domain: spi sde

text:
Adriane Clerc

Antoine Wautier

Stéphane Bonelli

François Nicot

Mesoscale inertial transition in granular materials

Granular assemblies can experience complex failure patterns along a given loading path, with a distribution of ephemeral inertial events marked by local outbursts in kinetic energy. However, investigating such mechanisms appears to be necessary to understand how a certain failure mode develops in a granular material. Using a discrete element method, this study highlights several microstructure reorganizations before the specimen reaches a proper failure state. Meso structures have proven to be efficient to understand the elementary mechanisms responsible for these outbursts in kinetic energy. Strain-like and stress-like quantities are thus defined at a mesoscale and they are used to characterize the nucleation and propagation of these local microstructural events.

Introduction

Granular materials are still fascinating by their complex behaviour. One of the difficulties lies in the description of a media that behave either like a solid or a fluid. The transition between quasi static to inertial regime is still an active research topic [START_REF]Micromechanics of granular materials[END_REF][START_REF] Vescovi | [END_REF]. Bursts of kinetic energy are seen as early evidence of mechanical instabilities [3,4], and their analysis is consistent with the search for precursors of regime changes [5,6]. Another main challenge when dealing with granular materials is that they can be considered as a continuous media macroscopically but their fundamental components are discrete. As a consequence, inertial transitions and mechanical instabilities are visible at the macro scale, but their nucleation results from micro scale mechanisms. Thus, multi-scale approaches have been developed in order to bridge the gap between the two scales. In this study, grain-loops [7,8] are used as an efficient way of tesselate a 2D sample domain and give relevant information on forces, strains and geometrical reorganizations.

This work is based on discrete element method simulations from YADE [9] in which grains are idealized by spheres interacting through linear elastofrictional laws [10]. Numerical experiments consist in the creation of an idealized quasi-2D a dense sample of 25,000 grains subjected to a biaxial test. The biaxial test is composed of two phases. First, an isotropic compression of intensity σ0 is applied. Secondly, a strain-controlled phase where the confining pressure 𝜎 0 is kept constant on lateral boundaries while horizontal walls are moved with a strain rate 𝜀. The characteristics *adriane.clerc@inrae.fr a Note that while the simulations are 2D, the mass and inertia of the grains corresponds to the one of spheres. Indeed, a of the sample and the loading are summarized in Table 1. DEM simulations give the expected response for deviatoric stress and volumetric strain corresponding to a dense granular material. For the sake of brevity the reader is referred to [START_REF] Clerc | Mesoscale signatures of inertial transitions in granular materials[END_REF] [START_REF] Clerc | Mesoscale signatures of inertial transitions in granular materials[END_REF] for more details.

Parameters

Dense sample

Grain density (kg/m

Focus on the bursts of kinetic energy

Kinetic energy is attached to the velocities of the grain and it is thus a microscopic quantity. However, it can be integrated and defined at a larger scale (macro and meso scales). For spherical grains, the kinetic energy is:

𝐸 𝑐 𝑔 = 1 2 𝑚 𝑔 ‖𝑐 𝑔 ‖ 2 + 1 5 𝑚 𝑔 |𝑤 𝑔 𝑅 𝑔 | 2
(1) where mg is the grain mass, Rg the grain radius, cg and wg are the translational and rotational velocity of the grain.

planar sample composed of one layer of spheres is considered. In order to use stresses, an out-of plane dimension equal to Dmax is used.

In order to detect a burst of kinetic energy, a threshold is defined based on the grain mean kinetic energy at the critical state (state where the sample deforms continuously with constant stress state and constant volume). From all the bursts that can be detected, we select four. For the sake of brevity, the results of a single burst are presented as the bursts present all the same patterns. The area of the burst propagation is separated from the rest of the sample domain to detect some microstructure features specific to the nucleation of the burst. It is easily done by setting an approximate control box around the location of the beginning of the burst (Fig. 1). Once the box is defined, preliminary investigations can be carried out. The sliding index Ip for each contact is defined as the ratio between the norm of the tangential force and the norm of the normal force multiplied by the friction coefficient. This index is an indicator of the stability of a contact. The extreme values it can take are 0 (no tangential force) and 1 (contact sliding). The comparison of the probability density function of Ip for contacts inside and outside the burst area reveals that the contacts inside the area are closer to their sliding limit just before the burst, while the probability density function outside the area does not change much during the burst. A sliding index close to 1 has already been shown to be a necessary condition to observe a burst of kinetic energy [4].

If we compare the different energies variations in the whole sample, we see that the kinetic energy goes through a peak corresponding. Meanwhile, the elastic energy decreases and the cumulative energy dissipated in plastic slips increases (Fig. 2). We can conclude that an excess of elastic energy stored into the contacts is transformed into kinetic energy but mostly dissipated through friction.

Mesoscale quantities

In the present case, meso-domains are considered in the form of grain-loops. They are defined from the tessellation of the sample area based on contacts between grains. The sample domain is seen as a unique pavement composed of grain-loops of different orders (i.e. number of grains forming the loops). High order grain-loops are on average more deformable than low order ones. This deformability is the base of microreorganizations and a way to adapt to external loadings. Non-contact or single contact grains called rattlers, often contained in high order loops, have a key role in the reorganizations and kinetic energy transfer as they can be absorbed in loop formation or be released when loops collapse.

We want to investigate the ability of mesodomains to develop kinetic energy with no external input. The second-order criterion [3,12,13] is relevant for this stability analysis, provided that the continuum mechanics framework holds. According to this criterion, if a given system is at balance initially and the external second-order work is null, the system evolves from static to inertial regime if and only if the internal secondorder work is negative. At mesoscale, the continuum framework is questionable and there is no reason for the meso-domains to fulfil the requirements for this criterion to anticipate bursts of kinetic energy. However, meso-stress and meso-strain can be defined (consistently with macroscopic definitions), and a mesoscale internal second order work is formed as:

(𝑤 2 ) 𝛺 𝑙 = ⟨𝛥𝝈⟩ 𝛺 𝑙 : ⟨𝛥𝜺⟩ 𝛺 𝑙 (2) with σ a stress tensor, ε a strain tensor and 𝛺 𝑙 the mesodomain of interest.

The meso-stress and meso-strain are averages of the respective quantities over 𝛺 𝑙 . Using Gauss theorem, the average strain rate on the domain is defined from quantities on the boundary of the domain. Centers of neighboring spheres belonging to the same loop are joined by branch vectors (Fig. 3a). They form the polygon 𝛺 𝑙 on which the calculation is based. The meso-incremental strain tensor is defined as a function of a linear interpolation of the incremental displacements of the grains [14,15]:

< ∆𝜺 > Ω 𝑙 = 1 |Ω 𝑙 | ∑ 1 2 (Δ𝒖 𝑘 0 + Δ𝒖 𝑘 1 )⨂𝒏 𝑘 𝑙 𝑘 𝑘∈𝛿Ω 𝑙 (3)
where u 0 k and u 1 k are the incremental displacement vectors of the vertices of the k th edge, l k is the length of the k th edge and n k is the normal to this same edge and |𝛺 𝑙 | is the volume of the polygon of domain 𝛺 𝑙 . The meso-stress we propose is defined as a spatial average over the polygon domain 𝛺 𝑙 of the grains micro stress (Fig. 3b). The main hypothesis is that the averaged stress calculated on the part of the grain included in the loop area is equal to the average stress of the grain. This definition is not restricted to a quasi-static regime and can be extended to dynamical regime as long as the contribution of rotations remains negligible.

〈𝝈〉 Ω 𝑙 = 1 |Ω 𝑙 | ∑ |𝑉 𝑔 ∩ Ω 𝑙 |〈𝝈〉 𝑉 𝑔 𝑔∈Ω 𝑙 (4)
Where V g is the solid domain of the grain. The macroscopic axial deformation between two steps used to calculate the incremental macro stress is very small (10 -6 ). Thus, we can make the following approximation:

〈∆𝝈〉 Ω 𝑙 = Δ〈𝝈〉 Ω 𝑙 (5)

Mesoscale changes during a burst of kinetic energy 4.1 Evolution of meso-structures during a burst of kinetic energies

The incremental evolution of grain-loops and rattlers is followed during the burst presented in this paper inside and outside the burst zone (box shown in Fig. 1). The incremental evolution is equal to the ratio between the incremental evolution of the number of structures ΔN over a small axial strain increment (10 -6 ) and their number N0 at the beginning of the recording. Figure 4 shows the incremental evolution of the four main groups of grain-loops inside the burst area (Fig. 4a) and outside (Fig. 4b). A small and equal amount of loops are lost and created for each type of loops. This observation is consistent with the fact that the loop decomposition of the microstructure is statistically at equilibrium at critical state. The burst does not induce noticeable statistical changes on the loop population. However, we can notice that low order loops are broken first (peak of lost loops before the peak of energy) and created after (peak of gain loops just after the peak of kinetic energy).

For the 6+ order loops, the maximum of created and lost incremental evolutions occurs simultaneously. The incremental evolution is also drawn for the rattlers and it shows that rattlers are first created and then lost, which can be related to the evolution of grain-loops. Before the maximum of kinetic energy, a significant proportion of loops of order 3, 4 and 5 are destroyed, transformed into higher order loops and creates rattlers. After the peak, these same orders of loops are reformed back and thus consume rattlers. Meanwhile, the high order loops are constantly created and lost and ensure statistical stability (in terms of loop composition) of the zone concerned by an inertial transition. By contrast, outside the burst zone, no significant changes are spotted neither for the grainloops (Fig. 4b) nor the rattlers. The changes due to the burst of kinetic energy remains in the neighborhood of its creation and immediate propagation.

Evolution of mesoscopic second order work during a burst of kinetic energy

In Fig. 5, the spatial distribution of the mesoscale second-order work (Eq. ( 2)) for macroscopic increments of axial strain of 10 -6 shows that the vanishing of the mesoscopic second order work follows the spatial evolution of the kinetic energy (Fig. 5) in the triggering mechanisms. It should be noticed that the burst area is not formed only from loops with negative values of second-order work. Positive and negative values follow the burst displacements, while the rest of the sample shows values close to zero. However, by looking at the volume-averaged second-order work in the burst domain, we can exhibit the predominance of negative values before the onset of the burst. The vanishing of the average second-order work based on meso-stress and meso-strain definitions can be seen as a signature of instability in the domain, while the followed increase indicates that the microstructure reorganizations stabilize the area and inhibit the growth of the burst. The box used for the delimitation of the burst is superimposed to the screenshot. We notice that the extension of the variations of the meso internal second order work is wider than the micro kinetic energy and highlight zones will be soon concerned by the burst of kinetic energy.

Conclusion and outlooks

We have shown the relevance of defining meso-domains as grain loops in granular material to analyze bursts of kinetic energy. Modifications in the number and of the nature of grain loops is synonym of microstructure reorganizations and release in kinetic energy. The microstructure after the burst is very similar to the one before, underlining the statistical equilibrium at critical state. Moreover, precursors of inertial transition have been pointed out in the zone of the burst of kinetic energy. A large number of contacts close to sliding in an area is necessary to trigger the kinetic energy release.

The variations in the second-order work, defined at mesoscopic scale, anticipate the burst of kinetic energy and give detailed information on its spatial origin. The influence of the material density (from loose to dense) will be studied to confirm and generalize the presented results. Mesoscopic quantities introduced in this work are based on several assumptions that need to be clarified and investigated in order to validate the interpretation of meso-second order work from a physical point of view. In particular, the contribution of inertial effects should be assessed.

.References

Fig. 1 .

 1 Fig. 1. Screenshot of the presented burst. The particles are colored in function of their kinetic energy. The box used for the delimitation of the burst is superimposed to the screenshot. It takes into account the slight displacement of the burst on the right direction (displacement not shown here).

Fig. 2 .

 2 Fig.2. Evolution of the energy dissipated through contact sliding Ep, of the elastic energy Ee (left y-axis), and of the kinetic energy Ec (in red, right y-axis) during the burst of kinetic energy presented (the duration of the burst is materialized by the black vertical lines). Only variations of energies are plotted, the reference energy levels being taken before the burst for an axial strain of 0.10416.

Fig. 3 .

 3 Fig. 3. Sketches to illustrate the calculation of the meso-strain (a) and meso-stress (b).

Fig. 4 .

 4 Fig. 4. Incremental evolution of grain-loops inside (a) and outside (b) the burst domain shown in Figure 1. A color is assigned to each order loops (L3, L4, L5 and L6+). Solid lines represent the creation of loops (ΔN>0) and dotted lines represents the loss of loops (ΔN<0). The duration of the burst is delimited by the vertical solid lines and the peak of maximum kinetic energy is displayed by the vertical dotted line.

Fig. 5 .

 5 Fig. 5. Screenshot of the presented burst. The meso domains are colored in function of their internal second-order work.The box used for the delimitation of the burst is superimposed to the screenshot. We notice that the extension of the variations of the meso internal second order work is wider than the micro kinetic energy and highlight zones will be soon concerned by the burst of kinetic energy.

Table 1 .

 1 Dense sample parameters for the triaxial test. D is the mean diameter of the grains.

	3 )	3000
	Friction coefficient	0.7
	kn/D (MPa)	356
	kt/kn	0.42
	Grain size distribution	Uniform with Dmax/Dmin=3.5
	Loading rate 𝜀̇ (s -1 )	0.01
	Confining pressure 𝜎 0 (kPa)	100

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).

EPJ Web of Conferences 249, 10004 (2021) https://doi.org/10.1051/epjconf/202124910004 Powders and Grains 2021


Jonas Biren

Muhammad Aufaristama

Lionel Cosson

Leire Del Campo

Hao Li

Joan Andújar

Aneta Slodczyk

Improving field lava flow temperatures with lab-based spectral emissivities for the 2014-2015 Holuhraun eruption

Spectral emissivity depends on λ and T [7]: ε increases linearly with temperature at 10.9 μm (TIR), and changes non-linearly and with greater amplitude at 1.6 μm (SWIR).

When lab-based emissivity maps are compared, derived ε values are higher in SWIR (0.9-1.0) than in TIR(0.8-0.9). High ε values are characteristic of molten lava (e.g., lava channel and levées are well visible) whereas lower ε values are characteristic of the lava flow surroundings (e.g., lava front).

When Thermal maps are compared, T distribution varies between RS-and Lab-based thermal maps. Lava channel shows lower temperatures whereas levées and lava front show higher temperatures. The temperatures of the cooled surroundings remain constant.

The mean di erence between RS-and lab-based thermal maps is ~50° for lava channel, while is greater for lava levées and lower for cooled surroundings.

METHOD

Spectral emissivity of basaltic magma from the 2014-2015 Holuhraun eruption was measured in situ. Spectra were systematically acquired over a wide spectral range (400-8000 cm -1

) covering TIR, MIR and SWIR, and up to ~1800 K using IR emission apparatus [4]. Then, we transformed the ε-T relationship into equations at two wavelengths of interest for RS; 10.9 μm (TIR), and 1.6 μm (SWIR). Finally, we implemented these equations in Aufaristama et al. ( 2018) [5] thermal model and run the refined model as follow: 1-First iteration with constant ε (0.97) to determine T. 2-Creation of emissivity map for each band using T to calculate ε.

3-Second iteration with ε

calculate to refine lava flow T.

Laboratory measurement

Lab-based Emissivity Maps CONCLUSIONS

Lab-based IR results help increasing accuracy in temperature retrieval by Remote Sensing techniques (by ≥50°). These observations imply that lava is less likely to loose heat radiatively thus taking longer time to dissipate. In turn, it allows for longer distances to be reached increasing ultimately the associated hazard especially in inhabited area. Consecutively, our results will help reduce the error related to thermo-rheological models [6] of lava flows and support hazard assessment during e usive volcanic crisis.

∆T

Difference in T due to lab-based Emissivity

High potential, high T (25-1800 K), wide υ (400-20 000 cm -1 ) in situ apparatus for Emissivity measurements [4]. 10.9 µm (TIR)

1.6 µm (SWIR)

Quanti. of Emissivity-Temperature relationship

Radiative eq.: R TIR-SWIR = [L(λ TIR-SWIR ) -L U-R (λ TIR-SWIR )]/τ ε TIR-SWIR

For more information, refer to «V23A-04, Thermal Radiative Properties of Bardarbunga Basalts: Importance of Emissivity in Magma Rheology and Volcanic Hazard», Jonas Biren et al.

1

INTRODUCTION

How to measure lava flow temperature more precisely?

Lava flows are one of the main hazards related to e usive basaltic volcanism. To minimize their impact during emplacement, we use lava flow distance-to-run predicted by propagation models. These models rely on surface Temperature (T), a key source term parameter that is commonly determined using infrared (IR) measurements of lava radiative heat fluxes by remote sensing (RS) techniques (ground-or satellite-based) [1]. Their results are however subjected to important errors related to the poor knowledge of spectral emissivity (ε), commonly considered constant (e.g., 0.97 for basalts) [2,3]. This oversimplification is an important source of uncertainties in derived temperatures, which restrain our capacity to accurately model active lava flows.

In this study, we confront thermal maps modeled with constant ε and based on ε laboratory measurements. We describe the methodology used to improve previous RS thermal maps using lab-based ε measurements. We discuss the potential impacts from improvements of temperature accuracy on lava flow thermo-rheological modelisation.

Remote Sensing

Emissivity is key for Remote Temperature determination

The 2018 eruption of Kilauea (Hawai'i)

Spectral emissivity (ε) is the fundamental and physical capacity of a material to emit heat radiation.

  t t o k n o w m o r e ? j o n a s . b i r e n @ c n r s -o r l e a n s . f r L o o k i n g f o r a P o s t D o c f e l l o w ? Derived eq.: ε TIR = 0.826 -8.235 10 -5 × T + 7.818 10 -8


domain: spi shs

text:
Guillaume Guimbretiere

Alexandre Lefevre

Sylvain Barbot

Fabrice Laurent

Fabrice Laurent Study

STUDY OF THE THERMAL DYNAMICS OF SOLAR COOKERS ON REUNION ISLAND : TECHNICS AND USES AT HOUSEHOLD AND COMMUNAL SCALES

Keywords: Low-tech, Thermal dynamic, Solar yogurt maker, Solar rice cooker, Solar Baker, French tropical island

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

CONSOLFOOD 2022 -International Conference on Advances in Solar Thermal Food Processing Faro-Portugal, 24-26 January, 2022

STUDY OF THE THERMAL DYNAMICS OF SOLAR COOKERS ON REUNION ISLAND : TECHNICS AND USES AT HOUSEHOLD AND COMMUNAL SCALES

Guimbretière 1,2 , G., Lefèvre 1,2 , A., Barbot 2 , S., Laurent 2 , F.

1 LACy (UMR8105, Université de la Réunion / CNRS / Météo-France) 2 Association Ekopratik -http://www.ekopratik.fr/ e-mail : guillaume.guimbretiere@univ-reunion.fr

Abstract: Within the desired framework of the overall transition of our civilization towards sustainable functioning, our study is interested in the adaptations of a modern society to solar cooking in tropical climates. Starting from the observation that the barriers limiting the adoption of solar cooking techniques are cultural before being technical, we have a contextual approach questioning both use and technique. The study setting is that of Creole cooking on the French island of Reunion located in the Indian Ocean (21° 6' 54.508" S 55° 32' 10.982" E). We identify three possible adaptations: the gesture, the recipe and the solar cooker.

By defining cooking as a journey in space, temperature as a function of time, following a map called a recipe resulting from the bio-physical-chemical properties of the ingredients and drawn by generations of previous explorers:

The objectives of this work are therefore: (i) to identify the usual cooking dynamics that can be carried out by the available solar cooking systems: adaptation of the gesture. (ii) Identify technical modifications to make the cooker more suitable for targeted use (iii) identify possible food transformations with available solar cooking systems: adaptation of the recipe. (iv) identify the synergies between different solar or alternative cooking systems to make a particular dish -Optimize the energy consumption of these synergies.

Inspired by the techno-critical philosophy of the low-tech movement, the method used is to design solar and alternative cooking systems in a citizen laboratory by constantly questioning usage. First, the thermal dynamics T(t) of all cooking systems are recorded. Then, a combined analysis of the thermal dynamics T(t) and the steps of associated traditional recipes, makes it possible to identify T(t) kinetic patterns that can be linked to the chemical processes of food transformation. The work on the adaptation of the gesture then consists of identifying the similarities between the T(t) patterns of traditional systems and those of solar and alternative systems, in order to reconstruct a sequence of gestures with the goal of achieving the desired recipe. Also, work will be done to modify a cooker to obtain a desired T(t). The work on adapting the recipe consists of comparing all the possible chemical food transformation processes and the original T(t) units obtained in solar and alternative cooking systems. This allows to explore new cooking methods of the same food.

At the time of submission of this abstract, the recording of T(t) dynamics and their analyzes just begun: Following a series of citizen workshops, several solar and alternative cooking systems are now available: 3 different box ovens, 1 Solar-Bro © tube oven, a Lytefire © -type solar concentrator with a set of removable targets (oven, plancha, wok) and two home-made rocket-stoves. As citizen expertise on solar cooking has been consolidated, each prototype can be modified to obtain a desired T(t) kinetics. Work on adaptations, however, began at two levels: domestic and community. On the domestic front, a "rougail saucisses" for 15 people was cooked using several solar cookers and rocket-stoves. This traditional recipe involves cooking sausage, rice and beans. In this first international presentation, in order to illustrate our scientific approach, we discuss the preparation of yogurt with the use of a solar yogurt maker, as well as the comparison between electric and solar rice cooking.

At the community level, we present our project in the process of establishing a network of solar artisan bakers on Reunion Island. The approach to characterizing the links between the solar cooking tool and the user's gesture is the same as at the domestic level, but the reading of temperature dynamics at a higher level of difficulty. However, we believe that learning a gesture and using a new tool may be less difficult for a professional rather than an individual. This is why we are working with artisan bakers: the analysis of the dynamics T (t) of a 28 kW artisan baker's oven made it possible to identify breads suitable for baking in our 4kW solar baker's oven, as well as interesting technical adaptations.


S Somaglino

R Desgranges

C Berti

D Patinote

F Langevin

R Lazeyras

A Salomir

C Polidori

Contino-Pépin

K Astafyeva

L Somaglino

S Desgranges

R Berti

C Patinote

D Langevin

F Lazeyras

R Salomir

A Polidori

C Contino-Pépin

W Urbach

N Taulier

Perfluorocarbon nanodroplets stabilized by fluorinated surfactants: characterization and potentiality as theranostic agent

Perfluorocarbon nanodroplets stabilized by fluorinated

surfactants: characterization and potentiality as theranostic agents

Introduction

Early detection of tumor and targeted drug delivery are two main objectives in treatments against cancer. A recent approach consists in using the well-known permeability of tumor vessels to large nanoparticles. Indeed, whereas normal vessels are permeable only to small molecules (< 12 nm), tumor vessels present large inter-endothelial gaps (most tumors exhibit a gap cut-off between 400 and 800 nm) allowing the passage of nanoparticles. [1][2][3][4] Nanoparticles with a mean diameter of 100 -300 nm have the best chance to use these gaps whatever the tumor type. In addition, tumors exhibit a dysfunctional lymphatic drainage system that induces the retention of nanoparticles into the tumor tissues. 1 These two properties represent the so-called enhanced permeability and retention effect (EPR) that allows a passive tumor targeting by nanoparticles that act as drug carriers or/and contrast agents. 5,6 The best imaging modalities, associated with contrast agents and suited for tumor detection, appear to be contrast echography and magnetic resonance imaging (MRI). On the one hand, contrast echography has realtime imaging ability, offers the cheaper imaging alternative, and is available in most hospitals. On the other hand, MRI offers the best tissue contrast. Unfortunately, commercial contrast agents currently available for both techniques are not compatible with EPR effect. Indeed, commercial ultrasound contrast agents are stabilized bubbles with a micrometric size (1 -12 µm) that prevent them to extravasate out of the vasculature into the tumor tissue. Such bubbles also exhibit a rapid blood clearance, representing a strong barrier for their use as quantitative tracers or drug carriers. To the contrary, commercial MRI contrast agents, commonly based on gadolinium, leak across even normal vessels wall. It may be possible to overcome the limitations of both imaging modalities by using perfluorocarbon (PFC) nanodroplets as contrast agents. Indeed, several studies has shown that perfluorocarbon droplets can be detected using 19 F MRI. [7][8][9] Unfortunately, the acoustic resonance frequency of such nanodroplets lies outside the clinical range of echography (1 -15 MHz). However, they still can enhance ultrasound contrast when accumulated in a specific region or bound to a targeted surface. 10,11 But the best approach to significantly improve their echogenicity is the vaporization of the nanodroplets. [12][13][14] Nevertheless, a major difficulty of the task comes from the ability to produce stable droplets with a sufficient lifetime to allow an accumulation into the tumor tissues using the EPR effect. Most perfluorocarbon droplets produced for imaging purpose were prepared as an emulsion and used as emulsifiers lipids, 10,13,15,16 surfactants, 17,18 proteins, 19 or diblock polymers. 20 Although alkanes, a constituted part of emulsifiers, and fluoroalkanes are both hydrophobic molecules, they are not miscible. [START_REF] Karsa | Fluorinated surfactants: synthesis properties applications[END_REF] Thus, the above emulsifiers exhibit a very low affinity for perfluorocarbons. Droplets coated with these emulsifiers are not very stable. To overcome this problem, the best way is to replace the (lipophilic) hydrocarbon part of the emulsifier by a (lipophobic and fluorophilic) perfluorocarbon part. A convenient approach is to use fluorinated surfactants, [START_REF] Krafft | [END_REF] a few of them are commercially available, mostly from Dupont like Zonyl® (available until 2010-2012), Cap-stone®, and Krytox®. These commercial surfactants were designed for industrial purposes but not for medical applications. Even if little is known about their toxicity, several studies have used them in contrast agent formulation. 19,23,24 Another fluorinated surfactant, called FTAC, was initially designed in the nineties as oxygen carrier 25,26 and drug carrier. 27,28 It was later used for the solubilization of membrane proteins. 29 FTAC exhibits a good biocompatibility (no hemolytic activity, LD 50 up to 4.5 g/kg in rats after i.v. administration), ubiquitous distribution in rat after i.v. or per os. route, and displays a long half-life (30 -50 h) without any degradation in both plasma and tissues. 27 Because of its biocompatibility, FTAC is an appealling candidate to produce perfluorocarbon-based colloids for theranostic purposes. However, there are still unknowns in FTAC chemical and physical properties. For these reasons, we have characterized the properties of this fluorinated surfactant at interfaces, in solution as micelles, and as emulsifier to stabilize droplets made of different perfluorocarbon liquids. Next, we have evaluated the overall characteristics of FTACperfluorocarbon nanoemulsions such as density, size distributions, aging, and ultrasound backscattering. Finally, we have assessed the theranostic capability of these emulsions, as drug carriers and 19 F MRI contrast agents.

2 Materials and methods

Materials

Perfluoropentane (PFP), perfluorohexane (PFH), and perfluorooctyl bromide (PFOB) were purchased from ABCR GmbH & Co (Germany). The purity is 90, 95, and 99% for PFP, PFH, and PFOB, respectively. For tension measurements, PFOB was further purified through a column of activated neutral alumina (purchased from Sigma-Aldrich). Water was purified using a Purelab Option Q system from ELGA Labwater. Fluorinated surfactants were FTAC telomers (Fig. 1), which synthesis was described in previous papers. 30,31 We followed the published protocol as summarized below. Surfactants were obtained by free radical polymerization of an acrylamide monomer derived from Tris, the tris(hydroxymethyl) acrylamidomethane (THAM), or from its peracetylated analogue (tris(acetoxymethyl)acrylamidomethane) in the presence of a perfluoroalkanethiol as a transfer reagent called "telogen". The physico-chemical parameters of these telomers (molec- ular weight, hydrophilic lipophilic balance or HLB, critical micelle concentration or CMC) can be adjusted through both the starting material and the experimental conditions. 30,32 Telomerization experiments were respectively performed in methanol (MeOH), when the monomer THAM was used as starting material, and in tetrahydrofuran (THF) for peracetylated THAM. The later monomer is required to obtain a Degree of Polymerization (DPn) higher than 15 according to Giusti et al. 33 due to the observed limited solubility of polyTris oligomers in methanol. Telomerization experiments (Fig. 2) were carried out by refluxing monomer 1 or 2 in dry and degassed appropriate solvent, under argon atmosphere, in the presence of 1H,1H,2H,2H-perfluorooctanethiol or 1H,1H,2H,2H-perfluorodecanethiol as transfer reagents and AIBN (α,α-azobisisobutyronitrile) as radical initiator. The AIBN concentration in the reaction mixture was ten times lower than the telogen one. [START_REF] Starks | Free radical telomerization[END_REF] The reaction was monitored by thin layer chromatography and pursued until complete disappearance of each monomer (12 to 24 h).

For telomers prepared from monomer 2, the solution was concentrated and subsequently precipitated in diethylether. The precipitate was dissolved in water and freeze-dried to give surfactants with DPn < 15 as white powders.

R F SH a) R F SH + b) R F S
As regards peracetylated telomers, after total disappearance of monomer 1, a final treatment under Zemplén conditions yielded the telomers with DPn > 15 in satisfactory yields and NMR analysis confirmed the total disappearance of acetyl groups. These telomers were all purified by precipitation in MeOH/diethylether. The resulting precipitate was dissolved in water, then dialyzed overnight (cut off of 1000 Da). The solution was eventually freeze dried to obtain telomers as white powders.

Monoadduct (DPn = 1) derivatives of each telogen were also synthesized. These compounds were easily obtained from Michael addition reaction of the perfluoroalkylated thiol on monomer 2 according to the previously described conditions. [START_REF] Contino | [END_REF] 2.2 Degree of polymerization determined by 19 F NMR.

All spectra were recorded on a 250 MHz Bruker Avance I or II spectrometer with a resonance frequency of 235.3 MHz for 19 F. All data collection was performed without spinning the samples. 19 F-NMR spectra were acquired using the inversegated decoupling technique, each spectrum was the result of 256 scans with 131,072 data points using a relaxation delay of 4 s. Peak areas were integrated using manufacturer's standard software (1D WinNMR). A coaxial capillary was filled with a known solution of trifluoroacetic acid (TFA) sodium salt in D 2 O (50 mg/ml) and put into a 5 mm diameter NMR tube in order to be employed as an external reference. 500 µl of solution was used in deuterated dimethyl sulfoxide (DMSO-d 6 ) for each sample (telomer or monoadduct) and the coaxial capillary was kept the same for all experiments. TFA salt was cho-sen because of the proximity of the signal ascribed to its CF 3 group compared to that of the monoadduct's fluorinated tail (i.e. its telogen part), respectively at -75.96 and -80.15 ppm, thus avoiding problem to keep uniform field over long range. The ratio of the integration of the external standard (ICF 3 of TFA) over the integration of the monoadduct (ICF 3 of telogen) was plotted against the monoadduct molar concentration value to create a calibration curve. This molar concentration of monoadduct can be referred as the molar concentration of its fluorinated telogen part. This calibration curve allows finding the molar concentration, M telogen , of the telogen moiety of each telomer. All measurements were performed on triplicate samples, where each sample contained a precise mass of telomer dissolved in DMSO-d 6 . The specific concentration of telomer, W telomer , was ranging from 3 to 12 g/l. Given that each telomer backbone contains a single telogen moiety, the average molecular mass of telomer ⟨M telomer ⟩ can be calculated using:

⟨M telomer ⟩ = W telomer /M telogen (1)
The average degree of polymerization (DPn) can thus be deducted through:

DPn = ⟨M telomer ⟩ -M F M m ( 2
)
where M F and M m are respectively the molecular mass of the perfluoroalkyl chain and of the monomer.

Emulsion preparation

About 10 -50 mM of fluorinated surfactant FTAC was first solubilized in 2 ml of an aqueous solution made of deionized water and 2 mM of NaCl. The surfactant concentration was higher than its critical micellar concentration (CMC), as given in Table 1. A volume of 0.6 ml of perfluorocarbon liquid was added to the surfactant solution so that the molar ratio, N r , of fluorinated surfactant molecules to perfluorocarbon molecules was known. Since the two liquids are immiscible, a two-phase solution was obtained, where the micelle aqueous solution was on the top and the perfluorocarbon liquid at the bottom due to its higher density (see Table 2). The two-phases solution was prepared in a 15 ml centrifuge plastic tube that was placed in iced water. The tip end of an ultrasound cell disruptor (Branson Digital Sonifier, model 450) was put inside the solution at the interface between the micellar and perfluorocarbon liquids. Ultrasounds were applied twice during 30 s using 0.5 s cycles at 20 kHz frequency with a waiting time of 10 mn between the two insonifications. The newly prepared emulsion was eventually stored at 4°C. Any volume of liquid perfluorocarbons that could not get encapsulated as a droplet would sediment after a few hours. If that was the case, only the top emulsion made of surfactant-stabilized perfluorocarbon droplets was retrieved and stored for further investigations.

Surface tension measurements

The surfactant surface activity at air/water interface was determined by the Wilhelmy plate technique using a Krüss K100 tensiometer controlled by Labdesk software (Krüss, Germany). The platinum plate was cleaned by flaming before experiments. All solutions were prepared a night prior to measurements in purified water, which surface excess tension was Γ S = 72.8 mN/m. A 20 ml initial volume of a surfactant solution was placed into a glass trough and surface tensions were determined by diluting the solution. All measurements were carried out at 25°C and repeated 3 times. The surface excess Γ S at the air-water interface was calculated using the Gibbs adsorption isotherm equation

Γ S = -1 RT dγ S d lnC
, where γ S is the surface tension (N/m) at the surfactant concentration C (mol/l).

Interfacial tension

The interfacial tension between water and perfluorocarbon liquid was measured with an error of 0.4 mN/m using a Tracker tensiometer (Teclis, France) at 25°C. The tensiometer analyzes the shape of a reverse pendant water drop in perfluorocarbon liquid and fits it using the Young-Laplace equation to derive the interfacial tension. During the experiment, the water drop volume was kept constant at 6 mm 3 in the absence of surfactant and at 2 mm 3 when the drop contained ∼ 6 mM of surfactant (above its CMC). We waited until the interfacial tension reached an equilibrium value to extract the interfacial tension value, γ I . As a test, we have also measured the in- terfacial tension of a sessile air bubble in water: a value of 72.5 ± 0.4 mN/m was measured.

Size by Dynamic light scattering measurements

Mean hydrodynamic diameters and size distributions were measured at room temperature using a ALV-Correlator Goniometer System (ALV-CGS) from ALV Company. This device is equipped with a 22 mW He-Ne laser (λ = 632.8 nm) and a goniometer with an angular range from 17 to 152°. Samples were measured for angles varying from 60 to 120°a t every 10°with a running time of 60 s for each angle. Measurements were performed in triplicate and the diameters were estimated with a precision of 0.5 nm. For emulsion samples, the droplet volume fraction, Φ, was in the range of (0.1 -0.2) × 10 -2 (i.e. 0.1 -0.2 %) to avoid multiple scattering effects. Micelle samples were prepared within a concentration range of 3 -6 mM, higher than the surfactant CMC.

Size by Scanning Ion Occlusion Spectroscopy (SIOS)

Size distribution of droplets was measured using a Scanning Ion Occlusion Spectroscopy (qNano model from Izon Com-pany, New-Zealand). 36 The device principle is based on the Coulter effect. 37,38 For a measurement we use an elastomeric and resizable nanopore (NP) that covered a size range of either 70 -200 nm (NP100), 100 -400 nm (NP200), 200 -800 nm (NP400), or 400 -1600 nm (NP800). These ranges can be shifted by stretching the nanopore, in our case the applied stretching values were 45 -48 mm. Voltage was set between 0.2 and 0.56 mV to keep the current baseline equals to approximatively 120 nA. For each nanopore a calibration was made using calibrated plain polystyrene particles (purchased from Izon Company). Each sample was measured at two pressures: 3 and 5 cm of H The closer to unity this index is, the more monodisperse the droplet size is. An error of less than 3% was obtained for the mean diameter and of 5 -10% for the mode diameter.

Density and concentration

Densities measurements were carried out at 25°C using a digital density meter from Anton Paar (model DMA 5000 M).

The device uses an oscillating U-tube sensor to derive densities with an accuracy of 5 × 10 -6 g cm -3 . Density measurements were first used to estimate the specific concentration C (in mg/ml) of droplets in the emulsion. To do so, the droplet volume fraction Φ was derived from mass conservation principle:

Φ = ρ -ρ o ρ droplet -ρ o ( 3
)
where ρ is the density of the emulsion, ρ o the density of the solvent used for the emulsion, and ρ droplet the density of a droplet. Measurements of the two first densities (i.e. ρ and ρ o ) were straightforward, but the measurement of ρ droplet was not possible without knowing the droplet concentration. However, it could be derived using the equation:

ρ droplet = ρ core • Φ core + ρ shell • (1 -Φ core ) (4)
where ρ core and ρ shell are respectively the densities of the per- fluorocarbon core and of the fluorinated surfactant composing the shell of a droplet. Φ core and (1 -Φ core ) are respectively the volume fractions of the perfluorocarbon core and of the surfactant shell. The value of ρ core was taken as the density ρ PFC measured for the corresponding bulk perfluorocar- bon liquid (values reported in Table 2), i.e. ρ core = ρ PFC . We assumed that the density of a fluorinated surfactant located in the droplet shell was close to the density of the same surfactant when it formed a micelle: ρ shell ≈ ρ micelle . An average value of ρ micelle = 1440 ± 30 kg m -3 was measured for all surfactants. The shell volume fraction (1 -Φ core ) could be calculated using an estimated value of the surfactant length and the value of the droplet mean radius. All estimations led to a value of (1 -Φ core ) smaller than 0.12. We stated that taking ρ droplet = ρ PFC instead of equation 4 gave rise to a dif- ference smaller than 3%. As this difference was reasonnably small, we made the approximation ρ droplet ≈ ρ PFC in all calculations. Thus, the mass concentration, C, is given by:

C = ρ droplet Φ ≈ ρ PFC ρ -ρ o ρ PFC -ρ o (5)
Finally, at a low concentration of droplets the partial volume V o of a droplet was equal to the droplet apparent volume φ V calculated using: 39

φ V = 1 ρ - ρ -ρ o ρC . ( 6
)

Ultrasound velocity measurements

Sound velocities of solutions were measured at 25°C using a previously described differential resonator method, [START_REF] Eggers | [END_REF][41][42][43] at a frequency of 7.5 MHz. The solution filled a thermostated cell of a minimal volume of 0.8 ml where two lithium niobate piezotransducers faced each other. The analysis of the frequency-amplitude characteristic of the resonator was performed by an Agilent (model E5100A) network/spectrum analyzer. From this analysis we calculated variations in sound velocities with a precision of 0.15 cm/s. We eventually derived the specific sound velocity increment, [u], due to the presence of a concentration C of droplets:

[u] = U -U o U o ×C (7)
where U and U o are the sound velocities in the solution and in its solvent, respectively.

Adiabatic compressibility

Adiabatic compressibility β of a solution was obtained using Newton-Laplace's equation:

β = 1/(ρU 2 ) ( 8
)
where U is the speed of sound in the solution that possesses a density ρ. The partial adiabatic compressibility of a solution was then calculated from:

K o S = β ×V o (9)
The apparent adiabatic compressibility φ k of a droplet could be calculated using equations 6, 7, and 8: 44,45

φ k = β o × ( 2φ v -2[u] - 1 ρ o ) (10)
where β 0 is the coefficient of adiabatic compressibility of the solvent. In our measurements, concentrations (in the 2 -7 mM range) were low enough so that the apparent adiabatic compressibility of a droplet was equal to its partial adiabatic compressibility, i.e. φ k ≈ K o S . Signal-to-Noise Ratio (SNR):

Ultrasound backscattering measurements

SNR( f ) = 10 × log ( PSD S PSD W ) (11)
where PSD S and PSD W are the mean Power Spectrum Densities over 100 PSD obtained in emulsion and in water, respectively. The calculation of an average PSD over many signals makes the SNR independent of particle configurations and, therefore, is representative of the so-called incoherent backscattered intensity. 46 Finally, the mean value of SNR( f ) over the transducer -3 dB frequency bandwidth, SNR mean , was extracted to characterize the echogenicity of an emulsion using a single quantity.

2.12

In vitro MRI 19 F MR spectroscopy and 3D imaging were performed on emulsions filling the bulb of a plastic Pasteur pipette. A transmiter-receiver, double frequency 19 F/ 1 H, saddle-type surface coil of 6 cm diameter was used with a 3T MR scanner (Siemens Trio, Erlangen, Germany). Fourier Transform was applied to the FID signal acquired from the whole sample (BW 15 kHz corresponding to 125 ppm, sampling size of 4096 points, flip angle ranges 20 to 90°, NEX = 200, TR = 205 ms, TE = 0.35 ms). 3D imaging was performed with a nonselective pulse RF-spoiled GRE sequence, of main parameters: TR = 10 ms, TE = 3.25 ms, FA = 45°, voxel size 1.1 × 1.1 × 3 or 3 × 3 × 3 mm 3 , NSA = 8, and acquisition time = 2 min 44 s.

Spectrofluorimetry

Fluorescence spectra were performed at 25°C on samples filling a 1 cm quartz cuvette using a JASCO FP-6200 spectrofluorimeter. An excitation wavelength of λ ex = 363 nm was used and spectra were recorded from 365 to 650 nm.

Results

Characterization of fluorinated surfactants

Taking into account published results about THAM telomerization, 18,30 we choose the values 3, 5, 15, 20, and 25 for the monomer over telogen ratio in order to obtain FTAC surfactants with a DPn (average number of repeating units on the polymeric backbone + 1 telogen moiety, Fig. 1) equal to 7, 13, 18, 22, and 27, respectively. DPn value was assessed after FTAC surfactant synthesis by quantifying the fluorine on the hydrophobic tail using a 19 F-NMR methodology. [START_REF] Contino | [END_REF]47 These measurements confirmed the expected DPn values with an error of ±1, in agreement with literature. However, to further validate these results we also performed high-performance liquid chromatography (HPLC) measurements. HPLC data showed the presence of impurities along with FTAC surfactants. Their amount was small (< 6%) for DPn = 7 -13, but significantly large (25 -50%) for DPn > 13. After purification on a reverse-phase column, the impurities identified as poly-Tris (without fluorinated tail) were completely removed. DPn measurements were performed again on purified solutions. Surfactants that were previously tagged as having DPn values of 18, 22, and 27 were found after purification to possess a DPn no larger than 13 ± 0.5. The surfactants were noted F i TAC n where n is the degree of polymerization, DPn, and i reflects the number of carbons bearing fluorine atoms. The above syntheses were performed for surfactants having C 6 F 13 C 2 H 4 or C 8 F 17 C 2 H 4 as hydrophobic moiety, i.e. i = 6 or 8. Eventually, we obtained the following surfactants: F 6 TAC 1 , F 6 TAC 7 , F 6 TAC 12 , F 6 TAC 13 , F 8 TAC 1 , F 8 TAC 7 , F 8 TAC 12 , and F 8 TAC 13 .

All these surfactants, except F 6 TAC 1 and F 8 TAC 1 , could be solubilized in aqueous solutions up to a concentration of 100 mg/ml. A critical micellar concentration (CMC) had been determined for all solubilized surfactants (second column of Table 1). There is an order of magnitude of difference in CMC values between surfactant containing 6 and 8 carbons bearing fluorine atoms. The hydrodynamic diameters of FTAC micelles were measured using light scattering and above the CMC. Diameters of ∼ 8 nm were measured for F 6 TAC n and of ∼ 11 nm for F 8 TAC n (third column of Table 1). The micelle density was derived from the micelle partial volume: ρ micelle = 1/φ V,micelle . Whatever the surfactant, we obtained ρ micelle = 1440 ± 30 kg m -3 . The measurements of the specific increment of sound velocity gave slightly different values depending of the surfactant. That is 35, 115, 105, 64, and 78 × 10 -6 m 3 /kg for F 6 TAC 7 , F 6 TAC 12 , F 6 TAC 13 , F 8 TAC 7 , and F 8 TAC 13 . Using these values we have derived the partial adiabatic compressibilities of the micelles (Table 1, fourth column). In addition, we measured surface tensions at the water/air interface in the presence of surfactants at their CMC (Table 1, fifth column) as well as the interfacial tensions at the water/PFOB interface (Table 1, sixth column) in the presence of 7 mM surfactant. Finally, none of FTAC surfactants could be solubilized in perfluorocarbon liquids.

Characterization of perfluorocarbons

Various properties of PFOB, PFH, and PFP are reported in Table 2. Among these properties we measured the densities of perflurocarbon liquids as well as the partial adiabatic compressibilities of perfluorocarbon droplets stabilized by the various FTAC surfactants using Eq. 9. The compressibility value of such droplets did not significantly depend on the surfactant structure as well on the droplet size. The average compressibility values is reported in Table 2 for each perfluorocarbon. For comparison, we calculated the partial adiabatic Table 1 Properties measured for several F i TAC n at room temperature. It includes the surfactant critical micelle concentration (CMC), the surfactant micelle diameter D micelle , the surfactant partial adiabatic compressibility in a micelle K o S,micelle , the surface tension γ S between air and water with surfactant at the CMC, and the interfacial tension γ I between water and PFOB in the presence of surfactant. A comparison is given for surfactants: sodium laurate (NaL) and sodium dodecyl sulfate (SDS), and several lipids: compressibility of a bulk perflurocarbon liquid using Eq. 8.

For each perfluorocarbon, the compressibility of a droplet is close to the compressibility of the corresponding bulk perfluorocarbon. Finally, we calculated the diffusion coefficient, D, of a perfluorocarbon molecule in water at 25°C as predicted by the Wilke-Chang equation: 52

D = 7.4 × 10 -8 (xM w ) 0.5 T ηv 0.6 ( 12
)
where η is the water viscosity, T the temperature of water, M w the water molar mass, x = 2.6 is the association parameter of water, and v = 1/ρ is the perfluorocarbon molar volume at the boiling point.

Optimization of the emulsion preparation

Emulsions were prepared in a 15 ml centrifuge tube using an ultrasonic homogenizer. We tested several tapered tips (with diameters of 3 mm, 5 mm, and 6.5 mm) and a 3 mm double stepped tip. In our experimental conditions, only the use of a double stepped 3 mm tip gives rise to a homogeneous onephase emulsion (as long as enough surfactant is added). Both light scattering technique and scanning ion occlusion spectroscopy showed that such emulsion was made of droplets of mainly nanometric size (a typical example is shown in Fig. 3). In addition, emulsions with the smallest droplet average diameter and the narrowest size distribution of droplets were obtained when: the tip was positioned right at the interface between the aqueous and perfluorocarbon liquids, the ultrasonic power has reached 160 W (output power value given by the manufacturer), and the total sonication time was more than 60 s. Consequently, all samples were prepared using these optimal conditions.

Characterization of the stabilized droplets in emulsion

Emulsions were successfully produced with three perfluorocarbon liquids: perfluoropentane (PFP), perfluorohexane (PFH), and perfluorooctyl bromide (PFOB). After preparation the emulsions were stored at 4°C to reduce aging process. Then, we regularly monitored at room temperature the change in their size distribution and mean diameter using scanning ion occlusion technique. Before any measurements, the emulsion was gently agitated. After a few minutes, a sample was taken from the upper part of the solution. In order to pinpoint which chemical and physical parameters affect droplet aging, we studied the size variation as a function of either the type of liquid core, the type of surfactant, the ratio of surfactant to fluorocarbon, or the temperature. An increase in the surfactant-to-fluorocarbon ratio N R value from 0 up to 0.005 induced a dramatic decrease in droplet diameter whatever the perfluorocarbon used but did not alter the polydispersity. An example is given in Fig. 4 for PFOB droplets stabilized with F 6 TAC 7 surfactant, where the droplet mean diameter was reduced from 600 to 240 nm, while d 90 /d 10 remains equal to 2.3±0.1. For larger ratios, no significant reduction in diameter was observed until a critical molar ratio, equal to 0.01 for PFOB and 0.006 for both PFH and PFP, where a stable foam was produced in addition to the droplet emulsion. Next, to draw a comparison between emulsions, an identical surfactant-to-perfluorocarbon molar ratio N R (= 0.005) was used. Typical size distributions are displayed in Fig. 5 for droplets made of PFOB (black), PFH (gray), and PFP (light gray) stabilized with F 6 TAC 7 surfactant at day 0 (i.e. the day emulsions were prepared) and ninety days after the emulsion preparation. At day 0, a similar right skewed size distribution was observed for the three perfluorocarbons. As time passed, the size distribution widened, still keeping a right skewed shape. This broadening was always larger for PFP where a substantial number of droplets were getting of micrometric size. This process was slower for PFOB where most particles remained of nanometric size. Droplets' mean diameters were extracted from these size distributions and plotted as a function of time (see Fig. 6). The initial diameters ranged from 230 to 320 nm between the three perfluorocarbons. All the emulsions exhibited an increase in their droplet mean diameter and a broadening in their size distribution over time with a rate dependent on the perfluorocarbon. This rate was always the smallest for PFOB and the largest for PFP. Despite the increase in droplet size, all emulsions remained stable, at least up to 100 days. Indeed, all perfluorocarbon liquid was still in the form of a colloid suspension as no phase transition was observed in the emulsions and no changes in sample density were detected.

1-17 | 7
To study the effect of surfactant chemical structure on droplet size distribution, we used only PFOB emulsions as they exhibited the slowest change in size variation. Emulsions freshly prepared with F 6 TAC n and F 8 TAC n produced stable droplets with similar mean diameter and size polydispersity whatever the DPn value (see Fig. 7 at day 0). However, increasing the length of the surfactant hydrophilic head diminished the droplet size growth (see Fig. 7).

We also monitored the change in droplet size distribution when emulsions made of PFOB and F 6 TAC 13 were stored at several temperatures (4, 25, and 37°C). As shown in Fig. 8, a small difference was observed between emulsions stored at 4 and 25°C. However, the emulsions stored at 37°C exhibited a faster growth in droplet mean size.

Finally, the aging process can be halted by freezing the freshly prepared emulsion, but the droplet coarsening is accelerated after thawing. Thus, the mean droplet diameter reaches 420 nm a day after thawing, whatever the time over which the emulsion was frozen.

Encapsulation

Encapsulation studies were performed using a thalidomide derivative. Thalidomide is a drug world-wide known for tragic teratogenic effects reintroduced as a promising anticancer and anti-inflammatory agent. 63 Although the overall mechanisms by which thalidomide exerts its anti-tumor activity still remain to be elucidated, it is clearly demonstrated that it reduces the levels of proangiogenic factors such as VEGF, bFGF, HGF, as well as TNF-α and several interleukins, the latter being key drivers of inflammation. In this way, thalidomide appears as a "multi-target drug" with promising therapeutic potency in various disorders. 64 In 2010 we reported on the therapeutic potenty of a 5-aminoalkylamino thalidomide analogue Fig. 6 Time variation of the droplet mean diameter when the droplet core was composed of perfluoropentane (△), perfluorohexane ( ), and perfluoro-octyl bromide (⃝). For all emulsions, the volume fraction of droplets was Φ = 24 × 10 -2 . The surfactant used was F 6 TAC 12 at an identical ratio N r = 0.005. The lines represents the fit of the data using Eq. 13: the derived oswald rates were w f (Φ) = 1.79 ± 0.1, 4.5 ± 0.3, and 14.1 ± 0.5 nm 3 /s for PFOB, PFH, and PFP respectively.

(called APA-thalidomide) in decreasing the clinical and pathological scores of experimental autoimmune encephalomyelitis (EAE). 65 A series of APA-thalidomide was prepared and evaluated on several biological targets for inhibition of angiogenesis and/or inflammation. 66 Among them, we recently developed a hydrophobic prodrug of APA-thalidomide, the N-benzyloxycarbonyl-glycine analogue of APA-thalidomide (called Z-Gly-Apathd), and use it as a model drug to investigate the capability of FTAC-stabilized perfluorocarbon nanodroplets for drug encapsulation. Actually, this derivative is a yellow fluorochrome which localization and release from droplets can be easily studied by spectrofluorimetry.

The solubilization in liquid perfluorocarbons of Z-Gly-Apathd was not possible. However, we determined that up to 15 g/l of Z-Gly-Apathd could be solubilized in triacetin. Consequently, during the emulsion preparation, a part of the PFOB volume was replaced by a triacetin solution containing 5 g/l of the drug. Three triacetin-to-fluorocarbon molar ratios were investigated, that were 0.137, 0.272, and 1.37. For the last two ratios, a second phase with a yellow color was visible after emulsion preparation at the bottom of the sample. This suggested that the volume of triacetin containing the solublized Z-Gly-Apathd could not be entirely encapsulated into the emulsion. Whereas the emulsion having a ratio of 0.137 was composed of only one phase homogeneously tinged with a yellow color, indicating that Z-Gly-Apathd was homogeneously distributed into the sample. For the latter ratio, 0.06 ml of PFOB was replaced by a triacetin/Z-Gly-Apathd solution during emulsion preparation, i.e. 10% of the droplet core volume

1-17 | 9
Fig. 7 Time-dependence of droplet mean diameter of of emulsions containing a volume fraction of PFOB droplet equals to Φ = 24 × 10 -2 . For these emulsions N r = 0.005 and the surfactants are F 8 TAC 7 (⃝), F 6 TAC 7 ( ), and F 6 TAC 13 (△). The behavior of triacetin-loaded nanodroplets made of F 6 TAC 7 surfactant is also displayed ( ). The lines represents the fit of the data using Eq. 13 and give as oswald rate values: w f (Φ) = 8.9 ± 0.7 nm 3 /s for F 8 TAC 7 , 7.5 ± 0.7 nm 3 /s for F 6 TAC 7 , 4.0 ± 0.3 nm 3 /s for F 6 TAC 7 with the presence of triacetin, and 2.0 ± 0.1 nm 3 /s for F 6 TAC 13 .

was occupied by triacetin/Z-Gly-Apathd. By using the same molar ratio of triacetin-to-fluorocarbon (i.e 0.137) we could also encapsulate Z-Gly-Apathd in emulsions made of PFH and PFP (data not shown).

After preparation, emulsions were carefully centrifuged (at 885 G, for a total time of 450 s), then washed (at every 90 s of centrifugation) from the stock solution. The fluoresence spectra at λ ex = 363 nm were measured for the washed triacetin- loaded emulsions in the absence and in the presence of Z-Gly-Apathd as well as for the filtered stock solution. No fluorescence signal was detected from the stock solution. The emulsion spectra were compared to spectra measured on triacetin solution (containing 5 mg/ml of Z-Gly-Apathd) and on pure PFOB liquid (see Fig. 10). The triacetin-loaded emulsion with no drug exhibited a single peak located at 412 nm as found for bulk PFOB. In the presence of Z-Gly-Apathd, the emulsion spectrum exhibited a second peak at 519 nm that was obviously characteristic of the drug signal. When the drug was solubilized in triacetin, a single peak was also observed but at 480 nm. Moreover, there was a negligible difference between the fluorescence spectra of the initial emulsion and the centrifuged and washed emulsion.

Additionnal emulsions were prepared by decreasing the ratio N r in order to obtain suspensions mainly made of microdroplets where a fluorescent probe, fluorescein isothiocyanate (FITC), was solubilized into triacetin. Fluorescent microscopy showed that triacetin did not mix with PFOB but formed a corona between the PFOB core and the surfactant shell (data Fig. 8 Change in the mean diameter of PFOB droplets stabilized using F 6 TAC 13 (Φ = 24 × 10 -2 ), when the emulsions were stored at 4 ( ), 25 (⃝), and 37°C (△). The lines represents the fit of the data using Eq. 13 and as oswald rate values: w f (Φ) = 1.3 ± 0.1 nm 3 /s for 4°C, 1.5 ± 0.1 nm 3 /s for 25°C, 2.8 ± 0.1 nm 3 /s for 35°C.

not shown).

Finally, the size growth rate was considerably reduced in the presence of triacetin. By following the time-dependence of the size of these triacetin-loaded PFOB droplets (see Fig. 7), we observed they had grown from an initial mean diameter of 240 ± 10 nm to 430 ± 20 nm after 60 days (the addition of Z-Gly-Apathd did not modify these results). Whereas the mean diameter of triacetin-free droplets reached 700 ± 25 nm over the same period.

Ultrasound backscattering measurements

All backscattering measurements presented herein were performed on F 6 TAC 13 -PFOB emulsions. The impact of volume fraction on SNR mean was evaluated on an emulsion prepared 7 days before experiments (mean diameter = 290 ± 10 nm, mode diameter = 200 ± 20 nm). For this purpose, dilutions were prepared from the initial emulsion solution to obtain several droplet volume fractions ranging from 0.1 × 10 -2 to 2 × 10 -2 . Each point in Fig. 11 represents a SNR mean value obtained from a backscattering measurement performed on one sample. A good reproducibility in SNR mean values was achieved for all volume fractions. Our data clearly show an Fig. 10 Fluorescence spectra of Z-Gly-Apathd are displayed for the case of Z-Gly-Apathd solubilized in bulk triacetin (circles) and when Z-Gly-Apathd is encapsulated in the F 6 TAC 7 -PFOB-triacetin droplets of an emulsion (continous line). As controls, the spectra of bulk PFOB (dash line) and of the emulsion (F 6 TAC 7 -PFOB-triacetin) devoid of drug (dotted line) are also displayed. All spectra were obtained at λ ex = 363. increase in SNR mean value as the volume fraction increases, and this increase is steeper for diluted suspensions (Φ = 0.1 to 0.5 × 10 -2 ) than for concentrated ones (Φ = 0.5 to 2 × 10 -2 ). It should be noted that the conditions of sonication didn't altered the stability of emulsions, as we did not observed significant changes in both size distribution and density after backscattering measurements.

Secondly, the impact of larger droplets on the SNR mean was evaluated by measuring ultrasound backscattering before and after gentle centrifugation (885 G, 45 s) of a fresh F 6 TAC 13 -PFOB emulsion (3 measurements for each solution). The droplet volume fraction Φ was kept at 0.5 × 10 -2 for all backscattering measurements. Size distributions were monitored by SIOS before and after centrifugation as displayed in Fig. 12 along with SNR mean values. We observed little differences in size distributions in the nanometric range as stated by the almost unchanged values of mean and mode diameters. However, a strong decrease in backscattered signals have been measured from the emulsion after centrifugation: the SNR mean value was divided by 2.7. Looking more precisely at size distributions, we can see that even using a small nanopore (NP200), a few microdroplets could be detected before centrifugation but not anymore after centrifugation. Optical measurements using a microscope allowed to detect the presence of microdroplets before centrifugation but only a few of them remained after centrifugation.

Potentiality of the emulsion as 19 F MRI contrast agent

19 F MRI data were acquired on emulsions made of PFOB droplets stabilized with F 6 TAC 13 surfactant, with a mean diameter of 400 nm and at droplet volume fraction ranging from 10 -2 to 5 × 10 -2 . All MRI spectra of emulsions exhibited five peaks (see Fig. 13) that are characteristic of pure PFOB since they were also observed for spectra measured on pure PFOB. They possess different longitudinal relaxation rates and, within the current precision of measurement, these relaxation rates are not modified between emulsion and pure PFOB. In addition, measurements were performed on triacetin-loaded emulsions and triacetin/Z-Gly-Apathd-loaded emulsions of similar droplet sizes and at Φ = 5 × 10 -2 . Presence of neither triacetin nor Z-Gly-Apathd in triacetin did not affect peaks location in the 19 F MRI spectra. Measurements were also carried with pure micelles of F 6 TAC 13 in water.

Discussion

FTAC surfactant in aqueous solutions

By convention, the named F i TAC n used here signifies that there is i carbons bearing fluorine atoms. It differs from some other publications 18,67 where i represents the total number of carbon atoms in the surfactant hydrophobic tail, in this case i includes two additional carbons. Initially, we wished to produce FTAC surfactants with a polar head of increasing length,

1-17 | 11
Fig. 12 Size distributions compared to backscattering measurements for a F 6 TAC 13 -PFOB nanoemulsion at Φ = 0.5 × 10 -2 before (black line) and after centrifugation at 885 g during 45 s (gray line). Mean and mode diameters were similar (within the error margin of the device): 235 ± 10 nm and 174 ± 20 nm, respectively, before centrifugation and 246 ± 10 nm and 175 ± 20 nm, respectively, after centrifugation.

from n (or DPn) = 1 to 30, by following published protocol on FTAC synthesis. We believed the expected DPn values were achieved according 19 F-NMR measurements. However, a HPLC analysis revealed that these results were biased due to the formation of polyTris oligomer or polymer (without fluorinated tail) as a side product in the synthesis of telomers with expected DPn over 12-13. The formation of this polyTris derivative can be ascribed to the faster consumption of the telogen compared to the monomer one, leading to a mixture made of low DPn (less than 13) fluorinated telomers and non-fluorinated oligomers or polymers. This sidereaction is probably due to the conditions of telomerization experiments applied for the synthesis of peracetylated telomers (see Fig. 2 conditions (a)) Indeed, the kinetic behavior of both monomer 1 (peracetylated THAM) and telogen reactants (perfluoroalkylthiol) seems to be strongly dependent on the nature of the solvent, as previously described by Loubat and Boutevin. 68 These authors reported an increase of the monomer consumption (resulting in high DPn values) when telomerization was performed in water rather than in organic media. In the future, mixtures of THF and water will be explored as reaction middles in order to reach a similar consumption of both monomer and telogen corresponding to the ideal case of telomerization (i.e. transfer constant CT = 1). For now, we obtained FTAC with DPn = 1, 7, 12, and 13, but larger values could not be reached. The water solubility of FTAC is directly correlated to their average degree of polymerization DPn. For FTAC having C 6 F 13 C 2 H 4 and C 8 F 17 C 2 H 4 fluorinated chains, it has been shown that their hydrosolubility appears for DPn > 4. [START_REF] Barthélémy | The synthesis and biomedical applications of various telomeric structures[END_REF] Indeed, we could solubilize all of our FTAC surfactants in aqueous solutions, except for monoadduct ones (i.e. for DPn = 1). When solubilized in water, FTAC forms micelles above a critical micelle concentration (see Table 1) to shield their perfluorocarbon chain from water. 49 These micelles possess a diameter of ∼ 8 and ∼ 11 nm for F 6 TAC n and F 8 TAC n surfactants, that does not seem to depend on DPn values. Because fluoroalkanes are more hydrophobic than their hydrogenated counterparts, fluorosurfactants are less soluble in water and their CMC is much lower. [START_REF] Mukerjee | Critical micelle concentrations of aqueous surfactant systems, Office of Standard Reference Data[END_REF] Pavia et al. did not observe a significant variation in CMC for DPn ranging from 4-5 to 12, whereas we did observe a difference. Our CMC value almost doubled from DPn = 7 to 13. We also observe that the addition of a CF 2 group decreases the CMC by a factor of 30 -60, while a factor 5 -10 times is obtained by the addition of a CH 2 group in the hydrophobic tail of regular surfactants. [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF]

FTAC surfactant at water/air and water/PFC interfaces

A characteristic feature of surfactants is to decrease the tension of an interface between an aqueous and hydrophobic environment like air or oil. Most of data about surfactants concerns the surface tension at the water/air interface. For comparison we performed such measurements and surface tensions of about 26 -31 mN/m were measured for FTAC surfactants. These values are close to what can be measured for nonfluorinated surfactants, that is in the range of 24 -54 mN/m. [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF] The measurement of the interfacial tension between water and perfluorocarbon liquid is more relevant for perfluorocarbon emulsions since this parameter will dictate the stability of the droplet as well as its temperature of vaporization. Unfortunately, data are scarce in this domain. Most published measurements were performed at PFOB/water interface, their values are reported in Table 1. In the absence of surfactants, our value of interfacial tension at the water/PFOB interface is about γ I = 48.7 mN/m, close to the values (51 ± 1 mN/m) reported in the literature. The addition of FTAC logically decreased the interfacial tension. While there is not difference in γ I values between F 8 TAC 7 and F 8 TAC 13 , we mea- sured a significant difference between F 6 TAC 7 and F 6 TAC 12 or F 6 TAC 13 . Surprisingly, the order of magnitude of these values is similar to what has been measured for non-fluorinated surfactants (7 -16 mN/m for NaL and SDS) and even larger than for lipids (1-10 mN/m for (C n ) 2 PC, 12-2-O, and DPPC) (see Table 1). Bertilla et al. showed that the interfacial tension in the presence of lipids can be further decreased by adding semi-fluorinated surfactants in the perfluorocarbon liquid: from ∼ 24 mN/m for DMPC, DLPC, and PLC8 down to ∼ 2 mN/m.

FTAC as emulsifier for perfluorocarbon/water emulsions

Various approaches exist for emulsion preparation, among them stirring, [START_REF] Abismaïl | [END_REF] high-pressure microfluidizing, 73 ultrasonic homogenizing, [START_REF] Abismaïl | [END_REF]74 and microfluidics. 75 Ultrasonic homogenizing was chosen because it is a technique that is more easily found in laboratories. On the downside, it has been shown that the result of an emulsion prepared by sonication depends on various parameters. 74 These parameters include the type of vessel containing the emulsion, the quantities of added solvent, the type of ultrasonic tip, the power applied on this tip, the time of sonication, and the position of the tip into the sample. We have optimized our ultrasonic parameters when plastic centrifuge tube of 15 ml were used and where the quantity of perfluorocarbon and aqueous solutions were always kept the same, i.e. 0.6 and 2 ml respectively. Our DLS and SIOS measurements showed that the prepared samples were a suspension of perfluorocarbon droplets as confirmed by our compressibility measurements. Indeed the value of the droplet partial compressibility was similar to the value of bulk perfluorocarbon liquid. In addition, it was possible to predict the emulsion density with a good accuracy based on the added volumes of bulk perfluorocarbon and aqueous liquids, which densities were separately measured. Thus, the surfactant contribution to density and compressibility appears to be negligible. At the day of preparation (i.e. day 0), the droplet exhibited a size that was mainly nanometric but with a significant polydispersity (d 90 /d 10 = 2.3 ± 0.1). If the initial mean diameter was 230 nm for PFOB, 280 nm for PFH, and 320 nm for PFP (Fig. 6), particles up to 700 nm (Fig. 5) were easily detected on SIOS using a strechable nanopore NP200 which initial (i.e. barely stretched) covered size range is 100 -400 nm. Larger microscopic droplets were also visible under microscope. Additionnal SIOS investigations using larger nanopores allowed to estimate that these large particles (> 700 nm) represent less than 1% of the total droplet volume fraction. It was possible to remove these microparticles using centrifugation, while filtering led to a destabilization of the emulsion.

In the absence of surfactant, droplets are expected to coalesce, exhibiting an exponential increase in mean diameter according to the van den Tempel theory. 76,77 The presence of FTAC surfactants should prevent coalescence through steric interactions if the whole droplet surface is coated by surfactant. 78 However, after sonication, the newly formed droplets are not immediately fully coated by surfactants, leaving some time to droplet coalescence. Once all the present surfactants are located on droplet surface, coalescence may still continue to take place until the droplet surface has reduced enough (i.e. increase in volume and decrease in number) to get fully coated. This process explains why adding less sur-factants leads to larger droplets as shown in Fig. 4. Whereas, if more surfactant is added than could bear all droplet surfaces, the surfactant will form micelles. At high concentration (N R > 0.006), these additional surfactants will be prone to stabilize the bubbles created by the sonication process and be responsible of the foam formation observed in our samples.

However, even if the coalescence is suppressed by surfactants, an increase in droplet mean diameter will still be observed over time. This behavior can be ascribed to the Ostwald ripening (OR) or molecular diffusion, that has been shown to occur for perfluorocarbon emulsions stabilized with phospholipids 50 and fluorinated surfactants. 53 This process is described by the Lifshitz-Slyozov-Wagner (LSW) model, [79][80][81] which predicts a linear relationship between the cubic mean radius R 3 and time t:

dR 3 dt = 8 9
Sγ I V 2 m D RT f (Φ) = w f (Φ) (13)
where in our case, γ I is the interfacial tension at the water/perfluorocarbon interface (in the presence of surfactant), S and D are respectively the solubility and the diffusion coefficient of the perfluorocarbon in water, V m is the perfluorocarbon volume, R is the gas constant, T is the absolute temperature, f (Φ) a correction factor taking into account the droplet volume fraction (= 1 at low dilution), and w is the rate of the molecular diffusion of a perfluorocarbon molecule. We used Eq. 13 to fit all our aging curves involving mean diameters and values of w f (Φ) are reported in the figure legends. In these fits, we systematically discarded the first points (i.e. at day 0 and day 1) to obtain an acceptable fit for PFOB and PFH, but we did not observe this problem for PFP. The problem is also reduced by increasing temperature, indeed for emulsions kept at 37°C only the measurements made at day 0 was discarded. This reflects the fact Oswald ripening started to be dominant after a few days. From our fits, we observe that the "corrected" Oswald rate w f (Φ) increases when DPn decreases (Fig. 7) or temperature (Fig. 8) increases. These results are understandable as surfactants with longer polar head provide a better barrier against the passage of perfluorocarbons and higher temperature increases perfluorocarbon solubility in water. w f (Φ) naturally depends on the perfluorocarbon liquid used in droplets (see Fig. 6) since PFC possess different properties. It was possible to directly derive w since all parameters in Eq. 13 have been determined. Several models provide an estimation of the value of f (Φ). 82 For a volume fraction of Φ = 24 × 10 -2 , f (Φ) equals to ≈ 2.2 ± 0.3 in most models. However, it should be emphasized that during emulsion storage droplets sediment. This may locally induce a higher fraction volume, hence the value of f (Φ) can be much larger. When taking f (Φ) ≈ 2.2, we obtain w f (Φ) = 1.7 nm 3 for F 6 TAC 12 and F 6 TAC 13 , in good agreement with the values derived from the fits in Figures 6,7, and 8. For PFOB, the calculation of w f (Φ) slightly varies, from 1.2 to 1.7 nm 3 , depending of the FTAC. Whereas fits of Fig. 7 show a variation from 2 to 9 nm 3 . As the properties of PFOB should be the same between the various FTAC and the error measured in γ I is small, this disagreement probably comes from differences in the values of f (Φ). Indeed, a larger droplet size induces a faster sedimentation and hence a larger local volume fraction. Besides, still keeping f (Φ) ≈ 2.2, we obtain for F 6 TAC 12 the values w f (Φ) = 67 nm 3 and w f (Φ) = 862 nm 3 for PFH and PFP, respectively. These values are too different from the values derived in Fig. 6 to be due only to a variation in f (Φ) values. This disagreement is probaly due to a wrong estimation in the perfluorocarbon solubilities in water. These values were, indeed, derived by Kabalnov et al. using Eq. 13 to fit experimental data recorded for several hours (up to a few days). 54,55 In their case the extracted Oswald rate are much larger than our rate measured over several months.

Taking Fig. 8, we observed that the Oswald ripening process takes place for 100 days, as a fit by Eq. 13 was only possible during this period. After this period the droplet mean diameter remained constant on longer time but there is no satisfactory explanation for this behavior.

Finally, for an emulsion made of F 6 TAC 13 and PFOB, the replacement of the solvent by a saline 9‰ NaCl solution (for intravenous injection purpose) did not change the aging behavior for 30 days.

Our data show that despite the fact that our emulsions are not a thermodynamically stable system, they exhibit a lifetime of a few months. Indeed, after droplets sedimentation, an homogeneous sample is easily recovered after gentle stirring. Consequently, the emulsions can be either simply stored in a fridge or put into a freezer for a longer storage time, depending of the maximum droplet mean size we wish not to exceed.

Ultrasound backscattering measurements

The two-step increase behavior of SNR mean observed with droplets volume fraction is well known. Many experimental and simulation studies, including those dealing with perfluorocarbon particles, 8,83 have reported such a result. In all these studies, the incoherent backscattered signal intensity also increases dramatically with volume fraction for dilute suspensions. Indeed, theoretical models (Morse and Ingard, [START_REF] Morse | Theoretical Acoustics[END_REF] Faran 85 ...) predict that for diluted small spherical particles solutions, the incoherent scattered intensity by N particles is the sum of the scattered intensity by each particle. Those models are valid only if: (1) the incident wavelength λ > 2πR (R is the particle radius), (2) the region F containing the scatterers is considerably larger than λ , and (3) the region F is far from the transducer. As all those criteria are met in the present study, it can be assumed that the first part of the curve is representative of such behavior, also often referenced as Rayleigh linear scattering. In the present study, SNR mean does also include attenuation mechanisms that prevent the curve to be fully linear. 86 Those mechanisms can be taken in account by applying to the measured signals some appropriate correction factors. In that case, only the incoherent backscattered waves are represented and a linear curve can be obtained. 23 For concentrated suspensions, the SNR mean reaches a plateau which is representative of multiple scattering as well as attenuation effects. Briefly, in concentrated suspensions, backscattering from the region F cannot be considered anymore as a simple sum of the contribution of every particles as the short distance between particles lead to strong interactions (re-scattering and absorption of scattered waves). [START_REF] Morse | Theoretical Acoustics[END_REF] Thus, concentration has a significant impact on backscattering intensity, but droplet size has even a higher impact on it. Indeed, Morse and Ingard predicted that the scattering cross section for a particle is directly proportional to its radius to the sixth power as well as to incident wave frequency to the fourth power (see Born approximation equation 8.2.19 [START_REF] Morse | Theoretical Acoustics[END_REF] ). Then, at a given frequency range, it is critical to check for the presence of microparticles in the emulsion, even if their concentration is very low. Our centrifugation experiment clearly illustrates that point with a SNR mean divided by almost 3 after centrifugation which means that Power Spectral Density was reduced by nearly a cube root. A more detailed quantification of these microparticles with SIOS technique as well as their precise impact on backscattered signal will be investigated in a future work.

In summary, the present study shows that backscattering measurement is a very sensitive tool for the detection of small amounts of liquid PFC microparticles in heterogeneous micro/nano-particles suspensions. Those microparticles can totally change ultrasonic properties of solutions and are usually formed in emulsions. Thus, a special care should be given to remove those microparticles. Finally our results show that the weak echogenicity of liquid perfluorocarbon nanoparticles prevents their use as ultrasound constrast agent in agreement with the investigation of Couture et al. 23

Potentiality of the FTAC stabilized nanodroplets as theranostic agent

Both hydrophilic and hydrophobic drugs can not be solubilized in liquid perfluorocarbons. Consequently, to help drug solubilization into perfluorocarbon droplets, an additive solvent is required. In our case, we were interested in the encapsulation of a fluorescent thalidomide derivative (Z-Gly-Apathd). This hydrophobic prodrug has recently exhibited an interesting and unexpected anti-apoptotic effect in a photodynamic therapy (PDT) induced apoptosis model (unpublished result). Since liposoluble drugs, like thalidomide derivative or paclitaxel, can be solubilized in oil, the more convenient way would be to use oil as a drug solvant. In the past, vegetable oils such as soya bean oil, olive oil, and canola oil have been mostly used in perfluorocarbon drug carriers. 7,87,88 Unfortunately, Z-Gly-Apathd exhibited a poor solubility in these oils (less than 0.1 g/l). Instead, we used triacetin, a simple and biocompatible triglyceride, which could dissolve up to 15 g/l of Z-Gly-Apathd. Our fluorescence results show, indeed, that the addition of a volume of solubilized drug in triacetin during emulsion preparation led to the drug encapsulation. However, the triacetin solution did not get solubilized into the perfluorocarbon, instead it formed a corona between the perfluorocarbon droplet and the surfactant shell. Since 5 g/l of triacetin was occupying 10% of droplet volume, a total of 3 mg of drug was encapsulated in the 2.6 ml of emulsion. Interestingly, the presence of triacetin reduced the growth rates of the droplet size (as well as its polydispersity from d 90 /d 10 = 2.3 to 1.9 ± 0.1). A similar result was described for perfluorocarbon emulsions prepared with the addition of hexadecane in the droplets. 89 In addition, our preliminary data show that PFOB nanoemulsions could be detected in vitro at a volume fraction of 1 × 10 -2 by 19 F MR spectroscopy and imaging at 3T, with isotropic 3×3×3 mm 3 voxel size. In our measurements, a 3D matrix sized 128 × 64 × 40 was acquired in 6 m with an average SNR value of 3.35 for the highest signal peak, determined after reduction of bias in GRE magnitude data according to Gudbjartsson and Patz. [START_REF] Gudbjartsson | Fig. 13 Result of 19 F MRI measurements performed on an emulsion made of PFOB-F 6 TAC 13 droplets having a mean diameter of 400 nm and at a volume fraction of Φ = 5 × 10 -2 . a) and b) Relative magnitude spectra, using low (20°) and respectively high (90°) flip angle, TR = 205 ms. c) Non-selective excitation heavily T1[END_REF] Note that the 19 F detection coil used in this study can be further optimized, for instance, by upgrading to a bird-cage quadrature type which should improve both the sensitivity and spatial homogeneity of the signal. The detected 19 F MRI signal of FTAC-PFOB nanoemulsion have mainly the characteristics of pure PFOB, even with the addition of triacetin. It is interesting to note that samples made of only fluorinated surfactant micelles in water can be detected and present a specific spectrum. However, in the spectra measured on FTAC-PFOB nanoemulsions samples, the characteristic peak of the FTAC surfactant is buried into the noise.

The benefit of having stable nano-agents with both imaging and therapeutic ability would be an asset in the evaluation of cancer treatment. Indeed, current commercialized nanodrug carriers such as liposomes (for example Doxil®/Caelyx®) cannot be imaged. Consequently, it is not possible to assess if these carriers have extravasated into tumor tissues (i.e. especially for tumor with a neovascularization that is not developed enough or that exhibits too small inter-endothelial gaps). The treatment fails if the carrier accumulation in such tissues is not sufficient, and precious time that could have been used for an alternate treatment is lost.

Conclusion

It was possible to prepare emulsions with PFOB, PFH, and PFP, where FTAC surfactants form the droplet shell and help to prevent droplet coalescence. The droplet mean diameter of an emulsion could be as small as 230 nm for PFOB but constantly increased for the first 100 days due to Ostwald ripening. All size distributions were right skewed with a small amount of microdroplets (< 1%) that can be removed by centrifugation. In addition, these microdroplets appeared to be the main contributor to the signal backscattered by emulsions in our ultrasonic measurements. In their absence, the Signalto-Noise Ratio is small that prevents any use of a suspension of nanodroplets as ultrasound contrast agent, unless they could be vaporized. However, the suspensions of nanodroplets could be detected in vitro in a clinical 3 T MRI scanner, which open the door for further in vivo investigations as 19 F MRI contrast agent. Furthermore, we succeeded in encapsulating a hydrophobic drug into the perfluorocarbon droplets by adding triacetin, which is a first step toward the study of the localized therapeutic ability of such agents. In the next step we will study the toxicity and therapeutic effect of our emulsions on tumor cells in vitro and assess their potential as theranostic agent in small animal.

Fig. 1

 1 Fig. 1 The chemical structure of fluorinated surfactants F i TAC n is composed of a polar head made of n repeating Tris units (n = DPn is the degree of polymerization) and of a hydrophobic moiety made of fluorine atoms (C i=6 F 13 C 2 H 4 or C i=8 F 17 C 2 H 4 ).

Fig. 2

 2 Fig. 2 Synthesis of fluorinated surfactants. Reagents and conditions: (a) AIBN/THF, reflux (62-66%); (b) AIBN/CH 3 OH, reflux (62-73%); (c) MeONa cat. /MeOH, room temperature (100%)

  Ultrasonic echogenicity of emulsions was determined from ultrasound backscattering measurements performed on a dedicated setup. Sample solutions were placed in a hollow cylindrical stainless steel chamber (30 mm in diameter and 3 mm in depth) maintained at 25°C by a water circulation bath. The chamber was sealed with a cellophane membrane outstretched on a transparent tube. An ultrasonic focused transducer (model PI 50-2, Panametrics Inc., USA) was immersed into the water-filled tube. Its focal spot was positioned into the sample solution using a micro-control translation stage (VT-80, PI miCos, Eschbach, Germany). An optimized distance of 1.25 mm between the membrane and the center of the focal spot was used to minimize the influence of both sample solution attenuation and membrane vibrations on backscattered signals. The transducer was a 41 MHz PVDF transducer (34.25 -47.75 MHz, -3 dB frequency bandwidth) with a 13 mm focal length and a 0.07 × 1 mm 2 (-3 dB) focal zone. Single short negative pulses (1 µJ energy) were generated in the sample at a 200 Hz repetition rate using a 200 MHz pulserreceiver (Panametrics Sofranel 5900 PR). Backscattered signals from the sample were received by the transducer/receiver set and digitized at a sampling rate of 2 GHz on a digital oscilloscope with a 8 bits vertical resolution (model WS424, Lecroy, USA). For each sample 100 signals were acquired and transferred to a personal computer for signal processing using MATLAB . To select the zone of interest inside the sample, the signal processing consisted in the multiplication of each acquired signal by a Hann window of 2671 points (corresponding to the 1 mm length of the focal zone). The Power Spectrum density (PSD) of each resulting signal s(t) was calculated. Both operations were made at once using the modified periodogram method of MATLAB. This method is almost equivalent of calculating PSD as follows: PSD = |S(ν)| 2 where S(ν) is the Fast Fourier Transform of s(t). The difference lies in the use of a normalization factor that compensates for energy losses due to windowing.Echogenicity of an emulsion was finally evaluated in comparison to control measurements in water by calculating the 1-17 | 5

  1,2-diacyl-sn-glycero-3-phosphocholines (C n ) 2 PC, dipalmitoylphosphatidylcholine (DPPC), and decaglyceroldioleate (12-2-O). a values extracted from Pavia et al. 18 ; b from Trevino et al. 48 ; c from Boyer et al.

Fig. 3

 3 Fig. 3 Size distributions measured by SIOS (histogram) and DLS (solid line) of an emulsion made of F 6 TAC 7 and PFOB in water.

Fig. 4

 4 Fig. 4 Droplet mean diameter as a function of the surfactant to perfluorocarbon molar ratio N r for F 6 TAC 7 -PFOB emulsion made of PFP (△), PFH ( ), and PFOB (⃝).

Fig. 5

 5 Fig. 5 Size distribution at day 0 (top) and day 90 (bottom) of droplets made of PFOB (black), PFH (gray), and PFP (light gray) and stabilized with F 6 TAC 13 surfactant.

Fig. 9

 9 Fig.9Structure of the hydrophobic drug Z-Gly-Apathd that exhibits high anti-angiogenic efficacy

Fig. 11

 11 Fig. 11 SNR mean as a function of droplet volume fraction extracted from backscattering measurements on F 6 TAC 13 -PFOB nanoemulsion (mean diameter: 290 ± 10 nm, mode diameter: 200 ± 20 nm).

  49 ; d from Kabalnov et al.50 ; e from Habif et al.51

	molecule	CMC (mM)	D micelle (nm)	K o S,micelle (m 3 kg -1 Pa -1 ) (mN/m) (mN/m) γ S γ I
		±0.005	±0.5	±0.2 × 10 -13	±0.4	±0.4
	F 6 TAC 7	0.36 0.35 a	7.9	1.4 × 10 -13	26	9.1
		0.38 c
	F 6 TAC 12	0.614 0.32 a	8.3	0.7 × 10 -13	27.8	12.1
	F 6 TAC 13 F 8 TAC 7	0.621 0.006 0.031 a	8.2 10.6	0.8 × 10 -13 1.2 × 10 -13	31	12.1 10.7 11.8 a
	F 8 TAC 12	0.020 0.035 a			31
	F 8 TAC 13 NaL	0.017 7.1 b	10.8	1.0 × 10 -13	31	10.4 7.5 b
	SDS				18 e	10 e
						16 d
	(C 6 ) 2 PC				31 d	9.8 d
	(C 7 ) 2 PC				28 d	7.3 d
	(C 8 ) 2 PC				25.5 d	5.8 d
	(C 9 ) 2 PC				24.8 d	5.3 d
	(C 11 ) 2 PC				24 d	4.4 d
	(C 12 ) 2 PC DPPC				24 d	4 d 1 e
	12-2-O					6 e

Table 2

 2 The table displays molecular weigh, M w , boiling point, B p , solubility in water S, diffusion coefficient in water, D, density ρ, sound velocity U, and adiabatic compressibility K o S,PFC of three perfluorocarbon liquids. In addition there is adiabatic compressibility K o S,droplet of a PFC droplet in water and the interfacial tension γ I between PFC and water. Values without a footnote have been measured or calculated by us. a are given by ABCR; b from Riess 53 ; c from Kabalnov et al.54 . d from Kabalnov et al.55 ; e measured at 25°C by Marsh et al.56 ; f measured at 21.3°C by Hall et al.57 ; g measured at 25°C by Cusco et al.58 ; h from Pavia et al.18 ; i from Kabalnov et al.50 ; j from Habif et al.51 ; k from Legrand et al.59 ; l from Nishikido et al.60 ; l from Clasohm et al.61 ; m from Halper et al.62

		PFOB	PFH	PFP
	Formula M w (g mol -1 )	C 8 F 17 Br 498.99 a	C 6 F 14 338.06 a	C 5 F 12 88.05 a
	B p (°C)	141-143 a	57 a	29 a
	S (mol m -3 )	5 × 10 -6 b , 5.1 × 10 -6 c	2.7 × 10 -4 d	4 × 10 -3 d
	D (m 2 s -1 )	5.2 × 10 -10	6.4 × 10 -10	7.0 × 10 -10
	ρ (kg m -3 )	1920, 1930 a , 1918 e	1670, 1682 a	1603, 1600 a
	U (m s -1 )	631.8 f , 623.7 e	548 g	477 g
	K o S,PFC (m kg -3 Pa -1 ) K o S,droplet (m kg -3 Pa -1 ) γ I (mN m -1 )	6.9 × 10 -13 6.7 × 10 -13 48.7, 50.7 h , 51.8 i , 50 j	1.2 × 10 -12 1.3 × 10 -12 38 k , 57.2 l , 55 c , 56.1 m	1.7 × 10 -12 1.9 × 10 -12 56 k , 55 c

Journal of Materials Chemistry B

| 1-17

Journal of Materials Chemistry BJournal of Materials Chemistry B Accepted Manuscript

Journal of Materials Chemistry B Accepted Manuscript

Acknowledgements

This work was supported by the grant ANR-10-NANO-06 overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir", a grant " Émergence UPMC 2010" (project NACUNAT) from the University Pierre et Marie Curie, and the Swiss National Foundation of Science grant number 31NM30 152045. The authors thank Dr. Jean-Noël Hyacinthe (from the Biomedical Image Center (CIBM), University of Geneva) for providing the 3D 19 F MRI sequence.


Sébastien Becker

Emilie Devijver

Rémi Molinier

Noël Jakse

Unsupervised topological learning approach of crystal nucleation in pure Tantalum

Unsupervised topological learning approach of crystal nucleation in pure Tantalum Sébastien Becker (1, 2), Emilie Devijver (2), Rémi Molinier (3), and Noël Jakse (1)

(1) SIMaP, Univ. Grenoble Alpes, CNRS, Grenoble INP (2) LIG, Univ. Grenoble Alpes, CNRS, Grenoble INP (3) IF, Univ. Grenoble Alpes, CNRS

We propose an unsupervised machine learning method for the autonomous structural analysis of materials based on original topological descriptors of local atomic structures computed from persistent homology [1,2]. From this protocol, a model is learned in course of nucleation in order to identify, without a priori on a system, clusters of atomic structures which arise in the process. This method has been applied to investigate the homogeneous nucleation of elemental Tantalum (Ta), on several molecular dynamics configurations of 10 million atoms at the nose of the time-temperature-transformation curve. A general behavior for all the nuclei (even the precritical ones) shows a concurrent emergence of the translational and orientational orderings in this pure metal.

Abstract Molecular dynamics simulations

 Large-scale simulations with LAMMPS [3]:

• (N,P,T) This unsupervised TDA-GMM approach opens the way to autonomous application in the studies of structural dependant phenomena at the atomic scale. Extension of the nucleation analysis on multicomponent systems is especially relevant for a deeper inspection and control of such mechanisms to enhance materials design. As a perspective, it would be interesting to extend the method to learn the time evolution, e.g., through recent generalization of the persistent homology to time series [8].

Perspectives

[1] H. Edelsbrunner, D. Letscher, and A. Zomorodian, Discrete Comput Geom 28, 511 (2002).

[2] A. Zomorodian and G. Carlsson, Discrete Comput Geom 33, 249 (2005).

[3] S. J. Plimpton, J. Comput. Phys. 117, 1 (1995).