Lucia Forte

Stéphanie Sarda

Christèle Combes

Fabien Brouillet

Massimo Gazzano

Olivier Marsan

Elisa Boanini
email: elisa.boanini@unibo.it

Adriana Bigi

Elisa Boanini

+ Adriana Bigi

Hydroxyapatite functionalization to trigger adsorption and release of risedronate

Keywords:

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

Introduction

Bisphosphonates (BPs) are widely and successfully employed for the treatment of diseases associated to bone turn-over disorders related to pathologies. such as osteoporosis, Paget's disease and bone metastases [1,2). ln fact, these drugs not only display a great affinity for the minerai phase of bone. preventing its dissolution. but also inhibit osteoclast activity [START_REF] Russell | Mechanisms of action of bisphosphonates: similarities and differences and their potential influence on clinical efficacy[END_REF]. However. their systemic pro longed use has been shown to provoke several negative side effects, including jaw osteonecrosis. gastrointestinal disorders. atypical subtrochanteric fractures (2.4.5). Moreover a low bioavailability is commonly observed for oral administration. Local release at spe cific bone sites exhibiting a risk of fractures has been suggested as a promising alternative strategy to deliver BPs without incurring in undesirable side effects [START_REF] Fazil | Bisphosphonates: therapeutics potential and recent advances in drug delivery[END_REF]. Severa! supports have been pro posed in the literature and apatitic calcium phosphates appear as good candidates as they are similar to bone minerai and largely used for bone substitute applications (6-13). BPs-functionalized CaPs can be prepared through adsorption from solution. as well as by direct synthesis in aqueous solution [START_REF] Verron | Calcium phosphate biomaterials as bone drug delivery systems: a review[END_REF][START_REF] Boanini | The effect of zoledronate-hydroxyapatite nanocomposites on osteoclasts and osteoblast-like cells in vitro[END_REF][START_REF] Errassifi | Infrared, Raman and NMR investigations of risedronate adsorption on nanocrystalline apatites[END_REF]. A study car ried out by Nancollas et al. using a constant composition method allowed to determine the binding affinity of several BPs to hydrox yapatite(HA) [START_REF] Nancollas | Novel insights into actions of bisphosphonates on bone: differences in interactions with hydroxyapatite[END_REF]. Moreover. previous studies on the mechanism of adsorption and desorption processes evidence the influence of the structure and composition of the apatitic surface on the parameters of adsorption of BPs and their kinetics of release [ 13, [START_REF] Pascaud | Interaction between a bisphosphonate, tiludronate, and biomimetic nanocrystalline apatites[END_REF][START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF].

ln this study we investigated the role of composition and surface charge of hydroxyapatite supports on the adsorption and release mechanisms of risedronate. To this aim, we utilized HA. HA with a partial substitution of zinc to calcium (ZnHA). and HA func tionalized with polyethyleneimine (HAPEI). PEI and Zn can indeed fulfill different useful roles. PEI is a polycationic polymer contain ing a high density of ionizable amino groups, widely employed to coat HA for chromatographie applications and complex transfec tion systems [START_REF] Murakami | Surface chemical analysis and chromatographic characterization of polyethylenimine-coated hydroxyapatite with various amount of polyethylenimine[END_REF][START_REF] Shkilnyy | Poly(ethylene imine)-controlled calcium phosphate mineralization[END_REF][START_REF] Sokolova | An outer shell of positively charged poly(ethyleneimine) strongly increases the transfection efficiency of calcium phosphate/DNA nanoparticles[END_REF]. Herein we synthesized hydroxyapatite in the presence of PEI in solution in order to get functionalized HA crystals with an increased number of positive charges on their surface with respect to pure HA. Enhancement of positive charge on the surface of the HA nanocrystals, thanks to the presence of the polycationic polymer, should promote the adsorption of negatively charged BPs from solution and control their release.

On the other hand, cationic substitution in HA can influence crystal growth and increase the specific surface area which in turn controls the adsorption ability [START_REF] Bigi | Ion substitution in biological and synthetic apatites[END_REF]. Zinc can partially substitute for calcium in the structure of HA and has been demonstrated to inhibit osteoclast formation and bone resorption [START_REF] Bigi | Ion substitution in biological and synthetic apatites[END_REF][START_REF] Shepherd | An in vitro study into the effect of zinc substituted hydroxyapatite on osteoclast number and activity[END_REF]. Its presence into HA structure might influence BPs interaction with the calcium phosphate surface. Moreover its co-presence with BPs in HA crystals should enhance the antiresorptive properties of the material.

In the present paper, we investigated the interaction between risedronate and different apatitic crystals (HA, HAPEI and ZnHA), through the study of the adsorption reaction of this BP on these different apatitic supports and physicochemical characterization of the solid products and of the supernatant solutions. Then, the release of risedronate from the three types of apatitic supports will be studied and discussed.

Materials and methods

Synthesis of the apatitic samples

The synthesis of HA was carried out in N 2 atmosphere using CO 2 free water [START_REF] Bigi | Microstructural investigation of hydroxyapatite-polyelectrolyte composites[END_REF]. 50 mL of a 1.08 M Ca(NO 3 ) 2 •4H 2 O solution (pH adjusted to 10 with NH 4 OH) was heated at 90 • C and 50 mL of 0.65 M (NH 4 ) 2 HPO 4 solution was added drop-wise under stirring. The precipitate was maintained in contact with the reaction solution for 5 h at 90 • C under stirring, then centrifuged at 10,000 rpm for 10 min and repeatedly washed with CO 2 -free distilled water. The product was dried at 37 • C overnight.

Hydroxyapatite at different poly(ethylenimine) contents (HAPEI) was obtained following the same experimental procedure as for HA except that PEI was added to the Ca(NO 3 ) 2 •4H 2 O solution, before adjusting the pH to 10 with NH 4 OH. Poly(ethylenimine) solution (Aldrich, MW ∼ 2000 g mol -1 ) was used. Concentrations of PEI tested were 1, 2 and 4 M (calculated with respect to the final volume of the precipitating medium) leading to HAPEI 1, HAPEI 2 and HAPEI 4 samples, respectively.

Zn-substituted hydroxyapatite (ZnHA) was synthesized following the same experimental procedure as for HA, but the cationic solution was prepared by dissolving the appropriate amounts of Ca(NO 3 ) 2 •4H 2 O and Zn(NO 3 ) 2 •6H 2 O in CO 2 -free deionized water before adjusting the pH to 10 with NH 4 OH. The total cationic concentration was 1.08 M, and the Zn/(Ca + Zn) molar ratio was 0.1.

Risedronate adsorption and release

Adsorption experiments were carried out on HA, ZnHA and HAPEI. The HAPEI samples used for risedronate adsorption study was HAPEI 4, from now onwards indicated as HAPEI for simplicity. 50 mg of apatitic sample were dispersed at physiological temperature (37 ± 1 • C) in 5 mL of risedronate (Aldrich) solutions (concentration ranging from 0 to 3 mM) in a polyethylene tube. The latter were prepared by dissolving the appropriate amount of risedronate in an aqueous 1 mM KCl solution (standard solution); the pH of the obtained solutions was adjusted to 7.4 using HCl or KOH solutions. After sonication for 1 min, the suspensions were incubated for 1 h without stirring and then centrifuged for 10 min at 5000 rpm leading to the various BP-functionalized apatites: HABP, HAPEIBP and ZnHABP samples. This equilibration time (1 h) was previously determined from kinetic experiments using a risedronate solution of 0.86 mM; this time allowed to reach the equilibrium of adsorption while minimizing the dissolution of apatitic supports. Blanks containing only apatite incubated in KCl solutions were used as controls. After centrifugation, the solids obtained were washed with deionized water and dried at 37 • C overnight. The supernatants were immediately filtrated on 0.2 m Millipore filters and then stored at 4 • C before titration.

The risedronate concentration in the filtrates was determined using UV spectrophotometric absorption at 262 nm (Hewlett Packard 8452 A diode array spectrophotometer). This wavelength corresponds to the maximum absorbance of the pyridine group of risedronate molecule.

Risedronate release profiles were obtained with a flowthrough cell system (USP Apparatus 4 Sotax CE6, Sotax AG, Switzerland) with 12 mm cells for powders and a peristaltic pump. In all experiments, laminar flow was used with one glass beads layer covered with each BP-functionalized apatitic sample, mixed with 2 g of glass beads. Different weights were utilized for the analysis of the different materials so that all the samples contained the same amount of adsorbed BP (about 1.8 mol/m 2 ). The release tests were carried out at 37.0 ± 0.5 • C under sink conditions according to European Pharmacopeia guidelines. The dissolution medium used was deionized water pumped through the column at a flow rate of 9 mL/min. A closed system was used, recycling 50 mL of dissolution medium. Fractions of 5 mL were collected periodically and risedronate content was determined by UV spectrophotometry at 262 nm. The same volume of dissolution medium was replaced back after each sampling in order to maintain the volume constant and sink conditions. Release study was performed in triplicate for each type of BP-functionalized apatite.

Sample characterization

X-Ray diffraction analysis was carried out by means of a PANalytical X'Pert PRO powder diffractometer equipped with a fast X'Celerator detector. Ni-filtered CuK␣ radiation was used (40 mA, 40 kV). The 2 range was investigated from 10 • to 120 • with a step size of 0.033 • and a time/step of 200 s. The determination of the cell and size/strain parameters was obtained by a full profile pattern refinement using the MAUD (Material Analysis Using Diffraction) routine [START_REF] Ferrari | Method for the simultaneous determination of anisotropic residual stresses and texture by X-ray diffraction[END_REF] with the Popa anisotropic size-strain model [START_REF] Popa | The (hkl) dependence of diffraction-line broadening caused by strain and size for all Laue groups in Rietveld refinement[END_REF]. The instrumental broadening was estimated by scanning the silicon NIST 640 e sample.

Ca, Zn and P contents in the solid products were determined by means of an inductively coupled plasma (ICP) mass spectrometer (ICP-AES, Horiba Jobin Yvon). Powders were previously dissolved in 0.6 M HNO 3 solution.

The infrared spectrum of each synthesized and functionalized apatite powder was recorded over the 400-4000 cm -1 range in transmission mode with KBr pellets (2 mg sample/300 mg KBr) using a Thermo Nicolet 5700 Fourier-transform infrared (FTIR) spectrometer.

Raman spectra of the samples were generated on a Horiba, Jobin-Yvon Labram HR800 confocal microspectrometer, equipped with a helium-neon laser ( = 632.82 nm). The spectral resolution was 2 cm -1 , the laser power was 2 mW and integration times varied from 30 to 120 s. All spectra were recorded over a wavelength range of 100-4000 cm -1 . Three spectral accumulations were averaged.

For TEM investigations, a drop of sonicated apatitic calcium phosphate suspension in ethanol was transferred onto holey carbon foils supported on conventional copper microgrids. A Philips CM100 transmission electron microscope, operating at 80 kV was used.

Thermogravimetric analysis was carried out using a PerkinElmer TGA-7. Heating was performed in a platinum crucible in air flow (20 cm 3 /min) at a rate of 10 • C/min up to 800 • C. The sample weights were in the range 5-10 mg. Results from this analysis represent the mean value of determinations for three different samples of each composition.

Zeta potential was measured using a Malvern Instruments Zetasizer Nano. 5 mg of powder sample was suspended in 50 mL of MilliQ water after sonication for 2 min. Each analysis was performed in triplicate.

The specific surface area was measured using a Carlo Erba Sorpty 1750 BET analyzer using constant volume N 2 adsorption with desorption at 80 • C.

Results and discussion

Characterization of the apatitic substrates

Chemical analysis of HA powder gave a Ca/P ratio of 1.67 characteristic of stoichiometric hydroxyapatite (Table S1). The powder XRD patterns of HA, HAPEI (PEI concentration in solution: 4 M) and ZnHA are presented in Fig. 1.

It is evident that all the samples are constituted of apatitic calcium phosphate as unique crystalline phase. However, the broadening of the XRD peaks varies with the type of apatite substrates synthesized. In particular, the reflections in the pattern of HAPEI are more sharp than those of pure hydroxyapatite. We can observe that the products obtained through the synthesis of HA in the presence of different PEI concentrations in solution, namely 1, 2 and 4 M, display an increase of the sharpness of the diffraction peaks on increasing PEI concentration (Fig. S1), which suggests an increase of crystallinity of the apatites precipitated in these conditions. This trend is confirmed by the Raman spectroscopic analysis of these samples (Fig. S2); indeed, the sharpness of the phosphates and hydroxyl vibration bands characteristic of HA increases on increasing PEI content. Moreover, the spectra of the samples containing the cationic polymer exhibit the presence of two absorption bands around 2800-2900 cm -1 characteristic of CH symmetric and asymmetric stretching bands ( NH stretching vibration band of PEI at about 3300 cm -1 cannot be observed probably due to their low intensity) [START_REF] Lakard | Theoretical study of the vibrational spectra of polyethylenimine and polypropylenimine[END_REF].

The lengths of the coherent domains ( hkl ) and the values of microstrain () were calculated from the microstructure parameters determined from the X-ray diffraction pattern refinement procedure. The results show that the main contribution to the broadening of the reflections is due to coherent length of the perfect crystalline domains, which increases significantly both along the c-axis direction and, even more, along the orthogonal direction on increasing PEI content in the solids (Table S1). At variance, the values of microstrain are of the order of 10 -4 and do not change appreciably as a function of composition. In agreement with the increase of crystallinity, the lattice parameters exhibit a slight but significant reduction of the a-parameter on increasing PEI content [START_REF] Gomes | On the effect of temperature on the insertion of zinc into hydroxyapatite[END_REF]. PEI content, determined through thermogravimetric analysis (Fig. S3) increases as a function of concentration in solution up to about 2.5 wt.%. The hypothesis of an electrostatic interaction between the polymer chain (rich in amino groups) and the surface of the apatitic crystals is supported by the values of zeta potential, which assume positive values and increase on increasing the content of the polycationic polymer (Table S1). The presence of PEI associated with apatite nanocrystals influences their morphology: when compared with HA nanocrystals, the HAPEI ones display a shorter mean length and a greater thickness (Fig. 1).

However, the morphological variation does not provoke significant modification of the specific surface area, which is quite similar to that of pure HA (Table 1). On the basis of their increased thickness and coherent length of perfect crystalline domains, it could be suggested that HAPEI nanocrystals can be considered as mesocrystals [START_REF] Song | olfen, Mesocrystals-ordered nanoparticle superstructures[END_REF] made up of HA nanoparticles aligned by PEI: PEI could interact preferentially with the hydroxyapatite crystal faces parallel to the c-axis and promote the oriented attachment of nanoparticles, leading to the observed increased thickness (Table 1).

ZnHA nanocrystals exhibit more perturbed shape, ill-defined edges and significantly reduced dimensions in comparison to HA (Fig. 1). Moreover, ZnHA displays a remarkably higher specific surface area when compared to HA and HAPEI, in agreement with its smaller crystal dimensions (Table 1). Zn inhibition of HA crystal growth is in agreement with previous studies [START_REF] Fuierer | A mineralization adsorption and mobility study of hydroxyapatite surfaces in the presence of zinc and magnesium ions[END_REF][START_REF] Bigi | Inhibiting effect of zinc on hydroxylapatite crystallization[END_REF] and it is supported by the observed broadening of the diffraction peaks of ZnHA with respect to those of HA (Fig. 1). Accordingly, the coherent lengths of the perfect crystalline domains of ZnHA evaluated from the line broadening of the (002) and (310) are significantly reduced with respect to those of pure HA (Table 1). Zn incorporation into HA crystals to about 7.9 atom.% provokes a reduction of the lattice parameters, in agreement with its smaller ionic radius with respect to that of calcium [START_REF] Ren | Characterization and structural analysis of zinc-substituted hydroxyapatites[END_REF], with no secondary crystalline phase observed.

Risedronate adsorption

The evolution of the amount of risedronate adsorbed on the solids Q ads (mol/m 2 ) from the dilute solutions as a function of the equilibrium BP concentration C eq (0-2 mM) is plotted in Fig. 2.

The isotherms obtained for HA and ZnHA are Langmuirian in shape (r 2 = 0.87 and 0.94, respectively) and reached the plateau at relatively low equilibrium concentrations (below 1 mM), indicating a high affinity of risedronate for these apatitic surfaces. Similar observations have been reported previously for the adsorption of bisphosphonate molecules (risedronate and tiludronate) on apatitic support [START_REF] Errassifi | Infrared, Raman and NMR investigations of risedronate adsorption on nanocrystalline apatites[END_REF][START_REF] Pascaud | Interaction between a bisphosphonate, tiludronate, and biomimetic nanocrystalline apatites[END_REF][START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF]. For same weight of apatitic powders, the risedronate content at plateau in presence of ZnHA was twice as much as that adsorbed on HA (about 40 and 100 mol/g for HA and ZnHA, respectively) mainly due to the higher specific surface area of ZnHA (86 m 2 /g) compared with that of HA (23 m 2 /g), (Table 1). The uptake of risedronate depended linearly on the amount of released phosphate ions in solution (Fig. S4). Thereby, the uptake of risedronate is proportional to the amount of phosphate ions released in solution indicating that the adsorption of risedronate on HA affects the amount of ionic species in solution and can be described as a chemisorption corresponding to an ion exchange process between bisphosphonate molecules in solution and phosphates species on HA and ZnHA, as previously published for bisphosphonates adsorption on apatitic surfaces [START_REF] Errassifi | Infrared, Raman and NMR investigations of risedronate adsorption on nanocrystalline apatites[END_REF][START_REF] Nancollas | Novel insights into actions of bisphosphonates on bone: differences in interactions with hydroxyapatite[END_REF][START_REF] Pascaud | Interaction between a bisphosphonate, tiludronate, and biomimetic nanocrystalline apatites[END_REF][START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF][START_REF] Al-Kattan | Medical potentialities of biomimetic apatites through adsorption, ionic substitution, and mineral/organic associations: three illustrative examples[END_REF]. The slope of the curve is close to 1 for HA and it increases for ZnHA. Indeed the number of phosphate groups released per adsorbed risedronate molecule varies as a function of the characteristics of the apatitic support, as observed in previous studies on BPs adsorption on apatitic substrates [START_REF] Pascaud | Interaction between a bisphosphonate, tiludronate, and biomimetic nanocrystalline apatites[END_REF][START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF][START_REF] Al-Kattan | Medical potentialities of biomimetic apatites through adsorption, ionic substitution, and mineral/organic associations: three illustrative examples[END_REF]. It can be noticed that the calcium and zinc concentrations in the supernatants after adsorption were low and not affected by the adsorption of risedronate (Ca concentrations for HA and HAPEI: below 0.5 mM; Zn and Ca concentrations for ZnHA: below 0.5 mM and 2 mM, respectively). These concentrations are related to slight dissolution of the supports during adsorption experiments [START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF].

The parameters of adsorption can be determined from the Langmuir Eq. ( 1), (Table 2):

Q ads = KNC eq / 1 + KC eq (1)
where N corresponds to the maximum amount of adsorbed risedronate (mol/m 2 ) and K is the affinity constant of risedronate for the solid surface (L/mmol). The values of N obtained for the HA and ZnHA supports are close (Table 2): 1.88 ± 0.05 and 1.20 ± 0.08 mol/m 2 , respectively, and correspond to the values previously obtained for the adsorption of risedronate molecules on apatitic surface [START_REF] Errassifi | Infrared, Raman and NMR investigations of risedronate adsorption on nanocrystalline apatites[END_REF]. At the same time, a significant decrease of the affinity K is observed for ZnHA (7 ± 1 L/mmol) compared with HA (21 ± 3 L/mmol), (Table 2), possibly related to changes in surface chemical composition.

The isotherm of risedronate adsorption on HAPEI can also be described by the Langmuir model (r 2 = 0.99). The amount adsorbed at saturation, N, was higher on HAPEI (7.9 ± 0.4 mol/m 2 ) than on HA and ZnHA but the curve does not reach a plateau even at high equilibrium concentrations in solution (C eq ). This can be due to the competition of several processes: a chemisorption process on HA surface and a physisorption process on PEI coating. The decrease of the affinity K for HAPEI (2.2 ± 0.3 L/mmol), (Table 2) can be explained by the presence of PEI on the apatitic surface. The evolution of the amount of risedronate adsorbed as a function of phosphate released in solution is still linear, but the slope appears lower than for HA. The ion exchange process proposed to occur at the surface of the apatite seems to be affected by the presence of PEI. The number of phosphate groups released per BP molecule is lower in the presence of PEI, in agreement with the presence of two different mechanisms of adsorption: risedronate chemisorption, which provokes phosphate release, and risedronate physisorption, which does not imply ion exchange.

Characterization of the solids after risedronate uptake

The results of XRD analysis of the solid products obtained after bisphosphonate adsorption show that the presence of risedronate does not influence the crystallinity of the apatitic samples and does not provoke precipitation of any other crystalline phase (Fig. S5).

Similarly, TEM images of HABP, ZnHABP and HAPEIBP show that the characteristic morphologies of the different apatitic samples used as substrates for risedronate adsorption are maintained after adsorption, as it can be appreciated by comparing the images reported in Fig. S6 with those in Fig. 1. Adsorption of BP does not significantly modify the values of zeta potential of HA and ZnHA, whereas it provokes a slight, but appreciable, decrease of the zeta potential of HAPEI (from 26.2 to 23.5 mV).

Raman spectra of HA and ZnHA after adsorption (Fig. 3) show the characteristic vibration bands of the apatitic structure [START_REF] Penel | MicroRaman spectral study of the PO4 and CO3 vibrational modes in synthetic and biological apatites[END_REF], especially those of apatitic phosphate groups: 2 (438-463 cm -1 ), 4 (580-614 cm -1 ), 1 (960 cm -1 ), 3 (1029-1077 cm -1 ), and the OH vibration band at 3560 cm -1 [START_REF] Eichert | Nanocrystalline apatite-based biomaterials: synthesis processing and characterization[END_REF]. All spectra display additional bands which can be attributed to the presence of adsorbed BP: in particular, two bands between 2900 and 3000 cm -1 , corresponding to C H stretching, and two intense bands between 1025 and 1055 cm -1 which might be assigned to C H pyridine ring deformation, are present. Moreover, the spectra show medium intensity bands between 1500 and 1600 cm -1 , associated with the substituted pyridine ring, and the characteristic Raman bands of phosphonate groups between 850 and 1230 cm -1 . Interestingly, we can see that these bands are shifted compared to those of risedronate sodium salt spectrum, showing a change in the envi- ronment of these groups after adsorption. These spectroscopic observations suggest a strong interaction between risedronate molecule and calcium ions at the surface of the apatitic samples after adsorption, as no insoluble calcium salts were observed by XRD and TEM (Figs. S5 andS6). These results are in accordance with the Langmuir model proposed for the adsorption isotherm, and the mechanism of interaction based on ion exchange process.

A shift of the characteristic bands of risedronate is also observed in the Raman spectrum of HAPEIBP after adsorption (Fig. 4), which confirmed that the process of adsorption of BP on the mineral part of HAPEI was similar. Moreover the presence of the vibration bands of PEI molecules (especially stretching vibrations of CH, CH 2 groups between 2800 and 3000 cm -1 ) on HAPEIBP confirmed that PEI was still on HA surface after adsorption experiments. Thus, PEI is able to participate to the process of BP adsorption.

Risedronate release

The results of kinetics of risedronate release from the different apatitic supports are presented in Fig. 5a. The release was fast during the first hour and then slowed down, as observed in previous studies for several apatitic supports [START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF]. All the samples release a quantity of risedronate that represents a small percentage of the initial adsorbed amount. However, the type of apatitic support is an important parameter for BP release control. In fact, the total amount of risedronate released was higher from HAPEI (about 14% of the initial quantity adsorbed) than from HA and ZnHA (about 5 and 9% respectively) probably due to different processes of release.

In order to describe and correlate the mechanism of BP release from each support, various usual mathematical models were tested [34]. The results of curve fitting with these models give interesting indications on the release behavior of risedronate from the different tested supports. First, the release of risedronate from the apatite supports without PEI (HA and ZnHA) cannot be directly described by a simple Higuchi diffusion model (r 2 = 0.66 and 0.83 for HA and ZnHA, respectively, Fig. 5b), suggesting another mechanism involving mainly dissolution of the apatitic support [START_REF] Costa | Modeling and comparison of dissolution profiles[END_REF]. In the case of HA and ZnHA, risedronate molecules were only slowly released from these apatitic supports because they were irreversibly bound by chemisorption. Indeed the exchanged species cannot be removed from apatitic surface by simple dilution of the exchange solution or simple washing of the solids, as previously published for adsorbed molecules on apatites, particularly bisphosphonates [START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF]. Therefore the release rate was limited by support dissolution keeping in mind the diminishing surface of the apatitic particles during dissolution; the dissolution deceleration may be explained on the basis of the reduction in particle size and surface as observed by several authors for degradation kinetic studies of calcium phosphates [START_REF] Hayakawa | In vitro degradation behavior of hydroxyapatite[END_REF][START_REF] Tang | Kinetics of dissolution of ␤-tricalcium phosphate[END_REF]. Moreover, assuming that the rate of dissolution depends on the surface area of the particle, the higher BP release rate observed from ZnHA compared with HA can be attributed to its higher specific surface area and solubility.

In contrast, the release mechanism from HAPEI seemed governed by simple laws of diffusion (r 2 = 0.98 from HAPEI, Fig. 5b) as generally observed from polymeric matrix [START_REF] Costa | Modeling and comparison of dissolution profiles[END_REF][START_REF] Fatnassi | Optimization of spray-dried hyaluronic acid microspheres to formulate drug-loaded bone substitute materials[END_REF]. Liquid penetrates the PEI surface and dissolves the trapped drug, which then diffuses into the release medium. However, if a total delivery of the drugs may be obtained for pure diffusion model applied to pure polymeric supports, it was not observed from HAPEI mineralorganic support (no more than 15% of the initial quantity adsorbed are released after 7 h of test) suggesting the involvement of a secondary mechanism related to the composite nature of the HAPEI. The fast release observed during the first hour can be attributed to the release of the drug molecules associated to the organic phase by physisorption, whereas the following slow release of BP can be ascribed to dissolution of the apatitic phase. This more complex mechanism of release explains the relatively higher quantity of drug delivered from HAPEI compared with those from HA and ZnHA.

Conclusions

The results of this study indicate that all the apatitic supports display Langmuir isotherms of adsorption. The mechanism of adsorption can be explained by ionic exchange between bisphosphonate molecules in solution and phosphate on the surface of apatitic supports. The values of the parameters of adsorption, N and K, obtained for the HA and ZnHA supports are close and correspond to the values previously obtained for the adsorption of risedronate molecules on apatitic surfaces.

Interestingly, in the case of HAPEI, the plateau of the Langmuir isotherm of risedronate adsorption was not reached even at high equilibrium concentrations in solution. Risedronate adsorption on HAPEI mineral-organic support occurs not only through chemisorption on apatitic phase, as for HA and ZnHA crystals, but also through physisorption involving PEI coating. Both mechanisms modulate bisphosphonate release. These results show that similarly to the adsorption process, risedronate release is directly related to the nature and the physicochemical characteristics of the apatitic supports. The characteristics and properties of these tailor-made hydroxyapatite supports could be exploited to develop delivery systems for antiresorptive agents directly on osteoporotic sites, allowing reduction of systemic treatments and associated drawbacks.

Figure S5

. XRD patterns of apatitic samples before (black) and after (red) the adsorption process (in risedronate solution at 3 mM). No difference can be appreciated before and after the adsorption process, as it can be seen also in the insets, where the order of plotting has been reversed in order to highlight possible dissimilarity. ε 002 (*10 -4 ) 9.9(8.5) 6.9(5.1) 6.9(2.7) 5.9(7.0) ε 310 (*10 -4 )

Fig. 1 .

 1 Fig. 1. Powder X-ray diffraction patterns and TEM images of the different synthesized apatitic samples: HA, HAPEI, ZnHA. Magnification in all TEM images is the same for direct comparison.

Fig. 2 .

 2 Fig. 2. Adsorption isotherms of risedronate on hydroxyapatite (HA), Zn-substituted hydroxyapatite (ZnHA) and PEI-modified hydroxyapatite (HAPEI) at pH 7.4 and 37 • C. The data fit the Langmuir isotherm.

Fig. 3 .

 3 Fig. 3. Raman spectra of risedronate sodium salt, HA, HABP and ZnHABP after adsorption (with Qads equal to the maximum value of the adsorption isotherm).

Fig. 4 .

 4 Fig. 4. Raman spectra of risedronate sodium salt, PEI, HAPEI and HAPEIBP after adsorption (with Qads equal to the maximum value of the adsorption isotherm).

Fig. 5 .

 5 Fig. 5. (a) Risedronate (BP) released (wt.%) from the different apatitic samples as a function of time. The initial amount of BP on each sample was the same, i.e. about 1.8 mol/m 2 . (b) Linear regression of Higuchi model (% BP released = KH × √ t, with KH constant) for the release kinetics of risedronate from HA, ZnHA and HAPEI.

Figure S6 .

 S6 Figure S6. TEM images of the different apatite samples obtained after risedronate adsorption.

Table 1

 1 Lattice parameters, coherent lengths ( hkl ) of the perfect crystalline domains in the direction normal to 002 and to 310 planes; Specific surface area (SSA); Zeta potential; PEI and Zn content of the different apatitic samples synthesized (HA, HAPEI and ZnHA).

		a (Å)	c (Å)	L 002 (Å)	L 310 (Å)	PEI content (wt.%)	Zn content (at.%)	SSA (m 2 /g)	Zeta potential (mV)
	HA	9.4378(3)	6.8862(2)	657(4)	311(3)	-	-	23	-15.6
	HAPEI	9.4298(2)	6.8872(2)	929(7)	543(5)	2.4	-	26	+26.2
	ZnHA	9.4241(9)	6.8696(2)	367(4)	148(3)	-	7.9	86	-15.3

Table 2

 2 Adsorption parameters of risedronate on HA, ZnHA and HAPEI samples, i.e. maximum amount at saturation (N) and apparent affinity constant (K) calculated from Langmuir equation plots.

	HA	1.88 ± 0.05	21 ± 3
	ZnHA	1.20 ± 0.08	7 ± 1
	HAPEI	7.9 ± 0.4	2.2 ± 0.3

N ± N ( mol/m 2 ) K ± K (L mmo1 -1 )

Acknowledgements

The authors thank the European MP 1301 COST action (New Generation Biomimetic and Customized Implants for Bone Engineering (NEWGEN); 2013-2017) and the University of Bologna (Marco Polo program 2016) for supporting this bilateral research work.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.colsurfb.2017.09. 055.

Supplementary Material

Hydroxyapatite functionalization to trigger adsorption and release of risedronate.

Lucia Forte, Stéphanie Sarda, Christèle Combes, Fabien Brouillet, Massimo Gazzano, Olivier Marsan, Elisa Boanini, Adriana Bigi Content :


+,# Iván Coto Hernández

Siddharth Sivankutty

Iván Coto

Hernández 1+

Nicolas Bourg

Guillaume Dupuis
email: guillaume.dupuis@u-psud.fr

Sandrine Leveque-Fort
email: sandrine.leveque-fort@u-psud.fr

Sandrine Lévêque-Fort

Supercritical Angle Fluorescence for Enhanced Axial Sectioning in STED Microscopy

Introduction

Many biological studies require imaging with superior axial resolution to specifically target cell membrane processes [START_REF] Steyer | A real-time view of life within 100 nm of the plasma membrane[END_REF][START_REF] Burnette | A contractile and counterbalancing adhesion system controls the 3D shape of crawling cells[END_REF] such as cell motility, adhesion or protein trafficking. However, the axial resolution of conventional fluorescence microscopy does not permit thin optical sectioning of the membrane from the volume of the cell. The improvement of the axial resolution has been a fundamental problem in optical microscopy. To date several progresses have been done to improve the lateral and axial resolution beyond the diffraction limit. However, isotropic resolution in all three dimensions is still a challenge in many superresolution techniques [START_REF] Huang | Super-resolution fluorescence microscopy[END_REF] Circumventing the diffraction limit in fluorescence microscopy became possible by exploiting molecular transitions of the fluorophore [START_REF] Hell | Far-Field Optical Nanoscopy[END_REF]. For instance, one of the most popular cellular imaging techniques is stimulated emission depletion (STED) microscopy [START_REF] Hell | Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy[END_REF][START_REF] Vicidomini | STED super-resolved microscopy[END_REF] known for its unprecedented spatial resolution. However, the axial resolution of a conventional STED microscope still remains similar to confocal microscopy and resolution enhancement [START_REF] Harke | Resolution scaling in STED microscopy[END_REF][START_REF] Harke | Three-dimensional nanoscopy of colloidal crystals[END_REF] along the axial direction comes at the cost of complex instrumentation and the reduction of lateral resolution. Furthermore, 3D-STED requires a greater power for the STED beam, which can have negative consequences on the sample.

In the specific case of membrane or flat-cells imaging, STED microscope has been coupled with Total Internal Reflection Fluorescence (TIRF) microscopy [START_REF] Leutenegger | Fluorescence correlation spectroscopy with a total internal reflection fluorescence STED microscope (TIRF-STED-FCS)[END_REF][START_REF] Gould | Total internal reflection STED microscopy[END_REF], which is based on evanescent excitation and provides subwavelength axial sectioning in the vicinity of the coverslip. However, it requires unconventional polarization states for the excitation beam [START_REF] Leutenegger | Fluorescence correlation spectroscopy with a total internal reflection fluorescence STED microscope (TIRF-STED-FCS)[END_REF] and suffers from the usual drawbacks of TIRF microscopy such as inhomogeneous illumination of the field of view and loss of axial confinement due to stray excitation [START_REF] Brunstein | Eliminating Unwanted Far-Field Excitation in Objective-Type TIRF. Part I. Identifying Sources of Nonevanescent Excitation Light[END_REF]. More importantly, it requires a modification of the excitation/depletion optical path, which can lead to a degradation of the lateral resolution.

Regardless, evanescent waves do appear as an elegant method to produce axial sectioning. Here, we therefore propose to take advantage of evanescent waves from the detection point of view rather than from the excitation, and thus preserve the qualities of an optimized excitation/depletion optical path [START_REF] Axelrod | Chapter 1 -Evanescent Excitation and Emission[END_REF]. Our alternate approach to TIRF-STED microscopy consists in exploiting the supercritical angle fluorescence (SAF) emission of fluorophore (see Fig. 1). It provides another way to achieve sub-diffraction axial sectioning by limiting detection to the immediate vicinity of the samplesubstrate interface. Indeed, when a fluorophore is close to the glass/medium interface, the evanescent near-field components of its emission becomes propagative in the medium with a higher refractive index, which manifests as light emitted above the critical angle [START_REF] Ruckstuhl | Forbidden Light Detection from Single Molecules[END_REF]. This SAF emission can represent up to 50% of the emission collected by the objective for a fluorophore located at the interface itself and sharply decreases when it is further away. The discrimination of the SAF components from the undercritical angle fluorescence (UAF) is the experimental key to achieve axial sectioning in a SAF-based imaging technique. Early implementations of this discrimination were based on a specifically designed objective lens that filtered the near-field components in the object space directly [START_REF] Ruckstuhl | Supercritical angle fluorescence (SAF) microscopy[END_REF]. However, this approach is not applicable here since it would affect both the excitation and detection paths and would result in a degradation of lateral resolution. The recent wide dissemination of SAF microscopy came with the demonstration that SAF microscopy is possible by filtering out the SAF components by inserting a dedicated amplitude mask in the detection pathway of the microscope at a position conjugated with the back-focal plane of a high-NA objective lens [START_REF] Barroca | Full-field supercritical angle fluorescence microscopy for live cell imaging[END_REF]. This method reduces complexity and increases the portfolio of applications since filtering only occurs in the detection path while the excitation path requires virtually no modification whatsoever. It has been demonstrated as versatile because it has been implemented both in widefield [START_REF] Barroca | Full-field supercritical angle fluorescence microscopy for live cell imaging[END_REF][START_REF] Barroca | Full-Field Near-Field Optical Microscope for Cell Imaging[END_REF] and confocal modes [START_REF] Sivankutty | Confocal supercritical angle microscopy for cell membrane imaging[END_REF]. Recently, the benefits of SAF detection have been combined with Single Molecule Localization Microscopy (SMLM) to yield an almost isotropic three-dimensional localization precision better than 20 nm [START_REF] Bourg | Direct optical nanoscopy with axially localized detection[END_REF][START_REF] Deschamps | 3D superresolution microscopy by supercritical angle detection[END_REF] In contrast with SMLM, STED microscopy is faster and compatible with live cells imaging. This motivates us to combine the strengths of these two methods to open new perspectives for superresolution imaging of thin samples [START_REF] Sivankutty | Towards STED microscopy with nanometric optical sectioning[END_REF]. Therefore, we report here a novel membrane-specific microscope, which takes advantage of supercritical angle emission (here onwards referred to as STED-SAF). Membrane-specific imaging is obtained without any change in the illumination path, simply by adding a SAF module in the detection path of any given STED microscope. This upgrade to STED microscopy enhances axial sectioning at the vicinity of the coverslip with no alteration of the excitation/emission path and will contribute to more applications of STED microscopy. We implemented a STED-SAF microscope compatible with green and yellow fluorescent dyes.

However, the same performance can be tuned to other wavelengths or multicolor regimes without any increase in the architectural complexity.

Materials and methods

STED-SAF instrumentation

We implemented the STED microscope on top of an existing custom made confocal SAF microscope [START_REF] Sivankutty | Confocal supercritical angle microscopy for cell membrane imaging[END_REF] based on a compact fiber-based supercontinuum (SC) source (SC450-HE, Fianium) that is adapted to the implementation of compact and tunable STED microscopes [START_REF] Wildanger | A compact STED microscope providing 3D nanoscale resolution[END_REF] with a wide choice of fluorophores (see Fig. 2). In the present configuration we set the wavelength of the excitation beam to λ exc = 488 ± 6 nm necessary for applications requiring visible fluorescent proteins (such as GFP and YFP) while the depletion beam was set at λ STED = 585 ± 10 nm. The use of the same laser for excitation and depletion reduces complexity and avoids problems with jittering or synchronization of the two lasers. We used two optical fibers to allow finer pulse-stretching to optimize the pulse width requirement and improve the beam quality. The low repetition rate of this laser (0.5, 1 or 2 MHz) significantly slows down the imaging speed but reduces photobleaching [START_REF] Donnert | Macromolecular-scale resolution in biological fluorescence microscopy[END_REF][START_REF] Donnert | Triplet-relaxation microscopy with bunched pulsed excitation[END_REF]. The STED beam passes through a polymeric mask imprinting 0-2π helical phase-ramps (VPP-A1, RPC Photonics) and is circularly polarized at the back-aperture of the objective lens by an achromatic quarter-wave plate (RAC 3.4.15, Bernhard Halle Nachfl.). The illumination beams are tightly focused on the sample with a 60x oil immersion objective lens with high numerical aperture (NA = 1.49). For 3D scanning of the sample we use a piezo-electric stage scanner (P-545) with a scan controller (E-710) from Physik Instrument. Using a stage scanner further improves the spatial resolution due to superior stability, nano-positioning and perfect overlap of the beams through the entire field of view. The fluorescence light is collected by the same objective lens and passes through the dichroic mirrors as well as through a fluorescence band pass filter (ET Bandpass 525/50 nm, AHF analysentechnik).

Optical alignments

The imaging performance of the STED-SAF microscope crucially depends on two factors, i) the spatial overlap of the excitation and the STED beams on the sample plane and ii) the positioning of the amplitude mask on the conjugated back focal plane. We employed standard techniques of optical alignment initially to co-align the beams on to the optical axis of the microscope. In order to inspect the fine spatial overlap of the beams on the sample plane and the quality of the excitation and the doughnut-like STED PSF, we imaged a sample of gold nano spheres (100 nm) in a backscattering configuration. We employed a thin pellicle beam splitter right below the microscope objective to ensure that part of the backscattered signal (<2%) from the beads was focused onto a photomultiplier tube (PMT, Hammamatsu) placed in a non-confocal configuration. Such an arrangement permitted the co-registration of the excitation and the STED beam by scanning the piezo-electric stage and allowed us to overlap the beams with a very high precision. This auxiliary system also allowed us to visually inspect the beam quality of both the beams, and thus provide a feedback to center and tilt the vortex phase mask for an optimal STED PSF.

For true comparison of STED-SAF with conventional STED the fluorescence signal is collected simultaneously into two confocal channels by a pellicle beamsplitter (BP145B1, Thorlabs). The specific collection of SAF emission was possible by inserting a SAF detection module in one of the two detection paths of our STED microscope. This module relies on a telescope with x1.2 magnification to access a plane conjugated with the back-focal plane of the objective lens where we placed a circular central amplitude mask (3.9-mm diameter) to block all the light emanating from under the critical angle. For the alignment of the SAF module, after an initial Koehler alignment of the conventional white light illumination on the microscope, we coarsely identify the position of the conjugate aperture stop on the detection channel. A flip-mirror placed downstream and an imaging system equipped with a Bertrand lens (f = 150 mm), allows us to image this plane on to a CCD camera (ORCA 4.0, Hamamatsu). For fine alignment, we then use a sample of 100 nm fluorescent beads (Yellow-Green, Invitrogen) and adjust the axial position of the camera such that the characteristic concentric pattern associated with UAF and SAF fluorescence emission is imaged crisply. Using this system, the size of the amplitude mask is verified, and its position is carefully adjusted and centered such that only the SAF components are visible and all the UAF components are blocked. After these alignments, both the pellicle beam-splitter below the microscope objective and the flip mirror is removed during the image acquisition.

STED-SAF acquisition

Both channels are focused (focal length 150 mm, AC254-150-A-ML, Thorlabs) into two fiberpigtailed single photon avalanche photodiodes (SPAD, Picoquant). The graded index multimode fiber with 62.5 µm and 102.5 µm cores respectively of the SPAD acted as confocal pinholes of 1.2 and 2.4 times the size of the projected Airy disk at 520 nm. To control the image acquisition we used a time-correlated-single-photon-counting-card (TCSPC) (HydraHarp 400, PicoQuant), synchronized with the reference signal provided by the Fianium laser and a trigger signal from the scanning system. All imaging operation and analysis was automated and managed by the software SymPhoTime 64 (SPT64, version 2.1, PicoQuant).

Sample preparations

PSF measurements

The experimental PSF of the instrument is obtained by imaging fluorescent 40-nm latex beads (~ 40 nm diameter, Yellow-Green, Invitrogen). We diluted the fluorescent beads in phosphate-buffered saline (PBS) by 1:3000 (v/v), we dropped 1mL of the diluted solution onto a glass coverslip placed in an open-bath imaging chamber and we waited 15 min for deposition of the beads on the coverslip.

Immunofluorescence assays

COS-7 cells (derived from monkey kidney tissue) are plated overnight on 18 mm diameter glass coverslips (No 1.5 ideal for superresolution) in DMEM supplemented with 5% FBS. The day after, the culture medium was removed and cells were immediately rinsed three times the cells in PHEM 1X (37° C) for 5 min before being incubated for 10 min in paraformaldehyde (4%), glutaraldehyde (0.02%) in PHEM and 0.5% Triton for 20 min at room temperature. After fixation, the cells were washed three times in PBS (0.1 M, pH 7.4) and one time in Triton (0.1%) for 7 and 10 min respectively. Cells are then washed in PBS and incubated for 20 min in NaBH4 (1 mg / ml) solution for reduction. Later, it was rinsed three times in PBS (0.1 M, pH 7.4) and rinsed again three times in PBS+ 1% BSA for 5 min for saturation. The cells were then incubated with the monoclonal mouse anti-a-tubulin antiserum (Sigma Aldrich) diluted (1:1000) in a blocking buffer (PBS + 1% BSA) for 1 h at 37 ° C. The cells were rinsed three times in PBS for 5 min. The α-tubulin antibody was revealed using Alexa Fluor 488 goat anti-mouse IgG (1:500, Molecular Probes in PBS + 1% BSA) for 45 min at 37° C and protected from light. After three washes in PBS, cells were rinsed in 3.6% formaldehyde in PBS during 16 min for post fixation. Cells are then washed three times in PBS for 5 min and rinsed during 10 min in NH4Cl (50 mM) in PBS for reduction. Finally the cells were washed in PBS and initially mounted on a coverslip and placed in an open-bath imaging chamber with an aqueous medium such as PBS. For STED-SAF imaging better results were found with a mount liquid antifade (4-0100-005-0, Abberior) with refractive index close to that of many biological samples (n=1.38), and lower than refractive index of glass to allow propagation and collection of SAF signal. Depending on the use of either PBS or a given mounting medium with a different refractive index, the size of the amplitude mask needed to be changed and adapted to the corresponding UAF/SAF distribution.

Results and discussion

Calculation of the molecular collection efficiency

Using our previous work in confocal-SAF instrumentation [START_REF] Sivankutty | Confocal supercritical angle microscopy for cell membrane imaging[END_REF], we simulated the molecular collection efficiency (MCE) for various experimental configurations to characterize the performance of our STED-SAF microscope in terms of lateral resolution and sectioning. In conventional STED imaging, the effective PSF in the observed superresolved image assuming no detection pinhole can be described as:

ℎ !"" 𝑟, 𝑧 = ℎ !"#$ 𝑟, 𝑧 × ℎ !"#$ 𝑟, 𝑧 × η(𝐼 !"#$ (𝑟, 𝑧)) (1)
where h conf (r,z) is the confocal PSF, h STED (r,z) is the depletion PSF and η describes an exponential decrease of the spontaneous emission probability with the STED beam intensity. Physically this describes that the only the molecules that contribute to the image formation lies at the zeros of the STED beam. Similarly, we already reported the general theory governing confocal-SAF detection [START_REF] Sivankutty | Confocal supercritical angle microscopy for cell membrane imaging[END_REF]: There exists an exponential dependence of the signal as a function of axial distance from the coverslip due to the evanescent decay of the near-field components. Hence, the MCE [START_REF] Fort | Surface enhanced fluorescence[END_REF] is given as:

𝑀𝐶𝐸(𝑧) = 𝑒𝑥𝑝 !! !" (2)
Therefore, we can model image formation in STED-SAF by accounting for both the spontaneous emission probability ℎ !"" 𝑟, 𝑧 and the MCE as:

𝐼𝑚𝑔 !"#$!!"# (𝑟, 𝑧) = ℎ !"" 𝑟, 𝑧) * 𝑂𝑏𝑗(𝑟, 𝑧 ×𝑀𝐶𝐸(𝑧) (3)
Intuitively, this can be understood as follows: The probability that a molecule will contribute to the image drops exponentially with increasing power of the STED beam or as it moves away from the interface. The strong ~160-nm axial confinement obtained according to the theory is similar to the experimental value we previously reported (see Fig. 3). This axial sectioning is in the same order of magnitude as the ~100-nm axial resolution accessible with a 3D-STED microscope, though limited to the vicinity of the coverslip. The improved sectioning in SAF mode arises due to the rapid decay of the MCE when the axial position of the emitter is further away from the interface. This result regarding the axial confinement of the signal anticipates a strong enhancement compared with conventional STED microscope.

STED-SAF imaging

For validation of the results obtained in the simulation we performed some experiments on calibration and biological samples. We first imaged the microtubule network in fixed COS-7 cells immunolabeled with AF 488 in both confocal and SAF modes (see Fig. 4). In SAF mode, nonconfocal detection presents the advantage of maximizing signal collection by avoiding signal loss at the pinhole. Besides out-of-focus fluorescence is inherently blocked by the central amplitude mask and we observed no degradation in the resolution. In the case of a more densely labeled sample, our previous results indicate that the use of a somewhat large pinhole does help reduce stray light from the system and improves contrast. In the case of the sample presented in Fig. 4, we can clearly see some features preserved in the SAF image while light from the volume of the cell is rejected. This underlines the improvement in axial sectioning permitted by SAF detection.

To highlight the benefits of STED-SAF microscopy, we imaged closely packed sub-diffraction sized (40 nm) yellow green fluorescence beads close to the surface (see Fig. 5) and compared confocal, confocal-SAF, STED and STED-SAF images. Beads that appear clustered together in confocal and SAF can be individually identified in STED and STED-SAF. A lateral resolution below 70 nm was evidenced in STED-SAF mode, which is similar to the results in conventional STED mode on the same sample (64 nm) (lateral resolution evaluated on 40 beads). The small loss in lateral resolution can be mainly attributed to the non-confocal detection of the STED-SAF signal.

In order to demonstrate the application of this STED-SAF microscope on biological samples, we imaged the microtubule network in fixed COS-7 cells immunolabeled with AF 488 (see Fig. 6). In the SAF and STED-SAF images we can clearly see surface-selective imaging of features close to the coverslip and the screening of the fluorescence from the volume. The ability of STED-SAF to efficiently remove background is particularly useful when imaging densely labeled 3D structures. In the case of biological samples, the resolution was mainly limited by the small number of photons associated with our slow acquisition and two simultaneous detection channels for true comparison.

However, the introduction of faster beam-scanning mirrors could easily facilitate faster image acquisition. When imaging thick and densely labeled biological samples in STED-SAF mode, we found that the STED beam generates a substantial amount of out-of-focus background. Therefore, in that case, the SAF amplitude mask is not sufficient to efficiently reject this stray light and the use of a detection pinhole becomes necessary and significantly improves the contrast. Conversely, a very small pinhole could drastically reduce the signal. Depending on the sample, a balance between good performances in resolution and contrast with regards to collection efficiency of the signal may have to be considered. Moreover, with an adapted pinhole, we evidenced a small increase in contrast for STED-SAF compared to confocal-SAF. We can suggest that the STED beam has the ability to turn off some of the fluorescence background, which in turns enhances the SNR.

Conclusion and outlook

This novel implementation gives access to membrane imaging with an axial sectioning of ~160 nm above the coverslip and effective sub-diffraction lateral resolution of 70 nm at moderate STED beam power. It could allow resolving and following dynamic events in the membrane of the cells.

This instrument achieves performances similar to the previously demonstrated TIRF-STED microscope with considerably lesser experimental demands. It should be noted that SAF detection comes along with a reduction of the fluorescence signal that forms the image. Therefore, it requires optimized collection efficiency. Here, for validation purposes and true comparison, the detection was divided into a dual-view type configuration for simultaneous surface and volume imaging of the sample, which resulted in the number of detected photons to be divided by two in each path.

However, the use of a flip mirror would restore the signal to its actual level and allow sequential imaging of the surface and the volume of the sample. Simultaneous dual depth imaging could also be obtained by introducing a module based on a parabolic mirror with a central hole, UAF components would be directly transmitted into one channel and SAF components reflected in the second one, allowing optimal signal detection.

SAF microscopy requires the samples to be embedded in a medium with a refractive index lower than the one of the glass coverslip. This refractive index mismatch induces optical aberrations, mainly spherical aberration. Usually, optical aberrations induced by imperfect coverslip thickness, inhomogeneous specimens or even temperature changes are compensated with the correction collar of the objective lens. However, it is not possible in STED microscopy because the collar adjustment deteriorates the zero of the doughnut beam. Nevertheless, it is not critical in the case of membrane imaging because the features to be imaged are not more than several tens of nanometers away from the coverslip. If necessary, image quality could be further improved by the use of adaptive optics in the detection path.

For a long time, the experimental complexity of STED microscopy has limited its wide adoption in the community to a small number of groups. Recent progress in the last couple of years have reduced the complexity for temporal and spatial alignment with the introduction of gated detection [START_REF] Vicidomini | Sharper low-power STED nanoscopy by time gating[END_REF][START_REF] Hernández | Gated STED microscopy with time-gated single-photon avalanche diode[END_REF] and easy doughnut [START_REF] Wildanger | A STED microscope aligned by design[END_REF][START_REF] Gorlitz | A STED MICROSCOPE DESIGNED FOR ROUTINE BIOMEDICAL APPLICATIONS[END_REF]. 3D-STED set-ups are also available, commercially or homemade, but the improved axial resolution comes at the cost of complex and expensive instrumentation due to the necessity of two separate STED beams for lateral (xy) and axial (z) resolution enhancement, respectively. For these reasons, our STED-SAF approach appears as an easy alternative to 3D-STED when imaging flat samples because it basically is an add-on in the detection path.

The proposed implementation is compatible with all STED microscopes (based on pulsed or cw lasers). Besides, this implementation relies on a one-photon-excitation architecture but is perfectly compatible with a two-photon-excitation system. In addition, this implementation was demonstrated with one color (namely green/yellow) but would also function in a multicolor STED microscope without any increase in architectural complexity in the SAF detection. The combination of these two imaging techniques offers a new tool to observe molecular phenomena on biological membranes at a nanometric scale for studying intracellular life processes. Furthermore, the demand for membrane imaging with sub-diffraction resolution is growing exponentially in many fields, and in particular in FCS-STED [START_REF] Eggeling | Direct observation of the nanoscale dynamics of membrane lipids in a living cell[END_REF][START_REF] Wang | A straightforward STED-background corrected fitting model for unbiased STED-FCS analyses[END_REF] and FCS-SAF [START_REF] Ries | Supercritical angle fluorescence correlation spectroscopy[END_REF] could be also improved with the benefits of this method (FCS-STED-SAF). We believe that ease of use of STED-SAF microscopy, could effectively open a wide dissemination of STED microscopy in cell membrane imaging/dynamic. P exc = 10 µW @ 488 ± 6 nm. P STED = 2 mW @ 592 ± 10 nm. Pixel size 39 nm. Scale bar 1.5 µm. P exc = 10 µW @ 488 ± 6 nm. P STED = 2 mW @ 592 ± 10 nm. Pixel size 39 nm. Scale bar 1.5 µm.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Principle of SAF emission

Fig. 3 .Fig. 4 .

 34 Fig. 3. Simulation of the molecular collection efficiency (MCE) (a) Confocal (b) Confocal-SAF (C) STED (D) STED-SAF

Fig. 5 .

 5 Fig. 5. Calibration sample. Shown are confocal with STED (left panel) and SAF with STED-SAF (right panels) recordings. P exc = 10 µW @ 488 ± 6 nm. P STED = 2 mW @ 592 ± 10 nm. Pixel size 39 nm. Scale bar 1.5 µm.

Fig. 6 .

 6 Fig. 6. Images of the microtubule network labeled with Alexa 488 in COS-7 cells.

Acknowledgments

We acknowledge the contribution of the Centre de Photonique BioMédicale to cell culture and labelling. We also acknowledge the help of Sandrine Lécart with cell culture. Finally, we thank Gaël Moneron for his help regarding STED alignment and fruitful discussions.

Funding

The authors acknowledge the ANRT, the Labex PALM and the DIM C'Nano for financial support.

Additional Information

Competing financial interests

The authors declare no competing financial interests.

Author contributions

All


Renaud Podor

X F Le Goff

T Cordara

Michaël Odorico

J Favrichon

Laurent Claparede

Stephanie Szenknect

N Dacheux

3D-SEM height maps series to monitor materials corrosion and dissolution

Keywords:

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

It is of strong interest to study and characterize the dissolution and/or corrosion mechanisms at the micrometer scale to evaluate materials' ageing or recycling. On the one hand, the materials durability is mainly limited at room temperature by corrosion mechanisms that yield to the degradation of materials by several well-known and often complex mechanisms. On the other hand, material recycling at the end of its lifecycle generally requires dissolution step in acidic or basic media to further separate the elements of interest. Both corrosion and dissolution of materials are controlled by surface reactions that are generally studied at the macroscopic scale by evaluating the element releases in solutions for various conditions. Nevertheless, the understanding of these processes generally requires data recorded at the microscopic scale. Indeed, it is now admitted that for several kinds of materials, the main weakness during dissolution/corrosion/leaching tests is associated to grain boundaries, triple junctions or pores which can be observed at this scale. While other defaults which are present in the material (stacking faults, dislocations…) are not directly observable at this scale, their consequences in terms of behavior during dissolution/corrosion/leaching (formation of voids, pitting…) can be observed by scanning electron microscopy (SEM). Thus, as most of the events occurs at the microscopic scale, there is a real need to observe directly the corrosion/dissolution of materials at the micrometer/submicrometer scale in order to characterize precisely the modifications occurring at the solid/liquid interface and to determine accurately the associated mechanisms.

Only few studies have been performed in order to evidence the evolution of materials surface at the micrometer scale. In this field, recent works [START_REF] Hsu | The effects of crystallization and residual glass on the chemical durability of iron phosphate waste forms containing 40 wt% of a high MoO 3 Collins-CLT waste[END_REF][START_REF] Horlait | Environmental SEM monitoring of Ce 1-x Ln x O 2-x/2 mixed oxides microstructural evolution during dissolution[END_REF][START_REF] Cordara | Kinetics of dissolution of UO 2 in nitric acid solutions: a multiparametric study of the non-catalysed reaction[END_REF][START_REF] Szenknect | Monitoring the microstructural evolution of Nd 2 Zr 2 O 7 pyrochlore during dissolution at 90 °C in 4 M HCl: implications regarding the evaluation of the chemical durability[END_REF] reported the description of a ceramic material dissolution in aqueous media. However, if the images recorded gave new insights in the changes occurring at the surface, no precise determination of the quantity of matter dissolved was done, due to the lack of information in the z-direction.

Various methods were used to characterize the surface microstructure at the microscopic scale: Atomic Force Microscopy (AFM) [START_REF] Dalmas | Quantitative AFM analysis of phase separated borosilicate glass surfaces[END_REF][START_REF] Urosevic | In situ nanoscale observations of the dissolution of {10-14} dolomite cleavage surfaces[END_REF], Scanning Tunneling Microscopy (STM) [START_REF] Damian | Electrochemical de-alloying in two dimensions: role of the local atomic environment[END_REF] or Vertical Scanning Interferometry (VSI) [START_REF] Luttge | Interferometric study of the dolomite dissolution: a new conceptual model for mineral dissolution[END_REF][START_REF] Daval | Linking nm-scale measurements of the anisotropy of silicate surface reactivity to macroscopic dissolution rate laws: new insights based on diopside[END_REF][START_REF] Fischer | Direct measurement of surface dissolution rates in potential nuclear waste forms: the example of pyrochlore[END_REF]. Each technique exhibits its own advantages and limits that will be shortly detailed hereafter. AFM images are characterized by a very good zresolution (close or higher than 1 nm) but the technique is limited to the observation of relatively smooth samples [START_REF] Weihs | Limits of imaging resolution for atomic force microscopy of molecules[END_REF][START_REF] Santos | The intrinsic resolution limit in the atomic force microscope: implications for heights of nano-scale features[END_REF] due to tip radius effects. The apparatus can be used directly when the sample is in contact with a solution. However, it can be very difficult (and time consuming) to find (and recover) the Region of Interest (noted hereafter ROI). Moreover, the size of the ROI is always relatively small compared to the size of the sample (maximum size of a few square micrometers). Last, the time to record an image can be very long when a high resolution is required. VSI images are characterized by a sub-nanometer resolution in the z-direction but also by a limited x-and y-resolution (in the order of 1 μm) due to the light illumination of the sample [START_REF] Arvidson | Lateral resolution enhancement of vertical scanning interferometry by sub-pixel sampling[END_REF]. The ROI is relatively easy to find as large zones can be observed and measured (few square millimeters). Last, https://doi.org/10.1016/j.matchar.2019.02.017 ⁎ Corresponding author. E-mail address: renaud.podor@cea.fr (R. Podor).

T

STM images are very accurate but difficult to record and limited to very small ROI (few square nanometers) [START_REF] Damian | Electrochemical de-alloying in two dimensions: role of the local atomic environment[END_REF].

The use of stereoscopic images recorded with an Environmental Scanning Electron Microscope (ESEM) to reconstruct and compare height maps of the surface of a material during its dissolution has not been reported previously. However, it appears as an interesting alternative to already reported methods. Indeed, the calculation of 3D surfaces from SEM tilted image series is now a well-established method. Several commercial softwares (Mountains®, Alicona Mex) are available and usually used in research and industry. This method is also sometimes directly implemented in SEM driving systems (Zeiss, Tescan SEM). Furthermore, the continuous development of optimized calculation procedures for 3D surface reconstructions by several research groups is also an active field of research, clearly evidencing the real possibilities offered by this technique [START_REF] Eulitz | 3D reconstruction of SEM images by use of optical photogrammetry software[END_REF][START_REF] Tafti | Recent advances in 3D SEM surface reconstruction[END_REF][START_REF] Gontard | Assessment of engineered surfaces roughness by high-resolution 3D SEM photogrammetry[END_REF][START_REF] Shi | Measuring topographies from conventional SEM acquisitions[END_REF][START_REF] Mignot | Color (and 3D) for scanning electron microscopy[END_REF]. Indeed, the reconstruction of 3D surfaces using this technique only requires a set of 2 (or 3) tilted SEM images. The recording of these images only last for few minutes and the 3D calculation process last for 5 to 30 min (depending on the computer power as well as on the image size).

In the present work, the experimental protocol for the acquisition of stereoscopic SEM images allowing 3D reconstruction is first reported. Then, the image processing developed using height maps is detailed and the obtained results are compared with AFM images in order to validate the method. Last, different ways to use the 3D-SEM height maps series to characterize materials corrosion and dissolution are described.

Materials and methods

Materials

The material used as reference in the present study was UO 2 pellet doped with 3 mol% metallic particles whose relative density was close to 95%. The microstructure of the obtained pellet consisted in UO 2 grains of 0.2-5 μm in size, mixed with 50-500 nm diameter metallic particles randomly located in the grains and at the grain boundaries, at the surface but also in their bulk of the pellets.

The aim of the experiment was to follow the modifications of the sample surface during its dissolution in 0.1 M HNO 3 at 60 °C. Two particular zones of the pellet, called hereafter "Region Of Interest" (ROI) were selected. Images of these zones were recorded at different magnifications prior the dissolution test, in order to find "easily" the ROI after the dissolution steps (Fig. 1).

Methods

Dissolution of sample

The pellet was put in contact with 25 mL of 0.1 M HNO 3 solution at 60 °C under stirring in a PTFE dissolution reactor. At regular intervals, the sample was removed from the dissolution device, washed with water three times and finally the excess of water was removed with an absorbent paper, in order to stop the dissolution process. Then, the sample was introduced in the ESEM chamber equipped with a Peltier stage. The Peltier stage was cooled down to 2 °C prior the introduction of the sample introduction. A great caution was paid to the pumping sequence in order to avoid any dehydration of the sample. This pumping sequence consisted in 8 differential pumping steps between 500 and 750 Pa of H 2 O. Finally, the water vapor pressure in the chamber was adjusted to 300 Pa which corresponded to a relative humidity of 42.5%. With this experimental procedure, the sample was never dried. The use of the ESEM under wet conditions prevented the dissolution experiment from perturbations induced by the sample observation.

After recovering the region of interest and recording the image series, the sample was put again in contact with the solution. This sequence was repeated several times up to the end of the dissolution test. Thus, the full experiment corresponded to a multistep observation sequence.

Recording of ESEM images

The ESEM used during this study was a Quanta 200 ESEM FEG (commercialized by the FEI Company). After the sample was introduced in the ESEM chamber, the images were recorded using a specific gaseous secondary electron detector [START_REF] Stokes | Principles and Practice of Variable Pressure/Environmental Scanning Electron Microscopy (VP-ESEM[END_REF]. The imaging conditions were defined in order to reduce the consequences of irradiation of the sample by the electron beam [START_REF] Royall | Radiation damage of water in environmental scanning electron microscopy[END_REF][START_REF] Egerton | Radiation damage in the TEM and SEM[END_REF]. Indeed, the irradiation of the sample could have strongly modified locally the reactivity of the sample surface and finally generated unexpected local modifications of the dissolution process (i.e. increase or decrease of the local dissolution kinetics). Thus, this effect had to be avoided -or limited -as much as possible. The image recording conditions resulted from a compromise between the final image quality required to reconstruct the sample surface (in terms of signal/noise ratio and limitation of the image deformation) and the irradiation of the sample surface by the electron beam (no observable sample surface modification of the ROI compared to the other parts of the sample).

3D-SEM surface image reconstruction and height map

The tilted image series were pre-aligned using Fiji software and the particular SIFT method [START_REF] Lowe | Distinctive image features from scale invariant keypoints[END_REF]. The image surface reconstructions were performed using the commercial Alicona Mex software with the three images recorded at the same magnification [START_REF]MeX | Alicona -high-resolution optical 3D measurement[END_REF] (Fig. 2a,b,c). Then the image of the sample surface was calculated, the 3D image was aligned by comparison with a reference plane which was the plane cutting the image in two parts with the same quantity of matter on the top and on the bottom sides (Fig. 2d). Thus, 16 bits images were extracted from the 3D surface reconstructions using a scale of 1 Å per pixel (corresponding to the grey scale). In these conditions, the maximum assessable scale was 6.5535 μm (Fig. 2e). Obviously, this scale must be modified and adapted by adjusting the length associated to a pixel, depending on the size of the studied sample. These images (hereafter called "height maps") contain the coordinates of each point of the sample surface in a three dimensional Cartesian system. They are the raw material that will be used to characterize the topographic changes of the surface sample as a function of the dissolution time.

Atomic Force Microscopy (AFM)

The sample was also characterized by Atomic Force Microscopy using a MULTIMODE 8 AFM apparatus (with a lateral resolution of approximately 8 nm and an optimal z resolution of 1 Å) equipped with a Nanoscope 5 controller from Bruker Germany. The observed sample was put in contact with the dissolution medium for 1064 h prior the microscopic characterization. The same Region of Interest (ROI) was also observed by ESEM before and after AFM.

AFM imaging was performed in the peak force mode, under dry conditions using SNL tips (silicon tip on silicon nitride cantilever) from Bruker Company with a spring constant of 0.24 N•m -1 . This mode has been used with specific parameters defined by the operator in order to minimize the force and to use the same tip for all the samples. Furthermore, the peak force mode has been used in order to minimize the energy that is dissipated at the sample surface during the AFM image recording with respect to their fragility (thin hydrated layers probably covers the sample). Last, a 16 bits height map with a 0.4 Å per pixel resolution was also extracted from the AFM topographic image.

Validation of the height maps

Mex height map versus AFM height map

The same region of interest (ROI) of the sample surface was observed using two types of microscopies (Fig. 3b andd) in order to compare both datasets and to validate the height values obtained with Mex by comparison with the AFM measurements.

The main difference between both techniques was the time required to record an image of the ROI. Concerning AFM, one day was necessary to recover the ROI (i.e. a 10 μm × 10 μm zone on a pellet of 5 mm in diameter with marks). Then, the time necessary to record an image with the desired resolution was 1.5 h. The precision in the height values was approximately 1 nm. Regarding the surface reconstruction, finding the ROI and recording the ESEM image series required 20 min for the 3 different magnifications. Then, it took 15 min to reconstruct the topographic image of the surface using the Mex software. The precision in the determination of the height values was approximately 30-40 nm (the determination of this value will be detailed later).

The height maps extracted from the Mex reconstruction and the AFM image were thus compared. Since AFM technique provided the most accurate measurements of the surface sample heights, these values were used to determine the correctness of the heights retrieved using the Mex software. Thus, the AFM height map was used as a reference to describe the real sample surface. Both AFM and Mex height maps of the same ROI (with the same scale) are reported in Fig. 3a andc and the image showing the difference between AFM and Mex height maps is reported in Fig. 3e. A more accurate comparison of both images was obtained by plotting the correlation map (Fig. 3h) between both images and by determining the cross-correlation coefficient [START_REF] Chinga | Quantification of paper mass distributions within local picking areas[END_REF]. In this case, the figure of merit (R 2 ) was equal to 0.85. This value reflects the very good correlation between the two height maps but also the defects present in both images and that are inherent to each type of characterization technique. The correlation map showed the defects of the AFM image as well as those of the Mex image.

The usual artifacts were observed on AFM images obtained on samples with large topography:

-The image of the AFM tip was observed on the steep edges of the grains. This defect was highlighted in Fig. 3e by a red rectangle in the image difference between AFM and Mex height maps and referenced as Zone 1 in Fig. 4a. -The deformation of the image arising from the high radius of curvature of the tip used relative to the geometry of the feature to be imaged (apparent increase of the sample size called tip artifact) [START_REF] Canale | Recognizing and avoiding artifacts in atomic force microscopy imaging[END_REF]. This defect was highlighted in Fig. 3e by a red circle on the image difference between AFM and Mex height maps and referenced as Zone 2 in Fig. 4a.

Artifacts of Mex images due to the reconstruction process were also observed: -The main one corresponded to the limit of the reconstruction resolution along the z-axis (estimated to 30-40 nm) which can be seen on the difference image on the top of the grains (shown by a red rectangle on Fig. 3e). There is much more topographic information at the nanometer scale on the AFM image than in the Mex image. -The general deviation of the baseline (that remained limited on this example, but still visible on the correlation map -Fig. 3g). It was related with a discrepancy of the reference planes between both height maps.

At this stage, the direct comparison between Mex and AFM height maps revealed a very good agreement between both datasets. This agreed with the conclusions of Raspanti et al. who showed the excellent visual match between Mex and AFM height maps recorded on biological materials [START_REF] Raspanti | A vision-based, 3D reconstruction technique for scanning electron microscopy: direct comparison with atomic force microscopy[END_REF].

In addition, profiles were drawn at the same location using both AFM and Mex height maps. The data and the position of the profiles on the selected ROI are reported in Fig. 4. Using these data, the accuracy of the Mex height values was determined by comparison with the AFM height values. The procedure used is described hereafter. First, the height difference between two points of the Mex profile was measured (HD Mex ). Second, the height difference between the same points was measured from the AFM height profile (HD AFM ) (Fig. 4a). Third, the percentage of height difference between AFM and Mex measurements was determined as follows:

= × %HD 100 ((HD HD )/HD ) Mex AFM AFM (1)
The %HD value is the relative difference between Mex reconstruction and AFM data.

This procedure was repeated several times on this profile in order to determine the %HD values for several HD AFM values. This set-up was also applied on four other profiles determined from the same AFM and Mex height maps. The obtained %HD values are reported as a function of the height difference determined using the AFM image, HD AFM , in Fig. 5a whereas the absolute values of the difference │HD Mex -HD AFM │ are plotted versus the height difference determined using the AFM image, HD AFM , in Fig. 5b. This dataset allowed determining the accuracy of the height values measured from the Mex reconstructed image as a function of the height difference. As an example, when the height difference between two details was equal to 30 nm, the accuracy reached ± 60%. The accuracy equaled ± 20% and 5% when the height difference was 130 nm and 1500 nm, respectively. In the conditions used for the present study, the average height difference between the HD Mex and HD AFM measurements was 38 nm. This value is represented by the dashed line in Fig. 5b. It corresponds to the resolution of the Mex image in the height direction.

As a conclusion, there was a good accuracy of the relative z positions determined as well as the {x,y} coordinates (depending on the initial SEM image magnification). This result indicates that the image was not significantly deformed by the 3D surface reconstruction process The HD Mex and HD AFM values corresponded to the height differences measured at the same locations from the Mex and AFM data, respectively. using the Mex software. This conclusion is also in good agreement with the results already reported in the literature [START_REF] Raspanti | A vision-based, 3D reconstruction technique for scanning electron microscopy: direct comparison with atomic force microscopy[END_REF].

Mex height maps recorded at different magnifications

Height maps of the same region of interest were reconstructed with Mex software at several magnifications. Three profiles determined on the same zone and the corresponding images are reported in Fig. 6a. The width of the line (integration zone) was adjusted as a function of the image magnification and it always corresponded to 33 nm (Fig. 6b,c,d).

A general good agreement between the three reported profiles was observed. On the basis of Fig. 6a, the baseline of the profile obtained from the image reconstructed at 20 kX was slightly shifted compared to the profiles obtained at 5 and 10 kX. This discrepancy was attributed to the automatic determination of the reference plane by the Mex software. Indeed, the image obtained after the reconstruction process could be tilted and straightened with respect to a reference plane. In this case, the reference plane was fixed in order to set one half of the volume below the plane and the second half of the volume under the plane. As a consequence, this plane was not necessarily the same for the two images (containing the same ROI) recorded at different magnifications. Thus, this yielded to a slight shift of the baselines for the profiles reported in Fig. 6a.

Another discrepancy was observed at the position of the grain boundary. The depth of the grain boundary measured from the 5 kX and 10 kX reconstructed images was higher than that obtained from the 20 kX 3D reconstruction. It probably corresponded to the presence of a crystallite that was not always exactly positioned at the same location depending on the magnification of the SEM image series. Nevertheless, the very good agreement between the 3 sets of data can also be considered as a proof of the quality of the surface reconstructions.

How to use the height map series?

Height maps coupled with SEM images

From the 3D surface reconstructions, the surface area of the solid/ solution interface was determined precisely. Thus, this method allowed calculating this parameter in the case of materials presenting low specific surface area that were not accessible by the usual techniques such as BET method using Kr adsorption. In addition, using stack of 3D reconstructions allowed monitoring of the evolution of the surface area of the sample during dissolution.

The Abbott-Firestone curve (or Bearing Area Curve) was used to describe the surface texture of the sample (for more details, please refer to Fig. 4 reported by Loberg et al. [START_REF] Loberg | Characterisation of titanium dental implants I: critical assessment of surface roughness parameters[END_REF]). From this curve, several parameters of interest for the kinetics of local dissolution processes were determined [START_REF] Franco | 3D surface parameters (ISO 25178-2): actual meaning of Spk and its relationship to Vmp[END_REF]:

o Core void volume (V vc ) expressed in cm 3 •m -2 o Core material volume (V mc ) expressed in cm 3 •m -2 o Valley void volume (V vv ) expressed in cm 3 •m -2
o Height of the core material (S k ) expressed in μm By considering that the surface of the sample was flat before the dissolution test, the value of V vc directly represented the quantity of matter that was dissolved (assuming that the highest points of the reconstructed surface where included in the initial surface of the sample) (Fig. 7). The evolution of the parameters associated with Abbott-Firestone curve extracted from the 3D reconstructions of the solid/solution interface of the sample during dissolution is reported in Fig. 8. First, the ratio between the core void volume (V vc ) and the core material volume (V mc ) was plotted for the stack of 3D reconstructions in order to detect anomalous reconstructions. From Fig. 8a, it appeared that the ratio between the volume of matter and the core void volume of the reconstruction was independent of the dissolution times, but slightly dependent on the magnification (i.e. the dimensions of the reconstructed zone). The average value and associated standard deviation of the ratio was 1.23 ± 0.09 and 1.12 ± 0.15 at ×5000 and ×10,000, respectively. The anomalous data that are evidenced from Fig. 8a correspond to images where detached grains are deposited on the sample surface. The evolution of the height of the core material and the void volume of the core are plotted in Fig. 8b andc, respectively. Sk and V VC were found to increase with the dissolution time. This result showed that the depth of the "valleys" dug during the dissolution of the pellet increased. This was a strong indication that the dissolution did not occur by normal retreat of the surface, which would lead to constant Sk and V vc values.

Height map series

During the study of the dissolution of materials, several reconstructions of the same ROI were obtained for various different dissolution times. As explained before, a height map was extracted for each reconstruction (where one grey level corresponds to 1 Å). Thus, these height maps were combined together into a stack. The images of the stack were aligned twice using alternatively the "Linear Stack Alignment with SIFT" [START_REF] Lowe | Distinctive image features from scale invariant keypoints[END_REF] and the "StackReg" plugins with Fiji software [START_REF]Stackreg plugin with Fiji software[END_REF]. One limit of this technique was the absence of invariant points during the dissolution process allowing an accurate alignment of all the images in the z direction, and thus the evaluation of the absolute dissolved volumes. However, this limit was overcome by considering one detail that remained recognizable from one image to the next one. Even if the error was not determined precisely, it was considered to remain relatively low (few nanometers to ten nanometers from one image to the next one).

The aligned stack of images offered the possibility to describe quantitatively the dissolution process at the surface of the material as a function of time, with images that were spatially resolved in the 3 directions.

Profiles in the height map series

Profiles in the height map series were drawn to quantify the local height variations as a function of the dissolution time. Two profiles were extracted from the stacks of images recorded with various magnifications (Fig. 9). The profiles reported in Fig. 9a andc correspond to 20 kX and 5 kX height map image series, respectively. They were aligned in order to keep the position of one point (point I) invariant in height with the dissolution time. From the high magnification images stack (Fig. 9a), the preferential dissolution at the grain boundaries was clearly evidenced. This preferential dissolution both corresponded to the increase of the depth and of the width of the grain boundary. From the low magnification images stack (Fig. 9c), the detachment of grains during the dissolution process was clearly evidenced. It corresponded to the fast depth modifications that were observed from one time to the next one.

The whole (or part of the) profile was integrated on a selected width of matter corresponding to the width of the line used to extract the profile. Thus local quantities of matter removed during the dissolution/ corrosion process were determined accurately. Using the data from the whole image series, the dissolution rates were evaluated at the microscopic scale.

Differences of height maps

The determination of differences of height maps can be useful to locate the zones of the sample where the dissolution process was predominant. This first required to reconstruct 3D images of the same zone at two different dissolution times and then to extract height maps. The difference between two aligned height maps was calculated using the Fiji software. The result was an image highlighting the preferential dissolution/corrosion zones at the surface of the material. Reconstructed surfaces after 287 h and 645 h of dissolution are reported in Fig. 10a andc, respectively, whereas the corresponding height maps are reported in Fig. 10b andd, respectively, and the difference map is shown in Fig. 10e (3D view) and Fig. 10f. From Fig. 10f, it is clear that a preferential dissolution occurred at the grain boundaries and at the triple junctions of the ceramic. As the x-, y-and z-scales were expressed in metric units, it was possible to derive the quantity of matter that was dissolved locally between 287 h and 645 h of dissolution.

The main limit of the comparison of two images obtained by 3D reconstruction method from SEM images was the necessity to have a reference plane, or "reference points", which remained at the same location in both images. In other words, this implies that a zone of the sample remained unaffected by the dissolution process. In the studies already reported, authors used a shadowing method to hinder the contact of the corrosive liquid with the sample in a specific zone. As example, platinum masks could be incorporated in the sample prior the dissolution test [START_REF] Taillon | Improving microstructural quantification in FIB/SEM nanotomography[END_REF], a part of the sample could be protected with a coating [START_REF] Fischer | Direct measurement of surface dissolution rates in potential nuclear waste forms: the example of pyrochlore[END_REF] that could not be dissolved or a particular assembly jig could be used to create a non-wetted reference zone [START_REF] Daval | Linking nm-scale measurements of the anisotropy of silicate surface reactivity to macroscopic dissolution rate laws: new insights based on diopside[END_REF][START_REF] Pollet-Villard | Experimental study of dissolution kinetics of K-feldspar as a function of crystal structure anisotropy under hydrothermal conditions[END_REF]. However, these techniques require to record large sized 3D images of the sample (from few hundreds of micrometers to millimeter scale) and they are impossible to implement with the reconstruction method reported herein (as the final image size only represents few square micrometers). As a consequence, when the dissolution mechanism occurred by normal retreat of the surface (i.e. general decrease of the sample thickness), no reference points were found on both images and the quantity of dissolved matter was not accurately determined. This limit was probably overcome by implementing reference points (or reference plane) in the sample that would remain unaltered during the dissolution experiment. This will be part of future technical developments.

More generally, if the dissolution process is not too fast, some unaltered zones could be found despite the dissolution progress. These invariant points could be used to align the different height maps by assigning the same absolute height (i.e. grey level) in both height maps.

Conclusions

An accurate method for the characterization of materials dissolution at the micrometric scale was reported. This method was based on (E) SEM tilted image series of the same zone at the sample surface after several exposition times to a corrosive solution. After each observation, a 3D surface reconstruction was obtained and these topographic images were compared to AFM images in order to validate the height values obtained. The quality of the 3D reconstruction from (E)SEM images was close to the AFM image one as the figure of merit of the correlation map between both images reached 0.85.

The main advantages of this characterization technique are the high quality of the 3D surface reconstructions, the fast acquisition of the data, the possibility to observe wet samples (by using an Environmental Scanning Electron Microscope) and the limited beam effects. This technique can be applied to the observation of topographic changes occurring at the surface of numerous materials due to various mechanisms such as dissolution and corrosion, formation of coatings or corrosion layers, cracking under mechanical stress… It could be also extended to the observation of high temperature transformations such as glass-ceramic crystallization, grain sintering, grain growth, etc.

Fig. 1 .

 1 Fig. 1. Series of images recorded at different magnifications prior the dissolution test that are used to find the same Region Of Interest (ROI) from one dissolution time to the next one.

Fig. 2 .

 2 Fig. 2. Tilted image series {-10°; 0; 10°} of the same zone of the sample (a, b, c) leading to the 3D surface image reconstruction using Alicona Mex software (d) and the corresponding extracted 16 bits height map (e). The features of the grains are recognizable on the 3 different representations of the surface.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Validation of the Alicona Mex surface reconstructions. Observation of the sample surface using several types of microscopies: (a) AFM height map; (b) AFM view of the sample; (c) Mex height map (using the same scale for the z pixel than for AFM height map); (d) 3D Mex reconstruction; (e) image of difference between AFM and Mex height maps; (f) SEM image; (g) correlation map between AFM and MEX height maps and (h) correlation plot between AFM and MEX height maps. (It must be noted that the ratio between the contrast and the brightness of the "Image of difference between AFM and Mex height maps" was enhanced in order to highlight the differences). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Fig. 5 .

 5 Fig. 5. Determination of the accuracy of the Mex height values. (a) Relative height difference (%HD) measured between Mex and AFM data at the same (x, y) coordinates and (b) absolute values of the height differences between Mex and AFM measurements (│HD Mex -HD AFM │). The line reported in (b) represents the average value of all the height differences measured (i.e. 38 nm).

Fig. 6 .

 6 Fig. 6. (a) Height profiles determined on the same ROI using Mex 3D-reconstructions of SEM images recorded at different magnifications; (b) height map and corresponding profile reconstructed from ×20,000 magnification SEM images (line integration on 10 pixels); (c) height map and corresponding profile reconstructed from ×10,000 magnification SEM images (line integration on 5 pixels); (d) height map and corresponding profile reconstructed from ×5000 magnification SEM images (line integration on 3 pixels). NB: The width of the integration line was adjusted as a function of the magnification and corresponded to 33 nm. The size of the images reached 2.82 μm × 3.78 μm.

Fig. 7 .

 7 Fig. 7. Abbott-Firestone curve and associated parameters considered to characterize the sample texture.

Fig. 8 .

 8 Fig. 8. Evolution of the parameters associated to the Abbott-Firestone curve determined from the 3D reconstruction of the topography of the sample during dissolution: (a) ratio between core void volume and core material volume (detection of anomalous reconstruction); (b) height of the core material; (c) core void volume used to calculate the amount of dissolved material.

Fig. 9 .

 9 Fig. 9. Height profiles determined on the same ROI for stack of height maps (a) and (c) recorded at (b) 20 kX and (d) 5 kX magnifications, respectively.

Fig. 9 .Fig. 10 .

 910 Fig. 9. (continued)