industrial applications, have been published so far.

Materials and Methods

Experimental procedure.

Synthesis. All reagents used were analytical grade. Starting materials were purchased from commercial sources and used as received. 1H, and 13C NMR spectra were recorded in CDCl3 unless otherwise specified on a spectrometer operating at 300, and 282 MHz, respectively. Mass spectra were measured on a JEOL MS-DX 300 mass spectrometer.

Tetraheptylammonium bis-trifluoromethylsulfonylamide

N(CF 3 SO 2 ) 2 - N(C 7 H 15 ) 4
To a solution of 5.9 mmol (2.9 g) of tetraheptylamine bromide in 10 mL of deionized water and 5 ml acetone, 6.5 mmol (1.86 g) of bis(trifluoromethane)sulfonimide lithium(1.85 g) in 5.0 mL of acetone was added at 25 ºC. The reaction mixture was stirred for 12h. Evaporation of the solvent under vacuum gave the crude compound. The product was extracted with dichloromethane (30 mL) and washed several times with aliquots of water (20 mL) until no longer bromide residues were detected by the AgNO 3 test.

Evaporation of the solvent yielded the compound as a transparent and slightly viscous liquid. Liquid Yield: 95%.

Active charcoal (10 wt%) was added to the ionic liquid and the liquid was stirred for 24 h. After adding 20 mL of dichloromethane to reduce the viscosity of the ionic liquid, the mixture was filtrated over a filter paper. The solvent was removed under reduced pressure. The ionic liquid was thereafter pumped at room temperature for 18 h and, additionally, at 50 °C for 10 h at 50°C. ).

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Triethylammonium 2,2-dimethyl-6,6,7,7,8,8,8-heptafluoro-3,5octanedionate

F F F F F F F O O H 3 C CH 3 CH 3 HN(C 2 H 5 ) 3
To a solution of 20 mmol (2.05g) of triethylamine in 10mL of anhydrous acetonitrile, 20 mmol (5.95 g) of 6,6,7,7,8,8,8-Heptafluoro-2,2-dimethyl-3,5octanedione in 5.0 mL of acetonitrile was added at 25 ºC .The reaction mixture was stirred for 24h. Evaporation of the solvent under vacuum gave the crude compound (yield 95%). The ionic liquid was thereafter pumped at room temperature for 18 h and, additionally, at 50 °C for 10 h at 50°C. ).

1-methylimidazolium 2,2-dimethyl-6,6,7,7,8,8,8-heptafluoro-3,5octanedionate

F F F F F F F O O H 3 C CH 3 CH 3 NH N
To a solution of 20 mmol (1.72 g) of 1-methylimidazole in 10mL of anhydrous acetonitrile, 20 mmol (5.95 g) of 6,6,7,7,8,8,8-Heptafluoro-2,2-dimethyl-3,5octanedione in 5.0 mL of acetonitrile was added at 25 ºC .The reaction mixture was stirred for 24h. Evaporation of the solvent under vacuum gave the crude compound (yield 95%). The ionic liquid was thereafter pumped at room temperature for 18 h and, additionally, at 50 °C for 10 h at 50 °C. It should be noted that ILs' viscosities are very sensitive to temperature 21 and there exists no well-established relation  = f(T).

Therefore, only viscosity data measured at T=25°C were retained for the modeling. The selected dataset contains four families of cations and 9 different anions (Table 1). The ILs involving the Tf 2 N -anion and fluorinated anions, empirically known to lower viscosity, represent about 80% of the data.

The data distribution on Figure 1 shows that only 20% of studied ILs are very viscous (> 200 cP).

Unlike UNIFAC-VISCO 22 and some other methods, we report here the models for the IL's viscosity itself rather than for its logarithm. In fact, the models for the logarithm of the viscosity were also obtained but they don't display any improvement of the predictive performance.

Descriptors.

The ISIDA descriptors were used to build the QSPR models. They represent the counts (occurrences) of some fragments in a molecular graph

23

. Three types of fragments are considered: sequences (type 1) and extended augmented atoms (type 2). A sequence is the shortest path connected two given atoms. For each type of sequence, the lower (l) and upper (u) limits for the number of constituent atoms must be defined. The program generates all ''intermediate'' sequences involving n atoms (l<=n<=u) recording both atoms and bonds. Extended augmented atom is a combination of types 1 and 2: an atom representing an origin of several sequences containing from l to u atoms. Three sub-types, AB, A and B are defined for each class. They represent sequences of atoms and bonds (AB), of atoms only (A), or of bonds only (B) 24 .

Since studied ILs represent the1:1 mixture of cation and anion, the descriptor vector of an IL has been generated by concatenation of the descriptor vectors of the constituted species, as it is shown on Figure 2.

Totally, 24 initial pools of descriptors corresponding to different fragmentation types have been generated for the training set.

Machine Learning Methods. The back propagating artificial neural networks (NN) implemented in the Weka 5.8 program 25 have been used. This is well reputed machine-learning method able to produce predictive models even on noisy and insufficiently prepared data. The network was trained using the early stopping procedure [START_REF] Sarle | Stopped training and other remedies for overfitting[END_REF] in which the model built on the training set was systematically applied to the tuning set containing 20% of the training data.

The training procedure was stopped as soon as the predictive performance deterioration was observed. For each initial pool of descriptors, the number of neurons in the hidden layer was systematically varied from 2 to the half of the number of descriptors. The optimal size of the hidden layer corresponds to models displaying the highest predictive performance in cross-validation calculations. Typically, this number ranges from 2 to 11.

The partial least square regression (PLS) implemented in the Weka5.8 Therefore, here we report only results obtained with the NN method.

Validation of individual models. In order to assess predictive performance of QSPR models, they must be validated on unknown data. Here, 5-fold crossvalidation (5-CV) procedure has been used. The initial dataset was split into 5 non-overlapping subsets; each subset was used as a test set, whereas an ensemble of other four subsets was used to train a model. Thus, each compound of the dataset was predicted using 80% of the data. This procedure has been repeated 3 times in order to estimate the fluctuations of statistical parameters of the models.

Two statistical parameters are used to evaluate the performance of the predictions: the determination coefficient [START_REF] Tan | Introduction to Data Mining[END_REF] should not be involve in property assessments. Here, as AD, we used the Fragment Control approach [START_REF] Horvath | [END_REF] discarding the model if a test compound possess the fragments absent in the initial pool of descriptor generated for the training set. The number of discarded models (and, hence, the number of models used for the consensus predictions) varies from one compound to another.

Results and Discussion.

Predictive performance of the consensus NN models assessed in 5-fold external cross validation is reasonably high: determination coefficient R 2 = 0.73 and RMSE = 67.5 cP. Prediction error represents about 10% of the viscosity range of the dataset. Despite of this rather big RMSE value, the models are able to distinguish several viscosity ranges -of weakly, medium and highly viscous ILs.

At the next step, the viscosity of 23 new ILs from Solvionic (Figure 3)

was measured and compared with the theoretically predicted values.

Prediction error is 73 cP, which is consistent with that observed during crossvalidation. A major underestimated outlier is tributyl(methyl)azaniumTf 2 N (structure 9 in Figure 3) for which calculated values are about 200 cP lower than the experimentally measured one (Figure 4). This could be explained by low population of viscous ILs in the initial dataset used for model building (Figure 1).

Finally, all cations and anions from the bibliographic dataset were combined to generate over 1000 new ILs. The models were used to predict the viscosity of each of them and a pool of either low viscous or high viscous ones was selected. Then, starting from these structures, and considering synthetic feasibility and availability of starting compounds, three completely new ILs have been suggested for the synthesis and experimental tests.

Conclusion

In this paper we report predictive models for viscosity of ionic liquids used to in silico design of new ILs with desirable properties. For the first time, QSAR modeling has been performed on the dataset of ionic liquids where both cation and anion varied. Relatively modest predictive performance of the models (about 70 cP) is attributed to inaccuracies in experimental data used for the model building.

To sum up, the models developed on the initial data set of 99 ionic liquids were able to predict with the reasonable accuracy the viscosity for new ILs recently synthesized by Solvionic. Moreover, three new ILs, whose viscosities were assessed theoretically before the synthesis, have been designed and tested experimentally.

The key point of our modeling is the technique of descriptors generation suggested in this work. This approach can be used to model properties of 1:1 two-component mixtures. New method of descriptors generation for any mixtures is in progress in our group. In particularly, this approach could be applied to ionic liquids containing mono-charged cations and doubly (as SO 4 2-)

or triply-charged (PO 4 3-) anions.

40 program

 40 has been used for the purpose of comparison. No significant changes of the predictive performance of the PLS vs NN models have been observed.

(R 2 ), the root mean square error 27 (

 227 RMSE) for the linear correlation Predicted vs Experimental viscosity values. Consensus predictions. The 5-CV calculations were performed on the training set systematically varying fragmentation type and the number of neurons in the hidden layer (N HN ). This resulted in 360 models. Then, 12 models with R 2  0.5 have been selected and the corresponding parameters (fragmentation type and N HN ) were further used to generate an ensemble of the final models on the entire initial dataset. All these models were then systematically applied to the compounds from the Solvionic catalogue 28 as well as to three new compounds synthesized in this work. For each test compound, the predictions were calculated as an arithmetic mean of the values calculated with the selected individual NN models. Applicability Domain. The Applicability Domain (AD) is a meta-model which decides if a QSAR model could be applied to a given test object. Indirectly, AD measures a similarity between the test object and the training set. If they are considered dissimilar, the QSPR model may lead to wrong value and, therefore,

40 TABLE 2 :Figure 1 .

 4021 Figure 1. Viscosity data distribution for the initial set of 99 ionic liquids.

Figure 2 .

 2 Figure 2. Generation of the ISIDA fragment descriptors for an ionic liquid by concatenation of those separately generated for the cation and anion. .

Figure 3 .

 3 Figure 3. Structure of 23 new ionic liquids from the Solvionic dataset.

Figure 4 .

 4 Figure 4. Prediction performance of the predictive neural networks models on the Solvionic dataset.

Table 2

 2

	shows

TABLE 1 .

 1 Cations and anions constituting 99 ionic liquids from the initial dataset.

	Cations	Number of ILs	Ref.		Anions		Number of ILs	Ref.
	imidazolium	47	0 4,5,39,4	Tf 2 N	-(CF 3 SO 2 ) 2 N	-	28	5,41-45
	tetraalkylammo nium	46	41-47	PF 6 -			5	5
	pyridinium	2	41,48	BF 4 -			5	4,39,41,44 ,48
	pyrolidinium	4	46,47	Fluorinated boron-containing alkyl	39	4,39,44
				chains

Acknowledgements.

The authors gratefully acknowledge the help of Dr. Christophe Melart and Dr.

Hervé Muller for their help in viscosity measurements. The authors are indebted to the company Solvionic (Dr. François Malbosc) for providing the ILs samples. The financial support of the Groupement National de Recherches (GNR) PARIS is highly appreciated.

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28 56


Sabine Bonnet

Abdelkarim Rjiba

Nizar Bchellaoui

Rachida Dorbez-Sridi

El-Eulmi Bendeif

Axel Gansmüller

Carole Gardiennet

Sabine Bouguet-Bonnet

Water dynamics in a mesoporous bioactive glass studied by NMR relaxometry

two-phase fast exchange model : exchange between bulk-like water et water adsorbed at the pore surface is fast compared to the longitudinal relaxation → measurement of an averaged relaxation rate Bioglass powders were dried during one day at 150°C before hydration with the wanted volume of distilled water : filling degrees of 33%, 66% and 99% were used (corresponding to the percentage of the mesoporous volume).

Samples were then kept at 25°C during 1 night for complete equilibrium before 1 H relaxometry measurement by Fast Field Cycling technique at 298K (Stelar SMARtracer relaxometer, 1 H 5kHz-10MHz).

1 H longitudinal relaxation rates as a function of the magnetic field (dispersion) as a tool to evaluate the dynamical behavior of the fluid embedded in bioglass

results and discussion

The microfluidic bioglass was filled at 99% with protonated or heavy water, and 1 H longitudinal relaxation rates were When the filling factor increases, p a decreases and R 1 tends toward R 1b .

The population in the adsorbed phase can be assumed to vary with the filling factor f as:

R 1 ( H )= p a R 1a ( H )+ (1-p a ) R 1b p a = R 1 ( H )-R 1b = (R 1a ( H ) -R 1b ) R 1a ( H )

  relaxometry allowed us to analyze water slow dynamics in confinement in both bio-glasses: adsorbed water has the same behavior in the mesoporous channels of both systems (made with microfluidic or sol-gel methods), but the microcapsule organization enhances slightly the rate of escaping of water molecules towards the bulk. conclusion Mesoporous bioactive glasses (MBG) are nanostructured materials possessing a high bioactive response. Many applications in tissue engineering and bone-tissue regeneration: formation of apatite-like layers (hydroxyapatite Ca 5 (PO 4 ) 3 OH ) at the surface of the bioglass when in contact with body fluids. Body fluids are mainly composed of water → it is crucial to study and understand the dynamics of confined water in these MBG. 2 , 6% CaO, 2% P 2 O 5 mol%) comparison of the dynamics when water is confined in two bioglasses having the same chemical composition but made with different methods Samples were prepared in 8 mm o.d. hermetically sealed capsules.

  measured for H 2 O protons ( ) or residual protons (HOD ) in 99.9% D 2 O. → HOD relaxation being purely intermolecular, the comparison of H 2 O and HOD dispersion curves shows that the 1 H lowfrequency relaxation of H 2 O is mainly due to intramolecular dipolar interactions modulated by molecular reorientations. measurements with deuterated water → two-phase fast exchange model dispersion as a function of the filling factor for comparing slow dynamical processes in confinement p a : population in the adsorbed phase longitudinal relaxation rate in the adsorbed phase longitudinal relaxation rate in the bulk phase (extreme narrowing, independent of the magnetic field)

.

  can thus be retrieved with the linear evolution of R 1 as a function of 1/f (with R 1b =0.41s -1 from an independent measurement) with  adsorbed water layer width, S porous surface area and V the porous volume S/V values are obtained from nitrogen adsorption/desorption isotherms, The apparent shift of experimental dispersion curves is mainly due to different S/V ratio for the two samples. * P.E. Levitz, J.-P. Korb, D.Petit, Euro Phys J. E (2003), 12, 29 and dispersion curves are analyzed according to Levitz's model * intermittent Brownian dynamics near a flat surface same dynamical behavior for the adsorbed molecule faster escaping to the bulk for water confined in the microfluidic bioglass