Thomas Dabat
email: thomas.dabat@univ-poitiers.fr

Patrice Porion

Fabien Hubert

Erwan Paineau

Baptiste Dazas

Brian Grégoire

Emmanuel Tertre

Alfred Delville

Eric Ferrage
email: eric.ferrage@univ-poitiers.fr

Influence of preferred orientation of clay particles on the diffusion of water in kaolinite porous media at constant porosity

Keywords: clay minerals, porous media, anisotropy, particle orientation, water diffusion

Solute transport in natural or artificial compacted clay porous media is receiving particular attention in the contexts of waste storage and the design of materials with tuneable physical properties. In these contexts, the porosity is commonly considered as a primary parameter controlling the diffusional properties of water and solutes in these systems. However, little attention has been given to the role played by anisotropy in the particle orientation. In this study, the influence of the preferred orientation of clay particles on the water diffusion anisotropy in two kaolinite porous media obtained by compaction and centrifugation methods (for a constant porosity value of ~0.5) was investigated by coupling experiments and simulations. An increase in the preferred orientation of kaolinite particles, as quantified by X-ray scattering analysis, was found to be logically associated with an enhanced anisotropy in water diffusion obtained from pulsed gradient spin echo attenuation measurements by nuclear magnetic resonance of protons.

Brownian dynamics simulations performed on three-dimensional virtual porous media, mimicking the shape and orientation of the particles in the samples, led to calculated water diffusion coefficients in agreement with experimental data. Once validated, this computational work was extended to a wide range of degrees in the preferred orientation of particles. The results showed that this parameter leads to an increase and a decrease in pore water diffusion coefficients along and across the mean orientation plane, respectively, up to a factor ~2. The directional diffusion anisotropy was also found to range between 1 and ~5 for the most isotropic and anisotropic organisations, respectively. This study hence provides quantitative insights into the impact of the preferred orientation for the prediction of water diffusion in compacted clay media.

Introduction

The understanding of solute transport in compacted clay-based porous media has considerable importance in the fields of nuclear waste storage in deep geological formations [START_REF] Altmann | Diffusion-driven transport in clayrock formations[END_REF][START_REF] Charlet | Diffusive transport and reaction in clay rocks: A storage (nuclear waste, CO2, H2), energy (shale gas) and water quality issue[END_REF] and the design of innovative materials with fluid barrier efficiency [START_REF] Aulin | High strength, flexible and transparent nanofibrillated cellulose-nanoclay biohybrid films with tunable oxygen and water vapor permeability[END_REF]. For these systems, macroscopic transport models based on the Fickian expression of the diffusion process of a non-sorbing tracer rely on its effective diffusion coefficient 𝐷 𝑒 , defined by [START_REF] Bourg | Tracer diffusion in compacted, water-saturated bentonite[END_REF][START_REF] Tournassat | Ionic Transport in Nano-Porous Clays with Consideration of Electrostatic Effects[END_REF][START_REF] Tinnacher | Ion adsorption and diffusion in smectite: Molecular, pore, and continuum scale views[END_REF]:

𝐷 𝑒 = 𝜀 𝐺 𝐷 0 ( 1
)
where 𝜀 is the porosity of the porous medium, 𝐷 0 the diffusion coefficient of the tracer in bulk liquid water, and 𝐺 the tortuosity factor related to the geometry of the pore network. The diffusion coefficient of the tracer 𝐷 in the pores, related to this 𝐷 𝑒 entity by 𝐷 𝑒 = 𝜀. 𝐷, is thus expressed as follows:

𝐷 = 1 𝐺 𝐷 0 (2)
In Eq. ( 2), all information regarding the geometry of the pore network, including the distributions in the size, shape, orientation, and connectivity of the pores, is contained in the entity 𝐺. Although different experimental methods such as microscopy techniques can be used to access specific properties of the porous network [START_REF] Keller | The Pore Structure of Compacted and Partly Saturated MX-80 Bentonite at Different Dry Densities[END_REF][START_REF] Gaboreau | Optimization of pore-network characterization of a compacted clay material by TEM and FIB/SEM imaging[END_REF][START_REF] Leu | Multiscale description of shale pore systems by scanning SAXS and WAXS microscopy[END_REF][START_REF] Backeberg | Quantifying the anisotropy and tortuosity of permeable pathways in clay-rich mudstones using models based on X-ray tomography[END_REF][START_REF] Takahashi | 3D-microstructure analysis of compacted Na-and Csmontmorillonites with nanofocus X-ray computed tomography and correlation with macroscopic transport properties[END_REF], the quantitative prediction of the geometric factor 𝐺 value for a given porous medium remains a challenging task in the field of macroscopic transport modelling.

Because of their lamellar shape, clay particles most often display a preferred orientation, leading to anisotropy in the morphology of the pore network and having a considerable impact on the transfer properties of water and solutes. For instance, experimental studies have evidenced a significant variation in the measured water effective diffusion coefficients in the direction parallel or perpendicular to the bedding of different natural argillaceous rocks [START_REF] Van Loon | Anisotropic diffusion in layered argillaceous rocks: a case study with Opalinus Clay[END_REF][START_REF] García-Gutiérrez | Largescale laboratory diffusion experiments in clay rocks[END_REF][START_REF] Xiang | Diffusive anisotropy in low-permeability Ordovician sedimentary rocks from the Michigan Basin in southwest Ontario[END_REF][START_REF] Gimmi | Anisotropic diffusion at the field scale in a 4-year multi-tracer diffusion and retention experiment -I: Insights from the experimental data[END_REF][START_REF] Jacops | The Dependency of Diffusion Coefficients and Geometric Factor on the Size of the Diffusing Molecule: Observations for Different Clay-Based Materials[END_REF]. Furthermore it was also demonstrated that the increase in the diffusion anisotropy was qualitatively linked to a more pronounced preferred orientation of clay particles in the different samples [START_REF] Wenk | Preferred orientations and anisotropy in shales: Callovo-Oxfordian shale (France) and opalinus clay (Switzerland)[END_REF]. Although the quantitative correlation between the water diffusion and porosity parameter has been subjected to a large number of studies [START_REF] Van Loon | A modified version of Archie's law to estimate effective diffusion coefficients of radionuclides in argillaceous rocks and its application in safety analysis studies[END_REF]Charlet et al., 2017 and references therein), little is known regarding the quantitative impact of the degree of preferred orientation on the diffusional properties of water and solutes. To obtain a complete understanding of this specific contribution, additional work on samples of model clay porous media with controlled porosity and anisotropic properties in the particle orientation is required.

In that context, the present study focuses on the water diffusion properties in two model porous media prepared from KGa-2 kaolinite particles with similar porosity but different particle orientations. The quantitative measurement of preferred orientation of the particles in these samples will be performed using X-ray scattering (XRS) analysis. An experimental analysis of the anisotropy in the water diffusion will be performed using pulsed gradient spin echo attenuation measurements by nuclear magnetic resonance (PGSE-NMR) of protons.

Information regarding the particle size, shape and orientation will then be used to build 3D virtual porous media, for which Brownian dynamics simulations will be performed to analyse the water diffusional properties in the pore network. This computational methodology was recently shown to be efficient in connecting the different time scales of the diffusional process of water and solutes in compacted clay porous media [START_REF] Tyagi | Multi-scale micro-structure generation strategy for up-scaling transport in clays[END_REF][START_REF] Bacle | Modeling the transport of water and ionic tracers in a micrometric clay sample[END_REF].

Once validated against experimental data, the computational methodology will be extended to a wide range of degrees in preferential orientation of particles. The obtained results will eventually help us to obtain quantitative insights into the role played by the preferential orientation in the variation of the diffusional properties in these systems.

Materials and methods

Starting material

The kaolinite KGa-2 from the Source Clay Repository of the Clay Mineral Society was used to prepare the different porous media. The average size of kaolinite particles is approximately 0.5 µm [START_REF] Hassan | AFM and lowpressure argon adsorption analysis of geometrical properties of phyllosilicates[END_REF] and their structural formula is [(Al3.80Ti0.13Fe 3+ 0.07) (Si3.84Al0.16) O5(OH4)] ( [START_REF] Mermut | Baseline studies of the clay minerals society source clays: chemical analyses of major elements[END_REF]. The original kaolinite powder was Na-saturated using three saturation cycles in a 1 mol/L NaCl solution to obtain homoionic samples. Dialysis in deionised water was then used to remove the excess salt until a silver nitrate test for Cl -was negative. Finally, the kaolinite dispersion was dried in an oven at 60°C and then sieved through a 50 µm mesh to remove coarse aggregates.

Preparation of porous media with contrasted anisotropy

Two porous media made of kaolinite powder were prepared in order to obtain a similar porosity value 𝜀 but contrasted anisotropy degrees in particle orientation. The first sample was obtained by uniaxial compaction of the initial powder in a poly(tetrafluoroethylene) (PTFE) cylinder with a diameter of 0.64 cm and a height of 7.5 cm. The kaolinite powder was introduced in the tube, the tube placed in a metallic cell with a bottom cap to prevent widening, and the powder then compressed to end up with a compacted kaolinite sample of 1 cm in height.

The second sample was obtained by a centrifugation process directly in the PTFE tube placed in a poly(methyl methacrylate) (PMMA) cell to avoid deformation. To do so, the initial kaolinite powder was first dispersed in water (50 g/L). A 1 mL aliquot of the obtained dispersion was then introduced in the PTFE tube and centrifuged horizontally at approximately 18 000 g (Centrifuge Avanti J 301 and rotor JS-24.38 from Beckman Coulter) for 10 min. After centrifugation, the excess of water was removed before the addition of a new dispersion aliquot.

Ten steps were sufficient to obtain a sufficient amount of kaolinite material. Finally, the sample was dried at 60°C and slightly compressed to a 1 cm height using the same protocol as for the first sample.

The final bulk porosity 𝜀 of 0.45±0.02 for both samples was determined based on the weight of the samples (488±1 mg in both cases), their height (measurement after compression: 1.0 to 1.1 cm), and the kaolinite grain density. This latter value was estimated at 2.62 g.cm -3 based on the structural formula mentioned above and the crystal structure parameters defined by [START_REF] Sakharov | Modeling Powder X-Ray Diffraction Patterns of the Clay Minerals Society Kaolinite Standards: Kga-1, Kga-1b, and Kga-2[END_REF] for KGa-2 kaolinite. Both samples were realised twice following exactly the same protocol. The first set of samples was used for quantifying the particle orientation using XRS measurements after sample induration (see Section 2.3). The second batch of sample was used for the PGSE-NMR attenuation measurements of protons to extract the self-diffusion tensor of the water probes (see Section 2.4).

Sample induration and X-ray scattering measurements

Both dried porous media were indurated and sliced to perform XRS measurements in transmission mode. For the induration, methyl methacrylate (MMA; C5H8O2) resin was chosen because of its fluidity higher than that of water allowing it to quickly fill the porosity, its small molecular volume compared to other organic molecules (19 nm 3 ), and its dipole moment being similar to that of water. The protocol used was based on the work of [START_REF] Sammaljärvi | Free radical polymerisation of MMA with thermal initiator in brick and Grimsel granodiorite[END_REF].

The first step consists of setting the sample under a primary vacuum in a hermetic cell for few minutes. This step is necessary to fully dehydrate the sample, as water molecules can disturb the polymerisation reaction of MMAwihtout impacting their orientation [START_REF] Hubert | Investigating the anisotropic features of particle orientation in synthetic swelling clay porous media[END_REF].

In the second step, MMA mixed with benzoyl peroxide (BPO; added in a BPO/MMA ratio of 0.5 wt.% as a thermal initiator of the polymerisation) is introduced in PTFE tubes under vacuum to facilitate the vaporisation of MMA and its condensation into the smallest pores to fill all the porosity. For both preparation conditions (compacted and centrifuged samples), the saturation of porosity by the resin was achieved after 3 days. The third step, consisting of the polymerisation of the MMA into PMMA, was achieved by transferring the saturated sample contained in the waterproof PTFE tube into a water bath at 55°C for 24 h. After induration, the cylindrical porous media were extracted from the PTFE tubes and sawed in both the longitudinal and transverse directions of the tube axis (Fig. 1a). These two directions were chosen to investigate the particle orientation in the two main directions relative to the compaction/centrifugation forces. The obtained slices were then polished into 500 µm thickness lamellas using grinding paper (with a grain diameter of 5 µm). The XRS measurements were performed at the Laboratoire de Physique des Solides (Orsay, France). A copper rotating anode generator (RU H3R, Rigaku Corporation, Japan) equipped with a multilayer W/Si mirror (Osmic) allows obtaining a monochromatic beam (CuKα = 1.5418 Å) of 600 x 600 µm² at the sample position. Two-dimensional (2D) X-ray scattering patterns were collected on a MAR345 2D-detector (marXperts GmbH, Germany, 150 µm pixel size). The sample-to-detector distance D was set to 250 mm with a sample-to-beam stop distance of 30 mm. This configuration allows us to obtain scattering vector moduli down to Qmin = 0.2 Å -1 (Q = 4π/λ sin(𝜃 𝐵 ), where λ is the incident wavelength and 2𝜃 𝐵 is the scattering angle), i.e., dspacings up to 31.5 Å (d = 2π/Q). Sample lamellas were mounted on a goniometer head and aligned perpendicularly to the incident X-ray beam with a typical exposure time of 300 to 900 s per sample position (Fig. 1b). For the XRS analyses, the limited thickness of the lamellas (i.e., 500 µm) is a compromise to optimise both the percentage of the transmitted beam and the quantity of particles analysed over a 600 x 600 µm² surface.

1 H NMR Pulsed Gradient Spin Echo experiments

The PGSE-NMR analyses were performed at the ICMN laboratory (Orléans, France). The dried kaolinite samples in their PTFE tubes (see Section 2.2) were first water-saturated by adding successive small drops of deionised water followed by equilibration over 2-3 days. As the samples were hydrated in unconstrained conditions, a limited decompaction occurred for both samples, leading to  values increasing from 0.45±0.02 to 0.50±0.02, a final value confirmed by helium pycnometry [START_REF] Porion | Water Mobility within Compacted Clay Samples: Multi-Scale Analysis Exploiting 1H NMR Pulsed Gradient Spin Echo and Magnetic Resonance Imaging of Water Density Profiles[END_REF].

The NMR measurements were performed using a Bruker DSX100 spectrometer with a static field of 2.35 T, equipped with a saddle detection coil and a micro-imaging probe (Micro5 Bruker) with gradient coils able to generate magnetic field gradients in three perpendicular directions. 1 H PGSE-NMR attenuation measurements [START_REF] Stejskal | Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient[END_REF][START_REF] Cotts | Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems[END_REF][START_REF] Callaghan | Principles of nuclear magnetic resonance microscopy[END_REF] were used to determine the macroscopic water mobility along any preselected direction within the sample. Fig. 2 illustrates the pulse sequence used to perform the PGSE-NMR attenuation measurements with which a wave vector 𝑞 may be associated [START_REF] Callaghan | Principles of nuclear magnetic resonance microscopy[END_REF] according to the relationship 𝑞 = 𝛾 𝑔 𝛿 𝜋 ⁄ , where 𝑔 is the intensity of the applied field gradient (between 0 and 1.6 T/m), 2𝛿 its effective duration (1 ms) and 𝛾 the proton gyromagnetic ratio

(2.675210 8 rad/s for 1 H). With the fixed duration 𝛿 of the pulsed field gradient set equal to 500 µs, the maximum value of the probed wave vector reaches 6.8 10 4 m -1 . As a consequence, our diffusion measurements are macroscopic and result from averages over sample sizes larger than 15 m with respect to the particle size (~0.5 µm). Under such macroscopic conditions [START_REF] Porion | Water Self-Diffusion within Nematic Dispersions of Nanocomposites: A Multiscale Analysis of 1H Pulsed Gradient Spin-Echo NMR Measurements[END_REF], the attenuation of the intensity of the NMR echo 𝐼(𝑞)/𝐼(0) evolves according to a Gaussian relationship from which the components of the self-diffusion tensor are easily extracted [START_REF] Cotts | Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems[END_REF][START_REF] Callaghan | Principles of nuclear magnetic resonance microscopy[END_REF]:

𝐼(𝑞) 𝐼(0) = 𝑒𝑥𝑝[-4 𝜋 2 𝑞 2 𝑒 𝑔 ⃗⃗⃗ 𝑇 𝐷 ⃡⃗⃗ 𝑒 𝑔 ⃗⃗⃗ (Δ + 3𝜏 2 ⁄ -𝛿 6 ⁄ )] (3)
where 𝑒 𝑔 ⃗⃗⃗ is the direction of the applied field gradient and 𝐷 ⃡ the self-diffusion tensor. This and the delay 𝜏 (760 s) are also displayed in Fig. 2. The PGSE-NMR attenuation measurements were performed at 292 K and the associated experimental bulk water selfdiffusion coefficient 𝐷 0 was measured at 2.0±0.2.10 -9 m 2 /s in these conditions.

Generation of 3D virtual kaolinite porous media and Brownian dynamics

Simulated porous media of kaolinite with contrasted anisotropy and controlled porosity

The 3D virtual porous media (VPM) mimicking the organisation of kaolinite porous media for different degrees of anisotropy in particle orientation were obtained using a one-by-one deposition algorithm of elliptic disc-shaped particles [START_REF] Ferrage | Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks[END_REF][START_REF] Ferrage | Influence of crystal structure defects on the small-angle neutron scattering/diffraction patterns of clay-rich porous media[END_REF]. This type of simulation was recently shown to be able to reproduce the organisation and porosity of discshaped particle packings [START_REF] Dabat | Mesoscale Anisotropy in Porous Media Made of Clay Minerals. A Numerical Study Constrained by Experimental Data[END_REF]. According to this algorithm, each particle with a set of Euler angles (𝜑, 𝜃, 𝜓) following the ZXZ convention [START_REF] Ferrage | Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks[END_REF], is introduced at the top of a square simulation box with periodic conditions along the x and y axes (z axis pointing upward; Fig. 3a) and settles to provide the steepest descent of the barycentre altitude.

The settling process of the particle, either at the bottom of the box or onto an existing bed of particles with fixed positions, is thus obtained through the repetition of individual movements around one or several contact points with one (or several) particles. The movements allow the particle to slide, swivel or rotate with a random amplitude ranging from zero to a maximum value to provide the steepest descent of the particle altitude. The variable parameters for the each simulation thus include a total number of particles (10 000), a width for the square simulation box set at 15𝑑 ̃, with 𝑑 ̃ the mean particle diameter, a total number of movement attempts (2400), an initial angle 𝜃 𝑖𝑛𝑖 of the particle introduced in the box, and a set of maximum amplitudes to swivel (𝐴 𝑠𝑤𝑖𝑣 𝑚𝑎𝑥 ), to rotate (𝐴 𝑟𝑜𝑡 𝑚𝑎𝑥 with here 𝐴 𝑟𝑜𝑡 𝑚𝑎𝑥 = 𝐴 𝑠𝑤𝑖𝑣 𝑚𝑎𝑥 ), and to slide (𝐴 𝑠𝑙𝑖𝑑𝑒 𝑚𝑎𝑥 ) [START_REF] Ferrage | Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks[END_REF]. For these simulations, the lognormal distribution in the geometric dimensions (i.e., basal surface, particle diameter, ratio between thickness and diameter, and ellipticity degree) of the individual elliptic particles was obtained from the work [START_REF] Ferrage | Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks[END_REF] and based on the experimental morphological study of [START_REF] Reinholdt | Morphological properties of vermiculite particles in size-selected fractions obtained by sonication[END_REF] for the 0.1-0.2 µm size fraction of vermiculite from Santa Olalla, Spain. This vermiculite sample was used here as a proxy, because it displays particles having very similar average aspect ratios (i.e., ratio between thickness and diameter of particles) to that of KGa-2 kaolinite (0.08 and 0.07 for vermiculite and kaolinite, respectively; [START_REF] Hassan | AFM and lowpressure argon adsorption analysis of geometrical properties of phyllosilicates[END_REF][START_REF] Reinholdt | Morphological properties of vermiculite particles in size-selected fractions obtained by sonication[END_REF].

The degree of anisotropy of particle orientation in the obtained packings was extracted by calculating the average of the second-order Legendre polynomial on the angular distribution of the particle orientations as follows:

〈𝑃 2 〉 = 〈𝑃 2 (𝑐𝑜𝑠𝜃)〉 = 〈3𝑐𝑜𝑠 2 𝜃 -1〉/2 (4)
with 𝜃 the angle between the normal unit vector of the particle and the z axis of the simulation box (Figs. 1c and3a). This 〈𝑃 2 〉 order parameter takes the value of 0 for an isotropic organisation and 1 when all particles are perfectly oriented in the bedding (all normal to particles aligned with the z axis of the simulation box). The 〈𝑃 2 〉 order parameter was previously used for the description of compacted clay porous media [START_REF] Perdigon-Aller | Preferred orientation in filtercakes of kaolinite[END_REF][START_REF] Ferrage | Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks[END_REF][START_REF] Dabat | Mesoscale Anisotropy in Porous Media Made of Clay Minerals. A Numerical Study Constrained by Experimental Data[END_REF] but is also referred to as 𝐻, the Hermans parameter in polymer sciences [START_REF] Hermans | Beiträge zur Kenntnis des Deformationsmechanismus und der Feinstruktur der Hydratzellulose[END_REF], or 𝑆, the nematic order parameter in colloid science [START_REF] Chaikin | Principles of condensed matter physics[END_REF][START_REF] Davidson | The measurement of the nematic order parameter by x-ray scattering reconsidered[END_REF]. To cover a large range of anisotropy degrees, 12 particle packings with 〈𝑃 2 〉 values varying from 0.03 to 0.92 were generated according to algorithm parameters reported in Table S1.

To allow investigating the dynamic behaviour of water tracers in these different VPM, additional numerical treatments are necessary. The generation procedure of these VPM indeed leads to different porosity values as a function of the 〈𝑃 2 〉 values [START_REF] Ferrage | Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks[END_REF]Dabat et al., 2018) and does not allow obtaining periodic conditions in the z direction. These effects are negative drawbacks for both Brownian dynamics calculations and comparisons with experimental data on compacted/centrifuged kaolinite samples. To overcome these limitations, a specific methodology was employed for the most isotropic VPM constituted by approximately 10 000 particles, as illustrated in Fig. 3. Each individual particle, originally defined by a set of three parameters (thickness and major and minor axes), is first polygonised considering 12 inplane vectors plus 2 vectors passing along the normal of the particle (Fig. 3b). A cubic subvolume containing ~2000 particles is then extracted (Fig. 3c). In order to allow the numerical investigation of water tracer mobility over a large spatial domain, periodic conditions under the form of minimum-image convention along the directors 𝑒 𝑥 ⃗⃗⃗ , 𝑒 𝑦 ⃗⃗⃗⃗ , and 𝑒 𝑧 ⃗⃗⃗ are required for the newly obtained simulation box (Fig. 3d). For Brownian dynamics simulations this convention indeed insures that a water tracer passing through one side of the box will re-appears on the opposite side of the simulation box. However, it requires avoiding the case where a particle protruding out of one side could overlap on the other side of the box. This is achieved by first detecting particle overlapping after application of minimum-image convention along the directors 𝑒 𝑥 ⃗⃗⃗ , 𝑒 𝑦 ⃗⃗⃗⃗ , and 𝑒 𝑧 ⃗⃗⃗ and its removal by reducing the length of the different vectors defining the geometry of the two overlapping particles. The two following numerical treatments consist of reducing the porosity of the VPM in order to reach an  value close to that of the water-saturated kaolinite samples analysed by PGSE-NMR, i.e.,  = 0.50 (see Section 2.4). First, each particle is allowed to grow along one of its 14 vectors, chosen randomly. The amplitude of the increase in the vector length is also chosen randomly between zero and a maximum value set at 10% of the initial vector length. In the case where the modification of the particle geometry induces an overlapping with another particle of the packing, the attempt is rejected. This first procedure allows increasing the volume of solid in the packing and thus decreasing the porosity until all particles become geometrically constrained by the other particles from the stack (Fig. 3e).

Second, if the porosity obtained still remains higher than the target value, new solid volume is added by injecting a new particle into the stacking on the surface of an existing one and letting the particle grow along its 14 vectors (Fig. 3f). The newly injected particles satisfy the distribution of the geometric dimensions but only the addition of the smallest ones is likely to be accepted during such a procedure. Depending on the initial porosity of the original VPM, the procedure is stopped during either the first or the second treatment, i.e., when the VPM reaches the porosity of 𝜀=0.50. Note that if the porosity is the same for all VPM, these two processes lead to a modification in the particle sizes and thus a change in the overall specific surface areas (SSAs). For instance, an increase in the volume of the individual particles leads to a decrease in the SSA values, whereas the injection of new particles, most often small in size, in order to fill the remaining porosity leads to an increase in the SSA values. Accordingly, the final step of the VPM generation procedure thus consists of applying a dilatation or contraction of the overall packing (and thus particle) dimensions (Fig. 3e). This leads to VPM with cubic lengths of ~4 µm (i.e., between 4.3 and 3.9 between 〈𝑃 2 〉=0.03 and 0.92, respectively) and SSA values of ~20 m 2 /g (similar to the experimental SSA value for KGa-2 kaolinite; [START_REF] Hassan | AFM and lowpressure argon adsorption analysis of geometrical properties of phyllosilicates[END_REF].

Brownian dynamics of water in virtual porous media

Brownian dynamics (BD) simulations represent a convenient way to investigate water diffusion at the representative time scale of the micrometre-sized porous media (typically several ms). In the framework of the general Langevin equation, the displacement of the molecular probes can be defined by [START_REF] Gunsteren | Stochastic dynamics for molecules with constraints[END_REF][START_REF] Tertre | Cation diffusion in the interlayer space of swelling clay minerals-A combined macroscopic and microscopic study[END_REF][START_REF] Porion | Water Mobility within Compacted Clay Samples: Multi-Scale Analysis Exploiting 1H NMR Pulsed Gradient Spin Echo and Magnetic Resonance Imaging of Water Density Profiles[END_REF]:

𝑚 𝑖 𝑑𝑣 ⃗ 𝑖 (𝑡) 𝑑𝑡 = -𝑚 𝑖 𝛾 𝑖 𝑣 𝑖 (𝑡) + 𝐹 𝑖 (𝑥(𝑡), 𝑡) + 𝑅 ⃗ 𝑖 (𝑡) (5)
where 𝑣 𝑖 , 𝑚 𝑖 and 𝛾 𝑖 are the velocity, molecular mass and frictional coefficient of probe 𝑖, respectively, 𝐹 𝑖 (𝑥(𝑡), 𝑡) is a systematic force acting on the probes and depending on their positions and 𝑅 ⃗ 𝑖 (𝑡) is a random force resulting from thermal collisions within the liquid.

Different algorithms can be used to solve the set of Eq. ( 5), mainly depending on the ratio between the friction coefficient and the time step (𝛿𝑡) used in the simulation. In the case where the time step is much larger than the velocity correlation time (i.e., 𝛾 𝑖 𝛿𝑡 ≫ 1) and considering the probe displacements to be completely independent, the solution of Eq. ( 5) becomes [START_REF] Gunsteren | Stochastic dynamics for molecules with constraints[END_REF]:

𝑥 𝑖 (𝑡 + 𝛿𝑡) = 𝑥 𝑖 (𝑡) + 𝑅 ⃗ 𝑖 (6)
with the random force 𝑅 ⃗ 𝑖 now satisfying a Gaussian distribution function with a zero mean and standard deviation given by the following:

〈𝑅 𝑖 2 〉 = 2𝐷 𝑖 𝛿𝑡 (7)
where 𝐷 𝑖 is the molecular self-diffusion of the probe 𝑖. For diffusion within isotropic media, the modulus of the random 3D displacements is quantified by the self-diffusion propagator, i.e., the density of the probability of the displacement distribution law [START_REF] Callaghan | Principles of nuclear magnetic resonance microscopy[END_REF][START_REF] Bacle | Modeling the transport of water and ionic tracers in a micrometric clay sample[END_REF]:

𝑃(𝑟 , ∆ | 𝑟 0 ,0) = {4𝜋𝐷∆} -3 2 ⁄ 𝑒𝑥𝑝 [- (𝑟 -𝑟 0 ) 2 4𝐷∆ ] ( 8
)
where ∆ is the diffusion time (see Eq. ( 3)). The self-diffusion propagator quantifying the mobility along any single director is then defined by the following:

𝑃 𝛼 (𝑟 𝛼 ⃗⃗⃗ , ∆ | 𝑟 𝛼 ⃗⃗⃗ 0 , 0) = {4𝜋𝐷 𝛼 ∆} -1 2 ⁄ 𝑒𝑥𝑝 [- (𝑟 𝛼 ⃗⃗⃗⃗ -𝑟 𝛼 ⃗⃗⃗⃗ 0 ) 2 4𝐷 𝛼 ∆ ] ( 9
)
where D is the component of the self-diffusion tensor describing the mobility of the probe along the selected 𝑒 𝛼 ⃗⃗⃗⃗ director [START_REF] Callaghan | Principles of nuclear magnetic resonance microscopy[END_REF]. Its spatial Fourier transform is also Gaussian and describes the probe displacement in the reciprocal q-space:

𝐸 𝛼 (𝑞, Δ ) = exp [-2 𝜋 2 𝑞 2 〈(𝑟 𝛼 ⃗⃗⃗ -𝑟 𝛼 ⃗⃗⃗ 0 ) 2 〉] = exp[-4 𝜋 2 𝑞 2 𝐷 𝛼 Δ] ( 10
)
where  is the diffusion time and 〈(𝑟 𝛼 ⃗⃗⃗ -𝑟 𝛼 ⃗⃗⃗ 0 ) 2 〉 the mean-squared displacement along the 𝑒 𝛼 ⃗⃗⃗⃗ director [START_REF] Callaghan | Principles of nuclear magnetic resonance microscopy[END_REF][START_REF] Porion | Anisotropy of the solvent self-diffusion tensor as a probe of nematic ordering within dispersions of nanocomposites[END_REF][START_REF] Porion | Water Self-Diffusion within Nematic Dispersions of Nanocomposites: A Multiscale Analysis of 1H Pulsed Gradient Spin-Echo NMR Measurements[END_REF]. In the scope of comparing simulations and experiments, as done in the present study, it should be pointed of that this Fourier transform of the self-diffusion propagator derived from BD simulations corresponds to the entity directly probed by PGSE-NMR measurements (see Section 2.4). Moreover it also corresponds exactly to the intermediate scattering function (𝐹 𝑞 (𝑡)) commonly probed, on a much shorter time-scale, by quasi-elastic neutron-scattering measurements [START_REF] Hansen | Theory of Simple Liquids[END_REF].

For the BD simulations performed here at 300 K, 𝑁 = 2500 water probes with the molecular self-diffusion 𝐷 0 set at 2.3.10 -9 m 2 /s were first introduced randomly into the porosity of the VPM. A time step 𝛿𝑡 = 5 ns was considered, and additional tests showed that smaller values did not provide any difference in the simulation results. An overall simulation time of 4 ms was used to extract the pore water diffusion coefficients 𝐷 𝛼 along a selected 𝑒 𝛼 ⃗⃗⃗⃗ director based on the asymptotic slope of the radial mean squared displacement as follows:

𝐷 𝛼 = lim Δ→∞ ∑ (𝑥 𝑖,𝛼 (0)-𝑥 𝑖,𝛼 (𝛥)) 2 𝑁 𝑖=1 2NΔ (11)
where 𝛼 refers to the single direction 𝑒 𝛼 ⃗⃗⃗⃗ on which the mobility is extracted (the uncertainty on the calculated 𝐷 𝛼 values is estimated at 10%). During the BD simulations, the collision with the surface of the kaolinite was treated as a Maxwell's 𝐴 wall with the angular probability 𝑓 𝐴 (𝜃, ) of water probes rebounding from the surface given by:

𝑓 𝐴 (𝜃, )𝑑𝛺 = cos 𝜃 𝑑𝛺/𝜋 (12)
where 𝜃 and  are the usual polar and azimuthal angles (with respect to the normal of the surface of the particle) and 𝑑𝛺 is the element of the solid angle. This condition mimics the fate of a molecule, which is supposed to reside at the interface of the wall and eventually leave the wall to return to the fluid [START_REF] Valleau | Comment on: Adsorption and diffusion at rough surfaces. A comparison of statistical mechanics, molecular dynamics, and kinetic theory[END_REF].

Results and Discussion

Preferred orientation analysis of kaolinite particles

Preferred orientation of the particles in both the compacted and centrifuged samples is based on the orientation distribution function (ODF) determined from 2D-XRS measurements (see Section 2.3). The orientation of a cylindrical particle can be described in an orthogonal laboratory framework by the direction of its normal Oz' through the spherical coordinates θ and φ (Fig. 1c). In addition, clay porous media are transverse isotropic systems with their z-axis as the unique symmetry axis [START_REF] Cebula | Neutron diffraction from clay-water systems[END_REF][START_REF] Perdigon-Aller | Preferred orientation in filtercakes of kaolinite[END_REF][START_REF] Wenk | Preferred orientation of phyllosilicates: Comparison of fault gouge, shale and schist[END_REF][START_REF] Hubert | Investigating the anisotropic features of particle orientation in synthetic swelling clay porous media[END_REF], leading to an equal probability of the particle orientation over the  angles.

Accordingly, the ODF only depends on the angle 𝜃, with the following general constraints:

𝑓(𝜃) ≥ 0 (13) 𝑓(𝜃) = 𝑓(𝜋 -𝜃) (14)
∫ 𝑓(𝜃) sin(𝜃) 𝑑𝜃 = 1 𝜋 0

(15)

Eqs. ( 13) and ( 14) indicate that the ODF 𝑓(𝜃) is positive and has an equal probability of the particles pointing upward and downward, respectively. Eq. ( 15) allows normalising the total number of particles in the system through the integration over all  angles [START_REF] Labarthet | Orientation Distribution Functions in Uniaxial Systems Centered Perpendicularly to a Constraint Direction[END_REF]. The experimental ODF can be extracted from the angular modulation of the scattered intensity of the 001 reflection of kaolinite along the detector angle  of the 2D-XRS patterns (Fig. 1b). Given the low values for the Bragg angle for the 001 reflection of kaolinite, the 𝜏 = 𝜃 The experimental 2D-XRS patterns for both the compacted and centrifuged samples on lamellas extracted in the longitudinal and transverse directions with respect to the tube axis are reported in Fig. 4 with their corresponding ODF. As seen for both samples, the 𝑓(𝜃) functions recorded for the lamellas extracted in the longitudinal direction display symmetric profiles, indicating that the lamellas were sliced perpendicularly to the preferred orientation plane and well aligned on the XRS setup. For lamellas corresponding to the transverse direction of the tube axis, the obtained ODF displays a constant intensity whatever the azimuthal angle, in agreement with the isotropic transverse nature of the sample and the correct methodology of the sample preparation and analysis. Based on the shape of the 𝑓(𝜃) functions for lamellas sliced in the longitudinal direction of the tube axis, the degree of preferred orientation can be obtained for both samples by calculating the average value of the second-order Legendre polynomial on the angular distribution as:

〈𝑃 2 〉 = ∫ 𝑃 2 (𝑐𝑜𝑠𝜃). 𝑓(𝜃) sin(𝜃) 𝑑𝜃 𝜋 0 (17)
As seen from the different shapes of the 𝑓(𝜃) functions (Fig. 4b), the two samples display very different order parameters, with 〈𝑃 2 〉 values of 0.21±0.02 and 0.59±0.05 for the compacted and centrifuged samples, respectively (Table 1). It is worth noting that the obtained 〈𝑃 2 〉 values are averages over several measurements for each sample. Although it can be expected that the successive centrifugation steps lead to a more heterogeneous sample organization, such a difference was not evident given the about 10% uncertainty of the structure parameter in both cases (Table 1). The different organisations for the two samples can likely be attributed to the preparation method for two reasons. First, the uniaxial compaction in air-dried conditions has been shown to provide rather poor preferred orientations for montmorillonite particles [START_REF] Lutterotti | Texture analysis of a turbostratically disordered Ca-montmorillonite[END_REF][START_REF] Suuronen | X-ray studies on the nano-and microscale anisotropy in compacted clays: Comparison of bentonite and purified calcium montmorillonite[END_REF]. Second, it is well accepted that the dispersion of particle aggregates as individual clay platelets in water followed by sedimentation promotes the preferred orientation, and a wide range of 〈𝑃 2 〉 values could be achieved, depending on the particle size, solid-solution ratio, and hydrostatic or shear forces applied on the sample (0.10  〈𝑃 2 〉  0.85; [START_REF] Perdigon-Aller | Preferred orientation in filtercakes of kaolinite[END_REF][START_REF] Méheust | Inferring orientation distributions in anisotropic powders of nano-layered crystallites from a single two-dimensional WAXS image[END_REF][START_REF] Perdigón | Neutron diffraction study of the orientational order in filter cakes made of kaolinite under laminar and turbulent cross-flow[END_REF][START_REF] Hubert | Investigating the anisotropic features of particle orientation in synthetic swelling clay porous media[END_REF][START_REF] Ferrage | Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks[END_REF][START_REF] Carrier | Effect of water on elastic and creep properties of self-standing clay films[END_REF].

Experimental analysis of water diffusion in kaolinite porous media

The contrasted organisations in the kaolinite particles (i.e., 〈𝑃 2 〉 = 0.21±0.02 and 0.59±0.05

for the compacted and centrifuged samples, respectively) for a similar porosity (ε = 0.50±0.02 in wet conditions; see Section 2.4) indicate that the two samples are well adapted to investigate in detail the impact of the preferred orientation on the anisotropy of the water diffusion. As illustrated in Fig. 5 for the centrifuged sample, the pulsed gradients are applied along six noncollinear directions [START_REF] Basser | Estimation of the Effective Self-Diffusion Tensor from the NMR Spin Echo[END_REF][START_REF] Skare | Condition Number as a Measure of Noise Performance of Diffusion Tensor Data Acquisition Schemes with MRI[END_REF] noted 𝑒 1 ⃗⃗⃗ = 𝑒 𝑥 ⃗⃗⃗ = (1,0,0), 𝑒 2 ⃗⃗⃗ = 𝑒 𝑦 ⃗⃗⃗⃗ = (0,1,0), 𝑒 3 ⃗⃗⃗ = 𝑒 𝑧 ⃗⃗⃗ = (0,0,1), 𝑒 4 ⃗⃗⃗ = (1,1,0), 𝑒 5 ⃗⃗⃗ = (0,1,1) and 𝑒 6 ⃗⃗⃗ = (1,0,1), respectively, with the direction 𝑒 3 ⃗⃗⃗ being parallel to the compaction/centrifugation axis of the sample. From the six corresponding components of the water self-diffusion tensor, one can easily extract its three principal axes and the corresponding eigenvalues describing the water mobility in the longitudinal or transverse direction of the tube axis (Fig. 1a). the components 𝐷 𝛼 of the self-diffusion tensor: 𝐷 1 =𝐷 𝑥 =1.14210 -9 m 2 /s, 𝐷 2 =𝐷 𝑦 =1.16510 -9 m 2 /s, 𝐷 3 =𝐷 𝑧 =0.61410 -9 m 2 /s, 𝐷 4 =1.17310 -9 m 2 /s, 𝐷 5 =0.86910 -9 m 2 /s and 𝐷 6 =0.87910 -9 m 2 /s.

As detailed in Table 1, the compacted sample exhibits a small anisotropy of the water self-diffusion tensor, which is consistent with the measured low values for the order parameter 〈𝑃 2 〉. Moreover, the pore water diffusion coefficient obtained for this sample along the z direction is consistent with a previous analysis from magnetic resonance imaging of the time evolution of the water concentration profiles during D2O/H2O exchange [START_REF] Porion | Water Mobility within Compacted Clay Samples: Multi-Scale Analysis Exploiting 1H NMR Pulsed Gradient Spin Echo and Magnetic Resonance Imaging of Water Density Profiles[END_REF].

In contrast, the sample obtained by the centrifugation method shows a larger anisotropy ratio 𝐷 𝑥,𝑦 /𝐷 𝑧 of the water diffusion tensor, in agreement with the increase of the 〈𝑃 2 〉 order parameter value for this sample. The water self-diffusion tensor can be better illustrated for these two samples by plotting the variation of the water mobility within two orthogonal planes (i.e., either parallel or perpendicular to the preferred orientation plane). The gradual variation of the pore water diffusion coefficients between the two principal axes of the diffusion tensor (i.e., 𝑒 ⊥ ⃗⃗⃗⃗ and 𝑒 ∥ ⃗⃗⃗ , directions perpendicular or parallel to the preferred orientation plane, respectively) can indeed be described by [START_REF] Porion | Water Self-Diffusion within Nematic Dispersions of Nanocomposites: A Multiscale Analysis of 1H Pulsed Gradient Spin-Echo NMR Measurements[END_REF]:

𝐷 𝑚𝑒𝑎𝑠 (𝛾) = 𝑒 𝑔 ⃗⃗⃗ 𝑇 𝐷 ⃡⃗⃗ 𝑒 𝑔 ⃗⃗⃗ = 𝐷 ⊥ cos 2 (𝛾) + 𝐷 ∥ sin 2 (𝛾) ( 18
)
where 𝛾 is the angle between 𝑒 ⊥ ⃗⃗⃗⃗ and 𝑒 𝑔 ⃗⃗⃗ . 𝐷 𝛼 and 𝐷 ∥ are the two eigenvalues of the diffusion tensor along the principal directions 𝑒 ⊥ ⃗⃗⃗⃗ and 𝑒 ∥ ⃗⃗⃗ . The diffusion tensor is illustrated in Fig. 6 for both the compacted and centrifuged samples. Calculations are performed either parallel or perpendicular to the preferred orientation plane based on the (x,z) or (x,y) planes, respectively.

The enhanced experimental anisotropy in the water mobility on the (x,z) plane for the centrifuged sample compared to the compacted sample well illustrates the role played by the preferred orientation of the kaolinite particles on the water mobility for a given 𝜀 value. In that regard, and compared to other diffusion experiment setups, the great advantage of the PGSE-NMR attenuation measurements is to provide a direct measurement of the water diffusion tensor in the sample. Such experimental data thus represent key constraints for assessing the representativeness of virtual porous media through a detailed comparison between the experimental and simulated water mobility dependences on the particle orientation. shown in blue and red, respectively. For the experimental data, the diffusion tensor is calculated from its eigenvalues 𝐷 𝑥 , 𝐷 𝑦 , and 𝐷 𝑧 according to Eq. ( 18). For the simulated data, the solid lines correspond to the limiting time evolution of the mean square displacements (see Eq. ( 11)), whereas the dotted lines represent the calculation of the diffusion tensor from its eigenvalues using Eq. (18).

Brownian dynamics of water diffusion in 3D virtual porous media

The pore diffusion coefficients in the 12 virtual porous media (with 0.04  〈𝑃 2 〉  0.92) are calculated along the 3 directors of the 3D virtual porous media reference framework (i.e., x, y, and z; Fig. 7) based on the mean square displacement (MSD) of the water probes according to Eq. ( 11). Additional calculations were performed every 10° in the (x,y) and (x,z) planes of the diffusion tensor. As illustrated in Fig. 7 for the VPM obtained for 〈𝑃 2 〉 = 0.92, the asymptotic time evolution behaviour of the MSD is rapidly obtained. The different MSD curves extracted in the (x,y) plane of the diffusion tensor are very similar (Fig. 7a). This feature confirms the transverse isotropy of the VPM, in agreement with the experimental data (see Section 3.1). Moreover, this lack of angular dependence of the calculated 𝐷 𝛼 values likely evidence that the VPM contain sufficient numbers of particles and thus can be considered as representative elementary volumes for the analysis of the dynamical behaviour of diffusive species. The situation differs when analysing the MSD curves in the (x,z) plane of the diffusion tensor (Fig. 7b). The 𝐷 𝛼 values are indeed significantly lower in the z direction compared with the ones in the x direction, with intermediate values of 𝐷 𝛼 for in-between directions. This observation is consistent with the plane (x,y) as the preferred orientation plane.

The pore water diffusion coefficients 𝐷 𝛼 derived from these different MSD curves are used to draw the water diffusion tensor in Fig. 6 for the two VPM having the closest 〈𝑃 2 〉 values to the experimental ones, i.e., 〈𝑃 2 〉 = 0.24 and 0.58. The overall 𝐷 𝛼 values are found to be in fair agreement when comparing the experimental and calculated water diffusion tensors. For the compacted sample, the simulated tensor displays a slightly more anisotropic pattern, likely due to the increased 〈𝑃 2 〉 value (〈𝑃 2 〉 = 0.24 and 0.21 for simulated and experimental media, respectively). In Fig. 6, the obtained simulated water diffusion tensor (solid line) is also compared to the tensor (black dotted line) only based on the extracted 𝐷 𝑥 , 𝐷 𝑦 , and 𝐷 𝑧 values from BD simulations and considering the angular dependence given by Eq. ( 18). The good consistency between the simulated and recalculated water diffusion tensors provides additional evidence of the good representativeness of the VPM as well as the correct consideration of the simulated 𝑒 𝑥 ⃗⃗⃗ , 𝑒 𝑦 ⃗⃗⃗⃗ , and 𝑒 𝑧 ⃗⃗⃗ directors of the simulation box as eigenvalues of the diffusion tensor.

The obtained VPM coupled to BD simulations can be used to further assess the influence of the preferred orientation of particles on the diffusional properties of water. In Fig. 8a, the obtained simulated 𝐷 𝛼 /𝐷 0 values extracted from the MSD curves are plotted in the 0.04-0.92 〈𝑃 2 〉 range, whereas the anisotropy ratio 𝐷 𝑥,𝑦 /𝐷 𝑧 of the water diffusion tensor is reported in Fig. 8b. Again, good agreement between the experimental and calculated diffusion coefficients is obtained for both samples. The 𝐷 𝑥,𝑦 /𝐷 0 and 𝐷 𝑧 /𝐷 0 values show steady increasing and decreasing behaviours, respectively, when increasing the degree of preferred orientation (Fig. 8a). For both directions, a factor ~2 is obtained for 𝐺 values between the more isotropic to more anisotropic systems. This amplitude observed for 𝜀=0.5±0.02 is in agreement with the computational results obtained by [START_REF] Tyagi | Multi-scale micro-structure generation strategy for up-scaling transport in clays[END_REF] using random walk simulations on 2D microstructure maps.

Such variation well illustrates the great importance of the preferred orientation on the diffusional properties of water. In the case of transport modelling, according to Eq. ( 1), the modification of the 𝐷 𝛼 /𝐷 0 values through the investigated 〈𝑃 2 〉 range has indeed the same impact on the 𝐷 𝑒 value as a change in the porosity value by a factor of 2. The anisotropy ratio 𝐷 𝑥,𝑦 /𝐷 𝑧 of the water diffusion tensor displays an exponentialshaped evolution with the 〈𝑃 2 〉 value (Fig. 8b). The observed variation of the 𝐷 𝑥,𝑦 /𝐷 𝑧 values between 1 and 5 is consistent with the reported experimental diffusivity anisotropies for water tracers in compacted clay-rich porous media, for pure clay-based materials (e.g., bentonite ;[START_REF] Sato | Fundamental study on the effect of an orientation of clay particles on diffusion pathway in compacted bentonite[END_REF][START_REF] Suzuki | Study on anisotropy of effective diffusion coefficient and activation energy for deuterated water in compacted sodium bentonite[END_REF], or for more complex polymineralic argillaceous rocks [START_REF] Van Loon | Anisotropic diffusion in layered argillaceous rocks: a case study with Opalinus Clay[END_REF][START_REF] García-Gutiérrez | Largescale laboratory diffusion experiments in clay rocks[END_REF][START_REF] Xiang | Diffusive anisotropy in low-permeability Ordovician sedimentary rocks from the Michigan Basin in southwest Ontario[END_REF][START_REF] Gimmi | Anisotropic diffusion at the field scale in a 4-year multi-tracer diffusion and retention experiment -I: Insights from the experimental data[END_REF][START_REF] Jacops | The Dependency of Diffusion Coefficients and Geometric Factor on the Size of the Diffusing Molecule: Observations for Different Clay-Based Materials[END_REF]. For these latter, the presence of elongated non-clay grains can provide additional contribution to the overall anisotropy in the water diffusion tensor [START_REF] Robinet | Effects of mineral distribution at mesoscopic scale on solute diffusion in a clay-rich rock: Example of the Callovo-Oxfordian mudstone (Bure, France)[END_REF].

Summary and conclusions

The results described in the present study further confirm the significant role played by the preferred orientation of the particles on the diffusional properties of water in compacted porous media made of clay minerals. The originality of this work is provided by a close connection between experiments and simulations on representative virtual porous media, allowing quantitative agreement between the measured and calculated 𝐷 𝛼 /𝐷 0 values. It is worth pointing out that such an agreement conceals significant differences in the probed spatial and dynamical domains between the experiments (~5 mm; 20 ms) and simulations (~4 µm; 4 ms).

Accordingly, the spatial heterogeneity in the porosity and anisotropy within the samples at higher length scales are not accounted for in the computed VPM used here, or are just averaged in such a limited volume. Moreover, the flexibility of the clay particles [START_REF] Honorio | Flexibility of nanolayers and stacks: implications in the nanostructuration of clays[END_REF] and the interfacial molecular forces on the dynamics of the water molecules are not considered in the present study in these mesoscopic simulations. Despite these limitations and in line with previous computational studies [START_REF] Tyagi | Multi-scale micro-structure generation strategy for up-scaling transport in clays[END_REF][START_REF] Bacle | Modeling the transport of water and ionic tracers in a micrometric clay sample[END_REF], the simulated VPM can be considered good toy models for estimating the underlying parameters of the pore network controlling the geometric parameter 𝐺 (i.e., distribution in size, shape, orientation, and connectivity of pores). This estimation is achieved in the present study based on the computation of the shape and the mean orientation of the particles, two parameters that are easily obtained experimentally. The validation of the computational methodology provides quantitative information on the role played by the preferred orientation of the particles on the 𝐺 values, as a variation by a factor up to ~2 of 𝐷 𝛼 /𝐷 0 for 𝜀=0.5±0.02 is observed when increasing the anisotropy in the particle orientation. Because the order parameter 〈𝑃 2 〉 values can significantly vary in compacted materials made from clay minerals [START_REF] Perdigon-Aller | Preferred orientation in filtercakes of kaolinite[END_REF][START_REF] Méheust | Inferring orientation distributions in anisotropic powders of nano-layered crystallites from a single two-dimensional WAXS image[END_REF][START_REF] Perdigón | Neutron diffraction study of the orientational order in filter cakes made of kaolinite under laminar and turbulent cross-flow[END_REF][START_REF] Lutterotti | Texture analysis of a turbostratically disordered Ca-montmorillonite[END_REF][START_REF] Carrier | Effect of water on elastic and creep properties of self-standing clay films[END_REF], this parameter undoubtedly deserves, as a porosity parameter, particular attention in the scope of predicting the macroscopic transport properties in compacted clay media. A logical continuation of this work could be, then, to expand the analysis of the influence of the preferred orientation on the water diffusion for different 𝜀 values. Using the same strategy combining experiments and simulations, another perspective could be to extend the analysis to other types of clay minerals, in particular to swelling clay minerals, leading to the presence of different type of porosities, and evaluating the overall diffusional properties of water.

Fig. 1 .

 1 Fig. 1. Experimental measurement of particle orientation within kaolinite porous media using X-ray

Fig. 2 .

 2 Fig. 2. Schematic view of the pulse sequence used to perform Pulse Gradient Spin Echo (PGSE-NMR)

  equation is usually simplified by replacing the tensorial contraction 𝑒 𝑔 ⃗⃗⃗ 𝑇 𝐷 ⃡⃗⃗ 𝑒 𝑔 ⃗⃗⃗ by the value of the self-diffusion coefficient 𝐷 𝑔 along the selected 𝑒 𝑔 ⃗⃗⃗ director. The diffusion time Δ (20 ms)

Fig. 3 .

 3 Fig. 3. Generation of virtual porous media with the same porosity but different anisotropy degrees in

Fig. 4 .

 4 Fig. 4. Extraction of orientation distribution functions of kaolinite particles from 2D X-ray scattering

Fig. 5 .

 5 Fig. 5. Illustration of water self-diffusion propagators obtained for the centrifuged sample from PGSE-NMR experiments. More details on the selected diffusion directors 𝑒 𝛼 ⃗⃗⃗⃗ are given in the text, leading to

Fig. 6 .

 6 Fig. 6. Water diffusion tensors determined from PGSE-NMR experiments (left) and Brownian dynamics simulations (right). The variations of the water mobility 𝐷 𝛼 /𝐷 0 in the (x,y) plane and (x,z) plane are

Fig. 7 .

 7 Fig. 7. Illustration of the time evolution of the mean square displacements (MSD) of the water probe obtained by Brownian dynamics simulations for the virtual porous media with 〈𝑃 2 〉 = 0.92.Displacements are extracted along the 3 directors of the 3D virtual porous media reference framework

Fig. 8 .

 8 Fig. 8. Influence of particle preferred orientation on the water diffusion properties. (a) Evolution as a function of the order parameter 〈𝑃 2 〉 of the mean water diffusion coefficients in the (x,y) plane 𝐷 𝑥,𝑦 (circles) or along the z direction 𝐷 𝑧 (squares), calculated from Brownian dynamics simulations (blue) or obtained experimentally by PGSE-NMR attenuation measurements (red). (b) Evolution of experimental (red) and calculated (blue) 𝐷 𝑥,𝑦 /𝐷 𝑧 ratios with preferred orientation of particles.

Table 1 .

 1 Experimental measurements of the anisotropy degree of particle orientation (order parameter 〈𝑃 2 〉) determined from XRS analyses and associated pore water diffusion coefficients 𝐷 𝛼 obtained from PGSE-NMR experiments on compacted and centrifuged samples (porosity 𝜀=0.50±0.02). The director 𝑒 𝑧 ⃗⃗⃗ is longitudinal whereas the directors 𝑒 𝑥 ⃗⃗⃗⃗ and 𝑒 𝑦 ⃗⃗⃗⃗ are transverse to the tube axis.

	Sample	〈𝑃 2 〉 order parameter	𝐷 𝑧 /𝐷 0	𝐷 𝑥 /𝐷 0	𝐷 𝑦 /𝐷 0	𝐷 𝑥,𝑦 /𝐷 𝑧
	Compacted	0.21±0.02	0.43±0.04	0.51±0.05	0.50±0.05	1.2±0.2
	Centrifuged	0.59±0.05	0.31±0.03	0.59±0.06	0.57±0.06	1.9±0.4

Acknowledgements

The results presented are part of the Ph.D. thesis of T.D. granted by "Région Nouvelle-Aquitaine", University of Poitiers, France. Claude Veit (IC2MP, Poitiers, France) is thanked for the design and conception of the compaction and centrifugation cells for the sample preparation. Claude Laforest (IC2MP, Poitiers, France) and Stephan Rouzière (LPS, Saclay, France) are also acknowledged for their technical assistance in the induration and polishing steps of the sample preparation and in the XRS measurements, respectively. Dr. Pascale Launois (LPS, Saclay, France) is thanked for constructive discussions about XRS measurements. The authors are grateful to the CNRS interdisciplinary "défi Needs" through its "MiPor" program (Project TRANSREAC) and the European Union (ERDF) and "Région Nouvelle Aquitaine" for providing financial support for this study. Additional support from Région Centre (France) is thanked for the funding of the DSX100 Bruker spectrometer used in this study. The authors gratefully acknowledge the anonymous reviewers for their constructive comments.


Sophie Bou

Xinyue Wang

Nicolas Anton

Andrey S Klymchenko

Mayeul Collot
email: mayeul.collot@unistra.fr

Near Infrared Fluorogenic Probe as a Prodrug Model for Evaluating Cargo Release by Nanoemulsions

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Introduction

Over the last 20 years nanoparticles (NPs) have drawn a particular attention in medicine, especially in the field of cancers. 1, 2 Indeed, NPs can improve three different aspects of cancer therapy: The tumor imaging, the diagnosis and the treatment. 3,4,5,6,7 The treatment of tumors can be achieved by specific drug delivery targeted by nanoparticles, 8 including polymeric NPs, 9, 10 inorganic NPs, 11 hydrogels, 12 lipid polymer hybrid NPs, 13, 14, 15 liposomes 16 and solid lipid nanoparticles, 17 thus avoiding side effects of the conventional chemotherapy. Although inorganic NPs (e.g. Quantum dots, iron oxide or gold NPs) and organic NPs (e.g. liposomes, polymeric NPs) can specifically target tumors by vectorization using ligands like RGD 18 or folic acid, 19,20 their drug loading remains overall limited. 21 Among NPs, nanoemulsions (NEs) that are composed of an oily core and a surfactant shell (see Fig. 1 A) display attractive features: First, their lipid core enables the encapsulation of an impressive quantity of lipophilic cargos. Then NEs are stealth and constituted of biocompatible components that can be injected in the bloodstream. Finally, their preparation, based on spontaneous emulsification, is readily accessible. 22,23,24 Unlike polymeric NPs, the functionalization of NEs by specific ligands for vectorization remains difficult and is still limited to the cellular level. 25,26,27,28 However, it was recently shown using in vivo fluorescence imaging that, when injected in mice, NEs spontaneously accumulated in tumors by enhanced permeability and retention (EPR) effect. 29,30 This phenomenon was observed for solid tumors and it was shown that molecules/particles tend to preferentially accumulate in tumor tissues allowing a faster growth of the tumor compared to other tissues. Consequently, NEs present appealing features to selectively deliver drugs to the tumors. However, loading NEs with cytoactive drugs requires the latter to be solubilized in the oily core and therefore is limited to highly lipophilic drugs. Previously, it was shown that Nile Red, a model of lipophilic drugs, should be modified with lipophilic groups to ensure efficient loading into NPs and to prevent its rapid leakage into biological media. 31 Unfortunately, most of the drugs do not display a sufficient lipophilic nature to fulfill this requirement. Indeed, common drugs used for chemotherapy medication to treat cancers including: docetaxel, bleomycin, vincristine, prednisolone or doxorubicin, possess several free polar hydroxyl groups. In order to circumvent this issue, a prodrug with a significantly enhanced hydrophobicity compared to its corresponding active drug could be used to be efficiently loaded in NEs. 32,33 In return, this chemical modification has to be reversible once the cell target reached in order to release the active drug (Fig. 1A). 34 In order to enhance the lipophilicity of the drugs, the abovementioned hydroxyl functions can be used to introduce a hydrophobic vector. Carboxylic acids and alcohol functions are readily chemically transformed into esters that can be hydrolyzed in cellulo by specific enzymes called esterases. 35 It is noteworthy that this strategy is actually used for decades since the most famous drug, namely aspirin is the acetylated prodrug of salicylic acid. 36 Although acetylation is a widely used prodrug strategy, it is not adapted for encapsulation in NEs due to the weak lipophilicity brought by the acetate group. Conversely, caprylic acid is a hydrophobic C8 fatty acid, naturally present in mammals' milk and coconut oil. Moreover, unlike esters with longer chain, caprylic esters have been shown to be readily hydrolyzed by lipases and esterases. 35 Consequently, esterification of drugs into caprylic esters could be used to transform drugs into prodrugs with enhanced lipophilicity. In order to confirm this hypothesis, we herein developed Pro-HD, a fluorogenic drug model based on the esterification of a fluorescent probe (Fig. 1B). The esterified HD called Pro-HD is virtually non-fluorescent and upon hydrolysis releases HD that provokes a fluorescence enhancement of 35-fold in the near-infrared thus making it an efficient system to evaluate the cellular delivery of prodrug by NEs.

Results and discussion

Design and principle

In this work we aimed at developing a pro-fluorophore as a prodrug model in order to study by fluorescence imaging its ability to be efficiently delivered by NEs as biocompatible nanocarriers. In addition to its ability to be transformed into the corresponding drug, the encapsulated prodrug should possess two main features: 1) It has to be soluble in oil to be efficiently carried by NEs. 2) It should not leak out of the NE before reaching its cellular target (Fig. 1A). 31 Indeed, if leakage occurs, the uncontrolled release of the cytoactive molecule can lead to negative side effects on healthy cells. Our work relies on the chemical transformation of an emissive fluorescent dye into a hydrophobic and non-emissive pro-dye. The latter bears a hydrophobic vector that quenches or decreases the brightness. After delivery of the pro-fluorophore into the cells, the vector must be cleavable by a cellular process to reveal the fluorescence of the corresponding dye (Fig. 1B). This last step implies that the vector must be biocompatible, avoiding side effects after its cleavage. Dihydroxyxanthene hemicyanines also referred to "Huda dyes" (HD) 37 are recently developed fluorophores, featuring high brightness and narrow emission band in the near-infrared region (NIR). 38 Due to these interesting features these fluorophores served to develop efficient probes for hypoxia, 39 hydrazine, 40 pH, 41, 42 calcium 43 and enzyme activity. 44 Moreover, their spectral properties, including emission in the NIR, make HD probes suitable for in vivo imaging. 39,45 For these reasons we intended to synthesize a fluorogenic probe based on HD that will display a high degree of hydrophobicity and that could be reversibly turned off by esterification (Scheme 1). To this aim, we designed Pro-HD that possesses several features: 1) The indoleninium moiety bears an octadecyl alkyl chains to maximize the hydrophobicity. 2) The phenolic moiety bears a chlorine atom at the ortho position to lower the pKa of the probe as shown previously. 41,46 The addition of the chlorine atom leads to a probe with a reported pKa of 6.2, thus ensuring formation of the brighter phenolate form of HD when exposed to the cytosol. 41 3) The hydroxyl group was esterified into a caprylic ester as a lipophilic, biocompatible and cleavable vector. 35 4) Finally, small hydrophobic counterion iodide was replaced with bulky hydrophobic counterion of tetraphenylborate family (F5-TPB), which is important to further increase lipophilicity of cationic dyes. 47

Synthesis of the probe

A common access to HD dyes consists in condensing an electron rich phenol on a carbocyanine 7-Cl. 38 Herein, Cy7-Cl bearing two octadecane chains was prepared (See SI) before being reacted with chlororesorcinol to obtain the NIR emitting HD. Then, caprylic acid was used to esterify HD into Pro-HD-I -. Finally, the iodine counter anion of Pro-HD-I -was easily exchanged for F5-TPB (Scheme 1). This last step is further detailed in the section: encapsulation in NEs (see below).

Scheme 1. Synthesis of HD and pro-HD. i) NEt3, DMF, 75°C, 2h ii) Caprylic acid, EDC, DMAP, DCM, RT, overnight iii) F5-TPB-Li, DCM, RT, 5 min.

Spectroscopic studies

In order to evaluate the performance of our system, spectroscopic studies of Pro-HD and HD were conducted. Due to the highly hydrophobic nature of HD and Pro-HD, spectroscopic studies could not be performed in aqueous solutions where aggregation occurred. Consequently, methanol was chosen as a polar and protic organic solvent that will mimic a cellular environment where these amphiphilic molecules are expected to end up, namely at the interface between biomembranes and cytosol. Oil (Middle Chain Triglycerides, MCT) was also used to study the properties of Pro-HD as it is its solvent when encapsulated in NEs. First of all, the results showed that Pro-HD displayed similar properties in methanol and oil (Fig. 2A,B) with broad multipeaks spectra with lAbs max at 585 and 595 nm, respectively with identical extinction coefficient (e= 64,000 M -1 .cm -1 ) denoting similar solubility in both solvents at this concentration.

Conversely to Pro-HD, HD displayed typical cyanine-shaped absorption spectra with lAbs max at 705 nm and a high extinction coefficient value (e= 127,000 M -1 .cm -1 ) (Fig. 2A). Fluorescence spectroscopy showed that Pro-HD was found to be virtually non-fluorescent in methanol and oil (f=0.006), whereas HD emits in the NIR (723 nm) with a quantum yield of 0.2 (Fig. 2B). Interestingly, when excited at 640 nm, which is a common excitation wavelength in bioimaging, the fluorescence enhancement between Pro-HD and HD was 35-fold (Fig. 2B), making Pro-HD a promising fluorogenic probe to evaluate its hydrolysis by the cell machinery. In order to demonstrate the possible hydrolysis of Pro-HD towards HD, a base (NaOH) was added in the methanolic solution. The fluorescence intensity at 723 nm was monitored over the time (Fig. 2C) and showed that, in these conditions, a plateau was reached after ∼15 min. It corresponded to a fluorescence enhancement of 32-fold which is in line with that between Pro-HD and HD (Fig. 2C). After hydrolysis of Pro-HD, the absorption and emission spectra were recorded and corresponded to those of HD (Fig. S1). As discussed above, a chlorine atom was introduced to the structure of HD to lower its pKa and thus to ensure an emissive specie when exposed to cytosolic environment (pH 7.4). Moreover, a lower pKa would also limit the acidification of HD in acidic environment like in early endosomes (pH ∼6). Indeed, in methanol and in the presence of acid, HD was found to be virtually non-emissive with a fluorescence intensity at 723 nm drastically reduced by 60-fold. Conversely, in the presence of a base (triethylamine), the fluorescence of HD was not significantly affected. (Fig. S2). In the light of these results, the Pro-HD/HD system was considered as a promising probe for encapsulation in NEs.

Encapsulation in NEs

Efficient encapsulation of a molecule in NEs requires a high lipophilicity in order to: 1) ensure a high solubility in the oil phase and 2) avoid its leakage out of the NEs. 29,31,47,48 As shown in the synthesis section, the iodine counter-ion of Pro-HD-I -was exchanged to F5-TPB to obtain Pro-HD using TPB-F5Li (Fig. 3A). Indeed, modifying the salt forms of a active pharmaceutical ingredients is a common approach to efficiently modulate their physicochemical and biological properties. 49 This approach was successfully used for enhancing the encapsulation of a potent antituberculosis drug in poly(lactide) microspheres by replacing the polar sodium counterion ion by a lipophilic tetraheptylammonium one. 50 Although Pro-HD-I -already displayed a hydrophobic structure with a C18 chain combined with a caprylic (C8) ester, its cationic This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins nature combined to the relatively polar iodine counter ion may lead to poor solubility of the dye and potential leakage into biological media. 47 As shown in figure 3A, the calculated logP (ClogP) of Pro-HD-I -is drastically increased when transformed in Pro-HD bearing F5-TPB, from -1.3 to 9.6, respectively. As an illustration of the counterion exchange's effect, the TLC plate is displayed on figure 3A and shows the impressive difference of migration distance on silica (from RF 0.06 to 0.96), in line with earlier reports for other dyes. 51 After solubilization of Pro-HD in oil at 0.5 wt% (corresponding to 3.4 mM), two types of NEs were formulated: 1) Stealth NEs (Fig. 3B), with highly PEGylated surface that prevents from non-specific interactions and thus do not interact with cells. They will be used as control to check whether Pro-HD leaks out of the NEs in the presence of cells. 2) Cell-penetrating NEs, cpNEs (Fig. 3B) that we recently reported, 25 to deliver the cargo to the cells. The cpNEs are obtained by dissolving poly(maleic anhydride-alt-1-octadecen) (PMAO) in the oil prior to formulation. This alternating polymer is composed of lipophilic carbon chains and cyclic anhydride functions. Upon formulation the latter get hydrolyzed to finally display negative charges at the oil surfactant interface. We reported that the negative charges lead to cell-penetration by endocytosis mediated by non-specific electrostatic interactions. 25 After formulation, their sizes were measured by DLS and were found to be similar: 97 and 91 nm, respectively (see Fig. S3). Absorption spectra confirmed the efficient encapsulation of Pro-HD in NEs as the optical density of Pro-HD (after correction of the scattering) was similar to those of Pro-HD in methanol at the same targeted concentration (Fig. S4). Fluorescence spectra, acquired in the same conditions, indicated that Pro-HD was not emissive in both NEs and cpNEs.

In order to assess the potential leakage of Pro-HD out of the NEs, the latter were put in the presence of a base, similarly to figure 2C. Indeed, if the Pro-HD leaks out of the NEs in the presence of NaOH, HD should be formed and should emit at 723 nm. In these conditions no fluorescence enhancement was obtained for both NEs and cpNEs denoting a strong encapsulation of Pro-HD without any apparent leakage (Fig. S5).

Figure 4. Epi-fluorescence microscopy imaging of fixed HeLa cells pre-incubated for 2 h in the presence of 0.5 wt% Pro-HD loaded NEs (top images) and 0.5 wt% Pro-HD loaded cellpenetrating NEs (bottom images). Final concentration of free Pro-HD and loaded Pro-HD was set to 1 µM and the images were acquired in the same conditions of illumination, recording and processing. HD was excited at 641 nm. The nucleus was stained with Hoechst (5 µg.mL -1 ). Scale bar is 10 µm.

Evaluation in cellular experiments

Initially, Pro-HD was incubated for 2h in the presence of HeLa cells as a positive control to evaluate the ability of Pro-HD to be hydrolyzed into fluorescent HD in cellulo. Indeed, due to its high hydrophobicity, Pro-HD was expected to spontaneously penetrate the cells in a fast manner. After incubation for 2h the cells were washed and presented only a dim signal in the nearinfrared channel. However, upon longer incubation, an increasing fluorescence signal was observed in the cytoplasm of cells, reaching a plateau of intensity after 3h (Fig. S6). This control experiment suggested that Pro-HD can be efficiently hydrolyzed in cellulo and that this conversion is not immediate, requiring several hours to occur. In a second time, both Pro-HD (0.5 wt%) loaded NEs and cpNEs were incubated in the presence of cells for 2 h before being washed. Fluorescence imaging showed that whereas cells incubated with stealth NEs displayed no red fluorescence over the time (Fig. 4A-D), those incubated with cell-penetrating NEs showed the progressive appearance of the red fluorescence over the time (Fig. 4E-H).

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Please do not adjust margins Quantification of fluorescence intensity confirmed these observations and showed that the maximum signal is reached after 6 h post incubation (Fig. 5). After 24 h the signal decreased probably due to the repartition of the probe during cell division. This experiment confirmed that Pro-HD is tightly confined in the NEs and does not leak out from the latter ensuring a controlled delivery. It also showed that cpNEs successfully delivered Pro-HD into cells. It was noteworthy that when Pro-HD was delivered by cpNEs, the fluorescence signal was lower in comparison with direct incubation of Pro-HD and required more time to reach a plateau of fluorescence intensity. Indeed, unlike free Pro-HD, the Pro-HD loaded cpNEs need to: first interact with cells in a non-specific manner and then internalize before being disintegrated to gradually liberate pro-HD within the cell. The summary of our experiments and the mechanism of release is presented in figure S7.

Conclusion

Visualization of prodrug delivery and release of active drug from nanocarriers is important for better understanding of the bottlenecks in nanomedicine. In particular, it concerns moderately hydrophobic cargos that could be reversibly modified into lipophilic prodrug in order to be loaded in nanoemulsions for controlled drug delivery. Here, we developed Pro-HD, a lipophilic near infrared fluorogenic probe as a model of prodrug to assess the controlled cargo delivery and release by nanoemulsions into cells. For this purpose, HD, our fluorescent drug model, was esterified with the hydrophobic and biocompatible caprylic acid, and its counter ion was exchanged for the hydrophobic F5-TPB giving rise to Pro-HD, a highly lipophilic fluorogenic prodrug model. We demonstrated that Pro-HD, which is virtually non-fluorescent, could be hydrolyzed into HD in cuvette as well as in cellulo, provoking a fluorescence enhancement of 35-fold in the near infrared region (lEm= 723 nm). Due to its high lipophilicity, Pro-HD was efficiently loaded into NEs with no leakage thus avoiding undesired premature delivery. Using cell-penetrating NEs, we were able to show that Pro-HD was delivered to cells and transformed into HD within ∼6h. We believe that this proof of concept can lead to the development of efficient prodrugs based on similar modifications of drugs requiring NEs as nanocarriers for efficient administration to target and treat tumors. As perspective, and taking advantage of the near infrared emission of HD, we also believe that this system is amenable to fluorescence in vivo imaging experiments, this will be the subject of a dedicated study.

Experimental Materials

The solvents were of analytical grade and dry, reagent and starting materials were purchased form TCI, Alfa Aesar or Merck Millipor. Labrafac WL® 1349 (medium chain triglycerides, MCT) was obtained from Gattefossé (Saint-Priest, France). Kolliphor ELP®, was from BASF (Ludwigshafen, Germany). Poly(maleic anhydride-alt-a-octadecene) (PMAO) was purchased from Sigma Aldrich (St. Louis, USA). Phosphate buffered saline (PBS) was from Eurobio (Gourtaboeuf, France) and fetal bovine serum (FBS) from Lonza.

Synthesis

Protocols and characterizations can be found in the supplementary information. NMR spectra were recorded on a Bruker Avance III 400 MHz spectrometer. Mass spectra were obtained using an Agilent Q-TOF 6520 mass spectrometer.

Spectroscopic studies

All the solvents were spectro grade. Absorption and emission spectra were recorded on a Cary 400 Scan ultraviolet-visible spectrophotometer (Varian) and a FluoroMax-4 spectrofluorometer (Horiba Jobin Yvon) respectively. For standard recording of fluorescence spectra, the emission was collected 10 nm after the excitation wavelength. All the spectra were corrected from wavelength-dependent response of the detector. Quantum yields were determined by comparison with Rhodamine 800 in EtOH (QY= 0.25) 52 as reference using the following equation:

where QY is the quantum yield, I is the integrated fluorescence intensity, n is the refractive index, and OD is the optical density at the excitation wavelength. R represents the reference.

Formulation of NEs

Nano-emulsions (NEs) were formulated with spontaneous emulsification method, as described previously. 25 In 100 mg of Medium Chain Triglyceride oil (MCT), Pro-HD (0.5 mg) in acetone was added before being heated at 80°C until complete evaporation of acetone and solubilization of Pro-HD in MCT. 67 mg of Kolliphor (surfactant) was then added at 80°C and after

QY = QY ! × !×!" ! ×! ! ! ! ×!"×! ! ! !
! This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins mixing for 10 min, 0.25 mL of pre-heated PBS was added to form nanoemulsions. For cell-penetrating NEs, PMAO (1 mg) was first dissolved in MCT prior to the addition of Pro-HD. The size of the obtained NEs was measured by Dynamic Light Scattering (DLS) using a Malvern Zetasizer Nano ZSP (Malvern, U.K.). For the size measurement, all the emulsions were diluted by 100 times and measured at a temperature of 25°C. Both size distribution and polydispersity index (PDI) were recorded.

Cellular imaging

HeLa cells (ATCC® CCL-2™) were grown in Dulbecco's Modified Eagle Medium without phenol red (DMEM, Gibco-Invitrogen) supplemented with 10% fetal bovine serum (FBS, Lonza), 1% L-Glutamine (Sigma Aldrich) and 0.1% antibiotic solution (gentamicin, Sigma-Aldrich) at 37°C in humidified atmosphere containing 5% CO2. Cells were seeded onto a 35 mm glassbottomed imaging dish (Ibidi®) at a density of 5´10 4 cells/well 24 h before incubation experiments. The cells were then washed 3 times with PBS and incubated 2h in opti-MEM in the presence of Pro-HD, Pro-HD loaded NEs and Pro-HD loaded cpNEs (1 µM based on absorbance of Pro-HD) before being washed again 3 times with PBS. The cells were then incubated at various times in Dulbecco's modified Eagle medium (DMEM, Gibco-Invitrogen), supplemented with 10% fetal bovine serum (FBS, Lonza) and 1% antibiotic solution (penicillin-streptomycin, Gibco-Invitrogen) at 37° C in humidified atmosphere containing 5% CO2. Prior to imaging, nucleus was stained with Hoechst (5 µg.mL -1 ) and the cells were washed with PBS and fixed with 4% PFA at room temperature for 5 minutes before being washed 3 times with PBS. The images were acquired with a Nikon Ti-E inverted epi-fluorescence microscope, using CFI Plan Apo × 60 oil (NA = 1.4) or CFI Plan Apo ×20 air (NA = 0.75) objective, and a Hamamatsu Orca Flash 4 sCMOS camera. Hoechst and HD were excited at 395 and 641 nm, respectively, using lightemitting diode (SpectraX, Lumencor). The images were recorded using NIS Elements and then processed with Icy software.

Figure 1 .

 1 Figure 1. Schematic principle of a prodrug for enhanced encapsulation in NEs (A) and of the developed HD/Pro-HD system as a model to monitor the drug delivery by NEs (B).

Figure 2 .

 2 Figure 2. Spectroscopic studies of Pro-HD and HD (1 µM). Absorption (A) and emission (B) spectra of HD in methanol and Pro-HD in oil (MCT) and in methanol. (C) In situ hydrolysis of Pro-HD to HD (1 µM in MeOH), evolution of the fluorescence intensity at 723 nm over 30 min and after addition of aqueous NaOH (at 90 s, 5 µL added in 1 mL, final NaOH concentration was 250 µM). Excitation wavelength was 640 nm. Pictures of cuvettes are Pro-HD (left) and HD (right) in methanol.

Figure 3 .

 3 Figure 3. (A) Anion exchange using F5-TPB as a lipophilic counter-ion, TLC (DCM/MeOH, 95:5) depicted the efficiency in decreasing the polarity from Pro-HD•I -to Pro-HD (F5-TPB - ). (B) Formulation by spontaneous nanoemulsification of Pro-HD loaded stealth NEs (NEs) and cell-penetrating NEs (cpNEs) using poly(maleic anhydride-alt-1-octadecen) (PMAO) as polymer. 25

Figure 5 .

 5 Figure 5. Mean fluorescence intensity of cells at various time points post incubation with NEs and cpNEs. Error bars are the standard deviation between images (10 images per condition, 10 cells per image).

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 5

Acknowledgements

This work was supported by ERC Consolidator grant BrightSens 648528. XW was founded by the China Scholarship Council PhD fellowship (CSC No. 201706240033). We acknowledge Dr. Delphine Garnier and Dr. Estefania Oliva from the Service de Chimie Analytique (SCA) for their assistance in the LC-MS and RMN analyses.

Conflicts of interest

There are no conflicts to declare