Phu Tuan

Anh Nguyen

Matthieu Vandamme

Artem Kovalenko

Collapse and cavitation during drying of water-saturated PDMS sponges with closed porosity

Keywords: Porous materials, drying, poroelasticity, cavitation, elastomers, mechanical properties

In this paper, we study the drying of water-saturated porous polydimethylsiloxane (PDMS) elastomers with closed porosity in which the evaporation of water is possible only via the diffusion across the PDMS. Starting from water/PDMS emulsions, we fabricate soft macroporous samples with different pore diameter distributions and average diameters ranging from 10 to 300 µm. In these materials, the drying may lead either to a collapsed state with low porosity or to the cavitation and reopening of a fraction of the pores. Using optical microscopy and porosity measurements, we showed the importance of the pore diameters and interactions on the result of drying. At pore diameters lower than 30 µm, the majority of pores remain collapsed. We attribute the permanence of the collapse of most small pores to a low probability of cavitation and to the adhesion of the pore walls. Pores with diameters larger than 100 µm tend to reopen after the water they contain cavitates. The behavior of pores with diameters ranging from 30 to 100 µm depends on the porosity and drying temperature. We also visualize collective cavitation upon drying of sponges initially saturated with a sodium chloride solution. In this case, the cavitation in the largest pores leads to reopening of small pores in a neighboring zone of the sample. To our knowledge, our results present the first experimental proof of the pore-size-dependent and cooperative nature of the response of soft sponges with closed porosity to drying.

Introduction

Porous polymers are widely used for acoustic and thermal insulation. In recent years, increasing attention is paid to soft porous elastomers, or sponges [START_REF] Zhu | Recent Progress in Fabrication and Application of Polydimethylsiloxane Sponges[END_REF] , due to their use as compressible parts in mechanical sensors and soft actuators. Moreover, these materials were used to fabricate novel acoustic metamaterials [START_REF] Brunet | Soft 3D Acoustic Metamaterial with Negative Index[END_REF] and gradient lenses [START_REF] Jin | Flat Acoustics with Soft Gradient-Index Metasurfaces[END_REF] due to extremely low values of the sound speed obtained at ultrasound frequencies [START_REF] Kovalenko | Tuning the Sound Speed in Macroporous Polymers with a Hard or Soft Matrix[END_REF] . To achieve a controlled porous structure, a template consisting of liquid droplets [START_REF] Silverstein | Recent Advances in Emulsion-Templated Porous Polymers[END_REF] or solid particles [START_REF] Tebboth | Inflatable Elastomeric Macroporous Polymers Synthesized from Medium Internal Phase Emulsion Templates[END_REF] is dispersed in the liquid prepolymer, usually polydimethylsiloxane (PDMS), which is then crosslinked to obtain an elastomer. The template is then removed by etching [START_REF] Turani-I-Belloto | Diffusion-Limited Dissolution of Calcium Carbonate in a Hydrogel[END_REF] (in the case of solid particles), washing and drying to obtain pores with sizes and volume fraction similar to that of the template. Ideally, the drying step should lead to air-filled porous materials with low mechanical moduli. However, it was reported previously that capillary forces during drying may lead to a collapse of the porosity and to a loss of the desired acoustic or mechanical properties [START_REF] Martina | Siloxane Elastomer Foams[END_REF][START_REF] Kovalenko | Tailoring of the Porous Structure of Soft Emulsion-Templated Polymer Materials[END_REF] . One solution to avoid this effect is to generate open porosity by using adhesive emulsions with aggregated droplet structure [START_REF] Kovalenko | Tailoring of the Porous Structure of Soft Emulsion-Templated Polymer Materials[END_REF] . The micron-sized "windows" between pores allow water evaporation and air invasion in the pores. This method suffers of the sensitivity to the emulsion fabrication conditions and spatial inhomogeneity of the aggregated porous structure. The second strategy is to use supercritical drying [START_REF] Jin | Flat Acoustics with Soft Gradient-Index Metasurfaces[END_REF][START_REF] Martina | Siloxane Elastomer Foams[END_REF] . This approach requires consecutive washing of the samples with an intermediate solvent (for example, ethanol) and liquid carbon dioxide which is then removed by supercritical cycle at high pressure. While it allows fabrication of materials with closed porosity and microscopically homogeneous pore distribution, such process is expensive and timeconsuming. Thus, it would be interesting to propose alternative approaches of drying for soft sponges with closed, homogeneously distributed porosity, which is impossible without rationalization of the collapse problem. However, neither the collapse mechanism during thermal drying nor the dependence of the final porosity on material parameters and drying conditions are yet well understood.

Interestingly, Milner et al. [START_REF] Milner | Creasing in Evaporation-Driven Cavity Collapse[END_REF] has recently shown that an "isolated" water-filled pore in PDMS with the diameter d ~ 1 mm reopens during drying via cavitation (i.e., via formation of a bubble inside the water it contains). The authors observed the shape of the pore and showed the presence of several drying stages. In the first so-called "breathing" mode, the pore contracted homogeneously and remained spherical. Next, a creasing instability was observed at the pore surface which leaded to a non-spherical pore shape. According to Cai et al. [START_REF] Cai | Osmotic Collapse of a Void in an Elastomer: Breathing, Buckling and Creasing[END_REF] , this instability is preferred to buckling for thick pore walls (corresponding to low porosities for sponges). The number of creases depends on the surface energy of the pore and on the high-strain mechanical properties of the elastomer. The next drying stage which takes place at a certain moment before or after creasing is cavitation of the water it contains [START_REF] Milner | Creasing in Evaporation-Driven Cavity Collapse[END_REF][START_REF] Bruning | Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks[END_REF] (i.e. nucleation of a water vapor bubble). This stage is followed by the release of the (negative) pressure inside the pore and by an expansion of the pore back to its initial size and shape. By tackling the bubble expansion velocity during this last stage, Bruning et al. estimated [START_REF] Bruning | Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks[END_REF] the cavitation pressure pcav ≈ -1.4 MPa, which absolute value is much lower than 20-30 MPa found for water in rigid monodisperse pores by Vincent et al [START_REF] Vincent | Drying by Cavitation and Poroelastic Relaxations in Porous Media with Macroscopic Pores Connected by Nanoscale Throats[END_REF] and synthetic trees by Wheeler et al [START_REF] Wheeler | The Transpiration of Water at Negative Pressures in a Synthetic Tree[END_REF] . This difference was explained by the highly hydrophobic nature of the PDMS which favors heterogeneous bubble nucleation.

Cavitation is the necessary but not sufficient condition for pore reopening. The stress in the matrix should be high enough to promote the cavity growth. This effect was intensively investigated in the literature related to such cavity growth in adhesives and elastomers [START_REF] Fond | Cavitation Criterion for Rubber Materials: A Review of Void-Growth Models[END_REF] , which is also called "cavitation" although no liquid is involved. We will refer to this process as to "solid cavitation", to avoid any ambiguity with the cavitation of the pore water in watersaturated porous solids, which was described in the previous paragraph. It was shown that a small pore inside an elastic matrix with Young's modulus E is unstable and will grow to the infinite size at mean tensile stresses higher than ⅚E: such dependence of the stress at which "solid cavitation" occurs on the modulus was observed experimentally [START_REF] Fond | Cavitation Criterion for Rubber Materials: A Review of Void-Growth Models[END_REF][START_REF] Gent | Surface Energy Effects for Small Holes or Particles in Elastomers[END_REF][START_REF] Dollhofer | Surface Energy Effects for Cavity Growth and Nucleation in an Incompressible Neo-Hookean Material--Modeling and Experiment[END_REF] . For the analysis of the stability of small pores, the polymer surface energy should be taken in account. Gent and Tompkins [START_REF] Gent | Surface Energy Effects for Small Holes or Particles in Elastomers[END_REF] introduced the surface energy term in the mechanical model of the pore deformation. They showed that the critical mean stress for the infinite inflation of the pore increases with a decreasing initial radius of this pore and attains hundreds of MPa for radius of few nanometers. The characteristic length scale of the action of surface forces is called the elasto-adhesive length 𝛾 𝐸 ⁄ , where γ is the surface energy of the elastomer. For a typical PDMS elastomer with γ = 40 mN/m and E ~ 1 MPa, the elasto-adhesive length is 0.04 µm. The model of Gent and Tomkins shows that a significant impact of surface energy on the tensile stress at which pore growth occurs is observed for pore dimensions lower than 0.1 µm [START_REF] Gent | Surface Energy Effects for Small Holes or Particles in Elastomers[END_REF][START_REF] Dollhofer | Surface Energy Effects for Cavity Growth and Nucleation in an Incompressible Neo-Hookean Material--Modeling and Experiment[END_REF] . For larger cavities, the growth should be observed at stresses of the order of the modulus E, i.e. about 1 MPa. This explains why the individual large pores in PDMS observed by Milner et al [START_REF] Milner | Creasing in Evaporation-Driven Cavity Collapse[END_REF] and Bruning et al [START_REF] Bruning | Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks[END_REF] reopen after cavitation at pcav ≈ -1.4 MPa.

The aim of this study is to characterize experimentally the effect of the size and number of pores on how porous elastomers with closed porosity initially saturated with water or a salt solution behave during drying. Using previously reported emulsion-templated protocols [START_REF] Kovalenko | Tuning the Sound Speed in Macroporous Polymers with a Hard or Soft Matrix[END_REF] , we synthesize macroporous polydimethylsiloxanes (PDMS) with pore diameters ranging from 1 to 100 µm. First, we use optical microscopy to observe the drying of "diluted" pores (5% of porosity) in thin (i.e. with a 0.5 mm thickness) water-saturated samples. We show that pore behavior differs regarding their diameters: after their total shrinkage, pores with diameters larger than 30 µm are most likely to reopen by cavitation while the major part of smaller pores remain in a collapsed state for at least 16 hours of observation. The part of reopened pores increases with increasing the drying temperature from 60°C to 110°C. Next, by using density measurements to measure porosity, we compare the drying of thick (i.e., with a thickness of about 10 mm) water-saturated samples with 30% porosity and two different pore size distributions. After drying, the sample with small pores (d ~ 70 µm) is almost completely collapsed while the sample with larger pores (d ~ 300 µm) shows reopening of a significant fraction of its pores. Finally, we show the cooperative nature of the cavitation of pores in samples initially containing sodium chloride solution in the pores. We observe that the opening of larger pores leads to reopening of neighboring small pores. To our knowledge, the observed size-dependent and cooperative effects were not reported before and present an interest for the soft matter physics.

Experimental

Materials

A two-component Sylgard®184 PDMS kit was supplied by Neyco. It is composed of vinylmodified PDMS base (SiVi) and silane-modified PDMS curing agent (SiH). We used deionized MiliQ water and NaCl from Sigma Aldrich.

Synthesis of porous PDMS samples

We used the previously reported emulsion-templated method of synthesis [START_REF] Kovalenko | Tuning the Sound Speed in Macroporous Polymers with a Hard or Soft Matrix[END_REF] . The continuous phase of the emulsions was obtained by mixing SiVi and SiH parts in the 10:1 ratio. After mixing, the continuous phase was degassed at room temperature to remove bubbles. The water phase was either MiliQ water or 1.5 wt.% NaCl solution. Surprisingly, stable emulsions with 5% or 30% volume fraction of water could be produced without adding surfactant. We explain this by the high viscosity of the PDMS and the presence of low-molecular species [START_REF] Stricher | How I Met Your Elastomers: From Network Topology to Mechanical Behaviours of Conventional Silicone Materials[END_REF] that can act as surfactants. The corresponding amount of water was incorporated in about 40 g of PDMS under gentle mixing with a spatula (at approximately 1 tour per second). The mixture was next stirred for 2 minutes via a mechanical mixer Heidolph RZR 2162 with a helical geometry with diameter of 3 cm. The stirring conditions are given in Table 1.

By controlling the stirring speed of the emulsions and, consequently, the shearing stress, one should be able to tune the size of the droplets. However, because of the high viscosity of the Sylgard 184, it was impossible to obtain narrow size distributions using simple mixing devices. After several tests, we determined empirically stirring protocols giving samples with significantly different drying properties. The pore diameter distributions Ni(di) were obtained by manual pore tracking of optical microscopy images on at least 1000 pores using ImageJ software. The pore distribution by volume φi(di) was calculated using the equation:

𝜑 𝑖 (𝑑 𝑖 ) = 𝑁 𝑖 𝑑 𝑖 3 ∑ 𝑁 𝑖 𝑑 𝑖 3 𝑖 (1)
where Ni are the numbers of pores with the diameters di.

To obtain samples for microscopy, the volume fraction of the aqueous phase was fixed to 5%. The emulsion was then poured between two PET-coated glass molds with a 0.5 mm rubber spacer and the molds were introduced in a sealed metallic box and heated at 60°C for 14 hours. These samples are designed as "thin" in the rest of the paper.

For density measurements, we fabricated samples starting from a 30% emulsion. The emulsion was poured in 60 mL plastic tubes and centrifuged at 1000 rpm for 5 min to remove gas bubbles. After polymerization at 60°C for 14 hours, the samples were unmolded and cut into equivalent pieces with an average weight of 5 g and thickness of about 10 mm. These samples are designed as "thick" in the rest of the paper.

In Table 1 we summarize the composition, stirring conditions and mean pore diameters for the samples and the methods we used to study their drying.

Observation of drying of thin samples with 5% porosity

The samples with 5% initial porosity and thickness of 0.5 mm were placed in a heating microscope stage HFS 91 (Linkam) under an optical microscope. The cell was connected to an air pump which maintained a flow of dry air equal to 0.5 liters/min through the chamber. After rapid heating to the desired temperature (about 1 min), the recording of images was performed every 10-30 s using a ×10 objective. Two drying temperatures, 60°C and 110°C, were used for each sample. The drying of the sample D200-5 was also performed at 90°C.

Drying and characterization of thick samples with 30% porosity

For thick samples (about 10 mm thickness), we desired to perform the drying at a wellcontrolled temperature and without any solid support which could create a tangential stress affecting the sample's shrinkage. Thus, the drying was done in a hot glycerol which homogenizes rapidly the temperature and does not diffuse into the pores (and hence does not swell the matrix). A 50 mL vial was filled with dry glycerol and heated to the desired drying temperature. Next, the sample was immerged in the bath for 7 days. This time was enough for complete drying, as deduced from the fact that the relative weight loss reached an asymptotic value close to the initial water mass fraction, with the difference between the relative weight losses at the 7 th and 8 th days being less than 0.2 %. The initial porosity of the samples was calculated from the amount of water lost during drying. Similar values, very close to 30%, were obtained for specimens extracted from the top and from the bottom of the centrifugation tube. Thus, we concluded that centrifugation did not create measurable gradients in the volume fraction of the emulsion.

The density of dried samples was measured by using a home-made hydrostatic balance which measures the force necessary to immerge a sample in a liquid using a thin rigid wire. To increase the precision, we used several liquids including pure water and NaCl solutions with concentration ranging from 3 to 7 wt.%. The density was calculated using the balance of the forces acting on the immerged sample:

𝑚 𝑠𝑎𝑚𝑝𝑙𝑒 + ∆𝑚 𝑝𝑢𝑙𝑙 = 𝜌 𝑙𝑖𝑞𝑢𝑖𝑑 𝑉 𝑠𝑎𝑚𝑝𝑙𝑒 (2)
We thus infer:

∆𝑚 𝑝𝑢𝑙𝑙 𝑚 𝑠𝑎𝑚𝑝𝑙𝑒 = 𝜌 𝑙𝑖𝑞𝑢𝑖𝑑 𝜌 𝑠𝑎𝑚𝑝𝑙𝑒 -1 (3)
where msample, Vsample and ρsample = msample / Vsample are the mass, the volume, and the mass density of the sample, respectively; ρliquid is the mass density of the liquid and Δmpull is the difference between the mass measured when the sample is forcibly immerged in the liquid by plunging the thin rigid wire and the mass measured in absence of sample but when the thin rigid wire is plunged in an identical position. The sample density was obtained from an affine fit of the curve of Δmpull/msample as a function of ρliquid, since, as Eq. ( 3) shows, the slope of this fit must be equal to 1/ρliquid (the curves are given in the SI-1a). By using the same method, we measured the density of the PDMS matrix ρPDMS = 1034 kg/m 3 , which is slightly lower than the reported value [START_REF] Stricher | How I Met Your Elastomers: From Network Topology to Mechanical Behaviours of Conventional Silicone Materials[END_REF] of 1100 kg/m 3 . To calculate the sample porosity Φ = 𝑉 𝑝𝑜𝑟𝑒𝑠 𝑉 𝑠𝑎𝑚𝑝𝑙𝑒 ⁄ (where Vpores is the volume of pores in the sample), we used the following equation:

Φ = 100% * (1 - 𝜌 𝑠𝑎𝑚𝑝𝑙𝑒 𝜌 𝑃𝐷𝑀𝑆 ) (4)

Other characterizations

The microstructures of the obtained porous samples were characterized with a TM-1000 scanning electron microscope (Hitachi). Prior to imaging, the samples were fractured in liquid nitrogen, dried at 60°C and covered with a thin gold layer by vapor deposition. The observation was performed on the fractured surface.

Tensile loading measurements on parallelepipedal samples of about 30×5×0.5 mm were performed using an Instron 5565 apparatus. In the linear elastic regime, the dependence of the axial force F with the axial strain  was obtained and treated according to Hooke's law:

σ = 𝐸𝜀 (5)
where σ = F/S is the axial stress, S the initial cross-section area of the sample, and ε = (L-L0)/L0 with L0 and L the sample's length before and during the test, respectively.

Results and discussion

Structure and mechanical properties of the PDMS sponges

For both the synthesized samples with 5% and 30% of the dispersed water (or salt solution) phase, the porosity is closed. This is confirmed by the electronic microscopy images of the sample sections shown on Figure 1a andb. The fact that the pores are less spherical than on the optical microscopy images (see next sections) may be due to the cutting and drying-induced stresses. The closed porosity is formed because of the isolated droplet structure of the emulsion [START_REF] Kovalenko | Tailoring of the Porous Structure of Soft Emulsion-Templated Polymer Materials[END_REF] ; moreover, at 5% and 30% of porosity, the pore walls are rather thick and are not connected by macroscopic windows between them. Like in the case of a unique water-filled pore [START_REF] Milner | Creasing in Evaporation-Driven Cavity Collapse[END_REF] , the drying of such samples happens by pervaporation through PDMS and not by the invasion of the pore network by a liquid-vapor meniscus.

We also checked that macroscopic mechanical properties of water-filled porous samples are qualitatively similar to the non-porous PDMS, as confirmed by the stress-strain curves on Figure 1c, which exhibits curves with similar shape. The Young's modulus of the wet nonporous PDMS is about 1.6 MPa and decreases to 1.16 MPa and 0.98 MPa for water-saturated porous samples with porosities equal to 5% and 30 %, respectively. The decrease of modulus for the water-saturated porous samples with respect to the dry bulk PDMS may be explained by the presence of pores and by the influence of humidity on polymerization. The fact that the difference in modulus between the wet non-porous PDMS and any of the two water-saturated porous samples is larger than that between the two water-saturated porous samples suggests that, for our samples, the modulus is more significantly impacted by humidity than by the presence of pores. Water may hydrolyze some of the Si-H groups in the curing agent and decrease the degree of curing [START_REF] Harley | Thermodynamic Study on Dynamic Water Vapor Sorption in Sylgard-184[END_REF] . However, the effect is minor and should not drastically impact the interpretation of the results in next sections.

Visualization of the pore collapse and reopening

First, we performed a microscopic observation of drying for the sample D200-5 with 5% porosity and very polydisperse pore diameter distribution (red bars on Figure 2a andb). The corresponding optical microscopy image in the initial water-saturated state is given on Figure 2c. When counting by number, the distribution is centered at about 20 µm, however, the volume-weighted distribution obtained via eq 1 is centered at about 200 µm. The volumeweighted distribution is more relevant for the porosity Φ which is, by definition, the volume fraction of pores. The images on Figure 2d-f show the microscopy images of pores in the D200-5 sample when dried at 110°C. For a video-stack of drying images, see the SI-2. First, we observe a rapid shrinkage of small pores which seem to disappear (Figure 2d). The pores with larger diameters also decrease in volume and show a transition to a creased state, as observed for the central pore on the Figure 2e. We define the time of collapse as the moment when pores are non-detectable. For larger pores the dissolution time is longer. This may be explained with the diffusive model of the pore shrinkage proposed by Milner et al. [START_REF] Milner | Creasing in Evaporation-Driven Cavity Collapse[END_REF] and Bruning et al [START_REF] Bruning | Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks[END_REF] . In this model, the diameter of the pore scales with time t as 𝑑 = 𝑑 0 √1 -𝑘𝑡 𝑑 0 2 ⁄ where d0 is the initial diameter and the kinetic factor k is mainly governed by the diffusion coefficient and the difference between the water concentration ceq in PDMS near the pore and c∞ near the sample's edge. In absence of impurities (such as salt), the values of ceq and the diffusion coefficient depend only on temperature. The concentration c∞ on the sample's edge is determined by the relative humidity in the chamber. Hence, we may suppose the value of k to be similar for all pores. The dissolution time scales as 𝑡 𝑐𝑜𝑙𝑙𝑎𝑝𝑠𝑒 ~𝑑0 2 , which explains the fact that the small pores reach full shrinkage faster than the large pores. However, quantitative analysis of the porous sample would not be straightforward, because the model was developed for a single pore and does not include interaction between pores with different drying dynamics.

Some pores reopen via cavitation, giving pores of diameters similar to the initial ones and located at places similar to the initial ones (compare the final state on Figure 2f and the initial sate on Figure 2c). The reopened pores show a higher contrast than in the water-saturated state because of the difference of the optical index between PDMS and water vapor. On Figure 2a, the comparison between the diameter distribution of the reopened pores and that of the pores before drying shows that most pores with diameters lower than 30 µm remain collapsed while the majority of larger pores reopen. However, on the volume-weighted diameter distribution (Figure 2b), the contribution of the small pores is almost invisible, meaning that their collapse will not strongly affect the total pore volume and hence the porosity. The fact that the number of reopened pores with a diameter around 40-50 µm is higher than the number of pores observed before drying may be caused by the change of the transparency of the sample during drying, because of which deeper pores may become visible. Because of the small pore size, the optical microscopy doesn't allow to determine precisely the nature of the cavitation (liquid or "solid" one). The results of Bruning et al [START_REF] Bruning | Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks[END_REF] on millimeter-scale pores in PDMS demonstrate that the cavitation occurs in the water phase and the pore reopening happens about 0.1 ms after cavitation. We did not observe any correlation between different cavitation events: reopening happened some time after the complete shrinkage of a given pore, with no obvious trend.

For a second experiment, we chose the sample D10-5 which contains exclusively the small pores (Figure 3a) with an average diameter of about 10 µm (the diameter distribution was obtained from the image of a thin layer of the emulsion used for the synthesis given in the SI-1b). In this case, the imaging of pores is very challenging because of their small diameters and the change of the transmittance of the sample with time (see the video-stack of drying images in the SI-3). However, once the pores reopen, their detection is quite easy. Only pores that were located near the focus plane and that appeared as black spots were counted as reopened. First, we performed a drying at 60°C, far below the boiling point of water. The images show that most pores remain collapsed and invisible in the shrunk state while only few pores reopen (Figure 3b). In the present configuration of the microscope, the effective depth of field (DOF), i.e. the distance which allows simultaneous detection of the reopened pores, was roughly estimated by changing the focus distance as DOF ~ 200 µm. Taking the image with lateral dimensions H×W = 1200×900 µm 2 , we assumed that pores are spherical and calculated the volume of the reopened pores Vpores 60°C ≈ 3*10 5 µm 3 . The estimated porosity is therefore as Φ 60°C ≈ Vpores 60°C / (DOF*H*W) ≈ 0.15 %. This value is at least one order of magnitude lower than the initial porosity equal to 5%. This confirms that the majority of the pores collapsed and did not reopen. The number of reopened pores does not change after 30 min of drying for at least 16 hours (Figure 3c). The background on the image at 16 hours appears darker and less homogeneous because of the low light intensity used to acquire this image. We also give images of initial and dry states at higher magnification in SI-1c. The D10-5 sample dried for 16 hours at 60°C was next heated to 110°C, which is above the boiling temperature of water. Figure 4 and SI-4 show that heating leaded to reopening of another small fraction of pores. Following the same methodology as at 60°C, the final porosity at 110°C may be estimated at about 0.3%, which is well below the initial one. This analysis confirms that small pores remain shrunk at least until the end of the experiment.

Macroscopic porosity measurements

We compare the samples D70-30 and D300-30 which have similar initial porosity Φinit ≈ 30% and different pore sizes. Figure 5 shows the optical images of a cross-section of the samples.

The number-weighted distributions as well as some additional images are given in the SI-1d.

In contrast to the transparent samples with 5% of porosity (section 3.2), the samples are opaque and the observation of the pores is possible only near the cross-section plane. The probability of a pore to be found in the cross-section is inversely proportional to its diameter [START_REF] Cheng | Errors in the Measurement of Bubble Size Distribution in Foam[END_REF] and thus 𝑁 𝑖 ∝ 𝑁 𝑖 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 /𝑑 𝑖 , where Ni section are the numbers of pore of diameter 𝑑 𝑖 observed in the crosssection and 𝑁 𝑖 the number of the pores of diameter 𝑑 𝑖 in the sample. Consequently, the volume fraction 𝜑 𝑖 of pores of diameter 𝑑 𝑖 is given by: (6) . The obtained distributions are displayed in Figure 5c.

𝜑 𝑖 (𝑑 𝑖 ) = 𝑁 𝑖 𝑑 𝑖 3 ∑ 𝑁 𝑖 𝑑 𝑖 3 𝑖 = 𝑁 𝑖 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑑 𝑖 2 ∑ 𝑁 𝑖 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑑 𝑖 2 𝑖

Figure 5 -Optical microscopy images of a cross-section of D70-30 (a) and D300-30 (b) samples and the corresponding volume-weighted diameter distributions (c).

The data of the samples dried in a glycerol bath at 60°C or 110°C are presented on Figure 6a. For both temperatures, the drying loss (which is equal to the ratio between the total volume of evaporated water and the initial volume of the sample, and is therefore an estimate of the initial porosity) was about 30%. Next, we show the porosity values calculated from density data obtained using the hydrostatic balance. The D70-30 sample's porosity after drying is very low, slightly increasing with drying temperature from 0.5 to 3%. By contrast, the D300-30 sample shows the reopening of almost a half of the pores (by volume). Again, the porosity increases with the drying temperature. The difference between the two samples is demonstrated by the flotation test in water on Figure 6b: the porous D300-30 sample rapidly rises to the surface while the collapsed D70-30 sample sinks. Note that we did not detect any change in the porosity after several months of storage at room temperature.

Factors affecting probability of reopening

The results of microscopy (Section 3.2) and macroscopic density measurements (Section 3.3) confirm that the pores with larger diameters are more likely to cavitate and reopen than small pores. Because of the large pore size distribution, it is difficult to demonstrate the existence of a critical pore diameter above which pores would reopen and below which pores would not. Also, we may expect the cavitation to be probabilistic and to depend not only on the pore diameter but also on small deviations of the pore shape and on the proximity to the neighboring pores.

We repeated the drying several times on different pieces of the sample D200-5 at temperatures of 110°C and 90°C to obtain a statistically relevant measurement of the fraction of pores of a given diameter that reopen during drying. The results at 110°C are displayed in Figure 7. The results at 90°C are very similar and are given in the SI-1e. We observe that, mostly, the larger a pore, the more likely it is to reopen. We fitted a sigmoid function of the form 1/(1 + exp(-(𝑑 -𝑑 𝑐ℎ𝑎𝑟 )/𝑝)) to this experimental data, where 𝑑 𝑐ℎ𝑎𝑟 is a characteristic diameter and 𝑝 a characteristic standard deviation. A least-squares fit yielded 𝑑 𝑐ℎ𝑎𝑟 = 33.6 ± 3.5 µm and 𝑝 = 4.0 µm. Above dchar, the pores tend to reopen during drying, and below dchar they tend to remain closed during drying. A fit of the same function to the data at 90 °C yielded 𝑑 𝑐ℎ𝑎𝑟 = 26.0 ± 2.0 µm and 𝑝 = 5.1 µm. We now perform some hypothesis testing, by assuming that, in samples D300-30 and D70-30, the likelihood for a pore of a given diameter to reopen during drying at 110°C is the same as for sample D200-5 and is therefore given by the sigmoid function F(di) displayed in Figure 7. We use the number-weighted distribution of pore diameters displayed in SI-1d, obtained from the cross-sections of the samples D300-30 and D70-30. Similarly to the derivation of the eq. 6, the probability of the pores to be found in the cross-section is inversely proportional to the pore diameter. Once all pores likely to reopen by cavitation have reopened, the number of reopened pores of diameter di must be equal to 𝐹(𝑑 𝑖 )𝑁 𝑖 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 , so that we can estimate the porosity Φ 𝑟𝑒𝑜𝑝𝑒𝑛 that samples should have recovered during drying:

Φ 𝑟𝑒𝑜𝑝𝑒𝑛 = Φ 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ∑ 𝐹(𝑑 𝑖 )𝑁 𝑖 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑑 𝑖 2 𝑖 ∑ 𝑁 𝑖 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑑 𝑖 2 𝑖 (7)
The initial porosity of both samples D300-30 and D70-30 was Φ 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 30%. With Eq. ( 7), we estimate that, after drying at 110°C, the porosity of those 2 samples should be Φ 𝑟𝑒𝑜𝑝𝑒𝑛 = 26% and Φ 𝑟𝑒𝑜𝑝𝑒𝑛 = 19%, respectively, while results displayed in Figure 6a show that the porosities of those 2 samples are only 3% and 17%, respectively. Therefore, we can conclude that the probability for pores to reopen after drying at 110°C is not the same for samples D300-30 and D70-30 as for sample D200-5. Consequently, this probability must not depend on the pore diameter only, but could depend also in particular on the porosity, since the initial porosity Φ 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 is the main difference between samples D300-30 and D200-5.

We now assume that, like for sample D200-5, there exists for samples D300-30 and D70-30 a characteristic size 𝑑 𝑐ℎ𝑎𝑟 𝐷300-30 and 𝑑 𝑐ℎ𝑎𝑟 𝐷70-30 , respectively, above which pores tend to reopen during drying, and below which pores tend to remain closed during drying. Using Eq. ( 7) and the data for pore diameter distributions for samples D300-30 and D70-30, we find that correct predictions of the porosity after drying are obtained for 𝑑 𝑐ℎ𝑎𝑟 𝐷300-30 ~100 -120 µm and 𝑑 𝑐ℎ𝑎𝑟 𝐷70-30 ~100 -120 µm. This characteristic size is quite similar for samples D300-30 and D70-30 and therefore seems to not be impacted much by the mean diameter of the pores in the sample. This characteristic size is much larger than the one measured on sample D300-5, namely 34 µm. Consequently, we infer that the characteristic size (separating the larger pores that tend to reopen during drying from the smaller ones that tend to remain closed during this same drying) depends, for a given temperature of drying, on the porosity. Note that it could also depend on the mechanical properties of the solid skeleton or on the size of the sample (which impacts the kinetics of drying). The dependence of the characteristic size on the porosity may be due to the fact that the effective elastic modulus of the medium decreases with an increasing porosity. Indeed, we previously observed 9 a strong effect of porosity on the modulus of airfilled porous PDMS, i.e. a decrease by factor ~3 of the modulus of a sample with Φ = 30% with respect to the non-porous one * . We thus may hypothesize that after reopening of one part of the porosity in the samples D300-30 and D70-30, pores that are still collapsed behave as if they are surrounded by an effective medium with much lower mechanical modulus, and hence the likelihood for those still-collapsed pores to reopen is significantly decreased. It is therefore possible that the characteristic size depends on the porosity as a consequence of its dependence on the elastic modulus of the medium.

Our observations do not allow to establish the mechanism of pore collapse and reopening. In accordance with the paper of Bruning et al. [START_REF] Bruning | Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks[END_REF] , we may expect that the condition necessary for cavitation in a water-filled pore should be that the (negative) pressure reaches a threshold value of about -1.5 MPa. The existence of such threshold value, which is independent of the size of the pore, does not explain directly the pore size-dependence of the pore reopening that we observed. However, since cavitation of water is a probabilistic process, one could argue that cavitation is likelier to happen in larger pores (which contain a larger amount of water) than in smaller pores, which would be in agreement with our experimental observations. The fact that the likelihood of cavitation increases with temperature [START_REF] Vincent | Drying by Cavitation and Poroelastic Relaxations in Porous Media with Macroscopic Pores Connected by Nanoscale Throats[END_REF] would also be in agreement with our experimental observations. The second condition for pore reopening is that the tensile stresses that prevail at the location of the collapsed pore after cavitation of the fluid it contains has occurred should be high enough to allow the pore to reopen, akin to what is observed for "solid" cavitation (following the denomination that we used in the introduction). For small pores with d < 0.1 µm, the threshold tensile stress [START_REF] Gent | Surface Energy Effects for Small Holes or Particles in Elastomers[END_REF][START_REF] Dollhofer | Surface Energy Effects for Cavity Growth and Nucleation in an Incompressible Neo-Hookean Material--Modeling and Experiment[END_REF] for the growth of the pore may be much higher (in absolute value) than the Young's modulus E = 1.6 MPa (which provides an order of magnitude of the tensile stresses that must prevail at the location of the collapsed pore). If we assume that the cavitation takes place in water inside pores after they shrink to a diameter d < 0.1 µm, the surface energy may prevent the pore from the reopening after the cavitation occurred. This would explain the dependence of the cavitation on the pore diameter. However, it is difficult to directly correlate the size and shape of an initially spherical pore in a highly deformed state with its initial size.

Drying in presence of NaCl

In this section, we present microscopy observations during drying of samples which contain a NaCl salt solution inside pores. Due to its hydrophobic nature, the PDMS is impermeable to the salt [START_REF] Naeimi | Novel PDMS-Based Membranes: Sodium Chloride and Glucose Permeability[END_REF] . Thus, drying leads to the concentration of the NaCl solution and crystallization of salt inside pores. The general image of drying is similar to the case without salt. However, a detailed investigation of the pore reopening shows the presence of cooperative effects. No cavitation is observed during the first 6 minutes of drying. Next, a cluster of pores reopens simultaneously in the area labeled "a" (Figure 8c). In the following 6 minutes, no new cavitation events happen. Next, a new cluster reopens simultaneously in the area labeled "b" (Figure 8d). Similar qualitative features are observed for sample D50-5NaCl (whose pores are smaller than for sample D300-5NaCl and filled with 3.65% NaCl solution), for which results are presented on Figure 9. Again, the pore reopening happens by clusters of pores (see also SI-6 and SI-1f). Interestingly, in the center of clusters we observe the largest pores and the diameter of the cluster is about 2-3 times the diameter of these largest pores. Figure 10a displays the diameter of some pores in the cluster "b" from Figure 8 versus the drying time. After creasing of the pore surface, we are not able anymore to measure a pore diameter; however, the times at which reopening occurs (which is indicated with star symbols on the figure) are clearly detected due to a good contrast of the vapor-filled pores. The dashed lines on Figure 10 are a linear extrapolation of the diameter evolution after creasing. While the collapse of small pores ("b2", "b3" and "b4") is expected to occur earlier than that of the large one ("b1"), we observe simultaneous reopening at about 900 s. Therefore, the reopening seems to be limited by the full shrinkage of the largest pore "b1". To better visualize this effect, we compare the reopening event statistics of samples D200-5 and D50-5NaCl on Figure 10b and 10c. Both samples contain statistically significant number of pores with diameters in the 10-100 µm range. The vertical bars correspond to the number of reopened pores between two imaging frames (about 10 s). Red bars show the events including at least one "large" pore with diameter > 50 µm. The comparison shows that in case of D200-5, many small pores reopen (black bars) independently of the large ones while in case of D50-5NaCl, most pores reopen simultaneously with the largest ones, i.e. are included in red bars. We attribute this difference to the osmotic pressure effect discussed in the following section.

Discussion on the physical origin of the cooperative pore reopening

In this section, we discuss why a cooperative pore reopening is observed in the samples whose pore solution contains NaCl. We will consider 2 factors successively: 1) osmotic pressure effects which slow the dissolution of small pores surrounding a large one; and 2) mechanical shocks caused by cavitation of a large pore that provoke the reopening of a cluster of pores.

We consider a large spherical pore "LP" of radius 𝑅 displayed in Figure 11a surrounded by a spherical shell of PDMS, which itself is surrounded by a "dry" air. The shell also contains a small pore "SP". In presence of salt, in any pore, the drying leads to an increase of the concentration C(NaCl) in salt in the pore which is inversely proportional to the volume V(t) of this pore, as: 𝐶(NaCl) = 𝐶 0 (NaCl) • 𝑉 0 /𝑉(𝑡) where C0(NaCl) and V0 are the salt concentration and pore volume in the initial state.

As mentioned in section 3.2, in a diffusion-limited model of pore collapse, the time to full collapse of an individual pore scales with the square of the pore diameter. Hence, a smaller pore should collapse faster than a larger pore. However, this is only expected to be true if we neglect flow of water between neighboring pores: indeed, if a small pore is very close to a large pore, flow of water from the large pore to the small pore is expected to significantly slow down the collapse of the small pore. In contrast, if the small pore is closer to the outer edge of the shell, the impact of the large pore on the kinetics of collapse of the small pore is expected to be more limited. In the next paragraphs, we aim at estimating a characteristic length 𝐿 𝑜𝑠𝑚 of influence of the large pore. We define this length of influence as the distance to a large pore below which, because of the presence of the large pore, the salt concentration in the small pore cannot become larger than the solubility.

At first, we calculate the water concentration distribution that would prevail in the PDMS around the large pore if the shell around the large pore contained no small pore. The thickness of the shell is noted Ldry and its diffusion coefficient (expressed in m 2 .s -1 ) is noted 𝐷. If we associate a spherical system of coordinates to the large pore with 𝑟 the radial coordinate, the concentration 𝑐 of water in the PDMS shell verifies: 𝑐(𝑅) = 𝑐 1 and 𝑐(𝑅 + 𝐿 𝑑𝑟𝑦 ) = 𝑐 2 . The concentrations c1 and c2 are equilibrium water concentrations in PDMS at water activities 𝑎 𝑤 𝐿𝑃 and 𝑎 𝑤 𝑜𝑢𝑡 , respectively, where 𝑎 𝑤 𝐿𝑃 is the water activity inside the large pore "LP", and 𝑎 𝑤 𝑜𝑢𝑡 is the water activity outside. We assume ideality of the solution, such that 𝑐 1 = 𝑘 𝐷 * 𝑎 𝑤 𝑆𝑃 and 𝑐 2 = 𝑘 𝐷 * 𝑎 𝑤 𝑜𝑢𝑡 , where 𝑘 𝐷 is a Henry's-type constant. For first-order estimations, literature data [START_REF] Harley | Thermodynamic Study on Dynamic Water Vapor Sorption in Sylgard-184[END_REF] show that this assumption is reasonable.

The flow of water through the PDMS shell verifies Fick's law 𝑗 = -𝐷∇𝑐, where 𝑗 (expressed in mol.m -2 .s -1 ) is the diffusion flux. Combined with the mass balance, Fick's law yields the classical diffusion equation: 𝜕𝑐/𝜕𝑡 = 𝐷Δ𝑐. We estimate the flow by considering that a steadystate has been reached, from which follows that Δ𝑐 = 0. Solving this equation with the abovementioned boundary conditions yields:

𝑐(𝑟) = 𝑅 • (𝑅 + 𝐿 𝑑𝑟𝑦 ) 𝐿 𝑑𝑟𝑦 • 𝑐 1 -𝑐 2 𝑟 + 1 𝐿 𝑑𝑟𝑦 (𝑐 2 • (𝑅 + 𝐿 𝑑𝑟𝑦 ) -𝑐 1 • 𝑅) (8)
As our drying was performed in dry air (𝑎 𝑤 𝑜𝑢𝑡 ≈ 0), we may assume 𝑐 2 ≈ 0, which gives:

𝑐(𝑟) = 𝑐 1 • 𝑅 𝐿 𝑑𝑟𝑦 • ( 𝑅 + 𝐿 𝑑𝑟𝑦 𝑟 -1) (9)
Now, we consider that a small pore "SP" is located in the shell at the characteristic distance Losm from the surface of the large pore "LP", and that the salt concentration in this small pore is at solubility. The water activity in this small pore is noted 𝑎 𝑤 𝑆𝑃 . With the definition of the characteristic distance Losm that we introduced, the small pore must be in thermodynamic equilibrium with the surrounding PDMS.

We assume that the size of the small pore is negligible and that the water concentration distribution in the PDMS in the vicinity of the small pore is determined by the large pore and may be found using Eq. ( 9), for r = R + Losm: We consider that the NaCl concentration in the small pore reached its solubility: its concentration 𝐶 𝑤𝑡 in g per g of solution is 27 wt%. The NaCl concentration in the large pore is taken to be the one prevailing in sample D300-5NaCl initially, which is equal to 1. and its approximate version 11a give Losm = 14.5 µm and Losm = 21.6 µm, respectively. If the small pore "SP" is at a distance larger than 𝐿 𝑜𝑠𝑚 from the large pore "LP", it can further shrink. But, in contrast, if it is at a distance smaller than 𝐿 𝑜𝑠𝑚 from the large pore "LP", the small pore "SP" will in rather gain water and will not go on shrinking until the large pore has significantly shrunk.

𝑐(𝑅 + 𝐿 𝑜𝑠𝑚 ) = 𝑐 1 • 𝑅 𝐿 𝑑𝑟𝑦 • ( 𝐿 𝑑𝑟𝑦 -𝐿 𝑜𝑠𝑚 𝑅 + 𝐿 𝑜𝑠𝑚 ) (10
In presence of multiple large pores, as on Figure 9, the dissolution of small pores between those large pores will be strongly slowed down until the large pore reaches the solubility limit of NaCl, at which point the water in large and small pores will be roughly the same and all osmotic effects will have vanished. Until then, osmotic effects may keep the magnitude of the negative pressure in the small pores low enough (in absolute value) to prevent cavitation. Such mechanism can explain that, in presence of NaCl, very few small pores reopen before the neighboring large pore has shrunk and is prone to cavitation itself (see Figure 10c). In absence of NaCl, there is no osmotic effect between neighboring pores, such that small pores are less impacted by neighboring large pores and can cavitate before the neighboring large pore has itself shrunk (see Figure 10b).

Figure 11 -a) The model used to estimate the osmotic length Losm: a small spherical pore "SP" with high concentration of NaCl is located near a large spherical pore "LP" in a PDMS shell of thickness Ldry. 𝑎 𝑤 𝐿𝑃 and 𝑎 𝑤 𝑆𝑃 and 𝑎 𝑤 𝑜𝑢𝑡 are the activities of water in the large pore, small pore and outside medium, respectively; 𝑐 1 and 𝑐 2 design the water concentrations in PDMS near the large pore and near the border. The schematic is not drawn to scale, in the sense that the characteristic distance Ldry of the large pore to the edge of the sample is, for most pores, much larger than the size of the pore b) The corresponding schematic of the radial distribution of water activity in the shell, when neglecting the impact of the small pore "SP".

The second factor explaining the observation in section 3.5 of a simultaneous reopening of neighboring pores is based on the recent work of Doinikov et al. [START_REF] Doinikov | Cavitation in a Liquid-Filled Cavity Surrounded by an Elastic Medium: Intercoupling of Cavitation Events in Neighboring Cavities[END_REF] . These authors proposed a model which predicts that the cavitation in a fluid-filled pore under negative pressure may provoke a cavitation in the neighboring pore at the distance of the order of the pore radius. This effect is due to the mechanical shock produced by the cavitation, which may instantly increase the absolute value of the negative pressure inside the neighboring pore. As shown by Vincent et al. [START_REF] Vincent | Drying by Cavitation and Poroelastic Relaxations in Porous Media with Macroscopic Pores Connected by Nanoscale Throats[END_REF] for rigid water-filled pores, the cavitation is very sensitive to the pressure and even relatively small changes may strongly increase the cavitation probability.

In conclusion, we explain the observed cooperative pore reopening in presence of NaCl by two effects: the osmotic pressure which tends to equilibrate the negative pressure between the neighboring large and small pores; and the mechanical shock transmission from a pore in which cavitation occurs to its neighbors.

Conclusions

In this paper, we investigated the drying of water-filled PDMS sponges with 5% and 30% of closed porosity. In these materials, the drying may lead either to a collapsed state with low porosity or to the cavitation and reopening of a fraction of the pores. Using optical microscopy and porosity measurements, we showed the importance of the pore diameters and interactions on the result of drying. At pore diameters lower than 20 µm, the majority of pores remain collapsed. This is most likely due to the adhesion of the pore walls and low probability of the cavitation in a pore with a small volume. Pores with diameters larger than 100 µm tend to reopen after the fluid they contain cavitates. The behavior of pores with diameters ranging from 20 to 100 µm depends on the porosity and drying temperature. In the last sections, we showed evidence of cooperative pore reopening in samples containing NaCl solution inside their pores. We explained this effect by the action of osmotic pressure and the transmission of mechanical shock from a pore in which cavitation occurs to its neighbors.

Our results show the complexity of the drying process for highly deformable materials such as elastomer sponges. Many open questions remain including whether small amounts of water are still present inside the collapsed pores or not, or what the role of adhesion and mechanical damage of the elastomer matrix on the collapse/reopening process is. To better understand the influence of pore sizes, one needs experiments on monodisperse sponges [START_REF] Giustiniani | Generation of Silicone Poly-HIPEs with Controlled Pore Sizes via Reactive Emulsion Stabilization[END_REF][START_REF] Wang | Macroporous Materials: Microfluidic Fabrication, Functionalization and Applications[END_REF] with controllable diameter distributions and porosities. We did not explore porosities larger than 30%, for which we may expect stronger cooperative effects between pores and the existence of collective buckling modes similar to those observed for polymer foams [START_REF] Gibson | The Mechanics of Three-Dimensional Cellular Materials[END_REF] .

Author Information

Corresponding author: * E-mail: artem.kovalenko@espci.fr Notes : The authors declare no competing financial interest.

Figure 1 -

 1 Figure 1a) and b) Scanning electron microscopy images of sections of the sample D200-5 with 5% porosity (a) and sample D70-30 with 30% porosity (b). c) Stress-strain curves of the same samples in wet state in comparison with a non-porous PDMS "swollen" in water at 60°C for 6 hours (red curve).For each type of porous sample, the measurement was performed on 3 samples.

Figure 2 -

 2 Figure 2a) and b) Distributions of pore diameters in the D200-5 sample obtained for initial, water-filled pores (red) and pores reopened via cavitation (semi-transparent green); c-f) optical microscopy images of the D200-5 sample during drying at 110°C. The overlap of the pore diameter distributions between water-filled and reopened pores appears as brown.

Figure 3 -

 3 Figure 3 -Optical microscopy images of the D10-5 sample during drying at 60°C: a) initial state (small pores are poorly visible); b) state after 16 min of drying; c) state after 16 hours of drying. The insert on the image a) shows the pore diameter distribution in the initial state. Some clearly identified pores are labeled with numbers.

Figure 4 -

 4 Figure 4 -Optical microscopy images of the same area in the sample D10-5 before (a) and after (b) increasing of the drying temperature from 60°C to 110°C.

Figure 6 -

 6 Figure 6a) Characteristics of the dried thick samples with different pore sizes; b) a photograph of the dried samples demonstrating flotation (D300-30) and sinking (D70-30) in pure water.

Figure 7 -

 7 Figure 7 -Fraction of pores in sample D200-5 that reopened after drying at 110°C. The data are obtained by adding results on 4 specimens. The parameters of the fitted sigmoidal function are 𝑑 𝑐ℎ𝑎𝑟 = 33.6 ± 3.5 µm and 𝑝 = 4.0 µm. The error bars are obtained as 1/√𝑁 𝑖 , where 𝑁 𝑖 are the numbers of pores of diameter 𝑑 𝑖 filled with water. The error on the fitted value of 𝑑 𝑐ℎ𝑎𝑟 is estimated by finding out the extreme values of 𝑑 𝑐ℎ𝑎𝑟 that make it still possible for the fitted sigmoid to remain in the experimental uncertainty.

Figure 8 -

 8 Figure 8 -Optical microscopy images of different drying stages of porous PDMS sample with 5% porosity at 110°C. Symbols a1-a3 and b1-b4 mark similar pores in zones a and b, respectively, before and after cavitation.

Figure 8

 8 Figure8shows the optical images of the sample D300-5NaCl in which the pores are filled with a 1.5% wt. NaCl solution. For a video-stack of drying images, see the SI-5. The drying was performed at 110°C. At first, the pores shrink (Figure8a and b), similarly to what was observed without salt (Figure2c-f). No cavitation is observed during the first 6 minutes of drying. Next, a cluster of pores reopens simultaneously in the area labeled "a" (Figure8c). In the following 6 minutes, no new cavitation events happen. Next, a new cluster reopens simultaneously in the area labeled "b" (Figure8d). Similar qualitative features are observed for sample D50-5NaCl (whose pores are smaller than for sample D300-5NaCl and filled with 3.65% NaCl solution), for which results are presented on Figure9. Again, the pore reopening happens by clusters of pores (see also SI-6 and SI-1f). Interestingly, in the center of clusters we observe the largest pores and the diameter of the cluster is about 2-3 times the diameter of these largest pores.

Figure 9 -

 9 Figure 9 -Optical microscopy images showing the reopening pore clusters during drying of the sample D50-5NaCl at 110°C.

Figure 10 -

 10 Figure 10a) Evolution of the pore diameter before (filled symbols) and after cavitation (open symbols) for the pores from cluster "b" on Figure 8. The points represent the data obtained when the pores had a well-defined ellipsoidal shape and were located close to the focal plane of the microscope. The supposed evolution of pore diameters after creasing instability or after eventual displacement out of the focus are represented by dashed lines to guide the eye. The moments at which reopening occurs are indicated with the star symbol. b-c) Number of cavitation events as a function of drying time at 110°C for samples D200-5 (b) and D50-5NaCl (c). The red bars correspond to reopening events of at least one pore with diameter > 50 µm.

Table 1 -

 1 Characteristics and drying investigation methods of the fabricated sponges

	Sample	Initial	Stirring	Volume-	Aqueous	Optical	Porosity
	name	porosity	speed	weighted	phase	microscopy	measurements
				mean pore		(thin samples)	(thick samples)
				diameter
	D200-5	5%	375 rpm	200 µm	MiliQ water	+	-
	D10-5	5%	1500 rpm	10 µm	MiliQ water	+	-
	D300-5NaCl	5%	375 rpm	300 µm	1.5% NaCl	+	-
	D50-5NaCl	5%	800 rpm	50 µm	3.65% NaCl	+	-
	D300-30	30%	200 rpm	300 µm	MiliQ water	-	+
	D70-30	30%	375 rpm	70 µm	MiliQ water	-	+

)

  After taking 𝑐(𝑅 + 𝐿 𝑜𝑠𝑚 ) = 𝑘 𝐷 * 𝑎 𝑤 𝑆𝑃 and 𝑐 1 = 𝑘 𝐷 * 𝑎 𝑤 𝐿𝑃 , we obtain the equation for Losm: Equation 11 may be simplified if R << Ldry, which is a strong but reasonable assumption for pores with R ~ 100 µm observed in depth of a rectangular sample with dimensions 10 mm × 10 mm × 0.5 mm (i.e. Ldry ~ 250 µm):

	𝐿 𝑜𝑠𝑚 ≈ 𝑅 ( 𝑎 𝑤 𝐿𝑃 𝑎 𝑤 𝑆𝑃 -1) (11𝑎)
	𝐿 𝑜𝑠𝑚 = (	𝑅 𝑆𝑃 + 𝑎 𝑤 𝐿𝑃 𝑅 𝐿 𝑑𝑟𝑦 𝑎 𝑤 ⁄	) (𝑎 𝑤 𝐿𝑃 -𝑎 𝑤 𝑆𝑃 ) (11)

  5 wt%. Since, assuming ideality, the water activity 𝑎 𝑤 verifies 𝑎 𝑤 = (1 -𝐶 𝑤𝑡 )/(1 -𝐶 𝑤𝑡 + 2 * 𝐶 𝑤𝑡 * 𝑀 𝐻 2 0 /𝑀 𝑁𝑎𝐶𝑙 ), where 𝑀 H 2 0 = 18.0 g.mol -1 and 𝑀 NaCl = 58.4 g.mol -1 are the molar mass of water and NaCl, respectively, the water activities corresponding to those concentrations are 𝑎 𝑤 𝑆𝑃 = 0.81 and 𝑎 𝑤 𝐿𝑃 = 0.99. The application of equation 11 (for 𝑅 = 100 µm and 𝐿 𝑑𝑟𝑦 = 250 µm)

* In the present manuscript, we measured a Young's modulus of wet samples with Φ = 30% which is only slightly lower than that of wet samples with Φ = 5% (0.98 MPa and 1.16 MPa, respectively), but such low effect of the porosity is due to the fact that, in our experiments, pores are filled with liquid water, whose bulk stiffness is very high (i.e. around 2 GPa).

Acknowledgments

We thank Andrea Aguiar for her help in formulation of the samples, Ludovic Olanier for help with the fabrication of the hydrostatic balance and Etienne Barthel for fruitful discussions. We also thank the DIM Respore ( http://www.respore.fr/ ) for having given the last 2 authors the opportunity to meet.


Yoann Farré

Federica Maschietto

Jens Föhlinger

Mike Wykes

Aurélien Planchat

Yann Pellegrin

Errol Blart

Ilaria Ciofini
email: ilaria.ciofini@chimie-paristech.fr

Leif Hammarström
email: leif.hammarstrom@kemi.uu.se

Fabrice Odobel
email: fabrice.odobel@univ-nantes.fr

A comparative investigation of the role of anchoring group on perylene monoimide dyes in NiO based dye-sensitized solar cells

The anchoring group of a sensitizer may strongly affect the overall properties and stability of the resulting dye sensitized solar cells (DSSCs) and dye sensitized photoelectrosynthetic solar cells (DSPECs). This article describes a comprehensive study of the properties of seven perylene monoimide dyes (PMI) for their immobilization on nanocrystalline NiO film. The PMI dyes differ only by the nature of the anchoring group, which are: carboxylic acid (PMI-CO 2 H), phosphonic acid (PMI-PO 3 H 2 ), acetyl acetone (PMI-acac), pyridine (PMI-Py), aniline (PMI-NH 2 ), hydroxyquinoline (PMI-HQ), and dipicolic acid (PMI-DPA). The dyes were investigated by cyclic voltammetry, spectroelectrochemistry, modeled by DT-DFT quantum chemical calculations. The mode of binding of these anchoring groups was investigated by infrared spectroscopy and the stability of the binding to NiO surface was studied by desorption experiments in acidic and basic media. Overall, we found that phosphonic acid group offers the strongest binding to NiO surface in terms of stability and dye loading. Finally, a photophysical study by ultrafast transient absorption spectroscopy shows that all dyes inject a hole in NiO with rate constants on a subpicosecond timescale and display similar charge recombination kinetics. The photovoltaic properties of the dyes show that PMI-HQ and PMI-acac gave the highest photovoltaic performances due to lower degree of aggregation on the surface. PMI-NH 2 0.83 -0.93 1.21 -0.91 -0.61 -1.

Introduction

NiO based dye-sensitized photocathodes have enjoyed a rising popularity in the scientific community because they are the key component of tandem dye sensitized solar cells (DSSCs) [1][2][3] and dye sensitized photoelectrosynthetic solar cells (DSPECs). [4-6] [7-8] These devices rely on chemically bound molecular components (sensitizers, or sensitizer + catalysts) to a NiO mesoporous electrode. [9] In DSPECS, the catalyst can be either covalently connected to the dye or co-adsorbed on the NiO surface. The primary role of the sensitizer is to absorb light and inject a hole in the valence band of NiO with the highest quantum yield upon photoexcitation. [10][11] This requirement demands a significant electronic coupling between the dye excited state and the valence band manifold. On the other hand, the catalyst must accumulate reductive equivalents and catalyze the reduction of substrates in solution before charge recombination takes place. This function requires slow charge recombination rate constant and consequently a weak electronic interaction between the injected holes in NiO and the reduced catalyst. Accordingly, the dye and the catalyst require different connectors if they are to be co-adsorbed on the surface. However, both dyes and catalysts must remain strongly attached to the NiO surface to sustain long operation lifespan. This condition is quite satisfyingly met in DSSCs, while it still remains an important challenge to solve in DSPECs, because the latter usually operate in harsher conditions than DSSC, most often in aqueous acidic or basic media. Thus, the anchoring group represents a very important factor to consider for the optimal design of sensitizers and dye/catalyst for NiO based DSSCs or DSPECs, because it controls both the electronic coupling and the stability of the anchored molecules on the NiO surface. The impact of different anchoring groups in TiO 2 based photoanodes has been quite thoroughly investigated, [12][13] although many of these studies are rather recent if one considers the large amount of work undertaken on Grätzel cells since 1991. [14][15] The development of NiO based photocathodes has been much less explored than the TiO 2 based photoanodes, therefore it is unsurprising that there are few studies of the role of the anchoring group on NiO dyes, for which carboxylic acid remains the most used one. [9] However, the electronic properties of the optimal binding group for NiO are certainly different as those for TiO 2 based photoanodes, because NiO is a p-type semiconductor and is composed of Ni(II) cation which is a weaker Lewis acid than Ti(IV) in TiO 2 . For a fast hole injection into the NiO valence band, the HOMO of the dye must mix with the valence band, which implies that the anchoring group orbitals must give a significant contribution to the HOMO. This is the opposite situation for TiO 2 sensitizers, which must be composed of electron deficient anchoring groups on which the LUMO should be delocalized. [16] We have investigated the replacement of carboxylic acid by catechol, [17] carbodithioic acid, [17] phosphonic acid, [17] acetyl acetone (acac), [18] silyl [19] and other teams have investigated pyridine, [20][21][22] di(carboxylic acid)pyrrole, [23][24] hydroxamic acid, [25] and di(carboxylic acid)triazole [26] as alternative anchoring groups for NiO photocathodes. Owing to the scarcity of systematic studies on NiO anchoring groups, we have been interested to investigate the properties of a series of dyes that differ only by the nature of the anchoring group (Chart).

Chart. Structures of the PMI dyes investigated in this study.

As dye for this study, perylene monoimide (PMI) was chosen as an ideal candidate for this study because previous work has shown that it is an effective NiO sensitizer and the radical anion displays a characteristic absorption band, which makes it easy to detect by transient absorption spectroscopy. [27][28] In this work, we prepared and investigated PMI dyes connected to seven different anchoring groups via an ethynyl spacer in order to promote electronic interaction of the -aromatic system of PMI with the anchoring group (Chart). The

Results and discussion

The synthesis and characterization of the dyes, preparation and sensitization of the NiO films and experimental methods are described in the Supporting Information.

Electronic UV-visible absorption and emission spectroscopy

First, the absorption and emission spectra of the all dyes were recorded in DMF solution at room temperature (Figures 1 and2). The spectroscopic data including wavelengths of maximum absorption wavelength ( abs ), extinction coefficient (),maximal emission wavelength ( em ) and the zero-zero energy level of the lowest singlet excited state (E 00 ) are collected in Table 1. shifted absorption band compared to the above dyes. This is attributed to the electron donating effect of the aniline and phenol groups that destabilize the HOMO level and consequently lower the optical gap and also leads to a charge transfer character of the optical absorption in which the PMI acts as an electron accepting unit (Figures 1 and2). This is also supported by DFT calculations (see below). Consequently, these two dyes display a broader absorption spectral coverage than the others. Moreover, all these PMI dyes exhibit a strong fluorescence band with a maximum emission located at 560-600 nm. From the absorption and emission spectra, we derive a singlet excited state energy (E 00 ) of about 2.2 eV (Figures 1&2 and Table 1). The absorption spectra of these PMI dyes were then investigated after chemisorption on thin NiO films (Figure 3). All dyes, except PMI-Py and PMI-NH 2 , turn the initially greyish NiO film into a reddish film after soaking the electrode into a DMF solution of these dyes.

Contrary to our expectation, the aniline and pyridyl groups do not show strong affinity to NiO surface, in spite of the fact that some previous reports showed that they could bind to some metal oxides, including NiO for pyridine. [20][21][22] The electron withdrawing effect of PMI might decrease the electron density on these amines and consequently diminish their ability to coordinate to nickel. Interestingly, the visible absorption band is blue-shifted and the intensity ratio of the vibronic peaks (between 450 and 550 nm) is inverted with respect to those in solution (Figures 12and S2 and Table 1). These characteristics are clear indications of the formation of H-type aggregates on NiO surface and is due to excitonic interaction between stacked chromophores. [29][30][31] Finally, the dye loading of these PMI dyes on NiO was determined by desorption experiments. Towards this end, we have not used the classical strategy consisting of soaking the NiO electrodes into a basic solution of hydroxyde, because PMI dyes are not fully stable under such conditions. Instead, the PMIs were cleanly and quickly desorbed from the NiO surface by a DMF solution of phenyl phosphonic acid which acts as a competing ligand. [32] The average values of dye loadings were determined from three independent runs and they are indicated in Figure 4. Phosphonic acid is undoubtedly the strongest binding group, then comes dipicolinic acid closely followed by carboxylic acid and finally hydroxyquinoline and acac, which gave the lowest loading on NiO. The dye loading and the stability of the linkage on NiO (see below)

are strongly related to the pKa of the anchor group, with the usual observation that strongly acidic binding groups displays higher affinity to the metal oxide surface. [12][13] Electrochemistry, spectroelectrochemistry and calculations of the charge transfer driving forces

These dyes were studied by cyclic voltammetry to determine the potentials for their first reduction and oxidation, as well as to calculate the hole injection (G°i nj ) and dye regeneration (G°r eg ) driving forces with iodine and tetrazole-thiol (T 2 /T -) based electrolytes (Table 2 and Figure S1 for the structures of T 2 /T -).

All the PMI dyes show similar behavior in cyclic voltammetry. For each dye, one reversible reduction process occurs at -0.9 V vs. SCE corresponding to the addition of an electron on the PMI unit. Conversely, in the anodic region, the PMI core is oxidized at around 1.1 -1.2 V vs.

SCE with a non-reversible wave for the dyes PMI-CO 2 H, PMI-acac, PMI-Py, PMI-DPA

and PMI-PO 3 H 2 . For the dyes PMI-NH 2 and PMI-HQ the first oxidation is cathodically shifted by circa 300 mV relative to the others PMI dyes reflecting the electron donating effect of the electron rich anchoring group (destabilization of the HOMO level) consistent with the spectroscopic properties.

The Gibbs free energies of hole injection into the NiO valence band after excitation of the dye and that of the regeneration reaction with iodine or tetrazole thiol based electrolytes indicate that all PMI dyes display sufficient exergonicity, by a large margin, for the charge transfer processes to spontaneously occur (Table 2). SCE. [33] c Calculated according to the equation: [34] d Calculated according to the equation: [35] The spectra of the radical anions of PMI-CO induces an important spectral change, which is accompanied by a bleach of the ground state absorption between 450-600 nm and the formation of a new band between 600-750 nm, which peaks at 654 nm. These changes are in perfect agreement with those measured with similar PMI dyes reported in the literature. [27][28] The same experiment run with PMI-HQ yields similar spectral changes except that the spectrum of the radical anion is broader and is stronger in the lower energy part of the visible spectrum ( max = 656 nm; Figure 5) as was also the case for the spectrum of the neutral dye above.

G reg = E Red (PMI/PMI -) -E(I 3 - /I 2 -• ) with E(I 3 - /I 2 -• ) = -0.32 V vs. SCE.
G reg = E Red (PMI/PMI -) - E(T 2 /T -) with E(T 2 /T -) = 0.25 V vs. SCE.

Binding mode of the anchoring group on NiO studied by infrared spectroscopy

Characterization of the dye binding modes on the NiO surface was made by FTIR spectroscopy, as there is extensive information available on the position of vibrational transitions of these anchoring groups on TiO 2 [12][13] but fewer on NiO. [18,20,[36][37] To interpret the data, we have compared the FTIR spectra of the bare NiO with those of the dye in KBr pressed disc and the dye grafted on NiO in order to determine the band shifts and disappearances (Figures S1-S5). Figure 6 summarizes the binding mode of each dye deduced from the analysis of the FTIR spectra. First, the spectrum of bare NiO displays two broad bands: a weak one at 1631 cm -1 attributed to the bending vibration mode of hydroxyl groups on the NiO surface [START_REF] Porta | C ianchi Confalonieri car[END_REF] and the more intense one at 1346 cm -1 assigned to the presence of adsorbed carbonate probably due to residual contaminants on the surface or coming from carbonization of the NiO paste used for screen printing. [39] Second, the intense C=O stretching band of the bisimide group, located at 1709 cm -1 is observed on the IR spectra of all the PMI dyes without any modification before and after grafting on NiO. Naturally, this moiety is not involved in the binding with NiO, but bear witness of the presence of dye attached to the NiO surface.

Starting with PMI-CO 2 H, after binding to NiO, the carboxylic C=O stretching band seen in KBr as a shoulder at 1727 cm -1 disappears upon binding on NiO. A new band appears at 1380 cm -1 , which is attributed to the symmetric stretching of O-C-O (Figure S3). The difference in wavenumber between the asymmetric and symmetric stretching of O-C-O is generally used as a diagnostic tool to determine the binding mode of CO 2 H. [40][41] Unfortunately, the asymmetric stretch of O-C-O, which is known to show up between 1610 cm -1 and 1650 cm -1 , [40,[42][43] cannot be distinguished here because this region overlaps with the NiO vibration modes of hydroxyl groups. Although, we can confidently conclude that the PMI dye is coordinatively bound via its carboxylic acid group and exclude the monodentate ester like binding, it is impossible to safely determine if it is a bidentate chelating or bidentate bridging mode (Figure 6). The IR spectrum of PMI-PO 3 H 2 is also very rich of information owing to the numerous vibrational modes on the phosphonic acid resonator (Figure S4). After binding, the P=O stretching band at 1210 cm -1 is not modified and is still intensely present, while the P-OH stretching bands between 925-940 cm -1 disappears and a new band appears at 968 cm -1 . [44][45][46][47] This suggests that P=O is not involved in the binding, but the two P-OH group are deprotonated and chelated to nickel, giving a bidentate binding mode as usually observed. [12] The interpretation of the IR spectrum of PMI-HQ can be made according to that of the Ni(II) quinolinol complex. [48][49] The (C=N) band of quinoline moiety, initially located at 1476 cm -1 before binding, is shifted to lower wavelength number (1468 cm -1 ) after chelation to NiO (Figure S5). This change is typical of quinoline group coordinated to Lewis acid metals. [48][49] The observation of the (OH) band of the phenol is more difficult as it appears as a broad band of medium intensity around 3400 cm -1 and it overlaps with those of the hydroxyl groups of NiO. However, the intensity of the (C-O) stretching band around 1030 cm -1 has decreased after binding, in agreement with formation of a metal-oxygen bond (Figure S5). Overall, we propose that both the nitrogen and the oxygen of hydro-quinoline moiety of PMI-HQ are bound to Ni(II) like in coordination complex of nickel tris(hydro-quinoline) because spectra of these species share similarities (Figure 6).

The dipicolinic acid anchoring group of PMI-DPA raises the questions whether both carboxylic acid groups are bound to the surface and if the nitrogen of pyridyl unit participates to the binding. The first interrogation can be quickly answered as the C=O stretching band at 1730 cm -1 has completely disappeared and an intense absorption at 1393 cm -1 (symmetric stretching of O-C-O) can be observed after grafting the dye on NiO (Figure S6). As a result, we can conclude that both carboxylic acid groups are involved in the binding with Ni(II).

Concerning the participation of the pyridyl unit, the breathing modes of the aromatic ring due to (C=C) and (C=N) located at 1414, 1446, 1464 cm -1 are not altered after binding, indicating that the pyridine is not coordinated to the NiO surface (Figure S6). [20,50] This is not surprising owing to the electron withdrawing nature of the PMI unit which most certainly diminishes the electron density on the nitrogen. As a consequence, the binding mode is either bidentate chelating or bidentate bridging mode but most probably bidentate chelating for geometrical reason (Figure 6). The mode of binding of acac group in PMI-acac was not analyzed, because the dye loading on NiO was not sufficiently high to obtain a good quality spectrum that would enable us to make a conclusive analysis (Figure S7).

Stability assessment of the dye-NiO linkage

The stability of anchoring groups in corrosive environment such as those in aqueous basic or acid conditions is an important factor to consider when designing dyes for DSPECs, because the electrode must sustain much harsher conditions than those in DSSCs. To assess the relative stabilities of each anchoring group, the stained electrodes were first soaked in acidic (acetic acid at 35 mM) or basic (tetrabutylammonium hydroxide at 1 mM) aqueous solutions, but no leaching of the dyes could be observed. This result is most certainly the consequence of the high insolubility of these hydrophobic and aromatic dyes in water as already observed with other systems. [51] Next, we turn to DMF solutions, which is a good solvent for all the dyes, to determine the relative stability scale of these series of anchoring groups. Towards this objective, the NiO electrodes, initially coated with each dye, were soaked in acidic (acetic acid at 35 mM) or in basic (tetrabutylammonium hydroxide at 1 mM) DMF solutions and the absorption of the DMF solution was monitored as a function of time for one hour (Figure 7).

The dye substituted with hydroxyquinoline (PMI-HQ) anchor was not investigated with this method, because the absorption spectrum of the desorbed solution was complicated by the presence of several species (broad absorption band very different from that of the dye implying degradation) preventing thus a quantitative analysis. However for a qualitative assessment, we have tentatively ranked the relative stability of PMI-HQ by using the pictures of the NiO films before and after 5 hours of soaking (Figure S9 ESI materials). First, in acidic conditions the phosphonic acid anchoring group is by far the most stable linker to NiO, a result in line with the high stability already reported on TiO 2 surface. [52][53] On the other hand, the least stable anchoring groups are acetyl acetone and carboxylic acid (Figure 7). Interestingly, dipicolinic acid (PMI-DPA) is less desorbed than the PMI-CO 2 H, which contains a single carboxylic anchoring group, most probably because DPA binds with the two carboxylic groups (see IR study above). Overall, in acid conditions, the relative stability towards desorption of the anchoring groups is: PO 3 H 2 > > DPA > HQ > CO 2 H > acac. Please note that PMI-HQ was ranked here only according to the qualitative observation of the electrode color as a function of the soaking time (Figure S9).

As far as the basic conditions are concerned, significant differences can be noticed. First, the stability of the linkage is lower in basic conditions than in acidic ones, because all binding groups detach faster from NiO surface. This result can be understood by the fact that hydroxyl anion is a stronger competitor than water to displace the anchoring group on the PMI dye from the NiO surface. Phosphonic acid remains the most stable anchor. Single carboxylic anchoring group (PMI-CO 2 H) is quickly desorbed as compare to the other binding group and it is followed by acac. Overall, in basic conditions, the relative stability of the linkage is:

PO 3 H 2 > DPA > HQ > acac > CO 2 H. Please note that PMI-HQ was ranked here only according to qualitative observation of the electrode color as a function of the soaking time (Figure S9).

In conclusion, the most stable binding group within this series is the phosphonic acid both in acidic and basic conditions. Accordingly, phosphonic acid remains among the best and most promising anchor to ensure slow desorption of a grafted molecular component on NiO surface. Dipicolinic acid does not provides as strong binding as phosphonic acid does, however, it is significantly more stable than the classically used carboxylic acid. Based on qualitative observation of the optical density of the soaked electrodes, it appears that hydroxyquinoline however provides a stronger stability than carboxylic acid.

Quantum chemical calculations

In order to get further insights on the structural and optical properties of the dyes, the ground and lowest excited electronic states of the dyes were investigated using Density Functional Theory (DFT) and Time Dependent DFT (TD-DFT) calculations, respectively. Solvent effects were included by the means of a Polarizable Continuum Model. [54] For the sake of clarity only results computed at the LC-PBE level of theory [55] are reported in the main text while corresponding data computed at the PBE0 level [56] are reported in Supporting Information together with a more extensive description of the computational protocol. The simulated absorption spectra are reported in Figure S8. All dyes are characterized by an intense absorption band centered around 475 nm corresponding to a  excitation of dominant HOMO-LUMO character. Although the computed absorption energies are shifted by roughly 50 nm with respect to the experimental values, calculations correctly reproduce the relative shift in absorption band maxima observed for the different dyes and, in particular, the observed sizable red-shifted absorption of PMI-HQ and PMI-NH 2 (Figure 8). Indeed, calculations show that due to the electron donating effect of the aniline and hydroxyquinoline groups, for these two dyes the HOMO lies at higher energy resulting in a consequently reduced HOMO-LUMO gap as reported in Figure 9. In particular, while the LUMO (of * character) is practically unchanged for all systems and always localized on the PMI moiety, the HOMO (of  character) shows a partial delocalization on the anchoring moiety only in the case of the PMI-NH 2 and PMI-HQ molecules and, to a minor extent, also in the case of the PMI-acac system. Therefore, the first electronic transition computed for all these systems of dominant HOMO-LUMO character displays a sizable intramolecular Charge Transfer (ICT) nature. This ICT character has been quantified computing the associated effective hole electron distance by the means of the D CT index. [57][58] Accordingly, PMI-HQ and PMI-NH 2 molecules display the greatest D CT value among the six molecules tested (Table 3), thus in principle providing the best hole-electron separation upon excitation followed by PMI-acac.

On the other hand, the smallest ICT character is computed for the PMI-DPA system. Calculation of the reduced form of the dyes allowed quantification of the spin density localized on each of the moieties that are here defined as the PMI core and the anchoring groups (-CC-X). The contribution of the anchoring group has been further dissected in the one localized on the carbon-carbon triple bond and on the terminal group (X) as reported in Table 4. In agreement with the LUMO localization on the PMI core, the spin density is mainly localized on it. Furthermore, the spin density distributes similarly among the terminal groups (-X) and carbon-carbon triple bonds. The terminal groups indeed carry from 3 to 4 % of the total spin density while the carbon-carbon triple bond carries from 2 to 4 % of the total spin density. The highest spin density contribution on the anchoring group is computed for the PMI-DPA (7.5%) while only in the case of PMI-NH 2 and PMI-CO 2 H an excess of beta spin density (resulting from a spin polarization effect) is computed. Nonetheless, these variations are relatively small and, in a general sense, we can conclude that the spin delocalization on the dyes is relatively insensitive to the anchoring group considered.

Transient absorption spectroscopy of the PMI dyes

The different anchor groups may lead to significant variations in electronic coupling to the NiO within the series of dyes. To investigate potential resulting differences in hole injection The ground state bleach is narrower (from 460 nm to 580 nm). There is no stimulated emission indicating that the singlet excited state has decayed within the experimental time resolution. The shape of the TA spectrum resembles the reduced state of PMI-CO 2 H

indicating ultrafast (<200 fs) hole injection, as commonly found for NiO-based DSSCs. [2, 11, To summarize, all investigated PMIs inject on a sub-ps time scale and show very similar recombination kinetics. Hence, the anchoring group does not seem to significantly influence the photophysical or electron transfer properties. Given the very different electronic structures of the anchoring groups, this is a surprising result. One possible reason is that hole injection and charge recombination does not occur through-bond but predominantly through space, as the dyes may lie close to the NiO surface. [61][62][63] Another possibility is that the hole injection is very fast and may be best described as adiabatic. In this case, the rate is not sensitive to small variations of the electronic coupling of the dye with the semiconductor. This is why there is no noticeable difference in the injection rate constants from one anchoring group to the others.

There are no obvious effects on the dynamics that can be attributed to dye aggregates (Figure 10). To study whether the aggregation has an effect on the conversion efficiency, PV measurements of DSSCs were conducted. The results are presented below.

Photovoltaic performances of the PMI dyes in p-DSSCs

The PMI dyes were used to fabricate p-DSSC with a NiO sensitized film assembled to a platinized counter electrode (See experimental part for fabrication details). A preliminary study was conducted only with PMI-CO 2 H dye with three electrolyte compositions in order to identify the optimized electrolyte for these sensitizers. Electrolytes with two different compositions of iodine/triiodide as redox couple and another one with 1-methyl-1H-tetrazole-5-thiolate (T-) and its disulfide dimer (T 2 ) [35] were investigated (Table 5). With the iodine based electrolyte, the one richer in triiodide (E1) gave the highest photocurrent density, while the redox couple T 2 /T-performs similarly in terms of Jsc but gives a higher Voc. Moreover and very importantly, the latter redox couple does not produce photocurrents from light absorption by the electrolyte, as observed for iodine based electrolytes, especially when they contain a high concentration of triiodide. [64][65] This is clearly visible in the photoaction spectra, which features a prominent band between 350-420 nm attributed to the photoactivity of triiodide (Figure S16). Therefore, the rest of the photovoltaic study was conducted with electrolyte E3 composed of the T 2 /T -redox mediator because it gives the highest performance and is not unreliably biased with artefacts on the photocurrent densities. The metrics of the solar cells of all the other PMI dyes fabricated with the T 2 /T -electrolyte are gathered in Table 6 and the IPCE spectra are given in Figure 12. Interestingly, the photovoltaic performances of these dyes differ significantly from one to another with PMI-HQ and PMI-acac being the most efficient within these series. There is a strong correlation between the dye loading and the short circuit photocurrent density, with the unusual behavior that J SC decreases with increasing dye loading. This is most certainly the direct consequence of the formation of aggregates on NiO, which decreases the injection quantum yield owing to quenching of the excited state. Consequently, the difference in photovoltaic performances of these dyes is not predominantly controlled by the anchoring groups in a direct way, but by the degree of aggregate formation. The latter increases with increasing dye loading that is, however, controlled by the affinity of the anchoring group with the NiO surface. Nevertheless, the IPCE spectra still show larger values at the higher vibronic peak (ca. 500 nm) than at the lower one (ca. 550 nm). Thus, it is clear that the aggregated dyes do contribute to the photocurrent, albeit with a lower yield than for the monomeric dyes. Probably, the aggregates already form in the dyeing bath before chemisorption.

Conclusion

In this study, we have investigated the largest series of anchoring groups for dyes sensitizing NiO. A series of seven different anchoring groups was explored with regard to their ability to form strong linkage with NiO and to mediate electronic coupling with the NiO valence band.

Overall, we found that phosphonic acid is the strongest binding group of the series and it leads to the highest dye loading. Conversely, acac and hydroxyquinoline are the weakest binding groups. Moreover, dipicolinic acid proved to be a stronger anchor than carboxylic. The photophysical study reveals that the PMI excited state of all dyes is quenched by fast hole injection into NiO at a sub-ps time scale, irrespectively of the binding group. Similarly, the anchoring group had no effect on the charge recombination kinetics. The weakest binding groups led to the lowest dye loading and consequently to the lowest degree of aggregation on NiO, which results in the highest photovoltaic performances, even if the differences are small. This demonstrates that, for dyes which have a strong tendency to form aggregates, the strongest binding group is not necessary optimal for application in DSSCs. This study also shows that the investigated anchor groups work equally well for hole injection and dye regeneration and therefore that the anchor-mediated electronic coupling of the dye with the semiconductor in NiO based DSSC may not be the primary parameter to consider to slow down the charge recombination between the reduced dye and the holes in NiO valence band.

However, for the fabrication of DSPEC, phosphonic acid is the most favorable binding group, within those investigated in these series, to attach a dye or a catalyst to NiO surface.

  PMI dye was substituted with pyridine (PMI-Py), aniline (PMI-NH 2 ), phosphonic acid (PMI-PO 3 H 2 ), hydroxyquinoline (PMI-HQ), acetyl acetone (PMI-acac), dipicolic acid (PMI-DPA), and naturally the carboxylic acid derivative (PMI-CO 2 H) was synthesized for purpose of comparison. The experimental electronic absorption, emission and electrochemical properties of the dyes were measured and analyzed by quantum chemical calculations. The dyes were also grafted on NiO mesoporous films and the stability of the linkage was assessed by desorption studies. The hole injection efficiency was determined by photovoltaic measurements in p-DSSCs and by ultrafast transient absorption spectroscopy.

Figure 1 .

 1 Figure 1. Electronic absorption (straight line) and normalized steady state emission (dashed line) spectra of the PMI-CO 2 H, PMI-acac, PMI-PO 3 H 2 and PMI-NH 2 dyes recorded in DMF solution.

Figure 2 .

 2 Figure 2. Electronic absorption (straight line) and normalized steady state emission (dashed line) spectra of the PMI-CO 2 H, PMI-DPA, PMI-Py and PMI-HQ dyes recorded in DMF solution.

Figure 3 .

 3 Figure 3. Electronic absorption spectra of the PMI-CO 2 H, PMI-HQ, PMI-DPA, PMI-acac and -PMI-PO 3 H 2 dyes recorded in thin films of NiO and pictures of the corresponding NiO thin films.

Figure 4 .

 4 Figure 4. Dye loading values (in nmol/cm 2 ) of the PMI dyes measured on NiO film of 1.3 m thickness. The average pKa value is given above each anchoring group.

Figure 5 .

 5 Figure 5. Evolution of the spectrum of the neutral for PMI-CO 2 H (left) and PMI-HQ (right) upon electrochemical reduction in dichloromethane. The initial spectrum of the neutral ground state is shown in black and the spectrum of the fully reduced dye is in red.

Figure 6 .

 6 Figure 6. Schematic representation of the binding mode of each anchoring group.

Figure 7 .

 7 Figure 7. Evolution of the relative absorbance of the DMF solution as a function of soaking time of NiO electrode coated with the PMI dyes. Left panel DMF with 35 mM of acetic acid and right panel DMF with 1 mM of tetrabutylammonium hydroxide.

Figure 8 .

 8 Figure 8. Simulated electronic absorption spectra of the dyes.

Figure 9 .

 9 Figure 9. HOMO-LUMO energies and gaps (in eV), where the former are given relative to the HOMO energy of PMI-DPA.

Table 4 .

 4 Computed Mulliken spin densities of the dyes, localized on the anchoring -CC-X group, along with the repartition on the carbon-carbon triple bond -CC and on the terminal group -X. PMI-CO 2 H PMI-NH 2 PMI-py PMI-DPA PMI-HQ PMI-Acac PMI-PO 3 H 2

  and recombination, transient absorption (TA) was performed on the dyes in solution and grafted on NiO. When exciting PMI-CO 2 H in THF solution, the transient absorption spectra show negative features from 480 nm to 650 nm and positive induced absorption features in the rest of the spectral range (Figure 10, left).

Figure 10 .PO 3 H 2 ,

 1032 Figure 10. Transient absorption spectra of PMI-CO 2 H in THF solution (left) and grafted on NiO films, immersed in propylene carbonate solution (right) at different time delays after excitation at 540 nm. The gray lines represent the corresponding ground state absorption (dotted) and fluorescence (dashed) spectra and the difference spectrum from spectroelectrochemical reduction (full) in arbitrary units.

Figure 11 .

 11 Figure 11. Kinetic traces of the TA at the maximum of the induced absorption and the minimum of the ground state bleach of PMI sensitized NiO films in propylene carbonate (upper/left) and the E3 electrolyte T 2 /T -(bottom/right) after excitation at 540 nm and normalized at 10 ps.

1 M

 1 E1 composition: [I 2 ] = 0.1 M, [LiI] = 1 M in CH 3 CN; E2 composition: [I 2 ] = 0.03 M, [1,2dimethyl-3-butylimidazolium iodide] = 0.6 M, [tBu-pyridine] = 0.5 M, [guanidinium thiocyanate] = 0.1 M, in CH 3 CN; E3 composition: [T 2 ] = 0.3 M, [T -] = 0.1 M, [LiTSFI] = 0.in propylene carbonate/CH 3 CN: 3/7 vol./vol.)

  However, we have tested the possibility to break the aggregates by loading the PMI-PO 3 H 2 dye in presence of increasing concentrations of chenodeoxycholic acid (CDCA) ([CDCA] = 2 mM, 5 mM, 10 mM and 20 mM) into the dyeing bath, hence a dye/CDCA ratios of 0, 10, 25, 50 and 100 were explored. However, the Jsc and the Voc was not changed within experimental errors resulting in no real improvement of the PCE. In a second series of experiments, we have also investigated the possibility to reduce the degree of dye aggregation by shortening the soaking time. The NiO electrodes were therefore soaked into the dye bath for 30 minutes, 2 hours, 4 hours and overnight. It turned out that after 2 hours, the Jsc and Voc plateau to almost the same values measured after 12 hours. When the soaking time was set to 30 min, both Jsc and Voc were reduced by about 20% relative to those after overnight in line with the lower dye concentration on the NiO film. Overall, we conclude that the control of the dye aggregation on NiO surface with PMI-PO 3 H 2 cannot be simply achieved neither with CDCA used as co-adsorbent in the dyeing bath nor by reducing the soaking time.

Figure 12 .

 12 Figure 12. IPCE spectra of the PMI dyes recorded with the electrolyte composed of the T 2 /T - redox mediator.

Table 1 .

 1 Wavelengths

		of maximal absorption ( abs ) with extinction coefficient (),
	wavelength of maximal emission ( em ) recorded at room temperature and zero-zero energy
	level of the lowest singlet excited state (E 00 ) of the PMI moiety.
	Dyes	a  abs /nm (/M -1 cm -1 )	b  abs /nm	 em /nm	c E 00 / eV
	PMI-CO 2 H	535 (48800) ; 421 (7300) ; 362 (10400)	495	592	2.21
	PMI-NH 2	555 (49900) ; 393 (10300)	-	601	2.14
	PMI-Py	529 (52800) ; 422 (7600) ; 338 (8200)	-	573	2.25
	PMI-DPA	534 (40100) ; 422 (6700) ; 357 (8500)	497	575	2.24
	PMI-HQ	546 (56200) ; 395 (14100)	514	575	2.21
	PMI-Acac	534 (54300) ; 419 (9100) ; 363 (11500)	497	584	2.22
	PMI-PO 3 H 2	535 (38500) ; 419 (5300) ; 366 (7400)	495	563	2.20

Table 2 .

 2 Redox Calculated according to the equation: E 1/2 (PMI*/PMI -) = E 1/2 (PMI/PMI -) + E 00 . b Calculated according to the equation: G°i nj =E VB (NiO)-E Red (PMI*/PMI -) with E VB (NiO) = 0.30 V vs.

	Dyes	E a,peak (PMI + /PMI)	E 1/2 (PMI/PMI -) (V)	a E (PMI*/PMI -)	b G°i nj	c G°r eg with I 3 -	d G°r eg with T 2 /T -
		(V)		(V)	(eV)	(eV)	(eV)
	PMI-CO 2 H	1.20	-0.93	1.28	-0.98	-0.61	-1.18

potentials recorded by cyclic voltammetry at room temperature in dichloromethane/DMF [95:5] solution with Bu 4 NPF 6 (0.1 M) as supporting electrolyte and referenced versus saturated calomel electrode (SCE). Calculated Gibbs free energies for hole injection (G°i nj ) and dye regeneration (G°r eg ) a

Table 3 .

 3 Computed

	Dye	 abs	Oscillator	D CT /Å
			Strength
	PMI-CO 2 H	473	1.71	1.83
	PMI-NH 2	479	1.85	2.64
	PMI-py	470	1.62	1.81
	PMI-HQ	479	1.77	2.33
	PMI-DPA	471	1.65	1.54
	PMI-acac	474	1.70	2.21
	PMI-PO 3 H 3	472	1.68	1.90

absorption energies ( abs in nm) and associated oscillator strengths (in au) and D CT values (in Å).

Table 5 .

 5 Photovoltaic properties of the p-DSSCs recorded under simulated AM 1.5 with

	PMI-CO 2 H sensitizer.

Table 6 .

 6 Photovoltaic properties of the p-DSSCs recorded under simulated AM 1.5 with all the PMI sensitizers with the electrolyte E3 composed of the T 2 /T -redox mediator.

	Dyes	Jsc [mA.cm -2 ] Voc [mV]	FF [%]	[%]	Dye loading [nmol cm -2 ]
	PMI-CO 2 H	1.52 ± 0.06	161 ± 7 25.4 ± 0.3 0.062 ± 0.001	22.3
	PMI-HQ	2.21 ± 0.09	164 ± 4 23.8 ± 0.6 0.086 ± 0.003	9.3
	PMI-DPA	1.33 ± 0.09	168 ± 6 24.6 ± 0.6 0.055 ± 0.005	23.7
	PMI-acac	2.08 ± 0.08	169 ± 8 27.9 ± 0.2 0.098 ± 0.002	7.7
	PMI-PO 3 H 2	1.27 ± 0.12	181 ± 7 17.7 ± 0.4 0.041 ± 0.004	38.2

a recorded in dichloromethane solution. b recorded on thin NiO film. c calculated according to

Acknowledgments

The authors are grateful to Agence Nationale de la Recherche (ANR) for the financial support of these researches through the program POSITIF (ANR-12-PRGE-0016-01) and Région des Pays de la Loire for the project LUMOMAT, to the Swedish Research Council (Project no 2014-5921) and the Swedish Energy Agency (Project no 4359-1). IC and FM have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 648558).

 59]However, the spectral shape does not completely follow the reference of the reduced state. This could be explained by a broadening of the peak at 650 nm due to different environment.

A similar broadening was observed earlier. 24 It could, however, also originate from dye aggregates on the surface, for which the anion spectra are different than for the monomers.

The other dyes show very similar TA spectra (not shown) and kinetic traces (Figure 11). However, PMI-HQ shows a contribution from stimulated emission in the initial spectra (< 1 ps) suggesting a slower injection for this compound (Figure S14 and Figure S15).

When comparing the normalized kinetics of the PMIs grafted on NiO in propylene carbonate solution, there is no significant difference between those of PMI-CO 2 H, PMI-acac, PMI-DPA, PMI-PO 3 H 2 , and PMI-HQ shows a fast component in the ground state bleach recovery, which is attributed to the disappearance of the stimulated emission, i.e. reflecting hole injection. This processes is, however, still on the sub-ps time scale. Except for this difference, the TA signal of the reduced PMIs decays non-exponentially to approximately 20% of the initial signal after 1.9 ns.

When adding the T 2 /T -electrolyte, the kinetics is slightly slower compared to the kinetics in propylene carbonate only. Also with T 2 /T -, the signal decays to approximately 20% of the initial value at 1.9 ns. There are previous studies where the dye anion has been more longlived in the presence of redox couple than without. [60] This counter-intuitive result must be attributed to changes in the fermi level (hole filling by the electrolyte), which slows down dye-NiO recombination. This makes it difficult to estimate the regeneration efficiency, and may obscure differences in recombination and regeneration rates between dyes. Especially for PMI-acac, the fraction of the initial signal that remains (20%) is smaller lower than the IPCE value (30 %, see below), indicating that (some) regeneration should take place on the sub-ns timescale.