Victor Malgras

Satoshi Tominaka

James W Ryan

Joel Henzie

Toshiaki Takei

Koji Ohara

Yusuke Yamauchi

Observation of Quantum Confinement in Monodisperse Methylammonium Lead Halide Perovskite Nanocrystals Embedded in Mesoporous Silica

Keywords: Methylammonium lead halide perovskite, iodide, bromide, mesoporous template, nanocrystals, solid state, optical properties, quantum confinement

Hybrid organic-inorganic metal halide perovskites have fascinating electronic properties and have already been implemented in various devices. Although the behavior of bulk metal halide perovskites has been widely studied, the properties of perovskite nanocrystals are less well understood because synthesizing them is still very challenging, in part because of stability. Here we demonstrate a simple and versatile method to grow monodisperse CH 3 NH 3 PbBr x I x-3 perovskite nanocrystals inside mesoporous silica templates. The size of the nanocrystal is governed by the pore size of the templates (3.3, 3.7, 4.2, 6.2 and 7.1 nm). In-depth structural analysis shows that the nanocrystals maintain the perovskite crystal structure, but it is slightly distorted. By tuning the size of the particles, we can observe quantum confinement, which provides an additional route to tune the optical bandgap of the nanocrystal, besides the ratio of bromide to iodide. The level of quantum confinement was modeled taking into account the dimensions of the rod-shaped crystals and their close packing along the channels of the template. Photoluminescence measurements on CH 3 NH 3 PbBr clearly show a shift from green to blue as the pore size is decreased. Synthesizing perovskite nanostructures in templates improves their stability and enables tunable electronic properties via quantum confinement. These structures may be useful as reference materials for comparison with other perovskites, or as functional materials in all solid-state light-emitting diodes.

INTRODUCTION

Hybrid organic-inorganic metal halide perovskites exhibit unusual electronic, optical and crystallographic properties enabling high mobilities 1,2 and long diffusion lengths. 3,4 They are promising candidates for photovoltaic applications and have rapidly achieved outstanding performances. [5][6][7][8][9] The chemical structure obeys the AMX 3 stoichiometry, where A is the organic cation (e.g., methylammonium (CH 3 NH 3 ) + , formamidinium (CH(NH 2 ) 2 ) + ), M is the metal cation (e.g., Pb 2+ , Sn 2+ ), and X is the halide anion (e.g., Cl -, Br -, I -). The optical bandgap can be tuned by selecting the appropriate A and X components: methylammonium and bromide lead to wider bandgaps than formamidinium and iodide, respectively. 10 While mixing bromide and iodide offers good control over the absorption band edge, these intermediate compositions can decrease the overall stability because it induces structural hindrances and can be prone to the formation of microdomains. 11 While numerous studies on bulk lead halide perovskites exist in the literature, less attention has been directed towards the synthesis and properties of CH 3 NH 3 PbX 3 quantum dots. The ability to tune the optical response of perovskites by altering their size or surface chemistry is useful for various light-emitting applications (e.g., LEDs, lasers). In addition, quantum confinement offers a different angle from which the electronic properties can be studied and manipulated. Many semiconductor nanocrystals (e.g., Si, Ge, GaAs, PbS, CdSe, etc) display interesting behavior when their radius is less than the exciton Bohr radius, such as bandgap expansion, increased Coulombic attraction of the paired charges, energy level quantization, and slower electronphonon relaxation. [12][13][14][15] Research on CH 3 NH 3 PbX 3 nanocrystals has been primarily limited to colloidal nanoplatelets [16][17][18][19] and nanoparticles, [20][21][22][23] through co-precipitation or seeding methods, as well as encapsulation in alumina. 24 Not only are these materials difficult to obtain (e.g., multiple steps, use of chemical vapor deposition, separation), but they also typically yield small amounts of material. In addition, the optical properties of the material can become difficult to assess and separate from the localized surface states induced by organic ligands. Compared to PbSe, InSb or even CdSe, the exciton Bohr radius of CH 3 NH 3 PbX 3 is rather small (r ~ 20 Å) 25 and thus quantum confinement will only be observed for crystals with a radius much smaller than 10 nm.

We used highly ordered mesoporous materials as templates to guide the confined growth of nanoparticles and keep them isolated from each other. Over the last three decades, zeolites and mesoporous templates have been used to synthesize inorganic nanoparticles such as metals, oxides, carbons or semiconductors with simple compositions in order to study their catalytic, magnetic, and optical properties. [26][27][28][29][30][31][32][33] LaCoO 3 and LaNiO 3 perovskites have been synthesized in mesoporous silica by impregnating them with aqueous solution of nitrate salts followed by calcination. 34,35 Here, we synthesized CH 3 NH 3 PbBr x I 3-x perovskite (with x = 0, 1, 2, 3) inside mesoporous silica templates to produce monodisperse 0D and 1D nanocrystals. Each template in this work is characterized by a specific pore size, limiting the crystal growth to a specific particle size, thus allowing us to control the level of confinement. We used mesoporous silica matrices having pores of diameters d pore ≈ 7.1, 6.2, 4.2, 3.7, and 3.3 nm. The N 2 adsorption/desorption isotherm data along with the calculated pore size distribution and small-angle X-ray scattering (SAXS) for each mesoporous silica template can be found in Figure S1. Our method uses capillary forces to fill the templates. Because of the relatively low interfacial surface tension between N,N-dimethylformamide (DMF) and silica, the dissolved perovskite precursors can be carried inside the channels with minimal resistance. Additionally, the chemistry underlying the formation of perovskite crystals does not involve the formation of any side-products that might require subsequent extraction. Crystallization of nanocrystals is induced by gradual supersaturation as the solvent evaporates. This method offers a simple, rapid, high-yield route to generate embedded perovskite quantum dots with an accurate control over the crystal size.

EXPERIMENTAL METHOD

Materials:

Lead iodide (PbI 2 , ≥ 99.0%) and lead bromide (PbBr 2 , ≥ 98.0%) were purchased from Sigma-Aldrich and hydroiodic acid (HI, 57% in water), hydrobromic acid (HBr, 48% in water), methylamine (MA, 40% in methanol solution) and N,N-dimethylformamide (DMF, ≥ 99.7%) were acquired from Wako Pure Chemical Industries, Ltd. The chemicals were used without further purifications.

Precursors synthesis:

The methylammonium iodide/bromide (MAX, X = I, Br) was prepared by mixing equimolar ratios of MA solution and HI or HBr under constant argon flow, with the flask sitting in an ice bath for 2 h. The precipitate was rinsed with diethyl ether three times and recrystallized from ethanol. Before use, MAX was left overnight in a vacuum oven at 60 °C. Each composition was prepared by mixing equimolar ratio of MAX and PbX 2 (i.e., x = 0, MAI + PbI 2 ; x = 1, MABr + PbI 2 ; x = 2, MAI + PbBr 2 ; x = 3, MABr + PbBr 2 ) in DMF. The concentration was 0.5 M for x = 0 and 1 and 0.2 M for x = 2 and 3.

Powders preparation:

The mesoporous silica powders with different pores of diameters d pore ≈ 7.1, 6.2, 4.2, 3.7, and 3.3 nm, were synthesized according to previously published methods, 36,37 and the organic template was removed by calcination treatment at 500 °C for 6 h. The silica powders were dried overnight under vacuum at 80 °C before use. 20 μL of each perovskite precursor was added dropwise to 40 mg of each mesoporous silica followed by vortex mixing for 30 min. The powders were then dried on a hot plate at 95 °C for 30 min before further characterization. Bulk perovskite used as a control sample was prepared by mixing the perovskite solution with non-porous silica nanospheres (~350 nm), which was found to promote the photoluminescence properties when compared to the bare polycrystalline bulk.

Structural analysis:

The wide-angle powder X-ray diffraction patterns (PXRD) were obtained with a Rigaku Rint 2500 diffractometer with monochromated Cu K radiation at a rate of 0.2°•min -1 . The high-resolution transmission electron microscope (HR-TEM) and scanning transmission electron microscope high-angle annular dark-field (STEM HAADF) images were obtained with a JEM-2100F TEM (JEOL, Japan) operated at an accelerating voltage of 200 kV with a spot size of 0.7 nm. Low-angle XRD profiles were acquired on a NANO VIEWER (Rigaku, Japan) equipped with a Micro Max-007 HF high-intensity micro-focus rotating anode X-ray generator. X-ray total scattering data for obtaining pair distribution functions (PDFs) [START_REF] Egami | Underneath the Bragg peaks: structural analysis of complex materials[END_REF] were collected on a Rigaku R-AXIS imaging plate detector at the BL04B2 beamline of SPring-8 at a beam energy of 61.39 keV (λ = 0.20196 Å). Details are available in the Supporting Information. The energy dispersive X-ray spectroscopy (EDX) was performed using a Hitachi FE-SEM S-4800 with an accelerating voltage of 15 kV. The nitrogen adsorptiondesorption isotherms were obtained with a high-precision Belsorp-mini apparatus (Bel Japan, Inc.) at 77 K and the Barrett-Joyner-Halenda (BJH) method was used to calculate the pore size distribution of each silica template. 39,40 Optical measurements: The UV-Vis-NIR absorption spectra of the solid powders were calculated from the reflectance spectra obtained on a JASCO V-570 at a scan rate of 400 nm•min -1 from 220 to 1000 nm using a deuterium or halogen lamp as a light source (for the 220-350 nm range and 350-1000 nm range, respectively). Photoluminescence (PL) spectroscopy was performed on a JASCO FP8500 at a scan rate of 500 nm•min -1 , with 10 nm slits. The photographs of the fluorescing powders were obtained under an AS ONE SLUV-8 UV lamp emitting at 254 nm. The PL lifetime measurements were carried out on a Hamamatsu Photonics Quantaurus-Tau at an excitation wavelength λ ex = 365 nm. Absolute quantum yield (QY) measurements were performed on a Hamamatsu Photonics PMA-12 equipped with an integrated sphere and a Xenon lamp set at an excitation wavelength of λ ex = 365 nm. To verify the accuracy of the system, prior to measuring the composites samples, Coumarin 6 (standard QY of 78%) and Rhodamine B (standard QY of 68%) dissolved in ethanol returned QY values of 78% and 66%, respectively.

RESULTS AND DISCUSSION

Each CH 3 NH 3 PbBr x I 3-x perovskite composition was obtained by combining equimolar ratios of PbX 2 and CH 3 NH 3 X (with X = Br, I) in DMF. EDX was used to confirm the final Pb:X ratios: 1.00:3.00 (± 0.06) and 1.00:3.07 (± 0.14) for the bromide-and iodide-based perovskite, respectively (Figure S2). The solutions were mixed with the mesoporous powders using vortex stirring at 2000 rpm for 30 min. After the solutions had thoroughly impregnated the pores, the powders were dried at 95 °C. The color of the powders changed within 5 min, as the solvent evaporated and the perovskites crystallized. The material was held at 95 °C for an additional 30 minutes to ensure complete evacuation of DMF from the pores. Qualitatively, the final color of each powder depended on the size of the template and the Br concentration, showing a clear spectral shift from black/brown to yellow/green as d pore decreases and x increases (Figure 1). From the N 2 adsorption/desorption isotherm data, the average pore sizes are found to be d pore ≈ 3.3, 3.7, 4.2, 6.2 and 7.1 nm (Figure S1). The SAXS patterns (Figure 2a) of the templates containing CH 3 NH 3 PbBr 3 can be observed. The pores exhibited periodic, long-range ordering, with peaks indexed to the (10), (11), and (20) of a 2D hexagonal mesostructure (P6mm). The pore-to-pore distance is calculated from , and the overall specifications for each template can be found in Table S1.

To test whether the perovskite grows into the typical cubic phase in the presence of silica, we performed a Rietveld refinement on synchrotron XRD data obtained on the bulk perovskite/silica nanosphere composite (x = 3). Figure 2c shows that the crystals grow into a typical CH 3 NH 3 PbBr 3 perovskite cubic phase (Pm ¯,3 m, a = 5.9286(4) Å). In conventional PXRD, the patterns of the perovskite nanocrystals inside the templates adopt the cubic crystal structure (Figure 2b), but gradual broadening of the Bragg peaks (e.g., 100 around 15°) is observed as the pore size decreases. Similar features could also be observed in the PXRD patterns for our CH 3 NH 3 PbI 3 samples (see Figure S3). Note that the broad peak centered at around 22° is attributable to the amorphous SiO 2 .

Although X-ray diffraction is sensitive to the crystallographic symmetry of the materials, much of the information on short to medium range ordering cannot be assessed from the Bragg peaks, especially in nanomaterials due to peak broadening. Pair distribution function (PDF) analysis is sensitive to the networks present in materials, and takes into account all the components of a sample including crystalline, nanocrystalline and amorphous phases. 41 Using PDF, we can examine the local to intermediate range ordering of nanocrystals to clarify the structure and detect the presence of amorphous phases. PDF measurements on the bulk perovskite sample fit the cubic perovskite model very nicely (Figure S4a). On the other hand, PDF measurements on nanocrystal samples show some discrepancies (Figure S4b). For example, in the 3.3 nm template, the material has a broad peak at 6.32 Å with a shoulder around ~5.93 Å, indicating there are two different Pb-Pb nearest neighbor distances. The typical CH 3 NH 3 PbBr 3 crystal has a lattice constant of ~5.93 Å, suggesting that the nanocrystals match the perovskite structure, but also has cells containing some expanded Pb-Pb distances or which possess a distorted structure. This was also observed at longer distances, such as the peak around 12 Å, explaining why the (100) peak in the PXRD becomes broad in the nanocrystalline systems (Figure 2a). To fit the PDF data we used the reverse Monte Carlo method to analyze the data assuming a ~2.3 nm CH 3 NH 3 PbBr 3 particle (Figure S4c). In this context, PDF is not used to determine the absolute structure, but as a comparative technique in combination with the PXRD data to conclude that the nanocrystals have a distorted perovskite network. A comparison between the PbBr 6 octahedra from the classic cubic structure and from the nanocluster model is shown in Figure 2d,e to highlight the distorted Pb-Br-Pb bonds (illustration of the whole cluster can be found in Figure S4d). Further details on these distortions will be reported in the future after performing additional PDF measurements.

The PXRD patterns for most samples have overlapping sharp and broad peaks. The sharpest peaks correspond to the {h00} diffraction planes, strongly suggesting that the perovskite inside the channels grows along the <100> direction forming elongated crystals or nanorods. In order to separate the broader contributions from the sharp ones, the peaks were fitted by a double Gaussian function and the Scherrer equation was used to estimate the average crystallite size in each sample (see Figure S5). Note that we used the peaks outside of the amorphous silica range, where the background could be subtracted clearly, and the results are reported in Table S1. For pore sizes ≤ 6.2 nm, the estimated crystallite sizes are 0.7 to 1.3 nm smaller than the pores. The ratio of spherical particles to nanorods is roughly estimated to be 5.1 ± 1.4, based on the integrated Gaussian fit.

Transmission electron microscopy (TEM) was used to image the CH 3 NH 3 PbBr 3 and CH 3 NH 3 PbI 3 nanocrystals encapsulated in the silica templates. This class of perovskite is notoriously sensitive to electron beam damage, so the TEM micrographs were taken with great care to minimize the exposure/dwelling times and avoid changes in morphology. The HR-TEM images (Figure 3ac) show the presence of a mixture of spherical and rodshaped particles that extend across the width of the channels. The Fourier transform of the HR-TEM images shows that the lattice fringes match the {211} and {200} crystal plane (d 211 = 2.68 ± 0.02 Å, d 200 = 2.99 ± 0.02 Å), the latter being oriented along the direction of the channels (Figure 3d,g). Exposure to the electron beam did not affect the morphology of the nanocrystals, and the observed lattice parameter is far enough from the Pb {111} crystal plane (d 111 = 2.852 Å), allowing us to rule out the possibility of electron beam-induced chemical reduction or precipitation. 19 The preferential growth of nanorods along the <001> direction matches the PXRD data and has been previously reported for CH 3 NH 3 PbBr 3 nanowires. 42,43 The STEM images (Figure 3e,f) show that the nanocrystals are closely distributed along the channels and that the templates do not suffer from any deformation or collapsing (see Figure S6). For each sample, the crystallized perovskite was observed inside the templated channels, as clearly shown by the bright particles/nanorods aligned parallel to each other. The spherical nanoparticles and nanorods size distribution histograms (over 100 nanocrystals), measured on both HR-TEM and STEM micrographs, closely match pore size distribution of the mesoporous silica calculated from the isotherms with the Barrett-Joyner-Halenda (BJH) method.

Figure 4 shows the UV-Vis-NIR spectra for the different silica templates and the four compositions. The reflectance data is reported as absorption spectra to enable better comparison with the previous literature. The data provides a clear measurement of the direct optical bandgap of the CH 3 NH 3 PbBr x I 3-x perovskites due to their sharp band edge. The bandgap energies measured for the various bulk compositions are similar to what was previously reported for comparable materials (the numerical values are reported in Table 1). 11,44 Small variations can be expected because the local crystal structure of hybrid perovskites is affected by the crystallinity and surface structure of the substrate. 8,33 The bulk samples include amorphous silica nanospheres to provide a similar perovskite/silica interface to the mesoporous templates. These measurements have no supplementary shoulder that would indicate the presence of both bulk and nanocrystals (example in Figure S7), confirming that the perovskite crystallized exclusively inside the mesopores and not at the surface of the grains. For each composition, a gradual shift of the band edge towards higher energies is an indication of how the bandgap increases due to confinement. With only four different compositions, one can easily cover the absorption spectrum from 1.52 to 2.62 eV with increments of less than 0.15 eV. The appearance of an excitonic peak is a signature of stronger electron-hole correlation as the crystal size is reduced. This feature appears to become more prominent as the Br content increases, to the point where a distinct exciton peak can be seen for the pure CH 3 NH 3 PbBr 3 even in the sample with 7.1 nm pore size. This could result from the fact that the exciton binding energy of the bromide-based perovskite is considerably higher than for the iodide-based one. 25 The slope of the band edge remains mostly unchanged.

The Stokes shifts (ΔE St , Table 1) obtained from comparing the absorption with the PL spectra (Figure 5a and S8) tends to be smaller for the pure halide composition (x = 0 or 3). For the intermediate compositions, light-soaking experiment resulting in gradual appearance of a new PL peak in the bulk perovskite and in the templates with larger pores (see Figure S9) confirms that the materials undergo phase segregation under light exposure, leading to the presence of instable Br-and I-rich microdomains, 11 contributing to the overall crystal disorder and resulting in a notably larger ΔE St . We can observe that the Stokes shift also increases significantly for the templates with 3.3 nm pore size compared to the other pore sizes. In addition, the PL emission spectra of the intermediate composition x = 2 reveals a split peak for d pore ≈ ∞, 7.1 and 6.2 nm, nm. d) Higher magnification centered on the selected area of the image displayed in a) and its Fast Fourier Transform pattern (g). STEM images of the impregnated silica with d pore ~ 3.7 (e) and 3.3 nm (f) for the bromide-based (x = 3) perovskite nanocrystals, along with the particle size distribution histograms (h and I, respectively) overlapping with the pore size distributions calculated from the N 2 sorption isotherms with the BJH method (including Gaussian fitting).

suggesting the coexistence of two phases (Figure S8). It should be noted, however, that while the smaller peak seems to match the position of the absorption band edge, and thus reflects the presence of a phase with the expected stoichiometry, a second peak is located in the Irich region for d pore ≈ ∞ and in the Br-rich region for d pore ≈ 7.1 and 6.2 nm. Also, below d pore ≈ 4.2 nm, only one phase, matching the absorption band edge, appears to be emitting (Figure 5a andS8). Not only do these results support what was previously reported on the formation of microdomains, they also suggest that spatially confining the perovskite crystals within static and inert walls has the potential to limit the degree of structural disorder responsible for certain stability issues.

The measured bandgaps for x = 0 and 3 were plotted against their respective crystal size (Figure 5b), highlighting the gradual displacement of their respective conduction and valence bands. To model quantum confinement in the nanoparticles, we plotted a simplified particle-in-a-box model for CH 3 NH 3 PbBr 3 and CH 3 NH 3 PbI 3 , taking into account coulombic interactions and the first zero point of the cylindrical Bessel function (see details in the Supporting Information). An approximation using cylindrical 1D structure is used here because we assume that, in addition to the significant proportion of rod-shaped particles, most of the nanocrystals are packed closely and are expected to behave as a 1D structure. Moreover, the asymmetry in the electronic environment (air vs. SiO 2 ) might also promote this effect. This model fits best for the smaller pore sizes (3.3-4.2 nm). However, even if the confinement energy is known to be more accurate for larger particles, the electrostatic term can quickly diverge when the size of the nanocrystals increases above the Bohr radius, especially for materials with small dielectric constants. 45 According to previous reports, the positions of the bandgaps measured for the smallest crystal with x = 0 and 3 are comparable to nanoplatelets with 3 to 4 atomic layers. 17,18,22 The pure bromide composition (x = 3), unlike the others, is characterized by a strongly emissive PL. Figure 6a clearly highlights the gradual shift of the emission from green to blue as the pore size is decreased, along with a significant peak broadening. We suspect that the increase in peak width might be caused by crystal distortion in the smaller particles, although it did not seem to affect the bandgap (as confirmed by the effective mass model). On the other hand, the PL lifetime tends to decrease with the pore size (Figure 6b) and the QY of the bulk reaches 7.2% while that of the composites remain relatively low (< 5.5 %) (Table S2). Even though previously reported CH 3 NH 3 PbBr 3 nanoparticles of size ranging from 6 to 8 nm reported PL quantum efficiencies up to 83 %, 46,47 it has been proposed that unpassivated crystals tend to exhibit lower emission yield. 48 The role of localized surface states is especially important in nanocrystals, and in organic perovskites this occurs mostly as Pb, Br or CH 3 NH 3 vacancies and substitutions. The shorter lifetimes could be the result of dominant surface trapping as the crystal size decreases. In such cases, we can surmise that the surface in contact with the silanol groups and/or air are not effectively passivated and thus cannot prevent non-radiative recombination through localized states.

Exposing these perovskite samples to UV light can potentially affect their response. The stability of each sample was studied by comparing the PL lifetime of the pure iodide-and pure bromide-based samples before and after UV irradiation exposure, as well as after an overnight recovery period in the dark (Figure S10-S11). The bulk samples were strongly affected by UV light, causing their lifetimes to decrease by factors of 13 and 8 for x = 0 and x = 3, respectively. There was very little recovery after UV irradiation of the bulk samples. The overall lifetime of the composite samples consistently decreased with crystal size, but the resting period resulted in the complete restoration, and in some cases of the optical properties, highlighting its strong resistance to UV irradiation. The PL decays best fit to triple exponential functions, so the exact mechanisms responsible for radiative recombination are difficult to discern here. These results, however, support once more the idea that confining CH 3 NH 3 PbX 3 crystals in a rigid template protects the structure from various types of degradation. It is possible that the energy imparted by UV exposure triggers two interrelated processes: 1) ion migration (mostly halide) and 2) annealing of the sample. In the bulk samples, ion migration can drive the components of the perovskite relatively far apart from their original location, which explains why the crystal might remain highly contorted even after recovery. The "rigid" spatial confinement provided by the template could limit how far the constituents can roam, so the system can eventually return to its original equilibrium state after the recovery period. In summary, we have successfully synthesized CH 3 NH 3 PbBr x I 3-x nanocrystals embedded in mesoporous silica templates. We show that the crystal size matches the pore size distribution and that the crystal structure is maintained even for particles down to 3.3 nm in diameter, although with slight distortions. TEM and X-ray diffraction data show the samples are a mixture of spherical and rod-shaped particles enclosed in the silica channels. Our optical measurements show that both the Br content and the size-dependent confinement are directly related to the bandgap. The gradual shift of the photoluminescence from green to blue (for the bromidebased perovskite) is additional evidence that fine tuning of the optical properties can be obtained from simply controlling the pore size of the template. A simplified particle-in-a-box model for 1D structures could fit nicely the confinement of the smaller quantum dots (< 4.2 nm), but fails for the bigger crystals because of the model's limitations. Because of their structural disorder, intermediate compositions also show larger Stokes shift values. The PL lifetime was directly dependent on crystal size, suggesting that localized surface states might induce non-radiative recombination pathways. Additionally, confining the crystals inside a rigid matrix such as mesoporous silica likely helps protect the structure from being damaged by UV irradiation. Our experimental procedure is simple and scalable, the results are proof of true quantum confinement and also showcase improved structural stability. For these reasons, we believe that this work will pave the way for extensive research on the topic, and ultimately find appropriate implementation in optoelectronic applications.

CONCLUSION

Supporting

Figure 1 .

 1 Figure 1. Photographs of the mesoporous silica powders after impregnation and crystallization.

Figure 2 .

 2 Figure 2. Structural analysis of CH 3 NH 3 PbBr 3 perovskite. (a) SAXS patterns of the perovskite-impregnated silica templates match the P6mm space group corresponding to the ordering of the mesopores. (b) PXRD patterns match the calculated pattern for the cubic (Pm ¯,3 m) structure. (c) Rietveld refinement of the synchrotron XRD data (λ = 0.20196 Å) obtained from the bulk perovskite/silica nanospheres system, confirming the cubic (Pm¯,3m) structure. Goodness-of-fit = 1.68, a = 5.9286(4) Å. Structural models of (d) the standard cubic structure compared to (e) the distorted cluster model. Note: the methylammonium ions were omitted from the models because of their negligible contribution to the X-ray scattering data.

Figure 3 .

 3 Figure 3. HR-TEM images of the perovskite/silica composite: a) x = 3, d pore ~ 7.1 nm; b) x = 0, d pore ~ 3.7 nm; c) x = 3, d pore ~ 3.3 nm. d) Higher magnification centered on the selected area of the image displayed in a) and its Fast Fourier Transform pattern (g). STEM images of the impregnated silica with d pore ~ 3.7 (e) and 3.3 nm (f) for the bromide-based (x = 3) perovskite nanocrystals, along with the particle size distribution histograms (h and I, respectively) overlapping with the pore size distributions calculated from the N 2 sorption isotherms with the BJH method (including Gaussian fitting).

Table 1 :

 1 Energy (in eV) of band edge maxima (or saddle point) obtained from the absorption spectra for each CH 3 NH 3 PbBr x I 3-x composition and pore size. The values in brackets correspond to the Stokes shifts ΔE St .

Figure 4 .

 4 Figure 4. UV-visible absorption spectra (calculated from reflection measurements) for each CH 3 NH 3 PbBr x I 3-x (x = 0, 1, 2, 3) sample and mesoporous silica template.

Figure 5 :

 5 Figure 5: a) Absorption (solid lines) and PL spectra (dotted lines) for each perovskite composition impregnated in mesoporous silica with d pore ≈ 4.2 nm (see Figure S8 for other pore sizes). b) Bandgap in function of the crystal/pore size for the iodide-and bromide-based hybrid perovskites, along with the expected trend calculated from the effective mass model for 1D structures. The dotted lines corresponds to the bandgap of the bulk samples.

  Information. Detailed characterization of each perovskite composition impregnated in mesoporous silica. PDFs data. EDX and XRD patterns. High magnification STEM of empty and impregnated host templates. Absorption and PL spectra. Light-soaking effect. PL lifetime measurements. Confinement model calculations. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author. Yamauchi.Yusuke@nims.go.jp

Figure 6 :

 6 Figure 6: a) Photographs and PL spectra of CH 3 NH 3 PbBr 3 impregnated in the various silica template (from bulk on the left to d pore ≈ 3.3 nm on the right) under black light (λ = 364 nm). b) PL decays measured for CH 3 NH 3 PbBr 3 impregnated in the various silica template (green) along with their respective triple exponential fitting (red dotted curves).

ACKNOWLEDGMENTS

The synchrotron radiation experiments were performed at the BL04B2 of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2016A1063).


Blanche Segrestin
email: blanche.segrestin@minesparis.psl.eu

Kevin Levillain

Jérémy Lévêque

SOCIAL, BENEFIT OR PURPOSE-DRIVEN CORPORATIONS: A CONCEPTUAL FRAMEWORK TO NAVIGATE BETWEEN THE NEW CORPORATE FORMS Communication at the European Academy of Management (EURAM) 2023, Dublin

Keywords: corporate purpose, sustainable governance, benefit corporation, société à mission, cooperative

In a context of grand challenges, states are increasingly using law to modify corporate governance in order to make business corporations more sustainable. They increasingly introduce new forms of corporations -labelled as profit-with-purpose corporations -with incorporated social and environmental goals. But the diversity of new legal forms is likely to create confusion, both for policy makers and for corporate leaders. This article offers a conceptual framework to distinguish between the different types of profit-with-purpose corporations, based on their type of purpose. It then derives several propositions to draw attention to the contingency criteria of the different purposes, and, more importantly, to the need to have governance rules appropriate to the pursued purposes, as a condition to avoid purpose-washing and ensure integrity.

emergence of a market of social enterprise law (Murray 2016), there are in practice even more options available for corporations, as several models can be combined to create hybrid organizations [START_REF] Battilana | In search of the hybrid ideal[END_REF]. A recent example of this is Patagonia. Its founder Yvon Chouinard has recently decided to change the legal structure and to create a hybrid form with a charity that owns the company's nonvoting stock and a purpose trust responsible for controlling the corporation.

The growing variety of corporate forms nonetheless comes with the risk of confounding heterogeneous models. While corporate legal forms create diverse commitments and obligations, the same words can sometimes be used to refer to them, resulting in confusion. For example, recent handbooks of social enterprise law [START_REF] Means | The Cambridge Handbook of Social Enterprise Law[END_REF][START_REF] Peter | International Handbook of Social Enterprise Law. Benefit Corporations and Other Purpose-Driven Companies[END_REF] refer to very different forms under the single term "social enterprises." The US benefit corporation is included as a typical form of social enterprise because, as Pollman writes, "the new form has provided a legal category with specific rules that give a structure and meaning that was lacking from the vague term social enterprise" [START_REF] Pollman | Social and Asocial Enterprise[END_REF]. This mix of terms not only creates a risk of harmful confusion in practice, it is above all indicative of a lack of clarity at the theoretical level.

We certainly do see the field as being filled with very open-ended terms that promote conceptual confusion. This is clearly the case of the concept of a social enterprise, which encompasses both the historical trend of the social and solidarity economy, and the more recent and originally more American "social business" movement [START_REF] Defourny | Conceptions of Social Enterprise and Social Entrepreneurship in Europe and the United States: Convergences and Divergences[END_REF]. But the concept of a purpose -"mission" in French and some of the English-language literatureaddress societal needs and maximize their social impact, and their way of operating because they implement specific business models based on collaboration, typically at the local level." is very generic too. Battilana and Yen define it as "a corporation's core reason (or reasons) for being, guiding what a corporation should be designed to do and whose interests it should serve" (Battilana and Yen, forthcoming). In doing so they pave the way for a very broad continuum extending from simple profit-driven corporations to those with "multiple purposes", some of which are not only for profit. We could say the same for other types of purposes, such as the "raison d'être" introduced in France alongside the concept of the société à mission.

These different factors motivate an effort of conceptual clarification in order to help corporations and policy makers to find their way in the field of corporate legal forms that add purposes to the profit motive.

Here, we are specifically interested in corporate forms recognized by law, and which combine the possibility of a profit-driven goal with another objective not related to profit. Usually, the literature differentiates between corporations based on their ownership regime: profit-driven corporations are owned by capital investors; cooperatives are owned by the workers; and "nonprofit enterprises are defined by their lack of allocated property rights" (Bandini et al., 2022: 5). We believe, however, that it is important to refine the typology of corporations by focusing exclusively on the "for-profit socially responsible corporation" category in the typology of Bandini et al. (2022). These corporations are held by capital investors and have a "broadened mission" oriented towards the stakeholders. However widely different configurations exist among them. We propose a conceptual framework of these particular purpose-with-profit corporations, that differentiates between the types of purpose, that is, the content of the legal commitments made. This framework questions the rules of governance and therefore the appropriate accountability to ensure the enforceability and credibility of these commitments. Our conceptual framework aims at positioning the different forms of purpose-with-profit corporations in relation to each other, but also at discussing the coherence of the possible combinations. Our conceptual frameworks identifies three different models:

-the model based on shared evaluation standards -the model based on a particular "socius" of different beneficiaries, -the model based on the enterprise or entrepreneurial project. These three models do not claim to be exhaustive, and it will be necessary to discuss their blind spots. Our objective in constructing this framework was to avoid the classic analysis bias of assessing variety through the prism of a single model. For example, if we analyze benefit corporations or French sociétés à mission through the lens of social enterprise criteria, we will conclude that they are particularly poor and undemanding social enterprises.. However, in doing so, we would be disregarding the intent and scope of these initiatives. In addition to conceptual clarification, the identification of archetypal configurations makes it possible to formulate several propositions, both for public authorities and for corporations. In particular, it provides an account of the contingency criteria for adopting one model rather than another; and above all, it makes it possible to discuss the coherence between governance and commitments, and the conditions for good integrity.

In this way, we contribute to the growing body of literature on corporate purpose [START_REF] Jensen | Value Maximisation, Stakeholder Theory, and the Corporate Objective Function[END_REF][START_REF] Stout | The troubling question of corporate purpose[END_REF][START_REF] Gartenberg | Corporate Purpose and Financial Performance[END_REF][START_REF] Davis | Corporate Purpose Needs Democracy[END_REF][START_REF] Levillain | From primacy to purpose commitment: How emerging profit-with-purpose corporations open new corporate governance avenues[END_REF] as we differentiate between multiple categories of profit-with-purpose corporations, based on their type of purpose. We also characterize the contingency parameters in which these categories are relevant. Moreover, we contribute to the literature on sustainable or responsible corporations by describing the governance and accountability rules adapted to each type of purpose. Our analysis thus allows to discuss the coherence of legislative proposals at the state level or the coherence of statutory rules of hybrid organizations at the corporate level. We conclude with the research questions that need to be addressed today if we want to limit the drift and promote the growth of sustainable corporations, or even of corporations that would be contributors to contemporary issues.

I-Conceptual framework: differentiating between profit-with purpose corporations based on their purpose

Before presenting our conceptual framework, we wish to emphasize that we are exclusively focusing on the legal corporate forms referred to as profit-with-purpose corporations, which make commitments to goals that cannot simply be reduced to profit [START_REF] Hemphill | The Benefit Corporation: Corporate Governance and the For-profit Social Entrepreneur[END_REF][START_REF] Hiller | The Benefit Corporation and Corporate Social Responsibility[END_REF]). These forms include, first and foremost, the benefit corporation and its multiple variants, depending on the state in question [START_REF] Rawhouser | Benefit Corporation Legislation and the Emergence of a Social Hybrid Category[END_REF][START_REF] Murray | Explaining the Adoption of Benefit Corporation Laws by the US States[END_REF], and the French société à mission. But cooperatives are also within the scope of our study, considering that they are in fact corporations, albeit with additional goals and governance rules. Therefore, even though the legal forms of profit-with-purpose corporations differ from one another, they have several features in common: (1) they define a purpose, which in this article refers to the goals or objectives that the corporation seeks to attain, other than generating profits or furthering shareholders' interests; (2) this purpose is legally binding, which means that the corporation requires managers and shareholders to commit to it; and (3) they establish a governance with a related accountability system.

As these forms are all optional, they are adopted -when applicable -on a voluntary basis.

Once adopted, they have legal effects. Specifically, one of their common features is what could be referred to as purpose lock-in, i.e. the stability induced by the statutes which can only be called into question by the partners under certain conditions. Let us also specify from the outset that the different forms we are considering are defined in heterogeneous legislative contexts and that consequently their meaning and scope may vary according to the contexts in which they are placed3 .

Three configurations which cannot be reduced to one another stand out from our analysis. Each of them is seen as the articulation of a particular purpose and specific rules of governance.

a. The model based on shared evaluation standards

The first configuration that we have looked at is the case in which the corporation commits to evaluate its practices according to a shared external reference framework. A typical example of this is the benefit corporation (at least in its first formulation [START_REF] Clark | White Paper: The need and rationale for the benefit corporation: why it is the legal form that best addreses the needs of social entrepreneurs, investors and ultimately the public[END_REF]), although there could be multiple forms of this model.

Purpose:

In this case, the purpose is therefore not peculiar to the corporation, but rather determined by existing and legitimate standards. These range from the Universal Declaration of Human Rights and the Fundamental Conventions of the International Labor Organization, to reference frameworks such as the GRI reporting framework or the UN Global Compact. For a corporation, the idea is to give an account of its position with regard to good practices or principles, which could, potentially, be incorporated into hard law.

Governance: Given that the goal is to benchmark or position the corporation's practices according to standardized reference frameworks, in terms of governance and accountability, the corporation should be expected to: 1) clearly communicate using the chosen standard; 2) publish a report on this evaluation; and 3) ensure that the said report is audited and certified by an independent third party.

Typical example: This appears to be the model of benefit corporations in the United States.

The legal framework for benefit corporations, following the legislative template and as initially drafted in Maryland, specifically requires "the measurement of general public benefit against a 'comprehensive, credible, independent and transparent' third-party standard", as well as the publication of an annual report in accordance with the said standard.

One of the benefits of this form is that it makes corporations accountable for their practices in accordance with international standards, beyond the scope of the regional legislation of the territory in which they are incorporated [START_REF] Lévêque | Concevoir la mission comme un engagement génératif : enjeux, écueils et principes de formulation pour les sociétés à mission[END_REF]. For example, benefit corporations can be evaluated in accordance with the B Corp Certification reference framework. If we consider the example of a corporation in the construction industry, the B Corp form includes the following questions: 1) if the corporation has adopted "occupational health and safety policies"; 2) if employees have access to a retirement plan; and 3) what percentage of employees are paid, at a minimum, the equivalent of a "living wage for an individual" or what percentage above the minimum legal wage is paid to the employee with the lowest salary. We see that these initial criteria might entail legal obligations in some countries. However, in addition to providing evidence that the corporation is complying with certain minimum standards, evaluation in accordance with shared standards can subsequently be enriched and specify good practices on an industry basis.

Contingency criteria: This model, which ensures third-party verification of compliance with shared criteria, is particularly useful in two situations:

-We can see from these examples that the interest of this device is first to ensure a form of proof that the corporation adopts minimum principles of foresight and vigilance, particularly when the legal rules are non-existent. In this context, a responsible corporation is one that undertakes "actions that appear to further some social good, beyond the interests of the firm and that which is required by law" (McWilliams & Siegel 2001: 117).

-In comparison to a classic certification approach (such as that proposed by B Lab), the legal corporate form addresses a need to protect corporate leaders in certain states. This is because corporate law, whether rightly or wrongly, is perceived in some states, particularly in the US, as requiring corporate leaders to pursue the interests of shareholders only [START_REF] Levillain | Profit-With-Purpose Corporations: An Innovation in Corporate Law to Meet Contemporary Corporate Social Responsibility Challenges[END_REF].

b. The model based on a commitment to a community of beneficiaries

The second configuration is based on the idea of building a corporation that is an alternative to the classic capitalist corporation by transforming the "socius" of the corporation: if we make sure that the associates are not (only) shareholders, then the corporation will be able to pursue a goal other than profit. In this sense, the governance has a specific objective, which is to give control to parties other than shareholders [START_REF] Hiez | The suitability of French law to B Corp[END_REF]. The typical example is of course that of cooperatives, where the employees are the majority shareholders.

Purpose:

The commitment is to serve a community in a way that is not limited to financial interests only [START_REF] Defourny | Conceptions of Social Enterprise and Social Entrepreneurship in Europe and the United States: Convergences and Divergences[END_REF][START_REF] Defourny | Defining Social Enterprise[END_REF] 4 . The service to the community must systematically prevail over profit seeking, which is therefore no more than a means to that end [START_REF] Dacin | Social Entrepreneurship: A Critique and Future Directions[END_REF]. It is therefore accompanied by a principle of limited profitability, especially when public resources are mobilized..

Governance:

In this model, governance is a tool of social commitment and the means for community service5 . In other words, the social purpose of service to a community is supported by principles of governance:

-Participatory governance, which grants members of the target community voting rights, or even democratic governance;

-Collective management, with the idea that some reserves cannot be distributed as dividends and profitability must remain limited.

In this case, governance thus differs significantly from the governance of a traditional commercial corporation, precisely because it is the corporate governance that ensures that the service will be provided to the community.

Typical example:

The typical example of this model is the cooperative. The goal of emancipation through work is rooted in cooperative governance via the requirement that the employees hold the majority of the control and that they have the same control rights (e.g. 1 person, 1 voice). Governance is therefore the expression and the guarantee of the targeted purpose.

Contingency criteria:

We can note that in the sphere of social enterprise, social utility can refer to communities other than that of employees. Moreover, the social utility of an activity is difficult to define. Amblard shows that in fiscal terms, an activity is recognized to have social utility when a corporation "intervenes in a domain in which needs are insufficiently covered by the profit-driven sector, or addresses a public which cannot normally access the services of the competition-driven sector. The search for social utility therefore correlates the product or service provided with the target public" (Amblard 2010). Most often, the primacy of the social factor is based on participatory governance, i.e. targeted publics (e.g. the elderly) must be be represented (either directly or indirectly) in governance bodies.

This configuration is particularly useful in the case of activities requiring the support of public actors. But it has been also particularly mobilized by social movements engaged in the development of alternative project of society.

c. The model protecting an entrepreneurial project

Our last configuration is based not on shared reference frameworks or the identification of a beneficiary stakeholder, but rather on the goals that the corporate activities pursue, and therefore a specific entrepreneurial project.

The typical example of this is the société à mission corporate form introduced in France in 2019, as well as social purpose corporations in the United States, initially called flexible purpose corporations [START_REF] Cormac | The Emergence of New Corporate Forms: The need for alternative corporate designs integrating financial and social missions[END_REF][START_REF] Cormac | New Corporate Forms: One Viable Solution to Advancing Environmental Sustainability[END_REF].

Purpose: The Notat-Senard Report, submitted to the French government in 2018, motivated the creation of this corporate form. It allows us to characterize the underlying model [START_REF] Notat | Designing Legal Frameworks for Social Enterprises[END_REF]. The idea is that ventures may have ambitious social or environmental goals, such as developing new therapies for chronic illnesses, CO2 capture technologies, etc. Ventures or enterprises must be distinguished from their legal vehicle, which is the corporation [START_REF] Robé | The Legal Structure of the Firm[END_REF]. As in corporation, shareowners have legally the ultimate control rights, the corporate governance enable shareowners to reduce the purpose of business ventures ultimately to that of producing shareholder value. Yet business ventures, when they operate in the collective interest, can be "a part of the solution" to large-scale contemporary challenges, instead of being a part of the problem. The idea was thus to allow corporations to include a "raison d'être" (or purpose) in their bylaws, in other words, a "guide for determining their strategic orientations and the resulting actions" (Notat and Senard, 2018: 6). This raison d'être would thus constitute the mandate for which directors should be directly accountable.

In this configuration, the purpose is thus peculiar to each corporation. It constitutes the mandate of corporate directors. This mandate refers to the purpose of the activities to be carried out in common, a purpose likely to mobilize the different stakeholders and build a desirable future [START_REF] Notat | Designing Legal Frameworks for Social Enterprises[END_REF][START_REF] Segrestin | When the law distinguishes between the enterprise and the corporation: the case of the new French law on corporate purpose[END_REF]. In that sense, it can require more than the respect for certain established rules or good practices. It can also include some commitments to explore new scenario and to look for social or environmental innovations. The purpose provides also the criteria for evaluating the corporate strategy and activities.

Governance: When the purpose relates to a unique entrepreneurial project, evaluation by external third parties is more complicated. Because evaluation concerns not only compliance with good practices but also potentially the quality of the strategy and innovation efforts, it can only be entrusted to a group of experts.

In the case of the French société à mission, the law requires the following:

-The formulation of a raison d'être (principle guiding the corporate strategy) as well as social and environmental goals that are written into its bylaws in more specific terms;

-The creation of a "comité de mission" (purpose committee) containing at least one employee and which is exclusively responsible for overseeing the strategy with respect to the purpose. This purpose committee has the broadest powers to investigate within the corporation.

-The law also requires an audit by an independent third-party every two years. This audit must control whether the purpose committee is functioning correctly, and whether the purpose is being upheld.

Contingency Criteria

This form becomes particularly useful when an business activity has (or could have) significant repercussions on society or the environment. Alternatively, it is also useful when a corporation is expected to go through a period of profound turbulence, and stakeholders need to be reassured in a credible way that the corporate goals will be maintained, regardless of who its future shareholders will be. Typically, a corporation developing cleantech will continue to pursue its goal of developing new technologies enabling the energy transition, and therefore of investing in R&D and so on, even if its potential could be financially harnessed in another way.

In other words, the société à mission is useful when the corporation can no longer be considered legitimate in pursuing only a private interest (the corporation's best interest). Given the deep transformational effects that its activities may have on its surrounding ecosystem, the corporation must instead make explicit the rules of responsibility that it sets for itself in designing and implementing its future strategies.

These three models are interesting in terms of the conceptual framework that they create. In the first case, shared evaluation standards allow a corporation to compare itself with its competitors. In the second case, social enterprises give some control rights to a community of stakeholders, but they leave much leeway with regard to strategy. In the last case, the société à mission invites each corporation to define its own purpose, but provides governance rules to ensure that strategies will respect this purpose and remain controllable.

II-Navigating among profit-with-purpose corporations: conditions of validity and integrity

The conceptual framework we have built around three models is probably far too simplified and is unlikely to capture the specific debates that animate each of them 6 . Nonetheless, at this point in time, profit-with-purpose corporations form a relatively heterogeneous and still underconceptualized set of forms. Types of purposes and commitments vary considerably from one legal form to another, and it is of utmost importance to provide some landmarks in order to avoid hasty confusion. To our knowledge, our conceptual framework is the first to characterize

6 For example, debates on that which should be included or not within the scope of "social enterprises" or "social utility" are endless. A typical example is the possibility of having "second-generation" cooperatives, in other words, cooperatives with shareholder classes which have ultimately different rights [START_REF] Mcdonnell | Three Legislative Paths to Social Enterprise: L3Cs, Benefit Corporations, and Second-Generation Cooperatives[END_REF]. Similarly, the tax breaks that should (or should not) be granted to some social enterprises are the subject of debates. While some participants expect that recognition as a social enterprise should grant access to a specific tax regime, others believe that there should be a "taxable not-for-profit" status specifically for social enterprises [START_REF] Tucker | Impact Investment and Alternative Capital Channels: Funding Social Enterprise Success and Scale[END_REF]. Société à mission status is still too recent, but it may well be the subject of similar debates when the time comes to discuss the purpose of the companies concerned.

the nature of the purposes of profit-with-purpose corporations and thus to discuss whether their governance is consistent with their purpose or not.

In this section, we will use this conceptual framework to formulate three propositions that may subsequently provide avenues for empirical research.

Guidelines for policymakers and contingency criteria

Faced with the risk of conceptual confusion, our framework differentiate among several models which it would be fallacious to reduce to a single category -whether that of the social enterprise, benefit corporation, engaged corporation or purpose-driven corporation. The table below provides a summary of the different models of profit-with-purpose corporations.

Model

Société à mission

This conceptual framework provides markers for introducing new legal statuses. In particular, it highlights the contingency parameters to guide policymakers according to context. For example, we can see that the US legislative context has been more favorable to the adoption of benefit corporations, since mandatory social and environmental standards are a priori stricter in Europe. The public authorities can however also encourage a diversified ecology of legal frameworks in order to offer more options to corporations. In this case, it appears necessary for legislation to clearly state the circumstances under which a given form of profit-with-purpose corporation is suitable and relevant.

The first proposition could therefore be the following:

Proposition 1: The introduction in law of a form of profit-with-purpose corporation is especially useful if: 1) this form is adapted to the local economic and legislative context; and

2) the underlying model and contingency criteria are made explicit to help corporations to make an informed choice based on their situation.

Guidelines for corporations and articulation between models

Our conceptual framework is also useful not only for describing certain hybrid empirical configurations, but also for analyzing new hybrid forms adapted to the specific situation of each corporation. In particular, corporations can combine several models when faced with specific concerns.

For example:

-In some US states, benefit corporations combine the requirement of evaluation in accordance with a third-party standard, and the possibility of stating a specific purpose.

-Certain activities involving sensitive or vulnerable publics can also experience ecosystem transformations that require them to carry out an in-depth overhaul of their activity. For instance, cooperatives and mutual insurance companies in France have chosen to adopt société à mission status in addition to their status as cooperatives or mutual insurance companies. The MAIF, for example, is a mutual insurance company which historically has been deeply committed to its members, who are also the group's shareholders. However, the insurance sphere is currently undergoing change, with the arrival of big data transforming individual risk assessment and encouraging the emergence of digital competitors. Likewise, climate change is also turning traditional actuarial calculation methods upside down, and the question has arisen of what this mutual insurance company can currently promise to its stakeholders. In this context, the MAIF adopted société à mission status in 2020, thus committing to several objectives: in addition to providing services to its members (objective 1), it promotes the self-fulfillment of its employees (objective 2), as well as the objective of building a society with more solidarity (objective 3: the fight against demutualization), and that of contributing to the ecological transition through its activities (objective 4).

-Another interesting case is that of corporations performing a public service. In the case of La Poste in France, the corporation did not have a distinct legal status, with the exception of two specific characteristics: the French government is the main shareholder of La Poste, thus ensuring that it works in the interests of the public; and the French government also has a plan implementation contract with La Poste defining the public services that La Poste must perform, even if they are not profitable, at the request and on behalf of the government (delivery of mail 6 days per week across the national territory). In 2021, La Poste also became a société à mission. The work of S. [START_REF] Ragot | L'identité de l'entreprise de service public au prisme de l'entreprise à mission[END_REF] shows that the purpose defined in its bylaws is not a reiteration of the public services that it must perform, but instead focuses on the efforts that La Poste must make to support transformations in society, detect risks of decohesion, and develop, when applicable, new public services. The purpose adopted by La Poste therefore mainly focuses on the dynamics of public service renewal [START_REF] Ragot | L'identité de l'entreprise de service public au prisme de l'entreprise à mission[END_REF][START_REF] Ragot | L'engagement de La Poste pour un numérique inclusif : un éclairage sur le rôle d'opérateur de service public[END_REF].

The second proposition could therefore be the following:

Proposition 2: Depending on their activity, the sustainability issues they face and the legislative context in which they operate, corporations will tend to hybridize several profitwith-purpose corporation models.

Preventing greenwashing or social washing and conditions of purpose integrity

Our conceptual framework highlights the importance of alignment between governance principles and the corporate orientation or ultimate goals. On the other hand, it also highlights the conditions in which integrity can be met. 7 The literature has thoroughly studied the risks of "mission drift" (Ebrahim, Battilana, and Mair 2014;[START_REF] Grimes | Anchors Aweigh: The Sources, Variety, and Challenges of Mission Drift[END_REF][START_REF] Lévêque | Is a Shift Always a Drift? Governing Hybrid Organizations with Innovative Purpose[END_REF], that is, cases in which the corporate practices do not follow its purpose or its social or environmental mission.

Our conceptual framework allows to warn against the risks of drift, or greenwashing, in cases where governance does not correspond to the nature of the purposes. Typically, vigilance is required as the evaluation standards, as well as the notion of "mission" are highly generic and can cover very broad fields.

In the case of benefit corporations, the B Corp Certification form includes for instance some provision to the community of employees. The chapter on governance contains questions on both participatory and democratic governance ("Is your company democratically governed or do employees have ESOP pass-through voting rights?") and employee ownership [START_REF] Lévêque | Concevoir la mission comme un engagement génératif : enjeux, écueils et principes de formulation pour les sociétés à mission[END_REF]). However, as points are cumulative, it is not necessary to answer "yes" to all cooperative prerequisites. A corporation could indicate that it has largely developed employee shareholding, while answering "no" to the principle of "1 person 1 voice", or without having a particular aim for its activities. As a result, it may present only a few elements of a cooperative, without being a cooperative. Likewise, it is possible to have extensive employee ownership without the associated voting rights. The method for calculating the number of points is such that on can get the higher rate only by "picking and choosing" from among the evaluation criteria.

The same applies to specific purposes. For instance, benefit corporations in Delaware can write a "special purpose" into their bylaws, which a priori categorizes them in our third model

7 Here, we use the term "integrity" as proposed by Selznick, when, like P. Nonet, he seeks to describe how the law can reconcile openness on one hand and integrity on the other hand [START_REF] Nonet | Law and Society in Transition: Toward Responsive Law[END_REF].

(protecting the entrepreneurial project). Yet these corporations are not required to have a specific governance body to oversee their strategy. This lack of appropriate governance body to control the strategy casts doubt on the credibility of this form (Murray 2016)8 .

Therefore, to prevent greenwashing, or what is called "mission drift" in the literature, it is necessary to ensure that the governance framework is consistent with the type of purpose, i.e.

with the contents of commitments.

The thrid proposition could therefore be:

Proposition 3: Washing risks are higher when governance is not aligned with the type of purpose the corporation claims to have.

Discussion and further research

Our article contributes to the literature on the purpose of the corporation, differentiating between types of purposes. So far the literature has grouped together all companies owned by capital investors pursuing profits but which were also subject to the restrictions of a broader purpose, under the single umbrella category of "profit-with-purpose corporations". As a result, this category simultaneously contained German codetermined corporations and American benefit corporations, both under the banner of "social enterprises" [START_REF] Means | The Cambridge Handbook of Social Enterprise Law[END_REF]Murray 2016;[START_REF] Peter | International Handbook of Social Enterprise Law. Benefit Corporations and Other Purpose-Driven Companies[END_REF]. Other authors however do not see cooperatives as for-profit socially responsible corporations, since the latter are defined by a social or environmental purpose, whereas cooperatives have a particular ownership structure but no specific purpose (Bandini et al., 2022). Yet cooperatives are for-profit corporations whose majority shareholders can only be employees (who therefore have dual status) and whose goal is to serve the economic or social needs of a community 9 (Defourny 2006). Thus, our article brings to light not only the variety of purposes pursued by companies, but also the combinations and hybridizations between archetypal models.

Our analysis furthermore contributes to the literature on mission drifts in hybrid organizations (Ebrahim, Battilana, and Mair 2014) and to current debates around the conditions that ensure responsible or sustainable governance. It draws attention to the contingency conditions under which various purposes are relevant for a corporation and for society as a whole. Above all, it enables a discussion around the governance principles that are appropriate for a stated purpose.

This analysis therefore provides markers for policymakers and for Europe in particular.

However, it should also help corporations to design structures that promote their long-term integrity.

Our work does however have limitations. The phenomenon of legal forms of corporations with a purpose is still recent and developing. The typology presented here must therefore be considered exploratory for the time being. It will require further empirical research to test the validity of the propositions that we have made, and for monitoring the effects of a purpose on 9 In the law of 1947, in France, a cooperative ("société coopérative") is defined as follows: "A cooperative is a company composed of several persons who have come together voluntarily in order to address their economic or social needs by means of their common efforts and the necessary means." The law of 1978 adds: "Cooperative production companies are formed by workers in all categories or with any professional qualifications, who have come together to jointly practice their professions at an enterprise that they manage directly or via the intermediary of authorized representatives appointed by them and from among themselves."

the management or strategy of corporations, as well as cases of mission drift. In particular, there is still much work to be done around the content of purposes specific to a given corporation. Questions to be explored include: how can they be formulated in such a way as to be effectively binding? What are the criteria for defining a purpose that is sufficiently precise to be verifiable, yet without forcing the corporation in a specific strategic direction? Clearly, this is essential if the société à mission model is to be robust, and current legislation, both in Europe and in the United States, provides no precise criteria for formulating a specific purpose or a mission.

From a more theoretical standpoint, the differences that we propose between corporate purposes also relate to different theories of the enterprise. If we distinguish between the enterprise (as an economic organization) and the corporation (as the legal vehicle of the enterprise) {Robé, 2011 #2259} {Deakin, 2017 #3514}, the different models of our framework refer to different conceptualization of the enterprise. Authors in the field of social enterprise define the enterprise in terms of economic criteria (in contrast with non-profit associations).

For them, the enterprise involves: a) a continuous activity, producing and selling goods and/or services, b) a high degree of autonomy, c) a significant level of economic risk and d) a minimum amount of paid work [START_REF] Defourny | Defining Social Enterprise[END_REF].

By contrast, sociétés à mission are grounded in the idea that an enterprise is not only an economic organization for producing goods and services; it is also an organization of "collective creation" that invents new technologies and develops new knowledge and expertise.

It consequently has a much more radical impact, negative or positive, on society and the environment. This innovation capacity induces radical uncertainty for the future and can potentially cause harm. Seeing the enterprise as an organization of collective creation [START_REF] Segrestin | Refonder l'entreprise[END_REF] leads thus to reconsider its responsibilities, as it can no longer pursue the private interests of its members, be they are capital investors or employees. It becomes necessary to require not only vigilance with respect to the observable impacts of its activities, but also responsibility with respect to the future that these activities contribute towards or aim to create. Introducing new legal forms of corporations is consequently also a critical subject for researchers since, depending on the models adopted, the very conception of the enterprise and its responsibilities are at play.

The EU has adopted a series of initiatives in this respect. Following the Non-Financial Reporting Directive (2014), Shareholder Rights Directive (2017), and Action Plan on Financing Sustainable Growth (2018), the idea of "sustainable companies" is clearly present on the Commission's agenda. This is evidenced, for example, in the "Sustainable Corporate Governance Initiative" launched in

(and the controversial report published by EY(Roe et al.

2021)), or through the "Corporate Sustainability Due Diligence" project.2 In its guide on social enterprises, the OECD defines social enterprises as follows: "Like any social economy organization, social enterprises distinguish themselves in two respects: their raison d'être, as they primarily

Note here that we are excluding from the field of our analysisat least temporarilywhat could be called a "vigilance clause" (French: "clause de vigilance"), which has now been made obligatory in France for all corporate forms. For example, since 2019, Article 1833 of the French Civil Code has required all corporations to be managed with due regard to the social and environmental effects of their activities. This rule echoes the wording of Article 172 of the UK Companies Act 2006 or a specific rule stated in benefit corporation legislation in the United States, according to which "Directors and officers shall consider effect of decisions on shareholders and employees, suppliers, customers, community, environment, together the 'stakeholders'". This form is however not compulsory everywhere, and both in the United Kingdom and in the case of benefit corporations, company administrators must take these factors into consideration in the best interest of the corporation.

Defourny Nyssens' definition of a social enterprise (2011) is based on

indicators (in addition to the economic criteria characterizing the enterprise):-An explicit aim to benefit the community -An initiative launched by a group of citizens -Decision-making power not based on capital ownership -A participatory nature, which involves the various parties affected by the activity -Limited profit distribution. 5 See, for example, the conditions for a social enterprise in the EU report: https://ec.europa.eu/social/main.jsp?catId=738&langId=en&pubId=8274.

As states have created more options around the proposed legislative model, the general framework can be summarized in relatively open terms.Pollman (year??) argues that, "[t]he common features of the benefit corporation form include the requirement that the corporate charter must contain a clearly articulated public or social purpose, the directors must consider stakeholder interests beyond shareholder profit, and the company must report on its efforts to promote its purpose." Murray pointed out that "[b]enefit corporations must be measured against a 'third-party standard,' but the standard does not have to be B Lab's B Impact Assessment.93 B Lab conducts on-site reviews of randomly selected Certified B Corporations, whereas no such review is mandatory for merely being a benefit corporation"[START_REF] Murray | Choose Your Own Master: Social Enterprise, Certifications, and Benefit Corporation Statutes[END_REF]. Furthermore, in the case of Delaware, the law no longer requires compliance with an independent third-party standard, and offers benefit corporations the option of pursuing a "general public benefit" or a specific purpose: "In short, Delaware's PBC law mostly pushes the Model's benefit corporation framework toward increased private ordering"(Murray 2016). In the initial scheme from Maryland, evaluation based on a third-party reference framework and an annual public report are nevertheless compulsory.


Scott Brown and Sontag : Women Who Have Shaped our Views on the Ugly and Ordinary

Yale symposium, February 8 th , 2023

As I was invited to contribute to the publication of Denise Scott Brown In Other Eyes and to participate in this symposium, I proposed to Frida Grahn to relate a Denise Scott Brown's writing with Susan Sontag's one.

As seen here, both women have been photographed by Lynn Gilbert in the late 1970s in the context of the publication of the volume Particular Passions : Talks with Women Who Have Shaped our times.

I have to say that at first glance, much separates Denise from Susan Sontag who I believe never met each other. While the former has endlessly fought elitism in the field of architecture, the latter has been the embodiment of the very same elitism in the literary and artistic milieu.

Denise Scott Brown is a woman of action who worked for half a century to change professional practices in the fields of architecture, urban design and pedagogy. Susan Sontag was a pure intellectual, a writer of avant-garde fictions and a sophisticated essayist who stayed out of academic circles.

£In Philadelphia, Denise worked closely with Bob Venturi within an architectural collective that she always promoted, while Susan Sontag was a prima donna of the New York high society.

But Denise Scott Brown and Susan Sontag also have things in common. They were both born within the same years and received their intellectual training in the late 1950s at the best American universities-Berkeley then Chicago for Sontag, Upenn for Denise.

In their respective domains, they actively participated in the great upheavals that marked the She explained that camp is both a sensibility which concerns an observer, and a quality that applies to the object that he or she observes.

On the sensibility side, "It is one way of seeing the world as an aesthetic phenomenon." On the quality side, "the hallmark of Camp is the spirit of extravagance," the excess, the too much.

In respect to the observer, "Camp sensibility is disengaged, depoliticized -or at least apolitical." One could add non-judgmental. The camp object, on the other hand, is characterized by "a seriousness that fails." Sontag claimed that there is only true camp in the combination of sensibility and quality.

Camp implies having a sense of irony to the extent that "behind the straight public sense in which something can be taken..." artifacts and people always play a role: "Camp sees everything in quotation marks. It's not a lamp, but a 'lamp;' not a woman, but a 'woman.'" And above all, as Sontag put it, camp affirms that there is "a good taste of bad taste". The ultimate slogan being "it's good because it's awful".

Camp sensibility belongs to an historical moment -the mid 1960s -but it clearly has antecedents and successors. Sontag claimed that "Camp is modern dandyism. Camp is the answer to the problem: how to be a dandy in the age of mass culture." The connoisseur of Camp indeed shows aristocratic tendencies, even if one takes enjoyment "in the coarsest, commonest pleasures, in the arts of the masses."

Camp shares certain attributes with kitsch, but it has more irony and self-awareness. At best, kitsch is "naive Camp", or "pure Camp." Pop also has some similarities, but it lacks for its part a bit of love for its object: "Pop Art is more flat and more dry, more serious, more detached, ultimately nihilistic".

Then, what about architecture? As Sontag put it, actually "there are 'campy' movies, clothes, furniture, popular songs, novels, people, buildings…"

Scott Brown's Las Vegas

Considering this, with all the flashy casinos and hotels, funny wedding chapels, and glittering giant billboards that sprung along the Strip, Las Vegas had it all to become the mecca of camp.

However, if I believe Benjamin Moser's recent biography, Susan Sontag has never paid a visit to the so called Sin City or has shown any interest into it. As a matter of fact, very few american intellectuals granted importance to Las Vegas in the mid 1960 aside from Tom Wolfe who wrote an exhilarating article for Esquire magazine.

Thus, Denise Scott Brown was a forerunner when she patrolled the Strip for the first time in 1965 a year after Notes on Camp was published.

She was actually predisposed to take a comprehensive look at the gaudy constructions since she had mingled with the New Brutalists in England in the 1950s. From that earlier experience Denise has learned that " beauty (albeit an agonized beauty) can be derived from hard reality, and that facing uncomfortable facts can sharpen the eye and refine one's aesthetic ability."

As she brought Bob Venturi to Las Vegas, Denise share with him a "rule-breaking outlook to aesthetic" and her interest into "ugly things". In Particular passions the book I mentionned previously she remembered: "Dazed by the desert sun and dazzled by the signs, both loving and hating what we saw, we were jolted clear out of our aesthetic skins."

As an outcome of this moving experience Learning from Las Vegas was first published in march 1968 in The Architectural Forum. As I already suggested, this text might be read as a manifestation of the camp sensibility, however it is not explicit.

Firstly, Denise and Bob actually considered Las Vegas as a purely visual phenomenon, if not an aesthetic one, as they described an "architecture of styles and signs". Moreover their study of the Strip, and more extensively of the commercial boulevard, focused on the more extravagant of its landmarks, from the Caesar's Palace to the Stardust Sign.

Secondly, the two architects' gaze could be described as camp inasmuch it seems to be non-judgmental, depoliticized, and amoral. Both made it clear on several occasions that they should not be bothered for a lack of social commitment. Resolute to keep the different concerns apart, they insisted that "the morality of commercial advertising, gambling interests, and the competitive instinct is not at issue here."

Thirdly, the second part of Learning from Las Vegas that has been published in The Architectural Forum during the fall of 1971 sounds more explicitely camp, as Denise and Bob playfully juggled with good and bad taste.

As they praised the "Ugly and Ordinary Architecture", they listed the features of the Guild House : "The technologically unadvanced brick, the old-fashioned, double-hung windows, the pretty materials around the entrance, and the ugly antenna not hidden behind the parapet in the accepted fashion..." Their design of the facade of the building, however, is cleverly elaborated, full of artifice. Obviously, the Guild House is rather camp than kitsch, not naive at all. Somehow in Learnign from Las Vegas Denise and Bob often saw things in quotation marks too : It's an "antenna", It's a "duck", it's a "monument", it's "Las Vegas"...Their texte is masterpiece of wit and irony. But, I insisted, the two authors showed true consideration and even love for the artifacts of commercial and popular culture. Learning from Las Vegas is in my view camp rather than pop.

Camp or not Camp?

If Denise and Bob never claimed to have a camp view on commercial architecture, the study of the reception of Learning from Las Vegas is suggesting that its readers thought differently.

For instance, Tomas Maldonado, Martin Pawley, and Kenneth Frampton have complained about "the camp cult of the ugly and the ordinary".

But it is Charles Jencks, in Modern Movements in Architecture, who picked up more seriously Sontag's idea and divided American architecture into "Camp" and "Non-Camp."

He focused on aestheticization and depoliticization, then he related camp to formalism and to the International Style.

Interestingly, Jencks pinned Venturi and Scott Brown as a non-camp architects who, although incorporating pop or camp materials, had nothing to do with formalism, and could even be considered "morally hot." Let's notice that with his binary classification, Jencks missed the irony and the second-degree of camp.

More relevantly, C. Ray Smith, considered camp in architecture as a matter of sensibility in his book Supermannerism: New Attitudes in Post-Modern Architecture.

He argued that educated people have long been confronted with the spectacle of consumerism, the obscenity of advertising, and the vulgar transformation of the visual environment.

As he summarized: "Artists, instead of being merely outraged and horrified by all of this, instead of rejecting it all as exclusively as possible, determined (in their hideous fascination) that the way to make those artifacts of our undesigned, uncouth, philistine, everyday culture better was to make fun of them, to make a big, joking, tongue-in-cheek put-down of them. " C. Ray Smith then related the camp sensibility in architecture to the work Morris Lapidus, Charles Moore and above all Venturi Scott Brown.

Which camp?

At this stage, I believe it is important to challenge Sontag's assertion that camp sensibility is "disengaged, depoliticized -or at least apolitical". Indeed, camp has always been used For Denise and Bob, being revolutionary for an architect did not mean dreaming of a utopia but rather showing empathy for people's true expectations and for the existing city as it isand as they like it.

In his book No Respect: Intellectuals and Popular Culture Andrew Ross is saying that: "Unlike the traditional intellectual, whose function is to legitimize the cultural power of ruling interests, or the organic intellectual, who promotes the interests of a rising class, the marginal, camp intellectual expresses his impotence as the dominated fraction of a ruling bloc as he distances himself from the conventional morality and taste of the ascendant middle class."

It seems to me that Denise followed such a narrow and perilous path, as she identified herself as an American architect who has to get her hands dirty.

In the 1970s, she and Bob had to deal with a political, social and economic context that was less and less favorable to the production of pure architecture. Then they had to look at the worl round them with irony, to laught at it so they don't cry as Denise said to Stanislaus von Moos in an interview in 1975.

To conclude I would like to suggest that Denise and Bob writing on Las Vegas expressed thereby a melancholy which could associate with the loss of a better world, but also the awareness that the one they lived in can still be enchanting.

  1960s and 1970s in the United States, before becoming key figures of the american culture in the late 20th century. But, as I will try today to expose resonances in the works of Denise and Susan Sontag, I will do it specifically out of the examination of two essays they've published a few years apart: "Notes on Camp" and "Learning from Las Vegas". Two essays that have made them at the same time famous and outrageous. My main hypothesis is that the notion of Camp helps us to understand the meaning of Learning from Las Vegas in the same way that Denise and Bob's views on Las Vegas architecture helps us to critically interpret Notes on Camp. Sontag's Camp Let me remind first what Susan Sontag said about Camp through the fifty-eight aphorisms that she have published in the Partisan Review during the fall 1964.

  since the 1950's to defend marginal cultural and social forms and behaviors. It flourished as a way to oppose to mainstream views of normality. The gay community has used it to confront heterosexuals with their prejudices. As Judith Butler observed, camp played a significant political role through its capacity to shake up preconceived ideas, to reverse understandings, and to exaggerate the artificiality of what the dominant cultural players perceived as natural. In a similar way, Denise and Bob challenged the architectural norms. They undermined Modernist orthodoxy by welcoming extravagant roadside constructions into the architectural repertoire. Denise did it too by redeeming the suburban home when she designed the Learning from Levittown studio in the early 1970's. Denise and Bob actually showed a new kind of commitment at the very moment social and political battles were loosing intensity. By questioning the founding of good taste and acknowledging the popular culture, they were opening a new front.