Emmanuel Siéfert

Etienne Reyssat

José Bico

Benoit

Benoit Roman
email: benoit.roman@espci.fr.

Bio-inspired pneumatic shape morphing elastomers

come

Morphing a thin plate into a programmed shape is a challenging problem, highlighted by Gauss: if the distances along the surface are not modified, the Gaussian curvature cannot be changed and only a limited family of 3D surfaces is achievable, as commonly observed with bilayer sheets [START_REF] Reyssat | Hygromorphs: from pine cones to biomimetic bilayers[END_REF][START_REF] Pezzulla | Geometry and mechanics of thin growing bilayers[END_REF] . However, Nature overflows with examples of geometrically complex thin objects, such as leaves or organs epithelia [START_REF] Dervaux | Morphogenesis of growing soft tissues[END_REF] . For instance, differential growth induces the elegant shape of flower petals [START_REF] Rebocho | Formation and shaping of the antirrhinum flower through modulation of the cup boundary gene[END_REF] , or may conversely crinkle an initially flat leave when the growth rate is deregulated 13 . While the growth process may be spatially homogeneous, the orientations of cellulose fibres may also induce anisotropic growth, which leads to the hygroscopic actuation of wheat awns [START_REF] Fratzl | Cellulose fibrils direct plant organ movements[END_REF] or to the chiral shape of some seed pods [START_REF] Armon | Geometry and mechanics in the opening of chiral seed pods[END_REF] .

Figure 1: Principle of pressure actuated baromorph plate. a, Schematic of actuation: the pressure inside the airways induces anisotropic inflation of the plate (higher strain normal to the airways than along the channels). b, 3D printed mould used to cast the baromorph illustrated in panel c. c, Actuation of the plate: suction (left) tends to contract the plate in the azimuthal direction, leading to a bowl (positive Gaussian curvature), while inflation (right) leads to an excess angle and a transformation into a saddle shape (negative Gaussian curvature). d, Evolution of the cap of an acetabularia alga from a bowl to a saddle shape due to a preferential growth in the azimuthal direction (adapted from Serikawa et al. [START_REF] Serikawa | An analysis of morphogenesis of the reproductive whorl of acetabularia acetabulum[END_REF] ) Inspired by biological morphogenesis, pioneering experiments have been carried out with hydrogel plates where the inhomogeneous isotropic [START_REF] Klein | Shaping of elastic sheets by prescription of non-euclidean metrics[END_REF][START_REF] Kim | Designing responsive buckled surfaces by halftone gel lithography[END_REF][START_REF] Huang | Ultrafast digital printing toward 4d shape changing materials[END_REF] or anisotropic [START_REF] Erb | Self-shaping composites with pro-grammable bioinspired microstructures[END_REF][START_REF] Sydney Gladman | Biomimetic 4d printing[END_REF] swelling properties were spatially distributed in order to obtain various 3D shapes once immersed in a bath of hot water. Nevertheless, the experimental realisations developed so far involve slow diffusive swelling processes and very soft objects that generally cannot sustain their own weight. In contrast, pneumatic actuation presents strong advantages such as large work load, reversibility, controllability and fast actuation, which have led to the recent development of multiple soft robotics actuators for twisting, contracting, expanding or bending motions [START_REF] Gorissen | Elastic inflatable actuators for soft robotic applications[END_REF] . However, such actuators generally rely on bilayers [START_REF] Shepherd | Multigait soft robot[END_REF] or are limited to surface texturing effects [START_REF] Pikul | Stretchable surfaces with programmable 3d texture morphing for synthetic camouflaging skins[END_REF] , which imposes strong constraints on the achievable states. Our approach bridges these two emerging fields, bioinspired shape-morphing and pneumatic soft robotics, with a new easy-to-build, easy-to-control object, referred to as a baromorph.

Baromorphs consist in elastomer plates embedding a network of airways (see Methods for fabrication details), which give rise to a programmed family of shapes upon air inflation or suction. Such structures can be viewed as pneumatic metamaterials [START_REF] Bertoldi | Flexible mechanical metamaterials[END_REF] . When the inner pressure is increased (or decreased), the elongated channels tend to inflate (or deflate) anisotropically [START_REF] Timoshenko | Theory of plates and shells[END_REF] :

The length of an inflated channel remains almost unchanged, while its width increases (Fig. 1a).

This anisotropy results in a controllable modification of the effective rest-lengths of the baromorph, mimicking the anisotropic growth of a biological tissue, with a magnitude that depends on the geometry of the inner channels and on the applied pressure. The plate deforms according to the new target metric imposed by the network of airways, and may buckle out of plane to reach an equilibrium 3D shape that minimises the total elastic energy -sum of stretching and bending energies.

In Fig. 1c, we illustrate the deformation of a baromorph plate with radial channels obtained by casting the 3D printed template shown in Fig. 1b: the target expansion is mainly circumferential.

Upon suction and consequent azimuthal contraction, the plate adopts a bowl shape (with positive Gaussian curvature). Conversely, inflation induces an azimuthal expansion and leads to an excess angle in the plate, which destabilises into a surface of negative Gaussian curvature.

These transformations are reminiscent of the morphing evolution of Acetabularia (Figure 1d) [START_REF] Dervaux | Morphogenesis of growing soft tissues[END_REF][START_REF] Serikawa | An analysis of morphogenesis of the reproductive whorl of acetabularia acetabulum[END_REF] . After initiation, the cap of this unicellular alga evolves from a bowl to a flat and eventually to a saddle shape, essentially for the same reason as our baromorph: biological growth in the cap is stronger in the circumferential direction than along the radius.

A first step in understanding and programming a baromorph is to predict the local deformation of airways in absence of external geometrical constraints, i.e. the target in-plane strains orthogonal ε t ⊥ and parallel ε t ∥ to the airway direction. The channel geometry (Fig. 2a) can be reduced to two relevant parameters in our minimal model: the relative channel height with respect to the total thickness of the sheet Ψ = h/(h + 2e) and the in-plane channel density Φ = d/(d + dw), where h, e, d, dw are geometrical parameters of the structure (Fig. 2b). Balancing stresses and making simplifying assumptions (detailed in Supplementary Text and Supplementary Figure 2), the target strains are then deduced following Hooke's law:

𝜖 ∥ ! = 𝑝 𝐸 ΨΦ 1 -ΨΦ (1 -2ν) = 0 𝜖 ! ! = 𝑝 𝐸 2 -Φ Φ Ψ 1 -Ψ - νΨΦ 1 -ΨΦ 1 + ν 1 -Φ Φ 1 -Ψ (1)
where E and ν are the Young modulus and Poisson ratio of the elastomer. We measured the target strains (Fig. 2b) by inflating a ring composed of only a few channels, therefore free of radial constraint. Within our crude hypotheses, the longitudinal strain is zero for ν = 1/2 as expected for an incompressible elastomer and we do observe that the longitudinal strain is much smaller than the transverse strain. We can account for the evolution of the parameters (Ψ, Φ) due to the deformation of the channels under pressure, as described in the Supplementary Information and input the actual values in Equation 1. The resulting non-linear prediction for the target strain is in very good agreement with experimental data, without any fitting parameter as illustrated in Fig. 2b (note that the calculations remain within the framework of Hookean linear elasticity: material stiffening at large strain is not considered in this simplified model). We now employ the concept of anisotropic target metric to program 3D shapes. As a first application, we target an axisymmetric shape, a cone. A configuration made of concentric and regularly spaced circular air channels is expected to induce a uniform radial target strain ε t r, while the azimuthal target strain remains null. Following elementary geometry (Fig. 2c), both target strains are satisfied if the airways keep their initial radii and the plate adopts a conical shape of slope α, with:

cosα = 1 1 + ε ! ! (2)
After a buckling transition, conical shapes with a tip regularised by the finite bending stiffness of the plate are observed for high-applied pressures (Fig. 2d, Supplementary Fig. 4). As in traditional buckling of slender structures, the finite bending stiffness of the plate indeed prevents out of plane buckling for small strains 24 (Supplementary Fig. 5). Both the buckling threshold and the evolution of the angle can be rationalised when inserting the incompatible target strain from Equation (1) within the Föppl-Von Karman equations for plates [START_REF] Efrati | Elastic theory of unconstrained non-euclidean plates[END_REF] (see Supplementary Text for a derivation and Supplementary Fig. 3).

In Fig. 2d, results from numerical integration of these equations for incompatible plates without any fitting parameter are plotted in solid lines and match the experimental angles. Equation (1) is not limited to uniform channels, but is also valid locally if the channels distribution follows a gradient. In the configuration illustrated in Fig. 3, the channel density decreases with the radius, which results in a spiky structure when inflated. Conversely, the channels tend to collapse upon suction leading to a negative value of ε t r. As a consequence, the structure adopts a saddle shape with negative Gaussian curvature, as theoretically predicted by Efrati et al. [START_REF] Efrati | Elastic theory of unconstrained non-euclidean plates[END_REF] . A continuous family of shapes is thus obtained when adjusting the pressure. Each shape corresponds to an equilibrium state and can be easily reached on demand.

Another key advantage of baromorphs relies on their fast pneumatic actuation [START_REF] Mosadegh | Pneumatic networks for soft robotics that actuate rapidly[END_REF] . In the example described in Fig. 3c, a reversible transformation of the plate could be achieved with a frequency of 3 Hz (Supplementary Video 1). The structures presented in this study have an initial diameter on the order of 10 cm and channels of a section close to 1 mm 2 . Baromorphs are however not limited to this size. For a given shape of the structure, the static mechanical response is independent of scale (Supplementary Figure 6 and Supplementary Video 2). Provided a sufficient power input, the actuation velocity is, in this case, limited by the natural frequency of the plate, ω ∼ h(E/ρ) 1/2 /R 2 , where ρ is the elastomer density, leading to a typical frequency of 10Hz. For small-scale structures, a poroelastic time scale could limit the actuation as in the context of water transport in plants [START_REF] Dumais | Vegetable dynamicks: The role of water in plant movements[END_REF] . Conversely, the finite compressibility of air may be a limiting issue for large baromorph structures. The actuation principle is moreover largely material-independent, so that any elastomer may be used, including relatively stiff, tough and wear resistant rubber, allowing meter-sized structures to resist their weight. Having captured the mechanical ingredients involved in the transformation of a baromorph, we now explore shape-programming issues. Elementary shapes can be programmed through simple computations. For instance, purely radial or azimuthal growth of uniform intensity leads to a cone or an e-cone [START_REF] Dervaux | Morphogenesis of growing soft tissues[END_REF] . This is confirmed by baromorphs with entirely azimuthal (Fig. 4a) or radial channels (Fig. 4c) at constant channel density respectively, displaying zero Gaussian curvature except at the apex (see details on scanning technique in Methods and Supplementary Figure 1).

A spherical cap with constant positive Gaussian curvature (see Fig. 4b and Supplementary Video 3) is programmed by azimuthal channels with a density according to equation ( 2) with a varying value of angle α = arcsin(r/R). As discussed in Supplementary information, less intuitive families of shapes can be simply obtained from the azimuthal growth of radial channels. Surfaces with constant negative Gaussian curvature may be programmed with radial channels with varying density (Fig. 4d, Supplementary Video 4). Fig. 4e shows how a flat annulus almost becomes a cylinder, by expansion of the inner circumference (see Supplementary Fig. 7a and Supplementary Video 5). Baromorphs are not limited to axisymmetric plates. For instance, a ribbon may spontaneously buckle into a helicoid as expected when a larger target strain is programmed along the edges as illustrated in Fig. 4f (see Supplementary Fig. 7b and Supplementary Video 6). Programming an arbitrary shape however involves a non-trivial inverse problem, as in other practical realisations of shape morphing. For instance, the direction of the anisotropic target growth (in nematic elastomers [START_REF] Aharoni | Geometry of thin nematic elastomer sheets[END_REF][START_REF] Aharoni | Universal inverse design of surfaces with thin nematic elastomer sheets[END_REF] ), or the isotropic growth factor (in swelling gels [START_REF] Kim | Designing responsive buckled surfaces by halftone gel lithography[END_REF] or auxetic materials 29 ), corresponding to a given target shape may only be computed through a numerical optimisation procedure with no formal guarantee for the existence of a solution. In the specific case of baromorphs, the possibility to select both the orientation and the density of the channels enables us to tune at each point both the direction and intensity of the local expansion. Taking advantage of this additional degree of freedom, we propose a straightforward and intuitive analytical recipe for programming a smooth surface that can be parametrised as z = h(x, y). In this procedure, each point of the baromorph is moving along the z-axis during activation, in a simple generalisation of the axisymmetric case (Figure 2c).

Contour lines (curves with equal h projected onto the reference plane z = 0) are conserved in the process, and no growth occurs along these curves, which we choose as centreline for the baromorph channels. The local slope angle α measured on the target surface perpendicularly to the contour lines, tan α = ∥∇h∥, determines through Eq.( 2) the lateral target strain

𝜖 ! ! = 1 + 𝜕ℎ 𝜕𝑥 ! + 𝜕ℎ 𝜕𝑦 ! -1 (3)
which in turn sets the width of the airways, i.e. Φ, for the desired pressure p using Eq.( 1).

This arrangement ensures that in the geometric limit, i.e. for thin enough plates, the baromorph will follow the target metrics (See Supplementary Text). Figure 4g shows the programming and the realisation of a face following the method described above. The results are qualitatively in good agreement with the target shape, except from the finest details, as the eyes, that are smoothed out by bending elasticity (Supplementary Video 7). Indeed, the size of the eyes is of the same order as the thickness of the sheet, and bending rigidity cannot be neglected at this scale. 32 . Basically, the 3D shape is inferred from the distortion of a pattern of stripes projected on the structure (Supplementary Fig. 1ab). The local height is thus deduced from the phase shift of the periodic pattern.

Although Fourier transform is generally used to extract the phase, the lack of periodic boundaries prevented us from using this method. We instead used a phase shifting profilometry technique, detailed by Van der Jeught et al. 33 . Four patterns are successively projected and recorded with the camera, each time shifted by π/2. The local phase φ(x, y) can thus be directly computed as:

φ x, y = arctan ( 𝐼 ! -𝐼 ! 𝐼 ! -𝐼 ! ) (4)
where I1-4 is the local fringe intensities at pixel (x,y) for the different phase-shifted patterns. The local phase is defined at each pixel modulo π. It is then unwrapped using a 2D unwrap Matlab code written by Muhammad F. Kasim (2D Weighted Phase Unwrapping) based on the work of Ghiglia and Romero 34 . The local surface height can be deduced from phase shift with respect to reference image ∆φ(x, y) using basic geometrical optics:

h x, y = ∆φL ∆φ -2πD/t (5)
where ∆φ = φ(x, y) -φ0(x, y), D is the distance between the video projector and camera, L is the height of both instruments with respect to the flat surface of reference and t is the spatial wave length of the fringed pattern (Supplementary Fig. 1c). The Gaussian curvature is finally deduced from a local quadratic fit of the surface (Supplementary Fig. 1d). 33. der Jeught, S. V., Soons, J. A. M. & Dirckx, J. J. J. Real-time microscopic phase-shifting profilometry.

Appl. Opt. 54, 4953-4959 (2015).

Ghiglia, D. C. & Romero, L. A. Robust two-dimensional weighted and unweighted phase

unwrapping that uses fast transforms and iterative methods. J. Opt. Soc. Am. A 11, 107-117 (1994). 14

3D scanning and computation of Gaussian curvature

As explained in the Methods section of the paper, the surface topography of inflated baromorph structures was measured with a 3D scanning system developed in the laboratory and based on the work of Cobelli et al. 37 . The 3D shape is extracted from the distorsion of a pattern of fringes projected onto the structure (Supplementary Fig. 1ab). The local height is deduced from the phase shift of the periodic pattern, which enables one to reconstruct the 3D shape of the structure and the field of Gaussian curvature (Supp. Fig. 1cd). 2 Theoretical framework Target strain. We aim at modelling the in-plane target strains induced by the pressurization of the baromorph. We thus need to determine the whole stress distribution in the material. We respectively define Ψ = h/(h + 2e) and Φ = d/(d + d w ) as the relative channel height with respect to the total sheet thickness and the in-plane channel density (Supplementary Fig. 2). A cross-section of the plate is sketched in Supplementary Fig. 2. The membrane region at the top and at the bottom of the plate is denoted with the subscript (1).

A simple force balance reads:

   σ (1)
⊥ = p Ψ 1 -Ψ σ (1) z ∼ 0 (1)
We denote the region of the walls separating the channels with the subscript (2). The force balance now leads to:

   σ (2) ⊥ = -p σ (2) z = p Φ 1 -Φ (2)
To derive the average stress σ mean in the direction e , we balance the force resulting from the pressure hd p in one channel with the stress integrated on the complementary area d w (h + 2e) + 2ed, which results into:

σ mean = p ΦΨ 1 -ΦΨ (3)
However, the distribution of σ in both regions remains undetermined. Nevertheless, the continuity of deformation along the direction of the channels imposes:

(1) = (2) (4)
Following Hooke's law, we obtain:

1 E (σ (1) -ν(σ (1)
⊥ + σ (1) z )) = 1 E (σ (2) -ν(σ (2)
⊥ + σ (2) z )) (5)
where E and ν are the Young modulus and the Poisson coefficient, respectively. The material properties of our silicone elastomer are E = 250 ± 15 kPa and ν = 1/2. We now assume that stresses along the channels in regions ( 1) and ( 2) are distributed according to their corresponding surface fraction, which leads to:

(1 -Ψ)σ (1) + (1 -Φ)Ψσ (2) = (1 -ΨΦ)σ mean (6)
We finally obtain a system of two equations and two unknowns that can be easily solved:

     σ (1) -σ (2) = ν(σ (1)
⊥ + σ (1) z -σ (2) ⊥ + σ (2) z ) (1 -Ψ)σ (1) + (1 -Φ)Ψσ (2) = (1 -ΨΦ)σ mean (7)
(2)

(3) Supplementary Figure 2. Schematic cross section of a baromorph plate.

In terms of strain in the parallel direction, we obtain:

     (1) - (2) = 0 (1 -Ψ) (1) + (1 -Φ)Ψ (2) = p E ΨΦ(1 -2ν) (8)
It is remarkable to notice that for incompressible elastomers, the Poisson ratio is equal to 1/2, which leads to (1) = (2) = 0. Knowing σ [START_REF] Ajaj | Morphing aircraft: The need for a new design philosophy[END_REF] and σ [START_REF] Cianchetti | Soft robotics technologies to address shortcomings in todays minimally invasive surgery: The stiff-flop approach[END_REF] , we can now determine the strain in the other directions. Following Hooke's law, we get for region (i):

                   (i) ⊥ = 1 E (σ (i) ⊥ -ν(σ (i) + σ (i) z )) (i) = 1 E (σ (i) -ν(σ (i) ⊥ + σ (i) z )) = 0 (i) z = 1 E (σ (i) z -ν(σ (i) ⊥ + σ (i) )) (9)
Shear is finally not accounted for in our simplified model. Assuming that the strain in the upper part of the walls (region (3)) is the same as in the channel part (region (1)) is not reasonable. We thus propose to make the following assumption:

(3)

⊥ ∼ Φ (1) ⊥ (10)
Indeed, in the two extreme cases, when Φ tends to 0,

⊥ also approaches 0 and when Φ tends to 1,

⊥ tends to

(1) ⊥ . The macroscopic homogenized radial strain is thus:

⊥ = Φ (1) ⊥ + (1 -Φ) (3) ⊥ (11)
The homogenized strains parallel and perpendicular to the local channel direction thus read:

           t = p E ΨΦ (1 -ΨΦ) (1 -2ν) = 0 t ⊥ = p E Φ(2 -Φ) Ψ 1 -Ψ - νΨΦ 1 -ΨΦ 1 + ν 1 -Φ Φ(1 -Ψ) -1 (12)
Note that both Ψ and Φ evolve with the pressure:

             Φ = d(1 + (1)
⊥ ) d(1 + (1) ⊥ ) + d w (1 + ( (2) ⊥ + (3) ⊥ )/2) Ψ = h(1 + (2)
z ) h(1 + (2) z ) + 2e(1 + (1) z ) (13)
This dependence of the geometry with the pressure constitutes a key feature in inflation: as the pressure increases, the cross-section of the plate resisting the load is reduced, which results in concentrated stresses. This behaviour explains the non-linearity of the amplitude of the deformation with the pressure. We limit our simplified model to linear elasticity and do not account for the stiffening of actual elastomers. Such stiffening would tend to regularise the divergence of the strain at large pressures.

Bending and elongation stiffness of inflated baromorphs. Estimating the bending and stretching stiffness of an inflated baromorph structure is critical to compute its shape. Since bending a slender beam conserves the volume, this deformation does not involve any work of the inner fluid. As a consequence, the inner pressure only prevents failure of the thin membrane and should not affect the bending rigidity. However, inflating the structure tends to thicken it, which slightly increases the bending stiffness. We measured the shape of baromorph beams sagging under their own weight for different pressures (Supplementary Fig. 3a andb). The dependence on the pressure remains modest, as expected. Similarly, a stretching deformation conserves the volume in the solid (ν = 1/2) as well as in the inner the fluid. As a result, the stretching stiffness should not change when the structure is stretched. A minor deviation from the ideal behaviour is however observed in Supplementary Fig. 3c due to material stiffening under large strains.

Axisymmetric plate equations. Consider a flat circular baromorph, embedded with circular concentric channels of constant relative height Ψ. The channel density Φ(r) may vary along the radial direction. The elastic energy stored in the plate corresponds to the sum of the stretching and bending energies:

U = U stretch + U bend (14)
U bend = 1 2 D(κ 2 1 + 2νκ 1 κ 2 + κ 2 2 )dS ( 16
)
where D is the bending stiffness of the plate (assumed here isotropic for simplicity) and (κ 1 , κ 2 ) are the principal curvatures of the plate. In the weak non-linear regime (within the limit of small slopes), the strain can be expressed at the second order in w as:

       r = u + 1 2 w 2 θ = u r (17)
where u and w correspond to the in-plane radial displacement and to the out-of-plane deflection, respectively. Using Hooke's law, we derive the stress distribution:

         σ r = E(1 -ΦΨ) 1 -ν 2 ( r -t r + ν( θ -t θ )) σ θ = E(1 -ΦΨ) 1 -ν 2 ( θ -t θ + ν( r -t r )) (18)
correspond to:

                             u(0) = 0 w (0) = 0 u (R) + 1 2 w (R) 2 -t r (R) + ν u(R) R -t θ (R) = 0 w (R) + ν w (R) R = 0 (23)
This system of equations can be solved using the boundary value problem function bvp4c from Matlab. Results of the integration of these equations for uniform target strain configurations corresponding to various channel densities Φ and relative channel heights Ψ are presented in Supplementary Fig. 4 and in the Fig. 2 from the main body of the article. These predictions are in good agreement with our experiments without any fitting parameter.

Scaling law for buckling threshold. The buckling threshold leading to out-of-plane deformations can be roughly predicted by comparing stretching and bending energies in the flat and bent plate, respectively. We expect the transition to occur when bending gets energetically more favourable than in-plane strain.

In terms of scaling, the stretching energy U stretch is proportional to:

U stretch ∼ E 2 r HR 2 (1 -ΦΨ) (24)
where H = h + 2e is the total thickness of the plate. Indeed if the plate remains flat, the azimuthal strain has to be of the same order of magnitude than the target radial strain (homothetic growth). Due to the presence of channels, the effective Young modulus in the azimuthal direction is now E(1 -ΦΨ).

We expect the bending energy per unit length U bend to scale as:

U bend ∼ EI R 2 κ 2 ( 25
)
where EI is the effective bending rigidity of the homogenised plate and κ is the typical induced curvature. Considering the presence of the channels, we expect the effective bending rigidity in the azimuthal direction to scale as

I ∼ H 3 (1 -ΦΨ 3 ) (26)
At the transition, radial strain and curvature are simply related by:

r ∼ κ 2 R 2 (27)
ratio of 1:10. From a practical point of view, smaller baromorphs could be made using soft lithography techniques, down to the millimeter scale and beyond.

Shape Programming and inverse problem

Geometric procedure for the inverse problem. In this section, we propose a simple and intuitive strategy to program any 3D surface on a baromorph structure in the geometric limit, i.e., when the bending energy can be neglected with respect to the stretching energy. This strategy is a generalisation of the programming of a conical shape following Eq. 2 from the main text. Consider a given smooth surface parametrised by z = h(x, y), that we want to reproduce, starting from a flat sheet. The first fundamental form reads:

ds 2 = (1 + h 2 x )dx 2 + 2h x h y dxdy + (1 + h 2 y )dy 2 , (31)
where h x and h y respectively correspond to ∂h/∂x and ∂h/∂y. This first fundamental form can be written in the matrix form:

a = 1 + h 2 x h x h y h x h y 1 + h 2 y (32)
Diagonalising this matrix leads to the eigenvalues λ 1 , λ 2 and corresponding eigenvectors u, v:

λ 1 = 1 u = 1 h 2 x + h 2 y -h y h x λ 2 = 1 + h 2 x + h 2 y v = 1 h 2 x + h 2 y h x h y (33)
Interestingly, the fact that the first eigenvalue is equal to unity implies that there is no extension along isodepth lines with respect to a reference flat sheet. A natural idea is thus to draw channels along the contour lines projected on the reference plane, since no expansion parallel to the airways is predicted by our model. The second step consists in matching the target orthogonal strain to the metrics in the direction of the gradient:

t ⊥ = λ 2 -1 (34)
According to our model, t ⊥ is a function of Ψ, Φ and p/E. Since airways are interconnected, p/E is uniform through the structure. In our manufacturing process, it is practically easier to tune the channel density Φ (i.e. the local channel width d) than the relative channel height Ψ. Equations ( 12) and ( 13) are thus solved using Matlab to find the relevant channel width to match the metrics along the gradient for fixed values of p/E and Ψ. Following this concept, a simple code can automatically generate the airways path for any target 3D shape of the form z = h(x, y). Nevertheless, the lateral expansion of the channels is limited by material properties ( t ⊥ max ∼ 2). As a consequence, only surfaces with slopes smaller than typically 45 • can be reproduced with this procedure.

Axisymmetric shapes In the case of an axisymmetric shape set by z = h(r), this procedure leads to the target strains:

   t θ (r) = 0 t r (r) = 1 + h 2 r (r) -1 (35)
For instance, in order to get a portion of a sphere of radius R as illustrated in Fig. 4b, the target radial strain should follow:

t r (r) = 1 1 - r R 2 -1 (36)
Programming a shape with constant negative Gaussian curvature. Although the previous procedure could, in principle, be used to program shapes of negative Gaussian curvature such as saddles, edge effects tend to distort the resulting structures. We propose a different strategy to produce saddle shapes based on azimuthal expansion of circular plates. The first fundamental form for a surface of constant negative Gaussian curvature K reads in cylindrical coordinates 33 , ds 2 = dr 2 -K -1 sinh(r √ -K))dθ 2 . Starting from a flat plate of first fundamental form ds 2 = dr 2 + r 2 dθ 2 , a straightforward solution to transform a circular plate in a saddle consists in keeping the distances in the radial direction unchanged and adapting the azimuthal expansion to the target metrics, t θ = -r 2 /6K + o(r 4 /K 2 ). In our baromorphs, this strategy involves purely radial channels. For the sake of simplicity, we approximate the target azimuthal expansion by a constant piecewise function and compute the corresponding channel density required to achieve the target at one given pressure. Despite such approximations, the actual shape obtained is very close to the programmed saddle shape (See Fig. 4d from main text and Supplementary Movie 4), mainly because elasticity tends to smooth the programmed deformations. Particular attention should however be paid to the boundary effects in the plate: the additional wall necessarily present at the outer edge of the baromorph in order to seal the airways induces an additional resistance to expansion. It is thus necessary to design this wall as thin as possible in order to minimise its influence.

Other examples of lateral expansion: truncated cones and helicoids. Using the lateral expansion of radial channels is not limited to programming negative Gaussian curvature. We employed the same strategy to program truncated cones. Consider a circular plate with a central hole and radial channels (Fig. 4e from the main text and Supplementary movie 5). Applying an azimuthal strain while conserving radial distances also results in a new shape. In the geometric limit when bending stiffness can be neglected, we obtain the local angle from elementary geometry (Supplementary Fig. 7a):

cos α = 1 + ∂ r θ ∂r (37)

Figure2:

  Figure2: Characterisation of baromorph expansion and deformation. a, Schematic vertical cut of the baromorph structure. The geometry of the channels can be reduced to two non-dimensional parameters: the relative height Ψ = h/(h + 2e) and the channel density Φ = d/(d + dw), where d is the width of the channels, dw the width of the walls, h the height of the channels and e the thickness of the covering membrane. b, Dependence of the targeted parallel and longitudinal strain on the pressure for different values of Φ with Ψ = 0.69 ± 0.05 and for different values of Ψ with Φ = 0.5 ± 0.02. Solid lines correspond to the model without any fitting parameter (in our simplified model ε∥ vanishes). c, Baromorph programmed to be a cone when pressurised. The slope angle is noted α. d, Experimental and theoretical (solid lines, no fitting parameter) evolution of α as a function of the applied pressure for baromorphs of different parameters: Red diamonds (Ψ = 0.78±0.05, Φ = 0.5, R = 50mm, H = 3.8±0.2mm); Blue triangles (Ψ=0.74,Φ=0.5,R=40mm,H=5.4mm); Purple flags (Ψ=0.68,Φ=0.2,R=50mm,H =6mm); Green squares (Ψ=0.6, Φ=0.5, R=40mm, H =6.7mm).

Figure 3 :

 3 Figure 3: Equilibrium states and dynamical response. a, Continuous family of equilibrium states obtained for a baromorph at different pressures. b, Corresponding network of channels embedded in the plate. Channels are more concentrated in the central region of the disk, which leads to a spiky structure once inflated. c, Dynamical response: actuation at approximately 3Hz of The pneumatic system (Supplementary Video 6).

Figure 4 :

 4 Figure 4: Collection of 3D shapes obtained by the buckling of baromorphs under pressure. Grey background paths represent the underlying airway network. Gaussian curvature K is plotted in insets. Circular concentric channels: cone (a) and portion of a sphere (b). Radial channels: econe (c) and saddle (d). e, Truncated cone of large angle. f, Helicoid . g, Shape programming of a face. From left to right: the target shape, the corresponding contour lines, the network of channels computed to give rise to the target metrics and two pictures of the deformed baromorph, made of Dragonskin 10 Medium from Smooth-On. Videos of the transformation of most structures are available as Supplementary Information (Videos 3-7).

  materials. ACM Trans. Graph. 35,1-11 (2016). 30. van Rees, W. M., Vouga, E. & Mahadevan, L. Growth patterns for shape-shifting elastic bilayers.Proceedings of theNational Academy of Sciences (2017). Methods Making baromorph plates. Baromorph plates are made of polyvinyl siloxane (Elite Double 8 from Zhermack or Dragon Skin 10 Medium from Smooth-On) by mixing equal quantities of "catalyst" and "base" liquids. The mixture is then poured on a 3D printed mould designed using OpenScad software and printed with Form2 printer from Formlabs. If necessary, the whole setup is placed in a vacuum chamber to efficiently remove trapped air bubbles. Curing takes respectively 20 minutes and 3 hours. At the same time, a sheet of thickness e of the same elastomer is spread on a flat surface and cured. The structure removed from the mould is finally closed by "gluing" the flat sheet on top of the moulded sheet using a thin layer of uncured mixture of the same material. Experimental strain data. Azimuthal and radial strains are measured experimentally using DIC (Digital Image Correlation) program CorreliQ4 on Matlab 31 . A random pattern of dots is generated on the surface by spraying paint. Top view pictures of the baromorph structure are taken at different pressures and the program tracks in-plane strain with respect to a chosen reference image. Mean strains perpendicular and parallel to the channels are then extracted. 3D scanning and computation of Gaussian curvature. The surface topography of inflated baromorph structures was measured with a 3D scanning system developed in the laboratory and based on the work of Cobelli et al.

  31. Hild, F. & Roux, S. Digital image correlation: from displacement measurement to identifica-tion of elastic properties-a review. Strain 42, 69-80 (2006). 32. Cobelli, P. J., Maurel, A., Pagneux, V. & Petitjeans, P. Global measurement of water waves by fourier transform profilometry. Experiments in Fluids 46, 1037 (2009).

Supplementary Figure 1 .

 1 3D scanning technique. (see Methods) a. Picture of one of the four reference patterns projected on a white planar surface. b. Distorted pattern on the 3D surface of the baromorph. c. Reconstruction of the 3D surface with our program. d. Gaussian curvature computed with a local quadratic fit of the surface.

Supplementary Figure 3 .

 3 Effect of the pressure on both bending and stretching stiffness of a baromorph cantilever beam for a fixed geometry (Φ = 0.5, Ψ = 0.69, H = 4.4 mm, w = 30 mm). a. Picture of a baromorph cantilever bending under its own weight. b. Shape of a sagging beam for different clamping lengths and applied pressures. Experimental shapes (continuous lines on the left side) are compared with theoretical predictions (dashed lines on the right side). c. Engineering stress as a function of the strain for different applied pressures. The theoretical prediction is plotted as a dashed line.withU stretch = 1 2 σ : ( -t )dS(15)

Acknowledgments This work has received the support of Institut Pierre-Gilles de Gennes (Équipement d'excellence, "investissements d'avenir", ANR-10-EQPX-34), and from ANR SMART.

We thank Cyprien Blanquart for developing the 3D scanning technique and Mathias Lebihain from the Institut Jean Le Rond d'Alembert for the technical support on 3D printing the moulds.

Data availability

The authors declare that the data supporting the findings of this study are available within the paper and its supplementary information files and from the corresponding author upon reasonable request.

Correspondence Benoit Roman (email: benoit.roman@espci.fr).

structures reversibly with fast actuation. Numerous extensions of this architectured active material are possible for practical applications: cuts 29 can be made in the plate to release some bending constraints and improve the shape programming (Supplementary Figure 8 and Supplementary Video 8); the target curvature tensor can also be programmed [START_REF] Efrati | Elastic theory of unconstrained non-euclidean plates[END_REF]30 using a bilayer composed of two independent networks of airways. In such a configuration, the homogenised sheet is free of constraint and the actuation does not involve any threshold.

Snapping instabilities can also be triggered with out of phase actuation of the layers, as shown in Supplementary Video 9. More generally, several intertwined networks may be embedded in one plate to program various shapes on demand. Rather than simple channels, controlled cavities with different sizes and shapes may be embedded in the plate to impose all three components of the target growth tensor, in contrast with current morphing techniques [START_REF] Klein | Shaping of elastic sheets by prescription of non-euclidean metrics[END_REF][START_REF] Kim | Designing responsive buckled surfaces by halftone gel lithography[END_REF][START_REF] Sydney Gladman | Biomimetic 4d printing[END_REF][START_REF] Aharoni | Universal inverse design of surfaces with thin nematic elastomer sheets[END_REF] (see Supplementary Figure 9 and Supplementary Video 10). Altogether, our study opens pathways in the numerous areas where shape morphing is believed to find new innovative applications, such as minimally invasive surgery, bio-printing, flow optimisation, architecture or more generally smart materials.

Author contribution

Competing Interests

The authors declare that they have no competing financial interests.

Supplementary Information

Bio-inspired pneumatic shape morphing elastomers Emmanuel Siéfert 1 , Etienne Reyssat 1 , José Bico 1 , Benoit Roman where, E is the Young modulus of the elastomer, ν the Poisson ratio of the material, t r and t θ are respectively the radial and azimuthal target strains computed in the previous section.

We have assumed that the effective stretching stiffness of the plate is isotropic, which is not strictly true. Indeed, we expect the effective Young modulus to be E(1 -ΨΦ) in the azimuthal direction, where (1 -ΨΦ) corresponds to the proportion of material surface in a transverse cut. In the radial direction, we obtain for the effective modulus

, by summing the compliance of the roof (region ( 1)) and the wall (region ( 2) and ( 3)). For typical values of Ψ = 0.5 and Φ = 0.66, we estimate a difference of approximately 30% in stretching moduli.

For the sake of simplicity, we thus use the value of the azimuths modulus for the other directions as well. The elastic stretching energy stored in the plate finally reads:

We now focus on the bending energy. For an axisymmetric surface parametrised by z = w(r), the two principal curvatures are determined by:

At the second order in w , the bending energy in the plate is given by:

The total energy can be minimized with traditional variational methods, which leads to:

The relevant boundary conditions, i.e. no torque and no forces at the boundary of the plate, The buckling transition should correspond to U bend ∼ U stretch , which leads for the critical strain:

We remark that we obtain the typical critical buckling strain (H/R) 2 corrected by the geometry of the plate. Similarly to I beams, our plates are indeed relatively stiffer in bending than in compression in comparison with full plates, since material is concentrated far from the neutral plane. As shown in the body of the article, the strain dependence on pressure reads:

which finally leads to the critical buckling pressure:

Supplementary Figure 5 shows how the buckling threshold collapses for various plates on a single point when internal pressure is normalised by the critical pressure presented in Eq. 30.

Scalability

From the mechanical point of view, when neglecting gravity forces, our system is scale free. As shown in the previous sections, stresses and deformations in the plate only depend on geometric parameters, Φ, Ψ -ratios between lengths-and a normalised pressure p/E. In order to highlight this property, we show in Supplementary Fig. 6a and Supplementary Movie 2 three baromorphs with the same design at three different scales allowed by the precision of the 3D printer, connected to only one pump. As the pressure is increased, all structures adopt the same shape, as predicted by our model.

Nevertheless, gravity forces do not have the same impact on all three objects. Indeed, the normalised deflection δ/R of a clamped baromorph scales as δ/R ∼ ρgR/(ES 2 ) in the small amplitude limit, where R is the radius of the baromorph and S = h/R the slenderness ratio, kept constant. The larger the object is, the less it can sustain its own weight, as highlighted in Supplementary Fig. 6b. The maximum size of a baromorph which would sustain its own weight is given by a balance between the bending energy in the structure and the moment due to the gravity forces: R max ∼ ES 2 /(ρg). This maximum size would be of the order of one meter for baromorphs made of elastomer of Young's Modulus of a few MPa and with a slenderness a b Supplementary Figure 7. a. Transformation of flat disk with a central hole based on azimuthal expansion (see also Fig. 4e and Supplementary movie 5). b. Twisting of a long rectangle into an helicoid by longitudinal extension along the edges (see also Fig. 4f and Supplementary movie 6).

The predicted shape is thus a truncated cone of angle α if the azimutal strain is of the form θ = cos α -1 + A/r. In practice, we approximate this form by a piece-wise function (fixed number of radial channels of uniform width in the inner part of the plate followed by a annular region without channels). The resulting shapes are in qualitative agreement with the prediction. We also developed long rectangular plates with channels following a fish-bone design (Fig. 4f and Supplementary movie 6). Applying pressure thus tends to expand the edges of the rectangle, leading to a helical shape. If the width b and the length of the middle line of the rectangle are maintained constant, imposing a pitch λ results in a longitudinal strain (Supplementary Fig. 7b):

The pitch obtained experimentally is in qualitative agreement with this relation.

A different shape-morphing strategy : baromorphs with cavities

Another possibility to achieve shape-morphing relies on non-uniform but isotropic growth: a hexagonal lattice of cylindrical bubbles interconnected by small channels is embedded in the elastomer plate. Similarly to Kim et al. halftone swelling technique 8 , we take advantage of different local sizes of the cavities to induce a controlled isotropic expansion upon pressure: the bigger the cavities are, the larger the local "growth" is. In Supplementary Fig. 6 Supplementary movies Supplementary Movie 1 Dynamic behaviour of a baromorph under inflation and deflation.

Supplementary Movie 2

Parallel actuation of three baromorphs with the same design, at different scales.

Supplementary Movie 3

Bowl-shaped baromorph fitting a spherical cap.

Supplementary Movie 4

Saddle-shaped baromorph.

Supplementary Movie 5

Large angle cone with a centred hole.

Supplementary Movie 6

Helicoid obtained from a baromorph ribbon with a programmed elongation along the edges.

Supplementary Movie 7

Face programmed with the geometric inverse recipe.

Supplementary Movie 8

Mask with a cut below the nose.

Supplementary Movie 9

Actuation of a double layer baromorph. Stacking two structures provides some control on the curvature of the structure. Snapping instabilities can be observed when the applied pressures variations are out of phase.

Supplementary Movie 10

Actuation of an isotropic baromorph with larger cylindrical cavities in the centre of the plate than at the periphery.


Jérémy Cure

Kévin Cocq

Adnen Mlayah

Teresa Hungría

Pierre Alphonse

Yves J Chabal

Valérie Maraval

Rémi Chauvin

Alain Estève

Carole Rossi

Teresa Hungria

Remi Chauvin

A Triptych Photocatalyst Based on the Co-Integration of Ag Nanoparticles and Carbo-Benzene Dye into a TiO 2 Thin Film

Keywords: carbo-benzene dye, silver nanoparticle, titanium dioxide film, triptych system, photocatalytic hydrogen production under pressure, water splitting

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

Introduction

Interest in hydrogen energy is greater than ever, notably because of the strong expectations for the development of new means of transport based on the improvement of fuel cell to cars, ships and even trains [START_REF]10th Stakeholder Forum -Fuel Cell and Hydrogen Technology: Europe's Journey to a Greener World[END_REF] to counterbalance the depletion of fossil fuels and global warming [START_REF] Dutta | A review on production, storage of hydrogen and its utilization as an energy resource[END_REF][START_REF] Ademe | the Role of Hydrogen in the Energy Transition[END_REF][START_REF] Pinaud | Technical and economic feasibility of centralized facilities for solar hydrogen production via photocatalysis and photoelectrochemistry[END_REF].

Alternately to water electrolysis and PhotoElectroCatalytic Water Splitting (PEC-WS) [START_REF] Abdi | Efficient solar water splitting by enhanced charge separation in a bismuth vanadate-silicon tandem photoelectrode[END_REF][START_REF] Luo | Bipolar membrane-assisted solar water splitting in optimal pH[END_REF][START_REF] Ager | Experimental demonstrations of spontaneous, solar-driven photoelectrochemical water splitting[END_REF][START_REF] Prevot | Enhancing the Performance of a Robust Sol-Gel-Processed p-Type Delafossite CuFeO2 Photocathode for Solar Water Reduction[END_REF][START_REF] Fujishima | Electrochemical Photolysis of Water at a Semiconductor Electrode[END_REF], achieving a pure PhotoCatalytic (PC) WS process from water and sunlight offers a promising approach for producing a sustainable costless and carbon free economy [START_REF] Hisatomi | Recent advances in semiconductors for photocatalytic and photoelectrochemical water splitting[END_REF][START_REF] Wang | Recent developments in heterogeneous photocatalysts for solar-driven overall water-splitting[END_REF][START_REF] Maeda | Photocatalyst releasing hydrogen from water[END_REF][START_REF] Melvin | M-Au/TiO2 (M = Ag, Pd, and Pt) nanophotocatalyst for overall solar water splitting: role of interfaces[END_REF]. The PC-WS concept is simple: sun irradiates a powdered photocatalyst dispersed in an aqueous solution and the hydrogen is readily produced [START_REF] Wang | Relation between the photocatalytic and photoelectrocatalytic performance for the particulate semiconductor-based photoconversion systems with surface phase junction structure[END_REF]. Rigorously, there is no need of a counter electrode, neither of a supporting electrolyte nor a pH-buffer: the photon energy is converted into electron-hole pairs and then into chemical energy [START_REF] Goto | A Particulate Photocatalyst Water-Splitting panel for Large-Scale Solar Hydrogen Generation[END_REF].

The PC-WS concept has been validated with numerous semiconductor materials [START_REF] Kudo | Heterogeneous photocatalyst materials for water splitting[END_REF][START_REF] Osterloh | Inorganic Materials as Catalysts for Photochemical Splitting of Water[END_REF][START_REF] Chen | Semiconductor-based Photocatalytic Hydrogen Generation[END_REF], and the majority of reports was based on Earth-abundant and stable semiconductors such as titanium dioxide (TiO 2 ) used for its moderate redox potential vs SHE (e.g. E°1 /2 (TiO 2 /Ti 2+ )= -0.50 V), large bandgap (Eg ~3.2 eV) and effective catalytic properties. However, the PC efficiency of semiconductors remains limited by several factors: (i) inability to harvest the visible light due to large band gap, only allowing the use of about 4% of the total solar radiation while the visible light contributes to ca 50% of the solar irradiance, (ii) fast recombination of photo-generated electron-hole pairs before they can migrate to the surface [START_REF] Tian | Mechanisms and applications of plasmon-induced charge separation at TiO2 films loaded with gold nanoparticles[END_REF][START_REF] Takai | Capture, Store, and Discharge. Shuttling Photogenerated Electrons across TiO2-Silver Interface[END_REF]. Therefore, various strategies have been explored to improve the WS efficiency under solar illumination. The band gap can be narrowed and light absorption extended to longer wavelengths by doping with non-metal atoms [START_REF] Khan | Efficient photochemical water splitting by a chemically modified n-TiO2 2[END_REF][START_REF] Varley | Mechanism of Visible-Light Photocatalysis in Nitrogen-Doped TiO2[END_REF], with organic dyes [START_REF] Rojas | All Solution-Processed, Hybrid Organic-Inorganic Photocathode for Hydrogen Evolution[END_REF] such as ruthenium complexes [START_REF] Reisner | Visible Light-Driven H2 Production by Hydrogenases Atteched to Dye-Sensitized TiO2 Nanoparticles[END_REF], porphyrins [START_REF] Watanabe | Visible Light-Driven Dye-Sensitized Photocatalytic Hydrogen Production by Porphyrin and its Cyclic Dimer and Trimer: Effect of Multi-Pyridyl-Anchoring groups on Photocatalytic Activity and Stability[END_REF], or graphene oxide [START_REF] Zhang | A green and facile synthesis of TiO2/graphene nanocomposites and their photocatalytic activity for hydrogen evolution[END_REF][START_REF] Huang | enhanced Photocatalytic Activity of Chemically Bonded TiO2/Graphene Composites Based on the Effective Interfacial Charge Transfer through the C-Ti Bond[END_REF][START_REF] Putri | Graphene oxide: Exploiting its unique properties toward visible-light-driven photocatalysis[END_REF][START_REF] Min | Dye-cosensitized graphene/Pt photocatalyst for high efficient visible light hydrogen evolution[END_REF]. Another strategy to improve the PC efficiency relies on the use of hybrid metal nanoparticles/semiconductor nanostructures [START_REF] Liu | Plasmonic Ag deposited TiO2 nano-sheet film for enhanced photocatalytic hydrogen production by water splitting[END_REF][START_REF] Yin | Fabrication of plasmonic Au/TiO2 nanotube arrays with enhanced photoelectrocatalytic activities[END_REF][START_REF] Liu | Design of cocatalyst loading position for photocatalytic water splitting into hydrogen in electrolyte solutions[END_REF][START_REF] Bai | Boosting Photocatalytic water Splitting: Interfacial Charge Polarization in Atomically Controlled Core-Shell Cocatalysts[END_REF][START_REF] Liu | Enhancement of photochemical hydrogen evolution over Pt-loaded hierarchical titania photonic crystal[END_REF][START_REF] Fraters | How Pt nanoparticles affect TiO2-induced gas-phase photocatalytic oxidation reactions[END_REF][START_REF] Zhang | Plasmonic Gold Nanocrystals Coupled with Photonic Crystal Seamlessly on TiO2 Nanotube Photoelectrodes for Efficient Visible Light Photoelectrochemical Water Splitting[END_REF][START_REF] Pu | Au Nanostructure-Decorated TiO2 nanowires Exhibiting Photoactivity Across Entire UVvisible Region for Photoelectrochemical Water Splitting[END_REF][START_REF] Gao | Plasmon enhancement on photocatalytic hydrogen production over the Z-scheme photosynthetic heterojunction system[END_REF][START_REF] Ge | In situ plasmonic Ag nanoparticle anchored TiO2 nanotube arrays as visible-light-driven photocatalysts for enhanced water splitting[END_REF][START_REF] Sreedhar | Ag nanoparticles decorated ionbeam-assisted TiO2 thin films for tuning the water splitting activity from UV to visible light harvesting[END_REF][START_REF] Chaudhary | Multifunctional plasmonic Ag-hematite nano-dendrite electrocatalysts for methanol assisted water splitting: Synergism between silver nanoparticles and hematite dendrites[END_REF][START_REF] Arunachalam | Activation effect of silver nanoparticles on the photoelectrochemical performance of mesoporous TiO2 nanospheres photoanodes for water oxidation reaction[END_REF][START_REF] Amin | In situ aqueous synthesis of silver nanoparticles supported on titanium as active electrocatalyst for the hydrogen evolution reaction[END_REF][START_REF] Amin | Cathodic activation of titanium-supported gold nanoparticles: an efficient and stable electrocatalyst for the hydrogen evolution reaction[END_REF], in order to reduce the electron-hole recombination and/or to harvest the visible light owing to plasmonic enhanced optical absorption [START_REF] Min | Dye-cosensitized graphene/Pt photocatalyst for high efficient visible light hydrogen evolution[END_REF][START_REF] Liu | Plasmonic Ag deposited TiO2 nano-sheet film for enhanced photocatalytic hydrogen production by water splitting[END_REF][START_REF] Zhou | Quantifying hot carrier and thermal contributions in plasmonic photocatalysis[END_REF]. Inorganic semiconductors based on transition-metal oxides, oxysulfides or oxynitrides with lower bandgap as compared to TiO 2 can also be used to increase the absorption of visible-light [START_REF] Hisatomi | Recent advances in semiconductors for photocatalytic and photoelectrochemical water splitting[END_REF][START_REF] Wang | Recent developments in heterogeneous photocatalysts for solar-driven overall water-splitting[END_REF][START_REF] Maeda | Photocatalyst releasing hydrogen from water[END_REF]. Finally, the formation of heterojunctions with other semiconductors (Bi 2 WO 6 , m-BiVO 4 , TaON, Bi 2 O 3 , Ag 2 O, Ag 3 VO 4 …) [START_REF] Wang | Synthesis of g-C3N4/TiO2 with enhanced photocatalytic activity for H-2 evolution by a simple method[END_REF][START_REF] Ong | Graphitic Carbon Nitride (g-C3N4)-Based Photocatalysts for Artificial Photosynthesis and Environmental Remediation: Are We a step Closer To Achieving Sustainability?[END_REF][START_REF] Chai | graphitic carbon nitride (g-C3N4)-Pt-TiO2 nanocomposite as an efficient photocatalyst for hydrogen production under visible light irradiation[END_REF][START_REF] Yan | TiO2-g-C3N4 composite materials for photocatalytic H2 evolution under visible light irradiation[END_REF][START_REF] Luo | Mechanochemically synthesized m-BiVO4 nanoparticles for visible light photocatalysis[END_REF][START_REF] Zhang | Mechanochemically synthesized CuO/m-BiVO4 composite with enhanced photoelectrochemical and photocatalytic properties[END_REF] has been proposed to induce beneficial charge separation and electronic properties in the stack.

Although significant advances have been achieved in the design of efficient materials for enhanced photocatalysis [START_REF] Marchal | Au/TiO2-gC3N4 Nanocomposites for Enhanced Photocatalytic H2 Production from Water under Visible Light Irradiation with Very Low Quantities of Sacrificial Agents[END_REF], the reported efficiencies are still far from those required for commercialization of operating devices. Moreover, powdered photocatalysts, which have attracted a large attention in the past years and constitute the subject of most of the published works on PC-WS, suffer from the possible dispersion of particles into the environment and are not advantageous for large-scale production.

Only a few concepts for scaling-up these technologies have been reported [START_REF] Turan | Upscalling of integrated photoelectrochemical water-splitting devices to large areas[END_REF][START_REF] Schröder | Hydrogen Evolution Reaction in a Large-Scale Reactor using a Carbon Nitride Photocatalyst under Natural Sunlight Irradiation[END_REF]. One remarkable achievement in 2018 is the 1 m² flat panel reactor composed of Al-doped SrTiO 3 powder photocatalyst, achieving a solar-to-hydrogen energy conversion efficiency of 0.4% by WS [START_REF] Goto | A Particulate Photocatalyst Water-Splitting panel for Large-Scale Solar Hydrogen Generation[END_REF], which is still too low for large-scale application of solar WS.

One challenge of solar to H 2 technology is the design of an efficient, long-lasting, scalable and low-cost photocatalyst, well-optimized for sunlight absorption to drive catalytic hydrogen evolution, which is the scope of the present study. The originality of the presented work is to assemble a triptych material (sparse examples in the literature) and demonstrate synergistic effects between its components. This is performed within a scalable, durable and low cost (mass fabrication compatible) technological pathway, based on a planar structure avoiding potential dissemination of nanoparticles in the environment. The hydrogen production is measured, for the first time, under slightly over-pressurized conditions, which we believe are closer to those of the device operation in envisaged applications. Results are compared to values of the literature, all recorded at the atmospheric pressure, pointing to the need of further investigation of this issue.

In more detail, we combine in an optimized assembly, a light harversting semiconductor thin film (TiO 2 ) with efficient and low cost noble metal (Ag) and a carbo-benzene macromolecule to prepare a hybrid nanomaterial for H 2 generation by PC-WS. For the first time, a carbo-benzene macromolecule functionalized with two NH 2 -primary amino groups (para-di(anilinylethynyl)tetraphenyl-carbo-benzene), hereafter denoted as Cbz is explored as photosensitizer. Carbobenzenes exhibit unique properties related to the "carbo-aromatic" character of their C 18 macrocyclic core: high -electron richness (~1.7 -e/C), persistent symmetry (quasi-D 6h ), emptiness (monocycle of ca 8 Å diameter) and associated residual flexibility [START_REF] Cocq | Carbo-aromaticity and novel carbo-aromatic compounds[END_REF]. The physicochemical properties of the di(anilin-4-ylethynyl) derivative Cbz selected for the present study are particularly adapted to its use as a redox-active photosensitizer [START_REF] Cocq | Synthesis of Functional Carbo-benzenes with Functional Properties: The C2 Tether Key[END_REF]: a structural propensity for high single molecule conductance ( ~100 nS) [START_REF] Li | Towards graphyne molecular electronics[END_REF] and a high molar extinction coefficient ( = 131 000 L mol -1 cm -1 ) [START_REF] Cocq | Carbo-aromaticity and novel carbo-aromatic compounds[END_REF][START_REF] Cocq | Synthesis of Functional Carbo-benzenes with Functional Properties: The C2 Tether Key[END_REF] at  max = 493 nm complementary with the frequency of Ag NPs surface plasmon resonance (SPR) [START_REF] Alenzi | Photoelectrochemical hydrogen production from water/methanol decomposition using Ag/TiO2 nanocomposite thin films[END_REF]. It is worth to notice here that the Cbz selected as photosensitizer in this work is, as most of other carbo-benzene molecules reported to date, very weakly photoluminescent, so that the possible contribution of its emission properties can be neglected in the present study [START_REF] Baglai | Difluorenyl-carbo-benzenes, hydrocarbon quadrupolar chromophores: synthesis, electronic structure, and two-photon absorption properties[END_REF][START_REF] Listunov | Steric/n-electronic insulation of the carbo-benzene ring: dramatic effect of tert-butyl vs phenyl crowns on geometric, chromophoric, redox and magnetic properties[END_REF][START_REF] Rives | Highly πelectron-rich macro-aromatics: bis(p-aminophenyl)-carbo-benzenes and their DBA acyclic references[END_REF][START_REF] Baglai | Towards fluorescent indolyl-carbobenzenes[END_REF][START_REF] Barthes | Spectral properties of Expanded π-systems: light absorption and emission of a tertaphenyl-carbo-benzene[END_REF]. This triptych TiO 2 /Ag/Cbz photocatalyst exhibits enhanced performances under visible light and pressure (2.2 bar) compared to those of binary TiO 2 /Ag and TiO 2 /Cbz systems pointing to the synergy between these three components.

Experimental Methods

All chemicals are supplied by Sigma-Aldrich. The glass wafers AF 32 are supplied by SCHOTT glass made of ideas®. Titania sols are prepared by hydrolysis of titanium alkoxide in a large excess of acidified water, according to the general procedure previously described [START_REF] Alphonse | Stable hydrosols for TiO2 coatings[END_REF] (see supporting information, Section A).

Synthesis of TiO 2 /Ag/Cbz photocatalyst

TiO 2 surface. Glass or silicon substrates are cleaned by an O 2 plasma (800 W, 5 min) prior to use. 0.5 mL of TiO 2 sol is deposited on the clean substrate by spin-coating (speed: 2000 rpm, acceleration: 2000 rpm, time: 30 s). The so-obtained glass/TiO 2 samples are annealed following 2 main steps: first at 110°C for 30 min to remove the solvent and organic molecules, then at 300°C under air during 1 hour, with a heating rate of 10°C.min -1 , to stabilize the titanium oxide structure. The glass/TiO 2 samples are diced into squares (1.5×1.5 cm 2 ) and cleaned using O 2 plasma (400 W, 5 min) prior to triptych processing.

For electron microscopy observation and spectroscopic characterization, silicon/TiO 2 samples (cleaned for 5 min with O 2 plasma at 400 W) are used.

Synthesis and deposition of Ag nanoparticles on TiO 2 . The Ag nanoparticles (NPs) are grown following a previously reported procedure. [START_REF] Cure | Controlled Growth and Grafting of High-Density Au Nanoparticles on Zinc Oxide Thin Films by Photo-Deposition[END_REF] The TiO 2 thin film is immersed in a mixture composed by 0.5 mL of AgNO 3 aqueous solution ([Ag + ] = 2.15 × 10 -3 mol/ L), 0.5 mL of sodium citrate aqueous solution ([citrate] = 0.05 mol/ L), 4.5 mL of DI water and 0.5 mL of ethanol and irradiated under UV (100 W, 2 min). The size of the nanoparticles is fixed by the irradiation duration. The samples are then annealed in air at 200°C during 30 min to ensure the grafting of Ag NPs into the TiO 2 film for a controlled localization of the plasmonic field close to the TiO 2 /Ag interface. After annealing, the substrates are vigorously cleaned with DI water (~50 mL for each substrate) in order to remove all the by-products arising from the thermal decomposition of the citrate ligands. Some of these, hereafter labeled as TiO 2 /Ag samples, are characterized prior to the deposition of Cbz molecules.

Synthesis and deposition of Cbz. Para-di(anilin-4-ylethynyl)tetraphenyl-carbo-benzene, a

carbo-benzene molecule functionalized by -NH 2 groups (Cbz) is synthesized by a 12 step process, according to previously described procedures [START_REF] Cocq | Synthesis of Functional Carbo-benzenes with Functional Properties: The C2 Tether Key[END_REF][START_REF] Leroyer | Synthesis and stereochemical resolution of a [6]pericyclynedione: Versatile access to pericyclynediol precursors of carbo-benzenes[END_REF]. The TiO 2 /Ag substrates are immersed overnight in an anisole solution of Cbz ([Cbz] = 0.05 g/L) under stirring at 50 rpm (round-per-minute) on a shaker platform. This final step affords the triptych TiO 2 /Ag/Cbz hybrid nanomaterial depicted in Figure 1. Some of the triptych samples are prepared, first, by spin-coating the Cbz on the TiO 2 followed by the deposition of the Ag NPs with the previously described procedure. Such samples are hereafter named TiO 2 /Cbz/Ag.

Materials characterization

Structural characterization of the triptych nanomaterials are performed using Scanning Electronic Microscopy (SEM) (FEI Helios 600i Nanolab) in the immersion mode at 20 kV and with a working distance of 4.2 mm. Transmission Electronic Microscopy (TEM) and High-Angle Annular Dark-Field Scanning Transmission Electronic Microscopy (HAADF-STEM) experiments are carried out in cross-section samples prepared by Focused-Ion Beam (FIB) process in a FEI Helios Nanolab. The surface of the samples is protected by a layer of sputtered carbon before the preparation of lamellas. These latter are observed on a JEM-ARM200F cold FEG at 200 kV with a probe Cs corrector reaching a spatial correction of 0.078 nm. Energy Dispersive X-ray Spectrometry (EDS) spectra are recorded using a JEOL CENTURIO SDD detector. Electron Energy Loss Spectroscopy (EELS) data are acquired using a GATAN GIF QUANTUM ER using a dispersion of 0.025 eV/channel (energy resolution of 0.3 eV), a collection semi-angle of 19.4 mrad and a convergence semi-angle of 15 mrad. Crystalline phases are detected using Grazing Incidence X-Ray Diffraction (GI -XRD, Bruker D8 Discover system) with a Cu k-alpha radiation as the source. For GI-XRD, the grazing angle is set to 1.2° and twotheta collection angle is ranged from 20° to 80° with a step of 0.05° and a dwell time of 0.1 s per point. The absence of Ag reflections for the diptych TiO 2 /Ag and triptych TiO 2 /Ag/Cbz samples is presumably correlated to the low content of silver on the TiO 2 thin film and the small dimensions of the samples. Note that the GI-XRD of the TiO 2 thin film provided in the supporting information is recorded from a whole silicon/TiO 2 wafer. The TiO 2 roughness and density are both characterized by Grazing Incidence X-Ray Reflectometry (GI-XRR, Bruker D8 Discover system): the grazing angle is set to 1.2° and two theta-omega collection angles is ranged from 0.4° to 3.0° with a 0.005° step and a dwell time of 0.1 s per point in all cases. X-ray photoelectron spectroscopy (XPS) (ESCALAB 250 X-Ray photoelectron spectrometer) with a monochromatized Al-Kα radiation, a concentric hemispherical electron energy analyzer under vacuum (10 -9 mbar) and a pass energy of 23.5 eV is used to characterize the chemical species at the interfaces of the triptych nanomaterial. The Raman scattering spectra are acquired using a Horiba-Jobin-Yvon XPlora set-up. The spectra are excited by a 532 nm laser beam focused onto the sample using a 100 × objectives (0.8 NA). The laser power intensity is kept as low as 0.1 mW in order to avoid sample heating and degradation of the organic Cbz layer. The absorbance spectra are recorded in the transmission mode from the triptych nanomaterials deposited on the transparent glass substrates using a Perkin-Elmer Lambda 950 UV-vis spectrometer equipped with an integration sphere (specular mode). The hydrophobicity of the Cbz layer is characterized by drop contact angle measurements using a Digidrop system. For each sample, three successive measurements are performed in order to check the reproducibility and estimate a mean value of the contact angle. Inductively coupled plasma -optical emission spectrometry (ICP-OES) measurements are performed at the "Service d'analyse élémentaire" of LCC-CNRS in Toulouse using a Thermo Scientific iCAP 6300 DUO spectrometer with a 3-channel, 12-roller pump and a 27.12 MHz solid state RF plasma generator. Typically, all the 10 mL (aqueous solution) involved in the photocatalytic experiments are evaporated overnight in a 50 mL Teflon tube. Concentrated nitric acid is added in the resulting mixture and then diluted in a 10 mL volumetric flask. The resulting solution (5 mL) is introduced during the ICP-OES analysis. Note that the calibration curve are realized by successive dilution of a 1000 ppm standard to give a series of standards with values at: 0.5; 1; 2; 5; 10 and 20 ppm. Each standard is analyzed in 3 replicates. The values of the working wavelength are 328.068 and 338.289 nm.

Measurement of Photocatalytic Activity

Lab-made quartz reactors are used to characterize the photocatalytic properties of the prepared samples (Figure S1). The hydrogen production is measured by gas chromatography (GC, Perkin-Elmer Clarus 580, thermal conductivity detector, PlotQ column (30 m) and PE-molisieve column (30 m), argon carrier gas). The samples (1.5 cm × 1.5 cm, 2.25 cm 2 ) are immersed into a 65:35 deionized water:ethanol mixture (10 mL). The quartz reactor is purged and pressurized at 2.2 bar under argon gas in order to remove the air. The samples are then irradiated with a Xenon lamp supplied by Cermax® (elliptical PE300B-10F, UV-visible, 300 W, wavelengths range from 300 nm to 1100 nm, sample placed at a distance of ~12 cm which corresponds to an optical irradiance at the sample of 28 mW.cm -2 ) during 48 h and the quantity of exhausted hydrogen is measured every 6 h. For each sample, several characterization are made to ensure reproducibility of the measurements. The relative spectral distribution of the Xenon lamp is presented in Figure S2. ± 2 nm, areal NP density: 349 ± 10 NPs/µm²) have grown not only on the TiO 2 surface but also in the grain interstices of the TiO 2 film, as revealed by the STEM-EDS chemical profile (Figure 2d). Silver nanocrystals exhibit typical (111) crystallographic planes (blue frame in Figure 2c) [START_REF] Cure | Monitoring the Coordination of Amine Ligands on Silver Nanoparticles Using NMR and SERS[END_REF].

Results

Structural and chemical characterization of the triptych material

The thickness, density and roughness of the TiO 2 film are estimated by GI-XRR at ~80 nm, 2.9 ± 0.01 g.cm -3 , well below the bulk density of 3.89 g.cm -3 and ~ 2 ± 0.1 nm, respectively [68]. The anatase single phase and the stoichiometry of the TiO 2 film are confirmed by the XRD patterns and XPS analysis, respectively. The latter gives the binding energies of the Ti 2p 1/2 , Ti 2p 3/2 and O 1s core levels at 464.5 ± 0.1 eV, 458.8 ± 0.1 eV and 530.0 ± 0.1 eV, respectively (see supporting information, Section B-1) [START_REF] Agarwala | Synthesis and tuning of ordering and cristallinity of mesoporous titanium dioxide film[END_REF].

The Cbz layer is visible (Figure 2c) as the well-defined black contrast on top of the Ag NPs; the grey region on top of the Cbz layer is attributed to the carbon layer used to prepare the FIB lamella. EELS analyses of this top layer (Figure 2e) shows a shift from 24. The Raman spectra of the triptych TiO 2 /Ag/Cbz nanomaterial measured in the 400-4000 cm -1 range are presented in Figure 3a. Sharp peaks are clearly observed in this spectral range owing to the Surface Enhanced Raman Scattering (SERS) effect produced by the Ag NPs. Indeed, SERS effect is here observable because the Raman excitation line (532 nm) is close to the surface plasmon resonances of the aggregated Ag NPs. As a matter of fact, the Raman spectra measured from the TiO 2 /Cbz substrate, i.e. without any Ag NP, reveal almost no Raman signal (black trace, Figure 3a) [START_REF] Persson | On the theory of surface-enhanced Raman scattering[END_REF][START_REF] Romero | Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers[END_REF].

It is worth mentioning that the weak signal/noise ratio of the SERS spectra shown in Figure 3a (red trace) is due to the fact that the Raman scattering was excited with a minimum laser power (0.1 mW) to avoid degradation of the Cbz layer which occurs at higher power because of heating resulting from the optical absorption by the Cbz and in the Ag NPs.

By comparison of these Raman spectra with the infrared spectra of Cbz and analogous paradianilinyltetraphenyl-carbo-benzene without exo-macrocyclic C≡C spacers, named Cbz* (Figure S5), the main sharp modes can be unambiguously assigned to -N(-H) 2 (3250 and 3053 cm -1 ), C≡C (2149 cm -1 and 2037 cm -1 ) and aromatic C=C (1580 and 1511 cm -1 ) stretching modes.

According to a combined experimental and density functional theory (DFT) computational study of the Raman spectra of a series of carbo-benzenes [75], the two bands at 2149 cm -1 and 2037 cm -1 can be assigned to the coupled vibrations of the exo-and endo-macrocyclic C≡C bonds together. The most intense one, at 2037 cm -1 , corresponds to the asymmetric mode, the other (at 2149 cm -1 ) corresponding to the superimposition of the in-phase and out-of-phase modes of the exo-C≡C bonds with respect to the totally symmetric vibration of the endo-C≡C bonds [75].

Remarkably, the intensity of band at 2149 cm -1 is much weaker than that at 2037 cm -1 when the Cbz layer is formed directly on the TiO 2 surface, which suggests a selective enhancement of SERS intensity of both the exo-and endo-macrocyclic C≡C modes in the TiO 2 /Ag/Cbz nanomaterial (Figure S6). Moreover, the enhancement of the Raman intensity of the C≡C and of the NH 2 modes in the triptych nanomaterial, indicates that the anilin-4-ylethynyl functions are localized in the close vicinity of the Ag NPs [START_REF] Persson | On the theory of surface-enhanced Raman scattering[END_REF][START_REF] Romero | Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers[END_REF], which suggests that the Cbz molecules are bound to the Ag NPs by the NH 2 groups.

Raman spectroscopy also reveals microstructure features, as well as the presence of electronic interactions in the diptych TiO 2 /Ag and triptych TiO 2 /Ag/Cbz materials. By increasing the time of the Ag NP growth, these phenomena are even more evident in the TiO 2 /Ag* series with larger Ag NPs (Figure 3b, see supporting information, Section B-3) compared to the TiO 2 /Ag series (see supporting information, Section B-4). The low-frequency (100-400 cm -1 ) Raman spectra (Figure 3b) exhibit a peak characteristic of the E g 1 phonon mode of anatase TiO 2 : it is located at 140 cm -1 in TiO 2 , at 147 cm -1 in both TiO 2 /Ag* and TiO 2 /Ag*/Cbz (Figure 3b) and at 140 cm -1 again in the reversed triptych TiO 2 /Cbz/Ag*, without TiO 2 /Ag interface. Moreover, the intensity of the TiO 2 Raman peak is clearly enhanced in TiO 2 /Ag and TiO 2 /Ag/Cbz with respect to TiO 2 and TiO 2 /Cbz/Ag. This clearly shows that the blue shift and the intensity of the TiO 2 Raman peak correlate with the formation of the TiO 2 /Ag interface. The observation of such a blue shift has already been reported in TiO 2 /Au films and was attributed to the deposition of Au NPs preferably on oxygen vacancies and edge sites which favors the charge transfer interactions between TiO 2 and metal nanoparticles [START_REF] Melvin | M-Au/TiO2 (M = Ag, Pd, and Pt) nanophotocatalyst for overall solar water splitting: role of interfaces[END_REF]. The charge transfer phenomenon may also enhance the photocatalytic activity since the photo-generated electron-hole pairs could be spatially separated and hence their lifetime significantly increased [START_REF] Seh | Janus Au-TiO2 Photocatalysts with Strong Localization of Plasmonic Near-Fields for Efficient Visible-Light Hydrogen Generation[END_REF]. The blue shifted Raman peak of the TiO 2 phonon also means that the Ti-O bond is stronger at the TiO 2 /Ag interface than in bulk TiO 2 , revealing a charge transfer from the metal nanoparticle to the semiconductor. Moreover, the blue shift of the Eg1 phonon mode can also result from the mechanical constraints applied in the TiO 2 network, confirming the complete filling of the TiO 2 pores by larger Ag NPs as discussed above. These interactions are expected since the annealing step performed after NP growth, should increase the intimacy and accommodate a transition between both TiO 2 and Ag crystalline networks. Note that no significant shift is observed in the Raman spectra when the Cbz is deposited on TiO 2 , pointing to the non-destructive interactions between the TiO 2 and the Cbz (violet trace, Figure 3b).

Additionally, XPS spectra given in Figure 3c clearly show an increase of the intensity of C 1s peaks and a decrease of the intensity of Ti 2p and O 1s peaks for the diptych TiO 2 /Cbz and triptych TiO 2 /Ag/Cbz nanomaterials which is expected when the Cbz layer covers the top surface (see supporting information, Section B-5). Finally, XPS spectra also show that N 1s core level (from -NH 2 groups) is exactly at the same position (399.8 eV) than for TiO 2 /Cbz which suggests a similar binding between Cbz and TiO 2 and the Ag NP surfaces (Figure 3c, see supporting information, Section B-5). Note that some carbon contamination coming from atmospheric adsorbed carbon species is detected on a few samples (without a coating of Cbz) with a C 1s peak of weak intensity (Figure 3c).

UV-visible spectroscopy and hydrogen production of the diptych and triptych nanomaterials

The optical absorption spectra of the investigated samples are presented in Figure 4a,b. The contribution of each component of the diptych and triptych nanomaterials can be clearly distinguished: (i) the strong band-gap absorption of TiO 2 is observed around 280 nm; (ii) the contribution of the Ag NPs SPR is visible around 430 nm in both TiO 2 /Ag and TiO 2 /Ag/Cbz compared to pure TiO 2 and is consistent with the SPR wavelength expected for spherical 7 ± 2 nm Ag NPs [START_REF] Ge | In situ plasmonic Ag nanoparticle anchored TiO2 nanotube arrays as visible-light-driven photocatalysts for enhanced water splitting[END_REF][START_REF] Sreedhar | Ag nanoparticles decorated ionbeam-assisted TiO2 thin films for tuning the water splitting activity from UV to visible light harvesting[END_REF]; (iii) the main absorption band of Cbz molecules resulting from the overlapping of the two strongest Gouterman transitions (HOMO-1/HOMO → LUMO/LUMO+1) appears around 494 nm as a shoulder in the TiO 2 /Ag/Cbz spectrum and is probably enhanced by the SPR of the Ag NPs [START_REF] Baglai | Difluorenyl-carbo-benzenes, hydrocarbon quadrupolar chromophores: synthesis, electronic structure, and two-photon absorption properties[END_REF][START_REF] Listunov | Steric/n-electronic insulation of the carbo-benzene ring: dramatic effect of tert-butyl vs phenyl crowns on geometric, chromophoric, redox and magnetic properties[END_REF][START_REF] Leroyer | From hexaoxy-[6]pericyclines to carbo-cyclohexadienes, carbo-benzenes, and dihydro-carbobenzenes: synthesis, structure, chromophoric and redox properties[END_REF][START_REF] Zhu | Carbo-biphenyls and Carbo-terphenyls: Oligo(phenylene ethynylene) Ring Carbo-mer[END_REF]. Note that in the reversed triptych system TiO 2 /Cbz/Ag, the Ag NPs are no longer in direct contact with the TiO 2 surface, which affects their LSPR properties by red-shifting and broadening [START_REF] Roldan | Optical response of silver nanoparticles stabilized by amines to LSPR based sensors[END_REF], resulting in an overlap of the Ag NPs LSPR peak with the absorption band of Cbz, leading to the observation of only one broad absorption band (Figure 4b). From these UV-visible analyses, the band gap of the TiO 2 thin films has been calculated for the different diptych and triptych systems and are found both close to ~3.4 eV (Figure S14). The H 2 production is measured by immersing the 2.25 cm² samples into 10 mL of a 35% aqueous ethanol solution in a hand-made quartz reactor. Importantly, the reactor is purged and pressurized with 2.2 bar of argon gas before analyses and is not placed under vacuum as it is the case in many literature reports. [START_REF] Wang | Recent developments in heterogeneous photocatalysts for solar-driven overall water-splitting[END_REF][START_REF] Takata | Particulate Photocatalysts for Water Splitting: Recent Advances and Future Prospects[END_REF] A sample of bare TiO 2 thin film is also studied as a reference.

The hydrogen production of all tested samples (Figure 4c,d) increases linearly during the two days tests and reveals a stable catalytic performance during 48 hours. The measured hydrogen production rates are determined: 0.03 mmol.m -2 .h -1 (0.13 mmol.g -1 .h -1 ) and 0.04 mmol.m -2 .h -1 (0.18 mmol.g -1 .h -1 ) for the diptych TiO 2 /Ag and triptych TiO 2 /Ag/Cbz nanomaterials, respectively. These rates exceed by more than a factor 2 those of the TiO 2 reference layer: 0.02 mmol.m -2 .h -1 (0.06 mmol.g -1 .h -1 ), of the TiO 2 /Cbz: 0.009 mmol.m -2 .h -1 (0.04 mmol.g -1 .h -1 ) and of the reversed triptych TiO 2 /Cbz/Ag nanomaterial: 0.02 mmol.m -2 .h -1 (0.07 mmol.g -1 .h -1 ), hence underlying the synergetic role of the TiO 2 /Ag in the PC process (Figure 4c,d, Figure 5). Moreover, the production rate of the triptych TiO 2 /Ag/Cbz is larger than that of the diptych TiO 2 /Ag by ~33% which gives an estimate of the contribution of the Cbz photo-sensitizer to the photocatalytic process.

The extension of the TiO 2 /Ag/Cbz triptych absorption over a large visible range (from 400 to 600 nm) as compared to TiO 2 alone may lead to a more efficient utilization of the visible light and thus enhance the hydrogen production. Furthermore, because the absorptions of Ag NPs (SPR) and Cbz (maximum absorption band) take place at two different wavelengths, their combination can also induce the observed enhancement of the photocatalytic efficiency.

Discussion

Influence of the respective spatial distribution of the three components

To better assess the respective role of the Cbz organic dye and plasmonic Ag NPs into the TiO 2 /Ag/Cbz nanomaterial, three different samples are assembled: (1) a sample without the organic dye: TiO 2 /Ag; (2) a sample without Ag NPs: TiO 2 /Cbz; (3) a sample where the Cbz layer is deposited before the growth of the Ag NPs i.e. preventing the contact between the TiO 2 pores and the environing medium: the reversed triptych: TiO 2 /Cbz/Ag. In the latter sample, no shift of the phonon mode E g 1 is measured (Figure 3b, Figure S10) indicating the absence of mechanical constraint on the TiO 2 lattice, as expected: the Cbz layer indeed covers the surface of the TiO 2 film and avoid the embedding of Ag NPs in the pores of the metal oxide film.

The samples are placed under Ar flow and irradiated in the presence of ethanol in the same conditions as those used for the TiO 2 /Ag/Cbz nanomaterial. In all the cases, the hydrogen production increases linearly over the 48 h (Figure 4c,d). The hydrogen production rate for each sample is represented in Figure 5. As expected, the TiO 2 /Ag substrate is more efficient than the pure TiO 2 thin film due to SPR effects, but the hydrogen production rate of this diptych is lower than that of the TiO 2 /Ag/Cbz triptych. The diptych TiO 2 /Ag nanomaterial is 1.9 times more efficient than pure TiO 2 if the H 2 production rate is expressed per m² (0.03 mmol.m -2 .h -1 ), and 2.2 times more efficient (0.13 mmol.g -1 .h -1 ), if this rate is expressed per gram. For the TiO 2 /Ag/Cbz triptych, a slight improvement of the production rate is observed, up to 2 times (0.04 mmol.m -2 .h -1 ), or up to 3 times more (0.18 mmol.g -1 .h -1 ) than pure TiO 2 depending on the considered unit (Figure 5). In contrast, the decreased efficiency observed for the TiO 2 /Cbz diptych clearly evidences a synergistic effect between the three components in the TiO 2 /Ag/Cbz triptych.

Additionally, the stability of the TiO 2 /Ag/Cbz triptych is tested by cyclic photocatalytic H 2 production monitoring (Figure 6). After 5 cycles, no significant decay in the photocatalytic activity is observed, suggesting that TiO 2 /Ag/Cbz have good stability in photocatalytic H 2 production under harsh environment: simulated sunlight illumination (optical irradiance at the sample of 28 mW.cm -2 ), room temperature and pressure (2.2 bar). The optical and SEM observations of the samples after the photocatalytic experiments show a better stability of the TiO 2 /Ag/Cbz triptych compared to the TiO 2 /Ag diptych on which the photoactive film is highly degraded (Figure S17). These observations reveal that the Cbz layer also acts as a protective layer against the TiO 2 photocorrosion [START_REF] Das | Electron-selective TiO2 / CVD-Graphene Layers for Photocorrosion Inhibition in Cu2O Photocathodes[END_REF][START_REF] Tang | Perfect Inhibition of CdS photocorrosion by graphene sheltering engineering on TiO2 nanotube array for highly stable photocatalytic activity[END_REF]. This remarkable enhancement of the hydrogen production rate observed with TiO 2 /Ag/Cbz and to a lesser extent with TiO 2 /Ag is attributed to the Ag metal link in the effective vertical Schottky junction between Ag NPs and TiO 2 . The plasmon mode corresponds to discrete states (interbands 4d -5s) of coupling between the incident light and the electronic density oscillation within the Ag NPs. The energy of the photon is transferred to electrons which can get over the Shottky barrier at the interface between TiO 2 and Ag and be injected into the conduction band of TiO 2 . This mechanism called plasmon induced electron transfer from metallic particles to a TiO 2 film is schematically represented in Figure 7. Importantly, the surface plasmon resonance of the Ag NPs spectral domain is overlapping with the optical absorption of the Cbz molecules, the latter giving a shoulder of the Ag NPs LSPR broad band (Figure 4b): this leads to a plasmonic enhancement of the photo-generation of electrons and holes and might explain the synergy observed in the hydrogen production with the triptych nanomaterials.

The lower hydrogen production activity of the reversed TiO 2 /Cbz/Ag triptych, close to the TiO 2 /Cbz level, can be tentatively explained by two effects. Ag NPs absorb light, but without the metal-link between Ag and TiO 2 , hot electrons cannot be transferred into the TiO 2 thus preventing the enhancement of hydrogen production. Nevertheless the energy is transferred to the Cbz dye which contributes to slightly increase the hydrogen production as compared to TiO 2 /Cbz [START_REF] Andrei | Plasmonic enhancement of dye sensitized solar cells via a tailored size-distribution of chemically functionalized gold nanoparticles[END_REF], and thus probably because of the electron transport ability of the Cbz molecule [START_REF] Li | Towards graphyne molecular electronics[END_REF]. The poor performance of the latter sample as compared to pure TiO 2 could be attributed to the hydrophobicity of the Cbz layer, hampering the interaction between the TiO 2 surface and water molecules.

Indeed, the contact angles systematically increases when the Cbz layer is deposited on the samples as compared to those measured for the same materials without organic layer (see supporting information, Section B-8). For example, the contact angle of 62 ± 3° of the TiO 2 /Ag diptych increases up to 100.2 ± 0.1° after deposition of the Cbz layer. The fact that the triptych system, despite the screening of charge in addition to the physico-chemical separation of water molecules from the catalytic surface sites, which is clearly visible from the diptych response, is a clear illustration of the synergy between Ag nanoparticles and Cbz molecules. With this respect, a better control of the Cbz layer thickness, as well as its organization at the molecular level, to facilitate water diffusion, is a potential source of enhancement of the triptych material performances.

All these observations clearly evidence the synergetic effect of the three components in the triptych materials and highlight the key role of electron transfer mechanisms for the H 2 production as illustrated in Figure 7.

Influence of the Ag loading and size

As the Ag-TiO 2 metal link was shown to play a crucial role in the hydrogen production performances of the TiO 2 /Ag/Cbz nanomaterial, this last section addresses the effect of loading and size of Ag NPs. The porosity of the TiO 2 films allows nucleation and growth of Ag NPs inside the pores, from molecular precursors such as AgNO 3 , which has a larger Van der Waals size than water or ethanol molecules. The size of Ag NPs can be easily tuned by modifying the time of irradiation inducing the process of photo-deposition of Ag NPs from their salt precursor.

Typically, the lengthening of the UV irradiation time for the photo-reduction process from 2 to 30 min induces an increase of the size of the Ag NPs in the corresponding TiO 2 /Ag* series. Two populations of Ag NPs are observed after a 30 min illumination: well-defined small particles with an average diameter of 18 ± 6 nm and larger ones with an average diameter of 30 ± 2 nm, the areal density being almost constant at ~ 344 ± 10 NPs/ µm² (see supporting information, Section B-3). Inside the pores of the TiO 2 film, the Ag NPs growth is limited by the volume of the pores, thus leading to the first population of smaller Ag NPs (18 ± 6 nm ), while the larger NPs (30 ± 2 nm) are those located at the TiO 2 film surface where their growth is not limited by any confinement. The smaller Ag NPs are thus the result of the growth inside the pores, whereas the bigger particles are those which grew on the TiO 2 surface.

The TiO 2 /Ag* diptych produces much less hydrogen than TiO 2 /Ag: 0.004 mmol.m -2 .h -1 (0.02 mmol.g -1 .h -1 ) and 0.03 mmol.m -2 .h -1 (0.13 mmol.g -1 .h -1 ), respectively (see supporting information, Section B-7). Three explanations can be proposed: (1) the aggregation of Ag NPs decreases the number and the accessibility of the active sites on the surface of the triptych material; (2) a too large covering of the surface by silver can shield the UV light absorption by the TiO 2 , and thus decrease the utilizing efficiency of photoelectrons [START_REF] Yang | Facile synthesis of Ag/ZnO heterostructures assisted by UV irradiation: Highly photocatalytic property and anhanced photostability[END_REF]; (3) the reduction of free TiO 2 surface accessible to water molecules since the pores are filled with ~18 nm plasmonic particles (Figure S9). The SPR effect of 18 nm Ag NPs completely embedded into the TiO 2 pores is characterized at ~380 nm (see supporting information, Figure S13) [START_REF] Cushing | Controlling Plasmon-Induced Resonance Energy Transfer and Hot Electron Injection Processes in Metal@TiO2 Core-Shell Nanoparticles[END_REF]. The maximum of the SPR absorption band resulting from the contribution of two Ag NP populations onto the surface (18 ± 6 nm and 30 ± 2 nm, Figure S8b) in TiO 2 /Ag* remains at ~430 nm, i.e. roughly at the same position as for ~7 nm Ag NPs obtained after a 2 min irradiation process. In the dual population case, we believe the largely predominant population (18 nm) to be responsible for the non-shifted TiO 2 /Ag* result (no shifting expected for NPs with diameter < ~20 nm), the population with larger diameter being minor, with a contribution also vanishing due to the broadening of the overall absorption peak.

So, the size of the Ag NPs has apparently no effect on the efficiency of the water reduction photocatalyst. However, a higher loading of NPs appears to be critical on the photocatalyst performances since it reduces the TiO 2 effective surface area in the final material.

Comparison with already published catalytic materials

Finally, the main characteristic and PC-WS performances of our TiO 2 /Ag/Cbz photocatalyst are reported in Table 1, together with other triptych materials (mostly in nanopowder form) described in the recent literature [START_REF] Marchal | Au/TiO2-gC3N4 Nanocomposites for Enhanced Photocatalytic H2 Production from Water under Visible Light Irradiation with Very Low Quantities of Sacrificial Agents[END_REF][START_REF] Wang | Yolk@Shell Nanoarchitecture of Au@r-GO/TiO2 Hybrids as Powerful Visible Light Photocatalysts[END_REF][START_REF] Sheu | Investigation of the appropriate content of graphene in Ag-TiO2-graphene ternary nanocomposites applied as photocatalysts[END_REF][START_REF] Wang | Verticallyheterostructured TiO2-Ag-rGO ternary nanocomposite constructed with {001} facetted TiO2 nanosheets for enhanced Pt-free hydrogen production[END_REF][START_REF] Wong | Photocatalytic H2 production of composite onedimensional TiO2 nanostructures of different morphological structures and crystal phases with graphene[END_REF]. Note that the comparison is difficult because the experimental parameters are highly variable. We characterize the H 2 production under 2.2 bar representative of practical applications whereas a major part of published works [START_REF] Wang | Recent developments in heterogeneous photocatalysts for solar-driven overall water-splitting[END_REF][START_REF] Takata | Particulate Photocatalysts for Water Splitting: Recent Advances and Future Prospects[END_REF] measure the photocatalytic activity in a quartz reactor under vacuum, which is highly favorable to hydrogen production because of the shift of the chemical equilibrium according to the Le Chatelier's principle: 2 H 2 O = 2 H 2 + O 2 . Nevertheless, our TiO 2 /Ag/Cbz photocatalyst thin film exhibits very good PC-WS performance (180 µmol.g -1 .h -1 ) under high pressure (2.2 bar). In addition, compared to other works, the manufacturing process is not only low costs but also provides robust material against photocorrosion compared to nanopowders (established over 48h (see supporting information, Figure S17 and Section B-13)).

(*)Note that the surface area of TiO 2 /Ag/Cbz is calculated from the dimension and mass of the thin film since the surface area is too weak to be measured by Brunauer-Emmett-Teller (BET) method.

Conclusion

In summary, the innovative TiO 2 /Ag/Cbz triptych system with an ultralow weight of photocatalyst, which is of paramount importance in the perspective of low-cost applications in the field of energy, benefits from synergy effect for hydrogen production by pure photocatalysis as shown by comparison with the diptych systems. The relevance of triptych materials for WS involving a semiconductor thin film, a plasmonic nanoparticle and a specific photosensitive molecule of the carbo-benzene genus is established. Thanks to an adapted procedure of photo-

Figure 1 .

 1 Figure 1. Schematic hybrid triptych nanomaterial combining a TiO 2 film (blue), Ag NPs (grey

Figure 2

 2 Figure 2 gives optical (a) and SEM (b) images and a TEM cross-section view (c) of a

  Figure 2e, both the contrast and shift of the C EELS peak reveal the information of a ~6 nm-thick

Figure 2 .

 2 Figure 2. a) Optical images and b) SEM observation (inset of the size distribution of Ag NPs

Figure 3 .

 3 Figure 3. a) Raman spectra of TiO 2 /Ag/Cbz in the 4000-400 cm -1 range recorded on a single Ag

Figure 4 .

 4 Figure 4. a) UV-visible spectra (in transmission) in the 200-850 nm region and; b) in the 350-

Figure 5 .

 5 Figure 5. The H 2 production rate per surface units (blue) and per gram (white) for the tested

Figure 6 .

 6 Figure 6. Cyclability of TiO 2 /Ag/Cbz triptych in H 2 production under visible light irradiation.

Figure 7 .

 7 Figure 7. Illustration of a possible electron transfer mechanism in the triptych TiO 2 /Ag/Cbz

Acknowledgement

All the synthesis and spectroscopic characterization and modeling were supported by ANR and the Université de Toulouse (IDEX MUSE project). This work was supported by LAAS-CNRS technology platform, a member of Renatech network. Jean-François Veyan is acknowledged for his help in the measurements of the XPS spectra. The authors thank Claudie Josse and Armel Descamps-Mandine (Centre de Microcaractérisations Raimond Castaing) for the preparation of lamelas and HAADF-STEM observations, Alain Moreau for the ICP measurements and Andréa Nicollet and Séverine Vivies for their help with XRD characterization. Tercio de Freitas Paulo is deeply acknowledged for his help in the assigment of the Raman spectra.

deposition, the pores of a TiO 2 thin film can be metallized by silver nanoparticles in one step. The present work not only demonstrates the high interest of carbo-benzene molecules in green hydrogen production applications, but also provides a mechanistic insight highlighting two key requirements: the need for a Schottky junction between silver and TiO 2 and the precise localization of the dye in triptych materials in order to promote a synergic effect for H 2 production by hydrogen evolution reaction.

Furthermore, although thin films-based systems are typically used in photoelectrochemical processes for hydrogen production, the improvement of thin films efficiency by their combination with adequate materials like plasmonic nanoparticles and/or photosensitive and innovative molecules was demonstrated, allowing their use in pure photocatalytic conditions i.e. without any need of electric energy to produce hydrogen from water and sunlight, and more importantly under usual conditions of ambient temperature and pressure.

Supplementary data

Supplementary material is available including detailed synthesis of TiO 2 sols; characterization of TiO 2 films; supplementar SEM, Raman, Infrared, UV-visible and XPS spectroscopies and angle contact measurements for the considered diptych and triptych materials.

Author Information

Corresponding author

Correspondence to: Jeremy Cure, jcure@laas.fr & Carole Rossi, crossi@laas.fr

Competting financial interests

The authors declare no competting financial interests.