Yang Zhang

Kun Qi

Ji Li

Bonito A Karamoko

Luc Lajaunie

Franck Godiard

Erwan Oliviero

Xiaoqiang Cui

Ying Wang

Yupeng Zhang

Yang Zhang

Yupeng Zhang

Huali Wu

Wensen Wang

Damien Voiry

Single-Pass CO 2 -to-CO Conversion Using Ni Single Atoms Supported on Ultra-Thin Carbon Nanosheets in a Flow Electrolyzer

Keywords: CO2 reduction reaction, single-atom catalysts, flow electrolyzers, threephase interface, single pass conversions

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Introduction

The intensive consumption of fossil fuels along with excessive emission of carbon dioxide (CO2) exacerbate global environmental problems, which severely limits the potential of sustainable growth. 1 The CO2 capture and utilization technologies are being investigated to mitigate the release of CO2 into the atmosphere. 2 Among the various strategies, the electrochemical CO2 reduction reaction (CO2RR) under ambient conditions, which can be coupled with renewable electricity sources, represents a promising approach to reuse the CO2 emissions, while generating value-added fuels and chemicals. [START_REF] Qi | Enhancing the CO2-to-CO conversion from 2D silver nanoprisms via superstructure assembly[END_REF][START_REF] Creissen | Solar-driven electrochemical CO2 reduction with heterogeneous catalysts[END_REF] In this context, a vast amount of efforts are currently being devoted to the development of novel electrocatalysts with optimum selectivity and activity towards the production of various C1-C3 molecules. [START_REF] Gao | Rational catalyst and electrolyte design for CO2 electroreduction towards multicarbon products[END_REF][START_REF] Chen | Water-dispersible CsPbBr3 perovskite nanocrystals with ultra-stability and its application in electrochemical CO2 reduction[END_REF] The discovery of single-atom catalysts has extended new directions for the rational design of heterogeneous catalysts with well-defined structure and maximum exposure of the active sites. [START_REF] Qi | Single atom is not alone: Metal-support interactions in single-atom catalysis[END_REF] Single-atom catalysts have been demonstrated with outstanding electrochemical CO2RR selectivity and high current densities thanks to the peculiar coordination environment of the single metal atom and the local electronic structures that differs from those of the nanoparticle counterparts. [START_REF] Yang | Atomically dispersed Ni(i) as the active site for electrochemical CO2 reduction[END_REF][START_REF] Zheng | Large-scale and highly eelective CO2 electrocatalytic reduction on nickel single-atom catalyst[END_REF][START_REF] Gong | Catalytic mechanisms and design principles for single-atom catalysts in highly efficient CO2 conversion[END_REF] Specifically, nitrogen-doped carbon with the inclusions of metal single atoms (M-N-C) has been investigated for several key electrochemical reactions including the hydrogen evolution reaction (HER), the oxygen reduction reaction (ORR) and also the CO2RR. [START_REF] Wang | Revealing the intrinsic peroxidase-like catalytic mechanism of heterogeneous single-atom Co-MoS2[END_REF][START_REF] Qi | Single-atom cobalt array bound to distorted 1T MoS2 with ensemble effect for hydrogen evolution catalysis[END_REF][START_REF] Choi | Review-Non-noble metal-based single-atom catalysts for efficient electrochemical CO2 reduction reaction[END_REF] The search for highly active CO2RR catalysts is typically carried out using traditional "H-cell" reactors. The performance is however severely limited by the relatively low CO2 dissolvability in the liquid electrolyte. H-cell designs also face mass transport limitation and high proton transfer resistance, thus leading to the current densities typically lower than 100 mA cm -2 which precluding its industrial applications. [START_REF] Qi | Single-atom cobalt array bound to distorted 1T MoS2 with ensemble effect for hydrogen evolution catalysis[END_REF] To unlock these bottlenecks, novel device architectures have recently been reported using solid-state electrolytes or flow reactors. Specifically, mass transport limitations can efficiently be overcame thanks to the continuously feed in the electrolyte and CO2 and current densities up to 1 A cm -2 have recently been reported. [START_REF] García De Arquer | H CO2 electrolysis to multicarbon products at activities greater than 1 A cm -2[END_REF][START_REF] Ren | Molecular electrocatalysts can mediate fast, selective CO2 reduction in a flow cell[END_REF][START_REF] Yang | Carbon dioxide electroreduction on single-atom nickel decorated carbon membranes with industry compatible current densities[END_REF] In flow electrolyzers, the reduction of CO2 occurs at the three-phase interface, which is formed by CO2 (gas), the electrolyte (liquid) and the catalyst (solid) respectively. This strategy ensures an efficient supply of CO2 meanwhile electrons and protons for the successive electronproton coupled transfers associated with the reaction pathway. 17 Two main strategies are usually adopted in order to enhance the CO2RR activity and selectivity using flow electrolyzers: i) improve the intrinsic activity of the catalysts and ii) engineer the structure of the gas diffusion electrodes (GDE). For example, by changing the structure of catalysts, the porosity of the carbon support, or the hydrophilic/hydrophobic properties of the electrode, the CO2 diffusion length can be greatly reduced and the mass transport will be significantly accelerated. [START_REF] Gabardo | Combined high alkalinity and pressurization enable efficient CO2 electroreduction to CO[END_REF][START_REF] Ma | Insights into the carbon balance for CO2 electroreduction on Cu using gas diffusion electrode reactor designs[END_REF][START_REF] Millet | Ni single atom catalysts for CO2 activation[END_REF][START_REF] Kim | Effects of composition of the micro porous layer and the substrate on performance in the electrochemical reduction of CO2 to CO[END_REF][START_REF] Gabardo | Continuous carbon cioxide electroreduction to concentrated multi-carbon products using a membrane electrode assembly[END_REF] In addition to the design of the catalyst and the manipulation of electrode those all focus on the optimizing of the solid phase for three-phase interface, the feed stream's conditions of both the electrolyte (liquid) and CO2 (gas) are therefore expected to play a central role in the kinetics of the CO2RR and the final CO2-to-product conversion efficiency. [START_REF] Tan | Modulating Local CO2 concentration as a general strategy for enhancing C-C coupling in CO2 electroreduction[END_REF] For example, by tuning the gas flow rates, the transport of CO2 to the surface of the catalyst as well as its local concentration can be directly controlled to optimize the equilibrium between the adsorption of CO2 and the desorption of the products on the active sites. [START_REF] Song | Effect of mass transfer and kinetics in ordered Cu-mesostructures for electrochemical CO2 reduction[END_REF][25][START_REF] Endrődi | Multilayer electrolyzer stack converts carbon dioxide to gas products at high pressure with high efficiency[END_REF] This is particularly crucial concerning the reaction processes at high conversion ratesi.e. at high current densities. For example, if we consider the conversion of CO2 to carbon monoxide (CO), a current density of 100 mA cm -2considered to be a threshold value for any industrial applicationinvolves a turnover of ≈ 6.2 × 10 17 cm -2 molecules of CO2 and protons per second. To date, the understanding of the influence of electrolyte and CO2 feeds on the overall CO2RR performancenotably the energy efficiency of the reactionin flow electrolyzers has remained elusive.

Herein, we investigate the behavior of single atom nickel supported on ultrathin nitrogen-doped carbon nanosheets (SA Ni-NC) in a flow electrolyzer for the electrocatalytic conversion of CO2-to-CO. The SA Ni-NC demonstrates excellent CO2RR stability together with a near-unity CO2-to-CO selectivity; making it an ideal platform to investigate the feedstock parameters in a flow electrolyzer. By tuning the electrolyte or CO2 flow rates, we explored the role of the CO2 and electrolyte feeds on the electrochemical CO2RR properties and the reaction rates at the three-phase interface. The optimum flow allowed achieving current densities as high as 170 mA cm -2 with an ultra-high energy efficiency ranging up to 85%. We finally demonstrate the scalability of our catalyst by connecting up to three flow electrolyzers in series to reach a single-pass CO2-to-CO conversion of 8.9 % and a yield rate of ≈ 31.5 L min -1 m -2 while maintaining a near-unity CO2-to-CO selectivity. Our work highlights the importance of the understanding of the flow dynamics in CO2RR to optimize the energy efficiency, the single-pass conversion as well as the yield rate of the reaction, which are key parameters for the development of industrial-scale processes towards the conversion of CO2-to-CO.

Results and discussion

Density functional theory calculations and catalyst selection

We first performed density functional theory (DFT) calculations to identify a model CO2RR catalyst for the conversion of CO2-to-CO with high efficiency and selectivity.

Figure 1a shows the successive steps associated with the CO2 electrochemical reduction pathways on the optimized structures of atomic nickel coordinated by four pyrrolic nitrogen: NiN4 supported on a carbon nanosheet. The reaction pathways for the CO2 electroreduction to CO is known to proceed via two successive proton-coupled electron transfer (PCET) associated with the formation of *COOH and *CO intermediates. [START_REF] Yang | Composition tailoring via N and S co-doping and structure tuning by constructing hierarchical pores: Metal-free catalysts for high-performance electrochemical reduction of CO2[END_REF][START_REF] Möller | Efficient CO2 to CO electrolysis on solid Ni-N-C catalysts at industrial current densities[END_REF] The energy profile associated with the CO2-to-CO conversion has been calculated for the NiN4 and Ni (111) for comparison (Figure 1b). We first note that the barrier energy associated with CO2-to-CO reaction on the NiN4 is 0.1 eV smaller than that on Ni (111). The corresponding Gibbs free energy plot for the abovementioned Ni-based catalysts suggests that the free energy change of Ni (111) for the formation of the *COOH intermediate is lower compared with that of NiN4 at 0.09 eV and 1.56 eV respectively. The formation of *COOH on NiN4 is endergonic and corresponds to the common rate-determining step for the CO2RR on the single-atom sites. This first PCET process is followed by the formation of *CO for both catalysts.

The *CO desorption from NiN4 is then exothermic with a free energy change of 0.75 eV contrary to Ni (111), for which the desorption is endergonic with an associated free energy change of 1.65 eV. We examined the influence of the applied potential on the electrochemical CO2RR performance for NiN4 and Ni (111), respectively. As shown in Figure 1c and 1d, the free energy change of the rate-determining step for NiN4 decreases with the applied potential increasing, while it remains virtually constant in the case of Ni (111). The predictions therefore suggest that the increase of the overpotential does not yield to an improved catalytic activity towards the production of CO for Ni (111). In addition, the DFT calculations of HER show that the first protonation step for Ni (111) is spontaneous, and the energy barrier for the formation of 1/2 H2 is estimated to be 0.36 eVmuch smaller than the *CO desorption energy barrier of 1.63 eV (Figure S1). Our results indicate that the NiN4 sites supported on carbon are promising to deliver high CO2-to-CO selectively thanks to an efficient desorption step, and a reduced barrier energy of rate-determining step at increasing overpotentials. Conversely the Ni (111) sites are likely to be poisoned due to the ratedetermining step associated with the desorption of *CO. To further understand the nature of binding of CO on NiN4 and Ni (111), the projected density of states (PDOS) was calculated in the presence and absence of CO, respectively. After the geometry optimization, we found that the 3d orbitals of the active sites on Ni (111) hybridize with the 5σ and 2π* orbitals of CO, presenting strong chemisorption of CO molecules on Ni (111) (Figure 1e). However, in the case of the NiN4 sites, CO spontaneously desorbs and no obvious orbital hybridization of CO and activate sites was observed. The distance between the nickel atoms of NiN4 and the carbon atoms of CO was estimated to be larger than 3 Å, suggesting weak Van der Waals' interactions and confirming facile desorption of the produced CO molecules. Our results thus predict again that the rapid desorption of CO on NiN4 plays a key role in the selectivity of the CO2RR towards the production of CO.

Catalyst characterization and electrode preparation

In the light of the DFT results, single-atom nickel with well-defined catalytically active sites on ultrathin supported on two-dimensional (2D) nitrogen-doped carbon nanosheets (SA Ni-NC) was prepared. The as-prepared catalyst exhibits a twodimensional structure with a smooth surface as confirmed by scanning electron microscopy and atomic force microscopy characterizations (Figure 2a We observe a positive shift of the binding energy compared with that of bulk Ni -expected at 852.4 eV and 869.6 eV for Ni 2p3/2 and Ni 2p1/2 respectively, which reveals a higher oxidation state for Ni as expected for the NiNx sites of the single atoms. [START_REF] Zheng | Large-scale and highly eelective CO2 electrocatalytic reduction on nickel single-atom catalyst[END_REF][START_REF] Nesbitt | Interpretation of Ni2p XPS spectra of Ni conductors and Ni insulators[END_REF] The high-resolution N 1s XPS spectrum of SA Ni-NC exhibits four peaks located at 398.0, 400.5 and 401.2 eV, which are assigned to the pyridinic N, pyrrolic N and graphitic N, respectively. [START_REF] Yang | Atomically dispersed Ni(i) as the active site for electrochemical CO2 reduction[END_REF] Besides, the peak at a binding energy of 399. S1). And the Fourier transform of the phase uncorrected EXAFS spectra of SA Ni-NC displayed a prominent peak at 1.42 Å (Figure 2g). Such a value is shorter than the Ni-Ni interactions in Ni foil at 2.15 Å and attributed to the presence of Ni-N interactions, in perfect agreement with the presence of isolated nickel atoms on the nitrogen-doped carbon nanosheet for SA Ni-NC.

Investigations of the CO2RR activity in an H-cell reactor

To gauge the electrochemical CO2RR performance, the SA Ni-NC catalyst was first tested using a traditional H-cell equipped with a cation exchange membrane between the anode and cathode chambers. A CO2-saturated solution consisting of 0.1 M KOH + 0.5 M K2SO4 was used as the electrolyte and the catalyst was immobilized on a mechanically polished glassy carbon electrode with a geometric loading of 0.044 mg cm -2 (See Experimental section for details). To observe the influence of the single-atom nature of the Ni sites on the CO2RR properties, we first compared the performance of SA Ni-NC with that of Ni nanoparticles supported on reduced graphene oxide (Ni-NPC) under the same conditions. The gas and liquid products were analyzed using gas chromatography (GC) and nuclear magnetic resonance (NMR) respectively. Hydrogen (H2) and CO were found to be the only products of the reaction for both SA Ni-NC and Ni-NPC catalysts. The linear scan voltammetry (LSV) curves demonstrate that Ni-NPC has a larger reduction current at a large range of applied potential compared with that of SA Ni-NC (Figure 3a), while most of the current works for hydrogen evolution. The onset potential of SA Ni-NC for CO2RR to occur is about -0.25 V vs. the reversible hydrogen electrode (RHE), which compares favorably with the recently reported values in the literature. [START_REF] Zheng | Large-scale and highly eelective CO2 electrocatalytic reduction on nickel single-atom catalyst[END_REF][START_REF] Yang | Carbon dioxide electroreduction on single-atom nickel decorated carbon membranes with industry compatible current densities[END_REF][START_REF] Zhang | Nickel-nitrogen-carbon molecular catalysts for high rate CO2 electroreduction to CO: On the role of carbon substrate and reaction chemistry[END_REF] Remarkably, the Faradaic efficiency of CO (FECO) for SA Ni-NC is much larger than that for Ni-NPC and the FECO reaches the highest value of about 80% at an applied potential of -0.75 V vs. RHE (Figure 3b). At this applied potential, the partial current density of CO (jCO) reaches -1.87 mA cm -2 and -0.77 mA cm -2 for the SA Ni-NC and Ni-NPC, respectively. We also observe that the reactions on Ni-NPC are dominated by the HER processi.e. the production of H2and the Ni nanoparticles are poorly selective towards CO2RR (Figure 3c). The high selectivity of the NiN4 sites compared with Ni nanoparticles is in line with our numerical predictions and attributed to the rapid desorption of *CO. To further assess the potential of SA Ni-NC as a CO2RR catalyst, we evaluated the electrochemical stability of the catalyst over 48 h at an applied potential of -0.8 V vs. RHE (Figure 3d). The current was continuously measured while the gas products were injected into the gas chromatograph every 3 hours. The SA Ni-NC catalyst exhibits a stable cathodic current density and negligible drop of FECO as demonstrated by retentions of 92.5% and 95% respectively (Figure 3d). We also measured the electrochemical double-layer capacity (Cdl) and the electrochemical impedance spectroscopy (EIS) of the two catalysts (Figure S7 and Table S2). The results show that SA Ni-NC catalyst exhibits a better interfacial charge transfer and more electrochemical active sites for CO2RR. All of the above results indicate that SA Ni-NC holds promises as a CO2RR catalyst with excellent selectivity and stability towards the production of CO from CO2.

Investigations of the CO2RR activity in a flow electrolyzer

The performance of SA Ni-NC was further evaluated in a liquid-electrolyte flow electrolyzer using CO2-saturated mixture of 0.1 M KOH+0.5 M K2SO4 solution as the electrolyte for both the cathode and the anode chambers. The catalyst was loaded on a GDE and the downstream products of the reaction were continuously analyzed using gas chromatography. The model 1 cm 2 flow reactor allows for the continuous diffusion of CO2 to the catalyst layer thanks to the position of the supported catalyst directly at the gas/liquid interface (Figure S8). To scrutinize the relationship between the CO2RR properties and the CO2/electrolyte feedstocks, the flow rates for both the electrolyte and CO2 were controllably tuned from 20 to 100 mL min -1 and 20 to 140 mL min -1 , respectively. The specific current density and Faradaic efficiency were measured at different potentials for each feed parameters, which allowed us to elucidate the behavior of SA Ni-NC in the flow electrolyzer. The electrochemical CO2RR properties of the SA Ni-NC were first assessed at a fixed stream of 60 ml min -1 CO2 with the variation of electrolyte flow rates (Figure 4a). The highest current reaches  170 mA cm -2 at -1.15 V vs. RHE for a 60 mL min -1 electrolyte flow rate while the FECO shows nearunity selectivity for all electrolyte flow ratessharply improved compared with that measured in H-cell (Figure 4b and Figure 3b). It should be noted that, due to the experimental errors introduced by the GC analyzes, the measured CO selectivity could sometimes be slightly higher than 100%, especially when H2 was suppressed to below 1%. [START_REF] García De Arquer | 2D metal oxyhalide-derived catalysts for efficient CO2 electroreduction[END_REF] To further study the effects of the electrolyte flow rate on the CO2RR performance from the viewpoint of three-phase interface, we analyzed both the electrochemical impedance spectra (EIS) of the catalyst and the double-layer capacitance (Cdl) (Figure 4c and4d). [START_REF] Jouny | High-rate electroreduction of carbon monoxide to multi-carbon products[END_REF] As shown in Figure 4d, the Cdl values get larger with the increase of the electrolyte flow rate and reaches a plateau for flow rates > 60 mL min -1 . We also found that the internal resistance (Rs) and the charge transfer resistance (Rct) simultaneously increase. In particular, the Rct sharply increases at the largest flow rates above 80 mL min -1 , suggesting an abrupt change in reaction kinetics attributed to the modification of the three-phase interface. Below 80 mL min -1 , larger flow rate may promote the penetration of the electrolyte inside the porous gas diffusion electrode (GDE) and therefore improves the reaction interface between the catalyst surface and the liquid electrolyte (Figure 4e). However, when further increasing the flow of electrolyte, the gas-liquid interface moves deeper inside the GDE resulting in a degraded three-phase interface and unfavorable conditions for the electrochemical reactions. [START_REF] García De Arquer | H CO2 electrolysis to multicarbon products at activities greater than 1 A cm -2[END_REF]33 Our experimental results highlight the critical role of interfaces for the CO2RR in a flow cell and the optimal electrolyte flow rate corresponds to the proper balance between the surface of catalyst in contact with the electrolyte and the position of the gas-liquid interface inside the GDE. To elucidate the influence of the CO2 feed, steady-state chronoamperometry was then recorded for different flow rates between 20 mL min -1 and 140 mL min -1 with a constant stream of electrolyte at 60 mL min -1 .

Remarkably, the selectivity of SA Ni-NC is not influenced by the gas flow and the catalyst performs with nearly 100% selectivity towards the formation of CO over the range of potential (Figure 4f). The onset potential for the production of CO reaches -0.35 V vs. RHE in the flow reactorslightly more negative than that in the H-cell (Figure 4a and4g). This can be attributed to the fact that the instantaneous concentration of CO at low potentials is below the detection limit of our instrument (See Experimental section for details). At an applied potential of -0.35 V vs. RHE, the SA Ni-NC shows similar current densities for all flow rates; therefore indicating similar levels of CO2RR activity (Figure 4g). At larger applied potentials, the current density increases as the CO2 flow rates increases from 20 to 60 mL min -1 due to the local depletion of CO2 near the site active at low flow rates. [START_REF] Jouny | High-rate electroreduction of carbon monoxide to multi-carbon products[END_REF] The lower current density for the CO2 flow rates higher than 60 mL min -1 points out a possible local decrease of the pH, which perturbs the CO2 activation and the free-energy barriers in CO2RR, in agreement with the endergonic nature of the first step. Indeed, a high feed in CO2 will result in a large excess of CO2 molecules not involved in the CO2RR, which will likely induce a reduction of the local pH as previously been identified. [START_REF] Li | Efficient electrocatalytic CO2 reduction on a three-phase interface[END_REF][START_REF] Singh | Mechanistic insights into electrochemical reduction of CO2 over Ag using density functional theory and transport models[END_REF] Overall, we identified optimal ranges for the electrolyte and CO2 flow rates to be 40-80 mL min -1 and 60 mL min -1 respectively depending on the applied potentials (Figure 5a). Our results demonstrate that the potential-dependent nature of the electrocatalytic reaction rate is also controlled by the supply of CO2 and electrolytes for the successive PCET steps. [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF] Remarkably, the FECO remains ≈100% even at current densities larger than 100 mA cm -2 and the CO2RR properties of SA Ni-NC in the flow electrolyzer are superior to those measured in the H-Cell (Figure 5b,c). For example, the jmass, jtotal and jCO values at -0.75 V vs. RHE in flow electrolyzer are 2.2 A cm -2 , 111 mA cm -2 and 109.18 mA cm -2 , respectively. However, the values in H-cell are 0.05 A cm -2 , 2.31 mA cm -2 and 1.87 mA cm -2 , respectively, which are all significantly smaller than those in the flow electrolyzer. This is attributed to the i) better exposure of the active sites, ii) larger local concentration of CO2 and iii) reduced amount of hydrated proton which is involved in the competitive HER. [START_REF] Nguyen | Mass transport control by surface graphene oxide for selective CO production from electrochemical CO2 reduction[END_REF] To better evaluate the performance of SA Ni-NC, we calculated the evaluative parameters of the system as a function of the CO2 flow rates at different applied potentials. The energy efficiency is found to be larger than 55 % for all the range of potentials. It reaches to 85% at -0.35 V vs. RHE with a current density of 7.2 mA cm -2 (Figure 5d). When considering the two important metrics, the specific current density and the energy efficiency, the SA Ni-NC catalysts in a flow reactor can achieve a current density larger than 170 mA cm -2 while maintaining a high energy efficiency of 56%. To gain some insight into the behavior of SA Ni-NC in the flow reactor, we also explored the role of the CO2 feed on the yield rate of CO (Figure 5e). The yield rate increases with the applied potential and reached values as high as 28.4 mL min -1 𝑚𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡 -1 at an applied potential of -1.15 V vs. RHE and CO2 flux of 60 mL min -1equivalent to a continuous CO production of 12.6 L min -1 m -2 of the electrode.

We further examined the single-pass CO2-to-CO conversion, which represents the percentage of CO2-to-CO conversion after one pass in the reactor which is the key parameter to assess the scalability of the CO2RR system. For example, a single-pass CO2-to-CO conversion of 10% is associated with a separation cost of 23% of the total operation cost for the production of CO. [START_REF] Jeng | Investigation of CO2 single-pass conversion in a flow electrolyzer[END_REF] Such a value is generally considered to be a threshold target to demonstrate the industrial viability of the process. According to Figure 5f, it can be observed that the single-pass CO2-to-CO conversion obeys the same trend as for jCO and the largest values are obtained for electrolyte flow rates around 60 mL min -1 . At this specific electrolyte flow rate, the highest single-pass CO2-to-CO conversion for the flow reactor reaches ≈ 3 % at a potential of -1.15 V vs. RHE for a CO2 flow rate of 20 mL min -1 (Figure 5g). We also note the tendency that for a constant feed in CO2, the single-pass CO2-to-CO conversion values increase with the applied potential, but decreases with the CO2 flow rate. Overall, reducing the CO2 flow rate results in larger single-pass CO2-to-CO conversion performance and improves the CO2 conversion efficiency but lower the CO yield rate. Trade-offs between single-pass CO2to-CO conversion and CO yield rate must therefore be chosen to meet the specific industrial recommendations.

To finally demonstrate the potential of our approach, we stacked three identical flow electrolyzer using the SA Ni-NC as a CO2RR catalyst (Figure 6a). The anolyte and catholyte were recycled using a peristaltic pump with a constant flow rate. The first flow electrolyzer was continuously fed with pure CO2 and the gas outlet was successively injected in the second and third flow electrolyzer, while the downstream gas products were continuously detected via GC analyses. The CO2-to-CO performances of each reactor were first examined and the specific current reached 160  20 mA cm -2 for each electrolyzer (Figure 6b). After the first two reactors, we measured a single-pass CO2-to-CO conversion and a CO yield rate of 4.4% and 35.3 mL min -1 mg catalyst -1

, respectively. These values were further improved after passing through the third reactor and reached 8.9% and 71.2 mL min -1 mg catalyst -1 equivalent to a continuous CO production of 31.5 L min -1 m -2 , respectivelypointing out the remarkable CO2RR properties of SA Ni-NC in a diluted CO2 environment (Figure 6c).

These results allowed the identification of a quasi-linear increase of the CO2-to-CO conversion and validated the scalability of our strategy towards higher single-pass CO2to-CO conversion by rationally designing the electrolyzer and the feedstock parameters.

According to the linear fitting, the SA Ni-NC in a flow reactor demonstrates a singlepass conversion of 2.6% per cm 2 of the electrode for the production from CO2-to-CO, which compares favorably to the best reports in the literature using flow electrolyzer (Table S3).

Conclusion

In summary, we have prepared single-atom nickel supported on two-dimensional nitrogen-doped carbon nanosheets using a salt template strategy. The controlled design of the single-atom Ni sites translates into high selectivity and high efficiency towards the conversion of CO2-to-CO. When implemented in a flow electrolyzer, SA Ni-NC exhibits near-unity selectivity towards the production of CO with a specific current density as high as 170 mA cm -2 . Importantly, our study reveals the influence of feed-in electrolytes and CO2 on the catalytic performance in a flow electrolyzer system. Using a model 1 cm 2 reactor, we determined the optimum flow rates for the electrolyte and CO2 at 40-80 mL min -1 and 60 mL min -1 , respectivelycorresponding to flow speeds of 8.3-16.6 cm s -1 and 12.5 cm s -1 . The feed parameters are found to modulate the catalyst behavior in the reactor by tuning the equilibrium of the three-phase interface between the electrolyte, the CO2 atmosphere and the surface of the electrocatalyst. This translates into a single-pass CO2-to-CO conversion of 2.6% cm -2 , corresponding to a total conversion efficiency of 8.9% when stacking three 1-cm 2 reactors without a notifiable drop of the catalyst performance when operating under diluted CO2 atmosphere. Our approach provides insight into the scalability of flow electrolyzers toward the mass production of CO from CO2 with high Faradaic efficiency using singleatom electrocatalysts. Future developments require the further optimization of the size of the electrodes and the number of stacks for optimizing the tradeoff between the single-pass conversion and the yield rate .

Experimental Section

Materials:

Nickel nitrate hexahydrate (Ni(NO3)2•6H2O, ≥ 98.5%), 2-methylimidazole (CH3C3H2N2H, 98%), methanol (CH3OH, ≥ 99.9%), sodium chloride (NaCl, ≥ 99.0%), ethylene glycol (HOCH2CH2OH, 99.8%), Nickel (II) acetate tetrahydrate (Ni(CH3COO)2•4H2O, 98%), graphene, urea (NH2CONH2, ≥ 99.5%), potassium sulfate (K2SO4, ≥99.0%) and potassium hydroxide (KOH, 90%,) were purchased from Sigma Aldrich. Nafion (5%) and hydrochloric acid (HCl, 37%) were purchased from Alfa Aesar. All the chemicals in the experiment were used without further purification.

The gas diffusion electrode (GDE, Sigracet 29 BC) and cation exchange membrane (CEM, Nafion 117) were both purchased from the Fuel Cell Store. The fresh cathode, anode, and CEM were used for each electrolysis test to avoid contamination.

Synthesis of SA Ni-NC:

SA Ni-NC was synthesized from the graphitization of a zeolitic imidazolate metalorganic framework (ZIF). In a typical synthesis of ultrathin ZIF-67 nanosheets, 200 mg of 2-methylimidazole and 50 mg of nickel nitrate hexahydrate were dissolved in 2.5 mL of methanol, respectively. [START_REF] Huang | In situ synthesis of ultrathin metal0organic framework nanosheets: A new method for 2D metal-based nanoporous carbon electrocatalysts[END_REF] After that, 20 g of the sodium chloride was mixed with the two solutions into a flask under vigorous magnetic stirring overnight at room temperature. The controlled ratio in MOF precursors and NaCl was adjusted to promote a thin coating on the salt crystals and favor the lateral growth of ZIF-67s. Subsequently, the NaCl@ZIF-67 nanosheets were obtained by the slow evaporation of the solvent at 35 ℃ followed by pyrolyzis at 800℃ for 2 hours under argon (Ar). After cooling down to room temperature, the product was soaked in 0.5 M HCl solution for 24 h at 60 ℃ to remove the redundant nickel nanoparticles. Finally, the sample was washed with deionized water for several times to remove the redundant NaCl, then centrifuged and freeze-dried for further storage.

Synthesis of Ni NPC:

The Ni nanoparticles were prepared by a modified chemical reduction method. 41 In a typical synthesis process, 0.349 g Nickel (II) acetate tetrahydrate, 17.5 mg graphene, and 1.394 g urea were mixed with 35 mL ethylene glycol through intense agitation for 0.5 h to form a homogeneous solution. Then the homogeneous solution was transferred into a 50 mL Teflon-lined stainless-steel autoclave and kept at 200 °C for 1 h. After cooling down, the mixture was washed with ethanol for six times and dried at 80 °C in a vacuum oven. The Ni-NPC composite was obtained by annealing the above mixture at 700 °C in an Ar atmosphere for 10 h.

Sample characterization:

Transmission electron microscopy images (TEM) were obtained using a JEOL 1400 microscope with an emission gun operating at 120 kV. High-resolution transmission electron microscopy images (HRTEM) were obtained using JEOL 2200 FS microscope with an emission gun operating at 200 kV. The samples for electron microscopy were prepared by dropping ethanol dispersions of the samples onto 300 mesh carbon-coated copper grids and then evaporating the solvent. Aberration-corrected high-resolution scanning ttransmission electron microscopy imaging (HR-STEM), and spatiallyresolved electron energy-loss spectroscopy (SR-EELS) were performed using an FEI Titan Cubed Themis microscope which was operated at 80 kV. The Themis is equipped with a double Cs aberration corrector, a monochromator, an X-FEG gun, and an ultrahigh resolution energy filter (Gatan Quantum ERS) which allows for working in Dual-EELS mode. HR-STEM imaging was performed by using high-angle annular dark-field (HAADF) and annular dark-field (ADF) detectors. SR-EELS spectra were acquired with the monochromator excited allowing an energy resolution of 1.1 eV with an energy dispersion of 0.4 eV/pixel. AFM images were obtained in Digital Instruments Nanoscope IV in tapping mode with cantilevers with a spring constant of 40 N/m and tip curvature < 10 nm and a frequency of 325 kHz (Dimension Icon, Veeco Instruments/Bruker, Germany). X-ray photoelectron spectroscopy (XPS) was performed using an ESCALAB-250 instrument (Thermo Fisher Scientific, USA), performed with a monochromatic Al-K α (1486.6 eV) radiation source and a hemisphere detector with an energy resolution of 0.1 eV. Peak positions were all corrected by the C 1s spectrum at 284.8 eV. X-ray absorption spectra (XAS) were measured at Beijing synchrotron radiation facility (BSRF) on beamline 1W1B. The storage ring is operated at a beam current of 250 mA with an electron energy of 2.5 GeV. The beam size for the sample position was ≈ 900 × 300 μm 2 . A Si (111) double-crystal monochromatic was applied. All of the experiments were conducted at ambient temperature and applied in the transmission mode. The curve fitting and data analysis were performed using the Artemis and IFEFFIT softwares. [START_REF] Rehr | Theoretical approaches to X-ray absorption fine structure[END_REF][START_REF] Newville | EXAFS analysis using FEFF and FEFFIT[END_REF] The energy resolution ( Δ E/E) for the incident X-ray photons was estimated to be 2 × 10 -4 .

Conventional transmission mode was adopted for the Ni K-edge EXAFS measurements.

To verify the reproducibility of the experimental data, at least two scans were collected and analyzed for each sample.

Electrode preparation for the H-Cell reactor:

The SA Ni-NC catalyst ink was prepared by mixing 2.5 mg of SA Ni-NC powder with 9.8 mL absolute ethanol and 200 µl of Nafion solution. Subsequently, 200 µL of the ink was drop-casted on the mechanically polished glassy carbon electrode to obtain a catalyst loading of 0.044 mg/cm².

H-Cell assembly:

The H-Cell reactor was assembled using a Ag/AgCl reference electrode, a Pt plate counter electrode (1.5 cm x 2 cm) and a glassy carbon working electrode (1.5 cm x 1 cm). The electrolyte consisted of 0.1 M KOH and 0.5 M K2(SO)4 mixture solution, the pH value was 13.03. Before each time CO2RR measurement, CO2 is saturated for 30 min. The CO2 flow is set to 5 mL min -1 for the long-term stability tests. All data are presented without iR-compensation.

Electrode preparation for the flow reactor:

The same amount of Ni catalyst (0.044 mg cm -2 ) was drop-casted on the surface of GDE. The geometrical area was fixed to 1 cm 2 by the coverage of epoxy. A standard cleaning procedure was used to clean the nickel foam anode by sonication in acetone and then deionized water. The fresh cathode, anode, and CEM were used for each electrolysis test to avoid contamination. The innner diameters for the inlet and outlet tubes was 3.17 mm.

Flow electrolyzer assembly:

The model flow reactor was composed of a sandwich of flow frames, electrodes, gaskets, and a membrane as illustrated in Figure S8 forming a three-compartment electrolyzer. One compartment delivered the CO2 from the backside and through the GDE (2.8 x 2.8 cm 2 , fixed with a PTFE frame), while the second compartment contained the catholyte solution (0.1 M KOH + 0.5 M K2(SO)4) between the GDE and the CEM. The exposed area of the GDE was estimated to be 1 cm 2 . A silver electrode was used as a quasi reference electrode. Before the experiment, the electrode was calibrated using a standard Ag/AgCl reference electrode. On the other side of the CEM, the anolyte was injected between the CEM and the nickel foam anode. The flow frames were made by PTFE, and the gaskets were made by rubber. Catholyte and anolyte were recycled using the peristaltic pump (Heidolph PD 5201).

Electrochemical measurements and gas-phase product analysis:

All of the electrochemical measurements were measured with a VSP potentiostat (Bio-Logic Science Instruments). All potentials were calibrated against the reversible hydrogen electrode (RHE) by the equation: ERHE = EAg/AgCl + 0.059 pH + 0.197. The products of the reaction were detected using a micro gas chromatograph (Agilent 490) and the micro-GC runs were initiated every 180 s. The GC was equipped with a packed MolSieve 5 A column and a packed HaySep D column. Argon (Praxair, 99.999%) was used as the carrier gas. A flame ionization detector with a mechanized was used to quantify CO, CH4, and C2H4 while a thermal conductivity detector (TCD) was used to quantify hydrogen. The GC was calibrated by injecting a mixture calibration gas (2500 ppm CO, 2500 ppm CH4, 2500 ppm, 2500 ppm C2H4, 2500 ppm C2H6 in CO2, Linde).

In the H-cell system, the electrolyte was first saturated with CO2 for 30 min and gas products were detected after 30 min of reaction under potentiostat conditions. When using the flow electrolyzer, the CO2 flow rate was tuned between 20 and 140 standard mL min -1 using a calibrated flow controller. The electrolyte was circulated through the anode and cathode compartments using a peristaltic pump. The gas outlet of the flow cell was directed to a condenser before being vented directly into the gas-sampling loop of the gas chromatograph. The EIS measurements were conducted at a constant potential of 0.7 V vs. RHE with an AC voltage of 10 mV between 100 kHz to 100 mHz in the flow cell. The Cdl was calculated from linear fit of the evolution of the cathodic and anodic current density with the potential scan rates.

FIGURES

  , Figure S2). To provide compelling evidence of the uniform distribution of the nickel atoms on the nitrogen-doped carbon nanosheets, we performed energy dispersive X-ray (EDX) mapping on the SA Ni-NC nanosheets. EDX analyses revealed that the Ni, C, and N elements are homogeneously distributed at the scale of the flake without noticeable metal aggregation or formation of the Ni nanoparticles (Figure 2b-2e). The nature of the Ni atoms in SA Ni-NC was further characterized by aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). Ni atoms are observed as brighter spots due to their larger atomic number compared with those of carbon and nitrogen. Ultra-small bright dots from the nickel single-atoms are found on SA Ni-NC confirming the uniform dispersion of the nickel with an average size of 0.15 ± 0.04 nm as confirmed by the HAADF-STEM and electron energy-loss spectroscopy (EELS) mapping (Figure 2f, Figure S3). To investigate the chemical composition and oxidation state of Ni, X-ray photoelectron spectroscopy (XPS) was performed on the SA Ni-NC (Figure S4). The Ni 2p spectrum of SA Ni-NC appears as doublets corresponding to Ni 2p3/2 (855.5 eV) and Ni 2p1/2 (873.5 eV) respectively.

  Figure S6b and TableS1). And the Fourier transform of the phase uncorrected EXAFS

Figure 1 .

 1 Figure 1. Theoretical and statistical predicational results on CO2 reduction and

Figure 2 .

 2 Figure 2. Characterization of the SA Ni-NC catalyst. a, Bright-field TEM image of

Figure 3 .

 3 Figure 3. CO2 electroreduction performance in the H-cell. a, LSV curves measured

Figure 4 .

 4 Figure 4. CO2 electroreduction performance in the flow electrolyzer. a, Current densities for the CO2 reduction at various applied potentials and electrolyte flow rates on SA Ni-NC catalyst. b, FECO measured at different applied potentials with different electrolyte flow rates. c, Nyquist plots of Ni SA-NC catalyst with CO2 flow of 60 mL min -1 and electrolyte flow rates ranging from 20 mL min -1 to 100 mL min -1 (solid symbols are experimental results and solid lines are fitting results). d, Cdl, Rs and Rct as a function of the flow rate of electrolyte for SA Ni-NC supported on the GDE in the flow cell reactor. Rs and Rct are simulated based on the equivalent circuit (Insert in Figure 4c). e, Schematic illustration of the change of the three-phase interface with the electrolyte flow rate. f, FECO measured at different applied potentials with different CO2 flow rates. g, Evolution of the current density with the applied potentials for different CO2 flow rates.

Figure 5 .

 5 Figure 5. CO2 electroreduction performance in the flow electrolyzer. a, Optimum electrolyte flow rates determined for each potential with a constant CO2 flow rate. b, FECO values from SA Ni-NC under different current densities. c, CO2RR performance from SA Ni-NC measured in the H-cell and in the flow electrolyzer (The bold values with different colors labeled in the graph are corresponding to the jtotal, jmass and jCO performance in H-cell, respectively). d and e, 2D map of the energy efficiency (d) and the yield rate of CO (YR of CO) (e) of electrochemical CO2 reduction from SA Ni-NC catalyst with different CO2 flow rates with a constant electrolyte flux of 60 mL min -1 at different applied potentials. f, Single-pass CO2 conversion for SA Ni-NC catalyst with different electrolyte flow rates at different applied potentials. g, Single-pass CO2 conversion for SA Ni-NC with different CO2 flow rates at different applied potentials.

Figure 6 .

 6 Figure 6. CO2 electroreduction performance in the stacked flow electrolyzers. a,

AUTHOR INFORMATION

Corresponding Author

*E-mail: damien.voiry@umontpellier.fr (D. Voiry).

Author


; De Herralde

; Elorduy

; Bartra

; Giraud-Heraud

; Gil

; Escobar

; Rodríguez

; Cela

; Tubío

; Savé

; Aranda

; Roudet

; Lecomte

; Thiery

; Fermaud

Multifactorial analysis of disease pressure and pesticide use in viticulture: reduction possibilities in South-western Europe

The indicators used in this study allow the evaluation of the pest pressure and pesticide use in a complex system in three regions. In 2017 we were able to see different patterns in pest type and pressure and in pesticide use in the different regions, significant relationships between pests and treatments. The variability in the relationships pest/treatments offers options for the reduction in pesticide use from the basis of the current practices. There is complexity in the factors that affect not only to wine quality, but also to yield. A new multipathogen approach in the field vs wine quality is tested. The multifactorial analysis will allow to evaluate the reduction in pesticide use in relation with the cost analysis and consumer preferences. 2018 has been a rainy spring and a rainy and hot summer, with a very different preliminary AIDB and IFT, which will provide a different range of results.

INTRODUCTION

Wine consumer preferences, along with the increasingly more restrictive regulations in pesticide use, represent a challenge for the European winegrowers and their viticultural practices, as well as for the winemaking sector competitiveness. The VINOVERT project integrates phytopathology, agronomy, economy and enology in order to develop feasible solutions for viticulturists in Spain, France and Portugal. This study evaluates the possibilities in the pesticide reduction at vineyard scale and the effect of such reductions in the quality of the resulting wines.

MATERIALS AND METHODS

The experimental layout consisted on a total of 30 commercial vineyards, distributed in Bordeaux, Galicia and Catalunya, half under conventional and half under organic management (Figure 1). Monitored variables (Figure 2) included epidemiological, agronomical, managemental and oenological parameters.

RESULTS AND DISCUSSION

The phytopathological profile (fig. 3) shows the diversity among regions and locations within each regions. In General in Bordeaux, the most severe attack is by Lobesia and Botrytis, in Catalunya, by Lobesia and Powdery mildew, and in Galicia there is mainly Downy mildew just in two locations. The AIDB was higher in Catalunya than in Bordeaux and in both higher than in Galicia (fig. 4 we can see a significant negative relationship but only explaining the 25%. There are many cases where the relationship is not accomplished, suggesting the need for more detailed and wider sample number. 2017 was also an atypical year with dry and hot spring and summer. There is high variability within each region and there is also a high variability of AIDB within the same range of IFT, indicating other factors due to the grape grower: we must take a deeper insight in the management practices: Crop Protection Practices Index (IPP) and grower's Technical Skills Index (ICT). The relationship between the Yield Achievement Rate (YAR,%) and the AIDB only shows the preliminary results not including Galicia. The pest pressure only explains the 25%. Other causes can be assumed to be due to water and nutrient requirements, uncertainty in measurements or grapegrowers statements, or the own relationship of each pathology to the actual yield loss. It appears to be a positive relationship between the organoleptic quality and the pathology pressure (fig. 6

  left top), because a lower IFT in Catalunya than in Bordeaux and lower in both than in Galicia (fig 4 left bottom). The AIDB was not significantly different between the organic (weak IFT) and the conventional (strong IFT) vineyards (fig 4 right top), but the calculated IFT was lower in the organic than in the conventional vineyards as expected (fig. 4 right bottom). Analyzing in detail the relationship between the pathologies (AIDB) and the treatments IFT (fig. 5 left)

  left), but in this case the most of the high AIDB values are due to Lobesia attacks not inducing secondary infections, so with no much impact in the cumulative liking score. When relating the Botrytis pressure with the cumulative liking (fig. 6 right), the relationship is negative, being Botrytis the cause of lower liking scores. ACKNOWLEDGMENTS: This work is funded by the Interreg SUDOE Project VINOVERT (ref SOE1/P2/F0246).

Figure 2 :

 2 Figure 1: Experimental layout in the three regions

Figure 4 :Figure

 4 Figure 4: AIDB and IFT without biocontrol products, mean for the three regions (left) and for the organic and conventional managements

Figure

  Figure 6: Organoleptic quality: AIDB vs Cumulative liking (left) and % of Botrytis severity (%) vs Cumulative liking in the young experimental wines


Nicolas Montagne
email: nicolas.montagne@enpc.fr

Cyril Douthe

Xavier Tellier

Corentin Fivet

Olivier Baverel

Voss surfaces: A design space for geodesic gridshells

Keywords: Voss nets, gridshell, geodesics, constructive geometry, Chebyshev nets, Gauss map

The design of envelopes with complex geometries often leads to construction challenges. To overcome these difficulties, resorting to discrete differential geometry proved successful by establishing close links between mesh properties and the existence of good fabrication, assembling and mechanical properties. In this paper, the design of a special family of structures, called geodesic shells, is addressed using Voss nets, a family of discrete surfaces. The use of discrete Voss surfaces ensures that the structure can be built from simply connected, initially straight laths, and covered with flat panels. These advantageous constructive properties arise from the existence of a conjugate network of geodesic curves on the underlying smooth surface. Here, a review of Voss nets is presented and particular attention is given to the projection of normal vectors on the unit sphere. This projection, called Gauss map, creates a dual net which unveils the remarkable characteristics of Voss nets. Then, based on the previous study, two generation methods are introduced. One enables the exploration and the deformation of Voss nets while the second provides a more direct computational technique. The application of theses methodologies is discussed alongside formal examples.

Introduction

The construction of complex shaped envelopes gives rise to great challenges in terms of manufacturing and assembling. The design of the support structure must conciliate competing requirements, ranging

Proceedings of the IASS Annual Symposium 2020 and the 7th International Conference on Spatial Structures

Inspiring the Next Generation 2 from mechanical efficiency, through architectural intents, to cost effectiveness. Two approaches coexist for the construction of complex shaped envelopes. Adopting the traditional way of building, the first one relies on stiff elements assembled with rigid connections (Schlaich and Schober [START_REF] Schlaich | Glass Roof for the Hippo House at the Berlin Zoo[END_REF], Mesnil et al. [START_REF] Mesnil | Non-standard patterns for gridshells: fabrication and structural optimization[END_REF], Tellier et al. [START_REF] Tellier | Surfaces with planar curvature lines: Discretization, generation and application to the rationalization of curved architectural envelopes[END_REF]) while the other strategy uses slender beams bent elastically. The later type of structure, referred to as active-bending structures (Lienhard et al. [START_REF] Lienhard | Active Bending, a Review on Structures where Bending is Used as a Self-Formation Process[END_REF]), presents the benefit to smoothly approximate the target geometry. In the great majority of cases, rectangular cross section beams are applied tangent to the surface (Harris et al. [START_REF] Harris | Design and construction of the Downland Gridshell[END_REF], Liddell [START_REF] Liddell | Frei Otto and the development of gridshells[END_REF], Colabella et al. [START_REF] Colabella | Structural Design with Reclaimed Materials: An Elastic Gridshell out of Skis[END_REF]). However, in such structures, the arrangement of the members often results in excessive stresses and the covering requires the use of tailor-made doubly-curved elements.

The problem of designing shells with actively bent rectangular elements was tackled by Natterer et al. [START_REF] Natterer | The roof structure "Expodach" at the World Exhibition Hanover[END_REF] who made use of geodesic lines. Geodesic lines are curves on surfaces with a vanishing geodesic curvature. Hence, a lath following a geodesic line is not bent sideways, along its strong axis and avoids excessive stresses and local instabilities. Inspired by Natterer et al. [START_REF] Natterer | The roof structure "Expodach" at the World Exhibition Hanover[END_REF], Pirazzi and Weinand [START_REF] Pirazzi | Geodesic Lines on Free-Form Surfaces: Optimized Grids for Timber Rib Shells[END_REF] proposed a framework for the design of shells with geodesic lines, called geodesic shells, and applied it for the realization of a pavilion.

Recently, discrete differential geometry, appeared as an elegant and powerful way to address the challenges faced during the design of complex shapes. The constructive expectations are translated as geometrical constraints on the mesh, mesh which is a discrete representation of the doubly-curved envelope. Using this point of view, geodesic lines were further studied for the mapping of surfaces (Pottmann et al. [START_REF] Pottmann | Geodesic Patterns[END_REF]) or for the modelling of developable surfaces (Rabinovitch et al. [START_REF] Rabinovich | Discrete Geodesic Nets for Modeling Developable Surfaces[END_REF]). In this context, Douthe et al. [START_REF] Douthe | Isoradial meshes: Covering elastic gridshells with planar facets[END_REF] presented a strategy for the covering of elastic gridshells with flat panels based on isoradial meshes. The covering property results from the duality of the grid structure, called a Chebyshev net, with a conjugate network of curves. However, the problem of covering geodesic shell with flat quad was not addressed in the literature.

Related works

In this paper, the design of geodesic shells is addressed through a special family of discrete surfaces called Voss nets. Resorting to these surfaces guarantees that the support structure can be built from initially-straight rectangular cross-section beams that are elastically bent and can be covered using only flat quadrilateral panels. Unveiled by the eponymous mathematician in 1888 in their smooth version (Voss [24]), discrete Voss surfaces, or Voss nets, are defined as quadrangular meshes in which opposite angles made by edges around a vertex are equal and where each face is planar (Sauer and Graf [START_REF] Sauer | Über Flächenverbiegung in Analogie zur Verknickung offener Facettenflache[END_REF]).

Voss nets have been studied since the first half of the 19 th century (Wunderlich [START_REF] Wunderlich | Zur Differenzemgeometrie der Flächen konstanter negativer Krümmung[END_REF], Sauer [START_REF] Sauer | Differenzengeometrie[END_REF]) and have recently resurfaced in the contexts of origami pattern and graphic statics.

Noticing their rigid-foldability property retrieved by Schief et al. [START_REF] Schief | On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces[END_REF], Tachi [START_REF] Tachi | Freeform Rigid-Foldable Structure using Bidirectionally Flat-Foldable Planar Quadrilateral Mesh[END_REF] identified Voss nets as a generalization of the well-known eggbox origami pattern. Indeed, this pattern can be modelled by a mesh with planar faces and whose opposite angles at edges are equal. In that approach, Voss nets are discussed in a jagged version, suited for the origami application. Such description decouples Voss nets from their comprehension as discretization of smooth Voss surfaces, and is consequently unrelated with the geodesic approach developed in this paper.

Mitchell et al. [START_REF] Mitchell | Structural Applications of the Graphic Statics and StaticKinematic Dualities: Rigid Origami, Self-Centering Cable Nets, and Linkage Meshes[END_REF] addressed Voss nets in the context of graphic statics, highlighting their duality with another family of nets called K-nets. K-nets are the discrete counterpart of surfaces with constant negative Gaussian curvature. They show that, using this duality, Voss nets and K-nets can be respectively interpreted as the form and the force diagrams. Accordingly, a generation method for Voss nets is presented. However, since it requires K-nets as input, which are non-trivial 3-dimensional nets, the methodology reveals laborious. The authors built an origami pavilion based on the rigid-foldability property of Voss nets.

Overview

In section 2. The Gauss map, the representation of Voss nets through normal vectors is examined. This approach gives rise to inherent nets on the unit sphere, the Gauss maps, and unveils unique characteristics of Voss nets. Then, two generation methods, based on the properties identified in the previous section, are presented in section 3. Morphogenesis. The first one addresses the design of Voss nets through their normals and results in the exploration of a linear space (Figure 1). The second uses two boundary curves and permits a more direct computation of Voss nets. Finally, these methodologies are applied for the creation of discrete Voss surfaces.

The Gauss map

The Gauss Map or spherical projection, in classical differential geometry, is the application mapping every normal vectors of a surface to its corresponding point on the unit sphere S 2 . As a result, the projection of all normals generates a new surface on S 2 , called without ambiguity the Gauss map. The new surface is unique and must be understood as a representation of the initial surface.

In discrete differential geometry, the notion of Gauss Map is not unique. Nets, or discrete surfaces, are defined by their sets of vertices, edges and faces, thus normal vectors can be defined upon any of these entities. Moreover, several definitions of normal vectors can concur on each sets. Hence, dealing with a new family of surfaces, the challenge is to find the most adapted set or sets of normals, i.e. the sets of normal vectors that represent the characteristic properties of the underlying surfaces the best.

Face normals PQ NETS:

Voss nets are a subset of the larger family of planar quadrilateral nets (PQ nets). In this context, the discrete Gauss map can be defined upon the faces and is the application associating each face normals of the net to a point on the unit sphere. Following this definition, the Gauss map produces a net on S 2 that is topologically dual to the initial net: each face, edge, and vertex of the initial PQ net is transformed respectively to a vertex, edge or face on the unit sphere, and conversely. The projection of the face normals around a vertex leads to a useful property on the angles on the unit sphere. Let's consider the situation depicted in Figure 2, where four normal vectors form a face on the unit sphere, dual to the central vertex on the PQ net. The angles made by the edges incident to the vertex are transformed by the Gauss map to their supplementary angles in the dual face on S 2 .

VOSS NETS:

The above property has an immediate consequence in the special case of Voss nets.

Recalling the equality of opposite angles around vertices of Voss nets, it follows that opposite angles in faces of their Gauss map are also equal. Thus, each face of the Gauss map is a spherical parallelogram, which by definition means that the Gauss map of a Voss net is a Chebyshev net of S 2 (Pinkall [START_REF] Pinkall | Designing Cylinders with Constant Negative Curvature[END_REF]). The Gauss map, defined upon the face normals of a PQ net, finds another interpretation with regards to dihedral angles. Dihedral angles, or angles made by the normal vectors of two adjacent faces, can be identified as the arc length of the edge which links the normal of these two faces in the Gauss map (Figure 3). For Voss nets, the faces of the Gauss map form parallelograms. Thus, each quad face of the Gauss map has equal opposite angles, which translate to the fact that these faces have equal opposite edge lengths. Therefore, following Figure 3, opposite dihedral angles around a vertex are equal. Extending this remark to the whole net, dihedral angles are constant along a coordinate lines in Voss nets. According to Schief et al. [START_REF] Schief | On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces[END_REF] , this property of constancy constitutes an alternative definition for Voss nets: they are PQ nets whose Gauss map forms a Chebyshev net on S 2 .

Vertex normals

Another possibility to define a Gauss map for Voss nets consists in describing it upon the vertices. This approach is based on the study of curves and more particularly on the definition of tangent and normal vectors. Considering 𝐶 a smooth regular curve, non-degenerate at arc length 𝑠, i.e. 𝐶'(𝑠) and 𝐶′′(𝑠) are not null, then the Frenet frame of 𝐶 at 𝑠 is defined as the orthonormal frame 𝐹 𝑠 𝐶 = (𝑡 𝑠 , 𝑛 𝑠 , 𝑏 𝑠 ), where 𝑡 𝑠 is the tangent vector, 𝑛 𝑠 the normal vector and 𝑏 𝑠 the binormal vector. A discrete counterpart of the Frenet frame can defined upon the vertices of polylines. With 𝑃 a polyline, non-degenerated at the vertex 𝑝 𝑖 , i.e. 𝑝 𝑖-1 , 𝑝 𝑖 , and 𝑝 𝑖+1 are not aligned, the Frenet frame 𝐹 𝑖 𝑃 = (𝑡 𝑖 , 𝑛 𝑖 , 𝑏 𝑖 ) at 𝑝 𝑖 is given by:

𝑡 𝑖 = 𝛿𝑝 𝑖̅ -𝛿𝑝 𝑖 ‖𝛿𝑝 𝑖̅ -𝛿𝑝 𝑖 ‖ , 𝑛 𝑖 = 𝛿𝑝 𝑖̅ +𝛿𝑝 𝑖
‖𝛿𝑝 𝑖̅ +𝛿𝑝 𝑖 ‖ , 𝑏 𝑖 = 𝑡 𝑖 ∧ 𝑛 𝑖 .

(1) QUAD NETS: Quadrilateral nets have the particularity to define a two-way grid of polylines, which is the equivalent of parameter-lines on continuous surfaces. Hence, two Frenet frames can be computed, one in each directions (see Figure 4). Following the analogy with the smooth setting, the normal at a vertex can be obtained from the tangent vectors of the Frenet frames at this point, 𝑡 1 and 𝑡 2 , by,:

𝑛 = 𝑡 1 × 𝑡 2 ‖𝑡 1 × 𝑡 2 ‖ . (2)
GEODESIC QUAD NETS: In the special case of geodesic quadrilateral nets, quad nets with equal opposite angles at each vertex, Rabinovitch et al. [START_REF] Rabinovich | Discrete Geodesic Nets for Modeling Developable Surfaces[END_REF] proved that the normal 𝑛 (described in equation ( 2)) is aligned with the two normals 𝑛 1 and 𝑛 2 of the Frenet frames (Figure 5). This result mimics the behaviour of smooth geodesic lines whose normal vector always agrees with the surface's normal. Furthermore, it gives an alternative way to compute the vertex normal 𝑛 using one Frenet frame only.

VOSS NETS:

In the case of Voss nets, the Gauss map defined from the projection of the vertex normals finds an interesting interpretation with regards to the other Gauss map defined upon the face normals. Indeed, the spherical projection of the normal vectors of four faces around a vertex produces a spherical parallelogram on the unit sphere, dual to the common central vertex on the Voss net (Figure 5). The normal of the common vertex is projected on the unit sphere to the centre of the parallelogram. The centre of the parallelogram is identified either as the centre or the intersection of the diagonals, or as the centre or the intersection of the medians.

Choice of Gauss Map

The above sections presented two definitions of the discrete Gauss map of Voss nets, one based on face normals, the other one based on vertex normals. The interaction between the two notions proves the pertinence of these definitions. Indeed, the superimposition of the discrete Gauss maps enriches significantly the representation of Voss nets on the unit sphere since it encompasses information on the net for both the vertices and the faces. The concomitance of the notions of Gauss maps will be advantageously exploited for the generation of Voss nets in section 3. Morphogenesis.

In the remainder, the Gauss map of Voss nets will only refer to the spherical projection of face normals since it produces a Chebyshev nets on the unit sphere, in the similar way as smooth Voss surfaces.

Morphogenesis

Following the study of Voss nets, and the presentation of their projection properties, this section addresses the design of this family of nets. Two significantly different generation processes are presented. The first methodology consists in the exploration of a linear space of Voss nets. Starting from the Gauss map, it enables the creation and deformation of Voss nets within the same framework. Then a more straightforward methodology is exposed, in which Voss nets are generated from two boundary curves.

Shape space exploration

The presented methodology starts from the generation of a Chebyshev net on the unit sphere, and explores an underlying linear space composed of parallel Voss nets. Indeed, different Voss nets can be projected on a same Gauss Map, and if so, they have parallel edges.

Voss nets have the particularity to be projected through the Gauss map onto Chebyshev nets. Chebyshev nets are a well-known family of discrete surfaces and their generation has been broadly studied (Otto et al. [11], Popov et al. [START_REF] Popov | Geometric Approach to Chebyshev Net Generation Along an Arbitrary Surface Represented by NURBS[END_REF], Bouhaya et al. [START_REF] Bouhaya | Optimization of gridshell bar orientation using a simplified genetic approach[END_REF], Sageman-Furnas et al. [START_REF] Sageman-Furnas | Chebyshev Nets from Commuting PolyVector Fields[END_REF]). In Masson et al. [START_REF] Masson | Existence and construction of Chebyshev nets and application to gridshells[END_REF], different strategies are exposed for the computation of Chebyshev nets on surfaces starting either from two boundary curves (primal conditions: Figure 6a) or based on the main diagonal and the next diagonal line (dual conditions: Figure 6b ). Each time the generation of the net relies on the length equality of opposite edge in each quad face. In addition, Masson et al. [START_REF] Masson | Existence and construction of Chebyshev nets and application to gridshells[END_REF] also studied the use of mixed conditions, the introduction of singularity, and the applicability of patches of Chebyshev nets on general surfaces (Figure 6). The method exposed allows to take advantage of the various possibilities for the generation of Voss nets. Then, from the Chebyshev net on S 2 interpreted as the Gauss Map of Voss nets, the direction of the edges of the underlying Voss nets can be retrieved. The edges common to two adjacent faces are parallel to the cross product of the normal vectors of these faces. The orientation of those normal vectors are defined by the position of the vertices in the Chebyshev net. As a consequence, all the possible Voss nets projecting on a same Gauss map have parallel corresponding edges. In fact, they form a linear space which only depends on the initially generated Chebyshev net on the unit sphere. Each vector of this linear space represent a Voss net.

Proceedings of the IASS Annual Symposium 2020 and the 7th International Conference on Spatial Structures

Inspiring the Next Generation 7

Thus, using an adapted basis, the linear space of parallel Voss nets can be explored to find a suitable geometry. Since all Voss nets belong to a same linear space, several nets can be added to one another and linear combinations can be formulated in order to blend different shapes together. Thus, from this point of view, each vector of the linear space is a Voss net but also correspond to a deformation mode if it is added to another element (Figure 7).

Explicit generation

In this section an alternative generation process is presented. Unlike the previous methodology which addresses the morphogenesis from an exploratory point of view, this method uses two curves in space and produces the single corresponding Voss net.

Let's consider two non-degenerate polylines in space starting at the same point which represent the boundaries of the Voss net to generate. Since the input curves are not degenerate, the Frenet frames can be computed. Understanding those curves as future geodesic lines on a Voss surfaces, the normal vector in the Frenet frame gives the normal at the vertices. In addition, the first edges of each polyline define the plane of the first corner face. The normal vector of this first face is given by the cross product of theses edges.

From the projection on S 2 of the vertex normals of the boundary curves as well as the first face normal, primal conditions for Chebyshev nets can be retrieve on the unit sphere. Therefore, the specification of two boundary curves of a Voss surface is sufficient to find and generate its Gauss map.

In a similar fashion as in the previous method, the direction of the edges of the Voss net can be computed from the Gauss map. Here, in contrast with the previous method, the resolution is made locally for each face and not on the whole mesh. The prescription of the boundary curves gives the possibility to compute the faces iteratively. Starting from the first corner face, the input curves provides with the knowledge of two edge lengths 𝑙 1 and 𝑙 4 in the quad (Figure 8). Therefore, since the direction of all edges are given by the Gauss map, the face is uniquely determined and the two lengths left 𝑙 2 and 𝑙 3 are given by: ( 𝑙 1 + 𝑙 4 . cos (𝛼) 𝑙 4 sin (𝛼) ) = ( cos (𝛽) cos (𝛼 -𝛿) -sin (𝛽) sin (𝛼 -𝛿) ) ( 𝑙 2 𝑙 3 )

(3)
Using the successive computation of faces, the Voss net is entirely determined. This methodology, inspired by the primal condition for Chebyshev nets and summarized in Figure 9, is permitted by the thorough knowledge of the properties of Voss nets, and particularly by the use of the interaction between the complementary notions of Gauss map upon the faces and the vertices. On the one hand, the first exploratory method starts from an abstract design space, dual to Voss nets, which is the family of Chebyshev nets on the unit sphere. No constraint is directly expressed on the Voss nets in Euclidean space. With a certain intuition, this approach reveals particularly interesting for the design of surfaces for it notably allows the use of all the expertise acquired on Chebyshev nets (Figure 10). In addition, the manipulation of the linear space, as opposed to a single net, gives the possibility to simply transform and interpolate Voss nets.

On the other hand, the second generation process is more simple and intuitive. The Voss net is specified using explicit boundary constraints in Euclidean space. This method enables to simply patch Voss nets together in a continuous way (Figure 11).

Conclusion

Voss nets constitute a proficient family of surfaces for the conception of doubly-curved structures. In this paper, they have been addressed for their capacity to model surfaces which can be built from elastically bent rectangular laths and covered with flat panels. In order to fully understand Voss nets, a thorough study is presented, which analyses normals vectors and their projection on the unit sphere. In particular, a rich interaction is identified between the Gauss map defined on the face normals and the one determined upon the vertices. This special characterization of Voss net is then used for the formulation of generation methods. Two methodologies are described, one permits the exploration and deformation of Voss nets while the other provides with a more explicit way to create them. Finally, the formal richness of this family is illustrated, thus supporting the relevance of the generation methods.

Further developments include the generation of the best-fit discrete surface to a target mesh. The fitting should be addressed from the Gauss map since it reduces the number of degrees of freedom for the optimisation process. In addition, further studies on transformations should identify a special conformal transformation which preserves the angle around a vertex, while deforming the net. This is supported by the fact that Voss surfaces are stable under conformal transformation in the smooth setting.

Figure 2 :

 2 Figure 2: Spherical projection of face normals. Angles around a vertex (left) are projected on the unit sphere to supplementary angles in the dual face (right).

Figure 3 :

 3 Figure 3: Spherical projection of dihedral angles of a Voss net. The angles made by adjacent face normals (left) are equal to the arc length of the edge in the Gauss map connecting these normals (right).

Figure 4 :

 4 Figure 4: Frenet frame of a discrete curve (left) and vertex normal vector of a quad net (right).

Figure 5 :

 5 Figure 5: Spherical projection of the vertex normal vector of a Voss net.

Figure 6 :

 6 Figure 6: Generation methods for Chebyshev nets : Primal (a), dual (b), mixed (c) and patch (d) conditions.

Figure 7 :

 7 Figure 7: Summary of the exploratory generation process of Voss nets.

Figure 9 :

 9 Figure 9: Summary of the explicit generation process of Voss nets.

Figure 8 : 8 3. 3 .

 883 Figure 8: Configuration for the determination of the position of vc using equation (3)

Figure 10 :

 10 Figure 10: Voss net (centre) generated from a rosette Chebyshev net on the unit sphere (left), inspired from the geodesic shell of the equine therapy centre of Uzwil (Switzerland) by J.Natterer et al. [10] (right) [reproduction authorization pending]

Figure 11 :

 11 Figure 11: Voss nets created from two boundary curves. Left: Geodesic gridshell inspired by the gridshell of Downland; Right: Geodesic gridshell canopy which can be repeated in both directions.

Acknowledgements

The authors warmly thank Romain Mesnil for the fruitful discussions on topics ranging from architectural geometry, to structural morphogenesis to implementation details, as well as Laurent Hauswirth for the enlightening advices in differential geometry. The authors also thank Arthur Lebée for valuable enlightenments in the domain of origami structures.


Botrytis Cinerea

E N Chile

Y Francia

Carolina Pañitrur-De

L A Fuente

Héctor Valdés-Gómez

Jean Roudet

Yaneris Mirabal

V Felipe Laurie

César Acevedo-Opazo

Marc Fermaud

EARLY EVALUATION INDICES OF BERRY SUSCEPTIBILITY TO BOTRYTIS CINEREA IN CHILE AND FRANCE EVALUACIÓN TEMPRANA DE LA SUSCEPTIBILIDAD DE BAYAS A

Keywords: Botrytis bunch rot, pectins, tannins, sustainable management. Resumen Botrytis bunch rot, pectinas, taninos, manejo sustentable

Substantial economic losses occur in grapevines due to Botrytis Bunch Rot (BBR). The control of this disease is still largely based on the periodical use of specific anti-Botrytis chemical pesticides. Therefore, protection strategies require to be optimized in order to reduce pesticides applications. Our main objective was to propose and evaluate disease risk indicators at early grapevine phenological stages related to the potential susceptibility of berries to BBR. The relationships between grapevine features, i.e. pectins and tannins content in berry skins, measured at berry pea-size stage, and BBR intensity at harvest were investigated. Between 2010 and 2016, two experimental plots of Merlot and Sauvignon Blanc were studied in Chile and France. Analyses of pectins and tannins compounds were performed to characterize berry susceptibility to BBR, and both the incidence and severity of the disease were evaluated at harvest. Furthermore, a potential berry susceptibility (PBS) index was calculated using pectins and tannins data. The results obtained showed positive and linear relationships between BBR intensity and pectins and PBS index, whereas negative and linear relationships between BBR intensity and tannins contents were observed. All these relationships were statistically significant, except for the correlation between pectins and BBR incidence. The Merlot cultivar evaluated in Chile showed the lowest PBS and pectins values, and the highest tannins content, which was related with a low disease development. This work points out key disease risk indicators, which could be useful before applying direct chemical-based control measures against BBR.

Pérdidas económicas sustanciales ocurren en los viñedos debido a Botrytis Bunch Rot (BBR). El control de esta enfermedad se basa en gran medida en la aplicación periódica de pesticidas químicos específicos. Así surge la necesidad de optimizar las estrategias de control con el fin de reducir las aplicaciones de pesticidas. Nuestro principal objetivo fue proponer y evaluar indicadores de riesgo relacionados con la potencial susceptibilidad de las bayas a BBR, medidos en estados fenológicos tempranos de la vid. Relaciones entre el contenido de pectinas y taninos en la piel de las bayas, medidos en el estado fenológico "tamaño de arveja", y la intensidad de BBR a la cosecha fueron investigadas. Entre 2010 y 2016, dos cuarteles experimentales de los cvs. Merlot y Sauvignon Blanc fueron estudiados en Chile y Francia. En estos se midieron las pectinas y taninos en la piel de las bayas para caracterizar la susceptibilidad a BBR, además de evaluar la incidencia y la severidad de la enfermedad a la cosecha. Un índice de potencial susceptibilidad de bayas (PBS) fue calculado usando los datos de taninos y pectinas. Los resultados mostraron relaciones positivas y lineales entre la intensidad de BBR y las pectinas y el índice PBS, mientras que relaciones negativas y lineales fueron observadas entre la intensidad de BBR y el contenido de taninos. Todas las relaciones fueron estadístiamente significativas excepto la correlación entre pectinas e incidencia de BBR. El cultivar

Introduction

Substantial economic crop losses (~ 2 billion $US per annum) occur worldwide in vines due to Botrytis cinerea [START_REF] Elmer | Epidemiology of Botrytis cinerea in orchard and vine crops[END_REF]. In this crop, the pathogen can reduce both yield and quality of wine (Ribéreau-Gayon et al. 1998). The control of this disease, still largely based on the use of periodic fungicide spraying. However restriction of fungicides have become necessary in order to reduce the negative effects on both, health and environment and to limit residues on harvest [START_REF] Damalas | Pesticide exposure, safety issues, and risk assessment indicators[END_REF]. Therefore, protection strategies aiming at the B. cinerea control require to be optimized in order to reduce pesticides applications. Under this context, and considering the main principles of Integrated Pest Management (IPM), risk disease assessment must be applied before direct control measures are used (IOBC 2007).

Risk disease assessment should consider factors related with the climate, the crop susceptibility and critical periods of disease development. The climate is considered the main factor involving in B. cinerea development and therefore several indices have been proposed. The susceptibility of grapevines to disease depends on various genetic and phenotypic traits, such as chemical features of the berry skin [START_REF] Latorre | Gray mold caused by Botrytis cinerea limits grape production in Chile[END_REF]. The cell walls is among the first structures that B. cinerea encounters when colonizing the berry skin and it can contribute to susceptibility as wells as resistance to the pathogen. An important component of cell walls are the pectins, considered a potential source of nutrients for the pathogens and the main cell wall targets during B. cinerea infections (Blanco-Ulate et al 2014). In contrast to pectins, other components including tannins, provide a protective barrier to Botrytis sp. The tannins are able to inhibit the cell wall-degrading fungal enzymes [START_REF] Goetz | Resistance factors to grey mould in grape berries: Identification of some phenolics inhibitors of Botrytis cinerea stilbene oxidase[END_REF], giving resistance to berries against the pathogen.

Regarding critical periods of disease development, a critical moment to disease control on grapevine is between flowering and bunch closure. Although B. cinerea appears and develops late in the growing season, early infections plays a key role in disease development [START_REF] Elmer | Epidemiology of Botrytis cinerea in orchard and vine crops[END_REF]. Then, fungicide applications are used during this period, in order to eliminate the fungal inoculum. Despite the importance of this critical stage, few studies have investigated the relationship between grapevine features evaluated at early vine phenological stages and the disease infection at harvest. Consequently, no risk assessment indices are available to evaluate early, grapevine susceptibility to the fungus. Thus, the main objective of this work was to evaluate early indices related to the potential susceptibility of grapevine to Botrytis cinerea. For that, the relationships between berry skin components (pectins and tannins) and BBR attack at harvest were investigated.

Materials and methods

Experimental field site: Experiments were carried out in two experimental fields of Merlot cultivar, one of them located in Aquitaine Region (France) and the other one situated in Maule Region (Chile). A second plot with the cultivar Sauvignon Blanc was also included in the Chilean experimental field. The experiments were carried out during seven seasons in France (2010 to 2016) and two seasons in Chile .

Experimental conditions:

In order to evaluate the grapevine susceptibility to B. cinerea at harvest, no fungicide with known activity against this pathogen was applied in any site and season.

Disease susceptibility assessment BBR incidence and severity: Berry incidence and severity were visually evaluated at harvest in environ 250 and 300 clusters in France and Chile, respectively. Disease incidence was obtained by dividing the number of clusters infected by the total number of clusters evaluated by replicate. Disease severity was calculated in each cluster as the percentage of the rotted and/or sporulating area. Both incidence and severity were expressed as a percentage.

Biochemical berry skin assessment:

Analyses of pectin and tannins compounds were performed to relate berry skin susceptibility/resistance to B. cinerea. For this, 20 grapes per experimental plot were randomly collected at berry pea-size stage and immediately stored at -20°C. Once in laboratory, berries were peeled to determine pectins and tannins compounds.

Pectins content in berry skin:

No-alcohol-soluble components (NAS fraction) were separated by a fractional process as proposed by [START_REF] Chenet | Résistance de la baie de raisin (Vitis vinifera) à Botrytis cinerea: é tude de la pellicule et de ses parois[END_REF]. Skins (5 g) were boiled for 10 min in 250 ml of ethanol 95%, grounded in a blender for 5 min and then centrifuged (10,000 g) for 20 min at 0°C. On a minimum of three occasions, the solid material component was resuspended in ethanol 95% and centrifuged similarly until the liquid supernatant was decolorized. The resulting NAS fraction was dried overnight at 60°C and ground to a fine powder (<100 um). After that, 0.1 g of NAS fraction were diluted in 20 ml of distilled water and 0.2 ml of ethanol 95% and shaken horizontally for 16 h at room temperature. The Water-soluble pectin (WSP) were extracted from the NAS fraction by centrifugation (10,000 g) for 20 min at 0°C. The supernatants were then diluted 1/10 and the concentration in galacturonic acid, expressed as mg g-1 NAS, was measured in three replicates using an adaptation to the colorimetric method described by [START_REF] Robertson | The fractional extraction and quantitative determination of pectic substances in grapes and musts[END_REF].

Tannins content in berry skin:

The tannins content was extracted and determined from berry skins (0.5 g) ground in liquid nitrogen. The extraction process was based on two successive macerations of berry skins for 3 h each, at room temperature. For that, berry skin were stirred with 5 ml of methanol containing 0.1% of 12N HCl, according to Gagné et al. (2006). The tannins content was determined by spectrophotometry and expressed as mg g -1 skin in three replicates, using the methodology proposed by [START_REF] Ribéreau-Gayon | Dosage des tanins du vin rouge et détermination de leur structure[END_REF].

PBS index:

A potential berry susceptibility (PBS) index was calculated dividing the pectins by the tannins data.

Statistical analyses:

The relationships between BBR incidence and severity with the explanatory variables pectins (WSP), tannins (TAN) and Potential berry susceptibility (PBS) index, were explored by using correlations and linear regressions. To determine if correlations were significant, Pearson's correlations coefficient were calculated based on the P-value = 0.05. All data analyses were performed using the SAS University Edition software.

Results and discussion

Disease incidence and severity:

In France, the Merlot cultivar showed mean values of disease incidence and severity for the seven studied years of 57.1% and 8.6%, respectively. Nonetheless, the disease level was different between years depending mainly on climatic conditions. On the other hand, the Merlot cultivar evaluated in Chile, presented disease incidence and severity values of 0 % in all studied seasons and the Sauvignon Blanc cultivar showed a mean disease incidence and severity for both seasons of 8.4 % and 1.2%, respectively (Figure 1). Then, BBR attack was much lower in Chile than in France mainly due to climatic conditions, specifically to rainfall before harvest (data not shown).

Relations between berry skin components and BBR at harvest

Positive and linear relationships were observed between BBR intensity and pectins and PBS, whereas negative relationships between BBR and tannins content were observed (Figure 2). The pectins appear to be the main cell wall targets during B. cinerea infections and their growth is enabled by the metabolism of sugars obtained from them. Although pectins were significantly correlated with BBR severity, this berry feature did not present a significant correlation with BBR incidence (Table 1). This could be explained because in addition to pectins, there are other types of polysaccharides presented in the primary cell wall, which are also considered substrates for the pathogen [START_REF] Kars | Extracellular enzymes and metabolites involved in pathogenesis of Botrytis[END_REF]. On the other hand, the tannins are constitutive antifungal compounds of berry skins which play an important role in resistance to B. cinerea [START_REF] Pezet | Plant microbe interaction: the Botrytis grey mould of grapes[END_REF], maintaining the pathogen in a quiescent stage.

The results of the present study suggest that these indicators measured in an early phenological stage, might be used to estimate the potential susceptibility of grapevine berries to B. cinerea. Nevertheless, they should remain as trend indicators as there are other factors such as vegetative growth, microclimatic conditions and interactions with microorganisms that may also affect the BBR development. Then, the interpretation of them should always consider environmental conditions as the climate and the vegetative growth, considered the two major important factors affecting B. cinerea development [START_REF] Valdés-Gómez | Grey mould incidence is reduced on grapevines with lower vegetative and reproductive growth[END_REF].

Conclusion

The results of the present study left in evidence early indices related with the potential susceptibility of grapevine to Botrytis cinerea. The pectins and the PBS index showed a positive relationship with BBR severity and incidence at harvest, whereas the tannin content showed a negative and linear relationship

Pectins

Figure 1 :

 1 Figure 1: Mean disease incidence (Inc) and severity (Sev) values (%) for each season under field conditions in France and Chile.

Figure 2 :

 2 Figure 2: Relationship between BBR Severity (%) with Pectins (a), Tannins (b) and PBS index (c); and BBR Incidence (%) with Pectins (d), Tannins (e) and PBS index (f). Merlot in France (), Merlot in Chile (), Sauvignon Blanc in Chile ( )

Table 1 :

 1 Statistical parameters for relations between BBR severity and incidence (%) and pectins, tannins and PBS index, in all study cultivars and seasons.

  disease attack. These indices, evaluated at berry pea-size stage (environ 100 days before harvest), could be used in IPM strategies as risk disease assessment before direct control measures are used. Nevertheless, they should remain as trend indicators as there are other factors such as vegetative growth, microclimatic conditions and interactions with microorganisms that may also affect the BBR development. Then, the interpretation of these indicators should always consider environmental conditions as the climate and the vegetative growth, considered the two major important factors affecting B. cinerea development

	with the final
						Tannins		PBS Index
		R 2	r	P-value	R 2	r	P-value	R 2	r	P-value
	Severity	0.49 0.70	0.02	0.38 -0.62	0.04	0.71 0.84	0.00
	Incidence 0.29 0.54	0.09	0.42 -0.65	0.03	0.46 0.68	0.02

Acknowledgments

The research was supported by the National CONICYT Doctoral Fellowship 2013 N° 21130505 and by the Chilean projects CONICYT-FONDECYT/Regular 1130763. We are grateful to Panguilemo Experimental Station, to the INRA Grande Ferrade experimental unit and INRA UMR EGFV (1287) for the vineyard plots and scientific and technical help. We are also grateful to the Conseil Interprofessionnel du Vin de Bordeaux (CIVB) for its financial support. This study has been performed in the framework of the French Cluster of Excellence COTE, Bordeaux.