Sandro Giuseppe Chiodo

Tzonka Mineva
email: tzonka.mineva@enscm.fr

Stability and Structures of Silver sub-nm Clusters in EMT Zeolite with Maximum Aluminium Content

Keywords: Ag-clusters, sodalite, EMT zeolite, DFT, Hydrogenation, Ion exchange, Formation energy, Density of state spectra

The stability of small silver clusters, Ag n with n=3, 4, 6, and 8, supported in a sodalite of EMT zeolite with a maximum possible aluminium content (Si/Al = 1) were studied with the Density Functional Theory based cluster approach. The results showed that various silver clusters, partially or compeltely reduced, can be stabilised in this zeolite with the maximum negative defects.

Computed formation energies for two reduction reactions reveals that completely reduced Agclusters can be stabilised trough hydrogenation, giving some preference to the formation of hydrogenated Ag 6 species. The hydrogenated neutral Ag n H m /EMT clusters remain stable at T=300 K as obtained from the analysis of the Born-Oppenheimer Molecular Dynamics trajectories. Ion exchange of Na + by Ag + cations is obtained to be exothermic with energy gain of 0.5 eV per Ag cation. The formation of Ag-O ionic bonds, known to stabilise metal clusters in zeolitic frameworks, is found to be preponderant in the structures with less than six silver atoms, which leads to strong geometrical deformations especially for Ag 3 and Ag 4 species. The largest possibly stabilised in the sodalite completely reduced silver cluster is Ag 8 . Partially reduced intact structures are obtained stable for silver clusters with n ≥ 4. Formation energies predict a co-existence of silver exchanged cations and partially reduced silver clusters with several oxidation states in the sodalite.

The density of state spectra (DOSS) of the supported completely and partially reduced Ag 4 and Ag 8 clusters are very similar despite the different cluster size, topology, and reduction degrees. DOSS of the host zeolite did not undergo any changes due to the interaction with silver clusters.

I. Introduction

Stabilization of silver aggregates inside the cavities in zeolites, alluminosilicate-based porous materials, has been extensively studied due to many applications in the chemical industry for their optical, redox and catalytic properties. [START_REF] Sun | Silver Clusters and Chemistry in Zeolites[END_REF][START_REF] Gao | Study of Structure and Optical Properties of Silver Oxide Films by Ellipsometry, XRD, and XPS Methods[END_REF][START_REF] Vosch | Strongly Emissive Individual DNA-Encapsulated Ag Nanoclusters as Single-Molecule Fluorophores[END_REF][START_REF] Richards | Oligonucleotide-Stabilized Ag Nanocluster Fluorophores[END_REF][START_REF] Xu | Water-Soluble Fluorescent Silver Nanoclusters[END_REF][START_REF] Sinclair | Density Functional Theory Calculations of Adsorption and Reactivity of Methanol at Alumino-Silicate Bronsted Acid Centres[END_REF][START_REF] Furusawa | Selective Reduction of NO to N2 in the Presence of Oxygen over Supported Silver Catalysts[END_REF][START_REF] Ju | The Local Structures of Silver(I) Ion Catalysts Anchored within Zeolite Cavities and Their Photocatalytic Reactivities for the Elimination of N 2 O into N 2 and O 2[END_REF][START_REF] Gurin | Self-assembling of Silver and Copper Small Clusters within the Zeolite Cavities: Prediction of Geometry[END_REF][START_REF] Kolobova | Formation of Silver Active States in Ag/ZSM-5 Catalysts for CO Oxidation[END_REF][START_REF] Shen | Gas-phase Selective Oxidation of Alcohols: In Situ Electrolytic Nano-Silver/Seolite Film/Copper Grid Catalyst[END_REF][START_REF] Dong | Silver Confined within Zeolite EMT Nanoparticles: Preparation and Antibacterial Properties[END_REF][START_REF] Zaarour | Progress in Zeolite Synthesis Promotes Advanced Applications[END_REF][START_REF] Miyanaga | Formation of Ag Clusters in Zeolite X Studied by in situ EXAFS and Infrared Spectroscopy[END_REF][START_REF] Mathisen | Irreversible Silver (I) Interconversion in Ag:ZSM-5 and Ag:SAPO-5 by Propene and Hydrogen[END_REF][START_REF] Golubeva | Stabilization of Silver Nanoparticles and Clusters in Porous Zeolite Matrices with Rho, Beta, and Paulingite Structures[END_REF] Metal clusters can be stabilised because of the negative charges at the substitution sites of Si 4+ cation by Al 3+ . [START_REF] Sun | Silver Clusters and Chemistry in Zeolites[END_REF][START_REF] Bogdanchikova | Role of Mordenite Acid Properties in Silver Cluster Stabilization[END_REF][START_REF] Kim | Two Crystal Structures of Fully Dehydrated, Fully Ag + -Exchanged Zeolite X. Dehydration in Oxygen Prevents Ag + Reduction without Oxygen, Ag 8 n+ (Td) and cyclo-Ag 4 m+ (near S4) Form[END_REF][START_REF] Anderson | Molecular Sieves: Science and Technology[END_REF] Small metal clusters are usually stabilised in the zeolites by applying ion-exchange procedure followed by an intra-zeolitical reduction process. Ag cations are reduced by heating, by reaction with reducing agents [START_REF] Furusawa | Selective Reduction of NO to N2 in the Presence of Oxygen over Supported Silver Catalysts[END_REF][START_REF] Gurin | Self-assembling of Silver and Copper Small Clusters within the Zeolite Cavities: Prediction of Geometry[END_REF][START_REF] Mathisen | Irreversible Silver (I) Interconversion in Ag:ZSM-5 and Ag:SAPO-5 by Propene and Hydrogen[END_REF] or via radiolytic reduction. [START_REF] Hornebecq | Stable Silver Nanoparticles Immobilized in Mesoporous Silica[END_REF] The Si/Al molar ratio in mordenite zeolites was reported to be the main parameter that permits to vary the size of formed metal species by reduction processes. [START_REF] Gurin | Self-assembling of Silver and Copper Small Clusters within the Zeolite Cavities: Prediction of Geometry[END_REF] Stable silver clusters with four and eight atoms were obtained in Rho, Pau and Beta zeolites with Si/Al molar ratio of 3.7 and 13 for Pau and Beta, respectively. [START_REF] Golubeva | Stabilization of Silver Nanoparticles and Clusters in Porous Zeolite Matrices with Rho, Beta, and Paulingite Structures[END_REF] This led to conclude that the surface acidity of Rho, Pau and Beta zeolites does not affect the stability of small silver clusters, which remained stable over a long time period. Silver sub-nm particles were obtained in various pores and on the surfaces of nanosized crystallite zeolites EMT, LTL, MFI, LTA, BEA with very different Si/Al ratio in each zeolite type. [START_REF] Zaarour | Progress in Zeolite Synthesis Promotes Advanced Applications[END_REF] Despite the enormous amount of information gathered, especially, in the last years, on the synthesis routes and reduction protocols, significantly fewer works have been devoted to a nonroutine description of the topology, geometrical structures, electronic properties and type of interactions of silver clusters with the oxide frameworks. For an extensive review about the challenges and earlier achievements on the characterisation of ionic clusters, including silver species, in zeolites we refer to the work of Anderson. [START_REF] Anderson | Molecular Sieves: Science and Technology[END_REF] More recently, inter-atomic distances in Agspecies formed in Y and A-zeolites [START_REF] Yamamoto | Stability of Silver Clusters in Zeolite A and Y Catalysts[END_REF] have been estimated from the extended X-ray absorption fine line structure (EXAFS) and the X-ray absorption near edge spectroscopy (XANES) measurements.

In this study, the relatively short Ag-Ag distance of 2.75 Å were attributed to Ag 4 + species in agreement with the Ag-Ag distances in ZSM-5. [START_REF] Shibata | Ag Cluster as Active Species for SCR of NO by Propane in the Presence of Hydrogen over Ag-MFI[END_REF] Applications of EXAFS, XANES and X-ray photoelectron spectroscopies to characterise Na-mordenite catalysts with 5, 10 and 15 wt% of silver loading revealed the co-existence of Ag + , Ag x O and Ag n + (n<10) structures in the same material. [START_REF] Aspromonte | Study of the Nature and Location of Silver in Ag-Exchanged Mordenite Catalysts. Characterization by Spectroscopic Techniques[END_REF] Recently, silver-containing LTA with the lowest possible Si/Al ratio was investigated using scanning transmission electron microscopy (STEM) with spherical aberration-corrected high-angle annular dark-field. [START_REF] Mayoral | Atomic Resolution Analysis of Silver Ion-Exchanged Zeolite A[END_REF] It was proposed that a neutral Ag 6 octahedron is formed in the sodalite cage with a Ag-Ag distance of 2.7 Å and coordinated to other eight silver cations, each located in the center of a 6-ring. [START_REF] Mayoral | Atomic Resolution Analysis of Silver Ion-Exchanged Zeolite A[END_REF] Ab-initio optical spectra of Ag 8 and Ag 14 , embedded in sodalite models, without and with Al 3+ substitution, were found dependent on the cluster size and charge; [START_REF] Cuong | Theoretical Modeling of Optical Properties of Ag8 and Ag14 Silver Clusters Embedded in an LTA Sodalite Zeolite Cavity[END_REF] however information about the interaction or formation energies has not been provided and charged Ag 14 /sodalite truncated cluster models have been considered. Theoretical studies, based on the Density Functional Theory (DFT) methods demonstrated that silver cluster topology, optical properties and geometrical parameters can be controlled by the Si/Al ratio in Ag n -ZSM-5(Al n ) (n=1-3). [START_REF] Yumura | Behavior of Ag3 Clusters Inside a Nanometer-Sized Space of ZSM-5 Zeolite[END_REF][START_REF] Yumura | Combined Experimental and Computational Approaches To Elucidate the Structures of Silver Clusters inside ZSM-5 Cavity[END_REF] In this article we present a systematic computational study on the stability of both neutral and charged Ag n (n=3, 4, 6, and 8) clusters embedded in the sodalite cavity of the EMT zeolite with Si/Al=1.0. This work was mostly stimulated by the recently obtained stable small Ag-clusters in the sodalite of EMT with Si/Al=1.1 that posses a crystallite ordering at nano-scale range and is expected to open a range of interesting new applications. [START_REF] Dong | Silver Confined within Zeolite EMT Nanoparticles: Preparation and Antibacterial Properties[END_REF][START_REF] Zaarour | Progress in Zeolite Synthesis Promotes Advanced Applications[END_REF] Our work aims at describing the hostguest interactions as a function of cluster size and oxidation states in the zeolite framework with the maximum of Al 3+ content.

II. Computational details and models of silver clusters hosted into the sodalite cage.

All calculations were performed at the density functional (DF) level of theory with the deMon2k code. [START_REF] Köster | deMon2k Version 4.2.0; The deMon developers[END_REF][START_REF] Geudtner | deMon2k[END_REF] The PBE exchange correlation functional [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] was used combined with the DZVP 31 basis sets. Automatically generated auxiliary basis sets were employed. [START_REF] Köster | Hermite Gaussian Auxiliary Function for the Variational Fitting of the Coulomb Potential in Density Functional Methods[END_REF][START_REF] Köster | Calculation of the Exchange-Correlation Potential with Auxiliary Function Densities[END_REF] An adaptive grid for numerical quadrature was used and the SCF convergence criterion of 10 -7 a.u. was set.

The EMT structure is composed of sodalite cages (or β-cages), consisting of 24 T atoms (T = Si and Al), rings with 4 or 6 T atoms connected by O atoms. Sodalite cages are linked through double 6-rings. The T atoms in the 4 and 6-rings lie in the same plane while the O atoms are in alternating sequence displaced slightly above and below these planes. The framework structure consists of super cages formed by the sodalite cages.

To prepare the EMT zeolite model with a Si/Al ratio of 1.0, we started from the EMT unit cell with parameters a = b =17.215 Å, c = 28.082 Å, α = β = 90.0°, and γ = 120.0° consisting only of Si and O atoms. Thus the unit cell was replicated and a truncated model, shown in Figure 1a, was cut from this periodic structure. The dangling bonds were saturated with hydrogen atoms. According to the Loewenstein rule, [START_REF] Loewenstein | The Distribution of Aluminum in the Tetrahedra of Silicates and Aluminates[END_REF] Si atoms were systematically substituted by Al in order to obtain Si/Al=1.

Owing to the presence of the three-valent Al atoms replacing the tetra-valent Si atoms, the zeolite framework is negatively charged and its neutrality is maintained by the insertion of Na + cations that were initially placed at the crystallographic positions of an EMT structure with Si/Al = 3.31 and the Na/Al = 0.949, as reported in the work of Livens et al. [START_REF] Lievens | Cation Site Energies in Dehydrated Hexagonal Faujaste (EMT)[END_REF] This model structure consists of 36 Na, 36

Al, 36 Si, 48 H, and 168 O. In order to find the distribution of Na + leading to the minimum energy, eleven input structures with different Na + positions were first selected and completely optimized.

We found that in the most stable model, which is displayed in Figure 1a, Na + are arranged as follows: one Na + interacting with each of the eight six-rings -four six-rings belonging to the hexagonal prisms and four six-rings from the side of the super cage -facing the central sodalite cage, but being slightly displaced toward the center of the sodalite cage; one Na + interacting with each of the four six-ring of the truncated sodalite cavities; one Na + in each of the three truncated six-ring of the four terminal sodalite cages; the remaining twelve Na + occupy the sites of the walls of the super cage located in front of the four-rings of the terminal sodalite cages. This Na + arrangement generally agrees with the crystallographic cation sites in faujasite structures. [START_REF] Smith | Faujasite-Type Structures: Aluminosilicate Framework: Positions of Cations and Molecules: Nomenclature[END_REF] Each Ag n (n = 3, 4, 6, 8) cluster was embedded in this sodalite model (denoted hereafter as

Ag n /EMT) by substituting nNa + , coordinated to the oxygens of the six-rings of the central sodalite cage, with nH + cations. In addition to these neutral clusters, species with a charge q were studied as follows: for n=3, q=1+, 2+, and 3+; for n=4, q=2+ and 4+; for n=8, q=2+, 4+, 6+, and 8+. For all the considered clusters, various possible H + locations in the neighbourhood of the silver structures were examined. Full geometry optimisation was applied in order to establish the minimum energy configurations in all the cases. In order to verify the stability of the obtained H + and Ag n positions, 1b.

Born
The formation energy was computed for two possible reduction reactions: (i) reduction with

H 2 EMT [nNa] + nAg + + (n-q)/2 H 2 → (Ag n ) q /EMT[(n-q)H] + nNa + (R 1 )
and (ii) reduction with N 2 H 4 :

EMT[nNa] + nAg + + (n-q)/4 N 2 H 4 → (Ag n ) q /EMT[(n-q)H] + (n-q)/4 N 2 + nNa + (R 2 )
The Mulliken population analysis and density of state spectra (DOSS) were computed.

Lorentzian functions with a constant half width of 0.1 eV was used to plot DOSS.

III. Results and discussion

III. 1 Stabilisation by hydrogenation of supported completely reduced clusters

The most expected locations of the hydrogen cations necessary to compensate the charges in the zeolite with completely reduced silver clusters are in the vicinity of the negative defects.

Because hydrogenation of metal clusters in zeolites was established for small rhodium and iridium clusters in HZSM-5 and HY, [START_REF] Ivanova Shor | everse Hydrogen Spillover onto Zeolite-Supported Metal Clusters: An Embedded Cluster Density Functional Study of Models M6 (M = Rh, Ir, or Au)[END_REF] The computed formation energies, E f , using eq. ( R1) and (R2), are reported in Table 1.

These results reveal that in all the neutral Ag n /EMT models, the hydrogenated silver structures

Structural deformation of embedded Ag n clusters

The hosting of Ag n in the sodalite cavity causes various degrees of structural deformations compared to their Ag n counterparts in gas-phase. These variations are particularly strong for three and four atomic structures and depend on the hydrogenation. The smallest Ag 3 H stable cluster in

EMT is an open triangle (Figure S1, (a) in the Supporting Information, SI) with Ag-Ag distances of 2.898, 2.952 and 3.296 Å. These distances are somewhat larger in comparison to the previous theoretical results. [START_REF] Yumura | Behavior of Ag3 Clusters Inside a Nanometer-Sized Space of ZSM-5 Zeolite[END_REF] The discrepancy can be attributed to the established by us energetically favoured Ag 3 H cluster in the sodalite containing more negative sites than in the previous models. Considering the larger size geometries Ag 6 and Ag S2 (a). An octahedron geometry of Ag 6 cluster hosted in sodalite of LTA with Si/Al = 1was proposed from the analysis of the experimental STEM images (vide supra), [START_REF] Mayoral | Atomic Resolution Analysis of Silver Ion-Exchanged Zeolite A[END_REF] which was not strictly corroborated by our results. This Ag-configuration has been proposed from the best fit between the experimental STEM and the simulated deconvoluted image, assuming perfect Ag 6 octahedron coordinated to eight Ag + cations, Ag 6 (Ag + ) 8 , in agreement with a model that has also been previously suggested from the single crystal XRD results. [START_REF] Sun | Silver Clusters and Chemistry in Zeolites[END_REF] The deformation of the Ag 6 H 2 octahedron is caused by the hydrogenation, which contributes to stabilise the supported silver structures (vide infra) in our models.

The observed tendency to decrease the Ag-Ag distances from hydrogenated to nonhydrogenated three-and four-atomic clusters, remains valid also in the case of larger silver 3.

In all the supported silver structures with n=3, 4, 6, and 8, the Ag-Ag distances are very similar, depending only on the hydrogenation. In the hydrogenated silver structures, r(Ag-Ag) are longer by 0.1-0.15 Å compared to these in the bare Ag n /EMT clusters. Different degrees of topology deformations occurred due to the stabilisation via silver-oxygen ionic bonds formation. In the clusters with three and four Ag atoms the Ag-O bonds dominate the Ag-Ag interactions that lead to the most pronounced structural changes. Small structural perturbations are found only for the bare Ag-clusters (b) and (c) in the sodalite that nearly preserved the same topology and bond lengths as those of their gas-phase counterparts. Formation of such structures is however energetically unfavoured as follows from the positive E f values in Table 1. Our computed Ag-Ag bond lengths are systematically longer than those from EXAFS [START_REF] Shibata | Ag Cluster as Active Species for SCR of NO by Propane in the Presence of Hydrogen over Ag-MFI[END_REF] and STEM [START_REF] Mayoral | Atomic Resolution Analysis of Silver Ion-Exchanged Zeolite A[END_REF] analysis reporting distances of ~2.7 -2.75 Å. Recent DFT study on the effect of the number of Al 3+ cations in a tenmember ring in a ZSM-5 cavity showed that Ag-Ag bond distances elongated with the increase of Al 3+ content and reported r(Ag-Ag) = 2.9 Å in Ag 4 cluster in a cavity with three aluminium cations. [START_REF] Yumura | Combined Experimental and Computational Approaches To Elucidate the Structures of Silver Clusters inside ZSM-5 Cavity[END_REF] The latter result agrees well with the Ag-Ag distances obtained by us for the hydrogenated Ag n H m clusters embedded in a cavity with the maximum possible Al 3+ cations (Si/Al=1).

The averaged Ag-O bond lengths in all the hydrogenated silver structures (a) are in the range of 2.40 -2.48 Å and in structures (b), and (c) -in the range of 2.50 -2.56 Å. In the averaging of the Ag-O bonds, bond distances ≤ 2.60 Å were taken in consideration. The number of shorter Ag-O bonds is higher in the hydrogenated clusters, which also contributes to the silver stabilisation. The Ag-H distances of 1.8-1.9 Å are formed in all the hydrogenated geometries.

Atomic charges computed within Mulliken population scheme showed that all the hydrogenated clusters are positively charged and the adsorbed hydrogen atoms bear a negative charge in the range of -0.16 ˗ -0.27 e. In Figure 4 are presented the atomic charges of the silver atoms, the adsorbed hydrogens and the binding oxygens in Ag 4 H 2 /EMT and Ag 8 H 3 /EMT clusters as representative cases. Similar charge distribution between the metal atoms and adsorbed hydrogen was found in hydrogenated rhodium and iridium clusters in zeolites, with -0.16e to -0.14e charge at H sites. [START_REF] Ivanova Shor | everse Hydrogen Spillover onto Zeolite-Supported Metal Clusters: An Embedded Cluster Density Functional Study of Models M6 (M = Rh, Ir, or Au)[END_REF] The electron density transfers towards the adsorbed hydrogens can be explained with the higher hydrogen electronegativity than that of Ag. We found that the total positive charge on

Ag n H m /EMT slightly decreases with the silver cluster size from 0.34 e (Ag 3 ) down to 0.20 e (Ag 8 ).

Hydrogenation causes the electron depletion of the silver particles, which enhances the Ag-O ionic bond strengths that stabilises Ag n H m in the sodalite with Si/Al=1.

Other possible Ag-configurations in sodalite cage

Further on, we have examined the hypothesis that more than one Ag-cluster with two or three atoms can co-exist in the cavity of a sodalite. Because, the hydrogenation of Ag 4 led to a splitting into two Ag 2 H...Ag 2 H-species, we have also considered the possibility to find two separate silver trimers in the sodalite. Starting from two separated hydrogenated Ag 3 clusters (with the minimum separation distance of 3.37 Å) the optimization led to a hydrogenated Ag 6 H 4 /EMT minimum structure, being more stable by 1 eV than Ag 6 H 2 (structure (a) in Figure S2). Therefore, two separated Ag 3 clusters would not remain stable in the sodalite and would preferably aggregate to intact Ag 6 clusters. The latter result agrees very well with the experimental suggestions. [START_REF] Sun | Silver Clusters and Chemistry in Zeolites[END_REF][START_REF] Anderson | Molecular Sieves: Science and Technology[END_REF][START_REF] Mayoral | Atomic Resolution Analysis of Silver Ion-Exchanged Zeolite A[END_REF] The initial geometry of the sodalite with the two separated silver trimers and the resulting optimized Ag 6 H 4 /EMT structures are shown in Figure 5a. Moreover, this Ag 6 H 4 /EMT cluster is the most stable among all the considered possibly formed neutral Ag n H m clusters as follows from the computed formation energies in Table 1. This result additionally suggests that various stable configurations can occur depending on the particular synthesis protocol.

We have also examined the possibility to stabilise large neutral silver species. Ag [START_REF] Mayoral | Atomic Resolution Analysis of Silver Ion-Exchanged Zeolite A[END_REF] experiments that an intact silver cluster co-exists with Ag + cations; however the proposed structure from these experiments is Ag 6 (Ag + ) 8 . In our computations, the initial intact Ag 14 /EMT structure split spontaneously, during the geometry optimisation, to a minimum energy structure with Ag 8 cluster embedded in the sodalite, coordinated to six silver cations, Ag 8 (Ag + ) 6 (Figure 5b). This revealed that the largest possibly embedded intact cluster in the sodalite with Si/Al=1 would be an octamer; however the formation energies in Table 1 predicted the hydrogenated hexamer to be the most favoured silver cluster among the completely reduced structures in line with the experimental suggestions for the sodalite with the maximum possible negative defects. [START_REF] Mayoral | Atomic Resolution Analysis of Silver Ion-Exchanged Zeolite A[END_REF] Despite it, the formation of other hydrogenated completely reduced silver clusters (especially with n ≥ 4) cannot be excluded, because they were also found energetically favoured from the computed formation energies.

In conclusion of this section, we note that the BOMD trajectories at T=300 K with initial optimized hydrogenated species, revealed stable hydrogen arrangement, which remained unchanged along the dynamics. Nevertheless our sampling is short because of the large size models; it suffices to estimate the influence of the fast vibrational motions on the hydrogenation.

III.2 Partially reduced (Ag n ) q /EMT

Energy stability and structural parameters of selected partially reduced Ag 3 , Ag 4 and Ag 8 structures supported in the same sodalite model (Figure 1a) were also investigated. The formation energies, computed from R 1 and R 2 reactions are reported in Table 1 in comparison with the completely reduced clusters. Charged Ag 3 /EMT clusters were not found intact. The three silver cations are separated by ≥ 4.2 Å for all the considered charges q = 1+, 2+ and 3+. Therefore partially reduced (Ag 3 ) q / EMT clusters are unlikely to be formed and will lead to various positions of Ag + cations in the sodalite with Ag + ions remaining well separated. Starting from an intact (Ag 3 ) 3+ cluster and optimising it in the sodalite led to a minimum energy configuration with the three Ag + ions, each displaced in the center of the 6-ring, thus occupying the positions of Na + cations in the minimum energy EMT model, Figure 1. Exactly the same situation occurs for (Ag 4 ) 4+ /EMT and (Ag 8 ) 8+ /EMT clusters as illustrated in Figures 6 and7, respectively. These optimized structures represent models of silver exchanged EMT and are characterised by the most negative formation energies for each cluster size, which confirms that reduction is necessary to form metal clusters.

Partially reduced (Ag 4 ) q /EMT with q = 2+ and (Ag 8 ) q /EMT with q = 2+, 4+ and 6+ were also studied following same computational protocol for the initial structures as that applied in the case of the completely reduced species. All the initial and final (Ag 4 ) q /EMT, and (Ag 8 ) q /EMT are shown in Figures 6 and7, respectively, where each initial geometry is presented left to the arrow and each optimized geometry is presented right to the arrow. Notice that all geometry optimizations were performed on the full EMT model, Figure 1a, but in the Figures 6 and7 As follows from E values, also reported in Figure 6, there is a manifold of partially reduced silver clusters that can be formed in the sodalite with very similar thermodynamic stabilities (relative energies are spread in the interval of 0. The initial structures in the geometry optimisation calculations of the studied (Ag 8 ) q /EMT clusters are those selected from snapshots along the BOMD trajectories using the small EMT model (Figure 1b). Hydrogenation stabilises only the silver clusters with q= 2+ and 4+. According to the reactions R 1 and R 2 , the formation energies of (Ag We have also evaluated the interaction energy per silver cation, E/Ag + estimating in this way the enthalpy of the ion exchange reaction. Using the total energies of the non-reduced minima structures (Ag 3 ) 3+ /EMT, (Ag 4 ) 4+ /EMT, and (Ag 8 ) 8+ /EMT in the relation

E/Ag + = 1/n {E [EMT(nNa)] + E[qAg + ] -E[(Ag n ) q
/EMT] -nNa + } , for q=n it was found thatE/Ag + in the three non-reduced minima configurations amounts to -0.5 eV. The latter result indicates an exothermic exchange of sodium by silver cations.

III.3 Density of states and analysis of the molecular structures

The variations of the electronic structures with the cluster size and reduction degrees were examined as well by analysing the density of the state spectra (DOSS) and frontier molecular orbitals of four and eight atomic silver clusters supported in the sodalite in comparison with the same features in the gas-phase clusters. First, DOSS of the EMT large and small models, used for the geometry optimisation and BOMD study, respectively, are compared in Figure 8a (see Figure 1 for the EMT sodalite models). The attribution of the band compositions to the atomic orbitals is also indicated in Figure 8. As follows both DOS spectra are similar and there is an expected difference in the intensity of the peaks, because of the different number of atoms. The bands attributed to Na + orbitals are shifted due to the different chemical environment of sodium cations in both models. The highest occupied molecular oribitals (HOMOs) in both sodalite representations are close in energy. The lowest occupied molecular orbital (LUMO) of the small model is downshifted by ~3 eV with respect to LUMO in the large mode, because of the smaller repulsion in a model with fewer electrons.

In Figure 8b, we report DOSS of the gas-phase Ag There is also a negligible difference with DOSS of Ag 8 -species in Figure 8c, where DOSS of Ag 8 H 3 /EMT, (Ag 8 H) 2+ /EMT, (Ag 8 H) 4+ /EMT, (Ag 8 ) 6+ /EMT and (Ag 8 ) 8+ /EMT are presented. The 4d contributions of the Ag 8 cluster in gas-phase are in the range from -9.18 to -7.14 eV and in the case of the supported eight-atomic clusters the Ag4d,5s, O2p and H1s orbitals form the band between -16.8 and -6.5 eV. As already observed for the (Ag 4 ) q /EMT species, the intensity of the peaks are, in general, related to the HOMO-LUMO energy gap. The most peaked DOSS is obviously given by the symmetrical (Ag 8 ) 8+ /EMT structure to which is assigned the largest HOMO-LUMO gap of 3.20 eV (see Figure 8c). The isolated and supported completely reduced Ag 8 species are characterised with similar width of the HOMO-LUMO energy gap, whereas a large difference is found for the isolated and supported completely reduced Ag 4 cluster. We attribute this difference to the strong geometrical deformations caused by the interaction of Ag 4 cluster with the sodalite (see Figure 2(a)). The structural features of Ag 8 in EMT were found to resemble those of the gas-phase counterpart, which is also reflected by the computed similar energies of the HOMO-LUMO gap.

The frontier orbitals of gas-phase Ag 8 and Ag 8 H 3 /EMT are shown in Figure 9b. Again, the major contributions to HOMO are those of Ag5s and O2p orbitals.

In summary, the DOSS of the small silver clusters supported in the sodalite is very little affected by the number of Ag atoms, cluster charges and particular geometries. The highest occupied band is dominated by the O2p and silver 4d and 5s orbitals. The support of silver clusters in the zeolite does not modify its O2p or other bands as follows from the comparison with DOSS of the solely EMT models in Figure 8a. This can be expected, because the stabilisation of silver clusters occurs via ionic bond formations with the framework oxygens.

Conclusion

We have studied the effect of the support of EMT zeolite with Si/Al=1 on the geometrical and electronic features of small Ag n clusters, n = 3, 4, 6, and 8. Completely and partially reduced species were considered in the sodalite cavity. Completely reduced silver sub-nm particles can be stabilized due to hydrogenation. Adsorbed hydrogens withdraw electron density from the silver atoms, causing a partial oxidation of the metal cluster and therefore enhancing the ionic Ag-O bonds. The hydrogenated structures were found stable also at T=300K as followed from the BOMD trajectories. Bare, completely reduced silver clusters were not found in the sodalite cage to be energetically favored. The Ag-O ionic bonds dominate the Ag-Ag bonds in the completely reduced clusters with n ≤ 6 causing therefore strong geometrical deformations. The Ag-Ag interactions are least perturbed and dominate in the hydrogenated Ag 8 species hosted in the sodalite, whose topology remains similar to that in their gas-phase counterparts.

Hydrogenation is also found energetically favorable for partially reduced (Ag 8 ) 2+ and (Ag 8 ) 4+ . Charged silver particles interact strongly with the zeolite than the hydrogenated completely reduced ones. Computed formation energies, including those of the non-reduced (Ag n ) q for q = n that were taken as reference values, predict that partial silver reduction can occur nearly spontaneously and explains the co-existence of silver exchanged cations and small clusters with several oxidation states in sodalites. DOS spectra of all the considered here Ag 4 and Ag 8 clusters in gas-phase, and supported in the sodalite do not vary with the size, charge and topology of the clusters. The Ag4d orbitals overlap with O2p in the energy interval of -17 --6.5 eV. The electronic structure of the host sodalite is found unaffected by the guest silver clusters.

  we have considered three different initial structures that represent the fully hydrogenated Ag n H m /EMT cases and partial hydrogenated Ag n with protons forming bridging O-H-Ag groups with the oxygen of the six-ring of the sodalite cage and Ag atoms. These models are exemplified for the initial and optimized neutral Ag 4 /EMT and Ag 8 /EMT in Figure 2. In Figure 2a are displayed the fully hydrogenated Ag n H m /EMT and in Figure 2b,c -the structures with bridging O-H-Ag groups. Structures (b) and (c) differ in the orientations of some of the hydrogen cations bound to the oxygens.

  Ag n H m (a) are the energetically favoured ones, independently on the cluster size. The formation energies computed for structures (b) and (c) with bare silver clusters are positive that indicates endothermic reduction reactions. The hydrogenation is well favoured for clusters with n ≥ 4 as follows from the large formation energy differences between products (a) and products (b), (c).

Indeed, in the bare Ag 3 /

 3 EMT species, (Figure S1(b), (c)) both Ag 3 /EMT structures form triangles with Ag-Ag distances of 2.752, 2.835 and 2.902 Å (b), and 2.790, 2.841 and 2.871 Å (c), in a better agreement with the previous results. The bare Ag 3 /EMT clusters are less stable by 0.70 and 0.87 eV, respectively, than Ag 3 H/EMT. The hydrogenated Ag 4 cluster in the sodalite cage, Figure 2 (a), which is more stable by 1.58 and 2.24 eV than the other two structures in Figure 2 (b) and (c), respectively, can be considered as split in two Ag 2 H...Ag 2 H species. Such a deformation is not observed for the bare Ag 4 /EMT structures that preserve their gas-phase rhombic form. The analysis of the bond distances, r, averaged by considering the Ag-Ag bond distances ≤ 3.40 Å, shows that in the hydrogenated Ag 4 H 2 configuration, the averaged Ag-Ag bond length elongates to 2.96 Å in comparison to the gas-phase Ag 4 cluster with an averaged r(Ag-Ag) = 2.80 Å. The cluster structural changes are notably smaller for structures (b) and (c): in Ag 4 /EMT the averaged Ag-Ag distances are 2.85 Å (b) and 2.83 Å (c).

  14 cluster was the largest size possible to introduce into the zeolite with Ag-O bonds of 1.4 Å and maintaining the Ag-Ag distances to their values in the gas-phase counterpart. In order to keep the neutrality in this case, eight Na + were replaced by eight hydrogen cations. During the optimisation procedure, the initial Ag 14 H 8 /EMT structure split into Ag 8 H 2 in the sodalite and six AgH species migrated to the six rings as shown in Figure 5b. The remaining Ag 8 H 2 intact cluster has almost the same structural parameters as those found for Ag 8 H 3 /EMT in Figure 2 (a). This result corroborates the suggestion from XRD 1 and STEM

  only the sodalite is shown for a better presentation of the silver clusters. In the structures in Figs 6 (a) and 7 (a) are shown the fully hydrogenated initial geometries and the optimized hydrogenated clusters. Analogously, in Figs 6 (b), (c) and 7 (b), (c) are displayed the partially hydrogenated Ag-clusters with protons forming bridging O-H-Ag groups in the starting geometries. The capital letters A and B in Figure 6 differentiate structures with protons interacting with different six-rings of the sodalite cage.

  4 cluster in gas-phase are in the range of -9.16 ˗ -7.25 eV. When supported, the Ag(4d,5s) orbitals overlap with O2p and give rise to the energy band in the interval -16.5 ˗ -6.8 eV. There is therefore a shift of the Ag4d band to the lower energies when supported in the zeolite. This down-shift can be associated with the partial positive charge at the silver clusters even in the completely reduced hydrogenated structures. The O2p band in the zeolite does not undergo any significant change due to the O-Ag ionic interactions as follows from the comparison of DOSS in Figure8afor the large EMT model. H1s orbitals, including those of the adsorbed on the silver cluster hydrogens or the bridging Ag-H-O hydrogens, lie in the same band. The highest occupied orbital, or the Fermi level, is composed predominantly by Ag5s and O2p orbitals and the plot of HOMO is shown in Figure 9a. Nevertheless, the three supported Ag 4 clusters are characterised by different geometrical parameters, charges, and chemical environment (hydrogen adsorption), their DOS spectra are very similar. The only difference of the electronic structures in the four types of Ag 4 -species is the HOMO-LUMO energy gap and the relative intensities.

Figure Captions Figure 1 .

 Captions1 Figure Captions

Figure 2 .

 2 Figure 2. Completely reduced Ag 4 Na 32 Al 36 Si 36 H 52 O 168 and Ag 8 Na 28 Al 36 Si 36 H 56 O 168 structures. Only sodalite is shown for clarity. The initial structures are reported left to the arrows and the optimized ones -right to the arrows. The structures are (a) fully hydrogenated silver clusters, and (b), and (c) partially hydrogenated silver clusters with protons forming bridging O-H-Ag groups. In the (c) structures some protons are not involved in the O-H-Ag bridge, pointing outside the sodalite cavity. The relative energies in eV are reported.

Figure 3 .

 3 Figure 3. Selected Ag-Ag, Ag-O, and Ag-H bond distances in Å of the ground-state (a) Ag 4 H 2 /EMT (top) and Ag 4 in gas-phase (bottom); and (b) Ag 8 H 3 /EMT (top) and Ag 8 in gas-phase (bottom).

Figure 4 :

 4 Figure 4: Atomic net charges in e obtained from Mulliken population analysis of the ground state (a) Ag 4 H 2 /EMT (top) and gas-phase Ag 4 (bottom); and (b) Ag 8 H 3 /EMT (top) and gas-phase Ag 8 (bottom).

Figure 5 .

 5 Figure 5. The (a) Ag 3 …Ag 3 /EMT input structure left to the arrow and the optimized Ag 6 H 4 structure -right to the arrow, shown only in the sodalite for clarity; and (b) the optimized Ag 14 /EMT structure presented in the full model. The full model is used in all the optimized structures.

Figure 6 .

 6 Figure 6. (Ag 4 ) 2+ /EMT and (Ag 4 ) 4+ /EMT structures. Left to the arrow are shown the starting geometries and right to the arrow -the optimized geometries. Only sodalite is shown for clarity. The (Ag 4 ) 2+ /EMT structures are (a) fully hydrogenated, and (b), and (c) partial hydrogenated with protons forming bridging O-H-Ag groups. In the (c) structures some protons are not involved in the O-H-Ag bridge, pointing outside the sodalite cavity. The capital letters A and B differentiate structures with protons interacting with different six-rings of the sodalite cavity. The relative energies in eV are reported.

Figure 7 .

 7 Figure 7. (Ag 8 ) q / EMT (q = 2+, 4+, 6+ and 8+) minimum energy structures. Only sodalite is shown for clarity.

Figure 8 .

 8 Figure 8. Density of state spectra of the ground state sructures: (a) EMT large (black) and EMT small (red) models; (b) gas-phase Ag 4 cluster (black), Ag 4 H 2 /EMT (red), (Ag 4 ) 2+ /EMT (cyan) and (Ag 4 ) 4+ /EMT (yellow); (c) gas-phase Ag 8 cluster (black), Ag 8 H 3 /EMT (green), (Ag 8 H) 2+ /EMT (blue), (Ag 8 H) 4+ /EMT (cyan), (Ag 8 ) 6+ /EMT (red) and (Ag 8 ) 8+ /EMT (yellow).

Figure 9 .

 9 Figure 9. Graphical representation of the HOMO and LUMO of the Ag 4 , Ag 4 H 2 /EMT, Ag 8 and Ag 8 H 3 /EMT minimum energy structures.

Figure 1 .Figure 2 .

 12 Figure 1. The EMT model structures: (a) large and (b) small. The (b) structure was derived from the optimized geometry of the large model (a) by fixing the positions of the atoms of the sodalite cage together with the four nearest Na + to the sodalite cage. These cations are necessary to keep the structure neutral. In structure (b) only the coordinates of the hydrogens were relaxed.

Figure 3 .

 3 Figure 3. Selected Ag-Ag, Ag-O, and Ag-H bond distances in Å of the ground-state (a) Ag 4 H 2 /EMT (top) and Ag 4 in gas-phase (bottom); and (b) Ag 8 H 3 /EMT (top) and Ag 8 in gas-phase (bottom).

Figure 4 :

 4 Figure 4: Atomic net charges in e obtained from Mulliken population analysis of the ground state (a) Ag 4 H 2 /EMT (top) and gas-phase Ag 4 (bottom); and (b) Ag 8 H 3 /EMT (top) and gas-phase Ag 8 (bottom).

Figure 5 .

 5 Figure 5. The (a) Ag 3 …Ag 3 /EMT input structure left to the arrow and the optimized Ag 6 H 4 structure -right to the arrow, shown only in the sodalite for clarity; and (b) the optimized Ag 14 /EMT structure presented in the full model. The full model is used in all the optimized structures.

  Oppenheimer Molecular Dynamics (BOMD) at T= 300 K was applied to each of the most stable Ag n /EMT geometry. The simulation time was 3 ps per structure. The BOMD simulations were carried out on a smaller model, consisting only of the sodalite cage (Na 24 Al 24 Si 24 O 84 H 24 ) with Na + cations fixed at their optimized positions in the large structure Na 36 Al 36 Si 36 H 48 O 168 . The small model is presented in Figure

  8 , we found that they remain intact upon hydrogenation giving rise to Ag 6 H 2 /EMT and Ag 8 H 3 /EMT species. The optimized Ag 6 H 2 /EMT and Ag 6 /EMT clusters are reported in Figure S2, SI section. As follows, the energetically favoured Ag

6 H 2 structure is formed by four in plane atoms that are coordinated to two atoms out of plane, bound to the zeolite oxygens. This topology can be viewed as deformed elongated octahedron with one too large Ag...Ag separation of 4.22 Å. Selected distances are presented in Figure

  Due to the Ag 8 cluster size it is possible to form a maximum number of Ag-O bonds without perturbing strongly the Ag-Ag interactions and leading to topological distortions. For the clusters with less than eight atoms, being significantly smaller compared to the sodalite diameter of ~7 Å, a stronger structural deformation occurs in order to enhance the stabilising silver-oxygen ionic interactions. The Ag-Ag distance variations of Ag 4 H 2 /EMT and Ag 8 H 3 /EMT with respect to the ground state structures of Ag 4 and Ag 8 in gasphase are illustrated in Figure

	particles, e.g. the averaged Ag-Ag separation in Ag 6 H 2 /EMT is 2.97 Å; in Ag 6 /EMT is 2.81 Å (b)
	and 2.76 Å in Ag 6 /EMT (c). The latter two bare Ag 6 /EMT structures are less stable by 1.80 and 2.39

eV, respectively. Similar are the averaged distances in Ag 8 H 3 /EMT in Figure

2

(a) and Ag 8 /EMT in Figure 2 (b), (c), computed to be 2.97, 2.87 and 2.88 Å in (a), (b) and (c), respectively. The larger size of Ag 8 cluster results in a more compact structure in the sodalite compared to the Ag-configurations with fewer atoms.

  6 eV). The minimum energy geometries, (b)-(A) for (Ag 4 ) 2+ /EMT and (Ag 4 ) 4+ /EMT, were verified by means of BOMD simulations using the smaller EMT model shown in Figure1b. Hydrogenated four-atomic clusters with q=2+ were not obtained among the low energy structures. In all cases (Ag 4 ) 2+ /EMT clusters remain intact with averaged distances of 2.88 -2.92 Å. The E f values in Table1suggest that (Ag 4 ) 2+ /EMT and (Ag 4 ) 4+ /EMT structures can coexist as concluded from the nearly equal formation energies. This predicts a spontaneous reduction to (Ag 4 ) 2+ in the zeolites. The formation of the completely reduced hydrogenated structure is less favourable as follows from the computed E f of Ag 4 H 2 /EMT that is by 36% smaller than E f of (Ag 4 ) 2+ /EMT.

  4 cluster, Ag 4 H 2 /EMT, (Ag 4 ) 2+ /EMT and (Ag 4 ) 4+ /EMT minimum energy structures. The obtained intensity trend (Ag 4 ) 4+ /EMT > Ag 4 H 2 /EMT > (Ag 4 ) 2+ /EMT correlates with the HOMO-LUMO energy gap tendency ΔE HOMO-LUMO ((Ag 4 ) 4+ /EMT) > ΔE HOMO-LUMO (Ag 4 H 2 /EMT) > ΔE HOMO-LUMO ((Ag 4 ) 2+ /EMT). The bands are narrow if clusters are not formed in (Ag 4 ) 4+ /EMT, thus increasing the peak intensities. The (4d,5s) orbital contributions of the Ag

Table 1 :

 1 Formation energies in eV computed for Ag n (n= 3, 4, 6 and 8) neutral and charged clusters in the sodalite cage of the EMT model as a difference between the energies of the products and the reagents in two reduction reactions R 1 and R 2 (see text). The capital letters A and B differentiate structures with protons interacting with different six-rings of the sodalite cavity (see Figure6). Structure obtained from an initial model with two separated Ag 3 clusters in the sodalite, Figure5.

	Structures (a) refer to the hydrogenated clusters.
	Species	Structure	R 1	R 2
	Ag 3 /EMT	(a)	-0.19	-0.22
		(b)	0.51	0.48
		(c)	0.68	0.65
	(Ag 3 ) 1+ /EMT	(a)	-0.98	-1.00
	(Ag 3 ) 2+ /EMT	(a)	-0.47	-0.48
	(Ag 3 ) 3+ /EMT	(a)	-1.64
	Ag 4 /EMT	(a)	-1.36	-1.39
		(b)	0.22	0.19
		(c)	0.88	0.85
	(Ag 4 ) 2+ /EMT	(a)-(A)	-2.15	-2.17
		(a)-(B)	-1.84	-1.85
		(b)-(A)	-2.17	-2.19
		(b)-(B)	-2.02	-2.03
		(c)-(A)	-1.89	-1.91
		(c)-(B)	-1.61	-1.63
	(Ag 4 ) 4+ /EMT	(a)	-2.14
	Ag 6 /EMT	(a)	-0.86	-0.91
		(b)	1.14	1.09
		(c)	1.53	1.48
	*Ag 6 /EMT	(a)	-1.87	-1.92
	Ag 8 /EMT	(a)	-1.31	-1.38
		(b)	0.27	0.21
		(c)	1.33	1.26
	(Ag 8 ) 2+ /EMT	(a)	-2.58	-2.63
	(Ag 8 ) 4+ /EMT	(a)	-4.12	-4.15
	(Ag 8 ) 6+ /EMT	(a)	-4.21	-4.23
	(Ag 8 ) 8+ /EMT	(a)	-4.29
	*

2.48 1.79 1.84 2.35 2.95 2.56 2.40 2.47 2.38 1.89 2.54 2.98 1.81 2.38 2.70 2.87 2.75 (a) (b) 2.79

ACKNOWLEDGEMENTS

The financial support from ANR TAR-G-ED is acknowledged. Part of the calculations was performed at the HPC resources of TGCC-CURIE under the allocation x2015087369 made by GENCI (Grand Equipement National de Calcul Intensif). We are grateful to Dr. Vincent De Waele and Prof. Svetlana Mintova for the fruitful discussions.

Supporting Information Available: Optimized Ag 3 and Ag 6 completely reduced structures hosted in EMT sodalite. This material is available free of charge via the Internet at http://pubs.acs.org.


Loïc Sauvée
email: loic.sauvee@lasalle-beauvais.fr

Latifa Daadaoui

Relationship governance within value creation systems Analytical framework applied to the biobased sector

Keywords: biobased, governance, inter organizational relationships, network, value

Relationship governance within value creation systems.

Analytical framework applied to the biobased sector Loïc Sauvée, Latifa Daadaoui

1-Introduction

Market and product innovations in the emergent biobased sectors are highly dependent upon the efficacy of knowledge transfer between research organizations and private firms. This is especially the case in the context of industrial clusters such as the French cluster 'Industrie et Agro Ressources', where public authority monitors and brings together private firms and research competences. The governance of these Industry-Research relationships (hereafter IRR) is thus critical to managers and appears to be a crucial element of their competitiveness. Our research explores this question in focusing on two main topics: firstly the role of institutional environment and more specifically of meta network forms such as industrial clusters, in the design of proper governance structures; secondly the identification of the main determinants of governance designs in this specific context of radical product innovations.

The context of the research is thus the biobased economy. The idea of biobased economy is not new [START_REF] Anex | Something new under the Sun? The Industrial Ecology of Biobased Products[END_REF]). In the 30s, the farm chemurgy movement already developed the necessity of industrial products coming from crops, aiming at reducing low prices and declining markets for farmers. But the new environmental context (global warming) and the risks of shortage for fuel or other non renewable products give a completely different landscape of what could be the biobased economy in the next decade. For [START_REF] Anex | Something new under the Sun? The Industrial Ecology of Biobased Products[END_REF], agriculture seen from an historical perspective is a 'conventional' biobased economy: in using "fuels and chemicals to produce the bountiful harvests that have allowed human population to grow beyond what was possible as recently as 100 years ago." (Anex, 2004: 1). But he adds: "attempts to reverse the trends of the last century and a half, and return to satisfying significant amounts of the human appetite for power and material using plantderived raw materials, will have complex social and environmental impacts" (Anex, 2004:2).

The paper is organized as follow. In a first part [START_REF]Regional consular for industry, commerce and agriculture[END_REF], after recalling the origin of the concept of interorganizational governance, we focus on the traditional views developed by researchers concerning IRR relationships. Then we show that in the specific contexts of radical innovations and value creating systems, the understanding of governance of IRR necessitates a global view upon the whole value creation process. In a second part [START_REF]two president of the regional council and the chef of department[END_REF] we develop this idea in reference to research works on value and organization. Then we turn to our proposal of an analytical framework and a set of propositions for the study of governance in biobased value creation systems [START_REF]Head of an administrative area[END_REF]. Some connections to real innovation processes in biobased businesses are done. A few concluding comments on the perspectives of the research as well as on the managerial implications are developed (5).

Governance of relationships between industry and research

In a first part we will define the notion of relationship governance in a functional perspective . Then we will summarize the main perspectives that have been usually devoted to the study of IRR . Finally we will turn to the interests and limitations of the concept of interorganizational governance in a context of radical innovations [START_REF]Regional consular for industry, commerce and agriculture[END_REF][START_REF]two president of the regional council and the chef of department[END_REF]. 2.1. Relationship governance: genealogy of a concept Generally the term of governance can be defined as the management of collective activities of a group [START_REF] Nye | Governance in a Globalizing World[END_REF]. Governance means the way of organizing transactions (Williamson, 1994) and by extension relationships. Its purpose is to achieve a correct public or private order through the use of coordination mechanisms. The governance structure is the design of an institutional model in which the integrity of a transaction or related set of transactions is decided [START_REF] Williamson | The mechanisms of governance[END_REF], or an institutional model that governs the exchange controlling the opportunism [START_REF] Dyer | Effective interfirm collaboration: how firms minimize transaction costs and maximize transaction value[END_REF]. [START_REF] Heide | Interorganizational governance in marketing channels[END_REF], in the vein of Palay, defines governance as a multidimensional phenomenon surrounding the introduction, the conclusion and maintenance of relationships between several parties. [START_REF] Ehlinger | Quelle gouvernance pour les réseaux territorialisés d'organisations[END_REF] build the notion of governance according to the roles assigned to the governance structure: adaptation to demand, coordination of actors and security to ensure taking into account the interests of various objectives. Governance and its structures are also seen as meta-management, which is assigned the role of developing the overall strategy, a responsibility to regulate the relationship between actors in terms of power, and the coordination of different strategies. Fréry determined the role of governance by defining the hub governing the network: "the design of the value chain, the coordination of the structure obtained by ensuring the governance of transactions between partners, and the control of the structure." (Fréry, 1997) In this vein and under a functional approach, we can define governance upon two functions: coordination and the regulation of exchanges [START_REF] Dyer | Does governance matter? Keiretsu and asset specificity as sources of Japanese competitive advantage[END_REF][START_REF] Heide | Interorganizational governance in marketing channels[END_REF].

-Coordination: not only related to: (i) formations exchange but also to (ii) decision making two issues which are sensitive to process, and in cooperation the difficulty is more important. Ansoff identifies three main levels of decision: strategic, tactical and operational. Organization theorists distinguished among several types of coordination: division of responsibilities, shared resources, meetings, communication technology (Cummings and Kielser, 2007). In terms of the nature of the information exchanged and the interfaces, [START_REF] Monateri | From value chain to value constellation: designing interactive strategy[END_REF] suggested an interesting typology of information exchanged: information utilities, spontaneous information, presentation and cohesion information. Each type requires a support: notes, records, meetings and working group, exchange meetings, team brainstorming, videoconferences, seminars, electronic mail, computer network, exchange of personnel.

-The regulation of exchanges: We will deal with the issue of regulation in terms of enforcement according to [START_REF] Dyer | Effective interfirm collaboration: how firms minimize transaction costs and maximize transaction value[END_REF]. By enforcement, we will consider three components: the control, incentive and adjustment [START_REF] Heide | Interorganizational governance in marketing channels[END_REF]. [START_REF] Dyer | Effective interfirm collaboration: how firms minimize transaction costs and maximize transaction value[END_REF] argue that most relationships are based on the form of self confidence. The adjustments in mutual monitoring procedures are almost nonexistent. The incentive to create value is maximized through the commitment and trust that increase with the maturity of the relationship. Thus governance will be more effective and the 'relational rent' will be greater. Because the cooperative relationship is a dynamic process, adaptability competence is required. It is therefore essential to see the evolution and dynamics of governance mechanisms and at the same time the factors that influence its evolution.

Dyer and Singh in the vein of Williamson assign to the governance a unique objective: costs minimization. The synthetic corporate governance theory [START_REF] Bouglet | Contribution à la connaissance de la gouvernance d'entreprise : cas des entreprises nationales[END_REF] proposes dichotomous function of governance which is interesting in the way that it gives a global and complete view of 'negative and positive' function of governance :

-A disciplinary function: mainly the aim is to reduce costs and avoid the opportunism of the actors. The governance system is the set of mechanisms that sustain the node of contract and secure the financial investment, the governance mechanisms role here is to create the rules of the interactions [START_REF] Brousseau | The Economics of Multilevel Governance[END_REF] ; -A cognitive function: the aim is to increase the gains arising from the cooperation. According to this productive point of view, governance mechanisms are seen as ways to invent opportunities and align patterns mentally. We believe that in the special context of innovation the governance structure is aimed to accomplish this role more than being the 'guard' of the system.

According to the functions assigned to the governance, contractual or relational mechanisms can be distinguished. The first one is more formalized by complex but incomplete contracts. The second one is inherent to the relationship between the partners. In the vein of [START_REF] Poppo | Do formal contracts and relational governance function as substitutes or complements?[END_REF], Hoetker and Mellewight (2004) we advocate the idea of complementarity between the two mechanisms instead of the idea of substitution that existed in the transaction-cost theory and the strategic management literature (Gulati, Dyer and Singh, Hill). Thus, well-tied contracts will guarantee the stability, preserve the longevity of relationships, and can build trust and cooperation. Relational governance helps to overcome the contracts limitations especially in the area of adaptation by nurturing commitment and trust.

We summarize in figure 1 the main components of relationship governance based upon our literature discussion and in a functional view. In exploring the research-industry literature, we have summarized in table 1 two research trends: one focusing on university-industry relationships and another one on laboratory and industry, the need for studies on broader research-industry definition is observed. By IRR in the process of developing new products, we means "any rapprochement between two or more organizations belonging to one or another sphere: research center and / or training center (e.g. university) and public or private firms. This rapprochement, including heterogeneous organizations from different organizational environments aims to fulfill a common vision and innovation which involves the accumulation of resources and coordination of actions" (adapted from [START_REF] Monateri | From value chain to value constellation: designing interactive strategy[END_REF]. We are interested in the broader relationship between the two spheres of business firms and research organization, more than punctual transactions because innovation collaborations need more frequent and regular transactions [START_REF] Brousseau | La gouvernance des processus de coopération[END_REF]. Cohen, Nelson and Walsh (2002) distinguished three possible uses of research output: (i) the results of research, (ii) prototypes, and (iii) the new instruments and techniques. According to the same authors the channels of the knowledge that flows from the academic sphere to the industry are varied. This could be patents, informal exchange of information, publications and reports, public conferences, the recruitment of young graduates, licensing, collaborations, research contracts, and consulting, temporary staff mobility. In the literature the main perspective is transactional, positioning the research among the industry in a classical design of value system. It is interesting to analyze the relationships between research and industry in the new project development from a relational perspective suggesting a great level of commitment, trust, a long term orientation, a high level of uncertainty and positioning them side by side in an interactive value constellation (Normann & Ramirez, 1993). This IRR has three main characteristics: [START_REF]Regional direction for Industry[END_REF] The organizational diversity of the various partners [START_REF]Regional consular for industry, commerce and agriculture[END_REF] The transfer of a mix of tangible and intangible assets (knowledge and technology) that will go along with the relationship (3) From an organizational point of view, no subordination link between the partners. These particular characteristics suggest a different mode of organization transaction (relations) in terms of coordination and regulation. In that way the question of studying governance is pertinent especially since a small but growing body of literature on transaction value is emphasizing the influence of governance on the value creation initiatives of alliance partners [START_REF] Dyer | Does governance matter? Keiretsu and asset specificity as sources of Japanese competitive advantage[END_REF]Barney & Hansen, 1997;[START_REF] Ring | Structuring cooperative relationships between organizations[END_REF][START_REF] Zajac | From Transaction cost to Trasaction Value Analysis: Implications for the study of Interorganizational Strategies[END_REF].

In the new biobased activities, the long-term orientation of relationships and the high uncertainty and ambiguity of the result and the future of research complicate the deal. Then the question is: what kind of governance is suitable for these particular relationships for an effective knowledge transfer? Table 1:

Two research streams on IRR

University-industry relationships Public laboratory-industry relationships

The most popular in the literature [START_REF] Anderson | Measuring the efficiency of university technology transfer[END_REF]: -Organizational structures, in particular the study of TTO-Technology Transfer Offices-; -Regional / international comparisons and case studies [START_REF] Owen-Smith | A comparison of US and European University-Industry relations in the life science[END_REF]Meyer-Kramer and Schmoch, 1998;[START_REF] Beise | Public research and industrial innovations in Germany[END_REF][START_REF] Lopez-Martinez | Motivations and obstacles to university industry cooperation: a Mexican case[END_REF] -The impact of university research [START_REF] Feller | Impacts of research universities on technological innovation in industry: evidence from engineering research centers[END_REF][START_REF] Cohen | Links and impacts: the influence of public research on industrial R&D[END_REF][START_REF] Shane | Organizational endowments and the performance of university start-ups[END_REF][START_REF] Siegel | Assessing the impact of organizational practices on the relative productivity of university technology transfer offices: an exploratory study[END_REF]) -The outputs of university research; -Effectiveness of university research [START_REF] Zucker | Commercializing knowledge: university science, knowledge capture, and firm performance in biotechnology[END_REF][START_REF] Anderson | Measuring the efficiency of university technology transfer[END_REF] According to [START_REF] Gonard | Public research/industry relationships: efficiency conditions in current innovation[END_REF] there are two types of research: -descriptive studies, which didn't discuss key factors for success or failure of these relationships, it was generally case studies;the evaluation studies which adopt various perspectives [START_REF] Gonard | Public research/industry relationships: efficiency conditions in current innovation[END_REF]: * the public policy -makers such as Mansfield, Rosenberg, Rosenberg and Nelson (1994); * the perspective of public R&D bodies or laboratories : Crow & Bozeman, Callon, Laredon, Mustar who studied the synergies which take place between the different activities of a laboratory * the industry perspective :which received little attention except the contribution of Bailetti, Callahan, Faulkner, Senker 2-3 Interests and limitations of the IRR research stream: Considering the dependence theory, dependence and uncertainty are the main key variables motivating the establishment of interfirm relationships [START_REF] Pfeffer | The external control of organizations. A ressource dependence perspective[END_REF], it is also correct for the IRR: they emerge and evolve more and more in a turbulent and uncertain surrounding and need each others to complete resources and competences. But this theory gives a short and global insight about the mechanisms within which these relationships are organized. A new analysis perspective of these relationships is needed. In the main researches the IRR have been studied as dyadic relations. We propose to analyse networked relationships between the two spheres in order to have a wide and complete idea of the logic and dynamic of interactions. This exchange involves more and more different types of organisations from different levels and different chains of value creation. Firms, universities, private and public laboratories deliberately create structure and negotiate and assign roles and goals. It's truer in the emergent biobased activities where a constellation of actors agreed to create a new activity with new value creation logic combining different and complementary resources and capabilities. The issue of governance is explicitly raised as a mean of steering the network and ensuring consistency of the projects of the various partners [START_REF] Ehlinger | Quelle gouvernance pour les réseaux territorialisés d'organisations[END_REF].

In our research we propose to full up the several shortcomings of the literature on IRR:

(i) The integration of new theories like network theory, the creation value logic, the synthetic corporate governance give a new vision to understand the governance of IRR; (ii) The lack of an integrative model of the different components of governance applied to the IRR in emerging Biobased activities; (iii) The issue of choice and determinants of governance is almost limited to the specificity of the exchange (Williamson, 1994), i. e. specific knowledge or physical assets [START_REF] Hoetker | Choice and performance of governance mechanisms: matching contractual and relational governance to sources of asset specificity[END_REF], and the structure of the exchange in terms of dependence, formalization, and socialization [START_REF] Gençtürk | Norms-and Control-Based Governance of International Manufacturer-Distributor Relational Exchanges[END_REF]. But we need to take into account other organizational aspects, as well as relational and contextual aspects. (iv) Mobilizing the network theory reconsider the different levels that constitute a net. The concept of governance levels borrowed from political science is interesting to consider in the networks. The combination in the context of IRR helps to understand the complementarity or substitution between the levels: project level, meta-organizational (relational) and institutional). The question is whether these levels are substitute or complementary? (v) We often forget that the IRR is a dynamic process. Its evolution leads to governance adaptation by the effects of positive or negative feedbacks. Studying these effects helps investigating the factors that trigger the positive feedbacks or avoid the negative ones. (vi) We find in the IRR: actors, resources and activities building a 'value net' or 'strategic net' [START_REF] Möller | Rise of strategic net -New modes of value creation[END_REF]. In this new business the uncertainty and ambiguity are higher and we believe that 'the value creation logic or system through which the net creates value has a fundamental role in influencing effective mechanisms for governance'. The aim of these relationships is to create value to develop a new business. The value creating logic is thus pertinent to analyse, describe and understand the governance of this special net [START_REF] Möller | Rise of strategic net -New modes of value creation[END_REF][START_REF] Parolini | The value net: a tool for competitive strategy[END_REF]. Our analysis unit is then the value-creating system-in biobased activities.

3-Value systems and governance

We consider the concept of value creation process and logic as the central point of our analysis. Thus we will define firstly the notion of value system . Then we will link this notion of value system with that of value creation . Then we will turn to the question of governance of the relationship within value systems, i.e. when innovation is at stake (3-3) 3-1 Value system: the core concept The objective of value creation is at the basis of any economy. The main difficulty of this notion of value creation is that it has been given many meanings throughout the literature. The definition of Porter's (1985) value chain referring to firm-level or industry-level activities has been criticized by many authors. For instance, Normann and Ramirez (1993) show that the linearity of vertical chains reflects only the reality of some value networks, and not when the nature of exchanges between partners is not solely business transactions but also intangible information.

Håkansson and Snehota (1995) also enrich the vision of value creation systems with their conceptualization of business relationship. They propose a broad descriptive framework centered on the substance and the functions of any relationship, defined as "a mutually oriented interaction between two reciprocally committed parties" (Håkansson and Snehota, 1995). The substance of any relationship is described in terms of resource ties, actor bonds and activity links. The functions can be conceived as the effects or the output any relationships will have at the individual partner, dyad and network levels. While not explicitly devoted to value creating systems, these authors provide a powerful theoretical apparatus for the study of industry-research relationships. [START_REF] Stabell | Configuring value for competitive advantage: on chains, shops and networks[END_REF] also propose an extension of the original value chain analysis in using Thompson's typology of 'long-linked, intensive and mediating technologies' (Stabell and Fjeldstad, 1998:414). For Thompson, the choice of technologies is to be related to the type of problem, in a particular competitive setting, the firm has to solve. For instance, the long-linked technology will transform object according to a predefined set and sequence of activities, while the intensive technology will solve problem by a custom combination of activities. The authors propose a value configuration analysis, defined as an 'analysis of firmlevel competitive advantage based on a theory of three value creation technologies and logics' (Stabell and Fjeldstad, 1998: 415). To identify discrete value configurations, the authors identify critical points to be studied: the primary technology, the primary activity categories, the main interaction relationship logic, the primary activity interdependence, the key cost and key value drivers, and the business value system structure. Doing so, the authors thus propose one of the first analytical frameworks that connect organizational configurations with value creation logics of firms.

In the chain and network science literature, the concept of value system has also been widely used. In their study of netchains, [START_REF] Lazzarini | Integrating supply chain and network analyses: the study of netchains[END_REF] propose an integration of social network and supply chain management approaches. They focused their analysis on the underlying link between interdependencies, following Thompson's typology and sources of value in different interorganizational settings. For instance, the reciprocal interdependency occurs when "one agent's input is another agent's output and vice-versa" [START_REF] Lazzarini | Integrating supply chain and network analyses: the study of netchains[END_REF]. This situation will produce knowledge co-specialization. Interestingly, the authors give the example of regional clusters, of small firms and of close-knit groups through the development of dense networks. Another idea of the netchain analysis is the alignment principle of interdependencies with distinct coordination mechanisms. In reciprocal interdependencies for instance, the mutual adjustment mechanism, i. e. the "mutual feedback processes with joint solving problem and decision making" [START_REF] Lazzarini | Integrating supply chain and network analyses: the study of netchains[END_REF] is the most efficient.

3-2 Value system and value creation: the question of innovation

In the chain and network science, [START_REF] Omta | Innovation in chains and networks[END_REF] suggests that "good innovation systems are possibly even more important at chain and network level than for innovation at the company level" (Omta: 2002:76). Following [START_REF] Uzzi | Social structure and competition in inter firm networks: the paradox of embeddedness[END_REF], Omta suggests that the network position, i.e. the positioning of the actor in the network, is critical to the success of innovation. For him, "one party can be in a strategic position for the implementation of innovations if it is a partner in more than one tightly-knit cluster of relationships such that it can serve as a bridge by introducing innovations from one network into the other. (…) This leads to the paradoxical situation in which the chance of achieving completely new innovations (the socalled radical innovations) decreases as more and more companies in the network establish mutual contractual arrangements" (Omta, 2002: 77). The role of network heterogeneity is also stressed: when markets and technologies are turbulent and prone to rapid changes, the diversity of contacts is a way to reduce insecurity. Finally the author identifies three elements critical for the success of innovations, with two of them directly related to business organization: structural position (of the firm), and social embeddedness in the network.

In their study of innovation networks, [START_REF] Dhanaraj | Orchestrating innovation networks[END_REF] also identify the fact that network form of organization has "profoundly impacted how companies innovate" (Dhanaraj and Parkhe 2006: 660). In many sectors such as pharmaceutical industry or other types of high-tech industries, the classical value chains disintegrated and innovations are carried out by complex sets of firms or organizations. For the authors, "such innovations typically involves high levels of transactional uncertainty and exchange of tacit knowledgeproblems that demand strategic actions from core actors to form and maintain a network and to extract value from it" (Dhanaraj and Parkhe, 2006: 660). In such innovation situations, where knowledge is at the core of the value configuration, firms should focus on the processes. For Dhanaraj and Parkhe, some firms or other entities within the network need to perform a leadership role: a role of pulling together the resources and capabilities of the network members.

With their study of biotechnology innovations, [START_REF] Salman | Indirect networks: an intangible resource for biotechnology innovation[END_REF] give an interesting illustration of these new modular organizational forms in relation with innovation processes. The authors suggest a distinction between direct and indirect networks, based on network position. Grounded in social network analysis, network position refers to the fact that network members are embedded in an array of relationships. Direct ties such as alliances between firms may provide benefits, but the authors suggest that indirect ties, i.e. firms that are affiliated to one another through their common direct partnerships, could also be a strategic resource. For the authors, in the emergent knowledge-based economy, channels of information between two firms stem "by virtue of their common partnership" to, for instance, a university. Thus the partner's partners also benefit from a community of knowledge. This is not only the relational content of the exchange that is relevant to the indirect partnership, but also the network position of the firm. The authors suggest that "indirect ties may potentially lead to access to a combination of non-mutually exclusive intangible resources such as information, knowledge, and skills that flow through the network" (Salman and Saives, 2005: 205).

In a recent article, [START_REF] Möller | Rise of strategic net -New modes of value creation[END_REF] provide an extension of the value creation approach to business organization. In considering that intentional business networks, i.e. networks that are created with the purpose of creating value, as the starting point of the analysis, Möller and Rajala open the vision of the value configuration continuum. Following [START_REF] Parolini | The value net: a tool for competitive strategy[END_REF] they define the value system of a business net as "a set of specific activities carried out by the actors constituting the net. (…) These activities are based on the resource constellations controlled by actors" (Möller and Rajala, 2007: 898).

But resources are not given per se. Instead, it can be seen as a set of dynamic capabilities: "the bundle of capabilities that a net has and controls influences directly the efficiency of its current value production and its renewal potential" (Möller and Rajala, 2007: 898). For them, any business net can be described in considering the level of determination of the system, in other words "how well known are the value activities of the net and the capabilities (resources) of the actors to carry them out, and to what extent can these activities be explicitly specified" (Möller and Rajala, 2007: 898). And, in turn, they consider that this level of determination of knowledge is directly related to its level of codification. This point of their framework is of tremendous importance when one considers the question of innovation. This continuum of knowledge codification underlies their classification of business nets. At one end of the continuum (high level of determination), the 'current business net' has a stable and well define value system. In the middle, the business renewal net' has an established value system, with incremental improvements. Finally, at the other end (low-level of determination), the 'emerging business net' has an emerging value system with radical changes. This situation concerns "radical, continuous and system-wide change. (…). It is characterized by dispersed and vaguely identifiable ideas about the future involving great uncertainty" (Möller and Rajala, 2007: 900).

3-3 Relationship governance within value systems

Knowledge, central to any innovation, is a combination of intangible information and of specific skills (or capabilities). Thus the role of the network architecture, defined by concepts such as centrality, interconnectedness, network level, complementarity, information flows… is to provide the conditions of access, distribution, protection of this knowledge between the network members. At the same time it shows the idiosyncratic nature of knowledge: considering the situation of innovation/value processes and its dynamics especially links to market and competition conditions, the approach must be contextual. But how to monitor value creation processes within one given value system?. Several authors have developed this specific question of monitoring applied to the broad question knowledge and innovation. In spite of theoretical heterogeneity, their main findings put the stress on a few characteristics and concepts that will be helpful to our analytical framework.

For [START_REF] Möller | Rise of strategic net -New modes of value creation[END_REF], innovation networks are loosely-coupled systems in a sense that several organizations without real business links are formed around collective actions. The main objective of some of their members is scientific discovery and for that reason the management of such networks cannot be centralized by one company. For Möller and Rajala, "a key managerial challenge on this early phase of emergence is the identification and sense making of widely dispersed and inherently the local nature of technological and breakthrough business ideas. Ideas are often fuzzy, that is, there is ambiguity about the possible cause and effect relationships between existing knowledge and the emergent knowledge" (Möller and Rajala, 2007: 904). The role of management is that of an environmental scanning, bringing new ideas of products, markets or business concepts.

Because of high uncertainty and poor heuristic content, the management of these emerging new business nets places the role of sense making ability and its enhancement as a central point. This early sense making has a better chance to form when firms are interconnected with a wide range of different networks, even if these connections are 'weak ties'. Weak ties usually bring a profitable context that will help sense making of new ideas.

Another interesting contribution is found in [START_REF] Möller | Managing strategic nets. A capability perspective[END_REF]: the distinction of explicit levels of network management, that provide "managers with an understanding of the stratified nature of the questions and decision they should face" (Möller and Svahn, 2003:226). For instance, applied to the emerging business nets, the macro network level deals with 'network visioning': the ability to evaluate the potentiality of new product development and to assess their value. Instead, at the strategic net level, the managers mainly deal with the questions of mobilizing and coordinating different value activities.

In a quite different approach but still in line with the question of innovation monitoring, [START_REF] Dhanaraj | Orchestrating innovation networks[END_REF] place the orchestration in innovation network at the center of their analysis. For them, three main tasks need to be performed by hub firms: knowledge mobility, innovation appropriability and stability. Knowledge mobility is defined as 'the ease with which knowledge is shared, acquired, and deployed within the network (Dhanaraj and Parkhe, 2006: 660).

Considering the double constraints of dispersion and of complexity of knowledge exchange, the 'orchestrator' (whatever its status) must be able to create the conditions of identifying the value of relevant knowledge. Moreover, the orchestrator must also be able to arrange the transfer of this relevant knowledge among the network members. To do so, the orchestrator has three main management tools:

-Innovation appropriability: this is an environmental property that, in the words of Teece's seminal work, "governs an innovator's ability to capture the profits generated by an innovation" [START_REF] Teece | Profiting from technological innovation: implications for integration, collaboration, licensing and public policy[END_REF].

-Legal protection of innovations usually comes with instruments such as patents or copyrights. They are part of the institutional environment: but in a rapidly evolving and uncertain environment, one must recognize the leading role of some network members is stimulating or even in creating the appropriability regime surrounding innovations.

-Stability of the innovation networks refer to the general atmosphere of trust that is necessary for the network members to perform efficiently. [START_REF] Dhanaraj | Orchestrating innovation networks[END_REF] consider specifically the dynamic stability "which aims for a non negative growth rate while allowing for entry and exit of network members" (Dhanaraj and Parkhe, 2006:661).

Analytical framework, research propositions and application to biobased sector

IAR cluster

The literature had extensive discussions on the issue of governance, but left in the shadow of the descriptive and explanatory framework, concrete structures and governance mechanisms [START_REF] Ehlinger | Quelle gouvernance pour les réseaux territorialisés d'organisations[END_REF]). We will present the IRR in Biobased activities within the cluster (4-1) and then apply our analytical framework of governance choice to the biobased activities (4-2). 4.1. The Industries and Agro Resources cluster ('pôle de compétitivité Industrie et Agro Ressources', hereafter IAR cluster): plurality and uncertainty Our empirical focus is on the emerging biobased industry where innovation has many facets. On the one hand, the origin of products for which it will give birth, 100% derived from renewable agricultural, functionality to the extent that they will produce no nuisance to the natural environment (biodegradability..), the technology that will be used to produce these products, which is still unknown in large part. But more important the framework which has been created in This new net (different actors detaining resources and capabilities and designing new activities) proposes to break with the existent technology a radical change that involve the creation of a new value system, ideas still fuzzy and exogenous uncertainty related to the project concerning the process, the results and the opportunities and endogenous one uncertainty associated to the difficulty of assessing performance are higher. Also, the net is characterized by a significant level of complexity relating to the subject of the relationship (biobased activities), the diversity of partners which belong to different organizational environment (Plewa et al, 2004), a complexity that induces a specificity of human, physical [START_REF] Heide | Interorganizational governance in marketing channels[END_REF] and relational (network, other relations) assets. Thus, the governance of this value net called innovation network in Möller and Rajala' acceptation is particular far from the classical governance modes (market, hierarchy and hybrids). [START_REF] Möller | Rise of strategic net -New modes of value creation[END_REF] suggest that these nets with weak ties require: self-coordination, informal leadership, and cannot be managed by one actor alone. The ambiguity suggests an environmental scanning, bringing new ideas of products, markets or business concepts and the uncertainty suggests the important of sense making role.

In the definition of the IAR cluster [START_REF] Jacquet | Les pôles de compétitivité[END_REF], each actor has a specific role, clearly defined and identified: the private sector is responsible for the cluster and the government represented by the public collectivities accompanying the device and participating in coordinating committees and funding. It is important to know the role of each one in terms of governance functions and mechanisms. The French model of clusters is different in the way that: [START_REF]Regional direction for Industry[END_REF] The French government was the initiator of those poles: strategic comity of Raffarin government 2002 and then the invitation to tender launched by the Villepin government in 2004. In the case of IAR cluster the Picardie and Champagne-Ardenne regional councils (the regional authority of two regions on the north of France) saw an opportunity to develop competences and visibility on the non food valorization of agricultural product and then they looked for researchers and industrials to support the project, while the American model cluster emerged from the industrial initiative (entrepreneur) to join the research in respecting a geographic and social proximity [START_REF] Saxenian | Regional networks and resurgence of silicon valley[END_REF]. ( 2) This geographic proximity is also at the origin of the 'pôle de compétitivité' but without being as close as 'the innovation campus'(the Silicon Valley or San Francisco Bay) or Marshallian district (Italian districts). ( 3) The idea of 'innovation project' or 'territory of projects' [START_REF] Blanc | Pour un écosystème de croissance[END_REF] is rooted in the design of the French clusters. For IAR cluster the development of non food valorization activities is the project that motivate all the actors to join the constellation (4) the conceptualization of the cluster as 'ecosystem of innovation' [START_REF] Blanc | Pour un écosystème de croissance[END_REF]. This organic view suggests that the system is alive, acting and reacting, evolving.

The IAR cluster joins the associative and the territorial governance [START_REF] Ehlinger | Quelle gouvernance pour les réseaux territorialisés d'organisations[END_REF]. The associative configuration is based on the appartenance to a solidarity community between pairs (no subordination link) on developing a community hub. It allows maintaining equilibrium between research and Industry, and also 'representativity' of the two regions (Picardie and Champagne-Ardenne). Its main challenge is to identify, accompany and help educate regional R&D projects in the field of agro resources (www.iar-pole.com). The local powers (regional council, DRIRE, CCI, CRA) and local collectivities help forming and maintaining the economic actors without participating directly in the cluster governance (Figure 3) via the 'Institutional partners committee'. The institutional frame plays a crucial role on governing the links between actors [START_REF] Brousseau | La gouvernance des processus de coopération[END_REF]. The association is organized around a steering committee that selects the projects with a view to their labeling by the pole based on an independent audit by a scientific committee. The labeling allows projects to be oriented, to be submitted to the committee for funding, and to the possibility of different funding related to its content (figure 3). To execute the plan of actions defined by the association, several working groups 'COS Comité d'Orientation Stratégique' (strategic orientation committee) have been established. They are spaces to meet, to think, to animate the network, to break boundaries and particularly project ideas incubation. We distinguish then three different network dimensions in terms of coordination and regulation: project dimension, relational dimension and institutional environment. Each dimension refers to different governance levels: project governance, meta-governance (private governance; [START_REF] Brousseau | La gouvernance des processus de coopération[END_REF] and institutional governance (figure 3).

Research propositions about relationship governance within the IAR cluster

In the innovation network, relationship governance influences the quality of the relationship in terms of trust, commitment, conflicts, willingness to invest on assets and the expectation of continuity which affects the knowledge/technology transfer between research areas and business firms (cf. figure 3). In this value system, the uncertainty makes difficult the establishment of contracts, so market governance seems risky. Also the diversity of partners which belong to different organizational environments makes hierarchy not appropriate or not realist to implement. The hybrid mode of governance seems to be the most appropriate and the most efficient in innovation network governance of Biobased sectors. The more the partners are various, different and the more the environment is uncertain, the more we need a specific governance structure far from market and hierarchy.

The lack of subordination link and the reciprocal interdependence of the various partners (Thompson, 1967) need the development of a specific function of governance in order to foster cooperation and to try to align the mental patterns of the various partners. In the case of innovation network in the emergent Biobased activities, it is needed to create an interactive space where different actors could exchange and help the fuzzy ideas to become project-ideas and then projects. This function could not be accomplished by the project governance because it is needed upstream on the value system. The intermediate level of the network is then competent. In describing the relations between industry and research in the biobased industry we found that there are different levels: (1) the institutional environment constituting by national public institutions but especially regional institutions ( 2

Relational governance

Relational and contractual governance The development of the biobased industry is a project of a defined territory (in our case Picardie and Champagne-Ardenne) and the creation of the cluster emphasize the choice to cooperate between different partners: research, industry and local communities. We believe that the relation has at its formation stage an initial capital of trust that we will describe as 'instantaneous'. The spatial proximity, to belong to the same territory, and the existence of a cluster based on spatial but also social proximity (pairs, friendships, ex-colleagues, alumni network, neighbors, etc.) create an instantaneous trust and commitment feelings. The willingness to cooperate (trust history) stressed by the instantaneous trust and reputation which are organizational determinants, results from the relational (interorganizational) factors (proximity) and the meta-organizational determinants materialized by the existence of an institutional environment that favors cooperation (figure 4). In addition, this proximity helps to build a collective sensemaking for organized action in innovation network. Looselycoupling occurs (Douglas Orton & Weick, 1990) in this network in the meta-level (relationlevel) sense making is thus crucial to create shared values and focusing attention on the most important relation in the system. The relation-governance have to assume this role in order to compensate the loosely links. More we are close to the project level, more ideas become précised, projects designed and the partners fixed, the system occurs tightly coupled.

Proposition 2: the interpersonal, organizational, relational determinants interact each other according to the context factors and influence the governance design. Depending on the level, the network is loosely or tightly coupled which influence the level governance.

The specificity of the exchange and the static view are not sufficient. The Biobased value system evolves and changes the governance functions and mechanisms by a game of positive/negative effect resulting from the quality evaluated of the relationship.

Proposition 3: the relationship governed by relational mechanisms favor positive feed-backs by promoting and nurturing trust and commitment (cf. figure 4).

Conclusion

For several years, many researchers stressed the need to pay attention to the black box of governance and yet few studies have been undertaken in this area. This gap is due in part to the difficulty of building a theoretical framework of relations which have borders in constant evolution and with multiple contingency factors. The interest of our research is to propose an integrative theoretical framework for understanding the governance in value creation system that is still missing in literature. From a managerial point the objective of this framework is to simplify a complex managerial situation in order to have a better understanding of the decision-making processes. We have seen that the governance of relations between knowledge-based and business activities in the biobased sector has multidimensional aspects: interpersonal, organizational, inter-and meta-organizational. Choosing the effective governance is required to improve the quality of the global relationships within the system and thus ensure the effectiveness of knowledge transfer. These governance relationships are characterized by the existence of different levels, and between them a complementarity of functions is suggested. A global level of governance, called relation-governance, is assuming cognitive function primarily via relational mechanisms. A second level is called project-governance, which in addition to the cognitive function will ensure a disciplinary one to ensure the safety and the continuity of the contracts. An overarching level of institutional-governance helps to identify the roles of institutional environment with regards to innovation atmosphere. Our research has yet to be fine-tuned by an analysis of the players' games that will identify the players involved, their degree of influence and some of their strategic challenges, the objectives of each actor involved and their level of divergence and convergence, in order to provide an in-depth understanding of the design of governance mechanisms in innovation settings.

Figure 1 :

 1 Relationship governance: aims, functions and mechanisms 2.2. The governance of industry-research relationships (IRR): main theoretical perspectives

  2005 for governing innovation by launching the French model of clusters called 'Pôles de Compétitivité'. The development of this process follows a model of encouraging open innovation industry-research-training relationships. The relationship in this context is tripartite between industry, research centers and training centers exchanging different streams of information and skills (cf. figure 2).

Figure 2 :

 2 Actors in IAR cluster

  ) the 'meta-governance' or 'relation-governance' materialized by the 'pôle de compétitivité' association where the different partners meet to maximize the benefits of the cooperation between the different actors and (3) the 'project-governance' governing the relation-project assumed by a pilot (generally a firm). There is a complementarity between the relation-governance assumed by the 'pôle de compétitivité' and the governance of the relation. We suggest that the relation-governance has mainly a cognitive function while the relation governance guarantees the double function. The effectiveness of the relation depends on the capacity to create the complementarity between the different governance levels. Proposition 1: In innovation network of Biobased activities there are three levels and different governance functions with different mechanisms with a complementarity in functions

Figure 3 :

 3 Figure 3: Governance levels in the IAR cluster

Figure 4 :

 4 Figure 4: Conceptual framework for relationship governance in biobased activities