Baoju Li

Zitao Wang

Zhuangzhuang Gao

Prof Jinquan S Suo

Ming Xue
email: xueming5@mail.sysu.edu.cn

Yushan Yan

Valentin Valtchev

Shilun Qiu

Qianrong Fang
email: qrfang@jlu.edu.cn

Prof Q Qiu

Fang

Prof M Xue

Prof Y Yan

Prof V Valtchev

Self-Standing Covalent Organic Framework Membranes for H 2 /CO 2 Separation

Keywords: Covalent organic framework, self-standing membrane, H2/CO2 separation

Abstract: Covalent organic frameworks (COFs) have been proposed as promising candidates for engineering advanced molecular sieving membranes due to their precise pore sizes, modifiable pore environment, and superior stability. However, COFs are insoluble in common solvents and do not melt at high temperatures, which presents a great challenge for the fabrication of COF-based membranes (COFMs). Herein, for the first time, we report a new synthetic strategy to prepare continuous and intact self-standing COFMs, including 2D N-COF membrane and 3D COF-300 membrane. Both COFMs show excellent selectivity of H2/CO2 mixed gas (13.8 for N-COF membrane and 11 for COF-300 membrane), and especially ultrahigh H2 permeance (4319 GPU for N-COF membrane and 5160 GPU for COF-300 membrane), which is superior to those of COFMs reported so far. It should be noted that the overall separation performance of self-standing COFMs exceeds the Robeson upper bound.

Furthermore, a theoretical study based on Grand Canonical Monte Carlo (GCMC) simulation is performed to explain the excellent separation of H2/CO2 through COFMs. Thus, this facile preparation method will provide a broad prospect for the development of self-standing COFMs with highly efficient H2 purification.

As the problems of global warming and environmental degradation become more and more serious, it is urgent to reduce carbon emissions and utilize clean energy. [1] Hydrogen is one of the most promising alternative energy sources due to its high energy efficiency and zero-carbon emission, yielding only water when burned. At present, the most commonly used hydrogen production technology is steam reforming of methane and the subsequent water-gas shift (WGS) reaction, in which carbon dioxide is the main by-product. [2] In order to obtain high purity hydrogen, it is necessary to find an efficient separation process of hydrogen and carbon dioxide, which is typical of pre-combustion capture. Compared with traditional separation processes, such as distillation, adsorption, extraction and crystallization, membrane-based separation is recognized as a powerful technology that guarantees high selectivity, low energy consumption and a small footprint for the separation process, satisfying the need for a new sustainable industrial process. [3][4][5] Therefore, using membrane separation technology to purify hydrogen and capture carbon dioxide is one of the most promising means but still remain elusive.

Covalent organic frameworks (COFs) are two-dimensional (2D) or three-dimensional (3D) open networks precisely woven by organic building units through covalent bonds to constitute predesignate topologies and tunable pore structures, presenting an emerging class of crystalline porous polymers. [6,7] COFs have potential applications in many fields, such as catalysis, [8] energy storage, [9] sensing, [10] photoelectric, [11] gas storage, [12] and separation, [13] because of their ordered and tunable pore structures, permanent porosity with a large surface areas, facilely tailored functionalities, outstanding thermal stability, and specific adsorption affinities. [14] It can be predicted that, amorphous membranes show uneven pores and a large amount of inaccessible pore volume, which will greatly affect their separation properties. On the contrary, due to the uniform channel sizes and more accessible functional sites, COF-based membranes (COFMs) are more likely to break through the trade-off between permeance and selectivity. Therefore, more and more scholars have currently made contributions to the development of COFMs. [15][16][17][18][19][20][21][22][23] For instance, to enable COFMs to meet the needs of gas separation, some effective strategies have been developed, including multilayer membranes, [24- 26] vertical membranes, [27] confined growth of metal-organic framework (MOF) inside a supported COF layer, [28] and staggered stacking in 2D COF nanosheets for reducing the pore size. [29] However, COFs are insoluble in common solvents and do not melt at high temperatures, which presents a great challenge for the fabrication of COFMs. There are still few truly universal approaches to make COFMs up to now. The classical method is to grow denser COFMs in situ on a modified porous substrate by a solvothermal reaction. [30][31][32] Other methods include interfacial polymerization, [17,23] layer-by-layer stacking of nanosheets, [18] electrophoretic deposition, [33] diffusion-induced, [34] baking, [35] and a compressed imine-based COF-aerogel. [36] It is worth noting that most of the reported membranes are fabricated on a support, and they cannot make full use of the pore of COF itself due to the shielding effect of other phases. [37] Therefore, the development of a new method for synthesizing self-standing COFMs is of great significance for making full use of the rich structural advantages of COFs.

Herein, we report a new strategy to construct continuous and intact self-standing COFMs for H2/CO2 separation, including 2D N-COF and 3D COF-300 membranes. Furthermore, these membranes exhibit high selectivity of H2/CO2 mixed gas with 13.8 for N-COF membrane and 11 for COF-300 membrane as well as excellent H2 permeance of 4319 GPU for N-COF membrane and 5160 GPU for COF-300 membrane, and especially the H2 permeance for COF-300 membrane is higher than those of previous reports from other COF-based membranes.

Notably, the overall separation performance of both COFMs exceeds the Robeson upper bound, and a theoretical study based on Grand Canonical Monte Carlo (GCMC) simulation further demonstrates the high separation power of COFMs in the H2/CO2 separation. To the best of our knowledge, it represents the first case of self-standing COFMs for H2/CO2 separation, which will greatly promote the development of COFMs for highly efficient H2 purification.

To obtain high-quality self-standing COFMs, we developed an ammonium acetateassisted steam induction strategy (Scheme 1). Typically, the appropriate proportions of amine and aldehyde organic linkers were mixed evenly in the first step. Subsequently, an appropriate amount of ammonium acetate was added and grind evenly with a mortar. In this process, a few drops of water were added dropwise to form a solid-liquid blend, and the bubbles were removed by ultrasound. The resultant blend was put into a round mold with a depth of 1 mm and a diameter of 15 mm, and was pressed flat with a glass sheet. Finally, the mold was put into a stainless-steel autoclave without contacting with dioxane and acetic acid solution directly, and reacted at 120 °C for 72 h. Notably, ammonium acetate will gradually decompose in the process of COFMs formation, providing enough space for the organic block reaction to obtain highquality COFMs. The resultant COFMs were gently rinsed with acetone (3 × 3.0 mL) and dioxane (3 × 3.0 mL) to remove potentially unreacted organic linkers, and then vacuum-dried overnight at 100 °C (Figure S1, Supporting Information).

The X-ray powder diffraction (PXRD) and grazing incidence X-ray diffraction (GIXRD) patterns of the fabricated COFMs showed typical crystal material characteristics, confirming a highly crystalline nature (Figure 1a and 1b and Figure S2, Supporting Information). These peak positions match with the crystal structures simulated by the Materials Studio 7.0 software. [START_REF]Materials Studio ver. 7.0[END_REF] It can be seen the absence of peaks at 1571 cm -1 and 1413 cm -1 from the Fourier-transform infrared (FT-IR) spectra (Figure S3, Supporting Information), indicating the complete removal of the ammonium acetate from COFMs. The C=O stretching vibration at around 1695 cm -1 and N-H stretching vibration at around 3100-3400 cm -1 were almost disappeared. Meanwhile, the new peaks of C=N bonds were displayed at around 1620 cm -1 and 1200 cm -1 , demonstrating that the Schiff-base condensation reaction occurred. Scanning electron microscope (SEM) images indicated that their surfaces were continuous and free of defects (Figure 1c and1d), which is particularly important for the selectivity of the separation. At the same time, the underlying crystals showed lots of pinholes from the decomposition of ammonium acetate and the agglomeration of COF microcrystals, which will greatly increase the mass transfer of channels. The thickness of both COFMs was about 800 µm, in which the part for dense membranes is only about 1 µm and the rest of membranes is mesoporous or macro-porous.

(Figure 1e and 1f as well as Figures S4 andS5, Supporting Information). Thermogravimetric analysis (TGA) profiles showed that no significant mass loss was observed for COFMs under a high temperature of 400 °C (Figure S6, Supporting Information).

In order to verify the porosity and surface areas of self-standing COFMs, N2 adsorptiondesorption tests were carried out at 77 K. The N2-adsorption isotherms exhibited classic type-I isotherms characterized by a sharp uptake under low relative pressures in the range of P/P0 =10 -5 -10 -2 (Figure S7, Supporting Information). The Brunauer-Emmett-Teller (BET) surface areas were found to be 845 m 2 /g for N-COF membrane and 834 m 2 /g for COF-300 membrane, respectively (Figure S8, Supporting Information). The pore size distribution of COFMs was calculated by nonlocal density functional theory (NLDFT, Figure S9, Supporting Information), and the pore diameters of N-COF and COF-300 membranes are 5.9 Å and 8.6 Å respectively, which is consistent with the previous reports. [START_REF] Dong | [END_REF]40] In the process of gas separation, the adsorption between the membrane material and the gas has a very important influence on the separation performance. Therefore, we investigated the adsorption isotherms of H2, CO2 and CH4 for two COFMs at different temperatures (Figure S10, Supporting Information). In previous report, COF-300 had the strongest adsorption effect for CO2 with the isosteric heat of adsorption (Qst) of 33 KJ/mol, CH4 with the Qst of 29 KJ/mol, and H2 with the Qst of 7 KJ/mol, respectively. [26] Meanwhile, we carried out CO2 and CH4 adsorption tests of N-COF at 273 K and 298 K, whereas the H2 isotherms were collected at 77 K and 87 K because the adsorption behavior of N-COF for H2 was not obvious under the condition of 298 K. Subsequently, the Qst was calculated by the Clausius-Clapeyron method.

The Qst value of N-COF for CO2 was 39.7 KJ/mol, which is much higher than those of H2 (7.4 KJ/mol) and CH4 (20.7 KJ/mol). Both COFMs showed strong adsorption of CO2 originating from the Lewis acid-base interaction of CO2 with abundant imine bonds in the porous frameworks of the COFs. This specific adsorption may have important guiding significance for gas separation performance.

Encouraged by the above results, we tested their H2/CH4 and H2/CO2 separation performance using the Wicke-Kallenbach system with an equimolar binary gas mixture as the feed and the Ar as the sweep gas on the permeate side at room temperature (25 °C). To avoid the risk of back flow of sweep gas during separation tests, an absolute pressure difference of about 0.1 bar across the membrane was used in this study (i.e., the feed pressure was fixed at about 1.1 bar of absolute pressure and the sweep pressure was kept at 1 atm, Figure S11, Supporting Information). As shown in Figure 2a, the selectivity of N-COF membrane for H2/CO2 is 13.8 with the permeance of H2 of 4319 GPU, and the selectivity for H2/CH4 is 5.8 with the permeance of H2 of 4634 GPU. Similarly, the selectivity of COF-300 membrane for H2/CO2 is 11 with the permeance of H2 of 5160 GPU, and the selectivity for H2/CH4 is 5 with the permeance of H2 of 5637 GPU (Figure 2b). Remarkably, the selectivity of two COFMs for H2/CO2 and H2/CH4 was higher than that of the corresponding Knudsen diffusion (H2/CO2: 4.7; H2/CH4: 2.8). Although the kinetic diameter of CO2 is smaller than that of CH4, both membranes showed even higher H2/CO2 selectivity, which indicates that the molecular sieving effect does not dominate the separation process. As reported previously, [41][42][43] this phenomenon can be explained by the synergistic effect of adsorption and diffusion of gas in the membranes instead.

When the gas mixture passes through the two self-standing membranes, only CO2 can be retained in the pore structure of the membranes while other small gas molecules will easily permeate through the framework since imine-based COFMs show a strong adsorption of CO2.

That is to say, the mobility of CO2 was retarded by this strong adsorption, while H2 can still pass through the pore network easily, leading to a high H2/CO2 selectivity. Notably, both COFMs also have very high H2 permeance, the possible reasons are as follows: (1) both COFMs have large intrinsic pore sizes, which facilitate the rapid transport of gas molecules; (2) the selfstanding membrane structure is not shielded by other phases, and there are abundant large pores stacked between crystals in the interior of the membrane, which also provide mass transfer channels for gas diffusion. Therefore, this unique membrane structure contributes to the high gas permeance of these self-standing membranes. When the transmembrane pressure difference is increased up to 0.2 bar, the selectivity of the N-COF membrane for H2/CO2 has been extremely reduced even below the Knudsen diffusion. Furthermore, the selectivity can be restored when the pressure is dropped to 0.1 bar, which indicates that the N-COF membrane still maintains structural integrity. The performance decline can be attributed to the low adsorption effect that is not enough to hinder the diffusion of CO2 under a high pressure.

Both COFMs exhibited outstanding running stability, which is reflected in the fact that the membranes have almost no performance degradation after 72 h of continuous testing (Figure 2c and2d). In addition, the separation tests were also carried out at 60 °C and 100 °C. As the temperature increases, the H2 permeance of two COFMs is almost unchanged, while the selectivity of H2/CO2 could be maintained at 12.2 and 10.6 for N-COF membrane and at 10 and 9 for COF-300 membrane, respectively (Figure 2e and2f). This trend can be explained by the interplay of adsorption and diffusion of H2 and CO2 in the pore structures of two self-standing COFMs. As the temperature increases, CO2 can diffuse more easily in the resulting free volume, which leads to an enhancement of CO2 permeance and hinders the diffusion of H2. It may be because these COFMs still have a strong adsorption effect of CO2 at high temperature, so the separation of H2/CO2 by two COFMs showed a good temperature stability and their separation performance did not decrease after running for 60 h at different temperatures (Figure S12, Supporting Information). The temperature dependence of H2 and CO2 permeance can be described by the Arrhenius equation (Figure S13, Supporting Information), indicating that the diffusion process of CO2 in two COFMs is mainly activated diffusion. While the constant H2 permeance of two membranes showed a weak dependence on temperature, this may be because the competitive diffusion of CO2 at high temperature hinders the penetration of H2. Moreover, after long-term testing at different temperatures, both COFMs kept its crystalline and structurally intact, which could be determined by PXRD tests (Figure S14, Supporting Information).

We summarized the permeance and selectivity of all reported COFMs for H2/CO2 (Table S1, Supporting Information). Both self-standing COFMs exhibited excellent selectivity, which considerably exceeds the corresponding Knudsen constants (4.7). In particular, both selfstanding COFMs showed ultrahigh H2 permeance, which is superior to those of COFMs reports up to now, such as COF-LZU1 (3684 GPU) [24] and vertically aligned TFB-BD (3802 GPU). [27] Furthermore, the overall performance of both self-standing COFMs surpasses the Robeson upper bound for H2/CO2 gas pairs (Figure 3, black line). [44] Notably, these self-standing COFMs exhibit high values for both permeance and selectivity, demonstrating an antitrade-off phenomenon. This is because self-standing COFMs are entirely composed of COFs without any interference from any secondary phase, ensuring high separation efficiency. The high permeance is also an inherent characteristic of these self-standing membranes since the cavities are inevitably formed in the membranes during the crystallization process, ensuring that the COFMs exhibit abundant CO2 adsorption sites and mass transfer channels. Therefore, COFMs show high flux and selectivity in the process of separating H2/CO2, despite their relatively thicker layer compared to the other composite membranes with the shielding effect of other phases or zigzag pathways. [27] We further performed a theoretical calculation to explain the separation of H2/CO2 by COFM materials. Grand canonical Monte Carlo (GCMC) simulation by the Sorption module of Materials Studio was used to simulate the competitive adsorption of CO2/H2 at fixed pressure. [45] The partial pressure of CO2 and H2 were set to be 50 kPa and the temperature was set at 298 K. The energy forcefield of Universal was utilized. The van der Waals interactions were calculated by the atom-based method with a fine cutoff distance of 12.5 Å, whereas the Ewald and group method summed the Coulombic interactions. The simulation parameters were set as 5 × 106 equilibration steps and 5 × 107 production steps. The 1 × 1 × 3 supercell of COF-300 and 2 × 2 × 5 supercell of AB stacking N-COF were used as adsorbents. The results showed that, in COF-300 cells, CO2 molecules tended to locate between the p-benzaldehyde structural units, whereas H2 molecules were dispersed in the open channels (Figure 4a). The average molecule loading in the supercell was 0.5 for H2 and 4.9 for CO2. The average isosteric heat was 7.1 kJ/mol for H2 and 16.5 kJ/mol for CO2. In this way, CO2 molecules were adsorbed in the stacked pores, and H2 molecules could flow in the pores, which explains why COF-300 has a large pore size but can still effectively separate CO2 and H2. Similarly, the average molecule loading in the AB stacking N-COF supercell was 4.2 for H2 and 82.7 for CO2 (Figures 4b andS15, Supporting Information). The average isosteric heat was 2.7 kJ/mol for H2 and 6.7 kJ/mol for CO2. Therefore, GCMC simulation results illustrated that both COFMs had high adsorption capacity for CO2 and relatively weak adsorption behavior for H2, leading to the excellent separation property of H2/CO2.

In conclusion, we developed a new universal method for preparing two self-standing COFMs for the first time, 2D N-COF membrane and 3D COF-300 membrane, and applied these COFMs to the separation of H2/CO2 gas pairs. The results showed that both self-standing COFMs exhibited outstanding selectivity for H2/CO2 mixed gas (13.8 for N-COF membrane and 11 for COF-300 membrane), and ultrahigh H2 permeance (4319 GPU for N-COF membrane and 5160 GPU for COF-300 membrane) based on the separation mechanism of adsorption diffusion, which is of great industrial importance for gas separation applications. In addition, the obtained membranes have excellent thermal stability and a long-term cycle stability, and their overall separation performance exceeds the Robeson upper bound. Furthermore, a theoretical simulation based on Grand Canonical Monte Carlo method is studied to illustrate the separation of H2/CO2 based on COFMs. Thus, this facile preparation strategy will provide a broad outlook for developing COFMs with highly efficient separation of H2/CO2 or other gas pairs in the future. S1).

Figures and Captions

Scheme 1 .

 1 Scheme 1. (a) Schematic representation of the COFM fabrication. (b,c) Structure and composition of N-COF membrane (b) and COF-300 membrane (c).

Figure 1 .

 1 Figure 1. (a,b) PXRD patterns of N-COF membrane (a) and COF-300 membrane (b). (c,d) SEM images showing the surfaces of N-COF membrane (c) and COF-300 membrane (d). (e,f) Cross-section SEM images of N-COF membrane (e) and COF-300 membrane (f).

Figure 2 .

 2 Figure 2. (a,b) Equimolar binary gas mixture separation performance of N-COF membrane (a) and COF-300 membrane (b). (c,d) Long-term test of N-COF membrane (c) and COF-300 membrane (d) for equimolar H2/CO2 mixture at normal temperature. (e,f) Selectivity and permeances of N-COF membrane (e) and COF-300 membrane (f) as a function of temperature.

Figure 3 .

 3 Figure 3. A comparison of H2/CO2 selectivity and H2 permeance for single-phase COFMs reported so far (the details of the H2/CO2 separation performance are shown in TableS1).

Figure 4 .

 4 Figure 4. Density distribution contours of H2 (red) and CO2 (green) mixture gas in COF-300 membrane (a) and N-COF membrane (b) based on GCMC simulation.

Acknowledgements

This work was supported by National Key R&D Program of China (2022YFB3704900 and 2021YFF0500500), National Natural Science Foundation of China (22025504, 21621001, and 22105082), the SINOPEC Research Institute of Petroleum Processing, "111" project (BP0719036 and B17020), China Postdoctoral Science Foundation (2020TQ0118 and 2020M681034), and the program for JLU Science and Technology Innovative Research Team. V.V., Q.F. and S.Q. acknowledge the collaboration in the framework of China-French joint laboratory "Zeolites".

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Conflict of Interest

The authors declare no conflict of interest.

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff))

Published online: ((will be filled in by the editorial staff))


Hugo Therssen

Laure Catala

Sandra Mazérat

Talal Mallah

Dominique Vuillaume

Thierry Mélin

Stéphane Lenfant

Electronic Properties of Single Prussian Blue Analog Nanocrystals Determined by Conductive-AFM

We report a study of the electron transport (ET) properties at the nanoscale (conductive-AFM noted C-AFM thereafter) of individual Prussian Blue Analog (PBA) cubic nanocrystals (NCs) of CsCo III Fe II , with size between 15 and 50 nm deposited on HOPG. We demonstrate that these PBA NCs feature an almost size independent electron injection barriers of 0.41 ± 0.02 eV and 0.27 ± 0.03 eV at the CsCo III Fe II /HOPG and CsCo III Fe II /C-AFM tip, respectively, and an intrinsic electron conductivity evolving from largely dispersed between ∼ 5x10 -4 and 2x10 -2 S/cm without a clear correlation with the nanocrystal size. The conductivity values measured on individual nanocrystals are higher by up to 5 decades than those reported on PBA films.

Introduction

Prussian Blue Analog (PBA) nanocrystals are nano-objects at the frontier between molecules and bulk materials, and have molecular properties that can be used for different applications 1,2 such as gas storage 3,4,5 , materials for energy issues, 6,7,8,9 magnetic properties for information storage, 10 electrochemical and biosensors, 11 catalysis, 12 environmental purification, 13,[START_REF] Lee | Improved adsorption properties of granulated copper hexacyanoferrate with multi-scale porous networks[END_REF] or biomedical applications. [START_REF] Busquets | Prussian blue nanoparticles: synthesis, surface modification, and biomedical applications[END_REF] The structure of PBA consists of a cyanidebridged bimetallic face-centered cubic (fcc) arrangement obtained from the reaction of a hexametallocyanate (negatively charged) and a hexa-aquometallate of transition metal ions (Fe in the pristine Prussian Blue) upon the substitution of water molecules by the nitrogen atoms of the metallocyanate molecules. [START_REF] Buser | Crystal-Structure of Prussian Blue -Fe4[Fe(Cn)6]3.Xh2o[END_REF] The neutrality of the network is ensured either by the presence of metallocyanate vacancies and/or by the insertion of positively charged alkali ions in the tetrahedral sites of the fcc structure. A wide variety of PBAs has been synthesized using different transition metal ions such as Cr, Mn, Co. [START_REF] Shriver | Environment of interstitial ions in a Prussian blue analog[END_REF][START_REF] Brown | Structures and solid-state reactions of Prussian blue analogs containing chromium, manganese, iron, and cobalt[END_REF] At the nanoscale, nanocrystals were prepared in water allowing the stabilization of nanocrystals with welldefined size and shape, [START_REF] Brinzei | Spontaneous stabilization and isolation of dispersible bimetallic coordination nanoparticles of CsxNi Cr(CN)(6) (y)[END_REF] that led using a seed mediated approach to the design of coremultishell heterostructures. [START_REF] Catala | Core-Multishell Magnetic Coordination Nanoparticles: Toward Multifunctionality on the Nanoscale[END_REF] The same approach is used here to prepare nanocrystals of increased size.

Here, we present an electrical study of the electronic transport (ET) through isolated PBA nanocrystals composed of Cs{Co III [Fe II (CN)6]} noted CsCoFe thereafter. Only few results exist in the literature, which describe ET properties of PBA. In particular the electron injection energy barriers at the contact interface and the intrinsic conductivity of PBA NCs have not been investigated so far. Previous experiments consisted in either ET experiments conducted at the microscale on film or powders, [START_REF] Cobo | Thin Films of Prussian Blue: Sequential Assembly, Patterning and Electron Transport Properties at the Nanometric Scale[END_REF][START_REF] Pajerowski | Electronic conductivity in Berlin green and Prussian blue[END_REF][START_REF] Lefter | Light induced modulation of charge transport phenomena across the bistability region in Fe(Htrz)(2)(trz) (BF4) spin crossover micro-rods[END_REF] or results obtained in our group at the nanoscale [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] demonstrating a weak attenuation of the electron transport through several (up to 3) CsCoFe NCs (15 nm in size) connected in series between two electrodes, i.e. a low electron transfer decay factor 𝛽=0.11 nm -1 , with the current I ∝ e -𝛽d , d the distance between the electrodes (15<d<45 nm). The current decay in these multi-NCs devices was ascribed to a multi-step coherent tunneling between adjacent NCs with a strong energy coupling (0.1-0.25 eV) between the adjacent CsCoFe NC. [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] Here, we report ET in individual CsCoFe NCs with various sizes in the same range (nominally: 15 nm, 30 nm and 50 nm). We prepared and deposited the CsCoFe NCs on highly ordered pyrolytic graphite (HOPG) surfaces and we characterized the electronic transport through individual NCs, i.e in HOPG/single PBA/C-AFM tip devices as a function of the PBA NC size. We found that the current increases with the NC size. To analyze the experimental current-voltage curves, we used two models. We first considered a quantum transport model as in our previous study of ET in one to three 15 nm NC in series. [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] In this single energy level (SEL) model, [START_REF] Datta | Electronic transport in mesoscopic systems[END_REF][START_REF] Cuevas | Molecular electronics: an introduction to theory and experiment[END_REF] the electrons are transferred between the two electrodes through a single molecular orbital (MO). Since the NC size is large compared to atomic-and molecular-scale (for which the SEL model was initially developed), we have also used a model suitable for nanoscale devices, i.e. a nano-Schottky diode as already used for C-AFM-tip/semiconductor nanocrystals, quantum dots and nanostructures interfaces. [START_REF] Tanaka | Local surface band modulation with MBE-grown InAs quantum dots measured by atomic force microscopy with conductive tip[END_REF][START_REF] Oh | Current-voltage and imaging of TiSi 2 islands on Si (001) surfaces using conductive-tip atomic force microscopy[END_REF][START_REF] Md | Direct detection of electronic states for individual indium arsenide (InAs) quantum dots grown by molecular beam epitaxy[END_REF] More specifically, we used a simple analytical model that consists in a double Schottky barrier (DSB) model [START_REF] Grillo | A Current-Voltage Model for Double Schottky Barrier Devices[END_REF] ii) The increase of the current with the NC size is not well explained by this model.

iii) With the DSB model, we found a Schottky barrier height (SBH) for hole injection of 0.41 ± 0.02 eV at the CsCoFe/HOPG interface and 0.27 ± 0.03 eV and CsCoFe/C-AFM PtIr tip, independent of the NC size. This finding is in contrast with size-dependent SBH observed in various non-ideal Schottky diodes, [START_REF] Rhoderick | Metal-semiconductor contacts[END_REF][START_REF] Tung | Electron transport of inhomogeneous Schottky barriers[END_REF][START_REF] Tung | Electron transport at metal-semiconductor interfaces: General theory[END_REF] or diodes with nanometer-scale contacts. [START_REF] Ruffino | Size-dependent Schottky barrier height in self-assembled gold nanoparticles[END_REF][START_REF] Hasegawa | Unpinning of Fermi level in nanometer-sized Schottky contacts on GaAs and InP[END_REF] and nano-diodes made of semiconducting nanocrystals or nanodots. [START_REF] Tanaka | Local surface band modulation with MBE-grown InAs quantum dots measured by atomic force microscopy with conductive tip[END_REF][START_REF] Oh | Current-voltage and imaging of TiSi 2 islands on Si (001) surfaces using conductive-tip atomic force microscopy[END_REF][START_REF] Md | Direct detection of electronic states for individual indium arsenide (InAs) quantum dots grown by molecular beam epitaxy[END_REF] iv) the intrinsic electron conductivity of the CsCoFe NCs is largely dispersed between ∼ 5x10 -

Experimental section

Sample preparation. The synthesis of the 15 nm CsCoFe nanocrystals has been reported elsewhere. [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF][START_REF] Trinh | Photoswitchable 11 nm CsCoFe Prussian Blue Analogue Nanocrystals with High Relaxation Temperature[END_REF] The larger size objects were obtained by the same approach used for the similar CsNiCr NCs (see details in the Supporting Information, section 1). [START_REF] Prado | Magnetization Reversal in (CsNiCrIII)-Cr-II(CN)(6) Coordination Nanoparticles: Unravelling Surface Anisotropy and Dipolar Interaction Effects[END_REF] The CsCoFe NCs are then deposited on a HOPG substrate by immersing a freshly cleaved HOPG surface in the colloidal suspension for 20 seconds. This step is followed by a thorough rinsing of the sample with deionized water and then with methanol, and finally a drying step under vacuum for several hours. The samples appeared stable over time in ambient air and at room temperature, but have nevertheless been kept in nitrogen environment for storage purposes.

C-AFM measurements were realized in an air-conditioned laboratory (Tamb = 22.5 °C, relative humidity of 35-40 %), with a Dimension Icon microscope (Brüker, US) equipped with a Nanoscope V controller and a PF-TUNA module with sensitivity factors comprised between 20 pA/V to 100 nA/V. Conductive (PtIr metal plated) tips have been used, both for topography imaging and I(V) measurements (SCM-PIT-V2 from Brüker with an apex radius ∼ 25 nm, a spring constant k = 2.8 N/m, and a resonance frequency of 75 kHz). Contactmode AFM was not used for sample imaging since it leads to the displacement of NCs outside the scanning area, even using a low scanning force (a few nN), due to the weak interaction force between the PBA NCs and the substrate. We instead imaged the sample topography in tapping mode, and addressed individual NCs electrically by switching from tapping to contact mode with the tip almost in point mode above a given NC. More precisely, the measurement procedure is conducted as follows: (i) the sample topography is acquired in tapping mode (TM-AFM); (ii) an isolated PBA NC is selected; (iii) the TM-AFM scan is progressively focused on the NC top (final scan size below 10 x 10 nm²) ; (iv) the AFM oscillation driving amplitude is suppressed to stop the cantilever oscillation; (v) the AFM tip is then gently brought into contact with the NC top, while monitoring the applied force as from the cantilever static deflection ; (vi) I(V) characteristics are recorded using a typical tip force of 15 nN (experimental data consist of a set of about 100-400 I(V) curves successively obtained by applying voltage ramps between -1 V to +1 V in the forward and then backward direction). All the I-V curves were acquired with the C-AFM tip positioned on the top surface of the PBA NC; (vii) after the I(V) data acquisition, the sample topography is imaged back in tapping mode to check for the integrity of the individual NC. For a given NC size, 2 to 3 NCs were measured on the same sample using the above-described I(V) measurement scheme.

Results

Topography by AFM after the NC layer deposition

Typical TM-AFM and scanning electron micrographs (SEM) images of the CsCoFe NCs for the different sizes and freshly deposited on HOPG substrates from a colloidal solution are presented in Figure 2. TM-AFM images confirmed the presence of NCs on the HOPG substrates with a sub-monolayer coverage. The surface coverage, however, differs from sample to sample (due to the simplistic deposition method). The samples with the 15 nm NCs have a surface coverage of ca. ∼220 NCs/µm², with a histogram/grain size analysis shown in Figure 2b given an average NC size of 15.8 ± 4.9 nm. The surface with the 30 nm NCs presents a lower surface coverage of around 57 NCs/µm², with an average NC height of 26.9 ± 7.2 nm and for the 50 nm NCs, we obtained ca. ∼110 NCs/µm² and an average NC height of and 42.4-± 18.1 nm. We notice a clear increase of the dispersion of the NCs size with the increase of the nominal size of the NC, this is due to the mutli step synthetic method to prepare nanocrystals with increased size (see SI for details). All samples (with nominal NC size of 15 nm, 30 nm and 50 nm) on HOPG substrates enabled to access individual NCs, as seen from the AFM images (and cross-sections) shown in figures 2d and 2e. Accessing individual NCs in a controlled way is a prerequisite to conduct ET transport measurements. In Figure 2d, an isolated nanocrystal of 15 nm, 30 nm and 50 nm of CsCoFe are presented with the corresponding height profile. We find the nominal height for each nanocrystal with, however, a larger lateral size due to the convolution effect with the radius of curvature of the AFM tip (estimated by the supplier around 25 nm).

Electronic transport properties by C-AFM

Figure 3 illustrates the evolution of current-voltage I(V) characteristics of NCs as a function of their size. For each size of CsCoFe NC, the current-voltage I(V) 2D histograms (Figure 3, middle) reveal low dispersed current values. The current histograms at fixed voltage (here +/-0.4 V) are fitted with a log-normal distribution given a log-mean current (log-Ī) and logstandard deviation log-s. We note a low log-s (lower than 0.3, see Table 1) indicating a reproducible and controlled acquisition of the I(V) characteristics with the C-AFM. By comparison, the I(V) 2D histogram realized on the same HOPG substrate (as a reference) presents higher current levels (e.g. log-Ī > -8.5, Ī>3x10 -9 A, at 0.4 V) (see Figure S2 in SI), thus the I(V) characteristics shown in Figure 3 correspond to the ET properties through the PBA NCs. The I(V) curves on NCs appear almost symmetric, with low ratios (inferior to 3 measured at +/-1 V). The same measurements were done on other NCs deposited on the same HOPG samples, the corresponding datasets are shown in section 3 in the Supporting Information, Fig. S3). Figure 4 summarizes the evolution of the mean current Ī (at +/-1V for all the measured samples). histogram from the fit with a Gaussian distribution (red lines), see fitted values in Table 1.

Discussion

Figures 3 and4 show that the current increases with the NCs size increasing from 15 nm to 50 nm nominal size, however, with a large dispersion from sample-to-sample. We started analyzing the I(V) datasets with the SEL model. [START_REF] Datta | Electronic transport in mesoscopic systems[END_REF][START_REF] Cuevas | Molecular electronics: an introduction to theory and experiment[END_REF] In this model, the ET occurs through a single MO (here the HOMO according to our previous results) [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] located at an energy ε0 below the Fermi energy of the electrodes. The MO is coupled (hybridized) to the electrodes, and these hybridizations are characterized by two coupling energies, Γ1 and Γ2 (see details in the Supporting Information). Fitting all the average I(V) of all the datasets shown Fig. 3 and Fig. S3, we found ε0 values between ∼ 0. NC size (nm) orbital). However, for the single PBA devices, we observed an increase of the current with the NC size in contrast to the current decay previously observed in the multi-NCs devices. [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] This latter behavior was explained by a strong coupling between the adjacent NCs and an ET dominated by hopping between them, 24 a mechanism not relevant here. In the case of single PBA NCs, with the SEL model the current increase is accounted for by an increase (a factor ∼ 7) of the coupling energies Γ1 and Γ2 with the NC size (Fig. S9 in the Supporting Information). Since the same electrodes (HOPG and PtIr tip) were used, the same NC/electrode interfaces were formed, it is difficult to understand why the interface hybridization would depend on the NC size. We note that the values of Γ1 and Γ2 in the present study are in the same range (here ∼ 0.2-0.8 meV) as in our previous work (∼ 0.5-1.5 meV) [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] supporting the fact that the same interactions with the HOPG and C-AFM tip are involved in the case of a single PBA NC of various sizes and in the case of interconnected multi-NCs as in Ref. [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] Moreover, the SEL model cannot be applied to the whole applied voltage range between -1V and 1V (see details on the validity of the SEL model in the Supporting Information), we considered another model. Materials of the PBA family are considered as large band gap semiconductors. Several works (on bulk and thin films of various PBA materials) have reported a band gap of around 2 eV [START_REF] Wojdeł | On the prediction of the crystal and electronic structure of mixed-valence materials by periodic density functional calculations: The case of Prussian Blue[END_REF][START_REF] Watanabe | Intra-and inter-atomic optical transitions of Fe, Co, and Ni ferrocyanides studied using first-principles many-electron calculations[END_REF] and a temperature activated behavior of electrical conductivity (in their partly oxidized state, the vacuum dried materials are insulators). [START_REF] Pajerowski | Electronic conductivity in Berlin green and Prussian blue[END_REF][START_REF] Rosseinsky | SITE-TRANSFER CONDUCTIVITY IN SOLID IRON HEXACYANOFERRATES BY DIELECTRIC RELAXOMETRY, VOLTAMMETRY AND SPECTROSCOPY -PRUSSIAN BLUE[END_REF][START_REF] Xidis | ON THE ELECTRONIC CONDUCTION IN DRY THIN-FILMS OF PRUSSIAN BLUE[END_REF][START_REF] Sato | Electric-fieldinduced conductance switching in FeCo Prussian blue analogues[END_REF][START_REF] Behera | Synthesis and Characterization of Ruthenium and Iron-Ruthenium Prussian Blue Analogues[END_REF] Given the size of the NCs, between the molecular scale and microscopic devices, the concept of nano Schottky is relevant, which takes into account non-ideal SB due to the low dimensionality of the metal/semiconductor interface (Refs. [START_REF] Tanaka | Local surface band modulation with MBE-grown InAs quantum dots measured by atomic force microscopy with conductive tip[END_REF][START_REF] Oh | Current-voltage and imaging of TiSi 2 islands on Si (001) surfaces using conductive-tip atomic force microscopy[END_REF][START_REF] Md | Direct detection of electronic states for individual indium arsenide (InAs) quantum dots grown by molecular beam epitaxy[END_REF][START_REF] Hasegawa | Unpinning of Fermi level in nanometer-sized Schottky contacts on GaAs and InP[END_REF] , see also a mini review in [ 44 ] and references therein). In these nano-Schottky diodes, the SBH values differ from those in their macroscopic counterparts, and ideality factors deviating far from unity (e.g. up to 2.5) [START_REF] Oh | Current-voltage and imaging of TiSi 2 islands on Si (001) surfaces using conductive-tip atomic force microscopy[END_REF] were observed. In particular, we found that the I(V) experimental datasets are well described by a double SB model 30 recently proposed to explain ET in several nanoscale devices (graphene 45 , MoS2 [START_REF] Liu | Scalable Submicron Channel Fabrication by Suspended Nanofiber Lithography for Short-Channel Field-Effect Transistors[END_REF] ). The double SB model consists of two back-to-back Schottky diodes at the interfaces in series with the intrinsic resistance of the NC (Fig. 5a): one diode accounts for the HOPG/CsCoFe interface (𝜙B1) and the other one (𝜙B2) for the interface at the CoCsFe/PtIr C-AFM tip. From the fit of I(V) curve, this analytical model allows extracting the two SB energy simultaneously albeit the two SBs are dissimilar (i.e. different energy barriers, ideality factors and contact areas), [START_REF] Grillo | A Current-Voltage Model for Double Schottky Barrier Devices[END_REF] and the intrinsic resistance of the NC. In this model, the current is always limited by the saturation current of the reverse-biased diode, the other diode being in the forward regime. Here, we consider a p-type NC in accordance with Bonnet et al. [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] since the ET occurs via the HOMO of the CsCoFe NC. Consequently, we measure the HOPG/CsCoFe diode (𝜙B1) at V>0 and the CsCoFe/PtIr tip diode (𝜙B2) at V<0 (voltage applied on HOPG, C-AFM tip grounded, see inset Fig. 5c).

The current IT between the two electrodes in the junction is written:

𝐼 ! = "# #$ # #% $%&'( &' %() ) # #$ * *&' %()+ $ +# #% * &' %()+ % ; 𝑈 = 𝑉 -𝑅𝐼 ! (1)
with q the elementary charge (q = 1.6 x 10 -19 C), V the applied bias, k the Boltzmann constant (k = 1.38 x 10 -23 J.K -1 ), T the temperature (here T = 293 K), n1,2 the ideality factors and IS1,S2 the reverse saturation currents, R the intrinsic NC resistance. The saturation current are expressed as:

𝐼 !",!$ = 𝑆 ",$ 𝐴 * 𝑇²𝑒𝑥𝑝 .- & !",!$ '( 0 (2)
with S1,2 the areas of the junctions, A* the Richardson constant (A* = 1.2 x 10 6 A.m -2 .K² for free carriers 47 ) and 𝛷 )",)$ the effective SBs. S1 corresponding to the surface area of the NC with the HOPG substrate was fixed to the nominal NC base surface value (square of the NC nominal size). S2 corresponds to the contact surface of the NC with the C-AFM tip, we estimate a surface S2 ~ 16 nm² for a loading force of 15 nN using a Hertzian model [START_REF] Wold | Fabrication and characterization of metal-molecule-metal junctions by conducting probe atomic force microscopy[END_REF] (see details in the Supporting Information Section 4). For example, the exact shape of the surface/tip contact (and thus its exact area value) depends on the precise shape of the tip (which can evolve during the successive C-AFM measurements), it also depends on the stiffness of the NC (not precisely known for CsCoFe NCs), but for Ni/[Fe(CN)6] it was observed that small NCs are stiffer than larger ones, 49 see details in section 4 in the Supporting Information). Also, albeit we used the same nominal loading force for all the measurements, the exact force applied by the C-AFM can vary and the pressure (around 1 GPa) at the tip/sample surface can also vary. It is known that the structural and electronic structures of PBA (and likely their ET properties) are dependent on the pressure. [START_REF] Bleuzen | CoFe Prussian Blue Analogues under Variable Pressure. Evidence of Departure from Cubic Symmetry: X-ray Diffraction and Absorption Study[END_REF] Another origin of the larger dispersion of the SBH at the NC/C-AFM tip interface could also come from the presence of the water meniscus (since measurements were done in air). It is known that the presence of water or humidity modifies the electronic properties of devices based on molecular nano-objects. [START_REF] Long | Effects of hydration on molecular junction transport[END_REF][START_REF] Zhang | Origin of the humidity sensitivity of Al/AlO(x)/MHA/Au molecular tunnel junctions[END_REF][START_REF] Smaali | Conductance Statistics from a Large Array of Sub-10 nm Molecular Junctions[END_REF] Albeit the measurements were done in an air-conditioned laboratory (see the Experimental Section), we cannot completely exclude that the fluctuations of the water meniscus (quantity of water and its ionic impurity contents) induce additional dispersion of the SBH values.

Thus, we conclude that this larger dispersion of the FB2 values are related to a less controlled interface at the C-AFM tip and that the SBH at the NC/C-AFM tip interface is also independent on the NC size with a mean value FB2 = 0.27 ± 0.03 eV. We also notice that the barrier height FB1 is always slightly higher than the barrier height FB2 by about 0.14 eV. This difference can be ascribed to the lower work function for the HOPG electrode (W = 4.47 eV) [START_REF] Hansen | Standard reference surfaces for work function measurements in air[END_REF] than for the PtIr electrode (W = 4.86 eV). [START_REF] Lee | The interlayer screening effect of graphene sheets investigated by Kelvin probe force microscopy[END_REF] The estimated SBH values are in agreement with previous works. From first-principles relativistic many-electron calculations of Fe, Co, and Ni ferrocyanide nanocrystals, the HOMO of CsCoFe is associated to the Fe 2+ -teg orbital at 0.2 -0.3 eV below the Fermi energy level. [START_REF] Watanabe | Intra-and inter-atomic optical transitions of Fe, Co, and Ni ferrocyanides studied using first-principles many-electron calculations[END_REF] From the I-V measurements on stacked layers of 15 nm CsCoFe NCs probed by C-AFM, Bonnet et al. [START_REF] Bonnet | Long-range electron transport in Prussian blue analog nanocrystals[END_REF] have shown that the ET in these samples involved the HOMO, which was measured at 0.42 -0.55 eV with respect to the Fermi energy of the electrodes. Concerning the ideality factors, we do not observe significant trends with the size of the NC (Figure 5, Figs S3 and S4 in the Supporting Information). From the analysis of all the datasets, we deduce n1 = 1.23 ± 0.07 and n2 = 1.47 ± 0.27 (Fig. S4). The n2 values are slightly higher than the n1 values, indicating that the HOPG/C-AFM interface is a less ideal than at the HOPG, in agreement with the discussion about the fluctuations of the SBH values (vide supra). In both cases, the n value deviates from ideality (n=1) which is due to any inhomogeneity, impurities and defects at the interface. For instance, at the HPOG/NC interface, the inhomogeneity of the electrical properties of the HOPG surface itself at different sheets, ribbons, step-edges 56 can play a role. At the NC/C-AFM interface the presence of impurities on the tip surface, water meniscus at the tip/surface interface can also play a role as mentioned above.

We note that the energetics of the PBA NC devices, deduced by the two models, are in reasonable agreement, with almost the same values for the SBH (position of the VB below the electrode Fermi energy) and the ε0 values (position of the HOMO below the electrode Fermi energy). This is consistent with the fact that the NCs are likely fully depleted (no band bending in the NCs). The very small C-AFM contact area (about 16 nm 2 , see the Supporting Information) makes capacitance measurements impossible (capacitance < ∼ 10 -18 F) in such C-AFM/NC/HOPG devices to check whether or not the capacitance is constant with the applied voltage (as expected for the fully depleted case). However, as evidenced by combining DSB model analysis and capacitance measurements in macroscopic Schottky diodes with few tens of nanometers thick semiconducting layers, [START_REF] Oswald | Field and Thermal Emission Limited Charge Injection in Au-C60-Graphene van der Waals Vertical Heterostructures for Organic Electronics[END_REF][START_REF] Kim | Capacitive behavior of pentacene-based diodes: Quasistatic dielectric constant and dielectric strength[END_REF] we can reasonably assume that this is also the case for the PBA single NCs. This feature makes the comparison of the interface energy barriers between the SEL and DSB models more pertinent in the absence of band bending in the Schottky diodes.

Figure 7a summarizes the estimated NC intrinsic resistance R for the whole datasets. From these values, we also estimate the intrinsic NC conductivity (Fig. 7b) using a simple equation and an idealized truncated pyramidal geometry for the HOPG/NC/PtIr tip with strongly asymmetric contact areas (see section 7 in the Supporting Information).

S3 (red circle symbols) and dataset #3 in Fig. S3 (blue triangle symbols).

The main feature is that the intrinsic electron conductivity is dispersed with values between ∼ 5x10 -2 -5x10 -4 S/cm for the 15 nm NCs. A less dispersed conductivity between 2x10 -2 -4x10 -3 S/cm is estimated for the 50 nm NCs. However, there is no clear correlation between the NC intrinsic resistance, nor the conductivity, with the NC size (i.e. no clear increase or decrease with size). This dispersion observed for the conductivity values on some nanocrystals mainly reflects the intrinsic dispersion of the NC structure probably inherent to the local inhomogeneities of the structure and/or chemical composition of these nanoobjects. We also note that the use of an idealized truncated geometry with the nominal NC size, instead of the real shape and size, is likely to induce some dispersion of the calculated conductivity. This dispersion of the structure is inherent to the synthesis route used to fabricate these nano-objects. A full statistical, much more time-consuming, study on a larger number of nanocrystals, would be considered in the future in order to better understand this conductivity dispersion.

Nevertheless, compared to sparse data in literature, the conductivity values reported above on individual nanocrystals are higher by up to 5 decades than those measured on PBA films:

1.5x10 -8 to 8x10 -7 S/cm for NaCo[Fe(CN6] films 42 and 5x10 -6 to 6x10 -3 S/cm for various Fe[Fe(CN6], Fe [Ru(CN6], KRu[Fe(CN6] films [START_REF] Behera | Synthesis and Characterization of Ruthenium and Iron-Ruthenium Prussian Blue Analogues[END_REF] . This work shows the importance of considering the nanocrystal individually to obtain a better estimation of its electronic properties and in particular a better estimation of its intrinsic electronic conductivity.

Conclusion

We have conducted a detailed analysis of the electronic transport properties of CsCoFe nanocrystals with nominal size between 15 and 50 nm. We have estimated the Schottky barrier heights at the interface with HOPG and PtIr tip of a conductive AFM. We show that they are independent of the nanocrystal size with a value 0.41 ± 0.02 eV at the HOPG contact and 0.27 ± 0.03 eV at PtIr C-AFM tip contact. These values of the hole injection barrier heights (PBA valence band offset with respect to the electrode Fermi energy) are consistent with a quantum transport model that estimates hole barrier heights of ∼ 0.3 -0.5 eV. The intrinsic electron conductivity of these CsCoFe nanocrystals was also estimated, with dispersed values between ∼ 5x10 -4 S/cm and 2x10 -2 S/cm without any correlation with the NC shape. The origins of the conductivity inhomogeneity remain to be established, but they might be related to the dispersion of the structure and/or chemical composition of the characterized nanocrystals.

Synthesis of the PBA nanocrystals

15 nm nanocrystals (CsCoFe_15). An aqueous solution (100 ml) containing 69.4 mg (4x10 -3 ML -1 ) of CsCl and 47.7 mg (2x10 -3 ML -1 ) of [Co(H2O)6]Cl2 is prepared. Then another aqueous solution (100 ml) containing 67.6 mg (2x10 -3 ML -1 ) of K3[Fe(CN)6] is prepared. The two solutions were mixed and vigorously stirred leading to the CsCoFe_15 nanocrystals. 30 nm nanocrystals (CsCoFe_30). An aqueous solution (240 ml) containing 122.2 mg (3x10 - 3 ML -1 ) of CsCl and 87.2 mg (1.5x10 -3 ML -1 ) of [Co(H2O)6]Cl2 is prepared. Then another aqueous solution (240 ml) containing 87.2 mg (1.5x10 -3 ML -1 ) of K3[Fe(CN)6] is prepared.

The two solutions were added simultaneously using a peristaltic pump (1 ml/minute) onto 50 ml of the previous solution containing the 15 nm nanocrystals, completed with 20 ml of water, that play the role of seeds for the growth of the objects leading to CsCoFe_30 nanocrystals. 50 nm nanocrystals (CsCoFe_50). An aqueous solution (180 ml) containing 92.4 mg (3x10 -3 ML -1 ) of CsCl and 65.4 mg (1.5x10 -3 ML -1 ) of [Co(H2O)6]Cl2 is prepared. Then another aqueous solution (240 ml) containing 89.4 mg (1.5x10 -3 ML -1 ) of K3[Fe(CN)6] is prepared.

The two solutions were added simultaneously using a peristaltic pump (1 ml/minute) onto 100 ml of the previous solution containing the 30 nm nanocrystals, completed with 40 ml of water, that play the role of seeds for the growth of the 50 nm objects leading to CsCoFe_50 nanocrystals.

The size of the objects corresponds to hydrodynamic diameter measured by DLS as depicted in the Figure S1. microscopy image of a sample of CsCoFe_50 showing the cubic shape of the nanocrystals as expected 1 and showing a relatively large distribution of size that is very narrow for the pristine objects. The large distribution is due to the two-step preparation process that leads from the 15 to the 50 nm samples.

Current-voltage 2D histogram measured on the bare HOPG substrates

It is known that bare HOPG substrates have a large dispersion of conductance (Fig. S2) depending on the exact sheets, ribbons, step edges contacted by the tip of the C-AFM with current from tens of nA (at low voltage <1V) up to µA and larger.

Supplementary I(V) datasets and analysis

On every samples, 2 to 3 NCs were measured following the same protocol as for the dataset shown and discussed in the main text (Figs. 4, 6, 7). 5. Statistical analysis of the dataset in Fig. 3 and in Fig. S3 The DSB model was fitted on all the individuals I(V) curves of the dataset to construct the statistical distribution of the model parameters shown in Fig. 3

Estimation of the NC conductivity.

The basic equation to estimate the conductivity σ from the resistance R is : G=(R) -1 =s S/L for a regular tube of surface S and length L, of equivalently G=(R) -1 =s V/L 2 with V the volume of the material contacted between the two electrodes. Here, we consider a truncate pyramidal device with asymmetric contacts at the HOPG/NC and at the NC/PtIr tip (see scheme in Figure S6). For a truncated pyramid inside the nanocube of side a, the volume is given by V = a(a 2 +ar+r 2 )/3, thus we used G=s(a+r+r 2 /a)/3 to estimate the conductivity, with a the NC size, r = 4 nm.

I(V) analysis using the single-energy level (SEL) model

The single-energy level (SEL) model (Eq. 3), considers that: i) a single molecular orbital (MO) dominates the charge transport, ii) the voltage mainly drops at the molecule/electrode interface and iii) that the MO broadening is described by a Lorentzian or Breit-Wigner distribution. 7,8 The simple energy scheme (inset Fig. S7) is described by ε0 the energy of the MO involved in the transport (with respect to the Fermi energy of the electrodes), Γ1 and Γ2 the electronic coupling energy between the MO and the electron clouds in the two electrodes, e the elementary electron charge, h the Planck constant. This analytical model reads:

(S3) This model is valid at 0 K, since the Fermi-Dirac electron distribution of the electrodes is not taken into account. However, it was shown that it can be reasonably used to fit data measured at room temperature for voltages below the transition between the off-resonant and resonant transport conditions at which the broadening of the Fermi function modify the I-V shape leading to sharpened increase of the current. [9][10][11] Moreover, for the sake of comparison with the I(V)s previously measured for multi-NCs devices, which were acquired

  (one Schottky diode at each interface) in series with the intrinsic resistance of the PBA NCs. The main observed features are the following: i) The SEL model gives an energy level of the MO involved in the ET at about 0.3-0.5 eV below the Fermi energy of the electrodes, independent on the NC size, in agreement with the values in Ref. [ 24 ].

Figure 1 .

 1 Figure 1. (a) Scheme of the unit cell of the fcc structure of CsCoFe PBA NCs (adapted from 24 ). The cell parameter is close to 10 Å. (b) Scheme of the conducting AFM experiments, in which an individual PBA NC with a characteristic size around 50 nm deposited on a freshly cleaved HOPG substrate is addressed, and statistics of I(V) characteristics are recorded using a given AFM tip force (see text). The AFM PtIr coated tip is grounded, the voltage V is applied on the HOPG substrate.

Figure 2 .

 2 Figure 2. (a) 5 x 5 µm topographic TM-AFM images for the three sizes of CsCoFe NCs (15 nm, 30 nm and 50 nm) deposited on a HOPG substrate; (b) Corresponding height histograms (function Statistical Functions / Distribution of heights in Gwyddion v2.60 software) (15 nm and 50 nm NCs). Histograms for the 30 nm NCs have been obtained using a grain recognition analysis (function Data Process / Grains / Mark by Edge Detection with a Laplacian fixed at

  and right respectively): log-mean current (log-Ī), the corresponding mean current Ī, and the log-standard deviation (log-σ).

Figure 3 .

 3 Figure 3. C-AFM 2D current-voltage I(V) histograms obtained with around 200 IVs traces (middle) and corresponding 1D histograms at -0.4 V (left) and +0.4 V (right) for three NCs of 15 nm, 30 nm and 50 nm deposited on bare clean HOPG (dataset #1). The average current at +/-0.4 V (log-Ī) and the log-standard deviation (log-s) were obtained on each 1D

Figure 4 .

 4 Figure 4. Mean current at 1V (filled symbol) and -1V (open symbol) for all the measured data set: for data shown in Fig. 3 (black square symbols), dataset #2 in Fig. S3 (red circle symbols), in blue dataset #3 in Fig. S3 (blue triangle symbols).

  3 and 0.5 eV, independently of the NC size (Figs. S7 and S8 in the SI). These values are consistent with those obtained for the one-tothree 15 nm NC in series and they were ascribed to the HOMO of the CsCoFe NC (Fe 2+ -t2g d

Figure 5 .

 5 Figure 5. (a) Energy diagram of the HOPG/NC/C-AFM tip junction with two SBs identified with red lines without applied bias for a p-type material, and the equivalent electrical circuit with the two Schottky diodes in opposite direction and the intrinsic resistance of the NC. (b)Energy diagram of the same junction at V<0 applied on the HOPG substrate. (c) Average Ī(V) curves (black line) corresponding to the C-AFM 2D current-voltage histograms presented inFig.3for the three nominal sizes of NC. Fits using a double SB model (Eqs 1 and 2) are shown as red lines. In the inset, the shaded diodes are in the forward regime. At V>0 (V<0, respectively), the measured current is the reverse current of the HOPG/CsCoFe (CsCoFe/PtIr tip, respectively) diodes, respectively. The fits converged with a coefficient of determination (R²) values between 0.98-099.

Figure 6 .

 6 Figure 6. Barrier heights 𝛷B1 (HOPG/NC) and 𝛷B2 (NC/C-AFM tip) extracted from the fits on all the I(V) dataset: dataset #1 shown in Fig. 3 (square symbols), dataset #2 in Fig. S3 (circle symbols), dataset #3 in Fig. S3 (triangle symbols), see the Supporting Information, Section 3, for the corresponding 2D histograms and mean Ī(V) fits. Lines correspond to the mean values for FB1 and FB2.

Figure 6

 6 Figure 6 shows the SBH extracted from all the I(V) datasets. At the HOPG/NC interface, the energy barrier height is constant with a mean value FB1 = 0.41 ± 0.02 eV. At NC/C-AFM tip interface, we measured more disperse values in function of the NC size. This feature can be rationalized because the C-AFM tip contact is flawed by various uncontrolled fluctuations.

f

  B1 : HOPG/NC interface f B2 : NC/C-AFM tip interface

Figure 7 .

 7 Figure 7. Evolution of the resistance and conductivity of the CsCoFe NCs extracted from the fits on the I(V) dataset: dataset #1 shown in Fig. 3 (black square symbols), dataset #2 in Fig.

2

 2

Figure S2 .

 S2 Figure S2. 2D histogram of the HOPG substrate used for the NC deposition with a mean current measured by C-AFM; log-Ī superior to -8.5 (corresponding to Ī > 3 x 10 -9 A) at 0.4 V.

Dataset # 2 Dataset # 3 Figure

 23 Figure S3. C-AFM 2D current-voltage I(V) histograms obtained with around 200 IVs traces for PBA NCs (Dataset #2 and #3) (Left), and the corresponding mean Ī(V) curves (black line) (Right) adjusted using the double SB model and by adjusting parameters: the effective SBs (𝛷 !",!$ ), the ideality factors (n1,2) and the intrinsic resistance R (red lines).

6 .

 6 , main text (Dataset #1) and in Fig S3 (Dataset #2 and #3). Ideality factors.

Figure S5 .

 S5 Figure S5. Evolution of the ideality factor of the two CsCoFe NC Schottky diodes. The values refer to the dataset #1 shown in Fig. 3 (square symbols), dataset #2 in Fig. S3 (circle symbols), and dataset #3 in Fig. S3 (triangle symbols).

Figure S6 .

 S6 Figure S6. Truncate pyramidal device with asymmetric contacts at the HOPG/NC and at the NC/PtIr tip considered for the estimation of the NC conductivity.

Figure S8 . 14 Figure S9 .

 S814S9 Figure S8. Energy levels ε0 obtained from the SEL model (fits shown in Fig. S7): dark squares (dataset #1), dark circles (dataset #2), dark triangles (dataset #3). The red symbols are the full statistics for the multi-NCs devices (from Fig. S18 in the ESI of Ref. 12 ).

Table 1 :

 1 Parameters of the log-normal fits of the current distributions at -0.4V and +0.4V

			15 nm NC	30 nm NC	50 nm NC
		log-Ī	-10.73	-10.35	-9.31
	-0.4 V	Ī (A)	1.86 x 10 -11	4.47 x 10 -11	4.90 x 10 -10
		log-σ	0.18	0.23	0.26
		log-Ī	-10.76	-10.76	-9.51
	+ 0.4 V	Ī (A)	1.74 x 10 -11	1.74 x 10 -11	3.09 x 10 -10
		log-σ	0.25	0.15	0.25

(Figures 3, left

Table 2

 2

	) confirm the results simply

Table 2 .

 2 Fitted

values of the SB heights at the HOPG/NC (𝛷B1) and NC/tip (𝛷B2) interfaces, the ideality factors (n1 and n2) and intrinsic NC resistance (R) for all the datasets. The table summarizes the mean values with the statistical dispersion, standard deviation (detailed in Supporting Information Section 5).

S/cm and 2x10 -2 S/cm without correlation with the NC size.

Acknowledgements

The IEMN SPM characterization facilities are partly supported by the French Network Renatech. This work has been financially supported by the French National Research Agency (ANR), project SPINFUN ANR-17-CE24-0004. We acknowledge D. Deresmes for his valuable help with the C-AFM instrument, and Anne Duchêne and Clément Jamme for the TOC graphic.

Author contributions

H.T. prepared the samples (NC deposition on HOPG) and carried out all the C-AFM and TM-AFM measurements as part of his PhD thesis (supervised by S.L. and T.M.). L.C., S.M. and T.M. synthesized the PBA NCs. H.T., S.L. and D.V. analyzed the data and did the modelization. S.L. wrote the manuscript with the contributions from all authors. All authors have given approval of the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Electronic Properties of Single Prussian

Blue Analog Nanocrystals Determined by

Conductive-AFM.

Hugo Therssen 1 , Laure Catala

Estimation of the contact area at the NC/C-AFM interface using a Hertzian model

We estimate the electrical contact surface for a loading force of 15 nN using a Hertzian model: 3

where R is the radius of the C-AFM tip (fixed at 25 nm according to the manufacturer), Fapplied the tip load force (15nN), E* the reduced effective Young modulus defined as:

with ENC/tip and 𝛾 .//123 the Young modulus and the Poisson ratio of the NC and the C-AFM tip respectively. The Young modulus of CsCoFe NCs is not known. A value of 43 GPa was reported for bulk material. 4 Values of about 30 GPa and 24 GPa were measured for 3 nm and 115 nm NCs of another material (Ni/[Fe(CN)6]). 5 By using the following values Etip = 204 GPa, 6 ENC = 24 GPa (by default, see above), 5 𝛾 123 = 0.37 6 and 𝛾 ./ = 0.36, 5 we estimate a surface S2 ~ 16 nm². This Hertzian model gives an estimation of the NC elastic deformation close here to 0.2 nm, negligible compared to the size of the NC.

Figure S4. Statistical distributions of the fitted model values obtained with the fitting with the double SB model and by adjusting parameters: the effective SBs (𝛷 !",!$ ), the ideality factors (n1,2) and the intrinsic resistance R, on a random sample of 20 I(V)s curves extract in

the complete datasets presented in Fig. 3 and Fig. S3 to obtain an estimation of the statistical distribution of the parameters. between -0.5 and 0.5 V, 12 we limited the fit of Eq. S3 to this voltage window. We verified that the condition of applicability of the 0K SEL model to room temperature experimental data is satisfied (here with ε0 < 0.5 eV, Γ1 and Γ2 around 0.1-1 meV, this condition is |V|<0.64 V). 13 The fits were done with the routine included in ORIGIN software (version 2019, OriginLab Corporation, Northampton, MA, USA), using the method of least squares and the Levenberg Marquardt iteration algorithm. Figure S7 shows the fits on the average I(V) of the three datasets shown Fig. 3


To build the welcoming city

Cyrille Hanappe

To cite this version:

Cyrille Hanappe. To build the welcoming city: Calais, Grande Synthe, Mayotte -Theotical and practical questions about cities and arrival. To re-invest existing and outdated housing units

«

  Build In My Backyard » : Les zones pavillonaires en déprise sont investies soit par une transformation des logements soit par la densification des parcelles. Des ensembles de logements prévus à la démolition type ANRU sont reprise et appropriés aussi bien par des familles que par des artistes en résidence pour créer un lieu de culture et de vie dans la ville.

The City as a borders. How cities shape migrants and how migrants shape the cities..

  Institut Convergences Migrations International Conference on Migration (ICM2) -Migration research at a crossroads. -Sanctuary cities and welcoming territories, Institut Convergences Migrations; Michel Agier, May 2021, Paris (en ligne), France. halshs-04270836

	To build the welcoming city Two situations : To think and to build The welcoming city To secure spontaneous neighborhoods and camps To build and run To build a new « migrants house » ecological welcoming inside the city neighborhood Calais and Grande Synthe Psychical Needs <-> Physiological Needs To squat and invest deserted building of the city To build new and adaptable building units transformable and To re-invest existing and outdated housing To secure spontaneous neighborhoods and camps To build and run « migrants house » inside the city To build a new ecological welcoming neighborhood To build new, To squat and invest transformable and deserted building of the city adaptable building
	Cyrille Hanappe

Calais, Grande Synthe, Mayotte -Theotical and practical questions about cities and arrival Babels -


De l'écran à la toile : l'absence à l'origine d'une expérience inédite 1

Yannick Lebtahi Maître de Conférences Habilitée à Diriger des Recherches en Sciences de l'Information et de la Communication, Université de Lille.

Zoom sur la fac 2 est un ouvrage collectif que j'ai initié dans le contexte de la crise sanitaire de 2020. L'imprévisibilité de celle-ci et le confinement imposé ont contraint les universitaires à se saisir du dispositif multimédia pour dispenser leur enseignement à distance et ainsi ne pas rompre les liens avec les étudiants et ne pas les abandonner à leur triste sort.

Dans l'urgence des préoccupations d'un monde incertain, les universitaires et les enseignants plus globalement ont inventé de nouvelles formes et de nouvelles pratiques fondées sur la reliance. Les problèmes individuels et collectifs dans leur complexité ont fortement teinté la transmission des savoirs.

L'incertitude selon Edgar Morin 3 « détermine le caractère aventureux de nos destinées, elle rappelle en effet à notre conscience que la vie de chacun est une aventure […] mais la vie d'une nation l'est également, et c'est valable pour toute l'humanité. C'est cette incertitude qui confère à une telle aventure d'être singulière. Ceux qui s'escriment à lui fixer des certitudes afin d'anticiper et de limiter les aléas ne peuvent qu'échouer dans leur entreprise. L'obsession de maitriser le futur en contrôlant les facteurs d'imprévisibilité est aussi inepte que délétère. Se camoufler, occulter le caractère incertain de l'aventure humaine est une illusion, et la pandémie de Covid19 sert peut-être à faire prendre conscience que l'incertitude ne résulte pas seulement d'un virus, mais est liée aussi à l'avenir et au destin de l'homme ».

Selon moi, face à l'écran de l'ordinateur ou du smartphone, l'aventure incertaine d'un réel fabulatoire nous a confrontés pleinement à notre désir de voir -à notre pulsion scopiquetout en nous plaçant face au vide (au rien) d'un espace infini.

En effet, face à l'écran -face au flux incessant -nous ne sommes en aucun cas passifs, mais plutôt engagés dans une confrontation avec nous-mêmes et avec les autres.

Devant nos écrans, nous sommes en activité, une activité qui siège dans l'inconscient sous la forme d'un vaste mouvement de régression narcissique.

Nous sommes en sur-perceptivité et en sous-motricité à l'image du petit enfant face au miroir primordial.

Poussé par la pulsion scopique, -elle-même issue de l'interdit du trou de la serrure de la chambre parentale que certains appellent voyeurisme dans mon domaine -s'instaure alors le leurre d'une vision complète, extensive et terminale, un inextinguible désir de voir, d'en voir toujours plus qui nous empêche de quitter l'écran, de quitter ce qui nous est donné à voir et à entendre.

Chacun communique avec lui-même au sens plein du terme, c'est-à-dire avec des phénomènes de feed-back, d'implication, de choc en retour et d'interaction entre ce que l'on est, ce que l'on a été et ce que l'on projette de soi, de nous.

Au travers de cet ouvrage, j'ai cherché à mettre en partage des expériences vécues dans la solitude face à l'écran -bien qu'irrévocablement reliés les uns aux autres -pour montrer combien le non-lieu que nous imaginons ouvre le champ du possible. La mise en lumière des postures réflexives et critiques participe au tissage des liens sociaux numériques et dessine leurs enjeux humanistes.

L'écran ou l'interface, à l'image de la toile ou de la feuille blanche, est un obstacle source de tensions que chacun à sa manière a dû franchir pour une créativité singulière.

Ce qui est inédit à ce moment-là se situe du côté de l'articulation entre la culture professionnelle des enseignants et la culture numérique, et les opérations de transferts de leurs savoir-faire propres à celle-ci qui s'imposent en retour dans leur pratique pédagogique.

En nous projetant davantage dans la société numérique, nous avons donc été confrontés aux pratiques sociales qui organisent les différents espaces symboliques et numériques. En les prenant en compte, nous avons pensé nos enseignements.

Parce que les modalités de l'expression qui les caractérisent envahissent malgré nous notre société et bouleversent nos interactions sociales.

Dans une forme d'errance à la Robinson Crusoé et avec une certaine curiosité, j'ai navigué à la découverte des potentialités du dispositif et des outils multimédias que j'allais me réapproprier pour imaginer les conditions de la rencontre avec l'étudiant.

C'est précisément à ce moment-là que s'engage une forme de passage à l'acte, un fort désir, et je cite Jean Nadal4 « d'habiter autrement le vide et que chaque peintre en fonction de son histoire, va s'y projeter ». C'est par la création artistique que « l'homme s'y confronte et qu'il peut trouver son autodépassement : aller vers le surhomme, que ses productions deviennent alors le reflet et le miroir de son pouvoir ».

Les dispositifs multimédias modifient nos sens et notre lien à l'autre. La pertinence du sensible repose sur la qualité de la relation que nous construisons avec notre public. Cette relation complice et complémentaire -qui s'appuie sur un réservoir culturel -ou un langage commun -et sur un référentiel éthique à partager -est un préalable à la transmission des savoirs au coeur de la société numérique.

La surface lisse de mon écran marque la ligne de partage avec les étudiants qui s'affichent chacun dans la galerie d'images -un écran morcelé. La combinatoire entre les différents contextes et les différents espaces-temps expose une architecture d'ensemble au travers de laquelle le jeu des regards et les champs du pouvoir s'orchestrent via l'interface.

 Quelques fois, les étudiants sont dans leur lit ou en pyjama sur leur canapé, en présence de leurs co-locataires qui interviennent dans la séance souvent de manière incongrue, d'autres déjeunent, des animaux de compagnie font intrusion dans l'écran et la plupart éteignent leur micro. Je suis en train de parler, ils m'écoutent en fond sonore tout en vaquant à leurs occupations et à l'image je les vois parfois discuter, rire avec des personnes qui sont dans le champ ou hors champ.  D'autres, connectés grâce à leur Smartphone, se déplacent pour se rendre au travail ou pour prendre un train par exemple et je les regarde au volant de leur voiture, dans le métro ou en train de marcher sur le quai de la gare tandis que j'explicite quelques notions théoriques à propos des images médiatiques.

Aux frontières entre la fiction et la réalité, « de l'hallucinatoire à l'imaginaire quantique », les sons s'entremêlent et la prégnance de l'image produit alors de vertigineuses sensations.

J'ai été très émue de regarder des fragments de vie -à la manière des surréalistes -à travers les fenêtres du temps mises en abyme ouvrant chacune sur des espaces productifs et en coexistence. Et, de me contempler en m'affichant à l'écran, ce qui est à la source d'un certain plaisir.

En surmontant, ensemble, les principales contraintes pédagogiques, sociales, culturelles et techniques, nous avons assisté à l'effacement du cadre de l'écran et à l'émergence de nouvelles lignes spatio-temporelles.

Face à « l'élargissement de l'espace public »5 , nous nous sommes déplacés vers d'autres écrans à la découverte de nouveaux univers aux dimensions impalpables, mais à re-configurer impérativement dans la perspective pédagogique.

La palette d'effets spéciaux et graphiques contribue à l'élaboration de la mise en scène de soi -de moi-même et de celle des étudiants -et apporte de nombreuses variations pour inscrire la relation interactive et la connoter selon la personnalité ou l'humeur de chacun.

 Certains choisissent d'intervenir sur fond de paysages ensoleillés ou pittoresques animés ou non ce qui confère à la séance une tonalité particulière.  D'autres optent pour le post d'une photo d'eux plutôt que d'être à l'écran, sans doute pour agir plus librement et sans le regard de l'autre.

Très hétérogènes, les photos montrent de jeunes gens dans de multiples représentations de soi qui me force à réagir, mais toujours sur le mode de l'humour et en référence à mes cours portant sur les enjeux de l'image dans la communication.

Comme la photo d'un jeune homme qui se dévoile la main sur le sexe et le smartphone dans l'autre à la manière de certains rappeurs ou celle d'une jolie jeune fille dénudée, un verre de bière à la main. J'ai orienté alors nos échanges sur les choix de leur photo pour se présenter et sur leurs enjeux dans la définition de l'identité numérique6 .  D'autres encore préfèrent tout simplement poster une photo en référence à notre espace médiatique ou fictionnel comme celle d'un présentateur de télévision connu, d'une star, d'un personnage de jeux vidéo ou de celle d'un super héros.

En référence à l'espace multimédiatique, tous ces choix esthétiques intentionalisent les modalités de nos interactions en contexte socio-pédagogique digital et révèlent combien notre identité plurielle au sein de la société numérique bouleverse le champ de l'apprentissage et de la transmission des savoirs.

Certains étudiants, bien évidemment, sont assis devant leur écran et je les entrevoisles yeux dans les yeux -reproduisant en quelque sorte la position de l'enseignant face à sa classe.

Le tchat disponible dans les logiciels de visioconférence renforce indéniablement l'interactivité et la créativité entre les membres du groupe. Au service de l'enseignement, il étoffe considérablement la manière de recenser, de partager et de sourcer l'information.

Et enfin, l'usage des symboles graphiques -le pouce levé ou baissé, les applaudissements, le coeur… -renforce l'activité spectatorielle et émotionnelle du moment.

Face à la multiplicité des écrans, j'acquiers une vision kaléidoscopique de la représentation esthétique de la société. L'agora virtuelle dans laquelle nous prenons place suscite des échanges humains originaux et une conscientisation planétaire 7 .

Cette prospective nous amène à nous interroger sur les sociétés dans leur globalité et convoque la responsabilité de chacun dans l'orientation démocratique que nous donnerons au monde numérique que nous bâtissons.

Non, nous n'étions pas "en guerre" pour reprendre les propos du président Macron, mais plutôt dans un état de turbulences où tous les possibles sont alors à imaginer collectivement.

1

  Ce texte a fait l'objet d'une communication dans le cadre du Colloque L'Image dans tous ses états, à l'initiative du Collège International de Psychanalyse et d'Anthropologie, sous la direction de Jean Nadal, Paris, 19/03/2023. 2 Zoom sur la Fac. Les Universités à l'épreuve du distanciel, Yannick Lebtahi (Dir.), Préface d'Edgar Morin, Paris, Éditions L'Harmattan, Collection De Visu, 2021, 208p. 3 Edgar Morin et Pierre Rabhi, Frères d'âme, Éditions de l'Aube, 2021.

Jean Nadal, Ils ont révolutionné la peinture, de l'hallucinatoire à l'imaginaire quantique, L'Harmattan, Paris, 2022.

Dominique Cardon, La démocratie Internet, Les Éditions du Seuil, Paris, 2010.

Dominique Cardon, « Le design de la visibilité. Un essai de cartographie du web 2.0 » In Réseaux sociaux de l'Internet, Réseaux 2008/vol. 6, n o 152, Lavoisier, Paris, 2008, p. 93-137.

Au sens d'Hervé Fischer dans L'âge hyper humaniste, Éditions de L'aube, 2019.