Dr Nabil Mroweh

Dr Cécile Mézière

Dr Flavia Pop
email: flavia.pop@univ-angers.fr

Dr Pascale Auban-Senzier

Pere Alemany

Dr Enric Canadell
email: canadell@icmab.es

Narcis Avarvari
email: narcis.avarvari@univ-angers.fr

Prof P Alemany

In search of chiral molecular superconductors: κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 revisited

Keywords: chirality, superconductivity, molecular conductors, band structures

The relationship between chirality and superconductivity is an intriguing question. The two enantiomeric crystalline radical cation salts κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 and κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 , showing -type arrangement of the organic layers, are investigated in search for superconducting chiral molecular materials following a 1992 report indicating the occurrence of a superconducting transition in the former compound. While the initial interpretation is presently challenged through in-depth temperature and pressure dependent single crystal resistivity measurements combined with band structure calculations, the two chiral conductors show metal like behaviour with room temperature conductivities of 10-30 S cm -1 at ambient pressure and stabilization of the metallic state down to the lowest temperatures under moderate pressures. Moreover, their structural and theoretical investigations reveal an original feature, namely the existence of two different  layers with

1D and 2D electronic dimensionality, respectively, as a consequence of an inter-layer charge transfer. The resistivity drop observed for one sample below 1 K and insensitive to magnetic field, possibly results from mixing in-plane and out-of-plane contributions to the measured resistance and suggests current induced charge order melting. This feature contradicts the occurrence of superconductivity in these chiral molecular conductors and leaves open the discovery of the first chiral molecular superconductors.

The quest for chiral molecular conductors [1] started in the middle of the eighties with the synthesis by Dunitz and Wallis of the first enantiopure tetrathiafulvalene (TTF) precursor, namely the (S,S,S,S) enantiomer of tetramethyl-bis(ethylenedithio)-TTF (TM-BEDT-TTF, Figure 1a), [2] together with the preparation of several chiral conducting salts. [3] The dimethylated precursor DM-BEDT-TTF (Figure 1a), containing only two stereogenic centres, was reported a few years later by Zambounis for the (S,S) enantiomer [4] and by Sugawara and Kawada for the (R,R). [5,6] The latter also described in the same report the (R,R,R,R) enantiomer of TM-BEDT-TTF. [5] While at that period chiral conductors were considered mostly from a chemical and crystallographic point of view as a means of variation of the library of available precursors for organic metals and superconductors, crystal packing issues and decrease of the structural disorder due to the flipping of the ethylene bridge in BEDT-TTF based conductors, their interest was revived and put in a new light thanks especially to the first experimental observations of the electrical magnetochiral anisotropy (eMChA) effect by Rikken. [7,8] This phenomenon, translating the direct influence of chirality on the electron transport properties measured in a longitudinal magnetic field, together with other indirect chirality triggered effects, such as the modulation of the structural disorder [9,10] or induction of different crystal packing between the enantiopure and racemic forms resulting in different conducting properties, [11] highly motivated intense efforts in the search of new chiral TTF precursors and conducting salts. [12] Accordingly, besides conducting salts with TM-BEDT-TTF [13][14][15][16] and DM-BEDT-TTF, [17,18] the new enantiopure EDT-TTF based donors dimethylethylenedithio-TTF (DM-EDT-TTF, Figure 1a) [19] and, very recently, methyl-EDT-TTF (Me-EDT-TTF, Figure 1a), [20] together with derived radical cation salts, have been prepared, culminating with the (DM-EDT-TTF) 2 ClO 4 salts which allowed the first observation of the eMChA effect in a bulk chiral crystalline material. [21] In this respect, particularly interesting is the recent observation of enhanced non-reciprocal charge transport in the superconducting state of the non-centrosymmetrical inorganic materials WS 2 nanotubes [22] and MoS 2 thin crystals. [23] Chiral superconductors are very intriguing since the degeneracy between electrons associated with k and -k wavevectors, i.e. the essential components of the Cooper pairs, is broken under magnetic field because of the electrical magnetochiral anisotropy. Besides, chiral superconductivity stimulates increasing endeavour in view of the exotic properties and functionalities that are predicted or observed, such as spontaneous generation of magnetic fields, [24] superconducting diodes [23] or quantum computing. [25] However, all these studies concern purely inorganic materials which, when they are obtained in crystalline forms, happen to crystallize in non-centrosymmetric structures, [26,27] yet this feature is impossible to predict as the initial components do not contain any chiral bias such as a stereogenic centre. Moreover, the two enantiomorphic forms and the racemate are hardly accessible in order to investigate and compare their properties in the superconducting state. As a consequence, the access to molecular chiral superconductors starting from enantiopure precursors with controlled chirality is of huge interest. We have therefore decided to explore the mixed valence salt κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 together with its (R,R) enantiomer, since the former is, paradoxically when considering the numerous examples of BEDT-TTF based superconductors, [28] the only chiral organic conductor to date claimed to show superconductivity, as described by Zambounis et al. back in 1992. [29] However, puzzling enough, no further report from the same group or others confirmed this initial statement, in spite of a result of fundamental importance in the fields of superconductivity and chirality. We describe herein the synthesis, structural characterization, conducting properties and in-depth extended Hückel and DFT band structure calculations of both enantiomers of κ-[DM-BEDT-TTF] 2 ClO 4 .

The two enantiomers (S,S) and (R,R) of DM-BEDT-TTF (Figure 1a) have been prepared according to the literature, [5,18] and then they were engaged in electrocrystallization, first in the experimental conditions described in the original paper, [29] that is in THF at room temperature (the temperature was not indicated though) under a current of 3 A in the presence of (n-Bu 4 N)ClO 4 as supporting electrolyte. In spite of numerous trials we did not obtain any crystalline compounds for either of the enantiomers, which determined us to slightly vary the donor/anion ratio, the temperature and current intensity. Performing the experiment at 3 °C with a current intensity of 0.5 A (details in the ESI) eventually allowed us to obtain black crystalline plates of both enantiomeric salts. Single crystal X-ray analyses were in agreement with the reported unit cell parameters for the κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 phase, the crystalline space group being the monoclinic non-centrosymmetric P2 1 (Table S1, ESI). The original structure, for which the reliability factor was rather high, i.e. 13.3%, was measured at room temperature (RT). While the authors pointed out that the perchlorate ions were disordered, they omitted to mention that in the asymmetric unit there are four independent donor molecules, hereafter noted A-D, and two anions, therefore the actual stoichiometry is 4:2 and not 2:1 (Figure 1b for the (R,R) and Figure S1 for the (S,S) enantiomers). We have measured our structures both at RT and T = 150 K with similar results.

Expected differences between the two measurements, such as volume decrease due to thermal contraction and better defined ellipsoids for some atoms at 150 K, have been observed but no disorder for either the anions or the ethylene bridges. Moreover, the reliability factors and Flack parameters for the structures at 150 K are indicating the high quality X-ray diffraction data for both enantiomers (see the ESI).

As discussed by Zambounis et al., [29] the most striking structural feature of this salt is the type arrangement of the donors (Figure S2-S5, ESI). However, a detail of utmost importance that has been overlooked in the original report is the existence of two different -type layers formed either by A-B dimers (layer 1) or by C-D dimers (layer 2) (Figure 2a for layer 1, layer 2 is formed by C-D dimers and shows the same architecture, vide infra). The C=C and internal C-S bond lengths values are rather similar for the four A-D donors (Table S2, ESI) and do correspond to a mixed valence state. While very few BEDT-TTF salts containing two different alternating layer types such as - 30 and -"pseudo-" [31] have been described, those possessing two different  layers are exceptionally rare and present potentially huge interest with respect to their electronic structures. As a matter of fact, to the best of our knowledge, there is only one reported example of such material and it concerns the -(BEDT-TTF) 4 PtCl 6 •C 6 H 5 CN salt which shows a very weakly activated conductivity down to 250 K where a first order phase transition takes place towards an insulating regime. [32] In that case it was proposed that the two different -layers [33] in the temperature range before the phase transition contain BEDT-TTF molecules in three different oxidation states. [34] In our enantiopure salts -(DM-BEDT-TTF) 4 (ClO 4 ) 2 every layer is built from two different donors A/B (layer 1, Figure 2a) or C/D (layer 2), making identical A-B or C-D dimers. There are six different intermolecular interactions in every layer (Figure 2a). Every dimer (interaction I) makes chains of dimers along the vertical axis b, through interaction II, and these chains are connected through four interactions: III / IV at one side of the chain and V / VI at the other side. To understand the electronic structure and transport properties of these salts we need to have a hint on the strength of the HOMO … HOMO interactions since there are the HOMO bands which are going to be partially emptied. This may be done by looking at the absolute value of the so-called HOMO … HOMO interaction energy, [35]  HOMO-HOMO , associated with each interaction. The calculated values for the six interactions in the two different layers of the two pure enantiomeric salts are reported in Table 1.

The calculated values of Table 1 clearly show that from the viewpoint of the HOMO … HOMO interactions (i) the salts of the two enantiomeric donors are practically identical and (ii) the two layers of the same salt exhibit noticeable differences. This is further confirmed when looking at the HOMO energies of the different donors. Whereas the difference between those of dimers C-D is practically nil (~ 0.001 eV in both the (R,R) and (S,S) salts) the difference is clear between those of dimers A-B (~ 0.030 eV in the (R,R) salt and ~ 0.090 eV in the (S,S) salt). Even if keeping the general topology of the band structure for  phases, the difference between the two types of layers leads to marked differences in their band structures (Figure 2b For a -type layer with one type of dimer as in the present salts, the separation of these two bands along this line depends on the values of the transfer integrals relating the dimers of different chains. When these interactions become very similar on both sides of the chain the two bands tend to collapse. As the values in Table 1 show, the interactions at both sides of the chains (III/IV vs V/VI) are very similar in type 2 layers but markedly different in those of type 1. Thus, it is understandable that the bands of layer 1 are well separated along X-M in Figure 2b (top left) whereas those of layer 2 are not (Figure 2b top right).

The Fermi surfaces calculated assuming an equal partition of the four holes between the two layers exhibit some important differences (Figure 2b As noted before [36] this kind of Fermi surface occurs in  phases when the donor layer becomes more one-dimensional (1D) along the direction of the donor chains. Such change in the shape of the closed portion of the Fermi surface is related to the fact that the Fermi level cuts the lower partially filled band very close to the  point (Figure 2b top left). Obviously, a very small electron transfer towards layer 2 would shift the Fermi level below this band at and the initially closed portion would disappear to become a warped line, something that may strongly affect the physical behavior. The two salts share all the mentioned features of the electronic structure (Figure S6 and S7, ESI, for the band structure and Fermi surface of [(S,S)-DM-BEDT-TTF] 2 ClO 4 ). Consequently, the question of the possible inter-layer charge transfer becomes a key issue in understanding the electronic structure of these salts.

Under such conditions only first-principles approaches treating on the same foot all components of the system and taking explicitly into account the interaction between donor and anion layers may lead to a correct description of the system. Thus, we have carried out a DFT study of the two salts. The calculated band structure for [(R,R)-DM-BEDT-TTF] 2 ClO 4 is shown in Figure 2c top. Among the four partially filled bands (in the full calculation the bands of the two different layers superpose) it is clear that two of them are clearly separated along the X-M line whereas the other two are much less. The first pair is associated with layer 1 whereas the second is associated with layer 2. The important feature of Figure 2c It is worth noting that if the hole transfer between layers is taken into account in the extended Hückel calculations, the correct Fermi surfaces are obtained (Figure S9). In summary, both the asymmetry in the interactions between chains of dimers and the important transfer of holes between the two types of layers work together to make the electronic structure of the two layers in -[(R,R)-DM-BEDT-TTF] 2 ClO 4 and -[(S,S)-DM-BEDT-TTF] 2 ClO 4 considerably different. Although some portions of the Fermi surface associated with layer 1 exhibit nesting, a large part of the Fermi surface would remain unaffected so that the metallic state of the present salts should be kept until low temperatures as far as the interlayer electron transfer does not change significantly as a consequence of thermal contraction. In addition, the electronic structure of the two layers is different enough so as to make the simultaneous electron localization in the two layers (which in addition have a non-integer number of electrons per layer), in principle, unlikely.

With the two crystalline enantiomeric materials in our hands, we set out to measure single crystal resistivity in order to track down the superconducting transition. Careful temperature dependent in-plane resistivity measurements at various pressures have been performed on several single crystals of each enantiomer. Since no abrupt decrease of resistivity has been observed for any of the investigated temperature range and pressures, we can safely conclude that, contrary to what was claimed in the 1992 report, [29] there is no indication of the occurrence of superconductivity in this compound (Figure 3a Both enantiomeric compounds are weakly metallic at ambient pressure down to 80 K, with a room temperature in-plane conductivity of 10-30 S cm -1 (the large range of values could be related to an anisotropy of the conductivity within the plane) and then a smooth metal to insulator (MI) transition occurs. Upon applying pressure the metallic regime is steadily stabilized down to the lowest temperatures, yet a small localization still occurs below 10 K at pressures as high as 14.5 kbar. This behavior strikingly differs from the one described in 1992. [29] First, the room temperature conductivity at ambient pressure was 0.05 S cm -1 , which is two orders of magnitude lower than in our case, and therefore could be tentatively assigned to an out-of-plane value (vide infra). Then, the weakly metallic conductivity down to 75 K followed by a MI transition observed at ambient pressure is comparable to our results, but the evolution under pressure is quite different. Unexpectedly, the insulating behavior was reinforced under pressures up to 10 kbar in the high temperature regime and was followed below 35 K by a sharp decrease of the resistivity. Structure determinations and DFT calculations (vide supra) suggest that in-plane transport data should combine 1D conduction in layers 1 and 2D conduction in layers 2 and their contributions are expected to vary differently with the temperature. In our experiments the room temperature in-plane conductivity shows a linear dependence with the pressure with a rate between +20 and +30%/kbar for both enantiomers (Figure S14-S15, ESI), as expected for 1D or 2D molecular metals. We have also checked the perpendicular (out-of-plane) resistivity  perp for -[(S,S)-DM-BEDT-TTF] 2 ClO 4 at ambient pressure. Its room temperature value is more than two orders of magnitude higher than the in-plane value and its temperature dependence is nearly proportional to in-plane data (Figure S16, ESI). This feature is commonly observed in 2D  phases of BEDT-TTF salts.

However, for one of the crystals of [(S,S)-DM-BEDT-TTF] 2 ClO 4 (#2) we observed a sharp MI transition below 80 K which is even preserved under a moderate pressure (Figure S11, ESI). This is reminiscent of a charge density wave transition typical of 1D conductors [37] or a charge ordering transition. The presence of steps on the large faces of the crystal or defects generated by microcracks during cooling down could imply a mixing of in-plane and out-ofplane contributions to the measured resistance. Moreover, amazingly, within this insulating regime, a variation of the current density (in the mA/cm 2 range) induced a sudden decrease of the resistance from several k to nearly 0 at very low temperatures (Figure 3c), very much alike to the resistivity drop reported by Zambounis et al. in 1992, [29] which was tentatively assigned to a superconducting transition. Nevertheless, this phenomenon is not altered under a magnetic field two times larger than the Pauli limit considering a SC critical temperature of about 1K (Figure 3d), an argument which is against the occurrence of a superconducting state.

Actually, this behavior reminds the current-induced melting of a charge ordered state, observed, for example, in the case of the so-called organic thyristors θ-(BEDT-TTF) 2 CsM(SCN) 4 (M = Co, Zn) exhibiting giant non-linear conduction at low temperatures, [38,39] or in the (EDT-TSF) 2 GaCl 4 phase. [40] The recent observation of the electrical magnetochiral anisotropy in a bulk chiral molecular conductor reopened the longstanding question of the relationship between chirality and superconductivity in bulk materials. This is especially attractive in the case of molecular conductors because of the many ways to tune their electronic structures and to control the absolute configuration. In this work we have prepared by electrocrystallization and thoroughly analyzed the two enantiomeric radical cation salts κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 and κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 , the former being previously described as possibly undergoing a transition towards a superconducting state under pressure, [29] although not confirmed later on by additional investigations. Single crystal diffraction on our materials revealed an original type of packing consisting of two different -layers formed of orthogonal dimers of crystallographically distinct donors. Band structure calculations suggest that these salts are very unusual because of the charge transfer between different cationic layers. As a result, the different layers have also a different electronic dimensionality (1D and 2D) which is unprecedented in -phases. Single crystal resistivity measurements showed weakly metallic conductivity at ambient pressure followed by a smooth metal to insulator transition at 80 K, while the metallic state is stabilized under pressure, a behavior in strike contrast from the one reported in 1992, since no abrupt decrease of resistivity was noticed in our study. The earlier results might find their interpretation in a current intensity induced melting of a charge order state, in line with our own observation of a current dependent resistivity drop under pressure in one sample possibly mixing in-plane and out-of-plane conductivity. Since this resistivity decrease remains unchanged under magnetic field, it unambiguously indicates that it is not related to a superconducting transition. This result is of utmost importance as it leaves open the quest for the first chiral molecular superconductor and spotlights the research on the growing family of chiral molecular conductors provided with intriguing properties. Table 1. Absolute values of the  HOMO-HOMO interaction energies [35]

R(F o ) = F o  -F c /F o ; R w (F o 2 ) = [[w(F o 2 -F c

  top). Whereas the two upper HOMO bands, which are partially filled, are almost degenerate along one of the borders of the Brillouin zone (X-M line in Figure 2b top) for the type 2 layers, they are substantially separated for the type 1 layers.

  bottom). Whereas that of layer 2 (Figure 2b bottom right) exhibits the typical shape for  salts, a series of overlapping almost circular sections and thus leading to formally open and closed portions separated by a small gap, that of layer 1 exhibits a different closed part, which looks as a rounded square (Figure 2b bottom left).

  top is that at  the Fermi level lies below the bottom part of the second band of layer 1 so that the closed part of the Fermi surface originating from layer 1 must have disappeared. The calculated DFT Fermi surface is shown in Figure 2c bottom where the portions associated with layers 1 and 2 are shown in blue and red, respectively. Whereas the contribution of layer 2 is that typical of  phases with the open and closed portions separated by a small gap, that of layer 1 is made of two open and warped lines perpendicular to the direction of the chains of dimers. All these results are shared by the two salts (Figure S8, ESI). Thus, (R,R)-and [(S,S)-DM-BEDT-TTF] 2 ClO 4 contain two structurally similar but electronically very different donor layers with different dimensionality. In order to further characterize the electronic structure of these phases we have evaluated the density of holes for each of the four donor molecules by integrating the associated projected density of states of the four partially filled bands. We obtained the values +0.62 (donor A), +0.58 (donor B), +0.39 (donor C) and +0.41 (donor D) for [(R,R)-DM-BEDT-TTF] 2 ClO 4 , and +0.63 (donor A), +0.57 (donor B), +0.40 (donor C) and +0.40 (donor D) for [(S,S)-DM-BEDT-TTF] 2 ClO 4 . Consequently, there is almost no charge difference between the two donors C-D of layer 2, only a slight charge transfer of +(0.04-0.06) between the two donors A-B of layer 1 and an important transfer of holes from layer 2 to layer 1 amounting to ~ 0.20 e. Thus, the bands of layer 1 are raised in energy and considerably depopulated mostly because of the asymmetry in the interactions between the chains of dimers so that the lowest band contribution to the Fermi surface evolves from closed to open. In contrast, the similarity of the interactions at both sides of the dimer chains of layer 2 keeps the typical shape of the Fermi surface for  phases, with both closed and open contributions separated by a small gap.

  ,b and Figure S10-S13, ESI).

Figure 1 .

 1 Figure 1. a) Enantiopure BEDT-TTF and EDT-TTF based donors including DM-BEDT-TTF, involved in this study. b) Crystalline structure of κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 highlighting the four independent donors and two anions in the asymmetric unit.

Figure 2 .

 2 Figure 2. a) Donor layer 1 of the -[(R,R)-DM-BEDT-TTF] 2 ClO 4 and -[(S,S)-DM-BEDT-TTF] 2 ClO 4 salts where the different donors and intermolecular interactions are labelled. b) (top panels) Extended Hückel band structure for the two donor layers of -[(R,R)-DM-BEDT-TTF] 2 ClO 4 : (left) layer type 1, and (right) layer type 2. The dashed line refers to the calculated Fermi level assuming two holes per layer.  = (0, 0), X = (a*/2, 0), Y = (0, b*/2), M = (a*/2, b*/2) and S = (-a*/2, b*/2). (bottom panels) Extended Hückel Fermi surface for the two donor layers of -[(R,R)-DM-BEDT-TTF] 2 ClO 4 assuming an equal partition of holes between the two layers: (left) layer type 1, and (right) layer type 2. c) DFT electronic structure of the -[(R,R)-DM-BEDT-TTF] 2 ClO 4 salt: (top) Band structure where the dashed line refers to the Fermi level and  = (0, 0, 0), X = (1/2, 0, 0), Y = (0, 1/2, 0), M = (1/2, 1/2, 0) and Z = (0, 0, 1/2) in units of the reciprocal lattice vectors. The partially filled bands associated with the two types of layers are labelled; (bottom) Fermi surface (section for c* = 0.0) where the blue and red contributions are those of layers 1 and 2, respectively.

Figure 3 .

 3 Figure 3. Temperature dependence of the in-plane electrical resistivity   for a single crystal of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 (a) and for a single crystal of κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 (b) at different pressures. c) Temperature dependence of the electrical resistivity  for a single crystal (#2) of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 in 4 points for different current intensities and under an applied pressure of 7.5 kbar. It shows a current induced insulator to metal transition below 1 K. d) Temperature dependence below 2 K of the in-plane electrical resistivity for a single crystal of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 (#2) at 7.5 kbar plotted for two different applied currents and different magnetic fields applied perpendicularly to the (a,b) plane.

  (eV) for the different donor•••donor interactions in the [(R,R)-DM-BEDT-TTF] 2 ClO 4 and [(S,S)-DM-BEDT-TTF] 2 ClO 4 salts.

The enantiopure mixed valence

  radical cations salts -[(S,S)-DM-BEDT-TTF] 2 ClO 4 and -[(R,R)-DM-BEDT-TTF] 2 ClO 4 , prepared by electrocrystallization of the chiral donor DM-BEDT-TTF, show metallic conductivity but no superconducting transition, unlike the conclusions of an earlier report. Original structural and electronic features consisting in two different -type layers having 1D and 2D electronic dimensionality are revealed by structural investigations and band structure calculations. Chiral conductors N. Mroweh, C. Mézière, F. Pop,* P. Auban-Senzier, P. Alemany, E. Canadell,* N. Avarvari* In search of chiral molecular superconductors: κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 revisited Table S1. Crystal Data and Structure Refinement for κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 and κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 , both at r.t. and 150 K.

Figure S6 .

 S6 Figure S6. Extended Hückel band structure for the two donor layers of -[(S,S)-DM-BEDT-TTF] 2 ClO 4 : (a) layer type 1, and (b) layer type 2. The dashed line refers to the calculated Fermi level assuming two holes per layer.  = (0, 0), X = (a*/2, 0), Y = (0, b*/2), M = (a*/2, b*/2) and S = (-a*/2, b*/2).

Figure S7 .

 S7 Figure S7. Extended Hückel Fermi surface for the two donor layers of -[(S,S)-DM-BEDT-TTF] 2 ClO 4 assuming an equal partition of holes between the two layers: (a) layer type 1, and (b) layer type 2.

Figure S8 .

 S8 Figure S8. DFT electronic structure of the -[(S,S)-DM-BEDT-TTF] 2 ClO 4 salt: (a) Band structure where the dashed line refers to the Fermi level and  = (0, 0, 0), X = (1/2, 0, 0), Y = (0, 1/2, 0), M = (1/2, 1/2, 0) and Z = (0, 0, 1/2) in units of the reciprocal lattice vectors. The partially filled bands associated with the two types of layers are labelled; (b) Fermi surface (section for c* = 0.0) where the blue and red contributions are those of layers 1 and 2, respectively.

Figure S9 .

 S9 Figure S9. Extended Hückel Fermi surface for the two donor layers of -[(S,S)-DM-BEDT-TTF] 2 ClO 4 where the DFT hole transfer between the two layers is taken into account: (a) layer type 1, and (b) layer type 2.

Figure S10 .

 S10 Figure S10. Temperature dependence of the in-plane electrical resistivity   (T) for a single crystal of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 (#1) at different pressures, in the whole measured temperature range (two upper graphs) and below 50 K (bottom).

Figure S11 .

 S11 Figure S11. Temperature dependence of the in-plane electrical resistivity   (T) for a single crystal of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 (#2) at different pressures.

Figure S12 .

 S12 Figure S12. Temperature dependence of the in-plane electrical resistivity   (T) for a single crystal of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 (#3) at different pressures, in the whole measured temperature range (top) and below 50 K (bottom). The resistivity of sample #3 under 17 kbar could not be measured below 130 K because of a contact to the ground of one of the wires in the feedthrough.

Figure S13 .

 S13 Figure S13. Temperature dependence of the in-plane electrical resistivity   (T) for a single crystal of κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 (#2) at P = 1 bar in linear (top) and logarithmic (bottom) vertical scale.

Figure S14 .

 S14 Figure S14. Pressure dependence of the in-plane electrical conductivity at room temperature for the three single crystals of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 measured under pressure. The black line is the linear fit to the data.

Figure S15 .

 S15 Figure S15. Pressure dependence of the in-plane electrical conductivity at room temperature for a single crystal of κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 (#1). The black line is the linear fit to the data.

Figure S16 .

 S16 Figure S16. Temperature dependence of the in-plane   and out-of-plane  perp electrical resistivity for single crystals of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 at ambient pressure.

Figure S17 .

 S17 Figure S17. Picture of the black crystalline plates of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 .

Figure S18 .

 S18 Figure S18. Different views of the measured single crystal of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 mounted on a loop fiber in fomblin oil.

Figure S19 .

 S19 Figure S19. Different views of the measured single crystal of κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 mounted on a loop fiber in fomblin oil.

Figure S20 .

 S20 Figure S20. Millimeter size single crystalline plates of κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 for single crystal resistivity measurements.

Figure S21 .

 S21 Figure S21. Millimeter size single crystalline plates of κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 for single crystal resistivity measurements.

Table S2 .

 S2 Selected bond lengths (Å) for κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 and κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4 at 150 K.

	Molecule	C═C (Å)	C─S (Å)	Molecule	C═C (Å)	C─S (Å)
	A	1.3540(98) 1.7438(84)	A	1.3581(73) 1.7269(49)
			1.7480(87)			1.7501(51)
			1.7587(86)			1.7435(61)
			1.7308(83)			1.7414(56)
	B	1.3586(99) 1.7428(86)	B	1.3553(76) 1.7423(60)
			1.7527(94)			1.7302(56)
			1.7368(87)			1.7365(56)
			1.7418(83)			1.7524(61)
	C	1.3512(148) 1.7546(91)	C	1.3560(65) 1.7576(49)
			1.7257(95)			1.736(5)
			1.7300(99)			1.7401(51)
			1.7552(100)			1.7477(49)
	D	1.3891(149) 1.7251(99)	D	1.3538(67) 1.7481(49)
			1.7317(99)			1.7455(51)
			1.7306(99)			1.7313(51)
			1.7391(99			1.7538(49)

κ-[(S,S)-DM-BEDT-TTF] 2 ClO 4 κ-[(R,R)-DM-BEDT-TTF] 2 ClO 4

) 2 ]/[w(F o 2 ) 2 ]] 1/2

Acknowledgements

This work was supported in France by the ANR (Project 15-CE29-0006-01 ChiraMolCo), the CNRS and the University of Angers. Work in Spain was supported by the Spanish MICIU (Grants PGC2018-096955-B-C44 and PGC2018-093863-B-C22), the MINECO (Grant SEV-2015-0496 and MDM-2017-0767) and by Generalitat de Catalunya (2017SGR1506 and 2017SGR1289).

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

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

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author. was added in the cathodic compartment of the electrocrystallization cell. Single crystals, as black crystalline plates, of the salt were grown at 2-3 °C over a period of 10 days on a platinum wire electrode by applying a constant current of 0.5 μA.

X-Ray structure determinations

Details about data collection and solution refinement are given in Table S1. Single crystals of the compounds were mounted on glass fibre loops using a viscous hydrocarbon oil to coat the crystal and then transferred directly to cold nitrogen stream for data collection. X-ray data collection were performed at 150 K on an Agilent Supernova with CuKα (λ = 1.54184 Å) and at 293 K on a Nonius Kappa CCD diffractometer, using graphite-monochromated MoK  radiation ( = 0.71073 Å). The structures were solved by direct methods with the SHELXS-97 and SIR92 programs and refined against all F2 values with the SHELXL-97 program 1 using the WinGX graphical user interface. 2 . All non-H atoms were refined anisotropically.

Hydrogen atoms were introduced at calculated positions (riding model), included in structure factor calculations but not refined.

Band structure calculations

Computational details

The tight-binding band structure calculations were of the extended Hückel type. 1 A modified Wolfsberg-Helmholtz formula was used to calculate the non-diagonal H  values. 2 All valence electrons were taken into account in the calculations and the basis set consisted of Slater-type orbitals of double- quality for C 2s and 2p, S 3s and 3p and of single- quality for H 1s. The ionization potentials, contraction coefficients and exponents were taken from previous work. 3 The first-principles calculations were carried out using a numerical atomic orbitals density functional theory (DFT) approach 4,5 which was developed for efficient calculations in large systems and implemented in the SIESTA code. [6][7][8] We have used the generalized gradient approximation (GGA) to DFT and, in particular, the functional of Perdew, Burke and Ernzerhof. 9 Only the valence electrons are considered in the calculation, with the core being replaced by norm-conserving scalar relativistic pseudopotentials 10 factorized in the Kleinman-Bylander form. 11 We have used a split-valence double- basis set including polarization orbitals with an energy shift of 10 meV for all atoms. 12 The energy cutoff of the real space integration mesh was 250 Ry. The Brillouin zone was sampled using a grid of (20×20×5) kpoints 13 in the irreducible part of the Brillouin zone. The experimental crystal structures were used for the calculations.

Conductivity measurements

Electrical resistivity was measured on platelet-shaped single crystals of both enantiomers using a four-point method. Four aligned gold contacts were evaporated on both large faces of the crystals for the in-plane configuration and two gold contacts were evaporated on each large face of the crystals for the out-of-plane configuration. Gold wires were glued with silver paste on those contacts. A low-frequency (<100 Hz) lock-in technique was used with a measuring current I ac = 10 μA. Lower values down to 0.1 µA were used for out-of-plane measurements and the non-linearity study in #2 of (S,S) enantiomer.

Resistivity measurements were also performed under high hydrostatic pressure in homemade clamped cells either a CuBe one up to 12 kbar or a NiCrAl one up to 20 kbar. The pressure is measured at room temperature when the pressure is varied using a manganin gauge and silicon oil (Daphne 7373) is used as the pressure transmitting medium. The loss of pressure during cooling is estimated to 2 kbar between 300 and 50 K, however the pressure indicated in the figures is the pressure measured at room temperature.

Resistivity measurements have been performed in the temperature range 4-300 K using a cryostat equipped with a 4 K pulse-tube (out-of-plane measurements, #1 of (S,S) enantiomer and (R,R) enantiomer) and in a dilution refrigerator down to 100 mK for the highest-pressure experiments (#2 and #3 of (S,S) enantiomer) equipped with a superconducting coil for generating the magnetic field.

In our measurements, the applied electric field is in the range 5-15 mV/cm and the maximum current density is 0.02 A/cm 2 for I = 10 µA.

The dimensions of the measured samples in ref. 40 are not given so that we cannot compare with our data in terms of electric field and current density. For the phase of BEDT-TTF salts (refs. 38-39) the dimensions of the measured samples are comparable to ours. We have studied a much smaller range in electric field and current density compared to these works: the current density reaches 18 A/cm 2 in ref. 39


Electrocrystallization of the BEDT-TTF organic donor in the presence of the [Fe(ClCNAn)3] 3- tris(chlorocyananilato)ferrate(III) paramagnetic anion in different stoichiometric ratios and solvent mixtures afforded two different hybrid systems formulated as [BEDT-TTF]4[Fe(ClCNAn)3]•3H2O

(1) and [BEDT-TTF]5[Fe(ClCNAn)3]2•2CH3CN (2). Compounds 1 and 2 present unusual structures without the typical segregated organic and inorganic layers, where layers of 1 are formed by Λ and Δ enantiomers of the anionic paramagnetic complex together with mixed-valence BEDT-TTF tetramers, while layers of 2 are formed by Λ and Δ enantiomers of the paramagnetic complex together with dicationic BEDT-TTF dimers and monomers. Compounds 1 and 2 show semiconducting behaviors with room temperature conductivities of ca. 6 x 10 -3 S cm -1 (ambient pressure) and 10 -3 S cm -1 (under applied pressure of 12.1 GPa) respectively, due to strong dimerization between the donors. Magnetic measurements performed on compound 1 indicate weak antiferromagnetic coupling between high-spin Fe III (SFe = 5/2) and mixed-valence radical cation diyads (BEDT-TTF)2 +• (Srad = ½) mediated by the anilate ligands, together with an important Pauli paramagnetism typical for conducting systems.

INTRODUCTION

Magnetic molecular conductors are a challenging class of multifunctional materials of special interest in contemporary material science, since coexistence or even interplay between delocalized π-electrons and localized d-electrons can lead to unusual and peculiar phenomena such as magnetic field-induced superconductors, magnetoresistance effects, magnetic field-switchable conductors etc., with technological applications in molecular electronics and spintronics. 1 Molecular π-d systems exhibit a variety of types of electron transport (conducting, semiconducting and insulating) which can be finely tuned by the π-d interactions and, therefore, by a wise choice of both the organic donor, carrier of conductivity, and magnetic counter ions, carriers of magnetic properties (ferro-, ferri-, antiferromagnetism). Among the organic donors, the BEDT-TTF molecule, 1d-e,2 along with its selenium derivatives, is the most successful donor which has produced the majority of known superconductors and several charge-transfer salts showing different conducting states (conducting, semiconducting, etc.). Tetrahedral and octahedral mononuclear complexes, such as [MX4] n-(M = Fe III , Cu II ; X = Cl, Br) 3 and [M(ox)3] 3-(ox = oxalate), 1e,4 respectively, have been reported as the most relevant charge-compensating magnetic anions used to construct magnetic molecular conductors; another important milestone has been achieved by using bimetallic oxalate-based layers of the type [M II M III (ox)3] -(M II = Mn, Co, Ni, Fe, Cu; M III = Fe, Cr), 5 showing a peculiar honeycomb packing pattern. Recently metal-complexes containing derivatives of the 2,5-dihydroxy-1,4-benzoquinone-3,6-disubstituted, hereafter called anilates, have been prepared by some of us and studied extensively, 6 because they have a delocalized moiety that can mediate magnetic interactions between metal centers coordinated to the ligand. Moreover these ligands, being redox-active, can form organic radicals which should lead to strong spin coupling with paramagnetic species. Anilato-based metal complexes are also versatile building blocks for constructing functional and multifunctional luminescent 7 or conducting/magnetic molecule-based materials. [8][9][10] Recently, by combining the BEDT-TTF organic donor, carrier of conducting layers, with the tris(chloranilato)ferrate(III) [Fe(Cl2An)3] 3- anionic magnetic complex, 6b a series of magnetic molecular conductors with different donor/anion stoichiometric ratio have been obtained. 9a,9d Furthermore, a complete series of chiral conductors with the chiral donor TM-BEDT-TTF 11 and a chloranilate-bridged heterobimetallic network was reported by Mercuri, Avarvari et al. [START_REF] Atzori | Complete Series of Chiral Paramagnetic Molecular Conductors Based on Tetramethyl-Bis(Ethylenedithio)-Tetrathiafulvalene (TM-BEDT-TTF) and Chloranilate-Bridged Heterobimetallic Honeycomb Layers[END_REF] Since the presence of different substituents at the 3,6positions of the anilate molecule can lead to the modulation of the π-π stacking, intermolecular halogen-bonding, hydrogen-bonding and dipolar interactions, we set out to use non-symmetric chloro-cyananilato based anionic complexes in molecular conductors where the variation of the ligand substituents should play a paramount role on the structural and physical properties of the obtained materials. Note that some of us reported on the use of the chlorocyananilato monoanion Crystal Structures. The crystal structures of the two hybrid systems consist of tris-anilate anionic Fe complexes and BEDT-TTF donors with different oxidation states. As a result of the different electrocrystallization solvents used, 1 crystallized with water molecules (three per formula unit according to the SQUEEZE program), while 2 contains two acetonitrile solvent molecules in its crystal structure. In both systems the metal complexes exhibit octahedral FeO6 coordination geometry, with the Fe III ion surrounded by three ClCNAn 2-chelating ligands. They are therefore chiral anions, yet both Λ and Δ enantiomers are present in the crystal structures. The magnetic anions are relatively isolated as shown by the Fe•••Fe distances of ca. 9.32 Å and 11.77 Å for 1 and 9.95 Å and 11.04 Å for 2 (Figure S1). In 1, one of the anilate ligands presents a structural disorder, since the chloro and cyano substituents are equally distributed over the two positions, as usually observed in chlorocyananilate coordination polymers. 10d The molecular structure of the anionic complex in 2 is represented in Figure 1. The metal-oxygen bond distances in compounds 1 and 2 vary in the 1.987(4)-2.034(5) Å range (Table 1) and are similar to the distances observed in the corresponding BEDT-TTF radical cation salt with the homosubstituted chloranilate complex. 9a The C-O bond distances are influenced by the coordination to the metal center. The oxygen atoms coordinated to the metal have C-O distances slightly longer than those of the peripheral oxygen atoms, which show a major double bond character.

RESULTS AND DISCUSSIONS

Compound 1 crystallizes in the monoclinic space group P21/c. The asymmetric unit contains four independent BEDT-TTF donor molecules (labeled as A, B, C and D) for one [Fe(ClCNAn)3] 3- complex (Figure S2). Analysis of the bond distances has been carried for each BEDT-TTF molecule following the procedure described by Day et al. [START_REF] Guionneau | Determining the Charge Distribution in BEDT-TTF Salts[END_REF] The results of the empirical equation Q = 6.347 -7.463δ, relating the charge Q to the parameter δ defined by δ =(b + c) -(a + d), where a-d represent averaged values of C=C and five-membered-ring C-S bonds, are reported in Table 2. The calculated Q value of the cationic part of compound 1 is +3, as expected from the sum of the charge calculated for each of the four BEDT-TTF donor molecules present in this salt (Table 2). 1.737( 14) 1.706( 14) 1.729(11) 1.742 (14) 1.724 (13) 1.716 (13) 1.743(11) 1.717 (14) 1.711 (13) 1.702 (13) 1.729(11) c

1.756( 14) 1.726( 14) 1.750( 14) 1.707( 12) 1.747 (14) 1.745( 13) 1.767( 14) 1.740( 13) 1.759 (13) 1.723( 16) 1.726( 14) 1.756 (13) 1.763 (13) 1.745( 14) 1.752( 13) 1.723(11) d 1.344( 18) 1.324 (20) 1.354( 20) 1.345(18) 1.329 (20) 1.381( 20 Intra-and inter-layer interactions between donor molecules are highlighted in Figures 7a-c, S4-S5. The central C꞊C and internal C-S bond lengths values (Table 3) confirm that the A and B molecules bear charges of +1, whereas C molecules are over-oxidised (charge +2). In this expression, J is the magnetic coupling and g is the average Landé factor which is assumed to be identical for the iron (III) ion and the radical. Least-squares best-fit parameters are J = -2.020(4) cm -1 , g = 1.990( 2) and TIP = 2.10(3) x 10 -3 cm 3 mol -1 . The calculated curve (solid line in Figure 8) matches well the experimental data in the whole temperature range investigated. The weak antiferromagnetic coupling between the iron(III) an the radical from the DC pair which occurs in 1 is mediated by the - interaction involving the BEDT-TTF donor molecule and the anilate ligand of the anionic complex. As far as the value of the TIP parameter is concerned,it is of the order of those previously reported for other molecular conducting radical cation salts, [START_REF] Williams | Organic Superconductor: Synthesis, Structure, Properties and Theory[END_REF] and S = solvent) family. 1a,b,4d,17 Alternatively, the magnetic data can be reproduced by ruling out the magnetic interaction between the iron(III) and the DA pair [that is J = 0 cm -1 in eq (1)] and introducing a Weiss parameter  as T-. In this mean-field approach, we obtain a  value of -1.374(7) K with the same values of g and TIP from the previous analysis but resulting in a poorer quality of the fit.

Unfortunately, the very small amount of compound 2 obtained precluded any accurate magnetic susceptibility measurements. However, from the analysis of the crystal structure one can infere that the donors will be essentially magnetically silent since A and B form strong dimers while C is a diamagnetic dication, therefore the magnetism should be dominated by the paramagnetism of high-spin Fe III (S = 5/2) ions.

Transport Properties and Band Structure Calculations. The conductivity measurements in compound 1 show room temperature conductivity between 2 × 10 -4 and 8 × 10 -4 S cm -1 . The resistivity increases as the sample is cooled down in agreement with a semiconducting behavior,  = 0exp(Ea/kT) with an average activation energy Ea of 164 meV (Figure 9, left). Compound 2 also shows semiconducting behavior at ambient pressure with r.t. conductivity of 1.8   S cm -1 and Ea of 2483 K (214 meV) (Figure 9, right). Then, temperature dependence of the resistivity under high pressure was measured only for compound 2. The r.t. resistivity and Ea decrease with pressure, while the compound shows semiconducting behavior at all measured pressures. At 12.9

GPa the room temperature conductivity was 10 -3 S cm -1 and Ea 92 meV (1068 K). flat so that the electronic repulsions will favor an electronic localization. Note that the HOMO levels splitting for the DA dimers is quite substantial (~ 0.6 eV). This indicates that (DA) + dimers with one hole in the antibonding combination of the two HOMOs should be quite stable whereas double occupation of this level in half of the dimers, as needed if the two lower levels are fully occupied, would be very unfavorable. In addition, a double occupation of the two lower bands would implicate the occurrence of two different types of DA dimers which would be at odds with the crystal structure. We thus conclude that the four DA levels must be singly occupied so that both donors A and D have an average +1/2 charge, in agreement with the results in Table 2.

CONCLUSIONS

Two radical cation salts based on BEDT-TTF and [Fe(ClCNAn)3] 3-tris(chlorocyanilato) ferrate(III) anionic complex have been prepared by electrocrystallization, by using CH2Cl2 for 1 and CH3CN for 2. In CH2Cl2, a 4:1 donor:anion salt 1 was obtained,containing mixed-valence and +1 oxidation states for the donor, while in 2, with a 5:2 donor:anion ratio, radical cations and dicationic donors coexist. The role of Cl•••S and N•••S intermolecular interactions on the crystal packing of compound 1 and 2 is also highlighted. 1 and 2 compounds present unusual donor-anion segregation and both are semiconductors. Applying high pressures of up to 12.9 GPa in the case of 2 allowed to increase the conductivity by two orders of magnitude.The thermal behavior of the MT product of 1 is quite interesting and corresponds to a spin sextet (SFe = 5/2) and a spin doublet (Srad = ½) with a weak antiferromagnetic coupling together with an important Pauli paramagnetism of the order of those previously reported for other related molecular conducting radical salts.

As perspective, BEDT-TTF-based radical cation salts where the tris(chlorocyananilato)ferrate(III)

anion is replaced by its Br or, in particular, I analogues at the 3,6 positions of the anilato moiety will be prepared, in order to perform a systematic study on the influence of the electronic nature and strength of the intermolecular interactions (including halogen bonding), due to the different halogen substituents, in affecting the crystal packing and, subsequently, the corresponding physical properties. The influence of electron-donating substituents in tuning the electron density of the anilato moiety will be also investigated. Of special interest would be the use of chiral donors in order to possibly select only one coordination stereochemistry around the metal center and also to combine chirality with conducting and magnetic properties. 18

EXPERIMENTAL SECTION

General Considerations. TPPh3[Fe(ClCNAn)3] was synthesized as previously reported. 6c BEDT-TTF (Zentek, TCI) was used as received. Electrocrystallization was performed using HPLC grade solvents (Termofisher Scientific Alfa-Aesar) previously dried under alumina and degassed with argon.

Synthesis. [BEDT-TTF]4[Fe(ClCNAn)3]•3H2O (1). Two CH2Cl2 solutions of the precursors

TPPh3[Fe(ClCNAn)3] and BEDT-TTF were prepared and respectively placed in the cathodic and anodic compartments of an H-shape electrocrystallization cell. Black blocks of single crystals of 1 were obtained on the anode electrode by appling a current density of 1 μA cm -2 at room temperature over a period of three weeks.

[BEDT-TTF]5[Fe(ClCNAn)3]2•2CH3CN (2). Black plates of single crystals of 2 were obtained in a similar experiment, by changing the CH2Cl2 solvent with CH3CN and applying a current density of 3 μA cm -2 over a period of two months.

X-ray Crystallography. Data collection was performed at 150 K on an Agilent Supernova diffractometer with Cu Kα (λ = 1.54184 Å). Single crystals of 1 and 2 were mounted on a glass fiber loop using a viscous hydrocarbon oil to coat the crystal and then transferred directly to the cold nitrogen stream for data collection. The structure was solved by direct methods with the SIR97

program and refined against all F2 values with the SHELXL-97 program using the WinGX graphical user interface. All non-hydrogen atoms were refined anisotropically, and hydrogen atoms were placed in calculated positions and refined isotropically with a riding model. The program SQUEEZE from PLATON was used for 1 to determine the nature of the disordered solvent molecules. The void space of 378.8 Å 3 containing 127 electrons/cell indicates the presence of 3 molecules of water that have been inserted in the formula. 1.071 1.069 a R1(F) = ΣǁF0|-|FCǁ/Σ|F0|; b wR2(F 2 ) = [Σw(F0 2 -FC 2 ) 2 /ΣwF0 4 ] 1/2 ; c S(F 2 ) = [Σw(F0 2 -FC 2 ) 2 /(n+r-p)] 1/2 . Single Crystal Conductivity. Conductivity measurements were performed on several needleshaped single crystals of 1 in the temperature range of 300-100 K. To perform the electrical contacts, gold wires were attached directly to the crystals with silver paint. Two-probe DC measurements were performed applying a constant voltage in the range 0-2V and measuring the current using a Keithley 6487 Picoammeter/Voltage Source. Low temperature was provided by a homemade cryostat equipped with a 4 K pulse-tube.

Four-probe DC measurements were performed for compound 2 by using a diamond anvil cell (DAC). A rectangular shape of single crystal (0.17 × 0.06 × 0.03 mm 3 ) was used for ambient pressure measurement, and a size of 0.16 × 0.04 × 0.02 mm 3 single crystal was used for highpressure measurements. The crystals were attached by four 5 μm gold wires with gold paint. A culet size 0.7 mm diamond anvil and Daphne Oil 7373 was used as the pressure-transmitting medium. A tension annealed stainless still (SUS301) was used as metal gasket. The pressure was determined by the shift of the ruby fluorescence R1 lines at room temperature. The Cryocooler helium compressor system (Sumitomo Heavy Industries, Ltd.) was used for cooling DAC with cooling rate of 1.5K/min. The KEITHLEY 224 Programmable current source and 182 Sensitive digital voltmeter were used for all measurements.

Computational Details. The tight-binding band structure calculations were of the extended Hückel type. [START_REF] Whangbo | The band structure of the tetracyanoplatinate chain[END_REF] A modified Wolfsberg-Helmholtz formula was used to calculate the non-diagonal H values. [START_REF] Ammeter | Counterintuitive orbital mixing in semiempirical and ab initio molecular orbital calculations[END_REF] All valence electrons were taken into account in the calculations and the basis set consisted of Slater-type orbitals of double- quality for C 2s and 2p, S 3s and 3p and of single- quality for H 1s. The ionization potentials, contraction coefficients and exponents were taken from previous work. [START_REF] Pénicaud | Hydrogen-Bond Tuning of Macroscopic Transport Properties from the Neutral Molecular Component Site along the Series of Metallic Organic-Inorganic Solvates (BEDT-TTF)4Re6Se5C19[END_REF]

ASSOCIATED CONTENT

The Supporting Information is available free of charge on the ACS Publications website at DOI:... Additional figures as mentioned in the text.

Accession Codes

CCDC 1945944-1945945 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

[

  HClCNAn] -in BEDT-TTF-based conducting radical cation salts, 10c yet no examples containing a [M(ClCNAn)3] n-anion complex have been reported to date. We describe herein two chlorocyananilate-based compounds formulated as [BEDT-TTF]4[Fe(ClCNAn)3]•3H2O (1) and [BEDT-TTF]5 [Fe(ClCNAn)3]2•2CH3CN (2) obtained by electrocrystallization, together with their in-depth crystal structures analysis and physical properties.

Synthesis.

  The tris(chlorocyananilato)ferrate(III) complex [PPh4]3[Fe(ClCNAn)3] 6c and the BEDT-TTF donor were combined in electrocrystallization experiments, by using different solvents and current density (see Experimental Section). Two different hybrid systems formulated as [BEDT-TTF]4[Fe(ClCNAn)3]•3H2O (1) and [BEDT-TTF]5[Fe(ClCNAn)3]2•2CH3CN (2) were obtained as reported in Scheme1. These systems mainly differ in the donor/anion ratio of 4:1 and 5:2 phase in 1 and 2 respectively, which, along with the different crystallization solvent molecules present in the structures, influence the crystal packing motif exhibited by the BEDT-TTF molecules and the resulting physical properties (vide infra).

Scheme 1 .

 1 Scheme 1. BEDT-TTF organic donor (D), [Fe(ClCNAn)3] 3-anionic complex (A) and experimental conditions used for the synthesis of compounds 1 and 2.

Figure 1 .

 1 Figure 1. Structure of the tris(chlorocyananilato)ferrate(III) anionic complex (Δ enantiomer) in 2.

  The unusual crystal packing of 1 consists of hybrid organic-inorganic layers formed by repeating units of D-A-B-C BEDT-TTF molecules along the a axis intercalated by [Fe(ClCNAn)3] 3- complexes of both chiralities as shown in Figure2. Very short S•••S contacts (3.29-3.61 Å) less than the sum of the van der Waals radii (3.65 Å) are present between the B and C molecules which form strong dimers (Figure3).

Figure 2 .

 2 Figure 2. Crystal packing of 1 in the bc plane (top) and the ba plane with A, B, C and D labels (bottom). Solvent molecules are omitted for clarity.

Figure 3 .

 3 Figure 3. S•••S interactions (Ǻ) in 1 shorter than the sum of the van der Waals radii (3.65 Å) :S4A-S28D 3.62, S16B-S24C 3.48, S13B-S21C 3.46, S14B-S22C 3.29, S11B-S19C 3.61, S12B-S20C 3.36.

Figure 4 .

 4 Figure 4. DABC BEDT-TTF molecules surrounded by metal complexes in 1. Solvent molecules are omitted for clarity. Intermolecular Cl•••S (violet) and N•••S interactions (blue) lower than the sum of the van der Waals radii between the BEDT-TTF molecules and the ClCNAn ligands are highlighted (Å). Cl2-S17C 3.51, Cl2-S23C 3.60, Cl2B-S19C 3.44, Cl2-S23C 3.60, Cl2-S29D 3.50, N3-S21C 3.59, N3-S13B 3.53.

  central C=C and internal C-S bond lengths confirm that B and C molecules, associated in strong dimers, bear a charge of +1, whereas D and A molecules are present in a mixed-valence state. The BEDT-TTF molecular packing in compound 1, along with the mixed-valence state of donorsA and D bearing 0.59 and 0.68 positive charge, respectively, are in principle favorable for delocalization of the charge, in agreement with the electron transport properties (vide infra). Compound 2 crystallizes in the triclinic centrosymmetric space group P-1. The asymmetric unit consists of two (A and B) and half (C) independent BEDT-TTF molecules (indicated as A-C in the Figures and discussion), one [Fe(ClCNAn)3] 3-anionic complex and one acetonitrile solvent molecule (Figure S3), thus providing the formula [BEDT-TTF]5[Fe(ClCNAn)3]2•2CH3CN. The crystal packing of 2 shows a pseudo-segregation of organic and hybrid organic-inorganic layers (Figure 5).

Figure 5 .

 5 Figure 5. Crystal packing of 2 in bc plane. Solvent molecules are omitted for clarity.

Figure 6 .

 6 Figure 6. AA and BB dimers and interactions of donors with complexes in 2 (top); representation of three consecutive hybrid layers with interlayer Fe•••Fe distances (bottom left) and π-π interactions in one hybrid layer (bottom right). Donor molecules A, B, C and complex are highlighted in red, green, violet and blue respectively. The dashed lines represent the intermolecular π-π interactions (pink), C-H•••S interactions (orange), Cl•••S and N•••S interactions (yellow). C•••S: 3.732(17) Å, Cl•••S: 3.980(5) Å, N•••S: 3.481(10) Å. Solvent molecules are omitted for clarity.

  e. the BEDT-TTF organic donor, CH2Cl2 and CH3CN solvents, when the [PPh4]3[Fe(Cl2An)3] salt was used instead of [PPh4]3[Fe(ClCNAn)3], different radical cation salts were produced with 3:1 and 5:1 ratios donor to complex, 9a as highlighted in Table 4. It is therefore clear that intermolecular interactions such as Cl•••S and N•••S contacts play a paramount role in the crystal packing of compounds 1 and 2TTF]5[Fe(ClCNAn)3]2•2CH3CN(2) 5:2 δ-[BEDT-TTF]5[Fe(Cl2An)3]•4H2O 5:1 Magnetic Measurements. The magnetic properties of 1 in the form of MT versus T plot [M being the magnetic susceptibility per one iron(III) ion] are shown in Figure 8. At roomtemperature, MT is 5.23 cm 3 mol -1 K. Upon cooling, MT exhibits a practically linear decrease until ca. 80 K and below this temperature it decreases abruptly to reach 3.0 cm 3 mol -1 K at 1.9 K.This plot is as expected for a spin sextet (SFe = 5/2) and a spin doublet (Srad = ½) with a weak antiferromagnetic coupling together with an important Pauli paramagnetism, this last accounting for the linear dependence of MT in the high temperature region. The zero-field splitting of the high-spin iron(III) is expected to be very small and then, the sharp decrease observed in the low temperature range of 1 has to be attributed to a relatively weak antiferromagnetic interaction between the local spins (the metal ion and the radical).

Figure 8 .

 8 Figure 8. Thermal variation of the MT product for 1: (o) experimental; ( __ ) best-fit curve through eq (1) (see text).

  Fe(C5O5)3] . CH2Cl2 16 and (ET)6[Fe(C6O2Cl2)3] . 3/2H2O . 1/2CH2Cl2 (C6O4Cl2 2-= chloranilate dianion) 9a,d as well as in other members of the ET4[(H3O)M((C2O4)3] . S (C2O4 2-= oxalate dianion

Figure 9 .

 9 Figure 9. Temperature dependence of the electrical resistivity ρ for single crystals of compounds 1 at ambient pressure (left) and 2 under various pressures (right).

Figure 10 .

 10 Figure 10. Calculated band structure for the donor lattice of [BEDT-TTF]4[Fe(ClCNAn)3]•3H2O where  = (0, 0, 0), X = (a*/2, 0, 0), Y = (0, b*/2, 0) and Z = (0, 0, c*/2). The red/black bands are those localized in the BC/DA dimers, respectively. The splitting of the HOMO levels for dimers DA and BC are also indicated.

Figure 11 .

 11 Figure 11. Calculated band structure for the donor lattice of [BEDT-TTF]5[Fe(ClCNAn)3]2•2CH3CN where  = (0, 0, 0), X = (a*/2, 0, 0), Y = (0, b*/2, 0) and Z = (0, 0, c*/2). The splitting of the HOMO levels for dimers AA and BB as well as the HOMO of C are also indicated.

Table 1 . Fe-O Bond Distances (Å) for the Anionic Complex in Compounds 1 and 2 Bonds Distances (Å) 1 2

 1

	Fe-O(1)	2.022(8)	2.006(4)
	Fe-O(2)	1.999(10)	2.022(3)
	Fe-O(5)	1.997(10)	2.027(3)
	Fe-O(6)	2.014(11)	1.987(4)
	Fe-O(9)	2.022(8)	2.034(5)
	Fe-O(10)	2.000(12)	2.015(4)
	Average	2.009	2.015

Table 2 : Bond Distance Analysis and Selected Bond Distances (Å) for the BEDT-TTF Donor Molecules in 1

 2

		A	B	C	D
	a	1.378(22)	1.366(20)	1.425(20)	1.356(16)
	b	1.710(16)	1.720(14)	1.706(14)	1.724(11)
		1.748(15)

Table 3 . Bond Distance Analysis and Selected Bond Distances (Å) for the BEDT-TTF Donor Molecules in 2.

 3

			A	B	C
		a	1.387(9)	1.391(8)	1.447(8)
		b	1.709(6)	1.721(8)	1.695(5)
			1.720(6)	1.717(6)	1.680(6)
			1.701(6)	1.714(8)
			1.722(4)	1.718(6)
		c	1.743(9)	1.745(6)	1.728(7)
			1.728(8)	1.740(8)	1.707(6)
			1.724(9)	1.727(6)
			1.728(8)	1.734(8)
		d	1.343(1)	1.360(1)	1.369(8)
			1.346(1)	1.348(1)
	δ=(b+c)-(a+d)	δ	0.71	0.709	0.589
	Q= 6.347-7.4638•δ	Q	1.03	1.05	1.95

Noteworthy, under the same experimental conditions, i.

  Table 5 details the crystallographic data and structure refinement results.

Table 5 . Crystallographic data for compounds 1 and 2

 5

		1	2
	Empirical formula	C61H38Cl3FeN3O15S32	C48H23Cl3FeN4O12S20
	Fw	2241.06	1651.10
	Crystal color	black	black
	Crystal size (mm3)	0.20 * 0.10 * 0.08	0.20 * 0.15 * 0.10
	Temperature (K)	150.00(10)	150.00(10)
	Wavelength (Å)	1.54184	1.54184
	Crystal system, Z	Monoclinic, 4	Triclinic, 2
	Space group	P21/c	P-1
	a (Å)	18.2791(10)	13.8508(5)
	b (Å)	21.9785(10)	14.5382(6)
	c (Å)	22.4369(11)	18.3072(7)
		90	67.487(4)
		111.722(6)	79.770(3)
		90	61.563(4)
	V (ų)	8373.9(7)	2994.6(2)
	ρcalc (g.cm -³)	1.778	1.831
	μ(CuKα) (mm-1)	10.334	10.338
	θ range (°)	2.602-72.810	2.613-73.623
	Data collected	35680	23006
	Data unique	16234	11621
	Data observed	12151	9812
	Number of	1015/58	811/9

ACKNOWLEDGMENTS

This work was supported in France by the CNRS, the University of Angers, the RFI Regional LUMOMAT project ASCO-MMM (grant to A.A.). The work in Italy was supported by the Fondazione di Sardegna-Convenzione triennale tra la Fondazione di Sardegna e gli Atenei Sardi, Regione Sardegna-L.R. 7/2007 annualità 2016-DGR 28/21 del 17.05.2015 "Innovative Molecular Functional Materials for Environmental and Biomedical Applicatons" (grant to S.A.S.) and INSTM. M.J.O. acknowledges support from the Ministerio Español de Ciencia e Innovación (Project CTQ2016-75068P) and Unidad de Excelencia María de Maeztu (Project MDM-2015-0538). Work at Bellaterra (Spain) was supported by the Spanish MICIU through Grant PGC2018-096955-B-C44 and the MINECO through the Severo Ochoa Centers of Excellence Program under Grant SEV-2015-0496 as well as by Generalitat de Catalunya (2017SGR1506).

DEDICATION

Dedicated to Professor Marius Andruh on the occasion of his 65th anniversary.

Notes

The authors declare no competing financial interest.


Anis Kaci

Angelica Torres

Frederic Giraud

Christophe Giraud-Audine

Michel Amberg

Betty Lemaire-Semail

Fundamental Acoustical Finger Force Calculation for Out-of-Plane Ultrasonic Vibration and its Correlation with Friction Reduction

This article presents a method for estimating the parameters of a biomechanical impedance approximation model for a finger interacting with a rigid beam vibrating outof-plane at ultrasonic frequencies, and illustrates correlation results of these parameter magnitudes with vibration amplitude friction modulation detection threshold.

I. INTRODUCTION

Ultrasonic out-of-plane vibration is one of the leading technologies to create friction modulation in haptic devices. By modulating the friction forces between a vibrating plate and a user's finger as a function of its position, illusions of out of plane shapes and textural patterns can be created [START_REF] Winfield | T-pad: Tactile pattern display through variable friction reduction[END_REF], [START_REF] Biet | Squeeze film effect for the design of an ultrasonic tactile plate[END_REF]. The intermittent contact between the finger pad and the plate, that occurs during out-of plane vibrations at amplitudes as low as few micrometers, is at the origin of the friction reduction [START_REF] Vezzoli | Friction reduction through ultrasonic vibration part 1: Modelling intermittent contact[END_REF], [START_REF] Wiertlewski | Partial squeeze film levitation modulates fingertip friction[END_REF]. It has been observed that the finger biomechanic help to predict the behavior of friction forces during tactile surface exploration. In [START_REF] Vezzoli | Friction reduction through ultrasonic vibration part 1: Modelling intermittent contact[END_REF], it is shown that soft stratum-corneum -with a low Young modulus -have lower friction reduction, while [START_REF] Fenton Friesen | The role of damping in ultrasonic friction reduction[END_REF] has established that the damping of the stratum corneum at ultrasonic frequencies greatly affects the subject's susceptibility to ultrasonic friction modulation.

Therefore, it is conceivable that certain finger mechanical properties are correlated to a measure of the textural perception. This is further supported by [START_REF] Ben Messaoud | Relation between human perceived friction and finger friction characteristics[END_REF], which has shown that the perceptual intensity of the tactile stimuli is a function of the friction contrast. This has been confirmed by [START_REF] Khurram Saleem | Psychophysical Evaluation of Change in Friction on an Ultrasonically-Actuated Touchscreen[END_REF], who has modeled this intensity by introducing also the change rate of the tangential force. Difference between falling and rising friction is observed, and is due to the viscoelastic properties of the fingertip.

Therefore, to obtain a same perceptual intensity of a tactile stimuli, the vibration amplitude should be adapted according to the scanning speed and pressing force, which can be measured with sensors, but also to the biomechanical properties of the finger pad, which change from one user to the other. In [START_REF] Monnoyer | Perception of ultrasonic switches involves large discontinuity of the mechanical impedance[END_REF], the measured acoustical impedance is correlated to the perception of simulated keyclick, since this measure is directly correlated to the biomechanical properties of the finger pad. The authors propose to use this *This work has been carried out within the framework of the Mint Project of IRCICA (Service and Research unit from CNRS) Lille, France 1 name.surname@univ-lille.fr 2 christophe.giraud-audine@ensam.eu measurement as a monitoring tool to produce a calibrated stimulation to each user.

This paper explores the application of the measurement of the acoustic forces in the case of friction reduction tactile displays. For that purpose, we first present the principle of an online measurement of the forces. We the present an experimental study which aim is to correlate the force measurement to the friction reduction. the results of this study are then presented in the final section.

II. PRINCIPLE OF THE FUNDAMENTAL ACOUSTICAL

FORCE MEASUREMENT

A. Definition of the acoustical finger force

We consider a vibrating plate which is actuated by piezoelectric cells supplied by a voltage v(t) around a pulsation denoted ω, and which vibration amplitude is named W . The voltage v creates an internal force f p such that f p = N v, which is used to compensate the internal friction force that exists due to the plate's particles motion, a phenomenon called internal damping. When a finger touches the vibrating plate, contact forces appear that can create additional damping and stiffness into the system formed by the plate and the finger. As a result, the voltage v needs to be adapted, so that f p can compensate the effect of the contact forces on the vibration, and maintain W constant [START_REF] Giraud | Design and control of a haptic knob[END_REF]. Therefore, the voltage difference between the no-load condition and the contact condition is related to the contact forces, and thus to the biomechanical properties of the fingertip.

Without lack of generality, we consider the model of a vibrating plate which is operated exactly at its resonance frequency, leading to the equation 1:

D ẇ = f p -f r (1)
with D the internal damping of the plate around a resonance pulsation, and f r , the acoustical force. In general, f r derives from the contact pressure p(x, y, t) which depend on time t and position {x, y}. The theory of vibrating plate helps to write the relationship between f r and p, by introducing Ψ(x, y), the modal shape of the plate when vibrating:

f r = S p(x, y, t)Ψ(x, y)dxdy ( 2
)
where S is the contact area.

It is then possible to observe f r by inverting the relation 1, leading to:

fr = N v -D ẇ (3)
where fr represents the observation of f r . It should be emphasized here that the acoustical finger force is not the contact force, but it derives from it. However, the variables w(t) and v(t) are high frequency signals, and solving the equation 3 in the time domain can be achieved at the expense of high sampling rate, and off-line calculation. Therefore, we transform the observation into the rotating reference frame.

B. Measurement in the rotating reference frame

Assuming that v is a sinusoidal function of time, one can use phasors to model it, hence:

v(t) = (V d + jV q ) e jωt (4)
where V d and V q represent the coordinates of v into a the rotating reference frame, and v is the phasor of v such that v(t) is the imaginary part of v. This representation is illustrated figure 3. In the same way, we define W d , W q , F rd and F rq . How to impose V d and V q and to control W d and W q is detailed in [START_REF] Ghenna | Vector Control Of Piezoelectric Transducers and Ultrasonic Actuators[END_REF].

In the remaining of this paper, the plate is controlled in such a way that W q = 0, leading to ẇ = jωW d e jωt ; the equation 3 leads then to two new equations, after projecting on axis d and q:

Frd = N V d , Frq = N V q -DωW d (5)

C. Theoretical examples

For the purpose of illustration, we present three examples of acoustical finger force observation. In the first example, we consider no contact conditions, and the probing finger is absent, leading to f r = 0. Then, the equation 5 yields:

V d = 0 , V q = N D ωW d (6)
Hence, at no load, V q is proportional to W d , and the slope gives D; this property is exploited later, in order to calibrate the measures.

In the second example, the finger is in contact with the vibrating plate; due to the acoustical impedance of the finger pulp, the contact force depends on the vibration itself. If we consider a typical model that includes the internal damping of the skin (denoted by D f ) and the vibrating mass, (M f ) [START_REF] Fenton Friesen | The role of damping in ultrasonic friction reduction[END_REF], the acoustical finger force is sinusoidal, and writes f r = D f ẇ + M f ẅ, leading to:

F rd = -M f ω 2 W d , F rq = D f ωW d (7)
The acoustical force is then shared between the axis: d axis contains the inertial force while q axis contains the damping force.

In the last example, we consider intermittent contact. When the contact is intermittent, f r shows pulses at the frequency of the vibration, and with a phase shift named Φ [START_REF] Vezzoli | Friction reduction through ultrasonic vibration part 1: Modelling intermittent contact[END_REF]. Each time the skin bounces on the plate, the force f r increases before returning to 0 when the skin is detaching from the plate. For illustration, we consider perfect rebound of the skin: the contact time equals zero, and the contact force is infinite when the plate touches the finger. Therefore, we write f r as a Dirac comb distribution ∆(.), The acoustical finger force f r contains a fundamental, which is at the resonance pulsation of the plate, and harmonics. Due to the resonant behaviour of the plate, the harmonic doesn't influence the plate's vibration, and therefore, only the fundamental can be observed with the equation 7. In the particular case of ideal intermittent contact condition, the fundamental of f r writes:

with f r = f 0 ∞ n=-∞ δ(t -n 2π ω -Φ).
Frd = 2f 0 cos(Φ) , Frq = 2f 0 sin(Φ) (8)
Hence, when the contact is intermittent, the observation of the acoustical finger force is not related to the acoustical impedance of the finger pulpe, and the components along the axis d and q are not related to a damping or a mass. However, the phase shift, which can be calculated from atan Frq Frd is related to the time at which the contact occurs.

III. EXPERIMENTAL SETUP AND PROTOCOL

A. Material

The setup is as shown in figure 3. An aluminum beam (18 × 119 × 2mm 3 ) is covered with a hydrophobic surface, and sustained by a structure equipped with a 6-dimensional force sensor (ATI Nano 43); an analog Standard Volume Indicator (SVI) gives an indication of the pressing force, with a specific guideline at 0.4N. Four piezoelectric ceramics of magnitude 16 × 4 × 0.5mm 3 are glued to the opposite surface of the beam to produce the vibration. The geometry of the beam, magnitude and position of the piezoelectric sensors are designed and simulated with an FE analysis in order to attain a pre-defined normal wave vibration mode at the plate's resonance frequency. We exploit the first bending mode of the beam, which is obtained with a resonant frequency of 24870kHz. Closed loop control of the vibration amplitude of the beam is achieved thanks to the use of a Digital Signal Processor (STM32F4 from ST Microelectronics). The acoustical force are observed online, and sent to a main computer through a serial connection for data collection. The vibration control is achieved at 10kHz. An external power amplifier (HSA 4051 from NF, Japan) amplifies the controller's output up to 200V peak-peak. The parameter N of the plate has been identified using the methodology described in [START_REF] Ghenna | Modelling, identification and control of a Langevin transducer[END_REF] and its value is N = 0.02N/V . The no-load test measurement presented figure 4 has been used to identify D = 0.2848N.s.m -1 .

B. Experimental procedure

Twelve healthy participants (3 females) aged from 22 to 60 participated to the experiments. They were asked to thoroughly wash and dry their hand before the tests. All participants gave written informed consent. The investigation conformed to the principles of the Declaration of Helsinki and experiments were performed in accordance with relevant guidelines and regulations.

Prior to any experiment, the participants train themselves to apply a constant pressure of 0.4N on the plate, by following the indication of the SVI. Two experiments were designed in this work. In the first experiment, the participants placed their finger in the middle of the plate, standstill, with an angle of 45deg, yet pushing with 0.4N with their finger on the plate. The location for the measurement has been chosen to have an almost constant deformation mode shape and to maximize the relation 2.

During the experiment, the vibration amplitude W d varies from 50nm to 1000nm peak in 20 steps of 50nm every 100ms, back and forth; 5 cycles are achieved, and the observed values of F rd and F rq are recorded at the end of each step.

In the second experiment, the participant moved their finger from left to right, in a lateral movement. They were asked to keep an inclination of 45deg and a pressing force of 0.4N. To control the finger's speed, a metronome emits sound at 1Hz and participants are asked to move their finger between two lines marked on the plate in two metronome beeps. The nominal speed is then equal to 70 mm/s. During this try, 10Hz vibration amplitude modulation from 0 to 1000 nm peak are produced on the plate, and the normal and tangential forces are recorded with a sampling rate of 100Hz.

The second experiment is achieved right after the second one, to keep the same experimental conditions, to get benefit of the training of the finger inclination and pressing force, as well as to keep the participants' skins in the same condition, IV. RESULTS

A. Result from experiment 1

During the tests, the participants controlled the pressing force with a higher pressure than required (mean = 0.515N), but maintained it almost constant over the test (SD¡0.07N over all participants). The result of the first experiment shows common features and differences from one user to the other, and the figure 5 presents the estimated values for all participants.

We notice that the observed acoustical finger force does not necessarily equally share on axis d and q, and that for some participants, there is a saturation in axis d which do not appear on the axis q. In order to establish a comparison between each participant, we have reported in figure 6 The results are sorted in the same order as for the figure 5. The value of the maximal acoustical force depend on each participant, and this figure is relevant to discriminate them. Moreover, the measure is robust, the standard deviation is small compared to the mean value over the five cycles of measurement.

B. Result from experiment 2

The results of the second experiment helped to characterize the friction modulation for each participant. The figure 7 depicts a typical friction measurement when the participant is sliding the finger over the tactile plate.

A positive friction coefficient (denoted as µ) is obtained when the finger is sliding from left to right, while a negative µ is obtained in the reverse direction. The modulation of µ is due to to the modulation of the vibrating amplitude W while sliding.

To characterize the friction modulation, we calculate, from the records of each participant, the maximum of µ, named µ max and the friction contrast denoted ∆µ. Since the value may change from one period of friction modulation to an other, we average the measurement over 6 periods This figure shows two groups of participants: The first group of participants (from 1 to 6) have a low friction coefficient (below 0.5) without vibrations; this group also have a low value of maximal acoustical finger force (less than 1.6). The other group of participants (from 7 to 12) have a high level of friction (above 0.5) and a maximum force of 1.5N. Therefore, it seems reasonable to consider a correlation between the acoustical force measurement, and the level of friction with and without ultrasonic vibration.

C. Correlation between acoustical finger force measurement and friction reduction

We report in figure 9 the friction contrast ∆µ as a function of the maximal acoustical finger force, and for each participant. We can propose a linear model to the data (Pearson correlation is 0.541), that helps to predict the friction reduction as a function of the maximal acoustical finger force. A linear regression gives ∆µ = A ∆ × max(F r ) + B ∆ , with A δ = 0.022 and B δ = 0.071 (norm of residual: 0.0506). To obtain this model, we have excluded two participants (8 and 11); including them would have resulted in other coefficients, but higher norm of residuals. The proposed model suits well for the 10 participants chosen for the linear regression.

We also depicts µ max as a function of max(F r ) in the figure 10. Also, we present a linear fitting to the data.

Here also, two participants have been removed from the linear fitting (7 and 10); The Person Correlation is 0.941, so a linear regression that gives µ max = A µ × max(F r ) + B µ , with A µ = 0.358 and B µ = -0.067 (norm of residuals: 0.192) is proposed. This model can predict the coefficient of friction without ultrasonic vibration for the 10 participants used for the linear regression, with a maximal error of 0.09.

V. DISCUSSION

The measurement of the fundamental acoustical finger force has been achieved on a light Digital Signal Processor, and does not require off line calculation. We obtained measures that have in common that the acoustical finger force increases as the vibration amplitude increases. However, we remark in figure 5 that for some participants, the force along the axis d saturates. We believe that this change in force slope corresponds to the beginning of the intermittent contact. The Fig. 10. µmax as a function of max(Fr) for each participant, and a linear fitting for the data; the participants marked by * have been removed from the model. amount of vibration amplitude from which the skin starts to bounce is different from one participant to the other. This might be due to the different mechanical skin parameters. Indeed, it has been shown that intermittent contact occurs for higher vibration amplitude for soft skin [START_REF] Vezzoli | Friction reduction through ultrasonic vibration part 1: Modelling intermittent contact[END_REF]. Surprisingly, the level of force is much higher than the pressing force (around 0.4N). The fact that intermittent contact produces pulses of forces, introducing a factor 2 into the fundamental acoustical finger force as shown in the equation 8 is not enough to explain the very large values obtained. The value of N might be overestimated, and further investigation are needed to address this issue.

The figure 8 shows that the participant are shared into two categories. Those with a high friction µ max have high acoustical finger forces, and vice versa. This correlation has been observed on the curve of the figure 10. This can be explained by the moisture level of the participants' finger. Indeed, [START_REF] Gueorguiev | the tactile perception of transient changes in friction[END_REF] demonstrate that higher level of moisture leads to higher level of friction coefficient, for all surfaces (without ultrasonic vibrations), while in the same time, [START_REF] Kuilenburg | Contact modelling of human skin: What value to use for the modulus of elasticity?[END_REF] shows that a moist skin also have lower stiffness than a dry one, and thus needs higher vibration amplitude to obtain the intermittent contact. Two participants (7 and 10) however have higher coefficient of friction than what is expected from the proposed model. The behaviour of Fr is different: it does not saturate, as if the finger skin has not reached the intermittent contact.

Finally, the measurements have shown that the friction contrast can be correlated to the acoustical finger force, for the surface considered in this paper.

VI. CONCLUSIONS

A conclusion section is not required. Although a conclusion may review the main points of the paper, do not replicate the abstract as the conclusion. A conclusion might elaborate on the importance of the work or suggest applications and extensions.

Fig. 1 .

 1 Fig. 1. Principle of the rotating reference frame (d, q).

Fig. 2 .

 2 Fig. 2. Evolution of fr in case of an ideal intermittent contact.

Fig. 3 .

 3 Fig. 3. The experimental setup; (a) is the vibrating plate and (b) is its deformation mode shape Φ(x, y).

Fig. 4 .

 4 Fig. 4. No-load relation between the applied voltage and the reference W d

Fig. 5 .

 5 Fig. 5. Estimated values of Frd (red) and Frq (blue) as a function of W for every participants;

Fig. 6 .

 6 Fig. 6. Maximal acoustical finger force observed for each participant.

Fig. 7 .

 7 Fig. 7.Typical friction coefficient µ as a function of time for one participant.

Fig. 8 .

 8 Fig. 8. Maximum of friction µmax and friction contrast ∆µ for each participant.

Fig. 9 .

 9 Fig.9. ∆µ as a function of max(Fr) for each participant, and a linear fitting for the data; the participants marked by * have been removed from the model.

Appendixes should appear before the acknowledgment.

ACKNOWLEDGMENT Thanks IRCICA And Maxime