Fabien Cassio

Nathalie Lorrain
email: nathalie.lorrain@univ-rennes1.fr

Parastesh Pirasteh

Luiz Poffo

Jonathan Lemaitre

Isabelle Hardy

Mohammed Guendouz

Porosity calibration in a 4-layer porous silicon structure to fabricate a micro-resonator with well-defined refractive indices and dedicated to biosensing applications

Keywords: Porous silicon, multilayers, porosity calibration, micro-resonator

teaching and research institutions in France or abroad, or from public or private research centers.   Porosity calibration in a 4-layer porous silicon structure to fabricate a micro-resonator with well-defined refractive indices and dedicated to biosensing applications

Introduction

Porous silicon (PSi) is a widely studied material that is used in many applications, particularly in the field of label free biosensors due to its large surface specific area and its biocompatibility [START_REF] De | Porous silicon optical biosensors: still a promise or a failure?[END_REF]. In addition, the adequate functionalization of the surface of the internal pores introduces the ability to specifically detect molecules of interest, which is necessary for early diagnosis of diseases. Due to the electrochemical anodization used process, the porosity and the thickness of the PSi layers are tunable, making it possible to manufacture many components that have been used for biosensing applications [2 -4]. Thus, double-layer structures for waveguides [5], interferometers [START_REF] Kim | Porous silicon integrated Mach-Zehnder interferometer waveguide for biological and chemical sensing[END_REF]7], optical grating [START_REF] Wei | Guided mode biosensor based on grating coupled porous silicon waveguide[END_REF], micro-resonators [START_REF] Shuren | Porous silicon ring resonator for compact, high sensitivity biosensing applications[END_REF][START_REF] Girault | Porous silicon micro-resonator implemented by standard photolithography process for sensing application[END_REF] and photonic crystals [START_REF] Rodriguez | Photonics crystal naobeam biosensors based on porous silicon[END_REF], or multi-layer structures for Bragg mirror [START_REF] Arroyo-Hernandez | Porous silicon optical filters for biosensing applications[END_REF][START_REF] Moretti | Periodic versus aperiodic: Enhancing the sensitivity of porous silicon based optical sensors[END_REF], microcavities [START_REF] Lorrain | Functionalization control of porous silicon optical structures using reflectance spectra modeling for bio sensing applications[END_REF][START_REF] Krismastuti | Porous silicon resonant microcavity biosensor for matrix metalloproteinase detection[END_REF] and rugate filters [START_REF] Kilian | Organic modification of mesoporous silicon rugate filters: the influence of nanoarchitecture on optical behaviour[END_REF] have been fabricated for biosensing applications in integrated optic.

In the field of integrated optic, micro-resonators (MRs) are certainly the smallest structures to obtain very sensitive sensors with low limit of detection compared to interferometers for example [START_REF] Chao | Design and Optimization of microring resonators in biochemical sensing applications[END_REF]. Most MRs are geared toward classical detection based on refractive index variations where the probed molecules interact with the evanescent wave [START_REF] Chao | Design and Optimization of microring resonators in biochemical sensing applications[END_REF][START_REF] Jokerst | Chip scale integrated microresontor sensing systems[END_REF]. MRs biosensors based on PSi technology offer an enhancement of the sensitivity, and so an improvement of the limit of detection compared to bulk MR biosensors, due to a direct interaction of specific biomolecules grafted on the internal surface of pores and the propagated light [START_REF] Girault | acetrack micro-resonators based on ridge waveguides made of porous silica[END_REF][START_REF] Azuelos | Optimization of porous silicon waveguide design for microring resonator sensing applications[END_REF], [START_REF] Rodriguez | Photonics crystal naobeam biosensors based on porous silicon[END_REF].

Waveguides made in PSi have higher optical losses than those made in a bulk material due to their porous nature. In order to reduce the losses in the whole optical biosensor, we planned to implement a hybrid structure by associating the PSi transducer MR with polymer waveguides that will ensure the transmission and recovery of the optical signal with lower optical losses [START_REF] Girault | ntegrated polymer micro-ring resonators for optical sensing applications[END_REF][START_REF] K K Tung | Polymeric optical waveguides using direct ultraviolet photolithography process[END_REF]. For this aim, the PSi MR will be butt-coupled to the polymer waveguides with the constraint that the refractive index of the PSi guiding layer corresponds to that of the polymer core waveguide. Moreover, to further fabricate this hybrid structure, a 4-layer PSi structure will be needed since guiding and confinement PSi layers will be subjected to a photolithography process inducing a resin deposit and then a polymer deposit. Consequently, both the guiding and the confinement layers have to be protected by a thin PSi barrier layers of low porosity to prevent from polymer or resin infiltration.

In PSi multilayer structures, the porosity and thus the refractive index of the guiding and confinement layers are often deduced from a calibration based on the elaboration and characterization of a single layer by assuming, as a first approximation, that the porosity of a single layer is the same than in a multilayer structure for the same fabrication parameters [5,[START_REF] Vincent | Optical properties of porous silicon supperlattices[END_REF][START_REF] Martin-Palma | Porous multilayers stacks for optical biosensing applications[END_REF][START_REF] Torres -Costa | Optical characterization of porous silicon films and multilayer filters[END_REF][START_REF] Nava | efractive index contrast in porous silicon multilayers[END_REF]. However, some authors mentioned that the so-determined refractive indices and also the anodization rate of PSi layers are modified in presence of a multilayer structure [START_REF] Mazzoleni | Application to optical components of dielectric porous silicon multilayers[END_REF]. It was reported that the measured refractive indices and anodization rates were systematically lower for thin and extremely high porous layers in presence of a PSi multilayer structure compared to a thick layer one [START_REF] Berger | nvestigation and design of optical properties of porosity superlattices[END_REF][START_REF] Pavesi | Porous silicon dielectric multilayers and microcavities[END_REF].

In this paper, a calibration of the porosity and the anodization rate of the guiding and confinement PSi layers is performed taking into consideration the presence of the thin PSi technological barrier layers. The objective is to define the current densities and anodization times that must be applied to obtain guiding and confinement PSi layers with well-defined refractive indices and thicknesses to be able to manufacture a 4-layer PSi MR. We first present the technological steps to fabricate the MR based on 4-layer PSi ridge waveguides. Then we present the method we have used to determine the porosity and thus the refractive index of each layer. The calibration results are presented and discussed. The 4-PSi layer MR is fabricated and characterized using scanning electron microscope observations and using an optical bench to measure its optical transmission spectrum. Simulations results are presented and compared to the experimental optical characterizations. Finally, as the MR will be used for biosensing applications, a preliminary theoretical study of the surface sensitivity and the limit of detection of the PSi MR for Bovin Serum Albumin (BSA) is presented.

Experimental

To fabricate a PSi MR that will be butt coupled with SU8 polymer waveguide, four PSi layers are needed since guiding and confinement PSi layers will be subjected to a photolithography process inducing a resin deposit and then SU8 deposit.

The refractive index of the SU8 polymer core waveguide is 1.57 at 1.55 µm. The refractive index at 1.55 µm of the porous confinement of both PSi and SU8 polymer core waveguides has been chosen to 1.41 in relation to a previous work [START_REF] Girault | ntegrated polymer micro-ring resonators for optical sensing applications[END_REF]. The target thickness of the confinement layer is about 5 µm. The target dimensions of the ridge core waveguide are a width of 2 µm and a height of 1.7 µm to obtain a single-mode propagation for the TM polarization.

The figure 1.a shows the four consecutive layers of porous silicon prepared by electrochemical anodization of a heavily doped P (100) silicon substrate with a 5 m.cm resistivity and using successive applied current densities for specific times. The electrolyte is a mixture of hydrofluoric acid (50 %) with ethanol and deionized water in the ratio of 2-2-1 respectively. The room temperature is maintained at 18 °C. The first and the third thin barrier layers with low porosities are obtained with a current density of 1 mA/cm². The target thicknesses of the four layers are respectively of 30 nm, 1.7 µm, 50 nm and 5 µm. In the waveguide structure, the first and the third layers do not exceed 50 nm to ensure single-mode waveguide @ 1550 nm.

To obtain the 4-layer PSi MR, a thin SiO 2 layer of about 30 nm is deposited on the first PSi barrier layer to further improve the impermeability of the porous structure. We have found that this thin SiO 2 layer directly deposited on the guiding PSi layer do not ensure the role of technological barrier to prevent from infiltration of resin in pores. Then, a positive S1805 photosensitive resin layer is deposited by spin coating on the technological barriers (SiO 2 layer and first PSi layer). Ridge waveguide patterns are then produced under UV exposure through a well-defined chrome mask designed using commercial Olympios software. The sample is immersed in the MF-319 to reveal the ridge PSi waveguide patterns. A trifluoromethane (CHF 3 ) Inductively Coupled Plasma (ICP) is performed in order to etch the first technological barrier layers and the guiding layer. The etching depth should be controlled to avoid the etching of the second PSi barrier layer. The photosensitive resin and the SiO 2 layers are then removed respectively with an oxygen (O 2 ) followed by a sulfur hexafluoride (SF 6 ) Reactive Ion Etching (RIE). The 4-layer PSi MR is then achieved as represented in figure 1.b.

Porosity determination method

In a PSi multilayer structure, it is reported by some authors that the refractive index and the etching rate of a PSi layer are modified compared to a single PSi layer [START_REF] Mazzoleni | Application to optical components of dielectric porous silicon multilayers[END_REF]. In a first approximation, the porosity of a layer in a multilayer structure is generally considered identical to that determined on a single layer. This was particularly the case in our previous studies with a good agreement between simulation and experimental results [START_REF] Lorrain | Functionalization control of porous silicon optical structures using reflectance spectra modeling for bio sensing applications[END_REF][START_REF] Hiraoui | Towards a biosensor based on anti resonant reflecting optical waveguide fabricated from porous silicon[END_REF] without any use of a technological PSi barrier of low porosity. In our 4-layer PSi structure, we must consider that the refractive index of the guiding and the confinement PSi layers may be affected by the PSi technological barrier layers.

To obtain refractive indices of the PSi guiding and confinement layers of 1.57 and 1.41 respectively, porosities of 69.6% and 76.3% are required. The current densities to be applied to produce these layers with well-defined porosities must be determined by a calibration taking into account the presence of the thin barrier layers.

We consider that changing the current density to perform another PSi layer does not affect the characteristics of the PSi layer previously formed because silicon dissolution occurs at the silicon electrolyte interface [START_REF] Lugo | Porous silicon multilayers structures: A photonic band gap analysis[END_REF]. But we assume according to literature [START_REF] Berger | nvestigation and design of optical properties of porosity superlattices[END_REF][START_REF] Pavesi | Porous silicon dielectric multilayers and microcavities[END_REF] that the porosity of a layer inside a multilayer structure is not the same as in a single layer.

In case of one single PSi layer (without any technological barrier layer) (figure 3.a), the porosity and so the refractive index are determined by a well-established methodology using reflectance measurements and the Bruggeman model [START_REF] Lorrain | Functionalization control of porous silicon optical structures using reflectance spectra modeling for bio sensing applications[END_REF][START_REF] Hiraoui | Spectroscopy studies of functionalized oxidized porous silicon surface for biosensing applications[END_REF][START_REF] Xiao | Structure characterization of porous silicon layers based on a theoretical analysis[END_REF][START_REF] Bethune | Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques[END_REF][START_REF] Bruggeman | Berechnung verschiedene physikalischer konstanten von heterogenen substanzen[END_REF]. Reflectivity spectrum of the Air/PSi layer/Si substrate interference system is measured in the range 900 -2000 nm using an Ocean Optics HR 400 spectrometer. The method consists in fitting on the experimental spectrum a theoretical spectrum calculated rigorously using a transfer matrix method [START_REF] Bethune | Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques[END_REF]. The transfer matrix method allows the reflectivity of the layers to be calculated from data including refractive index and layer thickness. The thickness of the PSi layer is determined by scanning electron microscopy (SEM). The refractive index of the layer is calculated using the approximation of Bruggeman [START_REF] Bruggeman | Berechnung verschiedene physikalischer konstanten von heterogenen substanzen[END_REF].

This method is commonly used in porous silicon [START_REF] A M Campos | Porous silicon dielectric function modeling from effective medium theories[END_REF] and can be applied in our case as the pores dimensions of 20 -40 nm are smaller than the optical wavelength so that the medium behaves homogeneously. This is an effective model that allows to take into account the different medium constituents and their volume fraction. Applied to a PSi layer, the Bruggeman model relates the porosity P and the refractive indices of air, silicon n Si and n, the effective index of the PSi layer according to following equation (1): Thus, for a PSi layer, the refractive index dispersion curve is obtained by knowing its porosity. By this method, the theoretical reflectance spectrum is compared to the experimental spectrum of the sample. The calculations are continued, by varying the porosity of the layers, until the two experimental and theoretical curves are fitted. The porosity value of the single PSi layer is then deduced from the best fit between the theoretical and experimental reflectance spectra. An example of an experimental and the adjusted theoretical spectra are reported in figure 2.a for a single layer; the thickness of the layer is obtained from the SEM cross section measurements (figure 2. b) with an accuracy of 0.05 µm. The determined porosity of the PSi layer is 71.1  0.6 % for an applied anodization current density of 80 mA/cm². Moreover, we have verified that the porosity of a 4.75 µm thick-layer is the same as that of a 1.7 µm thick-layer. The porosity of one single layer has been also determined using this method for current densities of 1 mA/cm² corresponding to the PSi barrier layers and in the range of 50 to 110 mA/cm² corresponding to the guiding and the confinement PSi layers respectively. In order to determine the porosities of the guiding and the confinement PSi layers in a 2 or 4layer PSi structure, we used the following method described in figures 3.b and 3.c which consists in reducing the study to a single-layer.

Precisely, in order to determine the porosity of the guiding layer which follows the first thin barrier layer, a 2-layer structure is prepared by applying J 1 = 1 mA/cm² for the barrier layer and another one for the guiding layer by applying a current density J 2 in the range of 50 to 110 mA/cm². Then, a SF 6 RIE etching is performed on the sample to remove the thin barrier layer (figure 3.b).

In the same way, to determine the porosity of the confinement layer, a 4-layer structure is performed by electrochemical anodization: current densities of J 1 = 1 mA/cm², J 2 = 85 mA/cm², J 3 = 1 mA/cm² and J 4 = 110 to 120 mA/cm² are applied successively.

In addition, in order to better identify the second 50 nm barrier layer both in the SEM images and in the RIE etch tracking, a larger thickness of about 300 nm was chosen for the calibration of the porosity of the confinement layer in the 4-layer structure. Then, a SF 6 RIE etching is performed on the sample to remove the three top layers: the two thin barrier layers and the guiding layer (figure 3.c).

Figure 3: (a) Study of the porosity of a single PSi layer: schema of the PSi layer corresponding to the guiding layer and prepared by electrochemical anodization by applying a current density J in the range of 50 to 110 mA/cm². (b) Study of the porosity of the guiding layer: schema of a 2-layer structure with the barrier layer in the top and the guiding layer prepared by electrochemical anodization by applying successively the current densities of J 1 = 1 mA/cm² and J 2 in the range of 50 to 110 mA/cm². Then a SF 6 RIE etching is performed to remove the first thin barrier layer. (c) Study of the porosity of the confinement layer: schema of a 4-layer structure with the barrier layer in the top, the guiding layer, the second barrier layer and the confinement layer prepared by electrochemical anodization by applying

successively the current densities of J 1 = 1 mA/cm², J 2 = 85 mA/cm², J 3 = 1 mA/cm² and J 4 in the range of 110 to 120 mA/cm². Then a SF 6 RIE etching is performed to remove the three top layers in order to get only one layer corresponding to the confinement layer.

Results and discussions

Porosity and anodization rate calibrations

The objective is to determine the porosity (P) and also the electrochemical anodization rate (Ra) of a single layer obtained either just after anodization, or after etching of a 2-layer or a 4layer structure using the method described in part 3 and to compare them. As an example, the results that have been obtained for the current density of 110 mA/cm² are reported in figure 4 with, in addition, the SEM cross-section observations that have been performed either just after electrochemical anodization ( In the 2-layer PSi structure (figure 4.b), after a RIE etching of the barrier layer and a part (about 500 nm) of the second layer performed with a current density of J 2 =110 mA/cm², the porosity P 2 has been estimated to 75.5  1 %. The 1 % uncertainty on porosity is mainly due to the uncertainty on thickness and related to the roughness created during the RIE etching step. The anodization rate of the second layer for J 2 = 110 mA/cm² is Ra 2 = 52.3  1.2 nm/s when a first layer with a current density of 1 mA/cm² is performed. Figure 4.c reports a 4-layer PSi structure that represents the multilayer structure that is needed to fabricate the micro-resonator, except for the second barrier layer which is thicker in this case for SEM observations and RIE etching tracking. Apart from the first barrier layer which is very thin and not visible on the SEM image, the other three PSi layers are well defined: the guiding layer corresponding to a current density of 85 mA/cm², the second barrier layer of 280 nm and the confinement layer corresponding to a current density of 110 mA/cm². The RIE etching of the three top layers reducing the structure only to the confinement layer to be characterized, provided the determination of a porosity P 4 of 75.7  0.7 %. This porosity P 4 is very similar to the porosity P 2 determined in the case presented in figure 4.b for the same current density of 110 mA/cm². The anodization rate of this confinement layer is Ra 4 = 51.6  1.1 nm/s which is also similar to the Ra 2 in the case of figure 4.b as the layer just above it is also a barrier layer performed with the same low current density of 1 mA/cm². These first results confirm that in a PSi multilayer system, there is an influence of the previous formed low porous layer on the anodization rate and on the porosity of the following layer. Indeed, the porosity of the PSi single layer performed with a current density of 110 mA/cm² is higher than that performed with the presence of a thin top PSi barrier. The porosity and the anodization rate of the layer seem to only depend on the structural characteristics of the previously formed PSi layer because the porosity and the anodization rate are very similar in the cases of figures 4.b and 4.c for which the layer just above the studied one is a barrier layer performed with the current density of 1 mA/cm². Taking into account these results, the influence of the presence of a thin top barrier layer on the anodization rate and the porosity of the considered PSi layer has been studied for other current densities over 50 mA/cm² and up to electro-polishing. Figure 5 compares anodization rate (figure 5.a) and porosity (figure 5.b) plotted as a function of the current density of the studied layer for three cases. In case A, the studied structure is a single PSi layer manufactured with a current density in the range of 50-100 mA/cm², without any barrier layer. Case B represents a 2-layer PSi structure constituted of the thin barrier and the studied guiding PSi layer performed with a current density in the range of 50-110 mA/cm². Case C concerns the 4-layer PSi waveguide structure constituted of the first barrier layer, the guiding layer prepared with a current density of 85 mA/cm², another thin PSi barrier and the studied confinement PSi layer prepared with a current density in the range of 110-120 mA/cm². Figure 5.a shows that for a current density of 50 mA/cm², the anodization rate is substantially the same for the cases A and B. Then, the difference in anodization rate between the two cases A and B increases even more with the current density applied. A previously formed barrier layer increases the anodization rate of the porous layer under study.

As already observed in figure 4.a, electropolishing phenomenon occurs on a single layer using current densities up to 110 mA/cm² (case A). It is not observed for the layer performed with the same current density of 110 mA/cm² in a 2-layer PSi structure (case B) or in a 4-layer PSi structure (case C) for which electropolishing occurs for higher current densities up to 120 mA/cm².

Figure 5: PSi layer (a) anodization rate, (b) porosity and (c) corresponding refractive index versus anodization current density J, (A) : for the case of one single layer; (B): for the case of the 2-layer structure with a barrier layer performed with 1 mA/cm² and the guiding layer with varying current densities in the range of 50-110 mA/cm²; (C): for the case of the 4-layer structure with a barrier layer performed with 1 mA/cm², the guiding layer performed with a current density of 85 mA/cm², a second barrier layer of 1 mA/cm² and the confinement layer performed with a current density of 110 or 115 mA/cm² (for J 4 = 120 mA/cm²: electropolishing).

The porosity calibration curve presented in figure 5.b also shows that the porosity is almost similar for a current density of 50 mA/cm² for the cases A and B. But for increasing current densities and in contrast to the anodization rate, porosity gets higher in the single layer (case A) than in the studied layer in cases B or C. The closer the porosity of the studied and the barrier layers are to each other, the more negligible the influence of the previously formed layer, as shown in figure 5.b. The diffusion of the reactive species responsible for pore formation is all the more limited through the barrier as its porosity is low. The composition of the electrolyte solution, in particular in hydroxide ion (pH), is therefore different in the underlying layers compared to a case without a barrier layer. The concentration of hydroxide ion would be higher in the presence of a barrier layer generating a less porous underlying layer [37][START_REF] Halimaoui | Porous silicon: material processing, properties and applications[END_REF]. In addition, as already observed in figures 4b and 4c, for the studied current densities, there is no difference in anodization rate and porosity between cases B and C. The characteristics of a PSi layer inside a multilayer structure would only depend on the porosity of the upper layer just previously formed and not on the other layers above it. In figure5.c, refractive index of the PSi studying layer, in cases A, B or C has been deduced from the layer porosity using the Bruggeman model [START_REF] Bruggeman | Berechnung verschiedene physikalischer konstanten von heterogenen substanzen[END_REF] and plotted as a function of the current density. From this plot, the current densities to be applied to obtain a guiding PSi layer with a refractive index of 1.57 and a PSi confinement layer with a refractive index of 1.41, both at 1.55 µm, have been determined: they are respectively of J G = 85 mA/cm² and J C = 110 mA/cm². To verify the porosity calibration which takes into consideration the presence of a thin barrier PSi layer, a reflectance measurement has been performed on the 4-layer PSi structure fabricated using these current densities J G and J C and using a thicker second barrier layer (280 nm) than in the waveguide structure presented in figure 1 in order to be able to make SEM measurements.

Then, the obtained experimental spectrum was adjusted to a theoretical one (figure 6.a) calculated using matrix transfer formalism [START_REF] Bethune | Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques[END_REF] from SEM thickness measurements (figure 6.b) and from the guiding and confinement layer porosities previously determined by the calibration. To obtain the theoretical reflectance spectra, refractive index and thus porosity of the two thin barrier PSi layers had to be determined. A single PSi layer performed with the low current density of 1 mA/cm² has been characterized to both estimate the anodization rate and the porosity using a 1.6 µm layer, thicker than the one which is used in the 2 or 4-layer system in order to have enough interference fringes. The anodization rate is 1.3  0.1 nm/s and the porosity is estimated to 43.5  1.5 %. The uncertainty on porosity is mainly due to the low number of interference fringes, the thickness of the layer being thin due to the very low anodization rate. Moreover, since the first barrier PSi layer thickness is difficult to measure precisely on SEM images in the 4-layer PSi structure, it has been adjusted so that the calculated spectrum corresponds as closely as possible to the experimental spectrum. We have verified that the obtained thicknesses of 30 and 280 nm for the first for the second barrier layer respectively well correspond to those that can be estimated from the anodization rate and time t. The adjustment parameters are reported on table 1. The fairly good adjustment of the experimental spectrum validates the PSi layer porosity calibration and thus of the refractive index as a function of the current density by taking into account the influence of the previously formed layers on the following ones. The slight mismatching could be due to inhomogeneous porosity through each layer and the interface roughness which is around 10 nm [START_REF] Charrier | Effect of interface roughness and polarization on the optical losses of porous silicon-based waveguides[END_REF]. Real improvement of quality and reproducibility of PSi layers could be obtained by performing the multilayers at low temperature [START_REF] Setzu | Temperature effect on the roughness of the formation interface of p-type porous silicon[END_REF] and by controlling the PSi formation in situ using for example photoacoustic method [START_REF] Ramirez-Gutierrez | n situ photoacoustic characterization for porous silicon growing: Detection principles[END_REF][START_REF] Ramirez-Gutierrez | Optical interferometry and photoacoustics as in-situ techniques to characterize the porous silicon formation: a review[END_REF][START_REF] Ramirez-Gutierrez | Design, fabrication, and optical characterization of one dimensional photonic crystals based on porous silicon assisted by in-situ photoacoustics[END_REF]. Moreover, improvement of the calculation of the theoretical reflectance spectra could be done taking into consideration interface roughness in the simulation [START_REF] Lujan-Cabrera | Effects of the interface roughness in the optical response of one dimensional photonic crystals of porous silicon[END_REF]. More adaptive optical measurement could also be used to characterize the porous silicon layer both in single and multilayer system [START_REF] Ghim | Simultaneous measurements of top surface and its underlying film surfaces in multilayer film structure[END_REF][START_REF] Santbergen | Optical model for multilayer structures with coherent, partly coherent and incoherent layers[END_REF].

Table 1: PSi layer fabrication parameters (current density and anodization time), theoretical reflectance spectra adjustment parameters of the 4-layer PSi system (thickness, porosity and refractive index of each layer).

PSi layer J (mA/cm²) t (s) Thickness (µm) Porosity (%) Refractive index

Porous silicon ridge waveguide MR fabrication

MRs based on PSi ridge waveguides have been manufactured from the 4-porous silicon layer structure using the process described in [START_REF] Girault | acetrack micro-resonators based on ridge waveguides made of porous silica[END_REF]. Following the fabrication steps, SEM measurements have been performed in order to verify the implementation of the PSi MRs. Figure 7 reports SEM images of a racetrack PSi MR with a radius R of 100 µm and a coupling length Lc of 70 µm. Moreover, in order to obtain a single-mode propagation for the TM polarization, the anodization time for the second barrier layer has been reduced to aim a thickness of 50 nm instead of the 280 nm previously chosen to facilitate its measurement by SEM observations and then to be able to adjust the experimental reflectance spectrum of the 4-layer system with the calculated one (figure 6). The top view SEM image of the characterized MR is reported in Figure 7.a. The separation between the straight and the racetrack MR ridge waveguides, which appears in dark grey light (Figure 7.b), shows that the gap has been successfully made along the coupling length of the racetrack. A mean waveguide width of 1.95 µm instead of the targeted 2 µm was measured. The gap between the access waveguide and the resonant cavity is 0.6 µm, which is slightly higher than expected (0.5 µm) due to low side etching during the photolithography steps and already observed in previous studies [START_REF] Girault | Porous silicon micro-resonator implemented by standard photolithography process for sensing application[END_REF][START_REF] Girault | acetrack micro-resonators based on ridge waveguides made of porous silica[END_REF].

The cross section of the etched ridge waveguide is reported in Figure 7.c showing the PSi guiding and confinement layers with almost the aimed dimensions (1.7 µm and 4.7 µm respectively). The observation at a higher magnification allows to measure the thickness of the barrier layer between the guiding and the confinement PS layer at about 50  10 nm (figure 7.d).

Optical simulations and characterizations

Before the optical characterizations of the fabricated PSi MR, some preliminary simulations of the waveguide schematized in figure 8.a have been carried out taking into consideration the experimental waveguide dimensions obtained by SEM observations. We have assumed a thickness of the first barrier layer of 30 nm with respect to the adjustment results of the theoretical and experimental reflectance spectra of the 4-layer PSi structure (figure 6). As the height of 1.7 µm of the guiding layer has been measured including the two barrier layers of 30 nm and 50 nm respectively (fig. 7.c and 7.d), we deduced the real height of 1.62 µm for the PSi core waveguide with a width of 1.95 µm (fig. 7.c).

Knowing the porosity, the refractive index evolution of each layer constituting the PSi waveguide could be determined as a function of the wavelength from the data in references [START_REF] Salzberg | Infrared Refractive Indexes of Silicon, Germanium and Modified Selenium Glass[END_REF][START_REF] Tatian | Fitting refractive-index data with the Sellmeier dispersion formula[END_REF]. Then, from these data and considering the 4-layer PSi waveguide represented in figure 8.a, the effective index of the TM single propagated mode has been calculated with a FMM (Film Mode Matching) full vector Solver from FIMMWAVE software commercialized by Photon design. The FMM solver is a versatile numerical method for vector mode field calculations and particularly adapted for waveguide structures with a rectangular geometry [START_REF] Sv | Film mode matching : a versatile numerical method for vector mode filed calculations in dielectric waveguides[END_REF]. The effective index variation as a function of the wavelength has been fitted by a linear function over the studied range (figure 8.b) and the group index of the PSi waveguide has been deduced from equation (2) in the studied wavelength range: n g . Effective refractive index have also been calculated as a function of the wavelength using Matlab software from the effective refractive index method [START_REF] A B Fallahkhair | Vector finite difference mode solver for anisotropic dielectric waveguides[END_REF], method that only consider a simple ridge waveguide constituted of a guiding and a confinement layer. Thus, using this method, we have neglected the upper and the lower technological barrier layers. This method is simple and regularly used in the field of integrated optics in the case of rectangular waveguides with low refractive index contrast (∆n  1) with a width/height ratio R >1. [START_REF] Chiang | Performance of the effective-index method for the analysis of dielectric waveguides[END_REF][START_REF] Batrack | Applicability of the effective index method for sumilatinf ridge optical waveguides[END_REF][53]. We have taken into consideration experimental waveguide dimensions: a width of 1.95 µm and a height of 1.7 µm. A group index of 1.646  0.001 in the studied wavelength range from 1.4 to 1.6 µm has been calculated, which is very close to the value determined by the FMM method, meaning that the barrier layers can be neglected.

The coupling factor between the straight waveguide and the resonant cavity has been calculated at 1550 nm using Marcatili model [START_REF] Marcatili | Dielectric ectangular Waveguide and Directional Coupler for ntegrated Optics[END_REF]. This model is also regularly used in the field of integrated optics in the case of rectangular waveguides for low index contrast and dimensions for single mode propagation and not small enough compared to wavelength [START_REF] Hunsperger | ntegrated optics: Theory and Technology[END_REF]. Precisions of the coupling factor determination method are given in [START_REF] Girault | acetrack micro-resonators based on ridge waveguides made of porous silica[END_REF]. The barrier layers are neglected again. The determined coupling factors for TE or TM modes are plotted as a function of the gap (separation distance between the access waveguide and the resonant cavity) in the range of 0.5 to 1 µm, that can be obtained from a process point of view (figure 9). We have taken into consideration experimental waveguide dimensions by neglecting the upper and the lower barrier layers: a width of 1.95 µm, a height of 1.7 µm, a coupling length Lc = 70 µm and a radius R = 100 µm.

For the mean gap of 0.6 µm that is experimentally obtained (fig. 7.b), a coupling factor of about 8 % and 5 % have been calculated respectivley for the TE and TM modes (figure 9). In order to verify that this fabricated PSi MR is optically operational, the spectral transmission was measured. Then, using the equations defined in our previous study on polymer micro-ring resonators [START_REF] Girault | ntegrated polymer micro-ring resonators for optical sensing applications[END_REF], the theoretical transmission TM has been calculated and then adjusted to match the experimental one by varying the following parameters: group index, coupling ratio and optical losses.

Figure 10 reports the experimental and the theoretical adjusted spectral transmission responses. The experimental spectrum TM shows three resonance wavelengths in the studied range that are separated by a Free Spectral Range (FSR) of 1.93 nm, with , where L is the cavity perimeter (

) and is the group index.

To match the experimental FSR, the group index n g was adjusted to 1.6551 ± 0.0001 which is in good agreement with the previous group indices of 1.646 or 1.643 that have been calculated using Matlab or FIMMWAVE simulations respectively.

The adjustment of the resonance shape is performed by varying the coupling factor and the propagation losses in the resonant cavity. A coupling factor κ² of 5 ± 1 % and a field attenuation constant a = 0.8835, which corresponds to propagation losses per length unit (α) of 14.0 ± 0.4 dB/cm, have been obtained in this case. The value obtained for the coupling factor well corresponds well to that estimated for the TM mode. As the minimum of transmission resonant wavelenght is about 0.4 , the critical coupling is not reached.

A width at half-height (δλ) of 06 nm is obtained, with a corresponding quality factor Q of 2.5 10 4 , which is better than those obtained in previous studies using another refractive indices [START_REF] Girault | Porous silicon micro-resonator implemented by standard photolithography process for sensing application[END_REF][START_REF] Girault | acetrack micro-resonators based on ridge waveguides made of porous silica[END_REF]. Morever, this quality factor could be yet improve by optimizing the coupling length to reach critical coupling and thus obtain a total extinction response at resonant wavelenghts. As the PSi MR is dedicated to biosensing applications, an estimation of the surface sensititvy of the MR for a BSA (Bovin Serum Albumin) detection have been calculated using previous results [START_REF] Lorrain | Functionalization control of porous silicon optical structures using reflectance spectra modeling for bio sensing applications[END_REF][START_REF] Hiraoui | Spectroscopy studies of functionalized oxidized porous silicon surface for biosensing applications[END_REF]. For biosensing, the PSi guiding layer has to be functionnalised for specific grafting of BSA molecule. Functionalization proccess of the PSi internal surface described in [START_REF] Hiraoui | Spectroscopy studies of functionalized oxidized porous silicon surface for biosensing applications[END_REF] has been used. It includes a silanization step using Aminopropyltriethoxysilane (APTES) and a coupling step using Glutaraldehyde (GL) molecules. We have supposed a functionalization of the PSi internal surface with one monolayer of APTES and one monolayer of glutaraldehyde to get the volume fraction of each component. Then using Bruggeman relation and modelling of the PSi surface described in [START_REF] Lorrain | Functionalization control of porous silicon optical structures using reflectance spectra modeling for bio sensing applications[END_REF], the refractive index of the functionalized PSi guiding layer has been determined. After BSA grafting step, the refractive index of the PSi guiding layer can also be deduced from Bruggeman model from a volume fraction of BSA (f BSA ) which is correlated to M BSA , the number of molecules grafted per surface unit of the functionalized PSi. M BSA can be estimated taking into consideration the surface specific area (Ss) of 90 m²/cm 3 calculated from [START_REF] Dribek | Theoretical study of the factor of merit of porous silicon based optical biosensors[END_REF], the volume of BSA (V BSA ) of 125 nm 3 [START_REF] Flecha | Determination of the molecular size of BSA by fluorescence anisotropy[END_REF] and the BSA molar weight (M mol BSA ) of 66.43 kDa [START_REF] Flecha | Determination of the molecular size of BSA by fluorescence anisotropy[END_REF]. The quantity of BSA in pg/mm² graffed on the internal surface of pore (M BSA ) is equal to Surface sensitivity S surf . depends on the variation of the effective refractive index of the propagated mode, taking into account the variation of the BSA mass per unit of surface (M BSA ) grafted onto the waveguide PSi internal surface. S surf. is defined as [START_REF] Azuelos | Optimization of porous silicon waveguide design for microring resonator sensing applications[END_REF]:

The refractive index of the waveguide confinement layer is assumed not to be affected by the functionalization process because of the presence of the second PSi barrier layer. The effective index of the TM mode of the PSi waveguide has been calculated by Matlab software using the effective refractive index method before and after BSA grafting on the internal surface of the PSi guiding layer. The calculation was carried out for a f BSA value of 0.1% corresponding to a M BSA of 10 pg/mm² in order to get a corresponding wavelenght shift inferior to the ISL of the MR.

A surface sensitivity of 0.06 nm / (pg/mm²) has been estimated which is slightly better than that estimated in a previous study [START_REF] Girault | acetrack micro-resonators based on ridge waveguides made of porous silica[END_REF][START_REF] Azuelos | Optimization of porous silicon waveguide design for microring resonator sensing applications[END_REF] with other porosity of the PSi guiding layer. As the quality factor is also better than those previously obtained in [START_REF] Azuelos | Optimization of porous silicon waveguide design for microring resonator sensing applications[END_REF][START_REF] Girault | ntegrated polymer micro-ring resonators for optical sensing applications[END_REF], a lower limit of detection (LOD) could be obtained with the studied PSi MR. Taking into consideration a minimal shift corresponding to the width at half-height (δλ) of 0.06 nm, and a minimum wavelength resonant shift of δλ /10 [58], a promising LOD of 0.1 pg/mm² could be obtained.

Conclusion

In this paper, the porosity of the guiding and the confinement PSi layers have been determined by taking into consideration the influence of low porosity barrier layers required to fabricate a 4-layer PSi structure. This 4-layer PSi structure consisting of a guiding layer with a well-defined refractive index of 1.57 at 1.55 µm is required to subsequently fabricate a hybrid MR with of a PSi MR and a straight access waveguide made of SU8 polymer with the same refractive index. Two PSi barrier layers fabricated with a current density of 1 mA/cm² and sandwiching the guiding layer in the 4-layer waveguide structure are also necessary for the technological realization.

The presence of a barrier PSi layer influences the porosity and the anodization rate of the guiding and the confinement PSi layers: their porosities are lower than if these layers had been manufactured separately as a single layer and the anodization rate is on the contrary higher. This effect is amplified for higher current densities.

Taking into account the influence of a PSi barrier layer and the porosity calibration results, current densities of J G = 85 mA/cm² and J C = 110mA/cm² have to be applied in the anodization process to obtain a guiding and confinement PSi layer with refractive index of 1.57 and 1.41 respectively.

The good fit of the experimental reflectance spectrum of the 4-layer PSi structure with a theoretical spectrum calculated from the SEM measurements and the targeted refractive indices certifies the validity of the porosity calibration.

Then a 4-layer PSi MR has been fabricated using these current densities. The parameters deduced from the adjustment of the experimental and theoretical MR transmissions are well consistent with those previously simulated from the target indices of 1.57 and 1.41 corresponding to the guiding and confinement PSi layers respectively.

The calibration of both the porosity and anodization rate of PSi layers taking into account the presence of barrier PSi layers is necessary for the future technological realization of the hydride MR that will be based on PSi and SU8 polymer.

Work will continue in our laboratory to focus on the manufacture of the hybrid MR. In parallel, the PSi layers will be functionalized for a specific grafting of molecules for biosensing applications. The calibration method which have been validated in this paper will be used to study the index variations at each step of the functionalization process as was done in reference [START_REF] Lorrain | Functionalization control of porous silicon optical structures using reflectance spectra modeling for bio sensing applications[END_REF]. Preliminary theoretical results of sensitivity for BSA detection of 0.06 nm/(pg/mm²) and a LOD of 0.1 pg/mm² are very promising.

Figure 1 :

 1 Figure 1: (a) Schematic representation of the four PSi layers. (b) Schematic representation of the 4-layer PSi MR after a standard photolithographic process.

Figure 2 :

 2 Figure 2: Example of adjustment of the experimental and calculated spectra (a) for the as prepared porous silicon layer (b).

  figures 4.a, b or c) or after etching of the tops of the layers to keep only one single layer in case of the 2-layer (figure 4.b) or the 4-layer (figure 4.c) PSi structure.

Figure 4 :

 4 Figure 4: SEM cross section micrographs of the PSi layers, anodization rate Ra, porosities P estimated by reflectometry adjustment method in a single layer for an applied current density of 110mA/cm²: (a) in one single layer (b) in a 2-layer PSi structure constituted by the barrier layer (J 1 = 1mA/cm²) and the studied guiding layer (J 2 = 110 mA/cm²) before and after RIE etching to reduce the structure to a single-layer study to determine the porosity P 2 . (c) in a 4layer PSi structure constituted by the barrier layer (J 1 = 1 mA/cm²), a second layer J 2 = 85 mA/cm², another barrier layer (J 3 = J 1 = 1 mA/cm²) and the confinement studied layer (J 4 = 110 mA/cm²) before and after RIE etching to reduce the structure to a single-layer study to determine the porosity P 4 .

Figure 6 :

 6 Figure 6: (a) Experimental and theoretical adjusted spectra of a 4-layer PSi structure. (b) Cross section SEM image of the 4-layer PSi structure.

Figure 7 :

 7 Figure 7: SEM images of the racetrack micro-resonator: top views at different scales: (a) whole racetrack MR, (b) the gap separation between the straigth and the cavity waveguides of the coupling area, (c) cross section of a PSi ridge waveguide, and (d) estimation of the barrier layer thickness at higher magnification.

Figure 8 :

 8 Figure 8: (a) Representation used in FIMMWAVE simulations of the 4-layer PSi waveguide constituted by a guiding layer sandwiched by two barrier layers and a confinement layer. The experimental dimensions have been taken into consideration. (b) FIMMWAVE calculated effective index evolution of the 4-layer PSi waveguide as function of the wavelength.

Figure 9 :

 9 Figure 9: Calculated coupling factor as a function of the gap between the straight waveguide and the cavity respectively for the TE and TM modes for a waveguide width of 1.95 µm, a height of 1.7 µm at 1.55 µm and for the following cavity parameters R = 100 µm and L c = 70 µm.

Figure 10 :

 10 Figure 10: Experimental and theoritical transmission spectra of the fabricated PSi MR and for the TM polarization.

Acknowledgments

This work is funded by Lannion Trégor Community (LTC22), Région de Bretagne. Technological processing of ridge waveguides was performed in the CCLO-Renatech clean room facilities of Institut Foton. Equipment funding of Institut Foton and CCLO was partly provided by the CPER Sophie


M H Noamane

] S Ferlay
email: ferlay@unistra.fr

R Abidi

] N Kyritsakas

M W Hosseini
email: hosseini@unistra.fr

X = Ch

Z = Oh

S Ferlay

N Kyritsakas

on ortho-imino-or ortho-amino-methylpyridyl appended p-tert-butylcalix[4]arene or p-tert-butyl-thiacalix[4]arene in 1,3-alternate conformation

Keywords: Calix[4]arene, Thialix[4]arene, tetranuclear complexes, Silver, Argentophilic

Discrete binuclear and tetranuclear silver complexes based

Introduction

Multivalent ligands are of interest for the formation of multinuclear metal complexes. For the design of such complexing agents, calix [4]arene (CA, 1, X = CH2, Z = OH), 1 thiacalix [4]arene (TCA, 2, X = S, Z = OH), 2 and its sulfonyl (Z = OH, X = SO, 3) 3 or sulfinyl (Z = OH, X = SO2, 4) 4 derivatives are backbones of interest (Scheme 1). Indeed, for steric reasons this class of molecule can not be planar and adopts four limit conformations (cone, partial cone, 1,2-Alternate and 1, 3-Alternate). For all conformers, the nature of the substituent Y in the para position of the phenolic rings (Scheme 1) may be varied.

Finally, using the reactivity of the phenolic OH group under basic conditions towards electrophiles, the backbone may be functionalized with a variety of groups. Over the past three decades, calix [4]arene and thiacalix [4]arene derivatives have been widely exploited in several areas of supramolecular chemistry 5,6 or catalysis, 7 for example.

Scheme 1: Generic representation of calix [4]arene derivatives 1-4 showing all possible modification sites (Y (upper rim), Z (lower rim) and X (bridge)).

Examples of nanometric multinuclear metal complexes based on calix [4]arene or thiacalix [4]arene derivatives in different conformations, have been well documented. 8,9,10 Among the four possible conformations adopted by calix [4]arene backbone, the 1,3-Alternate conformer is particularly well suited for the design of multivalent ligands. Indeed, the latter allows to position in an alternate fashion up to four interaction sites forming two distinct coordinating pockets above and below the mean plane of the macrocyclic unit. Multinuclear silver complexes with short Ag + -Ag + distances are of particular interest since, owing to argentophilic interactions, they emit light upon excitation, in the solid state and also in solution. 11 Here we report on a series of four new ligands 5-8 based on either p-tert-butylcalix [4]arene 1 or p-tert-butylthiacalix [4]arene 2 in 1,3-Alternate conformation (Scheme 1) bearing four orthoimino (ligands 5 and 6) or ortho-amino (ligands 7 and 8) chelating units and their propensity to form binuclear or tetranuclear silver complexes (Figures 1 and2). [4]arene 1 or p-tert-butylthiacalix [4]arene 2 in 1,3-Alternate conformation.

Results and Discussion

Design of ligands 5-8

With aim of preparing binuclear (Figure 2a and2b) and tetranuclear silver complexes (Figure 2c and2d) with short Ag + -Ag + distance, ligands 5-8 based on calix [4]arene CA (compounds 5 and 6 ) and thiacalix [4]arene TCA (compounds 7 and 8) macrocyclic backbones in 1,3-Alternate conformation were designed (Figure 1). The backbone is equipped with four ortho-imino-methylpyridyl (ligands 5 and 6) or ortho-aminomethylpyridyl (ligands 7 and 8) chelating units. Ligands based on ortho-iminomethylpyridyl coordinating group and their transition metal complexes have been scarcely documented in the literature. 12 Calixarene derivatives involved in complexes with silver cations have been widely described in the literature. 8,13 In the present work, the coordinating moieties are connected to the backbone through a propyl fragments using ether junctions. The choice of the pyridyl unit is based on its ability to bind metal cations such as Ag + or Hg 2+ . 14 The design principle discussed above should, on one hand, lead to the formation of binuclear species (Figure 2a and2b) through independent binding of the cation by the two chelates located on each face of the ligand and, on the other hand, to the formation of tetranuclear complexes resulting from binding of two silver cations by each coordinating pockets located above and below the macrocyclic backbone (Figure 2c and2d). Although the coordination mode for the binuclear complexes is rather classical and previously described, to the best of our knowledge, the coordination of two silver cations with argentophilic interactions within each coordinating pocket is unusual and has not been reported

Synthesis of ligands 5-8

The synthesis of the ligands 5-8 (Figure 1) was achieved using a stepwise strategy. Starting with either calix [4]arene derivative 1 or thiacalix [4]arene derivative 2, their condensation with N- (3bromopropyl)phthalimide 13 (Scheme 2) in the presence of Cs2CO3 afforded the amino-protected compounds 9 and 10 in 1,3-A conformation respectively (see experimental section).

Scheme 2: Starting compounds 1 and 2 and precursors 9-14 used for the synthesis of ligands 5-8.

The synthesis of 9 has been previously investigated. 15 It was reported that the formation of the cone conformer in high yield (83%) was favoured by the stepwise use of (i) K2CO3/acetonitrile for disubstitution and NaH/DMF for tetrasubstitution 15c or (ii) NaH/DMF (yield 55 %). 15b, 16 In our hand, the combination Cs2CO3 and DMF afforded the intermediate 9 in 1,3-A conformation in a relatively good yield (55%). The phthalimido derivative 10 in cone and 1,3-A conformation 17 18 was also reported with 68% yield for the latter. The deprotection of phthalimido derivatives 9 and 10 was achieved by treatment with hydrazine. 19 The amino compounds 11 and 12 were obtained in 98% and 97% yields respectively. The imino compounds 5 and 6 were obtained in 63% and 78% yields respectively upon condensation of 2-Pyridinecarboxaldehyde 14 with the amino derivatives 11 and 12 in DMF/EtOH (scheme 2). Compounds 5 and 6 are unstable under acidic conditions. Finally, the ortho-aminomethylpyridine ligands 7 and 8 were obtained in 84% and 85% yields respectively upon reduction of compounds 5 and 6 using NaBH4 in MeOH (or EtOH). All four ligands (5-8), in addition to usual characterisation methods, were studied in solution by 1 H-and 13 C-NMR spectroscopy. As expected, the 1 H-NMR study revealed that the imino N=CH group signals were downfield shifted (8.23 and 8.24 ppm for 5 and 6 respectively) with respect to signals corresponding to the amino HN-CH2 unit (3.83 and 3.78 ppm for 7 and 8 respectively) (see figure S1 in Supporting Information). The imino ligands 6 based on the TCA backbone and the amino ligand 7 based on the CA platform have been also characterized in the solid state by X-ray diffraction on single crystals.

Solid-state description of ligands 6 and 7

After many attempts, we were only able to grow single crystals for compounds 6 and 7. Crystals of compounds 6 were obtained upon CH3CN vapours diffusion into CHCl3 solutions of 6, whereas crystals of 7 were obtained upon Hexane vapours diffusion into a CHCl3 solution of 7. The structural investigations of ligands 6 and 7 were carried out by X-ray diffraction methods on single crystals (Crystallographic table S1 (Supporting Information) and Figure 3). In agreement with solution NMR studies, both compounds 6 and 7 adopt the expected 1,3-A conformation in the crystalline phase. Compound 6 and 7 crystallise in the P21/n and P2/n space groups respectively. Whereas crystals of compounds 6 contain CHCl3 molecules with no specific interactions with the ligand, for ligand 7, no solvent molecule is found in the crystal. For both compounds 6 and 7, metrics for the macrocyclic part are close to those observed for the parent CA and TCA and will not be detailed here. Relevant distances and angles are gathered in table 1. For compounds 6, one of the four tert-butyl groups was found to be disordered, the same holds for one of the four imino-pyridyl appended group. For the imino derivative 6, the C=N distances are in the 1.203 (7) -1.340(10) Å range (see table 1) with the CNC angles ranging from 108.0(7)° to 119.2(5)°. For the amino derivative 7, the HC-NH distances are in the 1.409(5)Å -1.435(6)Å range with CNC angles ranging from 111.8(6)° to 113.3(4)°. These bond distances and angles confirm the presence of sp 3 nitrogen atoms. Owing to the presence of propyl linker connecting the imino-or amino-pyridyl units to the macrocyclic calix [4]arene backbone, no rational trend could be spotted for the position and orientation of pyridyl groups (see Figure 3). The binding propensity of all four multivalent ligands 5-8 towards silver cation, in particular the formation of tetranuclear species, was investigated both in the solid state and in solution.

Silver complexes in the solid state After many attempts to prepare crystalline species upon combining ligands 5-8, with different silver salts (AgX, X = BF4 -, PF6 -, SbF6 -, AsF6 -, AsF6 -, NO3 -), only for ligands 6, 7 and 8 crystalline complexes have been obtained (see experimental section). All three ligands 6, 7 and 8, when combined with Ag + cation with Metal/Ligand (M/L) ratio of 2 or 3, form, independent of the nature of the anion, binuclear complexes (M2L, L = 6, 7 or 8) in the solid state. Interestingly, in the case of ligand 7, for M/L ratio greater than 4, tetranuclear species have been observed in the solid-state with two different counter-anions (BF4 -or NO3 -).

For all ligands 5-8, owing to the remote position of S atoms, the latter do not participate in the binding of silver cation. Since metrics associated with the calix backbones for the binuclear and tetranuclear complexes was found to be close to those observed for the parent compounds 6 and 7, they will not be discussed in detail here.

Binuclear silver complexes

As stated above, the role played by the anion on the formation of binuclear complexes was studied by using different Ag + salts with weakly (BF4 -, AsF6 -, SbF6 -, PF6 -) to strongly (NO3 -) coordinating anions. Furthermore, the role of the M/L ratio (2:1 or 3:1) on the stoichiometry of the complex was also investigated. The unit cell of all binuclear compounds 6-(AgX)2 (X = BF4 -, AsF6 -, SbF6 -and NO3 -) are isometric and crystallises in the orthorhombic system (space group Pccn for X = BF4 -, AsF6 -and NO3 -and Pna21 for SbF6 -) (table S2, Supporting Information). 20 . For the imino binuclear compounds 6-(AgX)2 (X = BF4 -, AsF6 -, SbF6 -and NO3 -), the C=N distances are in the 1.241 (16 -1.334(10) Å range with the CNC angles varying between 114.9(6)° and 120.1(13) ° (table 2).

Ortho-iminopyridine

7-(AgX)2 (X = BF4

For the amino binuclear compounds 8-(AgX)2 (X = AsF6 -and PF6 -), 7-(AgX)2 (X = BF4 -and PF6 -), C-N distances are in the 1.443(13) -1.537(19) Å range with CNC angles varying between 107.8(4)° and 115.8(9)° (table 3). For all the binuclear compounds 6-(AgX)2 (X = BF4 -, AsF6 -, SbF6 - and NO3 -), 7-(AgX)2 (X = BF4 -and PF6 -) and 8-(AgX)2 (X = AsF6 - and PF6 -), the metal centre is tetra-coordinated and the environment around the silver cations is similar and composed of 4 nitrogen atoms, two of them belonging to the amino (or imino) coordinating groups and two of the pyridyl type (Figure 3), for relevant distances see tables 2 and 3. The dAg-N varies between 2.197(6) and 2.499( 4 Owing to the distance between the two binding pockets composed of a N4 set of coordinating sites located above and below the mean plane of the ligand and the absence of electronic communication between them, they behave independently and each binds two silver cations leading thus to the tetranuclear silver complex 7-(AgBF4)4 and 7-(AgNO3)4 differing by the nature of the anion (BF4 -or NO3 -) (Figure 5). For the tetranuclear species, the set of two Ag + cations, located on the same side of the backbone, may be described as internal and external metal centres (Figures 1 and5). Interestingly, due to the proper positioning of the two chelating orthoaminomethylpyridine units on each side of the macrocyclic backbone, a rather short Ag-Ag distance of 2.8928( 7 As stated above, for the tetranuclear silver complex, two types of silver cations are present on each side of the ligand. The internal cation is di-coordinated and its coordination sphere is composed of two N atoms belonging to two amino units located on the same side of the backbone. The Ag-N distances are 2.173( 3 4) showing a slightly distorted linear coordination geometry around the internal silver cation.

The external silver cation is tetracoordinated adopting a distorted tetrahedral coordination geometry and is surrounded by a N2O2 set of coordinating atoms. The environment around the cation is composed of two nitrogen atoms belonging to two pyridyl units located on the same face of the ligand and two oxygen atoms either belonging to two H2O molecules in 7-(AgBF4)4 or to two nitrate anions in 7-(AgNO3)4 (Figure 5). For distances and angles see table 4.

Solid state emission

The rather short Ag-Ag distance of 2.8928( 7) Å in 7-(AgBF4)4, leads to strong d 10 -d 10 interactions 11 between vicinal silver atoms on each face of the complex. The emission due to argentophilic interaction was investigated using polycrystalline samples (Figure 6). The solid-state reflectance spectra recorded at 298K displays two major bands at ca 295 nm and 450 nm (Figure 6

Behaviour in solution

The binding of silver cation by the ligand 7 in solution was investigated. The complexation process was monitored by 1 H-NMR spectroscopy. Upon addition of AgBF4, in CD3CN, to a CD3CN solution of the ligand 7 at C = 8.05 10 -3 mol.L -1 signals corresponding to the pyridyl moieties, CH2NH and the CH2 bridging the aryl groups of the calix backbone were found to be shifted (Figure 7). The titration experiment in CD3CN consisting in addition of increasing amounts of the silver salt to a solution of 7 clearly showed the formation of the binuclear complex 7-(AgBF4)2. Indeed, after reaching the 2:1 M/L ratio, further addition of the silver salt had no effect on the displacement of signals. In marked contrast with the solid state structural investigations discussed above, the solution study revealed that, even in the presence of 5 equivalents of silver cation, no trace of the tetranuclear silver complex could be detected.

Conclusions

four new multivalent ligands 5-8 derived from calix [4]arene and thiacalix [4]arene backbones in 1,3-Alternate bearing orthoamino-and ortho-imino-pyridine chelating sites have been prepared and two of them (ligands 6 and 7) have been structurally characterized in the solid state by X-ray diffraction methods. Owing to the imposed 1,3-Alternate conformation of the backbone, they offer two coordinating pockets composed of two sets of chelates located above and below the mean place of the macrocyclic framework. Among the four unprecedented ligands, for compounds 6-8, the two coordinating pockets behave independently and form binuclear silver complexes independent on the nature of the anion associated with Ag + cation. This propensity was established both in the solid state and in solution using 1 H-NMR spectroscopy. Interestingly, ligand 7, based on four ortho-amino-pyridyl units, in addition to binuclear silver complexes, forms in the solid state tetranuclear silver complexes 7-(AgBF4)4, and 7-(AgNO3)4 in presence of two different auxiliary ligands (H2O or NO3 -). In the solid state, the tetranuclear complex 7-(AgBF4)4, due to a rather short Ag-Ag distance of ca 2.89 Å, displays argentophilic interactions leading, at 298 K, to an emission band at ca 425 nm (lemm = 295 nm). No such an emission was detected for the binuclear species. Finally, all attempts to generate the tetranuclear complexes in solution (CH3CN) failed. Combinations of the above mentioned ligands with other metal cations is currently under investigation.

Experimental Section

Materials and methods

1 H-NMR and 13 C-NMR spectra were recorded at room temperature on a Bruker (300, 400 or 500 MHz) NMR spectrometer.

Mass spectra (ESI) were obtained on a MicroTOF-Q (BRÜKER) equipped with an electrospray source.

Microanalyses were performed by the Service de Microanalyses de la Fédération de Recherche Chimie, Université de Strasbourg, Strasbourg, France.

Melting points were measured in capillar on a Stuart Scientific Melting Point SMP-1 apparatus.

Reflectance spectra in the solid state were recorded on a Perkin-Elmer Lambda 650 spectrometer.

Luminescence spectra in the solid state were recorded on a Perkin-Elmer LS55 spectrophotometer.

Single-Crystal Studies

Data were collected at 173(2) K on a Bruker Apex-II-CCD Diffractometer equipped with an Oxford Cryosystem liquid N2 device, using graphitemonochromated Mo-Kα (l= 0.71073 Å) radiation. For all the structures, diffraction data were corrected for absorption. Structures were solved using SHELXS-97 and refined by full matrix least-squares on F2 using SHELXL-97. The hydrogen atoms were introduced at calculated positions and not refined (riding model). [START_REF] Sheldrick | Program for Crystal Structure Solution[END_REF] They can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/datarequest/cif. CCDC: 1538265-1538276.

Synthetic procedures

General: All reagents were purchased from commercial sources and used without further purification. p-tert-butylcalix [4]arene 1 is commercial product and p-tert-butylthiacalix [4]arene 2 2 was prepared according to the literature procedures. The synthesis of 10 has already been reported. 17

All the reactions were performed under a N2 atmosphere.

Compound 9

A mixture of p-tert-butylcalix [4]arene 1 (1.50 g, 2.31 mmol) and Cs2CO3 (7.5 g, 23.11 mmol) in DMF (80 mL) was stirred at R.T. for 2 hours. N- (3bromopropyl)phthalimide 13 (6.19 g, 23.11 mmol) was added to the mixture and stirring was further continued for 3 days at 50 °C during.

After cooling to R.T., the reaction mixture was filtrated. The filtrate was washed three times with CHCl3 (3x50 mL). Washes were combined and evaporated. The yellow oil thus obtained was dissolved in 50 mL of CHCl3 and washed twice with HCl (1N, 2x50 mL). After evaporation, the residue was recrystallised twice from MeOH (50 mL) affording the pure product 9 in 1,3-A conformation as a white solid (1.77 g, 55%). mp = 256 °C. 1 H-NMR (500 MHz, CDCl3, 25 °C): δ(ppm) = 1.17 (36H, s, -C(CH3)3), 1.69 (8H, m, -CH2-CH2-CH2-), 3.47 (8H, t, -Phth-CH2-), 3.63 (8H, t, Ar-O-CH2-), 3.69 (8H, s, Ar-CH2-Ar), 6.95 (8H, s, Ar-H), 7.70 (8H, m, Ar-H), 7.82 (8H, m, Ar-H). 13 C-NMR (125 MHz, CDCl3, 25 °C): δ(ppm) = 29. 4, 31.5, 33.7, 35.2, 38.8, 68.6, 123.1, 126.3, 132.1, 132.9, 133.8, 143.7, 154.4, 168.1. Anal. Calcd. for C88H92N4O12: C, 75.62%; H, 6.63%; N, 4.01%; Found: C, 75.86%; H, 6.56%; N, 4.01%.

Compound 11

The synthesis was adapted from an already published procedure. 19 A mixture of 9 (2.00 g, 1.43 mmol) and hydrazine (14.1 mL, 286 mmol) in 70 mL of EtOH was stirred and refluxed for 24h. After cooling to at RT, 150 mL of distilled H2O was added and the reaction mixture was filtrated. The white solid thus obtained was washed three times with Et2O (3x30 mL). The white solid was dried for 4h under vacuum at 100 °C, affording the pure product 11 in 1,3-A conformation (1.22 g, 98%). mp = 248 °C.

1 H-NMR (500 MHz, CDCl3, 25 °C): δ(ppm) = 1.27 (8H, m, -CH2-CH2-CH2-), 1.28 (36H, s, -C(CH3)3), 2.48 (8H, t, NH2-CH2-), 3.43 (8H, t, Ar-O-CH2-), 3.79 (8H, s, Ar-CH2-Ar), 6.97 (8H, s, Ar-H). 13 C-NMR (125 MHz, CDCl3, 25 °C): δ(ppm) = 31. 6, 33.5, 33.9, 39.2, 39.6, 68.7, 125.9, 133, 143.6, 154.9. Anal. Calcd. for C56H84N4O4: C, 76.67%; H, 9.65%; N, 6.39% ; Found: C, 76.32%; H, 9.66%; N, 6.38%.

Compound 12

The synthesis was adapted from an already published procedure. 19 A mixture of compound 10 (2.00 g, 1.36 mmol) and hydrazine (13.3 mL, 272 mmol) in 70 mL of a THF/EtOH (1/1) mixture was stirred and refluxed for 24h. After cooling to room temperature, 150 mL of distilled H2O was added and the reaction mixture was filtrated. The white solid thus obtained was washed three times with Et2O (3x30 mL). The white solid was dried for 4h under vacuum at 100 °C, affording the pure product 12 in 1,3-A conformation (1.25 g, 97%). mp = 274 °C. 1 H-NMR (500 MHz, CDCl3, 25 °C): δ(ppm) = 1.23 (8H, m, -CH2-CH2-CH2-), 1.28 (36H, s, -C(CH3)3), 2.44 (8H, t, NH2-CH2-), 3.90 (8H, t, Ar-O-CH2-), 7.33 (8H, s, Ar-H). 13 C-NMR (125 MHz, CDCl3, 25 °C): δ(ppm) = 31. 3, 33.3, 34.3, 39.4, 67.1, 127.8, 128.1, 145.5, 157 3, 31.6, 33.9, 58.4, 68.3, 120.8, 124.5, 125.7, 133, 136.4, 143.8, 149.2, 154.6, 154.8, 161.3 λmax (nm)/ ε (mol -1 Lcm -1 )= 238(52064). IR (cm -1 ): νC=N: 1651.

Compound 6

2-Pyridinecarboxaldehyde 14 (560 µL, 5.84 mmol) and compound 12 (0.7 g, 0.73 mmol) were dissolved in 40 mL of a EtOH/DMF (1/1) mixture, and stirred at room temperature during 2 days. 100 mL of CH3CN was added and the white precipitate thus formed was filtrated and washed several times with petroleum ether (100 mL). The filtrate was placed during one week in a refrigerator to complete the precipitation. The solid was filtered and combined with the first batch, affording the desired compound 6 in 1,3-A conformation as a white solid (0.75 g, 78 %). mp = 182 °C. 1 H-NMR (300 MHz, CDCl3, 25 °C): δ(ppm) = 1.20 (36H, s, -C(CH3)3), 1.44 (8H, m, J = 7.5 Hz, -CH2-CH2-CH2-), 3.45 (8H, t, J = 6.5 Hz, =N-CH2-), 4.00 (8H, t, J = 7.5 Hz, -O-CH2-), 7.28 (4H, m, J = 5.5 Hz, Pyr-H), 7.33 (8H, s, Ar-H), 7.69 (4H, t, J = 7.5 Hz, Pyr-H), 8.00 (4H, d, J = 7.7 Hz, Pyr-H), 8.24 (4H, s, -CH=N-), 8.59 (4H, d, J = 5.0 Hz, Pyr-H). 13 C-NMR (125 MHz, CDCl3, 25 °C): δ(ppm) = 29.9, 31. 3, 31.4, 34.3, 58.3, 66.8, 120.8, 124.5, 127.6, 128, 136.4, 145.6, 149.2, 154.8, 156.8, 161.5

Compound 7

NaBH4 (0.31g, 8.1 mmol) and 3 (0.5 g, 0.4 mmol) were dissolved in 40 mL of MeOH and refluxed during 2 days. 50 mL of water was added carefully and the product was extracted three times with CHCl3 (3x50 mL). The organic phases were combined and then evaporated, affording the desired compound 7 in 1,3-A conformation as a white solid (0.42 g,

%

). mp = 122 °C. 5, 31.7, 33.9, 38.7, 46.7, 55.4, 69.4, 121.8, 122.1, 126.3, 133, 136.4, 143.4, 149.2, 154.6, 160.4

Compound 8

NaBH4 (0.12g, 3 mmol) and compound 6 (0.2 g, 0.15 mmol) were dissolved in 30 mL of EtOH and refluxed during 2 days before it was allowed to cool to room temperature. 50 mL of water was added carefully and the product was extracted three times with CHCl3 (3x50 mL). The organic phases were combined and evaporated, affording the desired compound 8 in 1,3-A conformation as a white solid (0.17 g, 85 %). mp = 172 °C. 7, 31.3, 34.2, 46.4, 55.4, 67.3, 121.7, 121.9, 136.3, 145.5, 149.1, 157.1, 160.3

Crystallisation conditions

Compound 6: A CHCl3 (0.5 mL) solution of compound 6 (5 mg, 3.82 mol) was placed in a closed beaker containing acetonitrile. Slow vapour diffusion of acetonitrile into the solution of the ligand 6 produced, after several days, colourless crystals suitable for X-ray diffraction (Formula: 2(C76H88N8O4S4)•CHCl3).

Compound 7: A solution in CHCl3 (0.5 mL) of compound 7 (5 mg, 4.03 mol) was placed in a closed beaker containing hexane. Slow vapour diffusion of hexane into the solution of 7 produced colourless, after several days, crystals suitable for X-ray diffraction (Formula: C80H104N8O4).

6-(AgSbF6

)2 : In a crystallization tube (20 x 4 mm), a solution of compound 6 (3.00 mg, 2.29 mol) in CHCl3 (1 mL) was layered with a CHCl3/ iso-PrOH (1/1) mixture (0.1 mL). A solution of AgSbF6 (1.70 mg; 4.95 mol) in MeOH (1 mL) was carefully added. At room temperature, slow diffusion in the dark produced, after several days, colourless crystals suitable for X-ray diffraction (3.39 mg, 63 % yield). Anal. Calcd. for C76H88N8O4S4•2(AgSbF6)•(CHCl3): C, 43.78%; H, 2.25%; N, 5.30%. Found: C, 43.42%; H, 2.20%; N, 5.26%.

6-(AgAsF6

)2 : In a crystallization tube (20 x 4 mm), a solution of 6 (3.00 mg; 2.29 mol) in CHCl3 (1 mL) was layered with a CHCl3/iso-PrOH (1/1) mixture (0.1 mL). A solution of AgAsF6 (2.02 mg; 6.80 mol) in MeOH (1 mL) was carefully added. At room temperature, slow diffusion in the dark produced, after several days, colourless crystals suitable for X-ray diffraction (2.60 mg, 60 % yield). Anal. Calcd. for C76H88N8O4S4•2(AgAsF6)•2(H2O): C, 47.16%; H, 4.79%; N, 5.79%. Found: C, 47.06%; H, 4.56%; N, 5.76%.

6-(AgBF4

)2 : In a crystallization tube (20 x 4 mm), a solution of the ligand 6 (3.00 mg; 2.29 mol) in CHCl3 (1 mL) was layered with a CHCl3/ iso-PrOH (1/1) mixture (0.1 mL). A solution of AgBF4 (1.30 mg; 6.67 mol) in MeOH (1 mL) was carefully added. At room temperature, slow diffusion in the dark produced, after several days, colourless crystals suitable for X-ray diffraction (2.00 mg, 51 % yield). Anal. Calcd. for C76H88N8O4S4•2(AgBF4)•2(H2O): C, 52.73%; H, 5.36%; N, 6.47%. Found: C, 52.65%; H, 5.16%; N, 6.50%.

6-(AgNO3

)2 : In a crystallization tube (20 x 4 mm), a solution of compound 6 (3.00 mg; 2.29 mol) in CHCl3 (1 mL) was layered with a CHCl3/ iso-PrOH (1/1) mixture (0.1 mL). A solution of AgNO3 (1.00 mg; 6.9 mol) in MeOH (1 mL) was carefully added. At room temperature, slow diffusion in the dark produced, after several days, colourless crystals suitable for X-ray diffraction (2.00 mg, 51 % yield). Anal. Calcd. for C76H88N8O4S4•2(AgNO3): C, 55.47%; H, 5.39%; N, 8.51%. Found: C, 55.30%; H, 5.44%; N, 8.41%.

8-(AgAsF6

)2 : In a flask, 3.0 mg of the ligand 8 (2.19 mol) dissolved in 0.5 mL of CH2Cl2 was mixed with 2.00 mg of AgAsF6 (4.74 mol) dissolved in 0.5 mL of MeOH. Slow vapour diffusion of Et2O produced, after several days, colourless crystals suitable for X-ray diffraction studies (2.70 mg, 66 % yield). Anal. Calcd. For C76H96N8O4S4•2(AgAsF6)•H2O: C, 47.41%; H, 5.13%; N, 5.82%; Found: C, 47.38%; H, 5.08%; N, 5.62%.

8-(AgPF6

)2 : In a flask, 3.0 mg of the ligand 8 (2.19 mol) dissolved in 0.5 mL of CH2Cl2 was mixed with 1.20 mg of AgPF6 (6.57 mol) dissolved in 0.5 mL of MeOH. Slow vapour diffusion of Et2O produced, after several days, colourless crystals suitable for X-ray diffraction studies (1.80 mg, 49 % yield). Anal. Calcd. For C76H96N8O4S4•2(AgPF6): C, 50.17%; H, 5.32%; N, 6.16%; Found: C, 49.86%; H, 5.28%; N, 6.08%.

7-(AgBF4

)2 : In a flask, 3.0 mg of the ligand 7 (2.41 mol) dissolved in 0.5 mL of CH2Cl2 was mixed with 1.40 mg of AgBF4 (7.25 mol) dissolved in 0.5 mL of MeOH. Slow vapour diffusion of Et2O produced, after several days, colourless crystals suitable for X-ray diffraction studies (2.20 mg, 52 % yield). Anal. Calcd. For C80H104N8O4•2(AgBF4)•2(CH2Cl2): C, 54.69%; H, 6.04%; N, 6.22%; Found: C, 53.16%; H, 6.13%; N, 6.35%.

7-(AgPF6

)2 : In a flask, 3.0 mg of compound 7 (2.41 mol) dissolved in 0.5 mL of CH2Cl2 was mixed with 1.20 mg of AgBF4 (6.16 mol) dissolved in 0.5 mL of MeOH. Slow vapour diffusion of Et2O produced, after several days, colourless crystals suitable for X-ray diffraction studies (2.20 mg, 52 % yield). Anal. Calcd. For C80H104N8O4•2(AgPF6)•2 (CH3OH): C, 54.37%; H, 6.23%; N, 6.18%; Found: C, 53.86%; H, 6.33%; N, 6.30%.

7-(AgNO3)4

: In a flask, 3.0 mg of ligand 7 (2.41 mol) dissolved in 0.5 mL of CHCl3 was mixed with 1.70 mg of AgNO3 (9.67 mol) dissolved in 0.5 mL of CH3CN. Slow vapour diffusion of Et2O produced, after several days, colourless crystals suitable for X-ray diffraction studies (2.7 mg, 50 % yield). Anal. Calcd. For C80H104N8O4•4(AgNO3) •2(C2H5OH): C, 51.07%; H, 6.04%; N, 8.12%; Found: C, 51.19%; H, 5.97%; N, 7.95%.

7-(AgBF4)4

: In a flask, 3.0 mg of ligand 7 (2.41 mol) dissolved in 0.5 mL of CH3CN was mixed with 1.90 mg of AgBF4 (9.75 mol) dissolved in 0.5 mL of CH3CN/H2O (9/1) mixture. Slow vapour diffusion of Et2O produced, after several days, colourless crystals suitable for X-ray diffraction studies (3.

Figure 1 :

 1 Figure1: ortho-imino-and ortho-amino ligands 5-8 based on either p-tertbutylcalix[4]arene 1 or p-tert-butylthiacalix[4]arene 2 in 1,3-Alternate conformation.

Figure 2 :

 2 Figure 2: Schematic representations of possible binuclear (a and b) and tetranuclear (c and d) silver complexes by ligands 5-8.

6 7 Figure 3 :

 73 Figure 3: The solid-state structures of 6 (left) and 7 (right) showing the 1,3-A conformation of both ligands. H atoms and solvent molecules in the case of compound 6, are not presented for clarity. For 6, disordered tert-butyl groups and imino-pyridine group are not presented. For bond distances and angles see text.

Figure 4 :

 4 Figure 4: Solid state structures of binuclear complexes 6-(AgAsF6)2, 7-(AgBF4)2 and 8-(AgPF6)2 formed by combination of the organic tectons 6, 7 and 8 with AgX salts. H atoms, anions and, solvent molecules, when present, are not presented for clarity. For bond angles and distances see text and tables.

Table 4 :

 4 useful angles and distances for the tetranuclear compounds 7-(AgX)4 (X = BF4 -and NO3 -). am and py indicate the localization of the N atom on either amino or pyridyl units.

Figure 5 :

 5 Figure 5: Solid state structure of tetranuclear complexes 7-(AgBF4)4 and 7-(AgNO3)4 formed by combination of the organic ligand 7 with AgBF4 and AgNO3 respectively. H atoms, solvent molecules and anions in the case of 7-(AgBF4)4 are not presented for clarity. For bond angles and distances see text.

  The NAgN angles are 177.80(19)° and 175.4(17)° and NAgAg angles are 91.10(10)°, 90.90(13) and 93.64(12)° (table

Figure 6 :

 6 Figure 6: Solid state spectra recorded on a polycrystalline sample at 298K a) reflectance spectra and b) excitation (black, lemm = 425 nm) and emission (blue, lexc = 295 nm) spectra for the tetranuclear complex 7-(AgBF4)4.

Figure 7 :

 7 Figure 7: Pyr-H, Ar-CH2-Ar and CH2-Pyr proton shift changes of the 1 H-NMR spectra (bottom) of 7 (top) with upon addition of increasing amount of AgBF4. (RM/L = Concentration of metal/concentration of ligand) C = 8.05 10 -3 mol.L -1

  1 H-NMR (300 MHz, CDCl3, 25 °C): δ(ppm) = 1.22 (36H, s, -C(CH3)3), 1.51 (8H, m, J = 7.0 Hz, -CH2-CH2-CH2-), 2.55 (8H, t, J = 7.0 Hz, -CH2-CH2-NH-), 3.46 (8H, t, J = 7.5 Hz, -O-CH2-), 3.69 (8H, s, Ar-CH2-Ar), 3.83 (8H, s, Pyr-CH2-), 6.93 (8H, s, Ar-H), 7.11 (4H, t, J = 5.5 Hz, Pyr-H), 7.28 (4H, d, J = 7.5 Hz, Pyr-H), 7.59 (4H, m, J = 7.5 Hz, Pyr-H), 8.50 (4H, d, J = 4.5 Hz, Pyr-H). 13 C-NMR (125 MHz, CDCl3, 25 °C): δ(ppm) = 30.

  1 H-NMR (300 MHz, CDCl3, 25 °C): δ(ppm) = 1.22 (36H, s, -C(CH3)3), 1.29 (8H, m, J = 7.0 Hz, -CH2-CH2-CH2-), 2.48 (8H, t, J = 7.0 Hz, -CH2-CH2-NH-), 3.78 (8H, s, -NH-CH2-), 3.91 (8H, t, J = 7.5 Hz, -O-CH2-), 7.09 (4H, m, J = 5.0 Hz, Py-H), 7.27 (4H, d, J = 7.5 Hz, Py-H), 7.30 (8H, s, Ar-H), 7.57 (4H, J = 5.5 Hz, m, Py-H), 8.48 (4H, d, J = 4.5 Hz, Py-H). 13 C-NMR (125 MHz, CDCl3, 25 °C): δ(ppm) = 29.

Table 1 :

 1 Useful angles and distances in 6 and 7.

		6	7
	d-(CAr-S) (Å)	1.760(5)-1.776(4)	-
	d-(CAr-C) (Å)	-	1.511(5)-1.516(5)
	d-(O -	1.360(5)	1.388(4)-

Table 2 :

 2 useful angles and distances for the imino binuclear compounds 6-(AgX)2 (X = BF4 -, AsF6 -, SbF6 -and NO3 -). im and py indicate the localization of the N atom on either imino or pyridyl units.

		6-(AgSbF6)2	6-(AgAsF6)2	6-(AgBF4)2	6-(AgNO3)2
	C=N	1.241(16)	1.255(7)	1.249(7)	1.260(8)
	(imino)	1.256(12)	1.275(9)	1.259(8)	1.334(10)
		1.294(13)

Table 3 :

 3 useful angles and distances for the amino binuclear compounds 7-(AgX2) (X= BF4 -and PF6 -) and 8-(AgX)2 (X = AsF6 -and PF6 -). am and py indicate the localization of the N atom on either amino or pyridyl units.

		7-(AgBF4)2	7-(AgPF6)2	8-(AgAsF6)2	8-(AgPF6)2
		1.465(7)
	C-N	1.481(7)	1.456(10)	1.443(13)	1.435(8)
	(amino)	1.488(6)	1.482(7)	1.537(19)	1.443(13)
		1.490(7)
		107.8(4)
	CNC	110.8(4)	111.0(5)	115.2(12)	109.5(10)
	(amino)	110.9(4)	111.4(6)	115.8(9)	110.9(5)
		111.0(4)
		2.273(4)
		(am)
		2.273(5)			2.331(6)
		(am)	2.307(6) (py)	2.299(8)	(am)
		2.281(4)	2.350(6) (py)	(am)	2.284(11)
	Ag-N	(am) 2.320(5)	2.355(6) (am)	2.359(12) (am)	(am) 2.403(5)
		(am)	2.358(5)	2.402(7) (py)	(py)
		2.366(4) (py)	(am)	2.468(6) (py)	2.449(16)
		2.449(4) (py)			(py)
		2.466(5) (py)
		2.499(4) (py)
	NAgN	73.52(15)-161.32(14)	74.45(19)-144.32(18)	73.9(3)-169.6(4)	68.5(8)-168.2(2)

  AgBF4)•6(H2O): C, 45.14 %; H, 5.49%; N, 5.26%; Found: C, 44.80%; H, 5.40%; N, 5.24%.

								C80H104N8O4•4(
	60	mg,	71	%	yield).	Anal.	Calcd.	For

Acknowledgements

We thank the University of Strasbourg, the C.N.R.S, the International centre for Frontier Research in Chemistry (icFRC), the Labex CSC (ANR-10-LABX-0026 CSC) within the Investissement d'Avenir program ANR-10-IDEX-0002-02, the Institut Universitaire de France, the Ministère de l'Enseignement Supérieur et de la Recherche for financial support and the Tunisian government for a PhD fellowship to M. H. N.

Entry for the Table of Contents

FULL PAPER

Formation of tetranuclear silver complexes in the solid state with short Ag-Ag distance displaying argentophilic interactions.

Supramolecular chemistry, Calixarene

Discrete binuclear and tetranuclear silver complexes based on orthoimino-or ortho-amino-methylpyridyl appended p-tert-butyl-calix[4]arene or p-tert-butyl-thiacalix[4]arene in 1,3alternate conformation