transition temperature, in contrast with metal/thermoplastics interfaces. 16,[18][19][20][21] Finally, when the adsorption is accompanied by a degradation of the polymer chain by cissions, the most reactive metals (e.g., Cr or Ni) form carbides or phosphides. 13,22 An important general observation of the above mentioned studies is that almost all metal/polymer bond creations or interactions correspond to a change in X ray photoelectron spectroscopy (XPS) spectra. Hence, XPS is very well suited for the determination of adsorption mechanisms at metal/polymer interfaces. But, as stated by Wolany et al."The main problems for line analysis are the exact calibration of the binding energy scale in the absence of a well defined aliphatic C 1s line and the number of peaks to be included into the fit of the C 1s line at a given energy resolution of the spectral data.". 14 This is one of the major limitations of XPS in complex systems that contain a variety of bonds and environments. There, the support of theoretical calculations is of great value. Several codes and methods are available in the density functional theory (DFT) or Hartree-Fock frameworks. [23][24][25][26][27][28][START_REF] Travaly | Calculation of C 1s core level shifts in poly(ethylene terephthalate) and comparison with x ray photoelectron spectroscopy[END_REF][START_REF] Haerle | sp2/sp3 hybridization ratio in amorphous carbon from C 1s core level shifts: X ray photoelectron spectroscopy and first principles calculation[END_REF][START_REF] Takahata | DFT calculation of core electron binding energies[END_REF][START_REF] Endo | Theoretical X ray photoelectron and emission spectra of Si and S containing polymers by density functional theory calculations using model molecules[END_REF][START_REF] Bureau | Accurate density functional calculation of core electron binding energies. 5. Application to nitriles. Model molecules for polyacrylonitrile revisited[END_REF][START_REF] Bagus | The interpretation of XPS spectra: Insights into materials properties[END_REF] We recently proposed a decomposition of the C 1s peak of the poly epoxy formed by polyaddition of diglycidylether of bisphenol A (DGEBA) and ethylene diamine (EDA), first with rough initial state DFT calculations [START_REF] Duguet | Toward a computational and experimental model of a poly epoxy surface[END_REF] and then with a high accuracy Hartree-Fock ΔSCF study that accounts for both initial and final state effects and simulates relative peak intensities. [START_REF] Gavrielides | A poly epoxy surface explored by Hartree Fock ΔSCF simulations of C 1s XPS spectra[END_REF] The high accuracy decomposition of the C 1s peak includes 9 contributions instead of 3 when performed empirically. Additionally, we demonstrate that whereas some C bonds are found at discrete binding energies, others allow quite large binding energy domains. This is due to different second neighbor interactions that may add further uncertainty to experimental decomposition. [START_REF] Gavrielides | A poly epoxy surface explored by Hartree Fock ΔSCF simulations of C 1s XPS spectra[END_REF] In the present work, we further study this system and its interaction with Cu. We use a different method by simulating XPS spectra by density functional theory (DFT) in the framework of the unrestricted generalized transition state theory (uGTS). Accurate simulations of XPS spectra have to take into account both initial state and final state effects. It can be achieved (i) at the Hartree-Fock (H-F) ΔSCF level of theory [START_REF] Gavrielides | A poly epoxy surface explored by Hartree Fock ΔSCF simulations of C 1s XPS spectra[END_REF][START_REF] Ziegler | On the calculation of multiplet energies by the hartree fock slater method[END_REF] and (ii) in the framework of the density functional theory using Slater's Transition State theory (TS). [START_REF] Slater | The Theory of Complex Spectra[END_REF] The latter method is based on the Taylor series expansion of the energy in terms of the shell occupation and the idea is to remove a fraction of electron from the molecular orbital of interest. Slater's transition state (TS) method leads to a calculation of the core electron BEs with eq 1

BE 1 2 k ε = - i k j j j y { z z z (1)
with ε k being the energy of the molecular orbital of interest, with an occupation number of 1/2 electron. This was generalized by Williams et al., [START_REF] Williams | Generalization of Slater's transition state concept[END_REF] who demonstrated that the core ionization energy is more accurate with eq 2

BE 1 4 (1) 3 1 3 k k ε ε = - + × i k j j j j i k j j j y { z z z y { z z z z (2)
with ε k being the energy of the molecular orbital of interest, with successively an occupation of 1 and 1/3 electrons. Chong et al. [START_REF] Chong | Accurate calculation of core electron binding energies by the density functional method[END_REF][START_REF] Chong | Accurate density functional calculation of core electron binding energies with a scaled polarized triple zeta basis set. Twelve test cases and application to three C2H4O2 isomers[END_REF] and Endo et al. [START_REF] Endo | Analysis of C 1s spectra of N , O , and X containing polymers in X ray photoelectron spectroscopy by ab initio molecular orbital calculations using model molecules[END_REF][START_REF] Endo | Simulation of C 1s Spectra of C and O Containing Polymers in XPS by ab initio MO calculations using model oligomers[END_REF][START_REF] Endo | IR, and C13 NMR spectral analysis of 6 polymers by quantum chemical calculations[END_REF][START_REF] Endo | Theoretical X ray photoelectron and emission spectra of Si and S containing polymers by density functional theory calculations using model molecules[END_REF] later showed that the most accurate results are obtained with an occupation of 1/3 and calculations performed as unrestricted. This latter development is known as the unrestricted Generalized Transition State (uGTS) theory.

Within the uGTS framework, we reproduce and improve the simulation of the XPS spectra of the pristine epoxy polymer as compared to our previous results. Then, we use simulated XPS to assess the bonding mechanisms responsible for the first step of formation of Cu thin films on the epoxy polymer. The experimental counterpart consists in the UHV evaporation of Cu thin films, followed by XPS and atomic force microscopy (AFM).

EXPERIMENTAL AND COMPUTATIONAL DETAILS

2.1. Experimental Details. The poly epoxy is formed by poly addition of diglycidylether of Bisphenol A (DGEBA) and ethylene diamine (EDA) poured on 1 × 1 cm 2 Si wafer coupons. Samples are obtained by slow polymerization at ambient temperature (24 h), followed by post curing above the glass transition temperature (2 h, 140 °C) in an Ar glovebox. This protocol (published elsewhere 17,[START_REF] Duguet | Toward a computational and experimental model of a poly epoxy surface[END_REF] ) maximizes the polymerization rate and limits the formation of surface defects to a minimum.

Samples are then transferred to a UHV chamber where pure Cu (99.999%) is evaporated in a chamber with a base pressure of 5 × 10 -10 mbar with a Mantis M-EV e beam evaporator (293 K, 8 × 10 -1 mbar, 6 min, 25 W, 23.2 nA). X ray photoelectron spectroscopy (XPS) is performed using a Thermo Scientific K alpha apparatus (hν(Al Kα) = 1486.6 eV). The pass energy is fixed at 40 eV. A Shirley background is systematically subtracted. Sputtering is achieved with Ar + ions (500 eV, 10 mA, Raster area of 2 mm 2 ) to remove the pollution layer formed during transfer to the XPS apparatus. For the latter, we monitor the recovery of metallic copper by analyzing the Cu 2p peaks and the shape of the Cu LMM peaks and by measuring the modified Auger parameter (α′ = BE Cu2p + KE CuLMM ). [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn[END_REF] After 60 s of sputtering, the Cu LMM and Cu 2p peaks are identical to our pure Cu 0 foil reference and the modified Auger parameters are almost equal: α′ Cu film = 1851.29 eV and α′ Cu ref = 1851.35 eV. Therefore, the O 1s signal after 60 s sputtering originates from the oxygen of the poly epoxy underneath the Cu film. The C 1s peak is also monitored: its intensity first decreases upon sputtering (for 5, 10, 15, and 20 s total sputtering time) before it increases again (for 25, 30, 60, 80, and 100 s total sputtering time). At the selected time of 60 s used in the study below, the C 1s peak then originates from the poly epoxy sample underneath. By doing so, we are able to analyze and discuss chemical bonding at the buried Cu/epoxy interface based on the fine decomposition of C 1s and O 1s peaks.

Finally, the surfaces of the Cu films are also characterized by atomic force microscopy (AFM, Agilent Technologies model 5500) in ambient conditions in Tapping mode with tips of k = 25-75 N/m (AppNano). The scanning rate is 2 μm/s. Images are processed with the software Gwyddion version 2.19. [START_REF] Necǎs | Gwyddion: an open source software for SPM data analysis[END_REF] 2.2. Computational Details. The molecular model that we use to simulate the surface properties of the epoxy polymer is composed of one DGEBA molecule connected to one EDA molecule (Figure 1). This model, called the "dimer model" in the following, is used to study the adsorption of Cu atoms on poly epoxy and to simulate the XPS spectra for the pristine surface and for the Cu covered poly epoxy surface. Carbon atoms are numbered first, from the right to the left, and then O atoms are numbered from the left to the right, as shown in Figure 1.

Identification of Cu-Adsorption

Sites. The geo metries of the systems were fully optimized using conjugate gradient methods with the Gaussian09 package. [START_REF] Frisch | Gaussian 09[END_REF] To identify the most favorable adsorption site(s) for Cu atoms, we initially positioned one Cu atom in many adsorption sites on the dimer molecule and we optimize the Cu/dimer molecule system without constraint. Two functionals were tested: the B3LYP hybrid functional [START_REF] Lee | Development of the Colle Salvetti correlation energy formula into a functional of the electron density[END_REF][START_REF] Becke | Density functional thermochemistry. III. The role of exact exchange[END_REF] and the gradient corrected PBE func tional. [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] The geometry optimizations were done with the 6 31G* basis set and the stationary points were characterized as minima by a vibrational analysis. This step was followed by a Mulliken population analysis to obtain the charge on each atom.

2.2.2. Simulation of XPS Spectra. The XPS spectra are simulated in the framework of the unrestricted Generalized Transition State theory (uGTS) using the PBE functional. [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] To this aim, the following computational scheme is used with the deMon2k code: [START_REF] Koster | deMon2k, version 4, The deMon developers[END_REF] (i) we fully optimize the systems with a relativistic valence basis set, GENA2 auxiliary functions, [START_REF] Calaminici | Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems[END_REF] and relativistic Stuttgart pseudopotentials [START_REF] Flores Moreno | Half numerical evaluation of pseudopotential integrals[END_REF] for all of the atoms, except for the H atoms (DZVP); (ii) we then remove the pseudopotential on the atom of interest, i.e., C or O atoms, to calculate the energy of the 1s orbital for this atom and we apply the large AUG cc pVTZ orbital basis set [START_REF] Dunning Thom | Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen[END_REF] to this atom to perform single point calculation of the energy of the neutral molecule and of the energy -εk(1) of the 1s orbital for the atom of interest; and (iii) finally, we perform a single point calculation of the energy on the ionized molecule, with 0.33 electron on the 1s orbital for the atom of interest. We obtain the energy -εk(1/3) of the 1s orbital; (iv) we then apply eq 2 and compose the simulated spectra with calculated binding energy shifts (ΔBE). Finally, these theoretical XPS results are compared to the experimental XPS data to estimate the ability of the limited size theoretical model to correctly capture the Cu/polymer interaction.

RESULTS AND DISCUSSION

3.1. Characterization of the Epoxy Polymer/Copper Thin-Film Interface by XPS and AFM. The experimental C 1s and O 1s XPS spectra of the clean epoxy surface are shown in black in Figure 2. The C 1s peak is composed of three features: the main peak centered at a binding energy (BE) of 284.6 eV, a high BE shoulder centered at 286.3 eV, and a shake up satellite centered at 291.2 eV. After Cu deposition, the shoulder is strongly diminished. The O 1s peak is centered at BE = 532.1 eV (FWHM = 1.8 eV), typical of organic environments. After Cu deposition, the O 1s peak shape is strongly modified with the occurrence of a metal oxide contribution at BE = 530.1 eV.

To decompose the spectra with a greater accuracy than by using database BEs, we use calculated BEs arising from the uGTS DFT calculations (namely from the molecular orbitals energies ε k (1) and ε k (1/3)) detailed in Section 2. Calculation results are summarized in Table 1. The orbital ID follows the numbering of the C atoms of the model dimer shown in Figure 1. Chemical shifts (ΔBEs) refer to the orbital with the lowest energy (C9), fixed at 0 eV.

The calculated chemical shifts and the relative intensities are used to fit the experimental C 1s spectrum. In other words, energies and intensities are all dependent on each other, but the absolute positioning and spectral intensity are fitted to the experiment. The FWHM is fixed at 0.9 eV for all contributions. The result is shown in Figure 2 (gray line), where the fitting is very satisfactory. Each individual contribution is identified with its originating bond (an asterisk pin points the carbon atom of interest when needed). As compared to our previous simulations of the same system in the framework of Hartree-Fock ΔSCF calculations, [START_REF] Gavrielides | A poly epoxy surface explored by Hartree Fock ΔSCF simulations of C 1s XPS spectra[END_REF] the positioning of the high BE peak is better. Anyway, bonds appear with the same increasing chemical shift order as in our previous work, and the qualitative result is similar.

The experimental C 1s XPS spectrum after Cu deposition is also shown in Figure 2 We further characterize the surface of the Cu thin film with AFM. The surface roughness, R a , is determined by the post processing of 500 × 500 nm 2 AFM images obtained in tapping mode with the Gwyddion software. [START_REF] Necǎs | Gwyddion: an open source software for SPM data analysis[END_REF] The pristine surface exhibits a low surface roughness R a = 0.23 nm. The Cu thin film shows an R a of 0.99 nm, i.e., greater than the initial surface, yet still limited. A 500 × 500 nm 2 AFM image of the Cu film is shown in Figure 3.

The morphology of the film is three dimensional and rough, with a peak to peak roughness R z = 6.01 nm, and some darker contrast holes that might point to uncovered substrate locations. Although the majority of the substrate is covered with Cu, we make sure that C 1s XPS spectra of the substrate/ film interface are still intense. With this buried interface method, we circumvent the problem of the exposure of the sample to air during its transfer from the evaporation chamber to the XPS chamber. Additionally, we determine that a 60 s mild sputtering (Ar + , 500 eV, 10 μA) is adequate to get rid of atmospheric contaminants and recover a pure Cu surface and the elements of the epoxy underneath. We thus monitor the Cu LMM shape and the C 1s and N 1s peaks' shape and intensity. We do not measure the Cu film thickness, but the large C 1s peak intensity indicates that it is well below 3 times the IMFP of electrons in Cu, i.e., ≪5.4-5.7 nm.

3.2. Identification of Cu-Adsorption Sites on Epoxy Polymer. The deposition of thin films with vapor phase deposition techniques mainly proceeds through an atom by atom mechanism (PVD) or can be simulated by an atom by atom process (CVD). [START_REF] Psarellis | Investigation of reaction mechanisms in the chemical vapor deposition of al from DMEAA[END_REF][START_REF] Aviziotis | Combined macro/nanoscale investigation of the chemical vapor deposition of Fe from Fe(CO)5[END_REF][START_REF] Aviziotis | Multiscale modeling and experimental analysis of chemical vapor deposited aluminum films: Linking reactor operating conditions with roughness evolution[END_REF] In the case of the deposition of Cu on several polymers, it is established that first atoms that adsorb on the surface undergo long distance surface diffusion (in the μm range sometimes!) before they stabilize. Once chemisorbed, they act as anchor points for the formation of Cu clusters, where the Cu-Cu interaction is favored at the expense of Cu-polymer surface atom interactions. [START_REF] Faupel | Metal Diffusion in Polymers and on Polymer Surfaces[END_REF] This is also well supported by the absence of interfacial adhesion in these metal/polymer assemblies in practical applications. 5,6,[START_REF] Zhang | Adaptation of a dry metalorganic chemical vapor deposition metallization process to a wet chemical pretreatment of polymers[END_REF] Therefore, a good practice in DFT calculations consists of evaluating the adsorption energies by optimizing the geometry of a molecule or a surface in close vicinity to an isolated atom. The limitations of modeling a surface with a representative molecule arise if one observes the deformation of the molecule around the metal atom. For instance, this is observed when a 4 atom cluster is used in the present work: the DGEBA-EDA molecule folds around the cluster, as a coordination complex would do (not shown). In this latter case, the molecular model is no longer relevant and should be replaced by a slab model, where the polymer "surface" is sufficiently cohesive to prevent strong deformation. Unfortunately, there is no surface model The two columns on the right show the number of orbitals and the corresponding relative composition in the stoichiometric mixture 2 DGEBA + 1 EDA used for samples' synthesis. Lines C1, C21, C22, and C23 show irrelevant results for bonds that do not actually exist in the fully polymerized epoxies. yet for most of the polymers in the state of the art; hence, the isolated atom in interaction with a molecular model of the surface remains the fairest option. Before we simulate the XPS spectra for the metalized polymer, we try to identify the most favorable adsorption site(s) for Cu atoms, by calculating the adsorption energy (E ads ), following the general eq 3.

E E E E ( ) ads Cu/dimer Cu atom dimer = - + (3)
where E Cu/dimer is the total energy of the system with one Cu atom adsorbed on the dimer molecule, and E Cu atom and E dimer are the total energies of an isolated Cu atom and of the isolated free dimer, respectively. The interaction energy (E int ) corresponds to the adsorption energy (E ads ), except when the dissociation of the O-H bond occurs, leading to a dehydrogenated RO dimer radical (see cases 2a and 2b, in Table 2). In this latter case, eq 4 is used instead.

where E RO-Cu is the total energy of the system with one Cu atom adsorbed on the RO dehydrogenated dimer molecule, and E Cu atom and E RO are the total energies of an isolated Cu atom and of the isolated free RO dehydrogenated dimer radical, respectively. The results are shown in Table 2. All sites that are tested are found to be stable for the adsorption of Cu.

The three bottom configurations that evaluate interactions with the O27 atom show the largest adsorption energies. Case 1 assumes that the Cu atom is adsorbed on the oxygen O27 and that the hydrogen atom remains. Cases 2a and 2b, on the other hand, assume the departure of the hydrogen atom from O27. The interaction energy in case 1 corresponds to the adsorption energy of Cu (-1.802 eV with B3LYP and -3.222 eV with PBE). For case 2a, the interaction energy calculated with eq 6 equals -5.175 eV for B3LYP and -6.508 eV for PBE. For case 2b, the interaction energy is -3.938 eV for the B3LYP calculation and -4.897 eV for the PBE calculation. These values show that the interaction of the Cu atom is much stronger with the dehydrogenated RO dimer radical than with the ROH dimer. Following the mechanism presented in eq 5, the strongest adsorption energy is found for case 2a (E ads = -2.980/-4.347 eV with B3LYP/PBE). It is worth noting that although the PBE functional predicts systematically larger adsorption energies, it reveals the same trend as the hybrid B3LYP functional. In addition, E ads reported here are not normalized by the bond numbers, which explains the somewhat large E ads values.

The optimized geometries for cases 1, 2a, and 2b are presented in Figure 4 (PBE calculations).

The Cu-O27 distances are 1.976/1.792/1.787 Å for cases 1/2a/2b, respectively. In case 1, the Cu atom is also bound to two carbon atoms of the phenyl ring (1.901 and 1.992 Å). In case 2a, the Cu atom is in interaction with two carbon atoms (C6 and C7) of the phenyl ring (1.909 and 1.965 Å) but also slightly with the O26 atom (distance Cu-O: 2.558 Å). For the last case (2b), the Cu atom is in interaction with O26 (distance Cu-O: 1.942 Å) and with C5 and C4 atoms (distance Cu-C: 2.423 and 2.306 Å, respectively). Therefore, the most favorable adsorption site is the O27 atom, preferably with the release of the H atom. In these cases, the Cu atom has a net charge of +0.34/+0.46e, i.e., it is oxidized. Unfortunately, the experimental methodology we use (interface burying, post mortem XPS + ion etching) does not allow the proper experimental monitoring of the Cu LMM Auger and Cu 2p peaks, where Cu oxidation is usually observed. [START_REF] Frisch | Gaussian 09[END_REF][START_REF] Lee | Development of the Colle Salvetti correlation energy formula into a functional of the electron density[END_REF] In our case, the proportion of bulk Cu within the nanometric thickness is largely superior to the proportion of interface Cu; hence, it is not possible to distinguish Cu-O contributions.

3.3. Cu-Polymer Surface Interactions as Evidenced from the Combined Theoretical and Experimental XPS Analysis. The 2a configuration corresponds to the strongest adsorption site for Cu. However, geometries 1, 2a, and 2b have been tested for further simulation of the XPS spectrum of the metalized surface to correlate with the experimental counter part. Case 1 calculations with a partial occupancy of the C 1s molecular orbitals do not converge or converge with unrealistic binding energy shifts, indicating either a numerical issue or an unstable configuration. Therefore, in the following, we present the results for cases 2a and 2b. Table 3 shows the chemical shifts calculated with the uGTS method in these two cases.

These computed data are used to build the simulated C 1s and O 1s spectra with the FWHM fixed at 0.9 and 1.6 eV, respectively. The resulting XPS decompositions are shown in Figure 5.

Black lines represent the experimental envelopes and gray lines represent the simulated spectra. The XPS C 1s spectrum simulated in case 2a is closer to the experimental counterpart. The high BE shoulder is attenuated as compared to the 2b case. Two differences explain this change of the spectrum shape. First, the C-O-Cu contribution is shifted by ΔBE = 1.33 eV in 2a, whereas it is shifted by ΔBE = 0.91eV only in 2b with regard to the reference BE(C* ph -C quater ). Second, a new contribution denoted C ph (Cu) appears in 2a because of the strong interaction between the adsorbed Cu atom and the C atom of the phenyl group. These two shifts of the binding energy are responsible for the concomitant decrease of the shoulder intensity and increase of the main peak intensity. However, in both cases, the shoulder is much less intense than on the pristine surface (Figure 2), where the C-OH bonds' contribution is strong (ΔBE = 2.13 eV). This shift toward lower binding energies from the initial C-OH contribution to the final C-O-M (M = metal) contribution (such as 2a or 2b) has already been observed experimentally on a variety of polymers. 14,[START_REF] Bebin | Comparative XPS study of copper, nickel, and aluminum coatings on polymer surfaces[END_REF][START_REF] Haight | Complex formation and growth at the Cr-and Cu-polyimide interface[END_REF][START_REF] Pertsin | An XPS study of the in situ formation of the polyimide/copper interface[END_REF] But these works refer to in situ and sequential Cu depositions, unlike our case with the buried Cu/poly epoxy interface. The former methodology permits the monitoring of Cu LMM and Cu 2p spectra, further confirming the hypothesis for the Cu partial oxidation. When Cu is deposited on the PMDA-ODA polyimide surface, [START_REF] Haight | Complex formation and growth at the Cr-and Cu-polyimide interface[END_REF][START_REF] Pertsin | An XPS study of the in situ formation of the polyimide/copper interface[END_REF] the initial C-OH contribution to the C 1s peak decreases to the benefit of a new contribution at lower BE, and a Cu + valence state is identified in the LMM Auger spectrum. The preferential interaction of Cu with the hydroxyl groups to form Cu-O-C bonds is further confirmed with a plasma pretreatment of the polyimide surface that increases strongly the concentration of hydroxyls and then the concentration of Cu-O-C (and Cu-N) bonds, a consequence being a large increase of the interfacial adherence. 14 The simulation of the O 1s spectrum gives similar results for cases 2a and 2b. Two contributions to the peak are taken into account in the model dimer, either Cu-O-C or C ph -O-C. ΔBE are found to be close: 3.00 eV in case 2a and 2.82 eV in case 2b, differences arising from the intensity of the interactions with the adsorbed Cu. The simulated spectra are then made of two distinct contributions that do not match the central part of the experimental O 1s peak. This is likely due to additional environments of O atoms that are not taken in the present model.

In the present work, it is clear from DFT calculations that hydroxyls are the preferential adsorption sites and that a dehydrogenation of the hydroxyl group proceeds simulta neously with the Cu oxidative adsorption. The XPS spectra are well reproduced with the formed Cu-O-C bonds; then, it may be the main chemical interaction at the Cu film/poly epoxy interface. Nevertheless, after the anchoring of the first atoms (Cu1) on hydroxyls, further Cu atoms aggregate on Cu1. Then, the Cu-O-C bond modeled in the present work is likely modified by the final coordination of the Cu1 atoms that share electrons with more Cu neighbors in the film. Hence, there is a possibility that charge transfers of Cu1 to O and C involved in the Cu-O-C bonds are slightly different from the one simulated with the single Cu atom DFT method, and that chemical shifts of O 1s and C 1s may be slightly different for the film. To test this mechanism further, we optimize final geometries 2a and 2b with 1 additional Cu atom, and obtain a final 2 Cu geometry. On this latter geometry, a third atom is placed in the vicinity of a Cu-Cu bridge position, and the geometry is optimized again to obtain the 3 Cu geometry. Then, a Cu atom is placed in the vicinity of the three fold Cu hollow site, and the geometry is again optimized to obtain the 4 Cu geometry. In 2 Cu, 3 Cu, and 4 Cu optimizations, the DGEBA-EDA atoms' positions are fixed to mimic a surface, and prevent the folding of the molecule around the Cu cluster. At the end, we obtain 8 stable n Cu/ poly epoxy configurations (1 < n < 4), on which we determine net charges of Cu atoms involved in the Cu-O-C bond. Net charges and optimized geometries are shown in Supporting Information. It appears that the charge on the first chemisorbed Cu atom (Q Cu1 ) is modified, following:

Q Cu1 (1 Cu) = +0.45e, Q Cu1 (2 Cu) = +0.38e, Q Cu1 (3 Cu) = +0.29e, et Q Cu1 ( 4
(3 Cu) + ∑Q neighbor = +0.35e et Q Cu1 ( 4
Cu) + ∑Q neighbor = +0.46e. Therefore, whereas there is a slight change due to neighboring Cu atoms, the total charge transfer to O27 remains similar (-0.15e < ΔQ O27 < -0.21e). Therefore, chemical shifts calculated by uGTS on the 1 Cu/poly epoxy system are valid to simulate the XPS spectra of the film/poly epoxy.

CONCLUSIONS

These DFT uGTS calculations on the DGEBA-EDA system confirm and improve our previous XPS simulations in the framework of Hartree-Fock ΔSCF calculations. [START_REF] Gavrielides | A poly epoxy surface explored by Hartree Fock ΔSCF simulations of C 1s XPS spectra[END_REF] Interest ingly, this methodology improves the accuracy of the description of the C 1s peak by allowing a fine decomposition with 8 components, unlike the standard empirical method that may include three contributions only. The evaporation of Cu leads to the formation of a covering thin film of about 5.5 nm thickness, therefore to the formation of a buried Cu/epoxy interface that can be probed by XPS. The XPS peaks arising from the interface are strongly modified as compared to the clean surface with the disappearance of the The metallization of polymers has been studied for quite a long time, originally driven by the microelectronic develop ment. In these times, a lot of knowledge has been acquired concerning the formation of metal thin films, including first steps, such as adsorption, nucleation, and growth. Never theless, while experimental evidence seems to converge, there are a limited number of theoretical studies to support and better explain the atomistic mechanisms involved. To that purpose, the major contributions of the present work are as follows:

• a substantial improvement of the decomposition of the XPS spectra as compared to purely experimental methods, with a DFT method that takes initial and final state effects and that has never been applied on such a big molecule. ■ ASSOCIATED CONTENT

* Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.9b07772.

  with the filled area. It shows a wide peak centered at BE = 284.6 eV. Discrepancies with the pristine surface are obvious with the drastic decrease of the high BE shoulder and the disappearance of the shake up satellite. Therefore, through Cu deposition, the contributions of C ph -O-C*, C-OH, and C ph *-O-C are modified or suppressed, indicating a strong interaction of Cu atoms with these groups. In addition, the shake up satellite that arises from π-π* transitions in phenyls groups disappears, further indicating interactions with C ph .

Figure 1 .

 1 Figure 1. Dimer model. The color code is as follows: blue for nitrogen atoms, gray for carbon atoms, and red for oxygen atoms.

Figure 2 .

 2 Figure 2. Experimental C 1s and O 1s XPS spectra of the pristine surface (black line) and of the Cu covered surface (filled area), along with the simulated spectrum (gray line), obtained by fitting experimental intensity at fixed (calculated) binding energies.

Figure 3 .

 3 Figure 3. 500 × 500 nm 2 AFM image of the Cu thin film.

aQ

  Cu is the Mulliken net charge on the Cu atom in the Cu/polymer system.

Figure 4 .

 4 Figure 4. Representation of the optimized dimer configurations with Cu in the vicinity of the O10 atom, with H (1) and without H (2a and 2b). The larger (yellow) ball corresponds to the Cu atom.

  Cu) = 0.16e. In cases 3 Cu and 4 Cu, another Cu atom

  • the identification of preferential adsorption sites for the first Cu atoms impinging and diffusing on the surface. Our calculations/experimental results match with the following scenario. Cu atoms interact preferentially with C-OH sites to form Cu-O-C bonds. These bonds are stabilized by a transfer of approximately 0.5 electrons from Cu to O; hence, Cu is partially oxidized. • a fair decomposition of the Cu/epoxy C 1s and O 1s spectra that is only rendered possible by the determination of ΔBEs through DFT. Without calcu lations, bonds' details are hidden in the broad C 1s peak with no possibility to decipher these. • a theoretical/experimental support for a nucleationaggregation scenario of the Cu thin film. In this assumption, first Cu atoms diffuse until they chemisorb, then additional atoms aggregate on these anchor points, and growth proceeds via a Wolmer-Weber mode.

Figure 5 .

 5 Figure5. Simulated XPS spectra using the uGTS theory. Both correspond to an oxidative adsorption of the Cu atom on the polymer (case 2). Top: the Cu atom is away from the phenyl (2b). Bottom: the Cu atom is close to the phenyl (2a). Hydrogen atoms are not shown.

Table 1 .

 1 Chemical Shifts, ΔBE (uGTS), Calculated for Each C 1s Orbital of the Model Dimer Identified by an ID and the Group to Which It Belongs a

	model dimer

Table 2 .

 2 Adsorption Energies of the Cu Atom on the Native or Dehydrogenated Dimer Molecule a

	adsorption site	E ads with B3LYP	E ads with PBE
	N	1.591 eV	2.593 eV
		( Q Cu = 0.14e)	(Q Cu = 0.13e)
	O26	1.022 eV	2.007 eV
		(Q Cu = +0.01e)	(Q Cu = +0.03e)
	phenyl ring	1.428 eV	2.867 eV
		(Q Cu = 0.09e)	(Q Cu = 0.08e)
	O27 (in O27 H case 1)	1.802 eV	3.222 eV
		(Q Cu = +0.11e)	(Q Cu = +0.13e)
	O27	2.980 eV	4.347 eV
	(H is removed case 2a)	(Q Cu = +0.46e)	(Q Cu = +0.45e)
	O27	1.742 eV	2.737 eV
	(H is removed case 2b)	(Q Cu = +0.39e)	(Q Cu = +0.34e)

Table 3 .

 3 O 1s and C 1s Binding Energy Shifts (ΔBE) Derived from uGTS Calculations for the Adsorption of the Cu Atom on the Dimer in Cases 2a and 2b and Functional Group to which the Atom of Interest (See Asterisk) Belongs

	ΔBE (uGTS) (eV)	BE (uGTS) (eV)
	case 2a	case 2b	functional groups
	0.00	0.00	C O* Cu
	3.00	2.82	C phenyl O* CH 2 C(OCu)
	0.00	0.00	C* phenyl C quaternaire
	0.01	0.02	C* phenyl C quaternaire
	0.01	0.06	C phenyl
	0.01	0.07	C phenyl
	0.08	0.08	C phenyl
	0.09	0.11	C phenyl
	0.14	0.11	C phenyl
	0.15	0.15	C phenyl
	0.21	0.19	C phenyl
	0.33	0.19	C phenyl
	0.35	0.34	CH 3
	0.38	0.34	CH 3
	0.48	0.70	C(OCu) C* NHC
	0.57	0.79	C*H 2 NH
	0.82	0.85	C quaternaire
	0.91	1.33	C* O Cu
	1.63	1.71	C* phenyl O CH 2 C(OCu)
	1.70	1.73	C* phenyl O CH 2 C epoxy
	2.02	1.95	C phenyl O C* C(OCu)
	2.46	2.51	C phenyl O C*

donates electrons, resulting in Q Cu1

  high BE C-O shoulder on C 1s, and the appearance of a metal oxide contribution on O 1s. These are first hints indicating the preferential interaction of Cu with oxygen. DFT is then used to check this hypothesis by adsorbing a Cu atom on different sites of the dimer molecule and to calculate adsorption energies. The three most stable adsorption sites are found on the hydroxyl group, with or without the H atom removal. XPS is then simulated in these configurations. It shows that the charge transfer from the Cu atom to the atoms involved in the chemisorption shifts the initial C-OH component of the pristine surface toward a lower BE for the new C-O-Cu bond, and new components are created such as C ph (Cu) that further modify the spectrum shape. For O 1s, two distinct molecular orbital energies are found: one for the organic O atoms of the C ph -O-C chain fragment and one for the newly formed Cu-O-C bonds.


Gaëtan Prigent
email: gaetan.prigent@laas.fr

Pedro Rynkiewicz
email: pedro.rynkiewicz@laplace.univ-tlse.fr

Anne-Laure Franc
email: anne-laure.franc@laplace.univ-tlse.fr

Synthesis of a Tunable Impedance Inverter Based on Variable Position of Capacitive-Loads

Keywords: Impedance inverter, tunable filters, synthesis

This work presents a topology to meet the demand of tunable quarter-wavelength impedance inverters. The proposed solution lies in a transmission line loaded by capacitors whose positions are variable. The associated synthesis is proposed and leads to the possibility of producing a quarterwave inverter operating at two different frequencies and with two characteristic impedances that can be optimized thanks to the degree of freedom provided by the position of the capacitors.

I. INTRODUCTION

Considering the spectrum spreading for embedded applications and the necessity of flexible data flows depending on the needs of end-users as well as the need for very high frequency multifunctional systems, the tunability appears as a key issue for low-cost integrated systems. Indeed, many functions only differ from center frequency or bandwidth [START_REF] Rebeiz | Tuning in to RF MEMS[END_REF]. Therefore, by promoting the design of tunable devices that can address all or part of the operating bands one can dramatically reduce the size, cost and complexity of the system. Moreover, the need for high capacity links the use of high frequency bands is required, notably with the imminent arrival of 5G systems [START_REF] Marcus | 5G and "IMT for 2020 and beyond[END_REF]. Within this context, the use of high-quality passive circuits is a key issue; they have to meet the system requirements in terms of selectivity and losses while maintaining their performance whatever the tunability. Unfortunately, for tunable functions the electrical performance are degraded with the tuning range. Thereby, one has to provide systems robust to the frequency change.

Among the passive functions filters are one of the most sensitive components, especially tunable filters. Most of planar filter topologies are composed of resonators and inverters whose characteristics, i.e. electrical lengths and impedance, control both center frequency and bandwidth. Fundamental components in the design of filters in millimeter frequency range are transmission lines. In the case of tunable filters, the center frequency can be controlled by changing the electrical length. However, the more the center frequency is far the nominal frequency, the more the filter response is degraded, especially the in-band return loss which is linked to impedance of the transmission line. It is therefore important to provide transmission lines whose electrical properties can be modified to fit the requirement in terms of frequency shift.

Although much work has been done to modify the electrical length of the line [START_REF] Issa | Loaded miniature transmission lines compatible with low cost substrates: Q-factor improvement[END_REF], few results are available on the characteristic impedance variation. The solution proposed in this work is to move capacitors along the transmission line in order to modify the equivalent impedance without affecting the electrical length. The displacement of series varactors was introduced in [START_REF] Lu | Single-Band and Switchable Dual-/Single-Band Tunable BPFs With Predefined Tuning Range, Bandwidth and Selectivity[END_REF] in order to produce a tunable resonator in central frequency and in bandwidth, but it was not treated from a transmission line point of view. So as to improve the mastery in design, essential in millimeter-and sub-millimeterbands, a synthesis in proposed for dual-band quarter wavelength inverter with tunable impedance.

II. CAPACITIVE LOADING WITH VARIABLE POSITION

A. Transmission line topology

In this part, a transmission line with a characteristic impedance of Z c is symmetrically loaded with capacitors located at a variable position defined by P (Fig. 1).

When P is 0, the two capacitors are overlapped on the center of the transmission line and when P = 1, they are arranged at each end. This variation of position is modeled by an electrical length of line dependent on P according to (1) and ( 2) where 𝜃 𝐻 = 2 • (𝜃 𝑃 + 𝜃 1-𝑃 ) is the electric length of the unloaded transmission line defined at the nominal highest frequency f H .

𝐴 𝑒𝑞 = 𝐷 𝑒𝑞 = cos 𝜃 -𝐶 𝑁 • sin 𝜃 + {𝐶 𝑁 2 • sin[2 • (1 -P) • 𝜃] • sin(2 • P • 𝜃)}/2  𝐵 𝑒𝑞 = 𝑗 • 𝑍 𝑐 • {sin 𝜃 + 𝐶 𝑁 • [cos 𝜃 -cos(2 • P • 𝜃)] + 𝐶 𝑁 2 •sin(2•P•𝜃)•sin 2 [2•(1-P)•𝜃] 2 }  𝐶 𝑒𝑞 = 𝑗 • {sin 𝜃 + 𝐶 𝑁 • [cos 𝜃 + cos(2 • P • 𝜃)] - 𝐶 𝑁 2 •sin(2•P•𝜃)•sin 2 [2•(1-P)•𝜃] 2 } /𝑍 𝑐  
The coefficient of the equivalent chain matrix (ABCDeq) of the loaded transmission line are given in APPENDIX 1. At a given low frequency f L , with lossless transmission lines, this matrix is then determined by ( 4)-( 7), with C N the normalized impedance such as:

𝐶 𝑁 = 2𝜋 • 𝑓 𝐿 • 𝐶 • 𝑍 𝑐  
From the chain matrix, the equivalent electrical properties of the loaded line can be obtained at any frequency f L .

B. Application to impedance inverters

In order to focus on the application of a tunable quarterwavelength inverter, the frequencies f H and f L are the two operating frequencies for which the line must have a behavior comparable to transmission line with electrical length of λ/4. The unloaded transmission line is quarter wavelength at f H (θ H =90 °).

The equivalent electrical lengths of the loaded line have to verify θ eq = 90 ° at f L , i.e. a chain matrix of the form (7).

[𝐴𝐵𝐶𝐷] 𝑒𝑞 = [ 𝐴 𝑒𝑞 𝐵 𝑒𝑞 𝐶 𝑒𝑞 𝐷 𝑒𝑞 ] = [ 0 𝑗𝑍 𝑒𝑞 𝑗𝑌 𝑒𝑞 0 ] 
Determining the capacitance value to reach an equivalent electrical length of 90 ° requires solving A eq =0 at f L . This calculation leads to a second order equation in C N and thus has two roots. The solution chosen is (8) because it vanishes for θ 1 =90° at f H . This means that no capacitor is needed to retrieve an impedance inverter behavior at f H , so the topology is simply that of the unloaded line.

 

Finally, the equivalent impedance can be recalculated from the chain matrix by applying the following relation:

𝑍 𝑒𝑞 | 𝜃=𝜃 𝐿 = √ 𝐵 𝑒𝑞 𝐶 𝑒𝑞  

C. Results

Fig. 2 presents the equivalent impedance variation with the capacitor position P. The unloaded transmission line is quarter wavelength at f H =100 GHz. The impedance of the transmission line depends on the application, in the study case it is considered to be 50-Ω. Three frequencies (f L ) are investigated for capacitive-loaded transmission lines: 40 GHz, 60 GHz and 80 GHz. Depending on its position (P), the capacitor value is modified following equation (8) to ensure quarter-wavelength behavior at f L . For instance, the C-loaded transmission line behaves as a 50-Ω quarter wavelength transmission line at 100 GHz whereas at f L =40GHz it has the behavior of a quarter wavelength transmission line with impedance range of [16 -22.7]-Ω depending on the capacitor value i.e. its position. Thereby, the degree-of-freedom introduced by the C-loaded transmission line allows designing dual-band impedance inverters with continuously variable impedance. This is fundamental in the design of many functions and especially on tunable filters. Indeed in numerous filter topologies the bandwidth and return loss level are controlled by impedance values. Thereby, as one can impose impedance while keeping constant the electrical length, the mastering in the design of passive devices is improved.

III. APPLICATION TO BANDPASS FILTER

For the sake of illustration of the interest of such an inverter synthesis, a ring-based bandpass filter is designed [START_REF] Rynkiewicz | Ring filter synthesis and its BiCMOS 60 GHz implementation[END_REF]. It is based on the use of two pairs of quarter wavelength transmission lines with different impedances Z 1 and Z 2 (Fig. 3). The synthesis of the unloaded nominal filter was given in [START_REF] Rynkiewicz | Ring filter synthesis and its BiCMOS 60 GHz implementation[END_REF]. The filter bandwidth is ruled by the impedance ratio between Z 1 and Z 2 . The nominal frequency f H is set to 60 GHz and the final frequency f L =45 GHz. The capacitor (C a1 , C a2 ) values are calculated according to equation (8). As depicted in Figs. 4-5 the use of continuously tunable impedance allows controlling the filter bandwidth while maintaining the center frequency and return loss level. The change of the capacitor position in the transmission line allows modifying the relative bandwidth from 15 to 20.8%.

IV. CONCLUSION

The synthesis of quarter wavelength impedance inverters with tunable impedance wave proposed. It allows determining the value and position of capacitors to reach specification in terms of equivalent transmission line impedance while maintaining a 90° phase-shift whatever the operating frequency. Thereby, the capacitive-loaded transmission line allows controlling its equivalent impedance while keeping constant its geometry (width and length), the impedance tunability being achieved changing the capacitor position. This concept was applied in the design of a ring bandpass filter which bandwidth is ruled by impedance ratio of quarter wavelength transmission lines. The filter bandwidth was controlled modifying the capacitor position while maintaining the center frequency and return loss which proves the efficiency of the proposed synthesis. Hence, this synthesis allows designing filters with double tunability: center frequency and bandwidth.

𝜃 1 -

 1 Fig. 1 Topology of the capacitive-loaded transmission line with variable position P.

  𝐶 𝑁 = sin 𝜃 𝐿 -cos 𝜃 𝐿 •√2 sin² 𝑃𝜃 𝐿 +tan 2 𝜃 𝐿 -sin 2𝑃𝜃 𝐿 • tan 𝜃 𝐿 sin 𝜃 𝐿 • sin 𝑃𝜃 𝐿 • cos 𝑃𝜃 𝐿 -cos 𝜃 𝐿 • sin 2 𝑃𝜃 𝐿

Fig. 2

 2 Fig. 2 Variations of the capacitor value and equivalent impedance of quarter wavelength inverter as a function of the capacitor position P.

Fig. 3

 3 Fig. 3 Topology of the capacitive-loaded ring-based bandpass filter.

Fig. 4

 4 Fig. 4 Electrical response of the bandpass filter depending on the capacitor positions.

Fig. 5

 5 Fig. 5 Evolution of the filter bandwidth as a function of the capacitors position.


Managing medicinal risks and treatment personalisation in the context of self-medication

Sylvie Fainzang

(Published in: Drug Safety, 37, 5, 2014, 333-342)

It is commonly thought that medicinal uses can be divided into "good uses" and "misuses", meaning, respectively, those conforming to medical recommendations, and those which fall into the category of inappropriate lay practices. In order to understand these practices, anthropology has shown the importance of not passing judgement in the light of medical knowledge, and of trying to decrypt their meaning, in particular by relating them to certain systems of thought or cultural representations. Lay medicinal uses follow their own logics, and are associated with how individuals perceive these medicines. In this respect, examining the uses of pharmaceuticals involves looking at perceptions of their efficacy and of their risks. If this question can be asked regarding patients holding a medical prescription -and this has indeed been the object of numerous social sciences studies [START_REF] Britten | Medicines and Society. Patients, Professionals and the Dominance of Pharmaceuticals[END_REF][START_REF] Fainzang | Médicaments et sociétés. Le patient, le médecin et l'ordonnance[END_REF][START_REF] Sarradon-Eck | Le sens de l'observance[END_REF][START_REF] Van Der | Popularité et scepticisme. Opinions contrastées sur les médicaments[END_REF] -it can equally be asked about users who are not in possession of a prescription, in other words within the framework of self-medication -a context in which choices have to be made between the various medicinal solutions on offer. The framework of self-medication is in effect more open to medicinal misuse than the context of prescription management, at least if the problem is perceived from the point of view of biomedical science [START_REF] Hughes | Benefits and risks of self-medication[END_REF][START_REF] Ruiz | Risks of Self-medication practices[END_REF] . As a matter of fact, the risk associated with medicinal use is a central element in the growing debate on self-medication in the French public domain, and is often invoked by its critics. The practice is considered to be uncertain and risky, and worries health professionals, even though the public authorities largely promote self-medication today. Their worry relates to the patients' ability or inability to know when they must consult a doctor and how to manage their medicinal uses. In contrast to the biomedical or pharmacological view of self-medication, the anthropological approach seeks to understand the logics that underpin it. The question is thus raised of knowing how users choose the medicines they take and how they construct the modalities of their use. It would be an error to believe, however, that individuals are not concerned with safety and that they are not aware of the risks associated with drug consumption and self-medication. Indeed, users devise strategies aiming to reduce these risks.

Yet, as we will see, though these practices sometimes escape biological logic, the mechanisms on which they are based do not necessarily break away from medical recommendations. Based on a study carried out on the conditions and motivations for selfmedication in France, I will examine the strategies adopted to reduce any associated risks. I will show that while the modalities of medicinal use result from symbolic logics unique to each subject, they are nevertheless inspired by principles borrowed from biomedical logic.

The question today

The studies relating to lay medicinal use all highlight the resistance individuals express to these substances [START_REF] Chamberlain | Forms of resistance to medications within New Zealand households[END_REF][START_REF] Fainzang | Religious Attitudes toward Prescriptions, Medicines and Doctors in France[END_REF][START_REF] Van Der | Popularité et scepticisme. Opinions contrastées sur les médicaments[END_REF] , or even their aversion to them [START_REF] Britten | The expression of aversion to medicines in general practice consultations[END_REF][START_REF] Britten | Resisting Psychotropic Medicines: a synthesis of qualitative studies of medicines use[END_REF] . These forms of resistance have resulted in some interesting typologies, that aim to account for the refusals and rearrangements that take place in terms of these medicines. In the direction taken by Dowel and Hudson [START_REF] Dowel | A qualitative study of medication-taking behaviour in primary care[END_REF] who distinguished between "passive users", "active users" and "rejecters", Pound et al. [START_REF] Pound | Resisting Medicines: a Synthesis of Qualitative Studies of Medicine Taking[END_REF] distinguish between "passive accepters", "active accepters", "modifiers" and "rejecters". Chamberlain et al. [START_REF] Chamberlain | Forms of resistance to medications within New Zealand households[END_REF] however remarked that these typologies do not take into account the functioning of the complex phenomenon of resistance, to the extent that attitudes differ according to the medicines (some people resist certain medicines and not others) and according to the context (indeed, some people can refuse one medicine in situation X but not in situation Y). They noted that resistance is complex and variable, as Britten et al. [START_REF] Britten | Resisting Psychotropic Medicines: a synthesis of qualitative studies of medicines use[END_REF] and Van der Geest [START_REF] Van Der | Why are pharmaceuticals sometimes liked and sometimes disliked[END_REF] also highlighted.

Such resistance to pharmacology has led Webster et al. [START_REF] Webster | Making sense of Medicines: Lay pharmacology and Narratives of safety and efficacy[END_REF] to believe that users act according to a logic of "lay pharmacology", since individuals carefully examine the medicines' actions, therapeutic properties and effects. However, it seems that we can go as far as considering that they realise a form of "lay pharmacovigilance", to the extent that these rearrangements are not only based on a desire to maximise the effects but also to minimise the risks [START_REF] Fainzang | Discourse on safe drug use, symbolic logics and ethical aspects[END_REF] . In these conditions, beyond the diverse causes of resistance brought to light in these studies, it is appropriate to examine the strategies that organise it and to unearth the symbolic logics of lay practices intended to manage the risks associated with consuming pharmaceuticals within the framework of self-medication.

This article rests on empirical research concerning the social, cultural and cognitive mechanisms underpinning individual practices as regards self-medication [START_REF] Fainzang | L'automédication ou les mirages de l'autonomie[END_REF] . To understand these mechanisms, anthropologists feel the need to question the categories usually used on this subject. Indeed, to learn that an individual resorts to self-medication only in benign situations, does not sufficiently illuminate what s/he regards as a "benign situation", what s/he calls "resorting to self-medication", her/his reasons for choosing such a drug or her/his strategies to reduce the associated risks or to increase its effectiveness. Such a decoding requires a critical approach of the very notions on which the public health discourse is based by testing their relevance through fieldwork. This involves studying a phenomenon without prejudging what the users do and think; thus, the practices and categories must be considered without any preconceptions. If the public health objective is to limit the risks involved in self-medication and to define the conditions of this recourse, the objective of anthropology is, not to attend to people's medical safety or to a safe use of drugs (a normative position that anthropologists should not assume), but to understand the social practices at work, the way in which individuals manage the risk associated with self-medication, and the meaning their practices take. This means that, even if the answers to these questions may ultimately contribute to improving public health, this must not be the prime and sole aim. Otherwise, we run the risk of formulating questions that prevent us from grasping some facets of social life. It is precisely these unexpected aspects of social life that can be highlighted by anthropology.

Research setting and method

The research was carried out in Paris and involved around 40 people from diverse social environments. The people participating in the research were for the most part met through the "snowball" method. The first informants, who were in keeping with the population chosen for the research, introduced us to other potential informants through their networks of acquaintances, who in turn referred us to other people who were added to the sample group, which was built in this way. This allowed us to approach a relatively diverse population, thanks to the diversity of the acquaintance networks used: some suggested members of their family, others work colleagues, and others again referred us to association members, friends or neighbours who by the end proved to be very different from the first informants (in their social, economic and ideological positions). By forming a group of informants using close personal contacts, we move away from the first types of people studied. Moreover, we chose to multiply the points of departure of the networks, favourising the constitution of what could be considered a plurality of "snowballs", each original snowflake coming along a different path. Indeed, this procedure reduced the difficulty of approaching people to discuss a topic as personal and intimate as treating one's body and affliction, without having to pass through the intermediary of health professionals.

It was not always possible here to observe, on the spot, people's actual actions and gestures. The research was carried out at people's homes, and thus consisted for a large part of interviews -even if, in some cases, the interviews were combined with in situ observation -concerning the choices people made when faced with a symptom. The research allowed me to collect a certain number of accounts of pathological episodes, in order to understand the different scenarios of self-medicinal use. The interviews concerned established facts. A technique frequently used in quantitative research on self-medication is to question informants as to how they intend to behave when faced with a hypothetical pathological or symptomatic situation. But this is an abstract situation, from which reality cannot be inferred. In this regard, an interview that only aims to ask questions such as: "What medicines do you take when you are ill?" as is often envisaged by questionnaire-based inquiries, does not provide much more information than if the subject is asked: "What medicine would you take if you were ill?" Interviews should resituate the practice of self-medication in its context and refer to lived events (past or present). In contrast to a study that deals with the "intended", it seemed preferable to study practice that has been carried out, when it is not possible to actually observe it. The past provides more information than the conditional.

Moreover, I collected information on the conditions in which drugs detained in the household pharmacies of the people studied were acquired and used in order to obtain complementary material and to verify their statements, which sometimes aimed to conform to what they judged to be socially appropriate. To avoid this pitfall as best I could, I avoided contacting the informants through the intermediary of a doctor, which could have risked associating my work with that of a health professional, and could have induced the subjects to produce discourses showing them to be "good patients".

Although the public authorities largely promote self-medication today (through a decree authorising direct access to medicines and delisting of a certain number of pharmaceutical products), the issue of safety in self-medication is a central concern; its practice is considered to be uncertain and risky, and worries health professionals. The principal risk they mention is that of inadvisable drug use (overdoses, drug interactions, etc.). To suppress this uncertainty and to limit these risks, public authorities together with medical authorities have produced several recommendations for users aiming to structure the practice and define the conditions of use. It is recommended that this recourse is limited to benign situations, that the remains of previous prescriptions should not to be used and that the advice of a pharmacist should to be sought. These practices can be summarized by the notion of "responsible self-medication". These recommendations are notably diffused through the ''ten commandments for self-medication'' circulated on several sites destined for the general public. Notable among these recommendations are the assertions that one must take note of patient information leaflets to be aware of any adverse side-effects (''Read the accompanying leaflet of a medicine carefully. It will tell you its indications, recommended dosages according to age, weight and potential adverse side-effects...''), and that one should not take medicines prescribed for somebody else (''A treatment that suits you may not suit someone else'', ''A medicine that worked very well for a member of your family could have no effect, or even be dangerous, for you'') and that one should ask advice from a pharmacist (''To provide the best advice, the pharmacist must know who the medicine is for''). So how do users respond to these recommendations?

In order to make their decisions, users refer simultaneously to various sources of informationprevious prescriptions, advice from friends and family, advertisements, Internet searches -and to their own experience. In this regard, although self-medication implies personal choice, individuals are never totally independent -they are subject to a thousand influences [START_REF] Massé | Ethique et santé publique. Enjeux, valeurs, normativités[END_REF] , from those around them as well as the whole society. Subjects are therefore never alone in dealing with their symptom and their medicinal options. They are surrounded by information coming to them from sources as varied as health campaigns, previous medical consultations, pharmacists, friends and family, pharmaceutical leaflets and the media, notably the press, the television and the Internet.

Clearly, the information found on the Internet does not only come from professional sites. Information distributed by specialists on sites for the general public, whether approved by health institutions or not, is collected together with information based on the experience of other web users, as told on discussion forums [START_REF] Hardey | Doctor in the house: the Internet as a source of lay health knowledge and the challenge to expertise[END_REF][START_REF] Akrich | Prendre ses médicaments / prendre la parole : les usages des médicaments par les patients dans les listes de discussion électroniques[END_REF] . The two are sometimes mixed in accounts given by patients. They search the Internet for several different objectives. While the aim may be to obtain information about an affliction, its causes and possible progression, it is also done in order to inquire about existing medicinal choices, precautions to be taken and conditions to be respected in order to assure the safety of the medicine, and to find out about any risks associated with its use. One user thus explained her problem on a forum and asked: "Is it possible to take Doliprane at the same time as Zelitrex? I have herpes on my lip which is very painful and a splitting migraine. I am desperate, please reply." Information gathered from the experience of other Internet users is thus added to advice from people close to the user (family, friends and colleagues). The aim is to benefit from the experience of others, despite their anonymity, concerning the effects of a medicine, the level of satisfaction or, inversely, on their potential side effects. Searching for opinions on forums can sometimes replace asking a pharmacist, either because it is embarrassing (a pharmacy does not lend itself to intimate talk about the body) or because it is more convenient (the advice arrives quicker), or simply to gain several points of view.

Quantitative logics/qualitative logics

Individuals' choices concerning medicines are constructed through various logics, some quantitative, others qualitative.

For example, concern over the consumption of too many pharmaceuticals leads some people, using quantitative reasoning, to decide to reduce the number of days they take a medicine for. However, these strategies can, in turn, generate risk, similarly to strategies that involve modifying the instructions (indications, dosages, precautions of use) that accompany medicinal prescriptions. This is the case for antibiotics, for which the high consumption levels in France, generally attributed to patient appetite for this type of medicine, presents serious problems for public health considering the drug resistance caused by this overconsumption, and the poor prospects of being able to find molecules that could replace today's antibiotics in the near future. This problem drove the Caisse nationale d'assurance maladie (The National Health Insurance Fund) to produce an information video-clip destined for the general public, entitled "Antibiotics are not Automatic", in which the explicit message is that one should not consume too many antibiotics. Thus, in response to this message, some patients, strongly convinced that excessive consumption of antibiotics carries risks, claim to be perfectly aware of this risk and ensure, when they do consume them, they stop the treatment as soon as the symptoms disappear, which often means after two days. It is precisely in accordance with the concern to not consume too many antibiotics that some users think it reasonable to reduce the time these drugs are taken for (whether they are prescribed or self-medicated), a strategy that responds to the advice diffused by the health authorities to not abuse this type of medicine. And so this practice results in an increase in drug resistant germs, even when the intention of the users is to reduce the phenomenon.

Likewise, managing the quantity of pharmaceutical products taken is seen as a means of reducing the iatrogenic effects of medicines. Thus, fear of medicinal interactions sometimes leads subjects to choose to limit the number of medicines they consume. Mrs N fears that accumulating and mixing several chemical products could induce harmful effects so she limits her medicinal consumption to three brands in order to reduce this risk. She believes that the iatrogenic risks are associated with the quantity rather than the quality of different pharmaceutical products.

Other mechanisms govern the choice of type or quality of medicines to be consumed. For instance, the pharmaceutical consumption may be refused when the risk is perceived to reside in the nature of the medicine, in the molecule it is composed of and in the danger inherent in its uncontrolled ingestion -that is to say, in the qualitative aspect of the medicine. This is what leads subjects to avoid, sometimes definitively, a certain class of products (such as anti-inflammatories for example). Other users systematically avoid taking two medicines at the same time when one is of a determined pharmaceutical class (anti-inflammatories, antibiotics). The perception of risk does not only depend on the perception a subject has of a medicine but also on what a medicine is. For example, some subjects claim to be against the consumption of psychotropic drugs but nevertheless choose to take a tranquiliser to treat sleeping problems (either difficulties in getting to sleep or waking during the night). This is partly explained by the status given to products such as hypnotic drugs, which are often simply considered to be "calming" and not to have a chemical action on the psyche. [START_REF] Britten | Medicines and Society. Patients, Professionals and the Dominance of Pharmaceuticals[END_REF] Moreover, some users do not consider a medicine to be risky if it is not a synthetic product. This goes for herbal medicines with which subjects freely practice selfmedication without caution despite the potentially noxious effects of their use -just like other medicines -, little aware of the fact that a medicine carries risk as soon as it has an action. Or indeed, some medicines are not considered risky if their consumption is not intended to solve a health problem. This is the case for medicines taken ''to lose weight'' which several patients take for aesthetic and non-medical reasons. Thus Mrs M does not distinguish between nutritional supplements based on green tea and weight-loss drugs which she considers to be cosmetic rather than therapeutic. The definition of a medicine here depends on the purpose for which it is consumed.

In parallel to risk management strategies, users develop strategies to maximise the efficacy of medicines. Thus, in the same way that the doses prescribed by a doctor may be increased in order to heighten the effects [START_REF] Van Der | The Context of Medicines in Developing Countries[END_REF][START_REF] Etkin | Side Effects: Cultural constructions and reinterpretations of western pharmaceuticals[END_REF] , certain medicines chosen for self-medication may also be taken at a higher dose than recommended in the leaflet or in a previous prescription, a practice resulting from quantitative logic. In some regards, the management of medicines consumed in the context of self-medication follows logics comparable to those that organise behaviour regarding prescribed medicines. In terms of how patients comply with their prescriptions, I have provided evidence of the various logics that underpin the modification of prescriptions. I have identified a cumulation logic, consisting of increasing dosages or even accumulating several medicines in order to increase the chances of recovery and an identity logic, consisting of modifying a treatment based on identifying a link between oneself and the product, whether one is (or considers oneself to be) fat or thin, strong or weak, adult or child, man or woman, resistant or frail, etc. [START_REF] Fainzang | Discourse on safe drug use, symbolic logics and ethical aspects[END_REF] . I have shown that such reasoning partly informs the choice as to whether to adhere to or modify the doses prescribed. These various logics also bear on how the medicines consumed within the framework of self-medication are managed. Thus we find both cumulative logic and identity logic within the practice of self-medication, both in the search for better efficacy and in order to reduce the negative effects of medicines. Recommended doses, either from a previous consultation resulting in a prescription, in the patient information leaflet of a medicine or given by a pharmacist, can thus sometimes be increased in order to boost efficacy, or in contrast, reduced to avoid inducing iatrogenic effects.

Risk in itself/risk for oneself

Exclusive or combined recourse to quantitative or qualitative logics may be done in order to manage the risk associated with medicines. The strategies adopted by subjects differ depending on whether they consider the risk to be inherent in the substance or linked to its modes of use. In the first case, subjects tend to eliminate the product in question from the arsenal of drugs they could potentially consume, in the second case, they try to neutralise the risks by modifying recommended doses or modes of consumption, whether the dosage is indicated in the patient information leaflet or figures in a previous prescription for the same medicine. The strategies thus follow mechanisms which differ both according to the individuals and to the medicinesthey depend on whether the risk is perceived to be linked to the nature of the medicine in itself (the type of pharmaceutical product, their adverse side effects on certain functions or certain organs), or to its incompatibility with the subject (in relation to their personal characteristics, or their ability to absorb the medicine, their sensitivity, susceptibility or responsiveness, etc.). A desire to limit medicinal risks then leads subjects to closely observe their effects in order to attempt to adapt the doses to their bodies, in connection with the recognition of a relationship between the medicine and the individual, in its singularity: ''I will need more than that! I am pretty tough,'' or ''I will only take a tiny bit, less than they say in the leaflet, because I am very responsive to medicines.'' The importance placed on this relationship leads individuals to choose to modify how the medicine is taken or the dosage when they deem the recommendations to be incompatible to their specific case.

Risk management associated with the practice of self-medication thus follows various logics organised around the duality between the risk of the medicine in itself and the risk of the medicine for oneself. This point is illustrated with two examples: Mr P, a 42-year-old industrial designer, not eager to practice self-medication, nevertheless decides to take an antiemetic with confidence because he has once given it to his dog, and that this experience, to which he now assigns the value of a test, led him to be sure of the absence of harmful effects. Mrs J, a speech therapist, on the other hand, gets her medicines ''tested'' by a radiesthesist to verify their safety and efficacy. She is driven by a suspicion of the medicine and a fear that taking it would be wrong (whether the product was recommended by a pharmacist or chosen by herself) to resort to divination in order to verify the suitability of the treatment in her case. ''He moves his antenna over the medicines to see if they react in order to test which ones respond, to check if they are safe and if they will work for me," she explained, her objective being to ensure that the medicine was well adapted to her particular case. It is in connection with the risk in itself that Mr P made sure his dog responded well to the anti-emetic before he took it. On the other hand, it is in connection with the risk of the medicine for oneself that Mrs J. relies on a radiesthesist to make sure a medicine suits her and is appropriate to herself and her body.

Undesirable effects and desired effects

The existence of adverse side effects is not necessarily an obstacle to self-medication in itself (neither is it necessarily an obstacle to compliance). While it is true that reading about the sideeffects in pharmaceutical leaflets sometimes dissuades patients from taking the medicines prescribed, the opposite can also apply where the subject interprets their presence as a sign of genuine efficacy to the point that however ''adverse'' this effect can be, the subject still does not envisage ending the treatment: the effects, good or bad, are a sign of the efficacy of the medicine and prove that one should keep taking it, without the subject considering the possibility of unfortunate consequences. For Mr B, "a good medicine is one that does something".

The significance here is in the type of effect more than its ''adverse'' or ''secondary'' characterof which the distinction is far from clear for the users, considering the ambiguity of these notions in the pharmaceutical leaflets. While, strictly speaking, a "secondary side effect" is a non-desired consequence, induced by the administration of a drug, and which is additional to the primary desired effect during the application of a treatment for a given indication, an "adverse side effect" is "a response to a drug that is noxious and unintended and occurs at doses normally used in man for the prophylaxis, diagnosis or therapy of disease, or for the recovery, correction or modification of physiological function". [START_REF] Fainzang | Médicaments et sociétés. Le patient, le médecin et l'ordonnance[END_REF] In this regard, in France, mentioning "side effects" on a pharmaceutical leaflet carries less negative connotations than saying "adverse side effects". It is in fact in this sense that the WHO intends these two notions to be used.

Yet it is noticeable that some medicines are chosen precisely for their side effects, and not for the intended indication of the medicine, transforming the side effect into the desired, and so primary, effect. In this case, the side effect is no longer simply a sign of efficacy, but the vector of a new efficacy, that leads to a drug use that is not in accordance with the indications but with the side effects or, we could say, because of the side effects. The side effect can thus be identified as a "side benefit". Indeed, some medicines are chosen precisely for their adverse sideeffects. For example, certain antihistamines (such as Polaramine), or cough medicines (such as Toplexil) are sometimes taken as hypnotics because of the drowsiness they induce. In this way Mrs L uses Neo-codion to curb the difficulties her child experiences in getting to sleep -she thinks he is too excited in the evening. Even though drowsiness is a "possible adverse side effect" of the medicine, induced by the presence of codeine, it is used precisely for this effect, and not for its indication as a cough mixture. Here the subjects choose the medicine because of its sedative qualities, their decision supported by the recommendation in the patient information leaflet to take the substance in the evening. This is the case for Lexomil which users often take not for the indicated use (which is a symptomatic treatment of manifestations of severe and/or incapacitating anxiety), but in order to induce drowsiness, considered to be one of the adverse side effects of this medicine. [START_REF] Sarradon-Eck | Le sens de l'observance[END_REF] Such forms of use show that a side effect normally deemed undesirable can in fact become a desired effect.

Users and biomedical logics

Just as users adjust the posology indicated in the leaflet partly in response to the concern to not over-consume medicines that could potentially harm their health, they also resort to such practices with the intention of arriving at an optimal use of the medicines, based on a realignment between cumulative logic and identity logic, and between efficacy and safety. The definitions or redefinitions of treatments in self-medication are based on a logic the subjects perceive to be medical, to the extent that they are convinced that in this way they are conforming to the safety precautions, and are adapting their self-prescription to their bodies and their unique characteristics (their age, sex, weight, etc.).

Certainly, some of the strategies devised by subjects to reduce the risk or maximise the efficacy of a treatment sometimes totally escape scientific logic. For example, using one's dog's experience or a radiesthesist's pendulum are techniques of validation which do not pertain to the biomedical field. However, my intention here is not to discriminate between ''good'' and ''bad'' practices when managing risks, but to understand the symbolic logic to which this risk management relates and the mechanisms according to which it is elaborated. Yet, when Mr P decides to take an anti-emetic drug only after he has made sure that his dog has tolerated it well, the aim is to be sure of the harmlessness and effectiveness of a drug from the experience of someone of his close circle (to which the dog belongs). His decision results from an approach which, in his eyes, makes his practice a validated, proven technique, opposing experience-based medicine with evidence-based medicine.

Likewise, when Mr J has her medicines ''tested'' by a radiesthesist to verify their safety and efficacy, she does this believing she is complying with medical recommendations and ensuring the medicine is suitable for her; she is perfectly aware of the need for a treatment to be adapted to each individual, and resorts to dowsing to test the drugs that are advised to her, in order to make sure that they are appropriate to her case. Thus, her strategy borrows from a medical discourse stressing that treatments must be adapted to individuals organisms and characteristics. This is an example of a strategy which is not only anchored in syncretic cultural logic but borrows from, while radically distorting, medical logic. The need for a treatment to be adapted to a person is in fact what the majority of health professionals underline, explaining (among the reasons justifying the need to ask for advice from a pharmacist), that each person reacts differently to drugs. By her behaviour, this lady seeks to conform to instructions diffused by the medical discourse, namely that the treatment should be personalised.

Therefore, although subjects may behave contrary to the recommendations of health professionals, they borrow their logics from medical discourse. After a lecture in which he explained the Filipino concept of hiang (which refers to the belief that a medicine should fit the person that takes it), Van der Geest [START_REF] Van Der | Discussing and testing efficacy[END_REF] writes that a pharmacologist perceptively remarked that this ''personal fitting/not fitting was what clinical pharmacologists were struggling with and trying to apply in new ways of testing". However, as we have seen here, the principle of personalising treatment exists well beyond such tests since it structures the medicinal practices of western patients with strategies that can prove to be totally foreign to medical logic.

Conclusion

The strategies employed within the practice of self-medication aim to both minimise the risks associated with medicines and to maximise their effect. There is thus a tension between two objectives: the search for efficacy and the prevention or management of risk. Safety and efficacy are considered simultaneously. Subjects seek to achieve a balance between the two, that is to say they search for efficacy with minimal risk by applying a balancing principle. This balancing between a given substance and one's body, which is considered according to an individual's personal rationality, is underpinned by symbolic, cultural or idiosyncratic logic.

The logics underpinning self-medication (to manage risk and obtain efficacy) are partly comparable to those underpinning prescription compliance (or non-compliance). However, the balance here leans towards a different recombination, in that these logics integrate more decisively the need for the subjects to establish an appropriate relationship, in accordance with personal rationalities, between a given substance and their bodies. The decision to modify the posology of a treatment or to verify the suitability of a medicine to one's personal bodily characteristics, by using what I have called cumulative logic and identity logic, or by means of the validation techniques mentioned above, is founded on the internalisation of learned behavioural norms, transmitted during the whole process of patient socialisation by health professionals.

However, these practices are not perceived to conflict with medical recommendations and although they do not echo professional logics, they borrow from biomedical ones. Subjects perceive them to be wholly in keeping with advice to be prudent, to be aware of the risks associated with medicines and to choose personalised treatments. Indeed, it is in order to reduce the risks of medicines that subjects adapt and personalise their treatments. As we have seen, the necessity for treatments to be adapted to an individual is highlighted by the majority of health professionals themselves; they point out in their recommendations to users that each person reacts differently to medicines. The methods of validation used by some subjects thus aim to respond to the instructions diffused by medical thinking, namely that treatments should be personalised. While their choices may be structured according to symbolic and cultural logics, subjects feed off medical notions to formulate their practices, taking recourse to strategies of validation, verification, experimentation or personalisation.

On the perception of "calming" medicine, see Haxaire[START_REF] Haxaire | Calmer les nerfs: automédication, observance et dépendance à l'égard des médicaments psychotropes[END_REF] .

According to the WHO and EU official definition.

We should note that the confusion between side effects and adverse side effects is maintained in the way the pharmaceutical information leaflets are written, where neuro-vegetative effects such as drowsiness, induced by certain molecules, are sometimes mentioned in the side effects and sometimes in the adverse side effects.