L Helfen

T Baumbach

P Mikulík

D Kiel

P Pernot

P Cloetens

J Baruchel

High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography

Computed laminography with synchrotron radiation is developed and carried out for three-dimensional imaging of flat, laterally extended objects with high spatial resolution. Particular experimental conditions of a stationary synchrotron source have been taken into account by a scanning geometry different from that employed with movable conventional laboratory x-ray sources. Depending on the mechanical precision of the sample manipulation system, high spatial resolution down to the scale of 1 m can be attained nondestructively, even for objects of large lateral size. Furthermore, high beam intensity and the parallel-beam geometry enables easy use of monochromatic radiation for optimizing contrast and reducing imaging artifacts. Simulations and experiments on a test object demonstrate the feasibility of the method. Application to the inspection of solder joints in a flip-chip bonded device shows the potential for quality assurance of microsystem devices. X-ray computed tomography ͑CT͒ was developed during the 1960s/1970s for cross-sectional imaging in medicine. 1,[START_REF] Hounsfield | Patent office[END_REF] Today, CT may be considered as one of the principal methods for volume imaging in medical diagnostics and nondestructive testing ͑NDT͒ for quality assurance of materials and devices. With the installation of x-ray imaging and CT setups at synchrotron-radiation ͑SR͒ sources, weakly contrasted materials could be distinguished [START_REF] Nugent | [END_REF][4][5] and highest spatial resolutions down to the submicrometer scale could be reached 6 in radiography. Despite the great success of CT in general, the CT inspection of flat, laterally extended objects ͑for instance equipped printed circuit boards͒ is rather problematic due to strong absorption in the directions parallel to the lateral elongation.

Another approach was followed by a method nowadays called classical x-ray tomography. Before the development of CT, it had been used to image specific cross sections of objects ͑or patients͒. An acquisition scan consists of synchronous movements of the x-ray source and detector with respect to the object and exposing the detector ͑film͒ during the scan. In this way object features on the so-called focal plane are imaged sharply whereas features with growing distance from this plane are rendered increasingly blurred and contribute to a background intensity in the image. The principle was proposed in 1932 by Ziedses des Plantes 7 for the acquisition of a few arbitrary slices by a single scan. To obtain large three-dimensional ͑3D͒ images with a multitude of slices, however, a time-consuming translational scanning of the object with respect to the focal plane has to be carried out. Nowadays, by combining digital projection data and computerized reconstruction, 8 the scanning procedure can be avoided: this so-called digital tomosynthesis has analogy to CT with limited angle access. Due to the availability of fast two-dimensional ͑2D͒ digital detector systems and the tremendous increase of computing power it has recently found renewed interest in medical 8,[START_REF] Lauritsch | Proceedings SPIE; Medical Imaging: Image Processing[END_REF] and technical [START_REF] Zhou | [END_REF]11 applications where the method is also called computed laminography ͑CL͒.

In this letter the development and implementation of synchrotron-radiation computed laminography ͑SRCL͒ is reported. SRCL combines laminography principles with advantages of SR imaging, owing to the use of monochromatic radiation and a high spatial resolution down to the scale of 1 m. In the following we first show the method's feasibility by simulations. Then, imaging of a test object of known geometry is used to demonstrate the instrumental implementation. Finally, the method's potential for nondestructive testing of microsystem technology and devices is outlined by an application to the inspection of flip-chip interconnections.

Medical tomosynthesis and laboratory CL systems are usually designed to operate with a stationary patient/object and synchronously moving x-ray tube and detector units. In a͒ Present address: Institut für Synchrotronstrahlung ͑ISS/ANKA͒, Forschungszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany; electronic mail: helfen@esrf.fr b͒ Now at: Institute of Condensed Matter Physics, Faculty of Science, Masaryk University, CZ-61137 Brno, Czech Republic. contrast to a mobile x-ray tube, the stationary position of the synchrotron source has to be accounted for by a modified scanning geometry involving fixed source and detector and a rotation of the object. As sketched in Fig. 1, for SRCL the rotation axis is inclined by an angle of Ͻ /2 ͑where the limiting case of = / 2 would correspond to CT͒ with respect to the quasi-monochromatic x-ray beam incident from the multilayer monochromator. From a coordinate system fixed to the sample and moving in the laboratory system, this scanning procedure corresponds to synchronous movements of the source and detector on circular trajectories where the x rays follow a conic envelope during the scan.

In general for all laminography methods, reciprocal space ͑i.e., the 3D Fourier domain of the sample space͒ is not sampled completely. In comparison to CT there exist unsampled regions which, quite generally, may lead to artifacts in the reconstructed images. According to the projectionslice theorem generalized to three spatial dimensions, 8 the region of reciprocal space sampled by a single 2D projection fills a plane perpendicular to the incident-beam direction, as spanned by the vectors k u and k v in Fig. 2. If the number of projections tends to infinity the sampled region corresponds to a rotation-symmetric body ͓of hyperbolic envelope k xy 2 ͑k z ͒ = k max 2 + k z 2 tan 2 ␣, with ␣ = /2-, k max =1/͑2s p ͒ and s p the pixel size͔ where two upwards and downwards directed inner cones of opening angle 2␣ contain no experimental information. Owing to the geometry and the anisotropy of the ͑nonaccessible͒ unsampled region in reciprocal space ͑see Fig. 2͒, the achievable spatial resolution of detail depends on the characteristic spatial features ͑and their corresponding frequencies͒ and, due to structure-dependent artifacts in the image, on their mutual arrangement in the object.

Contrary to the laboratory ͑strongly divergent͒ conebeam cases reported, [START_REF] Lauritsch | Proceedings SPIE; Medical Imaging: Image Processing[END_REF]12 the approximations of a parallel beam and monochromatic radiation can be very well fulfilled in the case of SR imaging setups: in the implementation developed at ESRF beamline ID19 ͑cf. Fig. 1͒ the high source-to-sample distance of 145 m leads to a divergence of only approximately 0.02 mrad across the field of view of 2.8 mm of the employed CCD-based detector system. At a pixel size of 1.4 m a maximum sample depth of up to 7 cm in the direction of the x-ray beam is allowed in order to stay within parallel-beam conditions to the precision of one pixel. Moreover, the wavelength bandwidth provided by a multilayer monochromator is ⌬ / Ϸ 10 -2 compared to ⌬ / Ϸ 1 for the laboratory case.

The 3D reconstruction method is based on filtered backprojection, taking into account the scanning geometry. A filtering of the 2D projection data yields an approximate inversion of the modulation transfer function ͑MTF͒ of the combined process of projection and simple ͑unfiltered͒ backprojection. [START_REF] Lauritsch | Proceedings SPIE; Medical Imaging: Image Processing[END_REF]13 Due to the missing information in the unsampled regions of reciprocal space ͑cf. Fig. 2͒, in general, exact inversion of the MTF is not possible, which manifests itself in characteristic laminographic artifacts in the reconstructed image. In summary, the experimentally achievable resolution is limited by the resolution of the detector system ͑presently down to 0.5 m at a pixel size of 0.2 m͒, by the mechanical precision of the sample manipulation system and due to intrinsic laminographic artifacts related to the sample structure itself. Besides the gain of intensity and resolution of SRCL, the monochromatic radiation and parallel-beam geometry reduces artifacts compared to laboratory whiteand cone-beam laminography.

For numerical and experimental investigations we chose a test object of a known, double-grid geometry: two electron microscopy grids made of copper ͑period 72 m͒ and of gold ͑period 12.7 m͒, respectively, were glued onto opposite sides of an approximately 400-m-thick plastic spacer. State-of-the-art laboratory laminography [START_REF] Zhou | [END_REF]11 was not able to image the 5-m-thick gold grid.

Initially, simulations were carried out with calculated projection data of an idealized computer-generated phantom of this double-grid geometry. Projection data sets were computed by means of a ray-tracing algorithm and used as input to the reconstruction program. Simulating a laminographic scan with a axis inclination ͑see Fig. 1͒ of = / 3 a series of 900 projection radiographs was computed for an x-ray energy of 14.7 keV over a scan range of 360°about the axis. Sharp images could be reconstructed ͑see Fig. 3͒, indicating the feasibility of SRCL for the chosen experimental parameters.

For the experimental investigations, the real test object was fixed by means of a cylindrical sample holder made from plexiglass on a rotation table ͑axis , see Fig. 1͒ in order to carry out the laminographic scan. The experimental scan was performed with the same parameters as used for the simulation.

A comparison of cross-sectional slices through the 3D data sets of the simulated and the real experiments is found in Fig. 3. In the two cases, both the coarse grid ͑period 72 m͒ and the fine grid ͑period 12.7 m͒ are clearly discernible. From the reconstructed slices of the test object their periods are determined to 9.0 and 50.8 voxels ͑of 1.4 m size͒ for the fine and coarse grids, respectively, reproducing the actual grid dimensions. Looking carefully, in both the experimental and the simulated reconstructed slices we observe dark shadows ͑instead of homogeneous areas͒ inside the grid windows which are slight intrinsic artifacts arising from the laminographic procedure rather than experimental instabilities. Nevertheless, high image contrast facilitates 3D renditions as shown in Fig. 4.

We demonstrate the capability of the method for NDT of microsystem technology by the example of a flip-chip bonded device. The solder joints of approximately 80-100 m diameter are hidden after the bonding process and thus are not accessible by visual inspection. Figure 5 shows a slice through solder joints of the device, reconstructed from 900 projections taken at an x-ray energy of 35 keV ͑adapted to the more absorbing object materials͒. The solder joints exhibit voids and solder splashes, entailing a reliability hazard of the electronic circuit.

The reported results of simulations and experiments demonstrate the feasibility of synchrotron-radiation computed laminography. We implemented a setup for data acquisition compatible with a stationary synchrotron source. Filtered backprojection adapted to the scanning geometry provides the basis for 3D reconstruction. The image quality obtained highlights the potential of the method. It can be applied to nondestructive testing of flat, laterally extended objects such as electronic components or flat samples of microstructured materials.

FIG. 1 .

 1 FIG. 1. Sketch of the experimental setup implemented at the imaging beamline ID19 of the ESRF.

FIG. 2 .

 2 FIG.2. Sampled region in reciprocal space: the z direction of the sample coordinate system is defined parallel to the laminographic rotation axis ͑, as shown in Fig.1͒. X rays are incident by an angle of with respect to the z axis ͑a͒. A single projection in reciprocal space samples a plane perpendicular to the incident-beam direction, cf. vectors k u and k v of ͑b͒. For a large number of projections the sampled region forms a rotation-symmetric body where two cones of opening angle 2␣ are missing.

  FIG. 4. Renditions of the reconstructed 3D data sets of the computergenerated phantom ͑a͒ and of the test object ͑b͒. The grids are segmented from the 3D data sets by simple thresholding.

This work was supported by an ESRF long-term project. The authors acknowledge R. Chagnon and D. Fernandez Carreiras for their contributions to the experimental setup. Support by the Sächsische Aufbaubank ͑Project No. 7719/ 1223͒ is acknowledged.


domain: phys chim spi

text:
Anna Dmochowska

Jorge Peixinho
email: jorge.peixinho@cnrs.fr

Cyrille Sollogoub

Guillaume Miquelard-Garnier
email: guillaume.miquelardgarnier@lecnam.net

Dewetting dynamics of sheared thin polymer films: an experimental study †

Rupture of thin liquid films, whether free or supported on a solid or liquid substrate, has long been studied. [START_REF] Vrij | Possible Mechanism for the Spontaneous rupture of thin Free Liquid Films[END_REF][START_REF] Sheludko | Thin liquid films[END_REF][START_REF] Ruckenstein | Spontaneous Rupture of Thin Liquid Films[END_REF] It can be attributed to the amplification of thermal fluctuations at the interface by long-range interactions or to the nucleation and growth of dry patches, leading to the formation of holes in the film. [START_REF] Oron | Long-scale evolution of thin liquid films[END_REF][START_REF] Craster | Dynamics and stability of thin liquid films[END_REF][START_REF] Moreno-Boza | Stokes theory of thin-film rupture[END_REF][START_REF] Kheshgi | Nucleation and growth of dry regions[END_REF] In the supported case, while retracting, the film generally pushes material into a rim around the hole which grows due to surface tension, until the rims coalesce to form droplets. The speed at which the holes grow (i.e. dewetting speed) results from an equilibrium between surface tension that draws the rim and viscous dissipation, and depends on the nature of the substrate and the viscosity of the film. Similar mechanisms occur in ultra-thin polymer films (thicknesses well-below 1 µm) when heated above their glass transition (or melting) temperature. They also have been thoroughly examined both from a theoretical and experimental point of view. [START_REF] Krausch | Dewetting at the interface between two immiscible polymers[END_REF][START_REF] Brochard Wyart | Liquid/Liquid Dewetting[END_REF][START_REF] Qu | Dewetting Dynamics at a Polymer-Polymer Interface[END_REF][START_REF] Reiter | Dewetting of thin polymer films[END_REF][START_REF] Vilmin | Dewetting of thin polymer films[END_REF] The effects of viscoelasticity, [START_REF] Mulama | Dewetting Rheology for Determining Viscoelastic Properties of Nonequilibrated Thin Polymer Films[END_REF] slip 14 or residual stresses [START_REF] Reiter | Residual stresses in thin polymer films cause rupture and dominate early stages of dewetting[END_REF] have been considered, as such films find many industrial applications in conformal, protective, optical or functional coatings [START_REF] Krogman | Anti-reflective optical coatings incorporating nanoparticles[END_REF][START_REF] Katsumata | Mussel-Inspired Strategy for Stabilizing Ultrathin Polymer Films and Its Application to Spin-On Doping of Semiconductors[END_REF][START_REF] Runser | Interfacial Drawing: Roll-to-Roll Coating of Semiconducting Polymer and Barrier Films onto Plastic Foils and Textiles[END_REF][START_REF] Lynge | Polydopamine/Liposome Coatings and Their Interaction with Myoblast Cells[END_REF] and electrical films. [START_REF] Shi | Recent advances in polymer thin films prepared by plasma polymerization. Synthesis, structural characterization, properties and applications[END_REF] A case less studied is the stability of multilayer structures, i.e. stratified thin liquid (or polymeric) films of different nature. [START_REF] Bertin | Capillary levelling of immiscible bilayer films[END_REF] They can be found in microfluidic applications, [START_REF] Lenz | Instability of confined thin liquid film trilayers[END_REF] pack-aging applications [START_REF] Langhe | Manufacturing and novel applications of multilayer polymer films[END_REF] or used for the fabrication of functionalized fibers, [START_REF] Nguyen-Dang | Controlled Sub-Micrometer Hierarchical Textures Engineered in Polymeric Fibers and Microchannels via Thermal Drawing[END_REF] and obtained through lithographic printing process, [START_REF] Lenz | Instability of confined thin liquid film trilayers[END_REF] thermal drawing, [START_REF] Nguyen-Dang | Controlled Sub-Micrometer Hierarchical Textures Engineered in Polymeric Fibers and Microchannels via Thermal Drawing[END_REF] layer-by-layer deposition, [START_REF] Park | Nanostructured Polymer Thin Films Fabricated with Brush-based Layer-by-Layer Selfassembly for Site-selective Construction and Drug release[END_REF] or multilayer coextrusion. [START_REF] Beuguel | Nanorheology with a Conventional Rheometer: Probing the Interfacial Properties in Compatibilized Multinanolayer Polymer Films[END_REF] Theoretical and numerical studies have evaluated the effect of thicknesses and viscosities in the modes of rupture in confined multilayers. [START_REF] Lenz | Instability of confined thin liquid film trilayers[END_REF][START_REF] Xu | Linear analysis of dewetting instability in multilayer planar sheets for composite nanostructures[END_REF] In recent works, aiming to elucidate the physical mechanisms responsible for layer break-ups during multilayer coextrusion, [START_REF] Bironeau | Sollogoub Existence of a Critical Layer Thickness in PS/PMMA Nanolayered Films[END_REF][START_REF] Feng | Breakup behavior of nanolayers in polymeric multilayer systems -Creation of nanosheets and nanodroplets[END_REF] we developed an experimental set-up to analyze the dewetting speed in a confined trilayer. [START_REF] Zhu | Kinetics of thin polymer film rupture: Model experiments for a better understanding of layer breakups in the multilayer coextrusion process[END_REF][START_REF] Chebil | Influence of outer-layer finite-size effects on the rupture kinetics of a thin polymer film embedded in an immiscible matrix[END_REF] This consisted of an ultra-thin (e ∼ 100 nm) polystyrene (PS) layer in between two micrometric poly(methyl methacrylate) (PMMA) layers. Basically, the holes' growth speed, v, can be described as the bursting of a Newtonian fluid film in a viscous environment [START_REF] Reyssat | Bursting of a fluid film in a viscous environment[END_REF] with dissipation occurring not in the PS film but in the surrounding PMMA. In this case v ∼ σ/η 0 = v 0 , where σ is the PS/PMMA interfacial tension, and η 0 the Newtonian PMMA viscosity.

Another barely studied question of interest is the role of shear on the dewetting. Shear is indeed applied in most of the processes used to produce these stratified structures, and understanding its effect on the stability and dewetting dynamics is then of fundamental importance. Numerical works in a bilayer flow, [START_REF] Kalpathy | Shear-induced suppression of rupture in two-layer thin liquid films[END_REF] for a thin liquid film [START_REF] Davis | Suppressing van der Waals driven rupture through shear[END_REF] or an ultra-thin polymer film [START_REF] Kadri | Dewetting of a thin polymer film under shear[END_REF] have shown that shear can delay or, above a critical shear rate, even suppress the rupture. From an experimental point of view, to the best of our knowledge, only two qualitative studies were conducted on sheared trilayer systems, but were mostly focused on the observation of the appearance of the holes. [START_REF] Sundararaj | Sheet formation in immiscible polymer blends: model experiments on initial blend morphology[END_REF][START_REF] Lyngaae-Jorgensen | Experimental methods for in situ studies of morphology development during flow: The case of instability of thin films studied by light scattering[END_REF] Since it appears no work aims at elucidating the role of shear in the evolution of the dewetting dynamics, we propose here such quantitative study in a PMMA/PS/PMMA trilayer.

First, the morphology of the holes varies significantly with shear rate, from a round shape at rest to an elongated (ellipsoid) one in the shear direction (see Figure 1), with an effect more pronounced as shear increases. Note that the shape of the rim also seems altered, with The PS layer is embedded between two PMMA layers with same thicknesses. The top plate is fixed, the bottom plate is moving with a speed V which value is set by the shear rate and the gap (or thickness of the trilayer) H ∼ 200 µm. The shear rate is then defined as γ = V /H. Hence, the PS layer and the holes, while growing, are moving at V /2 parallel to the shear. The dewetting of the film with thickness e is observed from the top. (b) Changes in the holes morphology with increasing shear rate (top view). The scale bars are 50 µm. The holes are circular with a radius R when dewetting occurs without shear, and have an ellipsoid shape when dewetting happens under shear, with a major radius R in the shear direction and a minor radius R ⊥ perpendicular to shear. The holes appear more elongated when higher shear is applied. The final dewetting stage is a series of long and thin holes all aligned in the shear direction. most of its volume gathered around the vertices of the holes instead of a regular shape around the hole. A similar change in the shape of the hole was also noticed in the case of PS dewetting from a stretched elastomer substrate. [START_REF] Schulman | Liquid dewetting under a thin elastic film[END_REF] We can describe the steady-state hole's growth speed v without shear (i.e. when the hole is circular) based on our previous studies. [START_REF] Zhu | Kinetics of thin polymer film rupture: Model experiments for a better understanding of layer breakups in the multilayer coextrusion process[END_REF][START_REF] Chebil | Influence of outer-layer finite-size effects on the rupture kinetics of a thin polymer film embedded in an immiscible matrix[END_REF] It is defined as R = vt, where R is the radius of the hole and t the time of the experiment. We assume that after a transient regime leading to the formation of a toroidal rim, the PS initially contained in the hole's volume is gathered into it. [START_REF] Brochard-Wyart | Dewetting of Supported Viscoelastic Polymer Films: Birth of Rims[END_REF] The change of capillary energy U may then be written as:

dU dt ∼ 4σRv (1)
where σ is the PMMA/PS interfacial tension in J/m 2 determined using Wu's empirical equation 40 σ = 3.2 -0.013(T -20) with T the temperature in °C.

In the present study, since H ∼ 1000e, confinement effects on the dewetting dynamics can be neglected [START_REF] Chebil | Influence of outer-layer finite-size effects on the rupture kinetics of a thin polymer film embedded in an immiscible matrix[END_REF] and in this range of viscosity ratio O(1), the dissipation shall occur within the surrounding PMMA. [START_REF] Zhu | Kinetics of thin polymer film rupture: Model experiments for a better understanding of layer breakups in the multilayer coextrusion process[END_REF][START_REF] Chebil | Influence of outer-layer finite-size effects on the rupture kinetics of a thin polymer film embedded in an immiscible matrix[END_REF] Consequently, the dissipated power can be set up as:

D ∼ η 0 ρ 2 R v ρ 2 = η 0 Rv 2 (2)
where η 0 is the PMMA Newtonian viscosity at the study temperature determined from the Carreau-Yasuda model (see Experimental Section) and ρ is the radius of the rim's crosssection.

Balancing equations ( 1) and ( 2), a constant growth speed is obtained in the case of dewetting without external shear:

v = A 0 σ η 0 = A 0 v 0 (3)
where A 0 is a numerical prefactor of order unity due to geometric simplifications from the scaling approach. For the five configurations (e, T ) tested, we obtain

A 0 = 1.3 ± 0.3.
As a first simple comparison with the case without shear, we define an effective radius for the sheared ellipsoidal holes, such as R = R + R ⊥ /2, where R is the semi-major axis and R ⊥ the semi-minor axis of the ellipsoid. At a given shear rate, monitoring the evolution of R over time leads to the average growth speed <v>, similar to the previous approach (see Figure 2). <v> increases sharply with increasing shear rate, for all tested conditions. Temperature variation has a bigger effect on the dynamics than changing the PS thickness, sug- For each hole, minimum 5 images were analyzed by ImageJ software to capture the growth evolution over time. The speed for each hole was obtained from a linear regression of R on t, and <v> is the average from all the holes' growth speed in their given interval.

gesting that viscosity still plays a major role on the dewetting. The increase of v is most pronounced at 200°C, from about 100 nm/s without shear to 400 nm/s at shear rate 1.6 s -1 .

Considering the effect of shear on both the increasing average growth speed of the holes and the differences in their morphology, we now try to go further and propose a model describing these observations. In the following, a more quantitative approach will consist in evaluating separately the growth speed in the shear direction, v , and perpendicular to shear, v ⊥ , from the temporal evolution of R and R ⊥ respectively.

The obtained results are plotted as a function of shear rate in Figure 3. Undoubtedly, for a given shear rate, v ⊥ is smaller than v and its increase with increasing shear is slower. Typically v ⊥ increased by a factor 2 from 0 to 1.6 s -1 , while the increase for v in the same interval is 5 to 8 times.

In the direction perpendicular to the applied shear, we first make the hypothesis that the growth speed can be described by the no-shear model (see Eq. 3), i.e. dewetting dynamics is only affected by shear parallel to the movement direction. However, we still must consider that PMMA displays shear-thinning behavior in the molten state, like most thermoplastics.

Hence the applied shear may modify its viscosity and consequently the dissipation in the vicinity of the rim. We can then use the Carreau-Yasuda equation (see Experimental Section) to modify Eq. 3 into:

v ⊥ = Av 0 [1 + (λ γ) a ] n-1 a (4)
Using the parameters obtained from the rheological measurements for PMMA (see Table 1), the best fits with only A as a fitting parameter are presented in Figure 3a. Though the data are somewhat scattered, the model captures reasonably well the trends for all conditions. Especially, at all temperatures the slight increase in growth speed with increasing shear rate can be described by the PMMA shear-thinning. Another experimental observation confirmed by the analytical model is that v ⊥ does not seem to depend on the initial PS film thickness (see green, orange and black points). Finally, all the values obtained for A are close to each other, A = 1.2 ± 0.3, in excellent agreement with A 0 obtained without shear.

Let us now move to the growth speed along the applied shear direction v . In this case there is a need to incorporate an additional term taking into account the external shear applied when balancing dissipated viscous power and the capillary energy changes:

ηρ 2 R v ρ 2 ∼ σRv + η γ2 ρ 2 R ( 5
)
where η is, same as for v ⊥ , a function of γ.

Reintroducing A and another geometric constant B for the term describing external shear, this leads to a solution of the form:

v = Aσ 2η + A 2 σ 2 4η 2 + B γ2 ρ 2 (6)
Here we can define a critical shear rate, γc , such as: γc = σ η 0 ρ

Through factoring and expanding the square root we simplify the solution by identifying two regimes for v :

v ≈            Av 0 [1+(λ γ) a ] n-1 a = v ⊥ if γ γc Av 0 2[1+(λ γ) a ] n-1 a + √ B γρ if γ γc (8)
To estimate the rim size, we use volume conservation and for the sake of simplicity will assume a toroidal shape. We also use an average value for the effective radius at a given set of parameters (e, T ). With these hypotheses, we can write ρ ≈ e R /2π. [START_REF] Chebil | Influence of outer-layer finite-size effects on the rupture kinetics of a thin polymer film embedded in an immiscible matrix[END_REF] It has been verified R indeed does not vary much from hole to hole nor during the limited experimental time nor with different shear rates (i.e. the morphology of the holes changes but their area does not). Coming back to Eq. 7, we obtain γc 0.1 s -1 for all the systems studied. In Figure 3b, we then use the equation from the second regime to fit the experimental data for 0.2 < γ < 1.6 s -1 , with only √ B as a fitting parameter. The model predicts well the growth speed evolution with shear rate for every condition studied. The obtained values for √ B are slightly scattered, √ B = 0.4 ± 0.2, while a constant value, similarly to A, shall be expected. Still, the variations do not seem to follow a monotonic trend with either PS thickness or PMMA viscosity, and may then be due to the simplifying hypotheses to estimate ρ.

To further examine the validity of our model, we conclude by analyzing the ratio R /R ⊥ as a function of the applied shear. The results are plotted in Figure 4. Starting from a circu- The lines represent the best fits using equations 4 and 8 respectively. The fits for v were obtained by fixing A with its averaged value obtained from the fits for v ⊥ . lar shape without shear (i.e. R /R ⊥ = 1), the holes deform more and more as shear is applied (see also Figure 1). Hence R /R ⊥ increases for all temperatures and all PS thicknesses, up to a value close to 3 for shear rates of 1.6 s -1 .

Considering that this ratio should be equal to v /v ⊥ , the previous model can be used to describe it, following Eq. 9:

R R ⊥ ≈                  1 if γ γc 1 2 1 + √ B A γ γc [1 + (λ γ) a ] n-1 a
if γ γc (9) Figure 4 shows the corresponding fits with the previously obtained values for A and B, i.e. without new adjusting parameters. The model captures semi-quantitatively the data, especially small changes at low shear rates, as well as the sharp increase at higher ones. More specifically, experimental trends such as a higher ratio for higher PMMA viscosities or thicker PS films, are also well-described. However, a slight overestimate of the predicted holes' elongation is observed in every cases. This could be due to the fact that shear plays a bigger role than only shear-thinning of the surrounding matrix in the dewetting dynamics Figure 4: Radius ratio as a function of shear rate. The proportion of semi-major axis R divided by semi-minor axis R ⊥ was calculated similarly to the sets of data presented for the growth dynamics. 5 different holes were monitored during each experiment and minimum 5 images were analyzed for each hole. From the experimental setup, a shear rate value was obtained for each hole by measuring its moving speed. The data was grouped into intervals of 0.15 s -1 and averaged over at least 5 points.

The ratio over time remains constant during a particular experimental run and the average value for each hole is taken as a mean value from all analyzed images.

perpendicular to it (see also Figure 3a).

In conclusion, the quantification of dewetting dynamics of ultra-thin polymer films under shear was achieved for the first time, and reported for different temperatures and film thicknesses. Though shear can delay rupture, [START_REF] Davis | Suppressing van der Waals driven rupture through shear[END_REF][START_REF] Kadri | Dewetting of a thin polymer film under shear[END_REF] once holes are created they grow faster with increasing shear. This was described satisfactorily by a simple analytical model balancing interfacial tension with the viscous dissipation occurring in the matrix, due to the rim's movement and the external shear applied. The model, assuming that shear does not affect the growth speed perpendicularly to the movement but only in the direction parallel to it, captures the experimentally obtained data. This study shall give insight to the instabilities happening during processes allowing the fabrication of such layered structures, such as multilayer coextrusion. Future work will aim at refining the proposed model. Especially, from a theoretical point of view we shall consider more precisely the effect of shear in the perpendicular direction, polymer-polymer interfacial slip, and focus experimentally on capturing more precisely the onset of dewetting as well as the shape of the rim. A set-up allowing to work at higher shear rates will also be of interest.

Experimental Section

Following our previous works, [START_REF] Bironeau | Sollogoub Existence of a Critical Layer Thickness in PS/PMMA Nanolayered Films[END_REF][START_REF] Zhu | Kinetics of thin polymer film rupture: Model experiments for a better understanding of layer breakups in the multilayer coextrusion process[END_REF][START_REF] Chebil | Influence of outer-layer finite-size effects on the rupture kinetics of a thin polymer film embedded in an immiscible matrix[END_REF] commercially available grades of PS and PMMA, namely PS 1340 (Total) and PMMA VM100 (Arkema), were selected for the study. The molecular weights and glass transition temperatures have been measured before. [START_REF] Bironeau | Sollogoub Existence of a Critical Layer Thickness in PS/PMMA Nanolayered Films[END_REF][START_REF] Zhu | Kinetics of thin polymer film rupture: Model experiments for a better understanding of layer breakups in the multilayer coextrusion process[END_REF] The viscoelastic properties of the polymers have been measured at three temperatures (180, 190 and 200°C) with a DHR 20 (TA Instruments) rheometer with a plate-plate geometry (25 mm diameter and 1 mm gap) under air flow. The experiments were performed on PS pellets and PMMA films samples with a similar thermal history to the trilayers. Frequency sweep tests were conducted in the range from 0.045 to 628 rad/s with an applied strain of 1%, in the linear viscoelasticity region. The zero-shear viscosity (η 0 ), relaxation time (λ), and shearthinning exponents (a and n) were obtained for the two polymers at three temperatures using the classical Carreau-Yasuda model (see Eq. PS thin films were prepared via spin-coating (Spin 150 v-3, SPS) PS in toluene (≥99.8%, VWR) solutions onto a silicon wafer (100 crystal orientation, Sil'tronix) at 2000 rpm/s and 2000 rpm/s 2 for 60 s. Three previously filtered concentrations (1.5, 2.5, and 4.0 wt.%) were used. Films with thicknesses e = 75±5 nm, 150 ± 10 nm, and 290 ± 15 nm were obtained and controlled for each sample by AFM (Nanoscope V, Veeco) in tapping mode. PMMA films were prepared by thermopressing pellets between two glass slides at 200°C in a laboratory press (Gibitre Instruments). Films with thicknesses from 70 to 170 µm were obtained, as determined by a digital length gauge system with accuracy of 0.2 µm (Heidenhain). The root mean square roughness values obtained by AFM was below 10 nm, in all cases considerably smaller than the PS thickness. Any possible impact of this roughness on the dewetting dynamics was neglected herein.

The PMMA films were sorted into pairs of similar thicknesses to ensure symmetric trilayers. The PS films were cut into small pieces (about 10 × 10 mm) and floated in a distilled water bath. A piece of PS film was then moved onto the PMMA substrate. The bilayer was left to dry at room temperature for about 12 h. Afterwards, the second PMMA film was placed on top. Such trilayer samples were kept in an oven at 60°C before the experiments to prevent water uptake. Shearing experiments were conducted in a shearing hotstage (CSS450, Linkam Scientific Instruments) placed under an optical microscope (Eclipse LV150N, Nikon). The trilayer samples were placed on a quartz glass in the cell and pre-heated at 160°C for 3 minutes. Next, the gap, H, was set to 97.5% of the trilayer's initial thickness and kept for another 3 minutes to ensure proper adhesion. Afterwards, the temperature was increased to the temperature of the measurement and the sample subjected to a chosen shear rate. Due to the limited observation window of the microscope and the movements induced by shear, this study only deals with γ < 2 s -1 . Such shear rates are nonetheless consistent with those typically achieved during multilayer coextrusion. [START_REF] Bironeau | Sollogoub Existence of a Critical Layer Thickness in PS/PMMA Nanolayered Films[END_REF][START_REF] Beuguel | Modeling of the rheological properties of multinanolayer films in the presence of compatibilized interphase[END_REF]

Figure 1 :

 1 Figure 1: (a) Schematics of the dewetting experiment with a zoom around a hole (side view).The PS layer is embedded between two PMMA layers with same thicknesses. The top plate is fixed, the bottom plate is moving with a speed V which value is set by the shear rate and the gap (or thickness of the trilayer) H ∼ 200 µm. The shear rate is then defined as γ = V /H. Hence, the PS layer and the holes, while growing, are moving at V /2 parallel to the shear. The dewetting of the film with thickness e is observed from the top. (b) Changes in the holes morphology with increasing shear rate (top view). The scale bars are 50 µm. The holes are circular with a radius R when dewetting occurs without shear, and have an ellipsoid shape when dewetting happens under shear, with a major radius R in the shear direction and a minor radius R ⊥ perpendicular to shear. The holes appear more elongated when higher shear is applied. The final dewetting stage is a series of long and thin holes all aligned in the shear direction.

Figure 3 :

 3 Figure 3: Growth speed perpendicular (a) and parallel (b) to shear as a function of shear rate.The lines represent the best fits using equations 4 and 8 respectively. The fits for v were obtained by fixing A with its averaged value obtained from the fits for v ⊥ .

  10):[START_REF] Bird | A nonlinear viscoelastic model for polymer solutions and melts-I[END_REF][START_REF] Stadler | Dependence of the zero shear-rate viscosity and the viscosity function of linear high-density polyethylenes on the massaverage molar mass and polydispersity[END_REF] |η * (ω) | = η 0 [1 + (λω) a ] η * the complex viscosity and ω the angular frequency in rad/s. The obtained parameters are displayed in Table 1 and show that PS and PMMA have a similar shear-thinning behavior. The analysis of the dewetting data was conducted assuming the classical Cox-Merz rule: 43 η( γ) = |η * (ω)|.

  Dependence of the average growth speed on the shear rate for different e and T .

		400	290 nm, 180°C
			290 nm, 190°C
			290 nm, 200°C
			150 nm, 190°C
	<v> (nm/s)	200 300	75 nm, 190°C
		100
		0
		0.0	0.2	0.4	0.6	0.8	1.0	1.2	1.4	1.6
						(s	-1 )
	Figure 2:

From the experimental setup, a shear rate value was obtained for each hole by measuring its moving speed. At least 5 different holes with very similar shear rates (intervals of 0.15 s -1 ) were observed. The radius of the hole R was calculated as an average from R and R ⊥ . The holes formed at various times of the experiment and only holes with radius of at least 5 µm were considered, hence in the steady-state regime.

Table 1 :

 1 Parameters of Carreau-Yasuda fits

		T (°C) (Pa•s) (s) η 0 λ	a	n
		180 58400 2.96
	PS	190 29200 1.48	0.91 *	0.37 *
		200 14600 0.74
		180 52800 0.91
	PMMA	190 29200 0.43	0.75 *	0.34 *
		200 13100 0.15
	* average values with standard deviations smaller than 0.01

Acknowledgement The authors thank Joshua McGraw and Frederic Restagno for fruitful discussions and critical reading of the manuscript. The Ecole Doctorale SMI (ED 432) is acknowledged for granting A.D. the fellowship for her PhD work.

Graphical TOC Entry


Marie Devreux

Céline Henoumont

Fabienne Dioury

Dimitri Stanicki

Sébastien Boutry

Lionel Larbanoix

Clotilde Ferroud

Robert Müller

Sophie Laurent
email: sophie.laurent@umons.ac.be

Robert N Muller

Bimodal Probe for Magnetic Resonance Imaging and Photoacoustic Imaging Based on a PCTA-Derived Gadolinium(III) Complex and ZW800-1

Introduction

Medical imaging plays a major role in medicine to facilitate diagnosis. One of the most widely used techniques is magnetic resonance imaging (MRI) because it has a high spatial resolution (10 µm -1 mm) and is non-invasive, based on the detection of water protons naturally present in the body. [START_REF] Wahsner | [END_REF] However, MRI is a non-sensitive technique (~ 100 µM) and requires in some cases the use of a paramagnetic contrast agent (CA), most often being a gadolinium(III) chelate, that reduces the relaxation times of protons present in its vicinity and consequently increases the contrast in the regions where it is located. However, since the gadolinium ion is toxic in its free form, it has to be injected as a complex characterized by a high kinetic inertness and a good thermodynamic stability in order to prevent the Gd(III) release into the body. The injectable dose of CA is quite high (approximately 0.1 mmol/kg) which can be problematic for people with kidney failure who could develop nephrogenic systemic fibrosis due to a slow elimination of the gadolinium complex and the liberation of free gadolinium ions, as previously described. [2] Moreover, new researches have shown the presence of gadolinium in the brain of the patients after several injections. [3] In such cases, an alternative could be to use a bimodal system where MRI would be combined with a more sensitive technique thus enabling to reduce the quantities of gadolinated species injected.

The concept of bimodal probe is very interesting because both modalities can be performed with a single injection for the patient. In the literature, there are different bimodal contrast agents, the most common combination of which is MRI, for its high spatial resolution, associated with another technique that can provide more information. The second modality is generally a more sensitive technique, such as PET, or optical imaging. To implement this model, different types of bimodal structures can be used such as dendrimers, liposomes, nanoparticles, or small organic molecules. [4][5][6] In this work, we decided to combine MRI with photoacoustic imaging (PAI), a quite new technique in biomedical imaging. PAI is based on the excitation of endogenous or exogenous molecules by a pulsed laser, followed by the detection of pressure waves resulting from the heat produced by the desexcitation. Heat is detected as pressure waves produced by the dilatation of the surrounding tissues, thus allowing images to be reconstructed. [8][9][10] Despite a lower spatial resolution (75 µm) than MRI, PAI would provide additional information since its sensitivity is higher (~ 100 pM).

Moreover, PAI is a noninvasive technique with a penetration depth limited up to 4 cm which is suitable for preclinical studies in mice and rats but limiting the applications in the clinical field to surface diseases such as skin cancers. The combination of the two modalities therefore appears to be a good solution to compensate for the weaknesses of each one of them, especially for preclinical studies. In the literature, only few researches can be found on this combination, all involving nanoparticulate structures. [7] Allowing more favourable pharmacokinetic properties than nanoparticles and faster elimination by kidney, an approach based on the use of a small organic molecule was chosen here, even if the ratio 1:1 of the two modalities seems not favourable considering the difference of sensitivity between the two techniques. [6,7,11] This can be rationalized by the fact that MRI and PAI images can not be recorded simultaneously, so that MRI scan could be performed at first, and followed by the PAI one during which a part of the agent would be eliminated from the body through the kidneys. It is also important to mention that, considering the limited penetration depth of PAI, this agent is at first dedicated to preclinical studies for which the PAI probe will allow a more precise detection of the targeted disease in the context of molecular imaging.

Most of the agents for MRI are based on 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA), which can form an eightcoordinated complex with gadolinium(III) with one coordinated water molecule. In this work, we decided to use a rigidified analogue based on pyclen framework: the 3,6,9,15-tetraazabicyclo[9.3.1]pentadeca-1(15),11,13-triene-3,6,9-triacetic acid (PCTA- [12], Figure 1). [12] PCTA- [12] has a lower denticity than DOTA so that the resulting gadolinium(III) complex can coordinate two water molecules in its inner-sphere. [13,14] This extended hydration number results in an increased relaxivity (at 20 MHz and 37 °C, r1 = 5.4 mM -1 .s -1 for Gd-PCTA- [12] compared to 3.5 mM -1 .s -1 for Gd-DOTA). Despite its slightly lower thermodynamic stability (log K is 20.4 for Gd-PCTA- [12], and 24.0 for Gd-DOTA), its faster complex formation, its satisfactory kinetic inertness as well as its in vivo-stability, make Gd-PCTA- [12] an interesting alternative to Gd-DOTA. [14][15] As proof of this valuable coordinating cage, P03277, a Gd-PCTA- [12] derivative, demonstrated a better tumor detection than a standard extracellular contrast agent (gadobutrol) and is currently undergoing human clinical trials. [19,[START_REF]Clinical Trials Registry[END_REF] ZW800-1 (Figure 2), the contrastophore chosen for PAI is an organic dye which is a derivative of indocyanine green (ICG) that absorbs in near-infrared (762 nm). This choice was guided to avoid noise resulting from the absorption of endogenous molecules such as hemoglobin, and melanine. [8][9][10] The linker chosen to connect the two parts for imaging modalities is L-lysine. Indeed, this natural amino acid acts as a trifunctionalizable platform with two amine and one carboxylic acid functions as potential sites for successive coupling steps. Two of these groups will thus allow the grafting of the two contrastophores, while the third one will remain free for conjugation to a biovector thus making the probe specific to a pathological tissue.

Results and discussion

2.1 Synthesis of the two parts of the bimodal probe:

2.1.1 PCTA(CO2tBu)3-COOH for MRI (part 1)
We previously reported the synthesis of PCTA(CO2tBu)3-COOH, [START_REF] Ferroud | [END_REF]24,26] as a precursor of a bifunctional derivative of PCTA- [12] bearing an additional carboxylic acid function anchored to the pyridine subunit that led to the corresponding Gd-PCTA-COOH chelate for application to the synthesis of targeted Gd-based CA (Figure 1). As previously discussed by us and other, [20,21,25] the preferred synthetic route to PCTA(CO2tBu)3-COOH was based on the assembly of two units bearing the final desired functionalities as it allows easier modulation of the nature and number of coordinating sites while avoiding post-macrocyclization functionalization steps with boring selectivity control. Herein, we described optimized protocols to produce higher quantities of this key synthon that is precursor of a variety of PCTA-based bifunctional chelators (BFC). The synthetic pathway involves a controlled macroring step performed by assembling pyridine unit 3 and triamine 6b (Scheme 1).

Compound 3 was prepared from 3-hydroxypyridine with a revised protocol as the three steps/two-pots synthetic route we previously described did not allow us to produce this synthon at tens of grams scale (Scheme 2). [START_REF] Ferroud | [END_REF]26] The first intermediate 1a (hydrochloric salt) was produced at some forty grams scale with a repeatable average yield of 74% according to Baldo's protocol. [27] The selective Oalkylation of the aromatic hydroxyl proceeded on the corresponding potassium pyridolate 1b resulting from the treatment of an ethanolic solution of hydrochloride 1a with an excess of K2CO3. [28] The desired dialcohol 2 was obtained by reaction with ethyl bromoacetate in warmed DMF in 65% yield higher than that previously reported by Hovland et al. for the dodecyloxy analogue. [28] As reported by Uenishi et al. for bipyridine substrates, [29] the Apple reaction with carbon tetrabromide and triphenylphosphine was used to give dibromide 3 in 64% yield. For this last step, it must be pointed that attempts to proceed in more concentrated medium (0.5 and 1.0 M) were damageable with formation of increasing amounts of a side-product of similar polarity (15%, and 35%mol respectively from 1 H NMR estimation). The synthesis of the triamine 6b starts from the selectively N,N''-protected diethylenetriamine derivative 4, [26] and was optimized as well for the last two steps -tri-N-alkylation with tert-butyl bromoacetate, then selective cleavage of sulfonamidic protections -rendered sequential in one-pot (Scheme 3). In the present work, both steps proceeded in warmed acetonitrile in the presence of K2CO3, and afforded synthon 6b in repeatable 72% mean yield at scales of more than ten grams. For that protocol, successive monitoring (mass spectroscopy) of the conversion of the intermediates 5a-b into 5c, then from 5c and 6a into the desired compound 6b were performed to avoid extending reaction times, particularly that for the second step, thus limiting the formation of the more polar lactamized side-product as reported before. [20] Our pathway constitutes an interesting alternative to that recently reported by C. Picard and coll. [25] that involves benzylic protections whose cleavage required pressure of dihydrogen that may be limiting for scaling-up.

The two previously prepared units 3 and 6b were then assembled on the basis of a recent published macroring process conducted in a diluted medium (reactants concentration 0.002 M) in rather "hard" conditions (refluxing acetonitrile for 2 days with a large excess of sodium carbonate) that gave access to small batches of only a few hundred milligrams. [25] The protocol was revised in the perspective of larger scales. We recently reported a new protocol involving equimolar amounts of compounds 3 and 6b occurring in DMF in more concentrated medium (reactants concentration 0.01 M) at room temperature for 1 day in the presence of a smaller excess of sodium carbonate that led to the desired macrocycle 7 in 76 % yield for a gram scale. [26] Herein, we found that replacing DMF by acetonitrile, a safer and more easily removable solvent, had no impact on efficiency of the macroring process: larger batches of several grams of compound 7 were obtained with yields above 70% (Scheme 4). At this stage, a specific spectral feature must be highlighted as the complexity of the 1 H NMR spectrum of the chromatographed material could be disappointing and lead to an erroneous conclusion about the efficiency of the process. Indeed, under milder conditions (lower excess of sodium carbonate, reaction conducted at room temperature), compound 7 was isolated as a mixture of two forms easily distinguished by NMR (Figures 3 andS1):

i) a NaBr adduct as evidenced by the elemental analysis, and in accordance with Na + species reported for such derivatives. [25] This NaBr The last step of this synthetic route was a selective cleavage of the masked carboxylic acid appended on the pyridine subunit. The corresponding ethyl ester was saponified in mild conditions, by action of a stoechiometric amount of sodium hydroxide in ethanolic solution at room temperature and afforded the desired conjugable prochelator 8 in quantitative yield. As expected, the NMR trace for coumpound 8 is also highly dependent of the pH (Figure 4). The CA for PAI (figure 2) was synthesized according to the route described by Choi et al. [10] This indocyanine derivative chosen for its absorption wavelength, in the near-infrared that is outside the absorption range of endogenous molecules and tissues, is ideal and allows a better signal/noise ratio. Moreover, this chromophore has a free carboxylic acid function to serve as functional site for subsequent grafting onto the linker.

Synthesis of the bimodal probe

Selective protections of the three functional sites of L-lysine were required to serve as a platform on which the two previously prepared imaging parts will be appended, as well as an additional biovector for targeting purposes.

First, the regioselective carboxybenzyl (Cbz) protection of the amine of the lateral chain was performed with 80% yield according to the protocol described by Balajhy et al (Scheme 5). [30] The carboxylic acid was then esterified as allyl ester using the thionyl chloride method that proceeds by an in situ activation as acid chloride. [30,31] In such conditions, compound 11a was obtained with a yield of 46%. This modest yield can be explained by the instability of the Cbz group in acidic medium evidenced by the formation of H-Lys(H)-OAl 11b as well. Moreover, this side-product 11b proved to have a polarity close to that of the desired compound 11a, and made the chromatographic purification with partial coelution of both products tedious.

The assembling of the two previously prepared parts 8 and 11a required preliminary optimization (Scheme 6). Different coupling conditions were tested (Table 1). The best results

Relaxometric analysis of the bimodal probe

NMRD profiles were recorded for all the Gd-complexes (Figure 5). By comparing Gd-PCTA-COOH to Gd-PCTA-Lys(H)-OAl 14, a damageable effect of the lysine linker grafting on the longitudinal relaxivity r1 can be deplored. Fortunately, a slightly higher relaxivity was obtained by subsequent grafting of the ZW800-1 fluorophore, with a dependence on the gadolinium concentration. The first verification to explain these results was the determination of the number of water molecules coordinated in the inner-sphere of gadolinium ions. PCTA-(CO2tBu)3-COOH is a N4O3-type heptadentate ligand that allows the presence of two water molecules in the coordination sites of the gadolinium ion. [17] In the present study, the impact of additional functionalization on the number of water molecules was thus measured by 17 O NMR. As already described, [32,33] the method consists in measuring the chemical shift difference of the water protons for pure water and for an aqueous solution of the studied gadolinium complex at a known concentration. Comparison with standard solutions of well-known gadolinium complexes allows the determination of the number of innersphere water molecules. The comparison with Gd-PCTA-COOH and Gd-DOTA having respectively two and one innersphere water molecules allows to deduce that both of the new complexes grafted onto the lysine linker have one water molecule directly coordinated to gadolinium (Figure 6). This is probably due to a new coordination between the carbonyl group on the linker and the gadolinium ion. This result explains the decrease in relaxivity observed for both complexes Gd-PCTA-Lys(H)-OAl 14 and Gd-PCTA-Lys(ZW800-1)-OAl 15. The relaxivity of Gd-PCTA-Lys(ZW800-1)OAl is nevertheless higher than that of Gd-PCTA-Lys(H)-OAl and depends on the gadolinium concentration, which can probably be explained by the modification of the size of the complex. Each NMRD profile was thus fitted with the Solomon and Bloembergen theory. [34][35][36] This model predicts that the relaxivity can be modified by different parameters that are: the rotational correlation time τ # , the electronic relaxation time at zero field τ $% , the correlation time that modulates the electronic relaxation τ & , the distance between the protons of the coordinated water molecule and the gadolinium (r) and the number of coordinated water molecules (q). The diffusion of water molecules in the vicinity of the gadolinium complex, known as the outersphere mechanism, will also influence the relaxivity. It is described by the distance of closest approach between the water molecules and the gadolinium ion (d) and by the relative diffusion coefficient of water (D). This mechanism has however a low and fixed contribution for all gadolinium complexes such that d and D were fixed to 0.36 nm and 3.10 -9 m 2 /s respectively during the fitting. The results of the fitting are presented in Table 2. r was fixed at 0.31 nm as previously described, and τ ' was fixed at 100 ns based on the standard evolution of the relaxivity of the small organic complexes without any amide bond with the temperature. [37] The continuous decrease of the relaxivity with increasing temperatures is indeed typical of a fast exchange of the coordinated water molecule, so that 100 ns is an appropriate value. [38] The value of q was fixed according to the results obtained by 17 O NMR, whereas the other parameters were let to vary. As expected, among those parameters, a modification of the rotational correlation time τ # is observed for the complex Gd-PCTA-Lys(ZW800-1)-OAl, which can be correlated with the increase of the molecular weight. Moreover, an increase of τ # is obtained when the concentration of the complex increases, which is probably the sign of a partial aggregation of the molecules by π-stacking, due to the aromatic structure of the ZW800-1.

Figure 5. NMRD profiles at 37°C. The straight lines correspond to the theoretical fitting according to the theory of Solomon and Bloembergen. It has to be noted that the fit at high field (above 100 MHz) is not so reliable considering the partial aggregation of the molecules, and is shown here to guide the eyes.

Table 2. Parameters extracted from the theoretical fitting of the NMRD profiles according to the Solomon and Bloembergen equations. d, the distance of closest approach and D, the diffusion coefficient of water characterize the outersphere contribution to the relaxation; r, the distance between the innersphere water molecule and the gadolinium, τR, the rotational correlation time, τM, the residence time of the coordinated water molecule, τs0, the Gd(III) electronic relaxation time at zero field and τV, the correlation time that modulates the electronic relaxation, define the innersphere contribution to the relaxation.

Gd-PCTA-COOH [b]

Gd-PCTA-Lys(H)-OAl [a] fixed parameters during the fitting procedure [b] the product -was prepared according to Guerbet's patent [START_REF] Guerbet | Lipophilic chelates and use thereof in imaging[END_REF] [c] obtained by the fitting of NMRD profiles

Phantom images

As a proof of concept, some phantom images were recorded (Figure 7). The MRI images are compared with Gd-DOTA, a commercially available contrast agent (Dotaremâ). As expected according to the previously described physicochemical characterization, the longitudinal relaxation time of water in the presence of Gd-PCTA-Lys(ZW800-1)-OAl 15 (r1 5,47 mM -1 s -1 )is shorter than with Gd-DOTA (r1 2,9 mM -1 s -1 ) [START_REF] Laurent | Contrast med[END_REF] at 9.4 T, leading to a better contrast. As explained above, this is mostly due to the bigger size of the molecule.

The PAI efficacy of Gd-PCTA-Lys(ZW800-1)-OAl 15 was compared to that of ZW800-1. As shown in figure 8, the photoacoustic signal in the therapeutic range, i.e. in the near infrared (660 nm to 930 nm), is more or less equivalent for Gd-PCTA-Lys(ZW800-1)-OAl 15 and for ZW800-1, the small observed difference being attributed to a small difference in concentration between the two compounds. These results show thus that Gd-PCTA-Lys(ZW800-1)-OAl is a promising bimodal molecule for imaging application.

Conclusion

The bimodal probe was successfully synthesized, each intermediate was characterized. The efficiency of this new bimodal probe for MRI and PAI was also assessed. These two imaging techniques could indeed be used jointly in the future to improve the quality of the images with a high spatial resolution provided by MRI and a high sensibility with optoacoustic imaging. Moreover, this probe allows in perspective to add a biovector. Indeed, the linker still possesses a carboxylic acid protected by an allyl group which is available after deprotection to graft for example a peptide specific to a biological disorder.

The efficacy of the MRI probe could also be improved by allowing the coordination of two water molecules in the innersphere as for the parent compound Gd-PCTA. In that aim, it could be possible to space out the free carboxylic function from the macrocycle in compound 1. It will be however necessary to verify that the length modification does not change the properties of the bimodal probe.

Acknowledgements

This work was performed with the financial support of the FNRS, FEDER, the ARC, the Walloon Region (Gadolymph, Holocancer and Interreg projects), the Interuniversity Attraction Poles of the Belgian Federal Science Policy Office and the COST actions. Authors thank the Center for Microscopy and Molecular Imaging (CMMI, supported by European Regional Development Fund Wallonia)

Thanks to the PhD De Winter J. and Prof Gerbaux P. from S 2 MOs lab for the mass spectra

Materiel and methods

Chemical and physical measurements

All reactions were monitored by mass spectrometry (Waters ZQ2000). Chromatographic purifications were performed on a the BiotageÒ flash chromatography system using pre-packed cartridges, and automatic fraction collection based on ELSD and/or UV detection (254, and 270 nm). The dialyses were performed on regenerated cellulose membranes fromSpectrum labs Ò characterized by pores of 500 to 1000 Dalton. The elimination of free gadolinium ions was realized with Chelex â 100 resin (sodium form). All synthetic intermediates were characterized by 1 H, 13 Compound 1a (36.7 g, 192 mmol) was prepared from 3-hydroxypyridine (24.0 g, 252 mmol) following the protocol described by Baldo et al.. [27] Yields 72-76% (five repeated trials). Yield 74% (mean).

Ethyl 2-{[2,6-bis(hydroxymethyl)-3-pyridyl]oxy}acetate, compound 2

Ethyl bromoacetate (22 mL, 199 mmol, 1.5 eq) was added to a solution of the crude potassium pyridolate 1b (26.2g, 131 mmol) in DMF (100 mL). The mixture was warmed at 80°C for 1.5 h than maintained in the hot bath allowed to cool to room temperature. Insoluble matter was filtered off, washed with CH2Cl2 and the filtrate was concentrated to dryness. The brown oily residue obtained was taken up in CH2Cl2 (150 mL) and water (50 mL). The mixture was vigorously stirred then neutralized by portionwise solid NaHCO3 addition. The two layers were separated and the aqueous layer was extracted with CH2Cl2 (2 x 150 mL). The combined organic layers were dried, and concentrated to give a brown oil that was purified by chromatography on silica gel (AcOEt) to afford the desired compound 2 (20.59 g, 85.35 mmol) as a yellow oil that crystallizes on cooling. [START_REF] Ferroud | [END_REF] Yield 65%. [START_REF] Wahsner | [END_REF] H NMR (400 MHz, CDCl3) δ (ppm): conform to reported data: [START_REF] Ferroud | [END_REF] 1.28 ( to add carbon tetrabromide (15.25 g, 46.0 mmol, 2.5 eq) in one portion followed by solid triphenylphosphine (12.06 g, 46.0 mmol, 2.5 eq) portionwise. After the end of the addition, stirring was maintained overnight in the cold bath allowed to raise up to room temperature.

The reaction mixture was concentrated. The brown oil obtained was taken up in CH2Cl2 (1000 mL), and washed with a saturated aqueous solution of NaHCO3 (80 mL). The organic phase was dried, and concentrated. The resulting coloured solid was purified by chromatography on silica gel (cyclohexane/AcOEt, 8/2 v/v) to give the desired compound 3 as a white powder (4.36 g, 11.88 mmol). [START_REF] Ferroud | [END_REF] Yield 64%. [START_REF] Wahsner | [END_REF] H NMR (400 MHz, CDCl3) δ (ppm): conform to reported data: [START_REF] Ferroud | [END_REF]

2-Nitro[N(2{2[(2-nitrophenyl)sulfonylamino]ethylamino}) ethyl]benzenesulfonamide, compound 4

A 2 M aqueous solution of sodium hydroxide (56 mL, 112 mmol, 2.0 eq) was added to a solution of diethylenetriamine (6.0 mL, 55.54 mmol) in diethyl ether (2 L). The mixture was vigorously stirred at room temperature to add dropwise (in about 2-2.5 h) a solution of 2-nitrophenylsulfonyl chloride (24.61 g, 111 mmol, 2.0 eq) in tetrahydrofuran (360 mL). Vigorous stirring was maintained overnight.

The white precipitate formed was filtered off, and washed with diethyl ether (30 mL). Volatiles were evaporated to afford the desired product 4 (20.9 to 21.5 g, 44.0 to 45.3 mmol) as a white solid. Yields 79-81% (three repeated trials). Yield 80 % (mean). [START_REF] Wahsner | [END_REF] H NMR (DMSO-d6, 400 MHz) δ (ppm): conform to reported data. [41]

tert-Butyl 2-{2-[(2-tert-butoxy-2-oxo-ethyl)-(2-[{2-tert-butoxy-2-oxo-ethyl}amino]ethyl)amino]ethylamino}acetate, compound 6b

Attention: store at -20°C to avoid lactamization. A suspension of the previously prepared disulfonamido amine 4 (21.46 g, 45.32 mmol), and K2CO3 (23.8 g, 172.2 mmol, 3.8 eq) in acetonitrile (284 mL) was refluxed for 15 minutes. tert-Butyl 2-bromoacetate (26.5 mL, 179.5 mmol, 4.0 eq) was added in one portion, and the resulting mixture was further refluxed until completion of the reaction (TLC and/or MS monitoring; 3 to 5 h). The reaction was cooled to room temperature. A second portion of K2CO3 (25.0 g, 180.9 mmol, 4.0 eq) was then added, followed by the addition of thiophenol in one portion (23 mL, 225.4 mmol, 5.0 eq). The resulting suspension was heated at 60°C until completion of the reaction (TLC and/or MS monitoring; 2 to 4 h). The insoluble matter was filtered off over a Celite ® 545 pad, and washed with CH2Cl2. The filtrate was concentrated then purified by chromatography on silica gel (CH2Cl2/MeOH, 100/0 to 95/5 v/v) to give the desired compound (14-15 g, 31.4 to 33.7 mmol)) as a clear sticky orange oil. Yields 70-74 % (three repeated trials). Yield 72% (mean). ESI-MS (C22H43N3O6) m/z 446.3 [M+H] + . [START_REF] Wahsner | [END_REF] H NMR (CDCl3, 400 MHz) δ (ppm): [26] The title compound was prepared according to our recently published protocol with slight modifications. [26] A suspension of triamino lower part 6b (3.09 g, 6.93 mmol), pyridinic dibromide upper part 3 (2.80 g, 7.63 mmol, 1.1 eq), and Na2CO3

(2.94 g, 27.74 mmol, 4.0 eq) in acetonitrile (700 mL) was stirred at room temperature for 2 days. The insoluble matter was filtered off.

The filtrate was concentrated then purified by chromatography on silica gel (AcOEt/MeOH, 100/0 to 90/10 v/v) to give the desired compound 7 (3.25 g, 5.00 mmol) as a beige solid. Yield 72%. [START_REF] Wahsner | [END_REF] H NMR (CDCl3+Na2CO3, 400 MHz) [START_REF]The NMR traces of the chromatographed fractions are variable with the presence of the two forms, NaBr adduct and free-Na form, in different proportions. Consequently, qualification (nature, purity) was preferred on samples treated to complete conversion in NaBr adduct. For that purpose, the solution in CDCl3 (0.5 mL) of the chromatographed compound 7 (12.3 mg) was treated with Na2CO3 (10.0 mg, 94.3 µmol, ca 5 eq) and vigorously stirred for 1 day at room temperature; the NMR spectra ( 1 H, and 13 C) evolved to the characteristic traces previously reported and presented on Figures 3-S1 (a). 20,23 After washings to neutrality with D2O (3 x 1 mL), both 1 H and 13 C NMR spectra are quite different (Figure 3-S1 (b)) and representative of that of the free-Na form with several species in equilibrium. Moreover, when a solution in CDCl3 (1 mL) of the chromatographed compound 7 (25.1 mg) was treated with aluminum oxide 60 activity IV (500 mg with 50 µl of H2O), a mixture of the two forms was obtained (Figure 3 (c))[END_REF] 13 C NMR (CDCl3+Na2CO3,100 MHz) [START_REF]The NMR traces of the chromatographed fractions are variable with the presence of the two forms, NaBr adduct and free-Na form, in different proportions. Consequently, qualification (nature, purity) was preferred on samples treated to complete conversion in NaBr adduct. For that purpose, the solution in CDCl3 (0.5 mL) of the chromatographed compound 7 (12.3 mg) was treated with Na2CO3 (10.0 mg, 94.3 µmol, ca 5 eq) and vigorously stirred for 1 day at room temperature; the NMR spectra ( 1 H, and 13 C) evolved to the characteristic traces previously reported and presented on Figures 3-S1 (a). 20,23 After washings to neutrality with D2O (3 x 1 mL), both 1 H and 13 C NMR spectra are quite different (Figure 3-S1 (b)) and representative of that of the free-Na form with several species in equilibrium. Moreover, when a solution in CDCl3 (1 mL) of the chromatographed compound 7 (25.1 mg) was treated with aluminum oxide 60 activity IV (500 mg with 50 µl of H2O), a mixture of the two forms was obtained (Figure 3 (c))[END_REF] δ (ppm): 14.2, 27.9, 28.

Figure 2 . 9 Figure 1 .

 291 Figure 2. Structure of the PAI probe ZW800-1

Scheme 1 .Scheme 2 .

 12 Scheme 1. Retrosynthesis to obtain PCTA(CO2tBu)3-COOH as precursor of a bifunctional chelating agent for Gd(III).

adduct is characterized by a 1 H 13 C

 113 Scheme 3. Synthetic scheme to obtain the triamine 6b. Reagents and conditions: (e) 2-NO2-C6H4-SO2Cl, NaOH, Et2O, THF, H2O; (f) i) BrCH2CO2tBu, K2CO3, CH3CN, reflux, 3-5h; ii) PhSH, K2CO3, 60°C, 2-4h.NH2

Figure 4 .Scheme 4 .Figure 3 . 1 H

 4431 Figure 4. Influence of pH on 1 H NMR trace of PCTA(CO2tBu)3-COOH (CDCl3, 500 MHz)

Scheme 5 .j

 5 Scheme 5. Preparation of the L-lysine derivative as a trifunctional linker. Reagents and conditions: (i) ref (30); (j) SOCl2, allyl alcohol, reflux, 1d.

Scheme 6 .

 6 Scheme 6. Preparation of the MRI part of the probe. Reagents and conditions: (k) HBTU, DIPEA, CH2Cl2, r.t., 4h; (l) TFA, CH2Cl2, r.t., 3d; (m) GdCl3, NaOH, water, pH 5-6.

14 Gd

 14

Figure 6 .

 6 Figure 6. Measurements of the 17 O chemical shift of water in the presence of different Gd-complexes.

Figure 7 .Figure 8 .

 78 Figure 7. Phantom image at 9.4 T: left: water; middle: Gd-PCTA-Lys(ZW800-1)-OAl 15; right: Gd-DOTA

Table 1 .

 1 Optimization

			Coupling reagent(s)	DIPEA (eq)	Solvent	Yield
	1	2.0	EDC.HCl (1.2 eq)	3.3	CH2Cl2	0%
			NHS (1.3 eq)
	2	2.0	DCC (1.1 eq)	2.0	CH2Cl2	34%
			HOBt.H2O (0.26 eq)
	3	2.0	EDC.HCl (1.2 eq)	3.0	CH2Cl2	21%
			HOBt.H2O (0.26 eq)
	4	1.5	EDC.HCl (1.2 eq)	3.0	CH2Cl2	20%
			HOBt.H2O (0.26 eq)
	5	2.0	EDC.HCl (1.2 eq)	3.0	DMF	9%
			HOBt.H2O (0.26 eq)
	6	1.2	HBTU (2.1 eq)	2.4	CH2Cl2	38%

of the coupling reaction between PCTA(CO2tBu)3-COOH 8 and H-Lys(CBz)-OAl 11a; all trials were made with ± 100 mg of compound 8 (limiting reagent).

Entry H-Lys(CBz)-OAl (eq) Scheme 7. Dual-modality probe synthesis. Reagents and condition: (n) EDC.HCl, water, pH 5-6.

  C and COSY NMR (Bruker ® AV 400 at 400 MHz, Bruker ® Avance II-500 at 500 MHz, Bruker ® BioSpin GmbH at 400 MHz or Bruker ® NEO at 600 MHz). If not mentioned, spectrum was recorded at 298 K. Chemical shifts d are reported in ppm using the residual deuterated solvent signals as an internal reference (CDCl3: dH = 7.26 ppm, dC = 77.1 ppm; D2O: dH = 4.80 ppm as internal standard, dC = 3-trimethylsilyl-1-propanesulfonic acid sodium salt as external reference; DMSO-d6: dH = 2.50 ppm, dC = 39.5 ppm; CD3OD: dH = 3.31 ppm). For 1 H NMR, coupling constants J are given in Hz and the resonance multiplicity is described as s (singlet), d (doublet), t (triplet), q (quartet), m (multiplet), and br (broad). The synthetic intermediates were also characterized by mass spectrometry (Waters, ZQ2000 or Synapt G2-Si). The relaxometric analyses were performed on Bruker Minispec 20 MHz and 60 MHz and the NMRD profiles were registered on the Stelar Spinmaster (Stelar, Italy).17 O NMR measurements were performed on a Avance II 500 NMR spectrometer (Bruker Ò ) at 37°C. The photoacoustic measurements were performed on InVision-256TF iThera Medical. The MRI measurements were performed at 1T on ICON (Bruker ® ) and at 9.4T on Biospec (Bruker Ò ) according to Rapid Acquisition with

	Relaxation Enhancement sequence (RARE), (TR=350 ms, TE=12 ms, resolution=156x146 microns, slice thickness=1,25 mm, RARE
	factor=2, 2 or 4 averages).
	5.2 Synthesis of the probe for MRI PCTA(CO2tBu)-COOH, compound 8
	5.2.1 2,6-bis(hydroxymethyl)pyridin-3-ol, hydrochloride salt, compound 1a

  1.44 (s, 9H, tBu); 1.45 (s, 18H, tBu); 2.4 * (br s, 2H, NH); 2.67 (t, 4H, J 6.0 Hz, CH2CH2N); 2.81 (t, 4H, J 6.0 Hz, CH2CH2N); 3.31 (s, 4H); 3.33 (s, 2H).

* Not always visible

5.2.7 tert-Butyl 2-[3,9-bis(2-tert-butoxy-2-oxo-ethyl)-12-(2-ethoxy-2-oxo-ethoxy)-3,6,9,

15-tetrazabicyclo[9.3.1]

pentadeca-1

(14)

,11

(15)

,

12

-trien-6-yl]acetate, compound 7

  δ (ppm): 1.26 (t, 3H, J 7.1 Hz, Et), 1.41 (s, 9H, tBu), 1.46 (s, 9H, tBu), 1.47 (s, 9H, tBu), 1.98-2.11 (m, 2H,CH2CH2N), 2.14-2.24 (m, 2H, CH2CH2N), 2.47-2.68 (2m, 4H, CH2CH2N), 3.10 (AB system, 2H, J 17.8 Hz), 3.29-3.48 (m, 4H), 3.65-3.76 (m, 2H), 3.92 (d of AB system, J 14.5 Hz, 1H), 4.12 (d of AB system, 1H, J 15.7 Hz), 4.21 (q, 2H, J 7.1 Hz, Et), 4.70 (AB system, 2H, J 16.3 Hz), 7.19 (AB system, 2H, J 8.4 Hz).

  1, 53.3, 53.81, 53.85, 54.1, 56.4, 56.5, 59.5, 59.8, 61.5, 61.7, 65.6, 82.6, 82.85,

82.94, 120.5, 122.3, 147.7, 149.8, 151.1, 168.2, 173.40, 173.2, 173.6. Elemental analysis (%): calcd. for 7.NaBr: C33H54BrN4NaO9 (MW 753.70): C, 52.59; H, 7.22; N, 7.43; found: C, 51.70; H, 7.22; N, 7.42.

N-CH2-CH2-N-) ; 4.66 (m broad, 1H, -NH-CH-CH2-) ; 4.80 (d, 2H, J 6Hz, -CH2-CH=CH2) ; 4.9 (S, 2H, -O-CH2-CO-) ; 5.31 (2d, 2H, J 17Hz, -CH=CH2) ; 5.96 (m, 1H, -CH=CH2) ; 7.32 (d, 1H, J 7Hz, -CHPyr) ; 7.44 (d, 1H, J 10Hz, -CHPyr).

Gd-PCTA-Lys(H)-OAl, compound 14

A solution of GdCl3.6H2O (6.95 mg, 18.7 µmol, 1.1 eq) in water (500 µL) was added dropwise to a solution of PCTA(COOH)3-Lys(H)-OAl 13 (10.6 mg, 17.0 µmol) in water (500 µL). pH was adjusted and maintained to 5 < pH < 6 with a 0.1 M aqueous solution of NaOH, and the mixture was warmed at 50°C overnight. The presence of free Gd 3+ was revealed by the colorimetric test with arsenazo. [42] The aqueous reaction mixture was treated with Chelex® resin, then freeze-dried to give the corresponding gadolinium complex 14 (8,6 mg) as a white powder. Yield 65%. ESI-MS (C28H39GdN6O10): m/z 779.2 [M+H] + , 801.2 [M+Na] + .

Gd-PCTA-Lys(ZW800-1)-OAl, compound 15

A solution of EDC.HCl (38.3 mg, 199.7 µmol, 8.3 eq) in water (300 µL) was added dropwise to a solution of Gd-PCTA-Lys(H)-OAl 14 (18.7 mg, 24.0 µmol) in water (600 µL). pH was controlled and maintained to 5 < pH < 6. A solution of ZW800-1 (18.9 mg, 0.02 mmol, 1 eq,) in water (200 µL) was then added, and the mixture was stirred for 4 h. The solution was first dialyzed for 2 days then lyophilized.

The resulting solid material was washed with dichloromethane (4 x 1.5 mL), then volatiles eliminated to give the desired probe 15 (29 mg) as a green solid. Yield 85%. ESI-MS (C79H104GdN10O18S2 + ): m/z 851.8 [M+H] 2+ .

Author contributions

Conceive and designed the experiments: SL, CH, FD, DS. Performed experiments: MD, CH, LL, SB. Analyzed data: MD, CH, LL, SB.

Contributed reagents/analysis tools/materials: SL, RNM, CF. Wrote paper: MD, CH, FD, DS, LL, SB, SL, CF. All authors read and approved the final manuscript

Conflicts of interest

The authors declare no conflict of interest Graphical Abstract Magnetic resonance imaging (MRI) has a low sensitivity. To improve this weakness, it is interesting to use a contrast agent and to couple MRI with a more sensitive technique like photoacoustic imaging (PAI). The probes used are Gd-PCTA for MRI and ZW800-1 for PAI.